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+{"query":"### SubjectName: Linear Equations ### ConstructName: Solve two-step linear equations, with the variable on one side, with all positive integers ### Question: Tom and Katie are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{4}-1=20\n\\)\nTom says you can write: \\( \\frac{m}{4}=21 \\)\nKatie says you can write: \\( m-1=80 \\)\nWho is correct?","positive":["Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount"],"negative":["Confuses the direction of vectors when adding or subtracting","Thinks a positive x value in a column vector means to move left rather than right","Subtracts instead of adds","Thinks positive values in a column vector denote movement left and down (and vice-versa for negative values).","Thinks a negative x value in a column vector means to move right rather than left ","Believes that the directions of positive and negative vectors are the opposite way around.","Ignores the negative signs when adding positive and negative numbers","When adding column vectors, multiplies rather than adds","Does not think that -n + n = 0","Adds instead of subtracts","Forgets to add starting value when calculating new coordinates","Does not realise that subtracting a negative is the same as adding it's additive inverse","Believes subtraction is commutative ","Ignores the negative sign","Confuses left and right","Thinks x = 0 is the x axis","Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round"," Does not believe that a negative multiple of a vector is in the opposite direction","Does not recognise the origin as the starting point for coordinates","Thinks a positive y value in a column vector means to move down rather than up ","When describing a translation, goes from the image to the original","Thinks a negative y value in a column vector means to move up rather than down","Heads towards zero when subtracting from a negative","Thinks signs are interchangeable when adding or subtracting positive and negative numbers","When subtracting a negative number, subtracts the absolute value rather than adding it","Believes that vectors of different magnitudes can be equal.","Believes adding two negatives gives a positive answer","In algebra, thinks it's ok to write (for example) 0x rather than just 0","Confuses negative and positive coordinates when working with graphs in four quadrants","Reflects instead of rotates","Rotates by the wrong center of rotation (not including the origin)","Does not know the y intercept is where the x coordinate is 0","Doesn't recognise commutativity of addition with negative numbers","Believes that the y intercept is where y = 0","Rotates instead of reflects","Thinks they find the length of a line between 2 points by adding coordinates, rather than subtracting","Assumes that an arrow on a number line starts at zero","Believes the centre of rotation is always the origin","Believes that adding a positive to a negative makes your answer more negative","Does not know that 7 and -7 are different","Does not realise addition is commutative","Does not realise that when you multiply by 0 the answer will always be 0","Believes the graph of x squared + c has the turning point of (-c, 0)","Does not know how to find the length of a line segment from coordinates","Believes we move down a number line when we add","When adding decimals with a different number of decimal places, lines up the digits incorrectly","When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored ","Reflects in an axis, instead of the given mirror line","When two digits sum to 10 or more during addition of decimals, does not carry across decimal point to preceding digit.","substitutes incorrectly"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Perimeter ### ConstructName: Given the area of a square, calculate a missing dimension ### Question: A shape is made up a square and regular pentagon.\nThe area of the square is \\( 144 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![Pentagon and square joined along one edge]()","positive":["Adds when calculating area instead of multiplying"],"negative":["Multiplies up without finding unit price in proportion question","Does not include units in answer.","Finds unit price then forgets to multiply up","Does not divide to get a unitary amount before scaling up","Finds unit price but doesn't multiply up for number in question","Subtracts rather than dividing to find unit price","Believes the amount given is for the whole rather than a part","Does not know how to calculate with exchange rates","Assumes a 1:1 conversion ratio between different currencies","Divides when converting to a larger unit","Multiplies when converting to a larger unit","Multiplied by the scale factor rather than divided in direct proportion problems","Multiplies up without finding unit amount","In a worded problem, does not complete all calculations","Believes they can round when converting units","Does not recognise inches (\") as a unit of length","When reading values from graphs, writes down the wrong units","Believes range does not need units","Believes direct proportion means a 1:1 ratio","Forgets to multiply up for the correct time frame in a worded question","Multiplies rather than divides when answering worded problems","Finds unit amount but doesn't multiply up","When given a non-unit fraction of an amount, treats it like a unit fraction","Believes they always divide by the conversion factor when converting units","Does not recognise a unit of length","Does not round up when an answer is non-sensical in a real-life context","Divides when converting to a smaller unit","In ratio where total is given, treats that as one part without dividing","Does not recognise a unit of mass","When multiplying, treats digits in other columns as if they are units","Ends up \u00a31 out when dealing with change in money","Rounds to the wrong degree of accuracy (rounds too little)","Rounds the wrong way when interpreting a real-life context","When converting compound measures into different units, thinks you multiply when the unit of the divisor has become smaller","Cannot spot a coefficient within a written scenario","Does not recognise litres as a unit of volume","Believes degrees can be used to measure length","Rounds to the wrong degree of accuracy (rounds too much)","Confusion over whether multiplication or division is the correct way to solve the problem.","Answers as if there are 100 minutes in an hour","Does not recognise a unit of time","Thinks grams and tonnes are the same","Multiplies the value as if the original recipe was for 1 person","Only includes full hours when measuring time in minutes","Difficulty with translating a mathematical answer into a real world context","Multiplies instead of divides to find one part given the total","Does not recognise feet (ft) as a unit of length","Divides rather than multiplies when answering worded problems","Believes you can go above an amount of money when finding how much of something you can buy","Does not consider fractional parts when solving proportion problems"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: BIDMAS ### ConstructName: Use the order of operations to carry out calculations involving brackets ### Question: \\( 4+12 \\div(2+2)= \\)","positive":["Performs addition ahead of division"],"negative":["Confuses reciprocal and quadratic graphs","Confuses quadratic and exponential graphs","Only recognises the negative form of a quadratic graph","Believes a reciprocal equation will have a quadratic graph","Does not recognise a quadratic graph","Only recognises the positive form of a quadratic graph","Confuses reciprocal and exponential graphs","confuses cubic and reciprocal graphs","Confuses linear and reciprocal graphs","Believes that a positive x squared coefficient in a quadratic equation results in an n shaped graph","Believes a cubic equation will have a quadratic graph","Confuses cubic and exponential graphs","Confuses cubic and quadratic graphs","Confuses the graph of a linear equation with a quadratic equation","Believes linear graphs can be curved","Believes both solutions of a quadratic will have the same absolute value, even when the graph is not symmetrical about the y axis","Believes a reciprocal graph comes from a cubic equation","Does not recognise a reciprocal equation","Believes a quadratic graph can be a straight line","Does not understand the term quadratic","Does not recognise the sin graph","Believes you can square root a negative number","Thinks a decreasing sequence cannot be quadratic","Does not think a square root can be negative","Only gives 1 value of x for a given value of y, when reading from a parabolic graph","Selects y>a solutions instead of y<a solutions for a quadratic inequality","Believes a reciprocal equation will have a linear graph","Believes a cyclic quadrilateral can be self-intersecting","Can not square root a negative number","Believes that graphs of inverse proportion meet the axes","Believes the solution of a quadratic is its turning point","Believes that reciprocals are undefined for negative numbers","Believes a direct proportion graph can have a negative gradient","Believes multiplying two negatives gives a negative answer","Believes a cubic equation will have a linear graph","When factorising a quadratic without a non variable term, tries to double bracket factorise","Writes a repeated root once, rather than in a squared bracket","Confuses the graph of 1\/x with 1\/x\u00b2 when both are shown","When sketching graphs of factorised quadratics, does not see that the negative of the non variable terms in the brackets give the x intercepts or the roots of the graph.","Incorrectly factorises a quadratic","Believes a polygon can have curved sides","Believes a reciprocal graph can be a straight line","Does not realise that a curved line represents a changing gradient","Believes an upward line has a negative gradient","Confuses the factorised form of repeated roots and the difference of 2 squares","Confuses the graphs of  direct and inverse proportion","Confuses negative and positive coordinates when working with graphs in four quadrants","Has an incorrect assumption about the definition of a reciprocal","Does not recognise factorising a quadratic","Believes the solutions of a quadratic equation are the constants in the factorised form"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Place Value ### ConstructName: Recognise the place value of each digit in integers ### Question: What is the value of the \\( 3 \\) in the number below?\n\\(\n43075\n\\)","positive":["Confuses the ten thousands and thousands place value columns"],"negative":["Does not think that a variable with no coefficient has a coefficient of 1.","Writes the variable before the coefficient in an algebraic term","Confuses a term with a variable","When collecting like terms, assigns positivity or negativity incorrectly.","Does not realise that two letters together, or a number and letter together, are multiplying","Does not understand when like terms can be collected","When collecting like terms, treats subtractions as if they are additions","Confuses an expression with a variable","Does not know that a single letter labels a vertex","Confuses a variable with a formula","In algebra, thinks it's ok to write (for example) 0x rather than just 0","Ignores coefficients when forming an expression from a question","When collecting like terms, only simplifies when there is an addition","Confuses collecting like terms with multiplication","Does not realize we can simplify a term that involves powers","Does not consider the variable when evaluating an expression that requires substitution.","Does not realise that two letters together are multiplying","Writes repeated letters instead of using index form of a variable","When substituting into an algebraic term, believes they can disregard the coefficient","Confuses an expression with a term","Cannot spot a variable within a written scenario","Believes a variable must remain unknown and cannot be substituted with a value","When substituting into an algebraic term, replaces variables with numbers without multiplying.","Confuses a variable with an equation","Confuses a constant with a variable","Thinks you can ignore the variable when simplifying algebraic fractions","Ignores the negative sign when thinking about the value of a term","Does not realize we can omit the multiplication symbol in algebraic expressions","Identifies a number as a common factor but doesn't identify a letter as a common factor","Does not include units in answer.","Does not understand how to multiply algebraic terms","Does not know the meaning of the identity symbol","Believes an algebraic term with the same coefficient as the value of a constant term can be subtracted to give zero","When factorising into single brackets, only factors out the numerical values and forgets to factorise possible variables","Confuses a term with an equation","Believes that n\/n = n, instead of 1","When simplifying, thinks they write 0 in front of a negative number in the final answer, instead of just writing the negative number","Does not understand use of the counters to represent algebra","Thinks that we can remove a division symbol and just write the variables next to each other","Uses 2 letters to describe an angle","Believes the variable should remain in place after substituting its value","Believes that 'zero' is read as the letter 'O'","Ignores numerical terms when setting up an equation from a question","Does not know how to identify common factors from algebraic terms","Does not know the correct notation for labelling a side length","When solving an equation forgets to eliminate the coefficient in front of the variable in the last step","Does not know how to simplify algebraic fractions","Tries to add or subtract unlike terms","\nHas incorrect belief about the meaning of \"expression\"","Multiplies all terms together when simplifying an expression"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Difference of Two Squares ### ConstructName: Factorise a quadratic expression in the form x\u00b2 - c ### Question: Which of the following answers shows a correct factorisation of the expression below? \\( x^{2}-9 \\)","positive":["Does not recognise difference of two squares"],"negative":["Assumes the item has not been replaced in a probability question where it has actually been replaced","Does not reduce the denominator when an item is not replaced in a probability question","Thinks the denominator in a combined probablity will be the same as the denominator in the probability of the first event.","Does not recognise that choosing 2 items at once means the first item does not get replaced in a probability question","Thinks the order of events does not matter in a question about combined probability with no replacement","Believes the numerator stays the same when calculating a second pick of the same type without replacement on a tree diagram","Believes the probability on all branches travelling in the same direction on a tree diagram are the same, despite changing events","Does not increase the denominator when an item is added in a probability question","Thinks they can just give the probability of the first event for a combined probability","Believes you always reduce the numerator and denominator by 1 when writing the probability for a second pick without replacement on a tree diagram","Believes when calculating a probability the denominator will be the total of one of the criteria rather than the overall total that is required (gives a given that answer)","Uses outcome as numerator in probability ","Adds rather than multiplies for combined probabilities","Believes 'given that a, what is the probability of b?' means 'given that b, what is the probability of a?'","Gives the probability out of the number of non-successes rather than the total","Does not work out all possibilites when given an 'at least' question in probability","Adds the numerators when working out a combined probability","Forgets the denominator in probability","Believes any sample gives an equal chance of selection","Believes data implies equal chance of selection","Thinks that probabilities of an event occurring or not occurring must be equal","When using the capture-recapture method, believes the number caught second is the numerator and the number marked second is the denominator","Includes too many possibilities when calculating a combined event in probability","Writes the numerator and the denominator the wrong way round in a probability","Confuses theoretical and experimental probability","Does not understand that the probability of something not happening is 1 minus the probability of it happening","Fails to consider all possible outcomes","Confuses dependent and mutually exclusive events","Confuses 'and' with 'or' in probability","Believes all possible outcomes must have equal probability","Uses the other part instead of total frequency as denominator for relative frequency","Believes P(success) in probability notation means the number of successes","Believes a sample space should show repeated outcomes, not just unique possible outcomes.","Includes too many possibilites when given an 'at least' question in probability","Believes biased selection methods can be random","Does not understand the effect of consecutive subtractions","Cannot identify mutually exclusive events","Misunderstands the capture-recapture method","Does not understand the effect of consecutive operations","Lists outcomes rather than counts how many outcomes","Confuses relative frequency and expected frequency","Has taken the percentage from the original ","Carries out operations from right to left regardless of priority order","Carries out operations from left to right regardless of priority order","When using the capture-recapture method of sampling, believes you divide the number caught second by the number marked second to find the best estimate of population size","In repeated percentage change, believes the second change is only a percentage of the first change, without including the original","When using the capture-recapture method for sampling, believes you subtract the number marked second from the number caught second to find the best estimate of population size","Does not understand that a probability of 0 represents something that is impossible","Does not understand how to maintain equivalence in fractions","Confuses all possible outcomes with options available"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Solving Linear Inequalities ### ConstructName: Solve linear inequalities in one variable where the unknown appears on boths sides of the equation ### Question: Solve\n\\[\n3 n+2 \\geq 4 n-5\n\\]","positive":["When solving an equation, uses the same operation rather than the inverse."],"negative":["When ordering integers, orders from the digits at the end of the number instead of the digits at the start","Ordered from largest to smallest","Mixes up smallest and greatest when ordering positive integers","Thinks the more digits a number has the greater it is, regardless of place value","Mixes up greater than and less than symbols","Orders integers based on first digits without taking into account place value","Believes negative numbers with a larger absolute value are greater","Believes digits of a number are read\/written from right to left","Assumes that a list is given in size order","Chosen the longest value rather than the greatest","Mixes up smallest and largest when ordering decimals","Lines up the digits incorrectly when doing a subtraction involving two numbers with a different amount of digits","When ordering decimals, believes the decimal point is not relevant","Lines up the digits incorrectly when doing an addition involving two numbers with a different amount of digits","Does not equate the value of a number with the place value column it is in","Mixes up smallest and largest when ordering fractions","Subtracts the smallest digit from the largest digit","When comparing unit fractions believes that fractions with larger denominators are greater in size.","When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right.","Believes you subtract the smaller digit from the larger digit in column subtraction, regardless of position","Writes digits in the order of the pictorial representation rather than using place value columns","Does not understand inequality notation","Counts on in the wrong direction on a number line","Counts in the wrong direction on a number line","Believes that the larger the dividend, the smaller the answer.","When asked for the value of a digit, gives an answer 10 times too big","Does not understand the meaning of \"value\"","Confuses the order of the digits in stick multiplication","Mixes up shortest and longest when ordering times","Does not understand the value of zeros as placeholders","Does not understand which place value is the one that determines if a number rounds up or down","When ordering numbers in standard form just looks at the decimal without multiplying by a power of 10","The student does not understand the place value of 3-digit numbers","Ignores zeros when giving the value of an integer","When asked for the value of a digit, gives an answer 10 times too small","Confuses the hundreds and hundred thousands place value columns","Believes that the larger the divisor, the larger the answer.","Believes the smaller number is always subtracted from the larger, regardless of the order of the calculation","Believes that fractions with larger denominators are greater in size","Believes a number written in standard form is smaller than another number written in standard form if the number between 1 and 10 is smaller","Does not know how to compare decimal numbers","Confuses the hundreds and thousands place value columns","Rounds up instead of down","Ordered fractions by comparing denominators rather than using equivalent fractions.","Confuses the hundreds and tens place value columns","Confuses the ten thousands and thousands place value columns","Changes wrong place value column when rounding","Ignores the negative sign","Believes that numbers are read aloud digit by digit ","When dividing decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant."],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Probability of Single Events ### ConstructName: Assign probabilities to single events using fractions ### Question: A box contains \\( 10 \\) coloured counters.\n\n\\( 3 \\) of the counters are pink\n\n\\( 3 \\) of the counters are blue\n\nThe rest of the counters are green\n\nWhat is the probability of choosing a green counter?","positive":["Forgets the denominator in probability"],"negative":["When finding the area of a parallelogram finds base x perpendicular height but divides the answer by 2 ","When finding a missing side of a parallelogram given the area completes an extra step of dividing by 2","When finding the area of a parallelogram does not understand which lengths to use","Calculates perimeter when asked for area","Has used slant height and base to find area of a parallelogram rather than perpendicular height and base","Does not realise we can find a missing length if we know the base of a parallelogram and its area. ","Has found the area of a triangle rather than an area of a parallelogram","Confuses perimeter and area","Multiplies rather than divides","Believes h in the formula for area of a trapezium stands for half the sum of the parallel sides","Adds when calculating area instead of multiplying","Calculates area when asked for perimeter","Divides rather than multiplies ","Calculates circumference when asked for area","Does not divide by 2 when calculating the area of a triangle","Multiplies all given dimensions when calculating an area","Uses formula for area of a parallelogram when finding the area of a trapezium","Finds the circumference instead of the area","Does not divide by 2 when calculating the area of a trapezium","Thinks they double rather than halve when finding the area of a triangle","Halves base but still divides product by 2 when finding area of a triangle","Thinks halving is the same as multiplying by 2","Thinks you multiply parallel sides to find the area of a trapezium","Subtracts instead of divides","Has used slant height and base to find area rather than perpendicular height and base","Does not half sum of parallel sides when finding area of a trapezium","adds all given dimensions when calculating area","Adds instead of subtracts when using an area model for multiplication","Uses an incorrect side length when splitting a composite shape into parts","Adds instead of multiples","Believes the area of a rectangle is calculated by length add width","Uses dividing fractions method for multiplying fractions","Thinks all dimensions given must be used when calculating the area","Divides by the index","Arithmetic error when dividing by 8","Confuses formulae for area of triangle and area of rectangle","Believes division is commutative ","Mixes up width and height of a rectangle","Counts half-squares as full squares when calculating area on a square grid","Uses only the base and perpendicular height when calculating the area of a trapezium","Thinks measures of area must end in squared","When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation","Adds when calculating volume instead of multiplying","Cannot identify the correct side lengths to use when asked to find the area of a face","Thinks the inverse of subtraction is division","Adds instead of multiplies","Does not have when calculating the area of a triangle","Thinks the inverse of addition is division","Thinks area of a circle = radius x pi ","Thinks the inverse of subtraction is multiplication"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Reflection ### ConstructName: Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object ### Question: Which is the correct point for E when reflected in the line \\( x=-1 \\) ? ![A set of axes: x-axis from -5 to 5, y-axis from -5 to 3. Four points are plotted and joined to make a rectangle: (1,1), (3, 1), (3, 3) and (1,3). Point (3, 3) is labelled with the letter \"E\". ]()","positive":["Thinks x = ? is a horizontal line through ? "],"negative":["Divides by 1000 instead of 100 when converting a percentage to a decimal","Divides by 1000 instead of 100 when converting a decimal to a percentage","Does not know how to convert percentages with a decimal point into decimals","When converting a percentage to a decimal, just writes all the digits after a decimal point.","Multiplies instead of divides by 100 when converting a percentage to a decimal","Divides instead of multiplies when converting a decimal to a percentage","Divides by 10 instead of 100 when converting a percentage to a decimal ","Multiplies by 1000 instead of 100 when converting a decimal to a percentage","Thinks you need to just remove the percentage sign to convert from a percentage to a decimal","Does not understand a percentage is out of 100","Does not know that you can have a decimal percentage","Multiplies by 10 instead of 100 when converting decimal to percentage","Assumes decimal point can be ignored when given a decimal percentage to convert to a fraction","Assumes that converting a decimal percentage to a fraction, they can just convert the decimal to a fraction, instead of writing the decimal over 100.","Thinks you need to just add a % sign to a decimal to convert to a percentage","Does not understand that you can have percentages greater than 100%","When converting a fraction to a decimal, divides the denominator by the numerator","Divided by 100 rather than multiplied by 100","Believes a fraction out of a number other than 100 represents a percentage","Believes a decimal with one significant figure is a multiple of 10 when converted to a percentage, regardless of place value","Believes percentages cannot be converted into fractions","Believes that dividing by 100 gives 10%","Believes that a greater percentage represents a greater quantity","Converts a fraction to a decimal by using only the numerator after the decimal point","Multiplied by 100 rather than divided by 100","Converts fraction to percentage by putting % sign after the denominator","Thinks they just remove the decimal point when converting a decimal to a percentage","Believes that dividing by 10 gives 1%","Does not understand a percentage can be applied to something not out of 100","Thinks that to decrease by a percentage you just multiply by the decimal equivalent to that percentage","Error finding percentage value after finding 1%","Thinks you just add a % sign to the numerator to make a fraction into a percentage","Thinks that a percentage can be converted to a fraction using a denominator of 10 ","Converts fraction to percentage by multiplying the denominator by 10","Converts a fraction to a decimal by placing all values of the fraction after the decimal point","Divided by 10 rather than 100","Converts a fraction to a percentage by placing a decimal point between the numerator and denominator","Believes they can reverse a percentage increase or decrease by dividing by the decimal multiplier of the original change","Does not understand changing decimals to fractions","Believes that any percentage of a larger number will be greater than any percentage of a smaller number","Believes you can divide the change by 100 to find the percentage change ","When the change in value is greater than the original amount, thinks percentage change = original\/change x 100","Thinks you need to just add a % sign to a number to make it a percentage","Converts a fraction to a decimal by using the denominator after the decimal point","Thinks when finding a percentage you divide by the percentage being asked","When writing a number as a percentage of another number gets them the wrong way around","Divided by 100 rather than 10","Found the percentage but forgot to add to 100%","Converts a fraction to a decimal by placing the denominator after the decimal point","Thinks they can convert percentages to fractions by writing the percentage value as both the numerator and the denominator"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Squares, Cubes, etc ### ConstructName: Calculate the square root of a number ### Question: What is the value of the missing number? ![\\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{\\( 15^{2} \\)} \\\\\n\\hline\\( \\square^{2} \\) & \\( 2 \\) \\\\\n\\hline\n\\end{tabular}]()","positive":["Thinks the sum of 2 numbers, each squared first, is the same as adding the two numbers and then squaring the total"],"negative":["Adds instead of multiplying when expanding bracket","Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets","Ignores negative sign when expanding bracket","When expanding brackets, multiplies out the first term correctly but adds together the number outside the bracket with the second term inside the bracket.","Believes multiplying a positive by a negative gives a positive answer","Only multiplies the first term in the expansion of a bracket","Adds instead of multiplies","Thinks signs are interchangeable when adding or subtracting positive and negative numbers","Adds instead of multiplies when multiplying algebraic terms","Only multiplies second term in the expansion of a bracket","Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets","Believes you can add or subtract from inside brackets without expanding when solving an equation","Believes they can ignore the coefficient when expanding double brackets ","Believes they only need to multiply the first and last pairs of terms when expanding double brackets","Adds instead of multiples","Believes the numbers in factorising should multiply to give the coefficient of x and add to give the constant","When multiplying out 2 or more brackets, does not multiply all the combinations of terms","Ignores the negative signs when adding positive and negative numbers","Only multiplies the numerical terms when expanding a bracket","Believes that adding a negative will increase the value of the original number","Expands when asked to simplify","Believes adding two negatives gives a positive answer","Believes multiplying two negatives gives a negative answer","Believes they only need to multiply the first pair of terms when expanding a double bracket.","Believes that multiplying variables is the same as adding them together","Does not understand the link between the sign of the root and the sign in the bracket","Thinks multiplying two or more negative numbers together always gives a positive answer, regardless of how many negative numbers there are in the sum","Thinks the multiplication sign means to add","Believes that the sign changes when factorising an expression into single brackets","When factorising into double brackets, finds the correct values for the non variable terms but swops the plus and minus sign","Thinks two variables next to each other represent addition","Multiplies by the index","Thinks a variable next to a number means addition rather than multiplication","When factorising into double brackets, believes the product of the constants in the brackets is of the opposite sign to the constant in the expanded equation.","Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant","Multiplies rather than adds ","Believes a cubic expression should have three terms","When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored ","Believes you can subtract from inside brackets without expanding when solving an equation","Believes cubing a number means you multiply it by 3","When completing the square in the form (x - a)^2 + b, believes b = a^2 + the original constant","Believes 0 multiplied by a number gives the number","Believes you add the terms together when multiplying like terms.","When multiplying with negative numbers, assumes any negative sign can be ignored","Believes the solutions of a quadratic equation are the absolute values of the constants in the factorised form","Adds the index to the number","When solving an equation, multiplies instead of adding","Thinks multiplication and addition are the same","Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x","Believes expanding a squared expression means writing it as a set of double brackets"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Estimation ### ConstructName: Round numbers to an appropriate degree to estimate the answer to a calculation ### Question: When estimating the answer to a complicated problem involving \\( 0.482 \\), you should instead use...","positive":["Rounds down instead of up"],"negative":["When comparing unit fractions believes that fractions with larger denominators are greater in size.","Believes that fractions with larger denominators are greater in size","Ordered fractions by comparing denominators rather than using equivalent fractions.","Mixes up smallest and largest when ordering fractions","believes that a fraction with the largest denominator will be smallest regardless of the numerator","Ordered from largest to smallest","When ordering integers, orders from the digits at the end of the number instead of the digits at the start","Believes negative numbers with a larger absolute value are greater","Mixes up greater than and less than symbols","Mixes up smallest and greatest when ordering positive integers","Mixes up smallest and largest when ordering decimals","Believes that fractions with the same denominator are equal","Does not find a common denominator when comparing fractions","Believes a smaller number of shaded parts represents a smaller fraction","When ordering decimals, believes the decimal point is not relevant","Assumes that a list is given in size order","Believes that a fraction means dividing the denominator by the numerator","Believes that the larger the dividend, the smaller the answer.","Believes that the smaller a divisor is, the smaller the answer will be","Believes that if the numerators of 2 fractions are equal then the fractions are equal, regardless of the denominator","Does not understand inequality notation","When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right.","Thinks a greater number of shaded parts represents a greater fraction","Believes -a is always smaller than a, ignoring the possibility that a is negative","Believes that the larger the divisor, the larger the answer.","Does not understand the 'less than' inequality notation","When converting a fraction to a decimal, divides the denominator by the numerator","Counts on in the wrong direction on a number line","Thinks numbers greater than 1 cannot be converted into fractions","When multiplying a fraction by an integer, multiplies the denominator instead of the numerator","Thinks the more digits a number has the greater it is, regardless of place value","Counts in the wrong direction on a number line","Assumes the denominator is divided by the numerator","When ordering numbers in standard form just looks at the decimal without multiplying by a power of 10","Does not know how to compare decimal numbers","Believes unit fractions with a difference of 1 in the denominator have no other fractions between them","Does not understand equivalent fractions","Gives the smallest whole when asked for the smallest fraction shaded, presented visually","Believes the sides of an inequality can be switched without changing the direction of the sign","Believes dividing by a unit fraction is equivalent to dividing by its reciprocal","Does not realise you can use equivalent fractions to break fractions up into smaller divisions","Does not know the units column is before the decimal point","Student thinks that negative decimals behave the same as positive decimals when positioning a decimal between two consecutive negative integers, placing the decimal with a greater absolute value to the right. ","Chosen the longest value rather than the greatest","Mixes up colder and hotter when comparing temperatures","Believes they must change the direction of the inequality when dividing through by a positive number.","Thinks subtracting a negative makes your answer smaller","Does not relate integers and fractions","Mixes up shortest and longest when ordering times","Confuses least and most"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Pie Chart ### ConstructName: Calculate the sector angle on a pie chart for a given group ### Question: A class of students were surveyed about how many siblings they have.\n\nA selection of results are shown in the table. \\begin{tabular}{|c|c|c|}\n\\hline Number of siblings & Frequency & Angle on a pie chart \\\\\n\\hline  0  & \\( 7 \\) & \\(  \\) \\\\\n\\hline 1  & \\(  \\) & \\( 144 \\degree \\) \\\\\n\\hline 2  & \\(  \\) & \\(  \\) \\\\\n\\hline 3  & \\( 4 \\) & \\( \\bigstar \\) \\\\\n\\hline 4 or more  & \\(  \\) & \\(  \\) \\\\\n\\hline  TOTAL  & 30  & \\(  \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\nWhat should replace the star?","positive":["Believes you find the angle for a pie chart sector by doing its frequency multiplied by total frequency"],"negative":["Thinks you need to just add a % sign to a decimal to convert to a percentage","Thinks you need to just add a % sign to a number to make it a percentage","Multiplies by 10 instead of 100 when converting decimal to percentage","Thinks you need to just remove the percentage sign to convert from a percentage to a decimal","Does not know how to convert percentages with a decimal point into decimals","Thinks you just add a % sign to the numerator to make a fraction into a percentage","Does not know that you can have a decimal percentage","Divides instead of multiplies when converting a decimal to a percentage","Multiplies by 1000 instead of 100 when converting a decimal to a percentage","Does not understand a percentage is out of 100","Thinks they just remove the decimal point when converting a decimal to a percentage","When converting a percentage to a decimal, just writes all the digits after a decimal point.","Assumes that converting a decimal percentage to a fraction, they can just convert the decimal to a fraction, instead of writing the decimal over 100.","Does not understand a percentage can be applied to something not out of 100","Divides by 1000 instead of 100 when converting a decimal to a percentage","Multiplies instead of divides by 100 when converting a percentage to a decimal","Believes a decimal with one significant figure is a multiple of 10 when converted to a percentage, regardless of place value","Thinks that to decrease by a percentage you just multiply by the decimal equivalent to that percentage","Believes a fraction out of a number other than 100 represents a percentage","Divides by 1000 instead of 100 when converting a percentage to a decimal","Assumes decimal point can be ignored when given a decimal percentage to convert to a fraction","Found the percentage but forgot to add to 100%","Does not understand changing decimals to fractions","Divides by 10 instead of 100 when converting a percentage to a decimal ","Converts a fraction to a percentage by placing a decimal point between the numerator and denominator","Converts fraction to percentage by putting % sign after the denominator","Only reads the percentage symbol as applying to the units digit","Error finding percentage value after finding 1%","Does not understand how to find percentages of an amount","Believes percentages cannot be converted into fractions","Converts a fraction to a percentage by writing the numerator followed by the denominator","Multiplied by 100 rather than divided by 100","Does not understand that you can have percentages greater than 100%","Divided by 100 rather than multiplied by 100","Multiplied by 10 rather than 100","Adds \"100\" to end of written value rather than multiplying by 100","When writing a number as a percentage of another number gets them the wrong way around","Does not understand the value of zeros as placeholders","Finds 10% of an amount rather than the percentage being asked","Does not know the units column is before the decimal point","Converts a fraction to a decimal by using only the numerator after the decimal point","Does not know how to compare decimal numbers","Believes that dividing by 100 gives 10%","Believes that when increasing by a percentage over 100, they do not need to add an extra 1 to the decimal multiplier for the original amount","Has considered the percentage rather than the percentage of the amount","Thinks that to decrease by a percentage you multiply by 1+ the decimal equivalent to that percentage","Believes that dividing by 10 gives 1%","Multiplied by 1000 instead of 100","Thinks they can convert percentages to fractions by writing the percentage value as both the numerator and the denominator","Converts fraction to percentage by multiplying the denominator by 10"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Converting between Fractions and Percentages ### ConstructName: Convert single digit integer percentages to fractions ### Question: \\( 4 \\% \\) as a fraction is....","positive":["Does not understand a percentage is out of 100"],"negative":["Multiplies up without finding unit price in proportion question","Does not divide to get a unitary amount before scaling up","Finds unit price but doesn't multiply up for number in question","Finds unit price then forgets to multiply up","Finds unit amount but doesn't multiply up","Multiplies up without finding unit amount","Believes direct proportion means a 1:1 ratio","Subtracts rather than dividing to find unit price","Multiplies the value as if the original recipe was for 1 person","Finds one part of a ratio but doesn't multiply that by the number of parts needed","Believes the amount given is for the whole rather than a part","In ratio question where one side of ratio is given, treats that as the total","Does not include units in answer.","In direct and inverse proportion, forgets to find the value of k, and carries out calculations as though k were 1","Multiplied by the scale factor rather than divided in direct proportion problems","Does not believe you can scale up a proportional statement","Cannot spot a coefficient within a written scenario","Adds rather than multiplies when scaling up in direct proportion problems","When given a non-unit fraction of an amount, treats it like a unit fraction","Finds the unit fraction when asked to find a non-unit fraction of an amount","Does not recognise when to find a multiple from a worded question","Shares equally instead of in given ratio","Thinks direct proportion rules apply to inverse proportion problems","Divides rather than multiplies when scaling up in direct proportion problems","Does not know the meaning of the word \"product\"","Does not know how to calculate with exchange rates","Forgets to multiply up for the correct time frame in a worded question","In ratio where total is given, treats that as one part without dividing","In ratio question where one side of ratio is given, uses that as one part in ratio without dividing","Assumes value of symbols in a pictogram without checking the key","Mixes up sides of a ratio","Gives number of sections of pie chart rather than the amount it represents","In a worded problem, does not complete all calculations","Multiplies instead of divides to find one part given the total","Finds a scale factor but forgets to multiply the original value in proportion questions","Assumes a 1:1 conversion ratio between different currencies","Believes every direct or inverse proportion question uses the formula p=kq","Arithmetic error when dividing by 8","Difficulty with translating a mathematical answer into a real world context","Finds the degrees for 1 person rather than the required number of people for a pie chart sector","Does not understand the meaning of \"value\"","Ignores numbers written as words in worded questions, and just calculates using those written in digits","Divides rather than multiplies in a related calculation questions","Subtracts rather than divides when scaling down in direct proportion problems","Mixes up constant and coefficient in a worded substitution problem","Estimates shares of a ratio instead of calculating","Believes that 1 part of a bar model will always have a value of 1","When interpreting a pictogram, thinks each symbol stands for 1","Is not able to spot a proportional relationship pictorially unless they are laid out in groups","Does not realise ratio in worded problem can be simplified"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Time Series and Line Graphs ### ConstructName: Identify when it is appropriate to use a line graph ### Question: Which of the following situations would a line graph be the most appropriate to use?","positive":["Does not understand that a line graph shows a relationship between 2 variables"],"negative":["Does not understand that factors are divisors which split the number into equal groups","Does not recognise when to find a factor from a worded question","Does not understand the term factor","Does not realise that division can be broken down into factors","Believes splitting a multiplication using the distributive property is the same as splitting it into factors","Does not understand a denominator represents equal parts","Does not know the meaning of common, eg. common factor","Does not realise you can use equivalent fractions to break fractions up into smaller divisions","Does not know how to interpret a fraction worded problem ","Does not realize we can write a division as a fraction","Is not familiar with the names of the different parts of a fraction","Does not understand equivalent fractions","Does not know how to say a fraction","Misunderstands the concept of common factors in algebra","When given a non-unit fraction of an amount, treats it like a unit fraction","Does not relate integers and fractions","Does not understand that the numerator and denominator of fractions represent groupings and have the same order of priority as brackets","Mixes up the terms for the parts of a fraction","Thinks the fraction 1\/n can express sharing n items between any number of people","Does not realise that multiplication can be broken down into factors","Does not know how to divide a fraction by an integer","Confuses factors and multiples","Confuses prime factors and factors","Believes factors add to give a number","Believes numbers are divisible by numbers which sum to their factors","Does not know how to solve linear equations involving fractions","Does not recognise difference of two squares","When asked for factors of an algebraic expression, thinks any part of a term will be a factor","Does not understand parts must be equal in a fraction diagram","Does not understand that a number is divisible by the factors of its factors","Does not understand how to simplify fractions","Does not know the meaning of bisect","Unable to equate two divisions with a single division","Thinks numbers are divisible by all multiples of their factors","When asked for factors of an algebraic expression, thinks a term will be a factor","When multiplying large numbers, splits numbers into addends rather than factors","Does not know how to simplify algebraic fractions","Thinks a factor of the final digit is also a factor of the whole number","Does not correctly apply the distributive property of multiplication","Does not understand the relationship between a ratio and fraction","Thinks the fraction 1\/n can express sharing any number of items between n people","Believes a factor pair doesn't have to be 2 integers","Can not recognise all factor pairs of numbers","Believes only the first term needs to be divided when factorising an expression","Does not know the term numerator","Believes factors of algebraic terms\/expressions will only be numbers","Believes stratified samples should be evenly split","Does not know how to identify common factors from algebraic terms","When dividing a fraction by an integer, divides both the numerator and denominator by the integer","Thinks you can divide terms by different factors when simplifying an algebraic fraction"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Basic Angle Facts (straight line, opposite, around a point, etc) ### ConstructName: Recognise the vertically opposite angles relationship ### Question: What is the relationship between these two angles? ![A pair of lines crossing to form an X shape. Two angles are marked, with one blank angle between them on each side.]()","positive":["Does not know the meaning of the word parallel"],"negative":["Believes you can have decimals in a simplified fraction","Converts a fraction to a percentage by placing a decimal point between the numerator and denominator","Does not fully simplify fraction","Forgot to simplify the fraction","Converts a fraction to a decimal by placing a decimal point between the numerator and denominator","Gives a fraction when asked for a decimal","Rounds a decimal instead of using a fraction in division","Does not understand how to simplify fractions","Has used the decimal point to separate numerator and denominator","Believes when simplifying a fraction you can divide the numerator and denominator by different values","Does not fully simplify ratio","Converts a fraction to a decimal by placing all values of the fraction after the decimal point","Does not understand changing decimals to fractions","Believes clock times can be written with a decimal point rather than a colon","Does not recognise when simplifying a fraction may be helpful","Does not understand that coordinates can be decimals","When converting a fraction to a decimal, divides the denominator by the numerator","Thinks you can multiply by a decimal to find a multiple of a number","When simplifying an algebraic fraction, only looks for number factors","Believes integers can have decimal places","When describing the relationship between the parts in a ratio, replaces the : with a decimal point to say how many times bigger a part is than the other","Converts a fraction to a decimal by using only the numerator after the decimal point","When adding fractions, adds the numerators and denominators","Thinks that a unit fraction can be simplified further","Believes fraction to decimal conversion is done by writing the numerator as a decimal","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","Thinks you cannot multiply by a decimal to get equivalent fractions","Believes the decimal point button writes a fraction","Thinks the fraction button on a calculator converts fractions to decimals","Divides instead of multiplies when multiplying by a decimal","When doing operations with decimals, ignores significant zeros after the decimal point","Does not understand equivalent fractions","Does not recognise when a fraction can be simplified","When multiplying fractions, multiplies both the numerator and denominator","Thinks you can divide the variables and the numerical values by different numbers when simplifying an algebraic fraction","Gives a rounded whole number instead of a decimal","Converts a fraction to a decimal by using the denominator after the decimal point","Converts a fraction to a decimal by placing the denominator after the decimal point","Expands when asked to simplify","Does not know how to simplify algebraic fractions","Thinks can combine the numerator and denominator after simplifying an algebraic fraction","When subtracting fractions, subtracts the numerators and denominators","Does not understand that a remainder can be written as a fraction","Believes that a fraction means dividing the denominator by the numerator","Does not realise you can use equivalent fractions to break fractions up into smaller divisions","Does not know how to convert percentages with a decimal point into decimals","Believes a quarter of 2 is 0.25","Assumes fractions with prime numerators cannot be simplified","Does not know that you can leave a fraction in improper form","Thinks the reciprocal of n, 1\/n = 0.n"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Real Life Graphs ### ConstructName: Given a situation sketch an appropriate real life graph ### Question: Water is poured into a glass at a constant rate.\n\nThis graph shows how the depth \\( (d) \\) of water in a glass changes over time \\( (t) \\).\n\nWhich of the following glasses is this most likely to be the graph of? ![A depth-time graph which is a curve starting at (0, 0), with a steep gradient to begin with but then the gradient decreases and the graph levels off to almost horizontal.]()","positive":["Does not spot the difference between a gradual change of gradient and 2 distinct line segments with different constant gradients"],"negative":["Struggles to visualise nets of 3D shapes","Does not know the definition of a cone","Confuses triangular prism with pyramid","Confuses pyramid with prism","Does not realise a triangular prism is a 3D shape","Thinks a cylinder is a prism","Does not know the definition of a prism","Names one of the faces of a 3D shape rather than the 3D shape name","Thinks all lines on a net will form edges in 3D","Does not know how to calculate the volume of a prism","Struggles to visualise 2D triangles in a cuboid","Struggles to draw 3D shapes on isometric paper","Struggles to visualise elevations of 3D shapes","Believes a line showing a constant rate of increase corresponds to a non-prism shape","Does not know that a solid is a 3D shape","Does not know the properties of a cylinder","Struggles to visualise how an object will look in 3D when given a plan view, front and side elevation","Only counts visible faces","Believes parts of a 3D diagram that look straight class as edges","Does not have when calculating the area of a triangle","Does not know the meaning of uniform cross section","Believes edges of a 3D shape do not include edges of base","Has multiplied base by slant height and perpendicular height to find area of a triangle","Thinks depth is marked on the cross section of a prism","Struggles to estimate 3D volume","Thinks cross section of a prism can be any face","Believes only straight lines count as edges on 3D shapes","Only counts visible vertices","Believes the number of edges on a 3D shape match those of the 2D cross section","Thinks cube numbers are triangular numbers","Tries to apply sohcahtoa to a non right angled triangle","Thinks that when drawing a plan view, you only include the top layer of the shape","Confuses scalene and right angle triangles","Think cross section of a prism is the biggest face","Gives 3-letter angle notation in the wrong order","In 3 letter angle notation, gives a wider angle that contains the shaded angle","Thinks depth always goes front to back in a diagram of a 3D shape","Believes the number of vertices on a 3D shape match those of the 2D cross section","Chooses the wrong 3 letters to describe an angle","Gives the vertex instead of the 3-letter angle notation","Confuses scalene and equilateral triangles","Believes triangle numbers are formed differently to the correct way","Thinks the orientation of the side view does not matter when identifying the direction of view","Does not understand the 3-letter convention for labelling angles","Believes that when constructing triangles, all sides should be measured from the same point","Only counts visible edges","Thinks the plan view is from the side of the shape","Thinks 3-letter angle notation has to use the nearest vertex on each side of the angle","Does not divide by 2 when calculating the area of a triangle","Draws both angles at the same end of the line when constructing a triangle"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Basic Calculator Use ### ConstructName: Perform calculator calculations with powers ### Question: Which button would you press to raise a number to a power? Which button would you press to raise a number to a power? ![A scientific calculator]() ![A scientific calculator]()","positive":["Thinks the fraction button on a calculator converts fractions to decimals"],"negative":["Believes the sides of a rectangle must be horizontal and vertical, not diagonal","Believes the sides of a square must be horizontal and vertical, not diagonal","Does not know how to find the length of a line segment from coordinates","Believes a rectangle has four equal sides","Does not know the properties of a rectangle","Makes an assumption about line segments being equal within a shape","Does not recall rectangle side length property","Believes a rectangle has one pair of equal sides","Mixes up width and height of a rectangle","Reflects in an axis, instead of the given mirror line","Uses the same value for both coordinates","Thinks x = ? is a horizontal line through ? ","Does not realise that if the horizontal and vertical measurements of a diagonal line segment switch it remains the same size","Includes the x variable when giving the equation of a horizontal line","Does not know how to find the y intercept when given two other sets of coordinates that lie on a straight line","Does not know how to find missing lengths in a composite shape","Believes a line segment can be opposite an axis","Believes that one point is enough to specify a line","Does not know that we can use the conservation of perimeter to find missing lengths","Mistakes lines as parallel","Does not know the meaning of the word parallel","Confuses left and right","Confuses lines of the form y = a and y= ax","Thinks y = ? is a vertical line through ?","Believes that points on an axis have equal x and y coordinates","Not considered the y value when reading coordinates","Forgets to add starting value when calculating new coordinates","Believes lines of reflection must be vertical or horizontal","Believes lines are parallel if they have the same y intercept ","Believes two lines of the same length are parallel","Reflects instead of rotates","Fails to reflect across mirror line","Believes the area of a rectangle is calculated by length add width","Thinks that only the sides need to be equal for a polygon to be regular","Thinks x = 1 at the x axis","Believes if a point is reflected in the line x=a then the x coordinate of the point will become 'a'","Believes the space diagonal is the same length as the diagonal on the bottom face of a cuboid","Mixes up the x and y values of the coordinates","Uses an incorrect side length when splitting a composite shape into parts","Believes lines can be parallel by having the same y intercept OR gradient","Believes there is more than one line which passes through a given pair of points","Believes that the y intercept is (0, y) where y is any y coordinate on the line","Believes a horizontal line can show a constant rate of change","Does not know what dashes on the sides of shapes mean","Does not know the information each vertical line of a box plot represents","Fails to identify mirror line","Thinks you can find missing values in a given table by treating the row as linear and adding on the difference between the first two values given.","Given a line segment with a midpoint that is not the origin, assumes that the two end points will still have the same absolute value","Thinks co-interior angles are equal","When a point is on an axis, gives both coordinates as the value it's at on the axis"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Properties of Quadrilaterals ### ConstructName: Identify the order of rotational symmetry of a shape ### Question: Which shape has the lowest order of rotational symmetry?","positive":["Does not know how to find order of rotational symmetry"],"negative":["Mixes up smallest and largest when ordering fractions","When comparing unit fractions believes that fractions with larger denominators are greater in size.","Ordered fractions by comparing denominators rather than using equivalent fractions.","Believes that fractions with larger denominators are greater in size","Ordered from largest to smallest","believes that a fraction with the largest denominator will be smallest regardless of the numerator","When ordering integers, orders from the digits at the end of the number instead of the digits at the start","Does not find a common denominator when comparing fractions","Mixes up smallest and greatest when ordering positive integers","Mixes up smallest and largest when ordering decimals","Believes negative numbers with a larger absolute value are greater","Assumes that a list is given in size order","Believes that fractions with the same denominator are equal","Mixes up greater than and less than symbols","When ordering decimals, believes the decimal point is not relevant","Believes a smaller number of shaded parts represents a smaller fraction","Does not understand inequality notation","Thinks a greater number of shaded parts represents a greater fraction","Believes that if the numerators of 2 fractions are equal then the fractions are equal, regardless of the denominator","Does not understand equivalent fractions","Does not know how to compare decimal numbers","Believes that a fraction means dividing the denominator by the numerator","Chosen the longest value rather than the greatest","When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right.","Does not realise you can use equivalent fractions to break fractions up into smaller divisions","Thinks numbers greater than 1 cannot be converted into fractions","Ignores the negative sign","Does not understand the 'less than' inequality notation","Believes that the larger the dividend, the smaller the answer.","Does not consider the denominator when adding\/ subtracting fractions. Adds\/subtracts the numerator and makes the denominator the one with the highest value.","Believes unit fractions with a difference of 1 in the denominator have no other fractions between them","Believes that the larger the divisor, the larger the answer.","Believes that the smaller a divisor is, the smaller the answer will be","Does not understand how to maintain equivalence in fractions","When converting a fraction to a decimal, divides the denominator by the numerator","Believes -a is always smaller than a, ignoring the possibility that a is negative","Thinks the more digits a number has the greater it is, regardless of place value","Mixes up shortest and longest when ordering times","When ordering numbers in standard form just looks at the decimal without multiplying by a power of 10","Counts on in the wrong direction on a number line","Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)","Counts in the wrong direction on a number line","Does not understand that the numerator and denominator of fractions represent groupings and have the same order of priority as brackets","Uses numerators to convert fractions to ratio despite different denominators","Believes the smaller number is always subtracted from the larger, regardless of the order of the calculation","Gives the smallest whole when asked for the smallest fraction shaded, presented visually","Thinks that a larger shaded area represents a larger fraction","Does not relate integers and fractions","Forgets to change the numerators when finding equivalent fractions","Believes the sides of an inequality can be switched without changing the direction of the sign"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: BIDMAS ### ConstructName: Use the order of operations to carry out calculations involving brackets ### Question: \\[\n9-8+5\n\\]\nJo and Paul are trying to make the calculation above equal to \\( 6 \\).\nJo says you can write it like this: \\( 9-(8+5) \\)\nPaul says you can leave it like this: \\( 9-8+5 \\)\nWho is correct?","positive":["Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)"],"negative":["Adds instead of multiples","Adds instead of multiplies","Has added the powers rather than multiplying them","Multiplied the powers rather than added them","Multiplies by the index","Arithmetic error when multiplying by 7","Adds the index to the number","Believes that when multiplying a number with a power, the multiplier is added onto the power","Adds instead of multiplies when multiplying algebraic terms","Thinks we have to add the base numbers as well as the powers when multiplying indices","When multiplying variables, thinks they add coefficients as well as powers","Thinks the multiplication sign means to add","Added the base numbers","Adds instead of multiplying when expanding bracket","Believes that multiplying variables is the same as adding them together","Believes squaring is the same as adding two","Thinks a variable next to a number means addition rather than multiplication","Multiplied the base numbers","Has multiplied the base number and the power","When multiplying algebraic terms written in the same base, adds the base variables and multiplies the powers.","Subtracts instead of multiplies","Thinks two variables next to each other represent addition","When adding variables with powers, thinks they can add the powers","Thinks index notation represents repeated addition rather than repeated multiplication","Divides by the index","Multiplies rather than adds ","Thinks multiplication and addition are the same","Mixes up squaring and multiplying by 2 or doubling","Multiplies coefficients and letters separately and writes as an addition","When substiting into an algebraic term, raises the coefficient to the power of the variable rather than multiplying the coefficient and the variable..","Ignores the zero when multiplying","Believes you multiply matching bases when carrying out a multiplication","Adds instead of subtracts","When two digits multiply to 10 or more during a multiplication problem, does not add one to the preceding digit","When multiplying fractions, adds the numerators and multiplies the denominators","Writes the index as a digit on the end of a number","When multiplying fractions, adds the numerators and the denominators","Added rather than multiplied by a scale factor","Adds rather than multiplies when asked for a product","Has increased by the value of the first value, rather than the difference","Has multiplied the value of the first term by the the term being asked","Believes you add the terms together when multiplying like terms.","Thinks multiplying by a variable is the same as raising to the power of that variable","When multiplying numbers with the same base, multiplies the powers ","Thinks the subtraction sign means multiply","Assumes they multiply by the numerator of fractional index","Believes addition of terms and powers of terms are equivalent e.g. a + c = a^c","When multiplying numbers with different bases, multiplies the powers and multiplies the base numbers.","Has multiplied by the root power","Added the values together instead of finding the percentage"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Volume and Capacity Units ### ConstructName: Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape ### Question: A regular pentagon has a total perimeter of \\( 17 \\mathrm{~cm} \\).\nWhat is the length of each of its sides?","positive":["When given the perimeter of a regular polygon, multiplies instead of divides to find each side length"],"negative":["Believes a curve can show a constant rate","Believes a horizontal line can show a constant rate of change","Believes a line showing a constant rate of increase corresponds to a non-prism shape","Does not know the properties of a cylinder","Does not know the meaning of uniform cross section","Believes infinite gradient is not possible in real life. ","Believes a direct proportion graph is a horizontal line","Does not realise that a curved line represents a changing gradient","Does not interpret a sloping gradient as a change in rate","Believes a steeper downwards line on a graph means a slower decrease","Believes all linear graphs show direct proportion","Thinks a cylinder is a prism","Believes a reciprocal equation will have a linear graph","Does not know the properties of a linear graph","Believes that a general trend of an increase or decrease over time, on a statistical diagram, means that the slope must be in the same direction for the whole time period","Confuses the graphs of  direct and inverse proportion","Believes a less steep gradient corresponds to a faster speed","Believes a direct proportion graph can have a negative gradient","Believes linear graphs can be curved","Confuses linear and reciprocal graphs","When reading value from graph, reads from the wrong axes.","Believes a reciprocal graph can be a straight line","Does not know the definition of a cone","Confuses a constant with a variable","Does not realise that gradient represents rate of change","Confuses pyramid with prism","Believes when you plot a linear sequence it doesn't give a straight line","Believes a cubic equation will have a linear graph","Believes that graphs of inverse proportion meet the axes","Thinks depth is marked on the cross section of a prism","Struggles to visualise elevations of 3D shapes","Assumes that a graph always starts at the origin","Does not understand that a line graph shows a relationship between 2 variables","Thinks depth always goes front to back in a diagram of a 3D shape","Confuses rest and movement on a distance time graph","Does not recognise that a linear sequence must increase or decrease by same amount","Believes an upward line has a negative gradient","Believes scales on graphs must match on both axes","Struggles to visualise nets of 3D shapes","Believes you cannot have a negative gradient when plotting a linear sequence","Does not know the meaning of the word regular ","Believes direct proportion means a 1:1 ratio","Thinks terms in linear sequence are in direct proportion","Reflects instead of rotates","Thinks the shape of the graph does not affect the area calculation","Believes a quadratic graph can be a straight line","Does not understand the term 'linear'","Assumes all journeys of the same distance take the same amount of time","Assumes regular shape refers only to a square","Confuses the dependent and independent variables on the axes of a line graph"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Horizontal and Vertical Lines ### ConstructName: Recognise the equations of horizontal lines from a diagram ### Question: What is the equation of this line? ![A graph showing a horizontal line going through 4 on the y axis.]()","positive":["Confuses the equations of vertical and horizontal lines"],"negative":["Thinks the more digits a number has the greater it is, regardless of place value","When ordering decimals, believes the decimal point is not relevant","When ordering integers, orders from the digits at the end of the number instead of the digits at the start","Believes negative numbers with a larger absolute value are greater","Ordered from largest to smallest","Mixes up smallest and largest when ordering decimals","Does not know how to compare decimal numbers","Orders integers based on first digits without taking into account place value","Does not know the units column is before the decimal point","Chosen the longest value rather than the greatest","When ordering numbers in standard form just looks at the decimal without multiplying by a power of 10","Student thinks that negative decimals behave the same as positive decimals when positioning a decimal between two consecutive negative integers, placing the decimal with a greater absolute value to the right. ","Does not equate the value of a number with the place value column it is in","When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right.","Does not understand that having values after the decimal point makes a number larger than a number with the same units but no decimal places","Believes -a is always smaller than a, ignoring the possibility that a is negative","Does not understand place value after the decimal point","Mixes up smallest and greatest when ordering positive integers","When asked for the value of a digit, gives an answer 10 times too small","Does not understand which place value is the one that determines if a number rounds up or down","Believes digits of a number are read\/written from right to left","Mixes up greater than and less than symbols","When dividing decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.","When multiplying decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.","When comparing unit fractions believes that fractions with larger denominators are greater in size.","Does not understand the value of zeros as placeholders","Mixes up colder and hotter when comparing temperatures","Counts on in the wrong direction on a number line","Believes a number written in standard form is smaller than another number written in standard form if the number between 1 and 10 is smaller","When asked for the value of a digit, gives an answer 10 times too big","Counts in the wrong direction on a number line","Believes a number written in standard form with a negative power creates a larger number than that with a positive power","Thinks subtracting a negative makes your answer smaller","Ignores the negative sign","Does not understand the meaning of \"value\"","Does not understand place value within a number","Mixes up smallest and largest when ordering fractions","Identifies wrong place value column after decimal point","Believes that fractions with larger denominators are greater in size","Rounds down instead of up","Lines up the digits incorrectly when doing a subtraction involving two numbers with a different amount of digits","Believes you subtract the smaller digit from the larger digit in column subtraction, regardless of position","Assumes that a list is given in size order","Ordered fractions by comparing denominators rather than using equivalent fractions.","Heads towards zero when subtracting from a negative","When subtracting decimals with a different number of decimals, subtracts one digit from more than one column","Believes an outlier is determined by the number of decimal places a number has","Changes wrong place value column when rounding","Thinks decimal place value works the same as integer place value, ones will follow tenths","Rounds to the wrong degree of accuracy (rounds too little)"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Adding and Subtracting Fractions ### ConstructName: Add proper fractions with the same denominator ### Question: Calculate:\n\\(\n\\frac{2}{7}+\\frac{1}{7}\n\\)","positive":["When asked to add fractions, multiplies instead"],"negative":["Does not recognise when simplifying a fraction may be helpful","Does not understand how to simplify fractions","Does not recognise when a fraction can be simplified","Does not understand a percentage is out of 100","Does not know that you can leave a fraction in improper form","Does not understand a percentage can be applied to something not out of 100","Only reads the percentage symbol as applying to the units digit","Does not realize we can write a division as a fraction","Believes percentages cannot be converted into fractions","Believes a fraction out of a number other than 100 represents a percentage","Does not know how to read information off a pie chart","Does not know how to simplify algebraic fractions","Does not know how to say a fraction","Does not understand equivalent fractions","Unable to equate a division and multiplication to a single division","Does not understand power notation","Does not understand how to find percentages of an amount","Does not think 'other' is an acceptable category for data","Does not know how to convert percentages with a decimal point into decimals","Does not fully simplify fraction","Does not understand the question","Does not understand changing decimals to fractions","Estimated when not appropriate","Forgot to simplify the fraction","Thinks they can convert a 2 digit percentage to a fraction by writing one number over the other.","Thinks that a unit fraction can be simplified further","Unable to equate two divisions with a single division","Does not understand the relationship between a ratio and fraction","Does not know how to write a fraction - just given an integer answer","Thinks you just add a % sign to the numerator to make a fraction into a percentage","Does not recognise difference of two squares","Does not relate integers and fractions","Thinks you need to just remove the percentage sign to convert from a percentage to a decimal","Does not understand that the numerator and denominator of fractions represent groupings and have the same order of priority as brackets","Does not realise ratio in worded problem can be simplified","Does not understand the value of zeros as placeholders","Does not realize we can simplify a term that involves powers","Assumes fractions with prime numerators cannot be simplified","Does not recognise a unit of time","Does not know that you can have a decimal percentage","Assumes that converting a decimal percentage to a fraction, they can just convert the decimal to a fraction, instead of writing the decimal over 100.","Believes you cannot find the angle size in a pie chart when given its percentage value","When converting a percentage to a decimal, just writes all the digits after a decimal point.","Believes you can make assumptions about size of pie chart sectors without enough information","Assumes decimal point can be ignored when given a decimal percentage to convert to a fraction","Does not realise you can use equivalent fractions to break fractions up into smaller divisions","Does not recognise factorising a quadratic","Does not understand inequality notation","Does not understand equivalent ratios","Thinks they can convert percentages to fractions by writing the percentage value as both the numerator and the denominator"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Substitution into Formula ### ConstructName: Substitute positive integer values into expressions involving powers or roots ### Question: When \\( h=10 \\)\nWhich of the following pairs of statements is true?","positive":["Answers order of operations questions with brackets as if the brackets are not there"],"negative":["Believes an interior angle in a regular polygon can be found using 180(n+2)\/n","Believes the only way to find the interior angle of a regular polygon is to subtract the exterior angle from 180.","Thinks rule for calculating interior angles only applies to regular polygons","Believes an interior angle in a regular polygon can be found using 360 subtract (180 over number of sides)","Does not understand to find each interior angle of a regular polygon you divide the sum by the number of sides","Thinks the interior angle of a regular polygon is 10n","Thinks the interior angles of any polygon add up to 180 degrees","Believes that you are unable to calculate the sum of the interior angles of an irregular polygon given the number of sides","Does not know how to calculate the sum of interior angles","Thinks the interior angles of any polygon add up to 360","Thinks the interior angles of a polygon add up to 100n","Does not understand what an interior angle is","Thinks that only the angles need to be the same for a polygon to be regular","Thinks that only the sides need to be equal for a polygon to be regular","Does not understand that all angles and sides must be equal for regular shapes","Does not recognise that interior and exterior angles are supplementary","Does not subtract 2 from the number of sides when finding the sum of interior angles","Does not know the meaning of the word regular ","Divides by (n-2) rather than n when finding an interior angle","Believes interior angles are outside a shape","Does not consider that all three angles in a triangle sum to 180 degrees","When given the perimeter of a regular polygon, subtracts instead of divides to find each side length","Does not know that angles in a triangle sum to 180 degrees","Assumes regular shape refers only to a square","Thinks the term polygons only applies to shapes with more than 3 sides","Only multiplies the first term in the expansion of a bracket","Does not recognise parallel lines angle rules applied inside a shape","Believes that an exterior angle can have a value of 360 degrees","Believes 1 is not a factor of a number","Does not realise that all regular shapes of a certain type will be similar","Does know know equilateral means the same as regular ","Thinks the value of an exterior angle is 360 degrees","Does not know what an exterior angle is ","Believes you add 2 instead of subtracting 2 to the numbers of sides when finding total interior angles","Confuses interior angles with exterior angles","Does not know that angles on a straight line sum to 180 degrees","Forgets to subtract sum of angles we know from 180 to find missing angle in a triangle","Identified the interior not exterior angle at a point","When given the perimeter of a regular polygon, multiplies instead of divides to find each side length","Only multiplies second term in the expansion of a bracket","Thinks only one variable can introduce bias","Does not understand that in the ratio 1:n the total number of parts would be 1+n ","Finds interior angle rather than given angle","Believes the constant only gives the y-intercept for linear graphs","Does not understand the question","Thinks only angles on parallel lines can be alternate","Believes only the first term needs to be divided when factorising an expression","Does not recognise that addition is the inverse operation of subtraction","Does not understand the concept of inverse operations in algebra","Assumes a fact without considering enough examples"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Reflection ### ConstructName: Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object ### Question: The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with a reflection line drawn and a triangle. The reflection line passes through the coordinates: (-1,-1) (0,0) (1,1) (2,2) etc. The triangle has coordinates: (2,2) (3,3) and (4,2). P is the coordinate (4,2).]()","positive":["Counts the squares rather than the diagonals when reflecting in y=x or y=-x "],"negative":["Mixes up greater than and less than symbols","Does not understand the 'less than' inequality notation","Does not understand inequality notation","Assumes that a list is given in size order","Ordered from largest to smallest","When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning.","When ordering integers, orders from the digits at the end of the number instead of the digits at the start","Believes the sides of an inequality can be switched without changing the direction of the sign","Believes negative numbers with a larger absolute value are greater","Confuses the shaded and unshaded regions on an inequality diagram","When asked to find data points below a certain value, gives the number of data points above this value","Counts on in the wrong direction on a number line","Confuses inequality symbols with equality","Counts in the wrong direction on a number line","When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right.","When asked to find data points above a certain value, gives the number of data points below this value","Believes that fractions with larger denominators are greater in size","When using inequality notation, thinks \"greater than\/less than or equal to\" symbols are instead the \"greater than\/less than\" symbols and vice versa","Confuses the lower and upper bound","Believes inequalities cannot be combined","Believes that 'less than' includes the number ","Thinks subtracting a negative makes your answer smaller","When comparing unit fractions believes that fractions with larger denominators are greater in size.","Believes a smaller number of shaded parts represents a smaller fraction","Believes greater than\/less than symbols include end values","Includes a data point with the value, when asked to find the number of data points below a value","Mixes up the inequality signs in an error interval","Confuses left and right","Believes they must change the direction of the inequality when dividing through by a positive number.","Believes an upward line has a negative gradient","Rounds down instead of up","When ordering decimals, believes the decimal point is not relevant","Confuses least and most","Thinks a dashed line marking a region means the line is included","Selects y>a solutions instead of y<a solutions for a quadratic inequality","Mixes up smallest and greatest when ordering positive integers","Mixes up colder and hotter when comparing temperatures","Confuses the union and intersection of inequalities","Ignores the negative sign","Believes reading from a cumulative frequency diagram will give the frequency above a certain value, rather than below","Subtracts from left to right, ignoring the word \u2018from\u2019","Believes they can multiply\/divide through by a negative number without changing the direction of the inequality","Student thinks that negative decimals behave the same as positive decimals when positioning a decimal between two consecutive negative integers, placing the decimal with a greater absolute value to the right. ","Believes inequalities can only include integers","Believes -a is always smaller than a, ignoring the possibility that a is negative","Believes digits of a number are read\/written from right to left","Cannot evaluate if an estimate is an underestimate or overestimate","Heads towards zero when subtracting from a negative","Believes rounding numbers down would give an overestimate","Thinks a greater number of shaded parts represents a greater fraction"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Equation of a Circle ### ConstructName: Given a sketch of a circle with centre at the origin, write its equation in the form x\u00b2 + y\u00b2 = r\u00b2 ### Question: What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]()","positive":["Mixes up squaring and multiplying by 2 or doubling"],"negative":["Does not find a common denominator when adding\/subtracting fractions","Forgets to change the numerators when finding equivalent fractions","Adds instead of subtracts","When adding fractions, changes to common denominator but leaves numerators the same","Does not understand how to maintain equivalence in fractions","When subtracting fractions, subtracts the numerators and denominators","Does not find a common denominator when comparing fractions","Subtracts instead of adds","Does not understand equivalent fractions","Does not consider the denominator when adding\/ subtracting fractions. Adds\/subtracts the numerator and makes the denominator the one with the highest value.","Does not understand how to subtract algebraic fractions","When subtracting fractions, divides the numerators","Removes the common denominator when making equivalent algebraic fractions","Subtracts numerators when dividing fractions with a common denominator","Believes they should multiply each numerator by its original denominator when adding\/subtracting fractions","Incorrectly cancels what they believe is a factor in algebraic fractions","Ignores the negative sign","Believes subtraction is commutative ","Performs subtraction in wrong order","Subtracts the smallest digit from the largest digit","When adding\/subtracting fractions, adds\/subtracts the denominators and multiplies the numerators","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","Performs addition ahead of subtraction","Does not compensate when subtracting","Believes that fractions with the same denominator are equal","Believes equivalent fractions are formed with addition not multiplication","When subtracting fractions, subtracts the numerators and multiplies the denominators","Multiplies the numerators when adding fractions with a common denominator","When adding fractions, adds the numerators and denominators","substitutes incorrectly","Thinks the fraction bar means subtract rather than divide","Subtracts instead of divides","Adds or subtracts from numerator first when solving an equation with a fraction","Adds instead of subtracts when asked to find the difference","Thinks the subtraction sign means multiply","Subtracts instead of multiplies","Carries out operations from left to right regardless of priority order","Uses numerators to convert fractions to ratio despite different denominators","Tries to add or subtract unlike terms","Does not realise that subtracting a negative is the same as adding it's additive inverse","When converting from an improper fraction to a mixed number, adds on the part left to make the whole, rather than subtracting it","Thinks the subtraction sign means divide","Confused mixed numbers with improper fractions","When adding fractions with identical numerators, leaves the numerator and adds the denominators","Does not recognise when one part of a fraction is the negative of the other","Does not know the term numerator","Thinks that when you cancel identical terms from the numerator and denominator, they just disappear","Does not know that 7 and -7 are different","when subtracting a fraction from an integer, just adds their absolute value and places a negative sign in front","Ignores the negative signs when adding positive and negative numbers"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Pie Chart ### ConstructName: Interpret a pie chart ### Question: A darts player hits his target \\( 40 \\% \\) of the time. Which pie chart represents his hits and misses?","positive":["Does not know how to read information off a pie chart"],"negative":["Does not understand the first significant value is the first non-zero digit number","Identifies second decimal place value when asked for the second significant figure","Identifies first decimal place value when asked for first significant figure","Gives the first significant figure when asked for the second","Rounds to wrong degree of accuracy (decimal places rather than significant figures)","Gives the second significant figure when asked for the first","Counts leading zero as a significant figure","Rounds to the wrong degree of accuracy (significant figures rather than decimal places)","Rounds to the wrong degree of accuracy (rounds too much)","Rounds to the wrong degree of accuracy (rounds too little)","Forgotten placeholders when rounding to significant figures","Rounds down instead of up","Does not understand which place value is the one that determines if a number rounds up or down","Does not understand the value of zeros as placeholders","Changes wrong place value column when rounding","Rounds up instead of down","Rounds down instead of up when next digit is 5","When ordering integers, orders from the digits at the end of the number instead of the digits at the start","Believes digits of a number are read\/written from right to left","Rounds to the nearest integer rather than one significant figure","Rounds to the nearest hundredth, rather than one significant figure","Orders integers based on first digits without taking into account place value","Rounds too early in calculation ","Rounded to wrong degree of accuracy (2sf not 1sf)","Ignores the negative sign","Ordered from largest to smallest","Does not understand the meaning of \"value\"","Rounds incorrectly by changing multiple place values","Does not know the units column is before the decimal point","When ordering decimals, believes the decimal point is not relevant","Thinks the more digits a number has the greater it is, regardless of place value","When doing operations with decimals, ignores significant zeros after the decimal point","Identifies wrong place value column after decimal point","Believes you subtract the smaller digit from the larger digit in column subtraction, regardless of position","Rounds up rather than to one significant figure","When rounding to decimal places and the only digits after the decimal point will be zeros, just gives the integer as the answer.","Believes an outlier is determined by the number of decimal places a number has","When rounding, believes that if the number, after the required degree of accuracy, is a 5 or below you round down","Mixes up greater than and less than symbols","Believes rounding to 1 significant figure means rounding to the nearest integer, regardless of the value of the number","Rounds too little when estimating","Believes that rounding must change the number","When subtracting decimals with a different number of decimal places, lines up the digits incorrectly","Thinks the first term in a sequence is the term before the sequence begins (0th term)","Counts on in the wrong direction on a number line","Thinks that the lower and upper bound for a truncated number can be found in the same was as when it has been rounded","Mixes up smallest and largest when ordering decimals","Does not equate the value of a number with the place value column it is in","When subtracting decimals with a different number of decimals, subtracts one digit from more than one column","Gives a rounded whole number instead of a decimal"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Mental Multiplication and Division ### ConstructName: Recognise and use efficient methods for mental multiplication ### Question: Tom and Katie are discussing ways to calculate \\( 21 \\times 12 \\) mentally Tom does \\( 12 \\times 7 \\) and then multiplies his answer by \\( 3 \\) Katie does \\( 21 \\times 6 \\) and then doubles her answer Who would get the correct answer?","positive":["Does not correctly apply the distributive property of multiplication"],"negative":["Thinks the sum of 2 numbers, each squared first, is the same as adding the two numbers and then squaring the total","Thinks 1 squared is 2","Square roots when asked for second multiple","Does not recall larger square numbers","Does not know what a square number is","Mixes up squaring and multiplying by 2 or doubling","Believes a power of 2 has no impact on its value","Has increased by the value of the first value, rather than the difference","Adds the index to the number","Mixes up squaring and addition","Believes squaring is the same as adding two","Believes the square of a negative will also be negative","Squares when asked to find the square root","Added the base numbers","Mixes up square numbers and cube numbers","Does not think a square root can be negative","Adds instead of subtracts","Mixes up square numbers and prime numbers","Only looks at the difference between one pair of terms when discerning the pattern","Halves when asked to find the square root","When completing the square in the form (x - a)^2 + b, believes b is the difference between a and the constant of the original quadratic","Believes 0 has no square root","Does not understand square root","Multiplies by the index","Believes the difference between triangle numbers remains the same","Ignores the negative sign","When comparing non like surds, does not square the surds","Adds instead of subtracts when asked to find the difference","Mixes up square numbers and even numbers","Thinks you can find missing values in a given table by treating the row as linear and adding on the difference between the first two values given.","Does not link Pythagoras Theorem to finding distance between two points","Believes square numbers are triangle numbers","When adding roots, adds the numbers under the roots","When completing the square in the form (x - a)^2 + b, believes b = a^2 + the original constant","Thinks you can find missing values in a given table by treating the row as a sequence of consecutive numbers","Ignores a more than question and just states one of the values","When completing the square in the form (x - a)^2 + b, believes b = the original constant","Adds instead of multiples","Mixes up squaring and multiplying by 2 or doubling, and not square rooted","Counts on by 1, when asked to count forward\/backwards in a step other than 1","When finding the distance between coordinates, includes the starting number","Subtracts instead of adds","Believes we can only take the square root of a perfect square","Chooses an example when asked for a counter-example","When finding the distance between 2 points, believes the distance is the coordinate of the furthest point from origin","Assumes a fact without considering enough examples","Adds rather than subtracts when using Pythagoras to find a shorter side","Believes the difference between triangle numbers decreases by 1 each time","Believes you can square root a negative number","Thinks that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Quadratic Equations ### ConstructName: Solve quadratic equations using the quadratic formula where the coefficient of x\u00b2 is not 1  ### Question: Mo wants to solve this equation using the quadratic formula.\n\\(\n5 h^{2}-3 h-2=0\n\\)\n\nWhat total should replace the square? \\( \\begin{array}{l} \\frac{ ?\\pm \\sqrt{9-(-40)}}{?} \\\\ = \\frac{ ?\\pm \\sqrt{\\square}}{?} \\end{array} \\)","positive":["When subtracting a negative number, adds the absolute values and then writes the answer with a negative sign"],"negative":["Believes the solution to mx + c = a is the x intercept of y = mx +c","Believes the solution to mx + c = a is the y intercept of y = mx +c","Thinks they solve mx + c = a, by substituting in the value of a for x and therefore calculating ma + c","Believes the solution of mx + c = a is x =a","When solving an equation, uses the same operation rather than the inverse.","When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value","Believes they solve mx + c = 0 by substituting in x = 0","Believes the solution of mx + c = 0 is x = m","When reading value from graph, reads from the wrong axes.","Finds the y intercept when asked to read the solution to a quadratic equation from a graph","Believes that the reciprocal of a number is equal to that number (1\/x = x)","Only gives 1 value of x for a given value of y, when reading from a parabolic graph","Solves for y=0 instead of given y-value when reading from a quadratic graph","Believes that in y=mx+c, m is the x-intercept","When solving simultaneous equations graphically, only gives one of two solutions","Subtracts instead of adds when using inverse operations to solve an equation","Stops iteration too early when solving equations","When finding an input of a function machine thinks you apply the operations given rather than the inverse operation.","Believes the solution of mx + c = 0 is x =0","Adds or subtracts from numerator first when solving an equation with a fraction","Believes the y-intercept of a line is the solution to its equation","When solving simultaneous equations, assumes every variable has equal value.","substitutes incorrectly","When asked to read a value from a graph, thinks they give the corresponding value on the other axis, rather than reading from the graph","Heads towards zero when subtracting from a negative","Believes that in y=mx+c, m is the y-intercept","Believes that the solution to ax + b = 0 is x = -a\/b","Does not reverse the order of operations when solving an equation","When solving an equation forgets to eliminate the coefficient in front of the variable in the last step","Believes the equation of a straight line is y=-mx+c","Believes solving an inequality gives a single value as a solution","Believes f(x) - a translates the function up a units","When solving an equation, subtracts instead of dividing","Thinks that in the equation x=a, a is the gradient","When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation","When solving simultaneous equations graphically, they think the solutions are the x or y intercepts","Believes the solutions of a quadratic equation are the constants in the factorised form","When solving simultaneous equations graphically, they think the solutions are the y-intercepts","Gives an answer of 0 when there are no solutions to an equation.","Includes the x variable when giving the equation of a horizontal line","Thinks x = ? is a horizontal line through ? ","Believes subtracting a positive number from a negative number makes the answer less negative","Believes that a number divided by itself equals the original number","Reflects in an axis, instead of the given mirror line","Believes the equation of a straight line is y=-mx-c","Thinks the sign of solutions in a quadratic equation is always the same as the constant term","When solving simultaneous equations graphically, they think the solutions are the x-intercepts","Has used the wrong data point on the graph","Believes subtraction is commutative ","Believes substituting the starting value into an iteration formula immediately gives the solution"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Mental Addition and Subtraction ### ConstructName: Complete missing number mental subtraction problems up to 100 ### Question: What should replace the star? \\( \\bigstar-37=38 \\)","positive":["When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit"],"negative":["Counts the starting number when counting on","Believes the number of jumps between two numbers on a numberline represents the sum of those 2 numbers ","Counts the starting number when counting backwards","Forgets to add on the starting value when identifying a position on a number line","Believes a gap of 2 is a gap of 1 on a numberline","Believes a negative number can be replaced with its positive equivalent when answering an addition problem from a numberline","Does not count end number when counting","When reading integers on a number line, assumes each dash is 2","Counts on by 1, when asked to count forward\/backwards in a step other than 1","Adds instead of subtracts","Ignores the negative sign","When reading integers on a number line, assumes each dash is 1","Assumes that an arrow on a number line starts at zero","Counts in the wrong direction on a number line","Counts on in the wrong direction on a number line","When finding the difference between two marks on a scale, counts lines instead of gaps","When finding the distance between coordinates, includes the starting number","Believes we move down a number line when we add","Does not include zero when counting over zero","Ignores the negative signs when adding positive and negative numbers","Miscounts when subtracting over zero","When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored ","When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.","Heads towards zero when subtracting from a negative","Out by 10 when subtracting","When reading integers on a number line, assumes each dash is 10","Subtracts instead of adds","Believes that adding a negative will increase the value of the original number","When describing a translation, miscounts when crossing an axis","Forgets to add starting value when calculating new coordinates","when reading a dash on a number line counts 1 dash too few when working out the divisions","Thinks the difference between a positive number and a negative number is equal to the positive number","When asked for a specific term in a sequence gives the term after","When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation","Subtracts the smallest digit from the largest digit","Treats zero as a ten when subtracting","Confuses left and right","When reading a dash on a number line does not take into account the number at the start or the width of each division","Ignores partial symbols on pictograms","Reads the position of a number from the space between the line marked, rather than the line marked","Believes subtraction is commutative ","Thinks positive or negative sign affects the term before it","Believes the arrow on a number line points to the middle value","Believes a quarter of 2 is 0.25","Does not compensate when subtracting","When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right.","Ignores position\/value of midpoint when trying to label a point on scale","Adds instead of subtracts when asked to find the difference","When subtracting a negative number, subtracts the absolute value rather than adding it"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Perimeter ### ConstructName: Use perimeter to write algebraic expressions ### Question: What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length a and side length b]()","positive":["Fails to use the properties of simple shapes to work out missing lengths"],"negative":["When reading value from graph, reads from the wrong axes.","When solving simultaneous equations graphically, only gives one of two solutions","Has used the wrong data point on the graph","Assumes that a graph always starts at the origin","When finding the difference between two points on a time series graph, only uses one of the points. ","When solving simultaneous equations graphically, they think the solutions are the x or y intercepts","When solving simultaneous equations graphically, they think the solutions are the y-intercepts","When solving simultaneous equations graphically, they think the solutions are the x-intercepts","When reading graph, chooses nearest marked value on axis instead of reading accurately","Misreads scale","Believes a direct proportion graph does not have to start at the origin","Believes scales on graphs must match on both axes","Makes an assumption about the squares on a scale representing either 1 or 10","Does not check the labelling of the axes ","Believes direct proportion means a 1:1 ratio","Does not understand the command word 'difference'","Believes change in y for gradient is always calculated from the origin, regardless of the y-intercept of the line","Believes the line y = mx - c will cross the y axis at c","Does not recognise the origin as the starting point for coordinates","Assumes every dash on a scale represents an increase of 1","Assumes the scale is the same when comparing two similar diagrams","Believes the solution to mx + c = a is the x intercept of y = mx +c","Confuses the dependent and independent variables on the axes of a line graph","Incorrect use of scale on a diagram","Believes it's not possible to solve simultaneous equations graphically","Counts squares instead of the correct scale when plotting coordinates","Ignores a more than question and just states one of the values","Believes a direct proportion graph is a horizontal line","When asked to read a value from a graph, thinks they give the corresponding value on the other axis, rather than reading from the graph","Believes the gradient is where the line intersects the y axis","Does not account for scale on diagram","Includes a data point with the value, when asked to find the number of data points above a value","Believes they solve mx + c = 0 by substituting in x = 0","Finds the y intercept when asked to read the solution to a quadratic equation from a graph","Believes the solution to mx + c = a is the y intercept of y = mx +c","Reads one point on a time series graph instead of all the values from a given time period","Believes that graphs of inverse proportion meet the axes","When comparing data, only compares one category of data rather than comparing the totals","Does not understand the difference between a value on a graph and the gradient of a graph","Believes the solution of mx + c = 0 is x =0","When finding the distance between coordinates, includes the starting number","Thinks that the scale on axes has to match with the number of squares","Reads 10,000 as 1000","When describing a translation, miscounts when crossing an axis","Believes that in y=mx+c, m is the x-intercept","Does not know the y intercept is where the x coordinate is 0","Not considered the y value when reading coordinates","Believes that the y intercept is where y = 0","Confuses negative and positive coordinates when working with graphs in four quadrants","Confuses left and right"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Expanding Double Brackets ### ConstructName: Expand two brackets with linear terms in the form (ax + b)(cx + d) ### Question: Alison is expanding these two brackets.\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the -4 in the first bracket and the -3 in the second bracket.]()","positive":["Believes multiplying two negatives gives a negative answer"],"negative":["Does not understand bar modelling in algebra","Believes that 1 part of a bar model will always have a value of 1","Does not understand what each part of a bar model represents as a fraction","When drawing bar diagram for ratio, shows the total amount as the total of one side","Believes the number of bars gives the total on a bar chart","Confuses section and whole when using a bar model","Does not know how to use a bar model to write division facts","Does not realise that two letters together, or a number and letter together, are multiplying","Does not take into account the whole amount when using a bar model to find a fraction","Confuses histograms with bar charts","Only multiplies the first term in the expansion of a bracket","Does not realise that two letters together are multiplying","When reading a composite bar chart, just reads total height of bar","Only multiplies second term in the expansion of a bracket","Thinks the longest bar has the highest frequency on a pictogram, even if the symbols aren't evenly spaced","Does not understand use of the counters to represent algebra","When drawing bar diagram for ratio, shows the total as the difference between parts","Confuses an expression with a term","Believes class width represents area of the bar in a histogram","Does not think that a variable with no coefficient has a coefficient of 1.","Does not know what the symbol for equal lengths means","Believes number of squares in a bar gives frequency on a histogram","Confuses a term with an equation","Writes the variable before the coefficient in an algebraic term","Confuses a term with a variable","Assumes the scale is the same when comparing two similar diagrams","Does not account for scale on diagram","Does not understand parts must be equal in a fraction diagram","Assumes value of symbols in a pictogram without checking the key","Only multiplies the numerical terms when expanding a bracket","Does not know the meaning of the identity symbol","Believes class width multipled by frequency gives the area of the bar in a histogram","Does not understand when like terms can be collected","Ignores coefficients when forming an expression from a question","Does not understand the interpretation of the fx column in a frequency table","Confuses an expression with a variable","Does not know the correct notation for labelling a side length","When interpreting a pictogram, thinks each symbol stands for 1","In algebra, thinks it's ok to write (for example) 0x rather than just 0","Does not know that a single letter labels a vertex","Ignores partial symbols on pictograms","Does not include brackets when attempting to multiply an expression","Uses an incorrect side length when splitting a composite shape into parts","Counts partial symbols as if they were whole on pictograms","Does not understand how to multiply algebraic terms","Confuses collecting like terms with multiplication","Does not realize we can omit the multiplication symbol in algebraic expressions","Mixes up total and part when forming expressions from worded problems","When factorising into double brackets, believes the sum of the two values in the brackets equals bx rather than b","Thinks the smallest bar in a bar chart is the mode"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Length Scale Factors in Similar Shapes ### ConstructName: Solve length problems involving similar shapes where the missing length is the shorter one ### Question: These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The bigger one has sides 9 cm and 7.5 cm. On the smaller triangle, the side corresponding to the 9 cm is 6 cm, and the side corresponding to the 7.5 cm is marked with a star.]()","positive":["Does not understand how to find a scale factor"],"negative":["Uses cos when tan is required","Uses cos when sin is required","Uses tan when cos is required","Uses sin when cos is required","Uses sin when tan is required","Uses tan when sin is required","Does not understand how to apply sohcahtoa","Believes the adjacent side is where the opposite side is in a right angled triangle","Confuses order of sides in a trigonometric ratio","Tries to apply sohcahtoa to a non right angled triangle","Believes the opposite side is where the adjacent side is in a right angled triangle","Misremembers the exact values of trigonometric functions at standard angles","Forgets to apply inverse trigonometric function when finding an angle","Confuses adjacent and opposite sides","Believes 0.5absin(c) requires only three sides (potentially confused with cosine rule)","Confuses tangent and radius","Believes the sin graph relates to the cos function","Does not find the angle being asked","Confuses tangent and chord","Is not able to identify a situation where Pythagoras' Theorem is needed","Believes any of the angles can be used in the trigonometric formula for area of a triangle","Mixes up sides of a ratio","Has an incorrect assumption about the definition of a reciprocal","Does not know that a right angle is 90 degrees","Uses 2 letters to describe an angle","Does not link Pythagoras Theorem to finding distance between two points","Does not understand equivalent ratios","Subtracts rather than adds when using Pythagoras to find the hypotenuse","Confuses tangent and circumference","Adds rather than subtracts when using Pythagoras to find a shorter side","Does not know the meaning of square sign for right angle","Thinks adjacent angles are equal","Forgets to include a marked right angle when performing angle calculations","Does not realise that the order is important in a ratio","Does not know the meaning of alternate","Believes the sin graph relates to the tan function","Gives 3-letter angle notation in the wrong order","Does not know the correct notation for labelling a side length","Confuses chord and radius","Does not rearrange the Pythagoras' Theorem formula accurately","Only uses the closest angle to the unknown when using the angles in a straight line relationship","Believes unrelated acute\/obtuse angles in a diagram are supplementary","Confuses obtuse and acute angles","Does not know the meaning of corresponding","Estimates angle rather than calculating","Does not understand that base angles in an isosceles are equal","Has used slant height and base to find area of a triangle rather than perpendicular height and base","Believes all triangles have a right angle","Does not know the definition of a rational number","Does not know the word and\/or does not know the function of a compass"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Adding and Subtracting Fractions ### ConstructName: Add proper fractions with different denominators which do not share a common factor ### Question: \\(\n\\frac{1}{3}+\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star?","positive":["Does not find a common denominator when adding\/subtracting fractions"],"negative":["Mixes up odd and even numbers","Mixes up square numbers and even numbers","Believes even numbers can have odd multiples","Believes two odd numbers multiply to give an even number","Believes all multiples of odd numbers are odd","Believes all triangle numbers are odd","Does not recognise that the intersection of a Venn diagram represents those belonging to both sets","Chooses an example when asked for a counter-example","Does not know what a square number is","Gives the intersect value of a Venn diagram when asked to find the value of a set only","Believes the intersection on a Venn diagram represents the total of one set","Includes the intersection of a Venn diagram when asked to find the value of a set only","Does not understand that 2n represents an even number","Believes that prime numbers cannot be even","Believes the number outside the circles in a Venn represents the intersection","Mixes up the sets in a Venn diagram","Assumes a fact without considering enough examples","Thinks numbers are a multiple of their index","Believes the square of a negative will also be negative","Mixes up square numbers and prime numbers","Mixes up squaring and multiplying by 2 or doubling","Believes sets are the same if the elements within them have a shared property","Believes raising a negative number to an odd power will give a positive answer","Only considers elements in one set when asked to find the intersection of multiple sets","Believes adding b to any integer gives a multiple of b","Believes square numbers are triangle numbers","Adds the index to the number","Does not understand how to answer generalised statements (eg. by testing values to check for always, sometimes, never)","Does not think a number can be a multiple of itself","Believes the intersection in a prime factor venn diagram does not contribute to the size of the number represented by a circle ","Thinks the term in a sequence is double the position value","Believes 0 has no square root","Confuses intersection and universal set","Thinks multiplying two or more negative numbers together always gives a positive answer, regardless of how many negative numbers there are in the sum","Believes that the complement of a set includes any elements which are also in another set.","Does not know the definition of a prime number","Thinks the sum of 2 numbers, each squared first, is the same as adding the two numbers and then squaring the total","Believes the total of the circle in a Venn should be included when intersections should be omitted","Believes 1 is a prime number","Thinks you cannot find the range if there are an even number of values","When finding the median for an odd numbered data set, find the midpoint of two values rather than giving the middle value","Forgets to include the intersection value when asked for total value of a set in a Venn diagram","Fails to consider all possible outcomes","Does not recall larger square numbers","believes the complement of a set consists of elements which only belong to one set","Does not know the definition of a composite number","When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle","Does not know the meaning of consecutive","Believes that the complement of a set in a triple Venn consists of the elements that only belong to one other set","Does not know the meaning of the word identity "],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Rotation ### ConstructName: Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object ### Question: John rotates rectangle \\( A B C D 90^{\\circ} \\) clockwise from the centre \\( (3,2) \\). What error has he made? ![A positive, coordinate grid with two rectangles drawn on it. The rectangle labelled ABCD has the coordinates: A(1,3) B(1,5) C(2,5) and D(2,3). The other rectangle has the coordinates: (4,3) (6,3) (6,2) and (4,2).]()","positive":["Mixes up clockwise and anticlockwise"],"negative":["Does not recognise the notation for parallel sides","Does not know the meaning of the word parallel","Thinks that if two lines do not intersect on a diagram then they will never intersect and are therefore parallel","Does not recognise a parallelogram","Does not recognise parallel lines angle rules","Does not know what dashes on the sides of shapes mean","Confuses the sign for parallel lines as being dashes","Mistakes lines as parallel","Does not know parallel lines have equal gradients ","Does not know that co-interior angles must be in parallel lines","Believes the arrows for parallel lines mean equal length","Does not recognise parallel lines angle rules applied inside a shape","Does not know the meaning of corresponding","Believes two lines of the same length are parallel","Does not know what the symbol for equal lengths means","Does not know the meaning of congruent","Does not understand the diagram given in the question","Describes lines when asked to describe angles","Does not know the properties of a rectangle","Does not know the meaning of alternate","Does not know how to compare size of angles on a grid without a protractor","Does not know the meaning of perpendicular","Thinks sign for parallel lines just means opposite","Does not recall rectangle side length property","Does not know the properties of a parallelogram","Does not know the term transversal","Believes lines can be parallel by having the same y intercept OR gradient","Confuses the meaning of parallel and perpendicular","Cannot identify a line of symmetry in a simple shape","Believes lines are parallel if they have the same y intercept ","Does not realise similar has a specific mathematical meaning","Believes parallel is the term used to describe two lines at right angles","Confuses the signs for straight lines as being dashes","Fails to identify mirror line","Believes it's not possible to solve simultaneous equations graphically","Does not understand that shapes are congruent if they have the same size and shape","Believes parallelogram is the term used to describe two lines at right angles","Does not understand how to find a scale factor","Does not realise the lines at an intersection have to be straight in order to show vertically opposite angles","Does not realise that if the horizontal and vertical measurements of a diagonal line segment switch it remains the same size","Believes mirror line must lie on a grid line, not in between grid lines","Fails to reflect across reflection line without a diagram","Does not know how to find the length of a line segment from coordinates","Believes any lines that cross are perpendicular","Believes parallel lines have gradients of opposite signs","Believes only angles on parallel lines can be called \"corresponding\"","Does not know the correct notation for labelling a side length","Does not know how to check tessellation","Does not recognise the properties of a kite","Does not recognise that a shape translated would not change orientation"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Multiplying and Dividing with Decimals ### ConstructName: Divide two decimals with a different number of decimal places ### Question: \\( 70.04 \\div 0.1= \\)","positive":["When dividing decimals, divides rather than multiplies when reinserting the decimal."],"negative":["Does not understand that area under a speed time graph gives distance because distance = speed x time","Believes distance = speed + time","Believes the length of the line in a velocity time graph gives the distance (rather than the area underneath that line).","Thinks the shape of the graph does not affect the area calculation","Believes distance is the area under the graph on a displacement time graph","Believes that when finding area under graph you can use the upper y value rather than average of upper and lower","When finding the difference between two points on a time series graph, only uses one of the points. ","Believes distance = speed\/time","Adds when calculating area instead of multiplying","Believes speed = time\/distance","Believes that addition should be used when finding the difference between two values on a time series graph","Believes the area of a rectangle is calculated by length add width","Believes scales on graphs must match on both axes","Believes speed is distance multiplied by time","Makes an assumption about the squares on a scale representing either 1 or 10","Reads one point on a time series graph instead of all the values from a given time period","Does not half sum of parallel sides when finding area of a trapezium","Estimated when not appropriate","Believes time = speed x distance","Believes the gradient of a speed-time graph is the distance","Calculates perimeter when asked for area","Believes the gradient of a speed-time graph is the speed","When calculating perimeter, only adds the marked lengths","When reading value from graph, reads from the wrong axes.","Confuses displacement-time graphs with velocity-time graphs","Does not divide by 2 when calculating the area of a trapezium","Does not divide by 2 when finding midpoint","Adds when calculating volume instead of multiplying","When reading graph, chooses nearest marked value on axis instead of reading accurately","Added rather than multiplied by a scale factor","Assumes a sequence is linear","Finds the difference in a coordinate pair rather than the midpoint","Has used the wrong data point on the graph","Uses formula for area of a parallelogram when finding the area of a trapezium","Believes a downward slope on a speed-time graph shows positive acceleration","Does not understand the difference between a value on a graph and the gradient of a graph","Forgets to add starting value when calculating new coordinates","Believes midpoint calculation is just half of the difference","Believes midpoints are plotted on histograms","Adds instead of multiplies","Adds instead of multiples","Assumes every dash on a scale represents an increase of 1","Does not have when calculating the area of a triangle","Assumes grouped data is evenly distributed within each group","Assumes all journeys of the same distance take the same amount of time","Thinks a variable next to a number means addition rather than multiplication","Believes the midpoint of grouped data is equivalent to the group width","Finds the median instead of the mean","Does not divide by 2 when calculating the area of a triangle","Does not know how to find the length of a line segment from coordinates"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Percentages of an Amount ### ConstructName: Express one quantity as a percentage of another mentally ### Question: What is \\( 50 \\mathrm{~m} \\) as a percentage of \\( 5 \\mathrm{~km} \\) ?","positive":["Thinks you need to just add a % sign to a number to make it a percentage"],"negative":["Does not recall rectangle side length property","Does not know the properties of a rectangle","Does not know the diagonals of a square bisect at right angles","Does not know the properties of a parallelogram","Does not know the properties of a rhombus","Does not believe the length of a diagonal line can be worked out based on horizontal and vertical measurements","Does not understand the question","Does not know that a right angle is 90 degrees","Believes a parallelogram cannot have right angles","Does not know what dashes on the sides of shapes mean","Does not recognise the properties of a kite","Does not know the meaning of perpendicular","Does not recognise a parallelogram","Does not realise that if the horizontal and vertical measurements of a diagonal line segment switch it remains the same size","Does not understand the diagram given in the question","Does not recognise parallel lines angle rules","Believes isosceles triangles cannot have right angles","Does not know a rectangle is a type of parallelogram ","Does not know the meaning of square sign for right angle","Thinks that perpendicular lines do not meet at 90 degrees","Believes you need to know the value of all algebraic variables before any general conclusions can be made","Does not recognise parallel lines angle rules applied inside a shape","Does not know the properties of an isosceles triangle","Does not understand how to answer generalised statements (eg. by testing values to check for always, sometimes, never)","Does not know the meaning of the word regular ","Does not know a rhombus is a type of parallelogram ","Believes any lines that cross are perpendicular","Believes particular is the term used to describe two lines at right angles","Believes the sides of a rectangle must be horizontal and vertical, not diagonal","Does not believe a shape can have two correct names e.g. rectangle and parallelogram","Assumes a fact without considering enough examples","Fails to reflect across reflection line without a diagram","Does not realise the lines at an intersection have to be straight in order to show vertically opposite angles","Believes a rectangle has one pair of equal sides","Is not able to identify a situation where Pythagoras' Theorem is needed","Believes a rectangle has four equal sides","Does not know that angles on a straight line sum to 180 degrees","Thinks rule for calculating interior angles only applies to regular polygons","Thinks that if two lines do not intersect on a diagram then they will never intersect and are therefore parallel","Does not know that co-interior angles must be in parallel lines","Believes a kite has bisecting diagonals","Does not know that we can use the conservation of perimeter to find missing lengths","Does not know the meaning of alternate","Given the length of the sides, still does not recognise there is enough information to find the area","Believes that angles that look like they are a right-angle are always 90 degrees","Fails to use the properties of simple shapes to work out missing lengths","Does not know the term 'diameter'","Does not know the definition of the range","Does not understand square root","Does not understand the meaning of the word commutative "],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Written Division ### ConstructName: Interpret and carry out mental division using a bar model ### Question: Find the value of \\( P \\). ![Horizontal green bar divided into 5 equal sections. Each section is labelled with a \"P\". Curly bracket shows that 3 of the sections sum to 615.]()","positive":["Believes the amount given is for the whole rather than a part"],"negative":["Multiplies by the index","Mixes up squaring and multiplying by 2 or doubling","Divides by the index","Has multiplied the base number and the power","Adds the index to the number","Has multiplied by the root power","Mixes up squaring and multiplying by 2 or doubling, and not square rooted","Believes a power of 2 has no impact on its value","Writes a variable to the power of n as nx","Multiplied the base numbers","Believes cubing a number means you multiply it by 3","Believes squaring a fraction requires you to double both parts","Reads a power as a normal digit","Believes the square of a negative will also be negative","Adds instead of multiplies","Has added the powers rather than multiplying them","When multiplying out 2 or more brackets, does not multiply all the combinations of terms","Adds instead of multiples","Mixes up cubing and squaring","Writes the index as a digit on the end of a number","Multiplied the powers rather than added them","Assumes they multiply by the numerator of fractional index","When substituting a value into a non-linear term with a coefficient, multiplies by the coefficient then calculates the power.","Has completed only one of the two operations.","Mixes up squaring and multiplying by 4","Believes term to term rule is applied to position number, not previous term","Believes multiplying two negatives gives a negative answer","Subtracted base numbers as well as powers","Thinks index notation represents repeated addition rather than repeated multiplication","When squaring a variable, believes they also need to square the coefficient","Believes squaring is the same as adding two","Divides by the order of the root","Subtracts instead of multiplies","Believes division is carried out before a power","Thinks that when raising a variable with a coefficient to a power, only the coefficient is affected by the power","Believes the inverse of square rooting is doubling","Believes squaring a negative number just changes the sign","Thinks numbers are a multiple of their index","Has cubed the base number and the power","Repeats the digits twice when squaring a number","Carries out operations from left to right regardless of priority order","When substiting into an algebraic term, raises the coefficient to the power of the variable rather than multiplying the coefficient and the variable..","Adds instead of multiplying when expanding bracket","Thinks halving is the same as multiplying by 2","Believes that when multiplying a number with a power, the multiplier is added onto the power","Multiplies before applying a power ","Multiplies rather than divides","Mixes up cubing and multiplying by 3","Thinks 1 squared is 2","Forgot to square both parts of the fraction"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Properties of Quadrilaterals ### ConstructName: Recall and use the intersecting diagonals properties of a rectangle ### Question: The diagonals of a rectangle with different length sides \\(_____________\\) intersect at right-angles ![A rectangle]()","positive":["Does not know the properties of a rectangle"],"negative":["Believes speed = time\/distance","Believes distance = speed\/time","Believes speed is distance multiplied by time","Believes time = speed x distance","Mistakes unit of speed for unit of time","Thinks the units for speed should not contain a measure of time","Assumes the denominator is divided by the numerator","Believes that a fraction means dividing the denominator by the numerator","When calculating a scale factor, thinks the division is the other way around.","Believes gradient = change in x\/change in y","Believes distance = speed + time","Divides by the index","When converting a fraction to a decimal, divides the denominator by the numerator","Believes division is commutative ","When adding fractions, adds the numerators and multiplies the denominators","when multiplying fractions multiplies by the reciprocal of the 2nd fraction instead","Believes gradient is the difference between the change in x and the change in y","Believes dividing by a unit fraction is equivalent to dividing by its reciprocal","Multiplies rather than divides","When substituting into an algebraic term, believes they can disregard the coefficient","Divides rather than multiplies ","When multiplying fractions, multiplies the denominator","When adding fractions, adds the numerators and denominators","When substituting into an algebraic term, replaces variables with numbers without multiplying.","Believes that dividing by a decimal is the same as dividing by its reciprocal","When subtracting fractions, subtracts the numerators and multiplies the denominators","When dividing fractions, does the reciprocal of the first fraction instead of the second","When dividing fractions, does the reciprocal of both fractions","Believes class width = frequency density","Confuses a variable with a formula","When finding the gradient from the equation of a line in the form ax + by = c, believes b\/a is the gradient","Mixes up the value of two terms when substituting","Thinks the fraction button finds the reciprocal","Believes you divide 1 by the number of values, rather than the total, when finding the mean","When substiting into an algebraic term, raises the coefficient to the power of the variable rather than multiplying the coefficient and the variable..","Uses term-to-term rule as numerical part of nth term rule","Gets their constants and coefficients the wrong way around when writing a formula from a given situation","Uses dividing fractions method for multiplying fractions","Believes a proportion of a whole is whole\/part not part\/whole","Believes gradient at a point = y coordinate\/x coordinate","When multiplying a fraction by an integer, multiplies the denominator instead of the numerator","Divides length of original by length of image to find scale factor, rather than image by original.","Multiplies by the index","Multiplies instead of divides when division is written as a fraction","Divides when converting to a smaller unit","When solving an equation, thinks the divisor and dividend are the opposite way around","substitutes incorrectly","Believes they always divide by the conversion factor when converting units","Believes the gradient of a line is given by the x intercept","Swaps the dividend and divisor in order to get an integer answer"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: 2D Names and Properties of Shapes-Others ### ConstructName: Understand the terms equilateral and regular, and recognise the notation for regular polygons ### Question: Tom and Katie are discussing regular polygons. Tom says this is a regular polygon ![A triangle with 3 equal sides and 3 equal angles]() Katie says this is a regular polygon ![A parallelogram with 2 pairs of parallel sides marked]() Who is correct?","positive":["Does not know the meaning of the word regular "],"negative":["When finding the gradient from the equation of a line in the form ax + by = c, believes b\/a is the gradient","Believes that for a line written in the form ax + by = c, a is the gradient","When solving an equation where there is a negative sign in front of the variable at the final stage, believes they can ignore it and treat it as if it's positive","Believes dividing a negative by a positive gives a positive answer","When given the equation of a straight line, believes the first term always gives the gradient, even when the first term is actually c","When solving an equation, uses the same operation rather than the inverse.","Believes dividing a positive by a negative gives a positive answer","When solving an equation forgets to eliminate the coefficient in front of the variable in the last step","When solving an equation, thinks the divisor and dividend are the opposite way around","Thinks signs are interchangeable when adding or subtracting positive and negative numbers","Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c","Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations.","Ignores the negative signs when adding positive and negative numbers","Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we do the operation inverse to the sign (- if positive, + if negative)","Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we do the operation matching the sign (+ if positive, - if negative)","Believes multiplying a positive by a negative gives a positive answer","Thinks they solve mx + c = a, by substituting in the value of a for x and therefore calculating ma + c","When solving an equation, believes that when they get to ax = b, b is the solution","When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value","Does not think that a variable with no coefficient has a coefficient of 1.","Believes subtraction is commutative ","When solving simultaneous equations, believes the terms must have the same sign in order to be eliminated.","Believes a downward line has a positive gradient","When solving an equation, adds instead of dividing","Believes the constant gives the y-intercept even when a line is not written in the form y = mx + c","Swaps the dividend and divisor in order to get an integer answer","When solving simultaneous equations, assumes every variable has equal value.","Believes gradient = change in x\/change in y","When solving simultaneous equations, finds the correct numbers to transform the equations, but uses them the wrong way around.","When collecting like terms, assigns positivity or negativity incorrectly.","Believes switching the x and y variables in a linear equation gives a perpendicular line","When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored ","Believes that in completed square form, the x co-ordinate of the turning point has the same sign as the constant in the brackets.","Believes they must change the direction of the inequality when dividing through by a positive number.","Believes they can change the subject of a formula just by swapping two letters","Believes that the solution to ax + b = 0 is x = -a\/b","Does not reverse the order of operations when solving an equation","Believes adding two negatives gives a positive answer","Believes the gradients of perpendicular lines are reciprocals of the same sign","Adds or subtracts from numerator first when solving an equation with a fraction","Believes that in y = mx+c, c is the gradient","Ignores the negative sign","Ignores negative sign when expanding bracket","When solving an equation, subtracts instead of dividing","Believes they can multiply\/divide through by a negative number without changing the direction of the inequality","Subtracts instead of adds when using inverse operations to solve an equation","Misunderstands the process of making a variable the subject of an equation","Believes that in y=mx+c, m is the y-intercept","Confuses the inverse operations of addition and subtraction when rearranging equations","substitutes incorrectly"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Converting between Decimals and Percentages ### ConstructName: Convert decimals less than 1 with 3 or more decimal place to percentages ### Question: How do you write \\( 0.909 \\) as a percentage?","positive":["Does not understand the value of zeros as placeholders"],"negative":["Does not know the definition of term or term-to-term rule","Thinks the first term in a sequence is the term before the sequence begins (0th term)","Describes position to term rule using term to term rule","When asked for a specific term in a sequence gives the term after","Goes the wrong direction in the sequence when identifying term-to-term rule","When asked for a specific term in a sequence gives the next term","Describes term to term rules using position to term rules","Thinks n=0 for the first term in a sequence","Thinks the first term of a sequence must be 1","Believes subtraction is commutative ","Uses term-to-term rule as numerical part of nth term rule","When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n.","Identifies the term-to-term rule rather than the next term","When asked for a specific term in a sequence just gives the next term","Identifies the first term rather than the next term in a sequence","Uses first term as numerical part of nth term rule","When asked for a specific term in a sequence gives the term before","Does not know how to calculate the position of a term in a sequence","Believes nth term rule can be given in words","Uses only the first two terms of a sequence to work out a term-to-term rule","Mixes up term in a sequence and position of a term","Thinks you subtract rather than add when finding the previous term in a descending linear sequence","Believes term to term rule is applied to position number, not previous term","When asked for a specific term in a sequence, just gives the position number","Identifies how much repeated use of the term-to-term rule changes a number but does not apply to the sequence","Identifies the term-to-term rule rather than the next term in a sequence","Believes they can find the nth term based on the first term only","When asked for a specific term in a sequence gives a different term, which is not the next","Believes the nth term of a descending sequence will have a positive coefficient of n","Thinks the nth term is when the value of the term is n","Thinks terms in linear sequence are in direct proportion","Believes the position number in a sequence does not have to be an integer","Thinks the term in a sequence is double the position value","When given a term to term sequence with multiple steps, applies one step per term","Only uses two terms of a sequence to work out a term-to-term rule","Uses difference as index instead of coefficient in nth term rule","Believes that in the nth term of a descending sequence, b is the difference between the term and the positive multiple of n","Believes the subscript in iteration notation is the value to be substituted","Believes substituting the starting value into an iteration formula immediately gives the solution","Adds instead of subtracts","Does not include zero when counting over zero","Believes you multiply the constant difference by the term number to get the term value","Does not know how to find the next term in a sequence","substitutes incorrectly","Ignores the negative sign when thinking about the value of a term","When finding the differences between terms in a sequence, believes they can do so from right to left ","When using a function machine, confuses the input and the output.","When finding an input of a function machine thinks you apply the operations given rather than the inverse operation.","Adds the index to the number","Does not recognise that a linear sequence must increase or decrease by same amount"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Equation of a Circle ### ConstructName: Given a sketch of a circle with centre at the origin, write its equation in the form x\u00b2 + y\u00b2 = r\u00b2 ### Question: What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]()","positive":["Confuses the radius with the radius squared in the equation of a circle"],"negative":["Does not find a common denominator when adding\/subtracting fractions","Forgets to change the numerators when finding equivalent fractions","Adds instead of subtracts","When adding fractions, changes to common denominator but leaves numerators the same","Does not understand how to maintain equivalence in fractions","When subtracting fractions, subtracts the numerators and denominators","Does not find a common denominator when comparing fractions","Subtracts instead of adds","Does not understand equivalent fractions","Does not consider the denominator when adding\/ subtracting fractions. Adds\/subtracts the numerator and makes the denominator the one with the highest value.","Does not understand how to subtract algebraic fractions","When subtracting fractions, divides the numerators","Removes the common denominator when making equivalent algebraic fractions","Subtracts numerators when dividing fractions with a common denominator","Believes they should multiply each numerator by its original denominator when adding\/subtracting fractions","Incorrectly cancels what they believe is a factor in algebraic fractions","Ignores the negative sign","Believes subtraction is commutative ","Performs subtraction in wrong order","Subtracts the smallest digit from the largest digit","When adding\/subtracting fractions, adds\/subtracts the denominators and multiplies the numerators","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","Performs addition ahead of subtraction","Does not compensate when subtracting","Believes that fractions with the same denominator are equal","Believes equivalent fractions are formed with addition not multiplication","When subtracting fractions, subtracts the numerators and multiplies the denominators","Multiplies the numerators when adding fractions with a common denominator","When adding fractions, adds the numerators and denominators","substitutes incorrectly","Thinks the fraction bar means subtract rather than divide","Subtracts instead of divides","Adds or subtracts from numerator first when solving an equation with a fraction","Adds instead of subtracts when asked to find the difference","Thinks the subtraction sign means multiply","Subtracts instead of multiplies","Carries out operations from left to right regardless of priority order","Uses numerators to convert fractions to ratio despite different denominators","Tries to add or subtract unlike terms","Does not realise that subtracting a negative is the same as adding it's additive inverse","When converting from an improper fraction to a mixed number, adds on the part left to make the whole, rather than subtracting it","Thinks the subtraction sign means divide","Confused mixed numbers with improper fractions","When adding fractions with identical numerators, leaves the numerator and adds the denominators","Does not recognise when one part of a fraction is the negative of the other","Does not know the term numerator","Thinks that when you cancel identical terms from the numerator and denominator, they just disappear","Does not know that 7 and -7 are different","when subtracting a fraction from an integer, just adds their absolute value and places a negative sign in front","Ignores the negative signs when adding positive and negative numbers"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Quadratic Sequences ### ConstructName: Given a description of an ascending sequence using quadratics in words, write some terms of that sequence ### Question: ![Square and then subtract \\( 4 \\)]() The first three terms of which sequence below is produced by this term-to-term rule?","positive":["Describes term to term rules using position to term rules"],"negative":["Only multiplies the first term in the expansion of a bracket","Only multiplies second term in the expansion of a bracket","Only multiplies the numerical terms when expanding a bracket","Ignores negative sign when expanding bracket","Does not understand equivalent fractions","Adds instead of multiplying when expanding bracket","Only applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction","When substituting into an algebraic term, replaces variables with numbers without multiplying.","Expands when asked to simplify","Believes you can subtract from inside brackets without expanding when solving an equation","Does not include brackets when attempting to multiply an expression","Believes only the first term needs to be divided when factorising an expression","Has removed brackets but not performed the operation","Does not consider the variable when evaluating an expression that requires substitution.","When subtracting fractions, subtracts the numerators and denominators","Does not understand how to subtract algebraic fractions","When subtracting fractions, subtracts the numerators and multiplies the denominators","When multiplying out 2 or more brackets, does not multiply all the combinations of terms","Incorrectly cancels what they believe is a factor in algebraic fractions","Believes that n\/n = n, instead of 1","Believes they only need to multiply the first and last pairs of terms when expanding double brackets","Does not think that a variable with no coefficient has a coefficient of 1.","Thinks you can ignore the variable when simplifying algebraic fractions","Believes you can add or subtract from inside brackets without expanding when solving an equation","Has multiplied the value of the first term by the the term being asked","Thinks that when you cancel identical terms from the numerator and denominator, they just disappear","Believes they only need to multiply the first pair of terms when expanding a double bracket.","Does not understand how to maintain equivalence in fractions","Does not apply the inverse function to every term in an expression","Adds or subtracts from numerator first when solving an equation with a fraction","Has completed only one of the two operations.","Answers order of operations questions with brackets as if the brackets are not there","Thinks only one variable can introduce bias","Does not include brackets when required","Assumes any variable in a sum on the numerator can be divided by the denominator","Thinks the subtraction sign means multiply","Thinks terms in linear sequence are in direct proportion","When factorising into single brackets, factorises the first term correctly but subtracts the number outside the bracket with the second term in the expression to find the second term in the bracket","Believes they must expand brackets before solving an equation","Believes multiplying two negatives gives a negative answer","When substituting into an algebraic term, believes they can disregard the coefficient","Removes the common denominator when making equivalent algebraic fractions","Does not know how to simplify algebraic fractions","Forgets to change the numerators when finding equivalent fractions","When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored ","Does not fully simplify fraction","When adding fractions, changes to common denominator but leaves numerators the same","Multiplies all terms together when simplifying an expression","When expanding brackets, multiplies out the first term correctly but adds together the number outside the bracket with the second term inside the bracket.","When factorising, finds a factor that goes into only the first term of the expression"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: BIDMAS ### ConstructName: Insert brackets to make a calculation correct ### Question: \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ?","positive":["Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)"],"negative":["When asked for a specific term in a sequence gives the term before","When asked for a specific term in a sequence just gives the next term","When asked for the next term in the sequence adds one to the last term given, despite the sequence not going up in ones.","When asked for a specific term in a sequence gives the next term","When asked for a specific term in a sequence gives the term after","When asked for a specific term in a sequence gives a different term, which is not the next","When asked for the next term in the sequence subtracts one from the last term given, despite the sequence not going down in ones.","Thinks the first term in a sequence is the term before the sequence begins (0th term)","Thinks you subtract rather than add when finding the previous term in a descending linear sequence","Does not understand that adding on to a multiple can give you the next multiple","Thinks the term in a sequence is double the position value","Does not know how to find the next term in a sequence","Does not count end number when counting","Believes 'inclusive' does not include the end value","Does not know the meaning of consecutive","Does not recognise that a linear sequence must increase or decrease by same amount","Identifies the term-to-term rule rather than the next term","Believes that 'less than' includes the number ","Thinks the remainder is the difference between the dividend and the next biggest multiple","Believes there is a multiplicative relationship between values of terms in a linear sequence e.g. 10th term is double 5th term","Thinks terms in linear sequence are in direct proportion","Identifies how much repeated use of the term-to-term rule changes a number but does not apply to the sequence","Believes the position number in a sequence does not have to be an integer","When asked for a specific term in a sequence, just gives the position number","Identifies the first term rather than the next term in a sequence","Believes that in the nth term of a descending sequence, b is the difference between the term and the positive multiple of n","Identifies the term-to-term rule rather than the next term in a sequence","Thinks positive or negative sign affects the term before it","Believes the position of a sequence cannot be an integer","Believes greater than\/less than symbols include end values","When ordering integers, orders from the digits at the end of the number instead of the digits at the start","Rounds down instead of up","Counts on by 1, when asked to count forward\/backwards in a step other than 1","Does not know the definition of term or term-to-term rule","Ordered from largest to smallest","Believes adding b to any integer gives a multiple of b","Counts the starting number when counting backwards","Does not notice all changes in a sequence of visual patterns","Assumes a sequence is linear","Believes inequalities can only include integers","Rounds up instead of down","When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit","Thinks it can't be called a sequence with a repeated number at the start","Counts on in the wrong direction on a number line","Counts in the wrong direction on a number line","Believes the nth term of a descending sequence will have a positive coefficient of n","Thinks the nth term is when the value of the term is n","Thinks the positive and negative terms in a sequence will have the same absolute values","Thinks you can find missing values in a given table by treating the row as a sequence of consecutive numbers","Assumes that a list is given in size order"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Adding and Subtracting Fractions ### ConstructName: Add proper fractions with the same denominator ### Question: Work out:\n\\(\n\\frac{3}{10}+\\frac{5}{10}\n\\)\nWrite your answer in its simplest form.","positive":["When adding fractions, adds the numerators and denominators"],"negative":["Does not find a common denominator when adding\/subtracting fractions","Forgets to change the numerators when finding equivalent fractions","Does not understand how to maintain equivalence in fractions","Does not consider the denominator when adding\/ subtracting fractions. Adds\/subtracts the numerator and makes the denominator the one with the highest value.","When adding fractions, changes to common denominator but leaves numerators the same","Does not find a common denominator when comparing fractions","Adds instead of subtracts","Does not understand equivalent fractions","When subtracting fractions, subtracts the numerators and denominators","Removes the common denominator when making equivalent algebraic fractions","Does not understand how to subtract algebraic fractions","Subtracts instead of adds","Believes they should multiply each numerator by its original denominator when adding\/subtracting fractions","Ignores the negative sign","Incorrectly cancels what they believe is a factor in algebraic fractions","Subtracts numerators when dividing fractions with a common denominator","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","When subtracting fractions, divides the numerators","Performs addition ahead of subtraction","Adds or subtracts from numerator first when solving an equation with a fraction","When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored ","Does not compensate when subtracting","Believes equivalent fractions are formed with addition not multiplication","Thinks positive or negative sign affects the term before it","Carries out operations from left to right regardless of priority order","Subtracts the smallest digit from the largest digit","Out by 10 when subtracting","Believes that fractions with the same denominator are equal","Thinks that when you cancel identical terms from the numerator and denominator, they just disappear","Multiplies the numerators when adding fractions with a common denominator","Believes subtraction is commutative ","Performs subtraction in wrong order","After multiplying to get a common denominator, simplifies back to the original fractions","When \u201cborrowing\u201d during a subtraction problem, does not subtract one from the preceding digit","substitutes incorrectly","When adding\/subtracting fractions, adds\/subtracts the denominators and multiplies the numerators","Done a different calculation to the one given","Thinks the fraction bar means subtract rather than divide","Believes that rounding parts of a fraction in different directions means the answer will be the same. ","When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit","Does not include brackets when required","When adding fractions with identical numerators, leaves the numerator and adds the denominators","Denominator used for other parts rather than total parts","Uses numerators to convert fractions to ratio despite different denominators","When subtracting fractions, subtracts the numerators and multiplies the denominators","Forgot to simplify the fraction","Does not realise that subtracting a negative is the same as adding it's additive inverse","Answers order of operations questions with brackets as if the brackets are not there","When subtracting decimals with a different number of decimal places, lines up the digits incorrectly"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Sequences-Others ### ConstructName: Write the next term of a descending integer linear sequence ### Question: What is the next term in this sequence?\n\n\n\\[\n23, \\quad 13, \\quad 3, \\quad \\ldots\n\\]","positive":["Identifies the term-to-term rule rather than the next term"],"negative":["Does not realise you can use equivalent fractions to break fractions up into smaller divisions","Cannot identify a fraction on a number line","Believes the arrow on a number line points to the middle value","Ignores position\/value of midpoint when trying to label a point on scale","When reading a dash on a number line does not take into account the number at the start or the width of each division","Does not understand a denominator represents equal parts","When reading decimals on a number line, assumes each dash is 0.5","Reads the position of a number from the space between the line marked, rather than the line marked","Believes a quarter of 2 is 0.25","Believes a gap of 2 is a gap of 1 on a numberline","Does not understand equivalent fractions","Estimates a measurement on a diagram rather than working it out","Converts a fraction to a decimal by using the denominator after the decimal point","Does not know the meaning of bisect","Does not understand parts must be equal in a fraction diagram","Converts a fraction to a decimal by using only the numerator after the decimal point","When finding a point on a line, assumes the point is always the midpoint","Does not know how to say a fraction","Believes unit fractions with a difference of 1 in the denominator have no other fractions between them","Does not know how to interpret a fraction worded problem ","Does not see fraction diagrams as equivalent if the shading is in a different pattern","When reading decimals on a number line, assumes each dash is 0.1","When converting a fraction to a decimal, divides the denominator by the numerator","When finding the median for an odd numbered data set, find the midpoint of two values rather than giving the middle value","Misunderstands dashed lines as being the midpoint","Does not divide by 2 when finding midpoint","Believes midpoints are plotted on histograms","When using interpolation to estimate frequency, assumes half the frequency of the class containing the value will be above\/below it, even if it is not the midpoint","Identifies the wrong part of a fraction model as the whole","Believes the frequency of the midpoint of a group is half the total frequency of the group","Believes midpoint calculation is just half of the difference","Forgets to change the numerators when finding equivalent fractions","Believes that fractions with the same denominator are equal","Believes that a fraction means dividing the denominator by the numerator","Converts a fraction to a decimal by placing the denominator after the decimal point","When finding which term represents the median, thinks you divide the total number of terms by 2","Does not understand changing decimals to fractions","Thinks you cannot multiply by a decimal to get equivalent fractions","When given a non-unit fraction of an amount, treats it like a unit fraction","When reading integers on a number line, assumes each dash is 1","Does not find a common denominator when comparing fractions","When adding fractions, changes to common denominator but leaves numerators the same","Does not understand what each part of a bar model represents as a fraction","Believes that if the numerators of 2 fractions are equal then the fractions are equal, regardless of the denominator","Thinks there are 50 minutes in 1 hour","Does not know how to write a fraction - just given an integer answer","When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle","When counting partial symbols on pictogram, uses the fraction rather than the amount it represents","When reading decimals on a number line, assumes each dash is 0.2","Chooses the correct scale when measuring angles on a protractor but starts from the wrong number when the angle is in between two labelled dashes"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Properties of Quadrilaterals ### ConstructName: Identify a rhombus from a description of the properties ### Question: Tom and Katie have been asked to give the name of a quadrilateral with four equal sides\nTom says arrowhead\nKatie says rhombus\nWho do you agree with?","positive":["Believes an arrowhead has four equal sides"],"negative":["When asked for the next term in the sequence subtracts one from the last term given, despite the sequence not going down in ones.","When asked for a specific term in a sequence gives the next term","When asked for a specific term in a sequence just gives the next term","When asked for the next term in the sequence adds one to the last term given, despite the sequence not going up in ones.","Thinks you subtract rather than add when finding the previous term in a descending linear sequence","When asked for a specific term in a sequence gives the term after","Does not know how to find the next term in a sequence","Identifies the term-to-term rule rather than the next term","When asked for a specific term in a sequence gives a different term, which is not the next","Counts on by 1, when asked to count forward\/backwards in a step other than 1","Does not recognise that a linear sequence must increase or decrease by same amount","When asked for a specific term in a sequence gives the term before","Identifies the term-to-term rule rather than the next term in a sequence","Identifies the first term rather than the next term in a sequence","Uses only the first two terms of a sequence to work out a term-to-term rule","Does not know the definition of term or term-to-term rule","Identifies how much repeated use of the term-to-term rule changes a number but does not apply to the sequence","Goes the wrong direction in the sequence when identifying term-to-term rule","Only uses two terms of a sequence to work out a term-to-term rule","Thinks the first term in a sequence is the term before the sequence begins (0th term)","Assumes a sequence is linear","Counts the starting number when counting backwards","Only looks at the difference between one pair of terms when discerning the pattern","Does not notice all changes in a sequence of visual patterns","Believes the nth term of a descending sequence will have a positive coefficient of n","Does not know the meaning of consecutive","Believes that in the nth term of a descending sequence, b is the difference between the term and the positive multiple of n","Believes subtracting a positive number from a negative number makes the answer less negative","Heads towards zero when subtracting from a negative","When given a term to term sequence with multiple steps, applies one step per term","Does not count end number when counting","Out by 10 when subtracting","Describes position to term rule using term to term rule","Does not understand the effect of consecutive subtractions","Thinks the term in a sequence is double the position value","Thinks it can't be called a sequence with a repeated number at the start","Believes a gap of 2 is a gap of 1 on a numberline","Thinks subtracting a negative makes your answer smaller","Thinks you can find missing values in a given table by treating the row as a sequence of consecutive numbers","Believes the difference between triangle numbers decreases by 1 each time","Does not understand that adding on to a multiple can give you the next multiple","Believes term to term rule is applied to position number, not previous term","When subtracting past zero, adds the absolute values and then writes the answer with a negative sign","Thinks the first term of a sequence must be 1","Believes you cannot have a negative gradient when plotting a linear sequence","Adds instead of subtracts","Thinks terms in linear sequence are in direct proportion","Thinks the remainder is the difference between the dividend and the next biggest multiple","Believes an arithmetic sequence can have a common second difference rather than first difference","Counts on in the wrong direction on a number line"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Adding and Subtracting Fractions ### ConstructName: Add fractions involving mixed number fractions with different denominators ### Question: \\(\n2 \\frac{1}{3}+\\frac{3}{4}=3 \\frac{\\bigstar}{12}\n\\)\nWhat should replace the star?","positive":["Finds an equivalent improper fraction when asked for a mixed number"],"negative":["Incorrectly factorises a quadratic","Does not recognise factorising a quadratic","Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant","Incorrectly cancels what they believe is a factor in algebraic fractions","Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x","Believes the solutions of a quadratic equation are the constants in the factorised form","Cannot identify a common factor when simplifying algebraic fractions","Believes the solutions of a quadratic equation are the negative of the absolute values of the constants in the factorised form","Thinks you can divide terms by different factors when simplifying an algebraic fraction","Thinks you can ignore the variable when simplifying algebraic fractions","When factorising a quadratic without a non variable term, tries to double bracket factorise","Believes that the sign changes when factorising an expression into single brackets","Does not recognise difference of two squares","Factorises difference of two squares with the same sign in both brackets","Believes only the first term needs to be divided when factorising an expression","When simplifying an algebraic fraction, only looks for number factors","Thinks that when you cancel identical terms from the numerator and denominator, they just disappear","When asked for factors of an algebraic expression, thinks a term will be a factor","Only applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction","Does not understand the link between the sign of the root and the sign in the bracket","Believes the solutions of a quadratic equation are the absolute values of the constants in the factorised form","When factorising, finds a factor that goes into only the first term of the expression","Believes the difference of 2 squares method of factorising also works for the addition of 2 squares","Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets","Thinks factorising a quadratic means factorising the variable terms into a single bracket, and leaving out the constant","Thinks can combine the numerator and denominator after simplifying an algebraic fraction","Believes the numbers in factorising should multiply to give the coefficient of x and add to give the constant","Believes factors add to give a number","Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term\n","When factorising a quadratic with a coefficient of x squared, believes the signs and\/or positions of the constants are interchangeable","Forgets to swap the sign of roots when placing into brackets","Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term\n\n","When factorising, believes they can choose different factors for each term","When asked for factors of an algebraic expression, thinks any part of a term will be a factor","Thinks a quadratic without a non variable term, can not be factorised","When factorising into single brackets, factorises the first term correctly but subtracts the number outside the bracket with the second term in the expression to find the second term in the bracket","Assumes any variable in a sum on the numerator can be divided by the denominator","Does not know how to simplify algebraic fractions","Thinks x^2 - a^2x is a valid form of difference of two squares","Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","Thinks you can divide the variables and the numerical values by different numbers when simplifying an algebraic fraction","Believes that when factorising a quadratic with a coefficient of x squared, the two constants in the brackets still add to give the coefficient of x","Thinks the sign of solutions in a quadratic equation is always the same as the constant term","When sketching graphs of factorised quadratics, does not see that the negative of the non variable terms in the brackets give the x intercepts or the roots of the graph.","Believes the solution of a quadratic is its turning point","When factorising into single brackets, only factors out the numerical values and forgets to factorise possible variables","Misunderstands the concept of common factors in algebra","Does not know how to identify common factors from algebraic terms","Believes numbers are divisible by numbers which sum to their factors"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Expanding Double Brackets ### ConstructName: Expand two brackets with linear terms in the form (x + a)(x + b) ### Question: What should replace the circle when these two brackets are\nexpanded and simplified?\n\n\\(\n(p-3)(p+3) \\equiv p^{2} \\color{purple}\\triangle\\) \\(p\\)\\(\\color{green}\\bigcirc\n\\)\n","positive":["Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets"],"negative":["Believes the solution of a quadratic inequality is always the interval between the roots","Selects y>a solutions instead of y<a solutions for a quadratic inequality","Believes inequalities cannot be combined","Confuses the union and intersection of inequalities","Believes any two inequalities can be combined into a double inequality","Mixes up greater than and less than symbols","Thinks two-tailed inequalities can have a constant in the middle","Does not understand inequality notation","Solves for y=0 instead of given y-value when reading from a quadratic graph","Confuses inequality symbols with equality","Finds the y intercept when asked to read the solution to a quadratic equation from a graph","Does not understand the 'less than' inequality notation","Believes solving an inequality gives a single value as a solution","Confuses the shaded and unshaded regions on an inequality diagram","Assumes that a list is given in size order","Believes the solutions of a quadratic equation are the constants in the factorised form","Believes inequalities can only include integers","When using inequality notation, thinks \"greater than\/less than or equal to\" symbols are instead the \"greater than\/less than\" symbols and vice versa","Believes the sides of an inequality can be switched without changing the direction of the sign","Believes the solution of a quadratic is its turning point","Does not understand the link between the sign of the root and the sign in the bracket","Confuses the lower and upper bound","Confuses the graph of a linear equation with a quadratic equation","Believes the solutions of a quadratic equation are the negative of the absolute values of the constants in the factorised form","Believes greater than\/less than symbols include end values","Thinks a dashed line marking a region means the line is included","Believes that a positive x squared coefficient in a quadratic equation results in an n shaped graph","Believes you can square root a negative number","Believes all quadratic equations have a solution of 0","Believes that the solutions to x<b or x>b also satisfy ax<b or ax>b","Ordered from largest to smallest","Mixes up the inequality signs in an error interval","Confuses maximum and minimum","Thinks the sign of solutions in a quadratic equation is always the same as the constant term","Believes both solutions of a quadratic will have the same absolute value, even when the graph is not symmetrical about the y axis","Believes the solutions of a quadratic equation are the absolute values of the constants in the factorised form","Believes the solutions to an equation have opposite signs from its x intercepts","Forgets to swap the sign of roots when placing into brackets","Only gives 1 value of x for a given value of y, when reading from a parabolic graph","Does not think a square root can be negative","Can not square root a negative number","Believes negative numbers with a larger absolute value are greater","Gives an answer of 0 when there are no solutions to an equation.","Ignores the negative sign","When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning.","When sketching graphs of factorised quadratics, does not see that the negative of the non variable terms in the brackets give the x intercepts or the roots of the graph.","Believes that in completed square form, they need to change the signs of both values to get the turning point","Believes a cubic equation will have a quadratic graph","Incorrectly factorises a quadratic","Does not understand the term quadratic"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Construct Triangle ### ConstructName: Construct a triangle using Angle-Side-Angle ### Question: Which of the following best describes how to construct a triangle with side length \\( 7 \\mathrm{~cm} \\) with angles of \\( 40^{\\degree} \\) and \\( 50^{\\degree} \\) either side?","positive":["Draws both angles at the same end of the line when constructing a triangle"],"negative":["Does not see fraction diagrams as equivalent if the shading is in a different pattern","Does not understand equivalent fractions","Does not understand parts must be equal in a fraction diagram","Does not find a common denominator when comparing fractions","Believes equivalent fractions are formed with addition not multiplication","Believes a smaller number of shaded parts represents a smaller fraction","Forgets to change the numerators when finding equivalent fractions","Thinks a greater number of shaded parts represents a greater fraction","Believes that fractions with the same denominator are equal","Does not understand how to maintain equivalence in fractions","Does not understand equivalent ratios","Believes that if the numerators of 2 fractions are equal then the fractions are equal, regardless of the denominator","Uses numerators to convert fractions to ratio despite different denominators","Does not understand a denominator represents equal parts","Does not recognise when a fraction can be simplified","Cannot identify a fraction on a number line","Gives the smallest whole when asked for the smallest fraction shaded, presented visually","Ordered fractions by comparing denominators rather than using equivalent fractions.","Does not realise you can use equivalent fractions to break fractions up into smaller divisions","Does not recognise when one part of a fraction is the negative of the other","Removes the common denominator when making equivalent algebraic fractions","When writing fraction from diagram, writes total as denominator","Does not fully simplify fraction","Believes when simplifying a fraction you can divide the numerator and denominator by different values","Does not find a common denominator when adding\/subtracting fractions","Denominator used for other parts rather than total parts","Can identify the multiplier used to form an equivalent fraction but does not apply to the numerator","When subtracting fractions, subtracts the numerators and denominators","Assumed each part of a fraction diagram is worth 10%","Forgot to simplify the fraction","When adding fractions, adds the numerators and denominators","Believes a rectangle has one pair of equal sides","Does not notice all changes in a sequence of visual patterns","Does not understand how to simplify fractions","Identifies the wrong part of a fraction model as the whole","When adding fractions, changes to common denominator but leaves numerators the same","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","Assumes the scale is the same when comparing two similar diagrams","Is not able to spot a proportional relationship pictorially unless they are laid out in groups","Thinks that a larger shaded area represents a larger fraction","Finds the shaded section rather than the specified section","Shares equally instead of in given ratio","Does not scale up a ratio to find an equivalent value","Believes that fractions with larger denominators are greater in size","Does not understand that the numerator and denominator of fractions represent groupings and have the same order of priority as brackets","Does not recognise the corresponding sides in similar shapes or enlargements","Thinks that when you cancel identical terms from the numerator and denominator, they just disappear","When converting a fraction to a decimal, divides the denominator by the numerator","When adding fractions with identical numerators, leaves the numerator and adds the denominators","Incorrectly cancels what they believe is a factor in algebraic fractions"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Linear Equations ### ConstructName: Solve linear equations with the variable appearing on both sides, involving negative integers ### Question: Tom and Katie are arguing about a first step to solve this equation:\n\\(1-4 v=3-9 v\\)\n\nTom says you can write: \\( 1+5 v=3 \\)\n\nKatie says you can write: \\( -4 v=2-9 v \\)\n\nWho is correct?","positive":["Does not realise that to maintain balance in an equation they must add or subtract the same amount from both sides"],"negative":["Reflects in an axis, instead of the given mirror line","Fails to reflect across mirror line","Rotates instead of reflects","Thinks x = ? is a horizontal line through ? ","Translates rather than reflects across a line of symmetry","Does not understand that a point on the line of reflection will stay the same when reflected ","Thinks x = 1 at the x axis","Believes if a point is reflected in the line x=a then the x coordinate of the point will become 'a'","Thinks x = ? is the y axis","Thinks y = ? is a vertical line through ?","Thinks x = 0 is the x axis","Reflects instead of rotates","Assumes every dash on a scale represents an increase of 1","Reflects horizontally or vertically instead of across a diagonal line of symmetry","Believes that when a shape touches the mirror line, all of its vertices will stay the same when reflected","Struggles to visualise elevations of 3D shapes","Believes a line of reflection must be touching the original shape","Thinks y = ? is the x axis","Confuses left and right","When describing a translation, miscounts when crossing an axis","Counts the squares rather than the diagonals when reflecting in y=x or y=-x ","Struggles to visualise the new position of an object after transformations","Rotates by the wrong center of rotation (not including the origin)","Believes that the third vertex of a triangle will share coordinates with both of the other vertices","Thinks y =1 is the y axis","Struggles to draw 3D shapes on isometric paper","Believes mirror line must lie on a grid line, not in between grid lines","Struggles to visualise how an object will look in 3D when given a plan view, front and side elevation","Counts squares instead of the correct scale when plotting coordinates","Believes parts of a 3D diagram that look straight class as edges","Believes point will move diagonally when reflecting in a horizontal or vertical line","Believes that reflection always switches the x and y coordinates","Only counts visible vertices","Thinks depth always goes front to back in a diagram of a 3D shape","Fails to identify mirror line","Believes that points on an axis have equal x and y coordinates","Thinks the x coordinate of a point on the y axis is 1","Confuses the equations of vertical and horizontal lines","Struggles to visualise 2D triangles in a cuboid","Believes each vertical line on a box plot represents 1 piece of data","Thinks x = ? or y = ? is y = x","In 3 letter angle notation, gives a wider angle that contains the shaded angle","Uses the same value for both coordinates","Has used the wrong data point on the graph","Misreads scale","Thinks x = y is an axis","Includes the x variable when giving the equation of a horizontal line","When reading value from graph, reads from the wrong axes.","Does not realise a triangular prism is a 3D shape","Confuses x and y axes"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Squares, Cubes, etc ### ConstructName: Calculate the square root of a number ### Question: What is the value of the missing number? ![\\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{\\( 13^{2} \\)} \\\\\n\\hline\\( \\ldots \\ldots \\ldots \\) & \\( 12^{2} \\) \\\\\n\\hline\n\\end{tabular}]()","positive":["Thinks the sum of 2 numbers, each squared first, is the same as adding the two numbers and then squaring the total"],"negative":["Does not notice all changes in a sequence of visual patterns","When asked for a specific term in a sequence just gives the next term","When asked for a specific term in a sequence gives the next term","Only looks at the difference between one pair of terms when discerning the pattern","Identifies the term-to-term rule rather than the next term","When asked for a specific term in a sequence gives a different term, which is not the next","When asked for a specific term in a sequence gives the term after","When given a linear sequence, cannot match it to a visual pattern","When asked for a specific term in a sequence gives the term before","When asked for the next term in the sequence adds one to the last term given, despite the sequence not going up in ones.","Does not know how to find the next term in a sequence","Uses only the first two terms of a sequence to work out a term-to-term rule","Identifies the term-to-term rule rather than the next term in a sequence","Identifies how much repeated use of the term-to-term rule changes a number but does not apply to the sequence","When asked for the next term in the sequence subtracts one from the last term given, despite the sequence not going down in ones.","Thinks the term in a sequence is double the position value","Identifies the first term rather than the next term in a sequence","Only uses two terms of a sequence to work out a term-to-term rule","Does not know the definition of term or term-to-term rule","Thinks you subtract rather than add when finding the previous term in a descending linear sequence","Does not recognise that a linear sequence must increase or decrease by same amount","Does not understand that adding on to a multiple can give you the next multiple","Thinks terms in linear sequence are in direct proportion","When asked for a specific term in a sequence, just gives the position number","Goes the wrong direction in the sequence when identifying term-to-term rule","Thinks the first term in a sequence is the term before the sequence begins (0th term)","When asked for more, find the total","Believes there is a multiplicative relationship between values of terms in a linear sequence e.g. 10th term is double 5th term","Believes term to term rule is applied to position number, not previous term","Describes position to term rule using term to term rule","Describes term to term rules using position to term rules","Adds instead of subtracts","Does not know the meaning of consecutive","Thinks it can't be called a sequence with a repeated number at the start","Thinks the positive and negative terms in a sequence will have the same absolute values","Thinks you can find missing values in a given table by treating the row as a sequence of consecutive numbers","Believes to find the next traingle number you add the previous two numbers together i.e. Fibonacci","Counts on by 1, when asked to count forward\/backwards in a step other than 1","Does not know how to calculate the position of a term in a sequence","Only counts visible vertices","Thinks you can find missing values in a given table by treating the row as linear and adding on the difference between the first two values given.","Uses term-to-term rule as numerical part of nth term rule","Believes you multiply the constant difference by the term number to get the term value","Does not count end number when counting","Believes they can find the nth term based on the first term only","Only counts visible edges","Thinks you add all the bricks in a row in an addition pyramid.","Only counts visible faces","Believes substituting the starting value into an iteration formula immediately gives the solution","Believes when you plot a linear sequence it doesn't give a straight line"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Graphs of Exponentials and Other Powers of x ### ConstructName: Calculate coordinates of points on the graph of y = ax, where x is a positive integer  ### Question: This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{9}^{x} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 0 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star?","positive":["Forgotten that anything to the power of 0 equals 1"],"negative":["When reading value from graph, reads from the wrong axes.","When asked to read a value from a graph, thinks they give the corresponding value on the other axis, rather than reading from the graph","Confuses the dependent and independent variables on the axes of a line graph","Counts squares instead of the correct scale when plotting coordinates","Multiplied by the scale factor rather than divided in direct proportion problems","When reading values from graphs, writes down the wrong units","Mixes up the x and y values of the coordinates","When reading graph, chooses nearest marked value on axis instead of reading accurately","Confuses x and y axes","Thinks that the scale on axes has to match with the number of squares","Believes a direct proportion graph is a horizontal line","Has used the wrong data point on the graph","Misreads scale","Only gives 1 value of x for a given value of y, when reading from a parabolic graph","Believes direct proportion means a 1:1 ratio","Not considered the y value when reading coordinates","Thinks x = ? or y = ? is y = x","Incorrect use of scale on a diagram","Uses the same value for both coordinates","Does not check the labelling of the axes ","Multiplies when converting to a larger unit","Believes scales on graphs must match on both axes","Added rather than multiplied by a scale factor","Mixes up the value of two terms when substituting","Thinks they solve mx + c = a, by substituting in the value of a for x and therefore calculating ma + c","When interpolating using a line of best fit, reads off the value for the closest point to the line rather than the value given by the line of best fit ","Thinks x = ? is the y axis","Assumes the scale is the same when comparing two similar diagrams","Reflects in an axis, instead of the given mirror line","Assumes every dash on a scale represents an increase of 1","Does not understand how to read both x and y coordinates","Thinks x = ? is a horizontal line through ? ","Believes the solution to mx + c = a is the y intercept of y = mx +c","Believes the solution to mx + c = a is the x intercept of y = mx +c","Makes an assumption about the squares on a scale representing either 1 or 10","Assumes a 1:1 conversion ratio between different currencies","When describing the relationship shown on a scatter graphs, gets the effect on the dependent variable backwards","Shares equally instead of in given ratio","Subtracted rather than divided by a scale factor","Believes that points on an axis have equal x and y coordinates","Does not understand the difference between a value on a graph and the gradient of a graph","Multiplies rather than divides","Believes that graphs of inverse proportion meet the axes","Mixes up width and height of a rectangle","Confuses the graphs of  direct and inverse proportion","Divides rather than multiplies when scaling up in direct proportion problems","Correct scale but wrong value on protractor reading.","Thinks y = ? is a vertical line through ?","Believes the solution of mx + c = a is x =a","Confuses the equations of vertical and horizontal lines"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Properties of Triangles ### ConstructName: Identify a right-angled triangle when presented non-conventionally ### Question: \\( A B C D \\) is a rectangle.\nWhat type of triangle is triangle \\( \\mathrm{BCD} \\) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]()","positive":["Confuses scalene and right angle triangles"],"negative":["Rounds to the wrong degree of accuracy (rounds too much)","Rounds to the wrong degree of accuracy (significant figures rather than decimal places)","Rounds to wrong degree of accuracy (decimal places rather than significant figures)","Rounds to the wrong degree of accuracy (rounds too little)","Rounds to the nearest hundredth, rather than one significant figure","Rounds too early in calculation ","Rounds to the nearest integer rather than one significant figure","Gives a rounded whole number instead of a decimal","Estimated when not appropriate","Rounds too little when estimating","Does not understand the value of zeros as placeholders","Counts leading zero as a significant figure","Forgotten placeholders when rounding to significant figures","When doing operations with decimals, ignores significant zeros after the decimal point","Rounds to the nearest integer when estimating","When rounding to decimal places and the only digits after the decimal point will be zeros, just gives the integer as the answer.","When given an error interval for a decimal that ends in a zero, thinks you give the error interval as if the zero was not present (e.g. 1dp rather than 2dp)","Rounds up instead of down","Rounds a decimal instead of using a fraction in division","Rounds down instead of up","Rounded to wrong degree of accuracy (2sf not 1sf)","Rounds to nearest 50 not 20","Believes substituting the starting value into an iteration formula immediately gives the solution","Rounds to the wrong degree of accuracy (nearest ten rather than nearest whole number)","Does not understand which place value is the one that determines if a number rounds up or down","Identifies first decimal place value when asked for first significant figure","Rounds to the wrong degree of accuracy (1 decimal place rather than nearest whole number)","Estimates angle rather than calculating","Does not understand the first significant value is the first non-zero digit number","Rounds every number to the same degree instead of rounding to significant figures when estimating ","Stops iteration too early when solving equations","Converts a fraction to a decimal by using only the numerator after the decimal point","Changes wrong place value column when rounding","Gives the first significant figure when asked for the second","Rounded to nearest 100 instead of 1sf","Removes a zero from within the digits when rounding","Rounds up rather than to one significant figure","Adds or subtracts the degree of accuracy from the original number","Believes they can round when converting units","When adding decimals, does not keep place value the same as the original digits","Thinks that the lower and upper bound for a truncated number can be found in the same was as when it has been rounded","Rounds every number up when estimating","Believes an outlier is determined by the number of decimal places a number has","When dividing, ignores any remainders","Removes the decimal point when asked to round a decimal to a whole number","Identifies second decimal place value when asked for the second significant figure","Misreads scale","Converts a fraction to a decimal by using the denominator after the decimal point","Cannot accurately estimate capacity","Rounds the wrong way when interpreting a real-life context"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Multiplying and Dividing with Decimals ### ConstructName: Divide decimals by 10 ### Question: \\( 43.2 \\div 10= \\)","positive":["When dividing a decimal by a multiple of 10, just divides the fractional place values "],"negative":["Believes if you changed all values by the same proportion the range would not change","Does not understand that removing an outlier will impact the range","Believes if you add the same value to all numbers in the dataset the range will change","Does not know the definition of the range","When calculating the range does not reorder the data to find the largest number minus the smallest number","Thinks that we cannot calculate the range of negative numbers","Does not know that a reflection would not change the size of the shape","Finds the mean instead of the range","Finds the median instead of the range","Thinks that we cannot calculate the range if values are repeated","Thinks you cannot find the range if there are an even number of values","To find the range adds the biggest and smallest number rather than subtract","Thinks the range is just the first value subtracted from the last value, without ordering","Does not include negative numbers when calculating a range","Believes range does not need units","Believes the range is largest add smallest","Thinks that scale factors, other than one, can leave the dimensions of shapes unchanged","Thinks a greater range means more consistent data","Confuses range and interquartile range","Believes subtracting a positive number from a negative number makes the answer less negative","Does not recognise that an equation will stay balanced if all terms are multiplied\/divided by the same amount","Believes when frequencies multiply by a scale factor in a table the median also multiplies by that scale factor","Believes the median is the midpoint of the range","Does not realise that subtracting a larger number will give a smaller answer","Finds the IQR rather than the range","subtracts the highest from the lowest when calculating the range","Believes extreme values can affect the median","Believes they can change only one side of a ratio and it will remain equivalent","Halves the radius to find the diameter","Finds the mode rather than the range","Does not realise we can scale the perimeter as a whole, rather than finding individual side lengths","Assumes the range of a set of data starts at zero","Thinks an enlargement of any scale factor keeps side lengths the same","Believes that we cannot calculate the median of a dataset that contains negative numbers","Does not understand that when dividing both sides of an equation by an amount every term must be divided by the same amount","Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount","Identifies the biggest value for the range","Does not understand that enlargements can make shapes make shapes bigger, smaller and the same size","Believes -a is always smaller than a, ignoring the possibility that a is negative","Believes midpoint calculation is just half of the difference","Does not realise that subtracting a negative is the same as adding it's additive inverse","Finds the range of possible values of the variable, rather than the range of recorded values","Assumes a fact without considering enough examples","Halves base but still divides product by 2 when finding area of a triangle","Believes interquartile range is the difference between one of the quartiles and the minimum value","Thinks halving is the same as multiplying by 2","Believes when frequencies multiply by a scale factor in a table the mean also multiplies by that scale factor","Thinks a lower average means the data is more consistent","Does not understand that a point on the line of reflection will stay the same when reflected ","Believes it's ok to change the scale on an axis for the negative values"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Simultaneous Equations ### ConstructName: Recognise whether you need to add or subtract linear equations in order to eliminate a variable ### Question: Tom and Katie are discussing this pair of simultaneous equations: \\( \\begin{array}{l}3 x-2 y=8 \\\\ 3 x+y=14\\end{array} \\) Tom says if you add the two equations together you will eliminate a variable\n\nKatie says if you subtract the two equations together you will eliminate a variable\n\nWho is correct?","positive":["When solving simultaneous equations thinks that identical terms in given equations can be eliminated by either adding or subtracting."],"negative":["Rounds up instead of down","Rounds up rather than to one significant figure","Rounds to the wrong degree of accuracy (rounds too much)","Rounds every number up when estimating","Rounds to the wrong degree of accuracy (rounds too little)","Rounds down instead of up","When rounding, believes that if the number, after the required degree of accuracy, is a 5 or below you round down","Believes that rounding must change the number","Rounds down instead of up when next digit is 5","Does not understand which place value is the one that determines if a number rounds up or down","Rounds to the nearest integer rather than one significant figure","When rounding up from a 9, does not add one on to the digit to the left","Rounds to nearest 50 not 20","Rounds to wrong degree of accuracy (decimal places rather than significant figures)","Rounded to wrong degree of accuracy (2sf not 1sf)","Rounds the wrong way when interpreting a real-life context","Rounds incorrectly by changing multiple place values","Changes wrong place value column when rounding","Gives a rounded whole number instead of a decimal","Forgotten placeholders when rounding to significant figures","Rounds too little when estimating","Does not round up when an answer is non-sensical in a real-life context","Rounds too early in calculation ","Rounds to the wrong degree of accuracy (significant figures rather than decimal places)","Believes rounding numbers down would give an overestimate","Rounds every number down when estimating","Believes rounding to 1 significant figure means rounding to the nearest integer, regardless of the value of the number","Thinks that the lower and upper bound for a truncated number can be found in the same was as when it has been rounded","Does not know how to round up when a decimal place value column contains a 9","Rounds to the nearest integer when estimating","Estimated when not appropriate","Does not understand you can round to numbers other than powers of 10","Believes that when finding bounds you round to the nearest whole number","Believes rounding to 1 decimal pleace means rounding to the nearest integer, regardless of the value of the number","Rounds every number to the same degree instead of rounding to significant figures when estimating ","Rounded to nearest 100 instead of 1sf","Mixes up greater than and less than symbols","Removes the decimal point when asked to round a decimal to a whole number","Rounds to the nearest hundredth, rather than one significant figure","Removes a zero from within the digits when rounding","Counts leading zero as a significant figure","Does not understand the first significant value is the first non-zero digit number","Rounds incorrectly when the nearest 10 is a multiple of 100","Cannot evaluate if an estimate is an underestimate or overestimate","Believes they can round when converting units","Adds or subtracts the degree of accuracy from the original number","Gives the first significant figure when asked for the second","Confuses place value when rounding to estimate","Ignores the negative sign","When using interpolation to estimate frequency that is above a certain value, believes they can add the estimated frequency up to that value in its class, rather than the estimated frequency after it"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Linear Sequences (nth term) ### ConstructName: Match linear sequences to other representations, such as tables and graphs ### Question: ![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \\begin{tabular}{|l|c|c|c|}\n\\hline Position & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline Term & \\(  \\) & \\( \\bigstar \\) & \\(  \\) \\\\\n\\hline\n\\end{tabular} What value should replace the star?","positive":["Thinks the term in a sequence is double the position value"],"negative":["Believes dividing two positives will give a negative answer","Believes dividing a negative by a negative gives a negative answer","substitutes incorrectly","Thinks a divide and a negative sign next to each other makes a minus","Believes a negative power results in a negative answer","Believes multiplying two negatives gives a negative answer","Correctly finds the reciprocal of a number, but believes it should be opposite in sign to the original number.","Thinks the subtraction sign means divide","Believes dividing a positive by a negative gives a positive answer","Believes dividing a negative by a positive gives a positive answer","When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value","Believes that reciprocals are undefined for negative numbers","Has used a subtraction sign to represent division","Believes division is commutative ","Believes multiplying two positives gives a negative answer","Subtracts instead of divides","Thinks the fraction bar means subtract rather than divide","When substiting into an algebraic term, raises the coefficient to the power of the variable rather than multiplying the coefficient and the variable..","Heads towards zero when subtracting from a negative","When substituting into an algebraic term, replaces variables with numbers without multiplying.","When there's a negative sign in the question, thinks the answer must be negative","when subtracting a fraction from an integer, just adds their absolute value and places a negative sign in front","When subtracting a negative thinks the answer must be negative ","Divides by the index","Believes that a fraction means dividing the denominator by the numerator","When subtracting a negative number, subtracts the absolute value rather than adding it","Thinks the division sign means to subtract","Assumes the denominator is divided by the numerator","Believes subtraction is commutative ","Does not recognise when one part of a fraction is the negative of the other","Believes division is sometimes commutative ","Does not consider the variable when evaluating an expression that requires substitution.","Thinks a divide and a negative sign next to each other makes a plus","Believes dividing by a unit fraction is equivalent to dividing by its reciprocal","When substituting into an algebraic term, believes they can disregard the coefficient","When dividing a fraction by an integer, divides the denominator by the integer","Makes the number negative when asked to find the reciprocal","Thinks the subtraction sign means multiply","Believes the square of a negative will also be negative","When subtracting a negative number, adds the absolute values and then writes the answer with a negative sign","Multiplies rather than divides","When subtracting past zero, adds the absolute values and then writes the answer with a negative sign","When dividing fractions, does the reciprocal of the first fraction instead of the second","Does not realise that subtracting a negative is the same as adding it's additive inverse","When solving an equation, uses the same operation rather than the inverse.","When dividing a fraction by an integer, subtracts the integer from the denominator","When dividing a fraction by an integer, divides both the numerator and denominator by the integer","Divides rather than multiplies ","Assumes the negative sign in a power has no meaning","Does not recognise that subtracting a larger number from a smaller number will give a negative answer"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Weight Units ### ConstructName: Convert between g and kg ### Question: \\( 4000 \\mathrm{~g} \\) is the same as \\( k g \\)","positive":["Thinks there are 100g in a kilogram"],"negative":["Thinks the reciprocal of a fraction is what number adds to that fraction to make one whole.","Thinks the inverse of multiplication is addition","Thinks if you multiply a fraction by itself you get a whole","When solving an equation thinks they add when in fact they need to multiply","Believes equivalent fractions are formed with addition not multiplication","When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation","Believes the fraction line represents addition","Adds or subtracts from numerator first when solving an equation with a fraction","When adding an integer to a fraction, thinks you add the integer to the numerator","When solving an equation, adds instead of dividing","Adds instead of multiplies","When solving a problem that requires an inverse operation (e.g. missing number problems), does subtraction when division is required","Thinks the inverse of subtraction is multiplication","Thinks the inverse of addition is multiplication","When solving an equation, multiplies instead of adding","When solving an equation thinks they divide when in fact they need to multiply","Adds instead of multiples","Thinks the fraction bar means subtract rather than divide","Thinks a variable next to a number means addition rather than multiplication","When solving an equation,  subtracts instead of multiplying","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","When asked to multiply fractions, uses the method for adding instead","When converting from an improper fraction to a mixed number, adds on the part left to make the whole, rather than subtracting it","Subtracts instead of adds","Adds instead of subtracts","Believes that a number divided by itself equals the original number","Divides by the numerator and multiplies by the denominator when finding a fraction of an amount","Does not understand how to maintain equivalence in fractions","Believes that the reciprocal of a number is equal to that number (1\/x = x)","when multiplying fractions multiplies by the reciprocal of the 2nd fraction instead","Forgets to change the numerators when finding equivalent fractions","When multiplying fractions, multiplies the numerator and adds the denominator","When solving an equation, uses the same operation rather than the inverse.","Believes they should multiply each numerator by its original denominator when adding\/subtracting fractions","Subtracts instead of multiplies","Multiplies by the denominator instead of dividing when finding a fraction of an amount","Uses numerator as whole part of a fraction","Thinks the inverse of addition is division","When multiplying a fraction by an integer, multiplies the denominator instead of the numerator","Thinks the inverse of subtraction is division","When finding a missing part in a ratio, divides rather than multiplies","Can identify the multiplier used to form an equivalent fraction but does not apply to the numerator","Believes factors add to give a number","When multiplying a vector by a fraction, adds the numerator to the top number of the vector, and the denominator to the bottom number of the vector. ","Thinks the multiplication sign means to add","Believes 0 multiplied by a number gives the number","Does not know how to solve linear equations involving fractions","Thinks two variables next to each other represent addition","When multiplying a fraction by an integer, multiplies both numerator and denominator by the integer","Believes to complete a part whole model you select a value already given in the model"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Expanding Double Brackets ### ConstructName: Carry out multiplication problems involving one negative integer ### Question: John is expanding these two brackets.\n\nWhat should he get when he multiplies the two terms indicated by the arrows? ![The two brackets are (x+5)(x-3). The arrows are pointing at the +5 in the first bracket and the -3 in the second bracket.]()","positive":["Adds instead of multiplying when expanding bracket"],"negative":["Confuses collecting like terms with multiplication","Does not realize we can omit the multiplication symbol in algebraic expressions","Writes the variable before the coefficient in an algebraic term","Multiplies all terms together when simplifying an expression","Does not realise that two letters together, or a number and letter together, are multiplying","Does not realize we can simplify a term that involves powers","Does not understand how to multiply algebraic terms","When substituting into an algebraic term, believes they can disregard the coefficient","Does not realise that two letters together are multiplying","Expands when asked to simplify","Does not think that a variable with no coefficient has a coefficient of 1.","Adds instead of multiplies when multiplying algebraic terms","Assumes you cannot use the fact that multiplication is commutative when simplifying an algebraic term. ","Does not think a factorised expression is equivalent to its multiplied out form","Does not include brackets when attempting to multiply an expression","In algebra, thinks it's ok to write (for example) 0x rather than just 0","Writes repeated letters instead of using index form of a variable","When collecting like terms, only simplifies when there is an addition","Only multiplies the numerical terms when expanding a bracket","When collecting like terms, assigns positivity or negativity incorrectly.","When substituting into an algebraic term, replaces variables with numbers without multiplying.","Confuses an expression with a term","Thinks index notation represents repeated addition rather than repeated multiplication","Multiplies by the index","Only multiplies the first term in the expansion of a bracket","Does not know how to simplify algebraic fractions","Thinks the subtraction sign means multiply","Confuses a term with a variable","When simplifying an algebraic fraction, only looks for number factors","Multiplies coefficients and letters separately and writes as an addition","Adds instead of multiples","Does not understand when like terms can be collected","Ignores coefficients when forming an expression from a question","Adds instead of multiplies","Thinks a variable next to a number means addition rather than multiplication","When multiplying just writes the numbers next to each other","Does not understand power notation","Thinks any 2 values multiplied together can be denoted with a squared symbol","When collecting like terms, treats subtractions as if they are additions","Misunderstands order of operations in algebraic expressions","Confuses a variable with a formula","Confuses an expression with a variable","When substiting into an algebraic term, raises the coefficient to the power of the variable rather than multiplying the coefficient and the variable..","Thinks you can ignore the variable when simplifying algebraic fractions","Does not understand the interpretation of the fx column in a frequency table","Cannot spot a coefficient within a written scenario","Writes a variable to the power of n as nx","Mixes up squaring and multiplying by 2 or doubling","Has multiplied the value of the first term by the the term being asked","Does not account for grammar when writing algebra e.g. ,then making a group"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Percentages of an Amount ### ConstructName: Calculate percentage of an amount mentally where the percent is greater than 100 ### Question: \\( 130 \\% \\) of \\( 40= \\)","positive":["Found the percentage but forgot to add to 100%"],"negative":["When subtracting fractions, subtracts the numerators and denominators","Incorrectly cancels what they believe is a factor in algebraic fractions","Believes subtraction is commutative ","Does not recognise when one part of a fraction is the negative of the other","Does not understand how to subtract algebraic fractions","When adding fractions, adds the numerators and denominators","When subtracting fractions, divides the numerators","Does not find a common denominator when adding\/subtracting fractions","Believes that a fraction means dividing the denominator by the numerator","Removes the common denominator when making equivalent algebraic fractions","Does not understand equivalent fractions","When subtracting fractions, subtracts the numerators and multiplies the denominators","Forgets to change the numerators when finding equivalent fractions","Mixes up the numerator and denominator","Assumes the denominator is divided by the numerator","When adding fractions, changes to common denominator but leaves numerators the same","When adding fractions with identical numerators, leaves the numerator and adds the denominators","Uses the numerator of an improper fraction as the denominator of the equivalent mixed number","Does not consider the denominator when adding\/ subtracting fractions. Adds\/subtracts the numerator and makes the denominator the one with the highest value.","When rationalising the denominator, confuses the numerator with the denominator","When adding\/subtracting fractions, adds\/subtracts the denominators and multiplies the numerators","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","Mixes up the numerator and denominator when writing a division as a fraction","Subtracts numerators when dividing fractions with a common denominator","Thinks that when you cancel identical terms from the numerator and denominator, they just disappear","Mixes up the terms for the parts of a fraction","Adds instead of subtracts","Does not understand how to maintain equivalence in fractions","Performs subtraction in wrong order","Uses the total as the numerator of the fraction rather than the denominator.","Believes that if the numerators of 2 fractions are equal then the fractions are equal, regardless of the denominator","substitutes incorrectly","When asked to subtract a fraction from a unit, removes the unit value from the denominator","Believes that fractions with the same denominator are equal","Thinks the fraction bar means subtract rather than divide","Subtracts from left to right, ignoring the word \u2018from\u2019","Believes the subtraction button writes a fraction","Does the reciprocal of both fractions when dividing fractions","Thinks can combine the numerator and denominator after simplifying an algebraic fraction","When adding fractions, adds the numerators and multiplies the denominators","Believes they can change the subject of a formula just by swapping two letters","When asked to subtract a fraction from a unit, removes the unit value from the numerator.","Ordered fractions by comparing denominators rather than using equivalent fractions.","Is not familiar with the names of the different parts of a fraction","Has not noticed the difference between 'subtract' and 'subtract from'","When converting a fraction to a decimal, divides the denominator by the numerator","Adds or subtracts from numerator first when solving an equation with a fraction","Does not know how to say a fraction","Does not know the term numerator","Thinks you can ignore the variable when simplifying algebraic fractions"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Mental Addition and Subtraction ### ConstructName: Given the solution to one problem, deduce the answer to a related problem using the same operation ### Question: Tom and Katie are discussing related calculations\nTom says if you know that \\( 4122+426=4548 \\), then \\( 4122+428 \\) must equal \\( \\mathbf{4 5 5 0} \\)\n\nKatie says if you know that \\( 4122-426=3696 \\), then \\( 4122-428 \\) must equal \\( \\mathbf{3 6 9 4} \\)\nWho is correct?","positive":["Does not realise that adding a larger number gives a larger answer"],"negative":["When multiplying numbers with different bases, multiplies the powers and multiplies the base numbers.","Multiplied the base numbers","Thinks we have to add the base numbers as well as the powers when multiplying indices","When multiplying numbers with the same base, multiplies the powers ","Has multiplied the base number and the power","When multiplying algebraic terms written in the same base, adds the base variables and multiplies the powers.","Believes you multiply matching bases when carrying out a multiplication","Has added the powers rather than multiplying them","Multiplies by the index","Believes that when multiplying a number with a power, the multiplier is added onto the power","When dividing numbers with different bases, divides the powers and divides the base numbers.","Thinks powers with different bases cannot be equal","Multiplied the powers rather than added them","Thinks multiplying by a number is the same as raising to the power of that number","When dividing numbers with different bases subtracts the powers but divides the base numbers.","Does not realise that multiplication can be broken down into factors","When dividing numbers with different bases, subtracts the powers and subtracts the base numbers.","Believes the columns in a base are multiples not powers of the base","Believes multiplying together all prime factors gives the highest common factor","Has multiplied by the root power","Confuses powers and multiples","Mixes up squaring and multiplying by 4","When dividing numbers with the same base divides the base numbers and the powers","When dividing numbers with the same base correctly subtracts the powers but divides the base numbers.","Mixes up squaring and multiplying by 2 or doubling","Repeats the digits twice when squaring a number","Believes a power of 2 has no impact on its value","Believes the lowest common multiple is found my multiplying the numbers together","Divides by the index","Added the base numbers","Believes when dividing numbers with the same base you divide the powers, rather than subtracting","When squaring a variable with a power, thinks that the power is squared rather than doubled. ","Believes multiply all numbers in a prime factor venn diagram gives the value of one sets number","When multiplying large numbers, splits numbers into addends rather than factors","Thinks any 2 values multiplied together can be denoted with a squared symbol","Believes all the multiples of a number will also be multiples of its multiples","When multiplying by a multiple of 10, gives an answer 10 times bigger than it should be","When converting between non standard form and standard form assumes changes to the base will not affect the power","Does not understand the root power of 4","Thinks that when raising a variable with a coefficient to a power, only the coefficient is affected by the power","When squaring a variable, believes they also need to square the coefficient","Thinks multiplying by a variable is the same as raising to the power of that variable","When multiplying surds in the form \u2713a \u00d7 b\u2713c, believes the answer is  \u2713(abc)","Thinks that doubling and then doubling again is not the same as multiplying by 4","Has added on the power of 1\/4 rather than raise to the power of 1\/4","Thinks multiplying a variable by a number is the same as raising that variable to the power of that number","Believes that if more than one number in a multiplication is divided by the same power of ten, the answer will be divided by the same power of ten. ","Thinks that dividing both numbers in a multiplication sum by the same power of 10 results in equal answers","Thinks a power raised to a power leads to addition of the powers","Counts repeated factors as two separate factors"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Volume and Capacity Units ### ConstructName: Convert between cl and l ### Question: \\[\n650 \\text { centilitres }=\\bigstar \\text { litres }\n\\]\nWhat should replace the star?","positive":["Thinks there are 10cl in a litre"],"negative":["When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal","When multiplying decimals, ignores place value and just multiplies the digits","Does not understand place value within a number","When multiplying decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.","When multiplying decimals, multiplies rather than divides when reinserting the decimal.","When multiplying a decimal less than 1 by an integer, gives an answer 10 times smaller than it should be","When multiplying a decimal less than 1 by an integer, gives an answer 100 times smaller than it should be","When multiplying a decimal less than 1 by an integer, gives an answer 10 times bigger than it should be","When multiplying a decimal by a power of 10, just adds a zero to the end of the number, not changing the place value of the digits","When multiplying just writes the numbers next to each other","Does not understand the value of zeros as placeholders","When dividing decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.","Believes multiplying by 0.1 is the same as multiplying by 10","When adding decimals, just adds the digits and ignores place value","When multiplying a decimal by an integer, ignores decimal point and just multiplies the digits","When multiplying, treats digits in other columns as if they are units","Believes you write the carried value in the number rather than adding it to the next place value column","Divides instead of multiplies when multiplying by a decimal","Does not understand place value after the decimal point","Adds instead of multiplies","Does not write the place holder zero when doing column multiplication","When subtracting decimals with a different number of decimals, subtracts one digit from more than one column","When dividing decimals, divides rather than multiplies when reinserting the decimal.","Identifies wrong place value column after decimal point","When subtracting decimals with a different number of decimal places, lines up the digits incorrectly","Multiplied by 10 rather than 100","Thinks that when multiplying decimals (less than 1), the number will get bigger","Changes wrong place value column when rounding","Believes multiplying two negatives gives a negative answer","When adding decimals with a different number of decimal places, lines up the digits incorrectly","Adds instead of multiples","Divides rather than multiplies ","When multiplying involving a multiple of 10, gives an answer 10 times smaller than it should be","When doing operations with decimals, ignores significant zeros after the decimal point","When dividing a decimal by an integer, divides by the wrong power of 10 when reinserting the decimal.","Subtracts instead of multiplies","When asked for the value of a digit, gives an answer 10 times too small","Believes that when multiplying by a power of 10 you add zeroes after the decimal point","When adding decimals, does not keep place value the same as the original digits","When two digits multiply to 10 or more during a multiplication problem, does not add carried value to the preceding digit","Believes dividing by 0.1 is the same as dividing by 10","Ignores the zero when multiplying","When finding the square root of a decimal, ignores place value","When dividing a decimal by a power of 10 adds zeroes to start of the number ignoring the placement of the initial decimal point","When multiplying multiples of ten and the answer requires an extra digit, leaves off that extra digit","Adds 3 decimal places rather than moving 3 places","Hasn't lined up the place value columns when writing out the calculation","When adding, just writes the digit to the right of the number without considering place value","When two digits sum to 10 or more during addition of decimals, does not carry across decimal point to preceding digit.","Multiplies rather than divides"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Averages and Range from Frequency Table ### ConstructName: Identify the mode from a frequency table ### Question: The frequency table shows the grade achieved by some students in a maths exam.\nWhat was the modal grade? ![\\begin{tabular}{|c|c|}\n\\hline Grade & Frequency \\\\\n\\hline \\( 1 \\) & \\( 3 \\) \\\\\n\\hline \\( 2 \\) & \\( 7 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 9 \\) \\\\\n\\hline \\( 5 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]()","positive":["Believes the mode is the most common frequency rather than the highest frequency"],"negative":["Multiplies the number of whole units by the numerator when converting from a mixed number to an improper fraction","Forgets to add the numerator when converting from a mixed number to an improper fraction ","Believes the number of wholes in a mixed number multiplies by the fraction part","Thinks you add the number of wholes to the numerator when converting a mixed number to an improper fraction.","Thinks you multiply by the numerator and add the denominator when converting a mixed number to an improper fraction","Confused mixed numbers with improper fractions","Finds an equivalent improper fraction when asked for a mixed number","Writes the numerator of an improper fraction as the number of wholes when converting to a mixed number","Believes a mixed number can contain an improper fraction","thinks when writing a mixed number fraction as an improper fraction, you need to multiply the denominator by the whole ","When converting from an improper fraction to a mixed number, just writes the tens digit as the number of wholes","Thinks the number of wholes in a mixed number represents the tens from the numerator of an improper fraction","Uses numerator as whole part of a fraction","Believes you add the whole to the numerators, ignoring denominators, when adding a mixed number to a proper fraction with the same denominator.","Believes the whole and remainder are the other way when changing an improper fraction to a mixed number","When subtracting a fraction from a mixed number, assumes they just subtract the numerator from the integer of the mixed number","When multiplying mixed numbers, forgets to multiply the fraction","Uses the numerator of an improper fraction as the denominator of the equivalent mixed number","When subtracting a fraction from a mixed number, assumes they subtract the numerator from the integer and the numerator of the mixed number","When converting from an improper fraction to a mixed number, adds on the part left to make the whole, rather than subtracting it","Simplifies integers when simplifying a mixed number","Thinks converting an integer to a fraction means both the numerator and denominator are equal","When the dividend is a mixed number and the divisor is an integer, thinks they only perform the calculation with the integers.","When the dividend is a mixed number and the divisor is an integer, thinks they only divide the fraction by the integer.","Multiplies the numerators when adding fractions with a common denominator","When multiplying mixed numbers thinks they add the integers","Believes when changing an improper fraction to a mixed number you divide the numerator by 10, regardless of the denominator","Mixes up the terms for the parts of a fraction","When subtracting mixed numbers, does not realise that a negative fractional answer needs to be taken away from their integer answer","When given a non-unit fraction of an amount, treats it like a unit fraction","Assumes they multiply by the numerator of fractional index","Finds unit amount but doesn't multiply up","Thinks numbers greater than 1 cannot be converted into fractions","Mixes up the numerator and denominator","Does not know how to write a fraction - just given an integer answer","Believes they should multiply each numerator by its original denominator when adding\/subtracting fractions","Does not know how to interpret a fraction worded problem ","Identifies the wrong part of a fraction model as the whole","Forgets to change the numerators when finding equivalent fractions","Denominator used for other parts rather than total parts","Uses the total as the numerator of the fraction rather than the denominator.","Multiplies up without finding unit amount","Is not familiar with the names of the different parts of a fraction","Misunderstands mixed number notation ","Finds the unit fraction when asked to find a non-unit fraction of an amount","Believes mixed numbers cannot be simplified","Believes the amount given is for the whole rather than a part","Mixes up the numerator and denominator when writing a division as a fraction","Adds instead of multiples","Does not know the term numerator"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: BIDMAS ### ConstructName: Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and\/or division ### Question: What does the following equal?\n\\[\n3-5+4 \\times 2\n\\]","positive":["Subtracts instead of adds"],"negative":["Ignores the negative signs when adding positive and negative numbers","Believes that adding a negative will increase the value of the original number","Believes adding two negatives gives a positive answer","Ignores the negative sign","Thinks signs are interchangeable when adding or subtracting positive and negative numbers","Performs addition ahead of any other operation","Believes a negative number can be replaced with its positive equivalent when answering an addition problem from a numberline","Believes that adding a positive to a negative makes your answer more negative","Thinks two variables next to each other represent addition","When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit","Performs addition ahead of subtraction","Adds instead of subtracts","Thinks positive or negative sign affects the term before it","When adding, just writes the digit to the right of the number without considering place value","Believes we move down a number line when we add","Multiplies rather than adds ","Believes multiplying a positive by a negative gives a positive answer","Believes the range is largest add smallest","Doesn't recognise commutativity of addition with negative numbers","Performs addition ahead of multiplication","Multiplied the powers rather than added them","Added the base numbers","When adding an integer to a fraction, thinks you add the integer to the numerator","Thinks multiplication and addition are the same","Lines up the digits incorrectly when doing an addition involving two numbers with a different amount of digits","When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored ","Thinks they find the length of a line between 2 points by adding coordinates, rather than subtracting","Carries out operations from left to right regardless of priority order","When collecting like terms, treats subtractions as if they are additions","To find the range adds the biggest and smallest number rather than subtract","When two digits sum to 10 or more during addition of decimals, does not carry across decimal point to preceding digit.","Believes adding b to any integer gives a multiple of b","Has increased by the value of the first value, rather than the difference","Does not realise that adding a larger number gives a larger answer","When adding decimals with a different number of decimal places, lines up the digits incorrectly","Thinks the difference between a positive number and a negative number is equal to the positive number","When subtracting a negative number, subtracts the absolute value rather than adding it","Confuses the direction of vectors when adding or subtracting","Does not realise addition is commutative","Thinks a divide and a negative sign next to each other makes a plus","Does not think that -n + n = 0","Multiplies the numerators when adding fractions with a common denominator","When adding fractions, changes to common denominator but leaves numerators the same","Adds instead of multiples","When solving an equation, multiplies instead of adding","When adding variables with powers, thinks they can add the powers","Does not divide by 2 when finding midpoint","When adding fractions, adds the numerators and denominators","Ignores negative sign when expanding bracket"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Direct Proportion ### ConstructName: Use direct proportion to solve non-unitary missing amounts in problems (e.g. recipes) ### Question: Twelve rulers cost \\( 96 p \\).\nHow much do five rulers cost?","positive":["Multiplies up without finding unit price in proportion question"],"negative":["Does not know that sample size affects reliability","Confuses relative frequency and expected frequency","Gives frequency when asked for relative frequency","Believes any sample gives an equal chance of selection","Believes 'data' and 'sample' are interchangeable","Believes the frequency represented by a pie chart sector can be judged visually, without considering the total it represents","Confuses theoretical and experimental probability","Believes biased selection methods can be random","Cannot evaluate if an estimate is an underestimate or overestimate","Believes data implies equal chance of selection","Confuses objective and subjective","Estimated when not appropriate","Thinks a higher average means more consistent data","Thinks only one variable can introduce bias","Misunderstands how to adjust proportions for different sample sizes in stratified sampling","Thinks that probabilities of an event occurring or not occurring must be equal","Thinks a greater range means more consistent data","Believes the mean is always representative","Thinks a lower average means the data is more consistent","Thinks that we cannot calculate the range if values are repeated","Does not understand the question","Confuses random and stratified sampling methods","Uses the other part instead of total frequency as denominator for relative frequency","Misunderstands the capture-recapture method","Cannot accurately estimate capacity","Does not understand equivalent fractions","Believes you can make assumptions about size of pie chart sectors without enough information","Fails to consider all possible outcomes","Does not understand that a probability of 1 represents something that is certain","Believes all possible outcomes must have equal probability","Believes stratified samples should be evenly split","Confuses the method of selection with the group selected in statistics","Believes that any percentage of a larger number will be greater than any percentage of a smaller number","Does not understand equivalent ratios","Believes we can categorise data as primary or secondary without knowing the source","Does not know how to read information off a pie chart","Uses numerators to convert fractions to ratio despite different denominators","Believes it is not possible to calculate the frequency for a pie chart sector despite being given enough information to do so","Confuses least and most","Mixes up quantitative and qualitative data types","Ignores a more than question and just states one of the values","Does not think 'other' is an acceptable category for data","Does not understand that a probability of 0 represents something that is impossible","Believes that fractions with the same denominator are equal","Believes if you changed all values by the same proportion the range would not change","Does not know the meaning of attribute data","Does not find a common denominator when comparing fractions","Doesn't take into account cost when calculating expected return\/profit","Believes you do not include an \"other\" category when finding a total frequency","Does not recognise that probabilities of all possible outcomes will sum to 1"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Adding and Subtracting Negative Numbers ### ConstructName: Carry out missing number subtraction problems involving negative integers ### Question: ![Number line with -7 and -5 marked on it. From the -7 there is an arrow to the right labelled +5. Then there is an arrow pointing to the left labelled b and ending at -5.]() What is the value of \\( b \\) ?","positive":["Counts the starting number when counting backwards"],"negative":["Thinks that only the sides need to be equal for a polygon to be regular","Thinks that only the angles need to be the same for a polygon to be regular","Assumes regular shape refers only to a square","Does not know the meaning of the word regular ","Does know know equilateral means the same as regular ","Does not understand that all angles and sides must be equal for regular shapes","Does not realise that all regular shapes of a certain type will be similar","Does not remember that a rhombus has equal sides","Thinks rule for calculating interior angles only applies to regular polygons","Does not recognise a parallelogram","Does not know the properties of a rectangle","Believes a rectangle has four equal sides","Thinks the term polygons only applies to shapes with more than 3 sides","Does not know the properties of a rhombus","Does not know the properties of an equilateral triangle","Does not know the meaning of equilateral","Does not recall rectangle side length property","Believes a rectangle has one pair of equal sides","Believes a rhombus has one pair of equal sides","Confuses isosceles and equilateral triangles","Does not understand the naming structure of polygons","Does not understand that shapes are congruent if they have the same size and shape","Does not recognise the properties of a kite","Does not know the meaning of uniform cross section","Does not know a rhombus is a type of parallelogram ","Does not know a rectangle is a type of parallelogram ","Does not know the definition of a prism","Does not believe a shape can have two correct names e.g. rectangle and parallelogram","Believes a polygon can have curved sides","Thinks the interior angle of a regular polygon is 10n","Does not know the properties of an isosceles triangle","Does not understand to find each interior angle of a regular polygon you divide the sum by the number of sides","Believes an arrowhead has four equal sides","Does not know the properties of a parallelogram","Thinks rectangles have rotational symmetry or order 4","Does not know the meaning of congruent","Does not realise that all circles are similar","Does not realise similar has a specific mathematical meaning","Does not understand that base angles in an isosceles are equal","Does not know what dashes on the sides of shapes mean","Thinks congruent shapes are the same shape but can be different sizes","Believes a parallelogram has one pair of equal sides","Believes only straight lines count as edges on 3D shapes","Does not know the meaning of the word equidistant ","Believes there is only one orientation for the isosceles triangle base angles","Does not know how to find order of rotational symmetry","Cannot identify a line of symmetry in a simple shape","Does not know that a single letter labels a vertex","When given the perimeter of a regular polygon, subtracts instead of divides to find each side length","Only counts visible vertices"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Converting between Decimals and Percentages ### ConstructName: Convert decimals less than 1 with 2 decimal place to percentages ### Question: Convert this decimal to a percentage\n\\(\n0.07\n\\)","positive":["Thinks you need to just add a % sign to a decimal to convert to a percentage"],"negative":["Believes an outlier is a value that does not fit the same characteristics as the other values","Believes an outlier is the value in a data set with the biggest denominator, even if this value is close to the mean","Believes an outlier is the smallest value in a data set, even if this value is close to the mean","Believes an outlier is not determined by distance from the mean","Believes an outlier has to be a whole number","Believes extreme values can affect the mode","Believes extreme values can affect the median","Does not understand that removing an outlier will impact the range","Thinks a higher average means more consistent data","Believes an outlier is determined by the number of decimal places a number has","Identifies the biggest value for the range","Thinks a greater range means more consistent data","Thinks only one variable can introduce bias","Believes that fractions with larger denominators are greater in size","Ignores the negative sign","Chosen the longest value rather than the greatest","Does not understand equivalent fractions","Thinks a lower average means the data is more consistent","Believes when identifying the mode you look at all values, not just frequencies, for the highest number","Does not think 'other' is an acceptable category for data","Mixes up odd and even numbers","Rounds up instead of down","Ordered fractions by comparing denominators rather than using equivalent fractions.","Finds the mode instead of the median","Believes that fractions with the same denominator are equal","Includes a data point with the value, when asked to find the number of data points above a value","Believes the mean is the middle number","When comparing unit fractions believes that fractions with larger denominators are greater in size.","When asked for the mean of a list of data, gives the mode","Does not understand inequality notation","Believes you can only have one mode","Finds the mode rather than the range","Does not find a common denominator when comparing fractions","Thinks that we cannot calculate the range if values are repeated","believes that a fraction with the largest denominator will be smallest regardless of the numerator","Believes the lower quartile is the lowest value in a list","Believes the mode is the most common frequency rather than the highest frequency","When asked for the mean of a list of data, gives the median","Believes even numbers can have odd multiples","Confuses objective and subjective","Finds the median instead of the mode","Mixes up smallest and largest when ordering fractions","Estimated when not appropriate","Does not understand the meaning of \"value\"","Does not know that 7 and -7 are different","Ordered from largest to smallest","Has increased by the value of the first value, rather than the difference","Does not know the term numerator","Thinks the difference between the numerator and denominator determines how close the fraction is to 1","Believes you don't need to numerically order the data before calculating the median"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Written Multiplication ### ConstructName: Multiply 3 digit integers by 2 digit integers using long multiplication ### Question: What is a correct way to set up this problem to solve it using long multiplication?\n\\[\n128 \\times 26\n\\]","positive":["Hasn't lined up the place value columns when writing out the calculation"],"negative":["Mixes up sides of a ratio, when working with vectors for line segments.","Assumes a ratio is part to part instead of part to whole","Mixes up total and part in ratio","Thinks ratios are written as 1:total","Mixes up sides of a ratio","Does not know how to find the length of a line segment from coordinates","In ratio where total is given, treats that as one part without dividing","In ratio question where one side of ratio is given, treats that as the total","In ratio question where one side of ratio is given, uses that as one part in ratio without dividing","When finding a point on a line, assumes the point is always the midpoint","Divides total amount by each side of the ratio instead of dividing by the sum of the parts","Shares equally instead of in given ratio","Believes angles on a straight line add to 360 degrees","Thinks the number in the ratio is the total","Gets order of ratio wrong","When converting ratio to fractions, puts the other side of the ratio as the denominator rather than the total","Finds one part of a ratio but doesn't multiply that by the number of parts needed","When drawing bar diagram for ratio, shows the total amount as the total of one side","When finding a missing part in a ratio, divides rather than multiplies","Forgets to add starting value when calculating new coordinates","Divides length of original by length of image to find scale factor, rather than image by original.","Thinks that all angles anywhere along a straight line add to 180","In ratio question where the difference between the sides is given, uses that as one part without dividing","When reading a dash on a number line does not take into account the number at the start or the width of each division","When drawing bar diagram for ratio, shows the total as the difference between parts","When describing the relationship between the parts in a ratio, replaces the : with a decimal point to say how many times bigger a part is than the other","Does not divide by 2 when finding midpoint","Believes adding coordinates of endpoint and midpoint of a line will give the other endpoint","Believes the amount given is for the whole rather than a part","Beileves you can use the full length when finding an area of part of a composite shape, when part of the length is needed","Finds the circumference of the whole circle instead of arc length ","Believes the total of a part whole model is always 1 (or equivalent) instead of the given total","Makes an assumption about line segments being equal within a shape","Does not understand that in the ratio 1:n the total number of parts would be 1+n ","When calculating a scale factor, thinks the division is the other way around.","When finding the distance between coordinates, includes the starting number","Believes a proportion of a whole is whole\/part not part\/whole","When writing ratio, writes total as one side","Believes the gradient of a line is given by the x intercept","Believes ratios can be combined without equalizing common terms","Does not realise that the order is important in a ratio","Believes quartiles are at 1\/4 and 3\/4 through the range of the data","Thinks they find the length of a line between 2 points by adding coordinates, rather than subtracting","When enlarging a shape, thinks the scale factor divides the movement from the centre of enlargement to a vertex rather than multiplies","Believes that 1 part of a bar model will always have a value of 1","Divides length of original by length of image rather finding length of image divided by length of original to find an enlargement scale factor.","Confuses section and whole when using a bar model","Thinks the gradient of a line is found from 2 points by finding the length of that line between those points","When converting fractions to ratios, puts the other side of the ratio as the total of the numerator and denominator","Thinks co-interior angles sum to 360 degrees"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Time Series and Line Graphs ### ConstructName: Interpret continuous data using a line graph ### Question: This graph shows the amount of potatoes consumed by a restaurant in a week.\n\nHow many more potatoes were consumed on Sunday compared to Saturday? ![Chart of potatoes consumed with kilos against day of week]()","positive":["Reads one point on a time series graph instead of all the values from a given time period"],"negative":["When converting from an improper fraction to a mixed number, adds on the part left to make the whole, rather than subtracting it","When asked to subtract a fraction from a unit, removes the unit value from the numerator.","Confused mixed numbers with improper fractions","Writes the numerator of an improper fraction as the number of wholes when converting to a mixed number","When asked to subtract a fraction from a unit, removes the unit value from the denominator","When converting from an improper fraction to a mixed number, just writes the tens digit as the number of wholes","Believes the whole and remainder are the other way when changing an improper fraction to a mixed number","Believes that n\/n = n, instead of 1","Uses numerator as whole part of a fraction","Uses the numerator of an improper fraction as the denominator of the equivalent mixed number","When expressing one quantity (x) as a fraction of another (y), believes the answer is 1\/x.","When subtracting a fraction from a mixed number, assumes they subtract the numerator from the integer and the numerator of the mixed number","When subtracting a fraction from a mixed number, assumes they just subtract the numerator from the integer of the mixed number","Finds an equivalent improper fraction when asked for a mixed number","Thinks the fraction 1\/n can express sharing any number of items between n people","Does not know how to interpret a fraction worded problem ","Thinks numbers greater than 1 cannot be converted into fractions","Believes a mixed number can contain an improper fraction","Thinks that a unit fraction can be simplified further","Simplifies integers when simplifying a mixed number","Forgets that a number divided by itself is 1","Forgot to simplify the fraction","When asked to take off a fraction of an amount, subtracts the fraction itself","Multiplies the number of whole units by the numerator when converting from a mixed number to an improper fraction","Thinks converting an integer to a fraction means both the numerator and denominator are equal","Does not know that you can leave a fraction in improper form","Thinks you add the number of wholes to the numerator when converting a mixed number to an improper fraction.","Does not know how to say a fraction","Forgets to add the numerator when converting from a mixed number to an improper fraction ","When given a non-unit fraction of an amount, treats it like a unit fraction","When subtracting fractions, subtracts the numerators and denominators","Thinks the fraction 1\/n can express sharing n items between any number of people","Thinks you multiply by the numerator and add the denominator when converting a mixed number to an improper fraction","Only applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction","Thinks if you multiply a fraction by itself you get a whole","Does not understand that a remainder can be written as a fraction","When adding fractions, adds the numerators and denominators","Does not understand equivalent fractions","Identifies the wrong part of a fraction model as the whole","Uses the total as the numerator of the fraction rather than the denominator.","Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator","Thinks that fractions involving a fraction as the denominator can just be read as mixed numbers","Does not consider the denominator when adding\/ subtracting fractions. Adds\/subtracts the numerator and makes the denominator the one with the highest value.","when subtracting a fraction from an integer, just adds their absolute value and places a negative sign in front","Mixes up the terms for the parts of a fraction","Does not fully simplify fraction","Believes that a fraction means dividing the denominator by the numerator","Writes fraction rather than fraction of amount","Denominator used for other parts rather than total parts","Believes when changing an improper fraction to a mixed number you divide the numerator by 10, regardless of the denominator"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Converting between Fractions and Decimals ### ConstructName: Convert fractions less than 1 to terminating decimals of 2 decimal places ### Question: \\( \\frac{6}{25}=? \\)","positive":["Converts a fraction to a decimal by placing a decimal point between the numerator and denominator"],"negative":["Believes multiplying a positive by a negative gives a positive answer","Believes multiplying two negatives gives a negative answer","Believes dividing a negative by a positive gives a positive answer","Believes dividing a positive by a negative gives a positive answer","Believes adding two negatives gives a positive answer","Believes dividing a negative by a negative gives a negative answer","Thinks signs are interchangeable when adding or subtracting positive and negative numbers","Believes multiplying two positives gives a negative answer","Thinks multiplying two or more negative numbers together always gives a positive answer, regardless of how many negative numbers there are in the sum","When multiplying with negative numbers, assumes any negative sign can be ignored","Believes the square of a negative will also be negative","Ignores negative sign when expanding bracket","Ignores the negative signs when adding positive and negative numbers","When factorising into double brackets, believes the product of the constants in the brackets is of the opposite sign to the constant in the expanded equation.","Believes raising a negative number to an odd power will give a positive answer","Believes that the sign changes when factorising an expression into single brackets","When subtracting a negative number, subtracts the absolute value rather than adding it","Does not realise that subtracting a negative is the same as adding it's additive inverse","Confuses negative and positive correlation","Believes a number raised to a power will always give a positive answer","Believes two odd numbers multiply to give an even number","Believes that the directions of positive and negative vectors are the opposite way around.","When solving simultaneous equations, believes the terms must have the same sign in order to be eliminated.","Believes dividing two positives will give a negative answer","Does not understand the link between the sign of the root and the sign in the bracket","When calculating the power of a negative number, thinks they can ignore the sign when multiplying and then put a negative sign back on at the end, regardless of the power ","Factorises difference of two squares with the same sign in both brackets","Only multiplies the first term in the expansion of a bracket","Adds instead of multiplying when expanding bracket","Only multiplies second term in the expansion of a bracket","Does not think a square root can be negative"," Does not believe that a negative multiple of a vector is in the opposite direction","Ignores the negative sign","When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored ","When multiplying out 2 or more brackets, does not multiply all the combinations of terms","When subtracting from a negative thinks the answer must be positive","When subtracting a negative thinks the answer must be negative ","Believes reflection in y = -x changes sign of x coordinate only","Believes they only need to multiply the first and last pairs of terms when expanding double brackets","Believes multiplication is not commutative","Thinks the subtraction sign means multiply","Believes the centre of rotation is always the origin","Does not understand that the negative outside the bracket means answer will be negative","Thinks the difference between a positive number and a negative number is equal to the positive number","Does not know that 7 and -7 are different","Believes reflection in y = -x changes sign of y coordinate only","Does not realise that when you multiply by 0 the answer will always be 0","Thinks positive or negative sign affects the term before it","Believes they can multiply\/divide through by a negative number without changing the direction of the inequality","Believes squaring a negative number just changes the sign"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Pie Chart ### ConstructName: Calculate the sector angle on a pie chart for a given group ### Question: A diver wants to make a pie chart of his trip. \\begin{tabular}{|c|c|c|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline Conger Eel & \\( 12 \\) & \\( \\mathrm{~F} \\) \\\\\n\\hline\n\\end{tabular} Which one of these is a correct method for finding F?","positive":["Finds the degrees for 1 person rather than the required number of people for a pie chart sector"],"negative":["When completing the square, believes the constant in the bracket is the coefficient of x","When completing the square, believes the constant in the bracket is double the coefficient of x","When completing the square in the form (x - a)^2 + b, believes b is the difference between a and the constant of the original quadratic","When completing the square in the form (x - a)^2 + b, believes b = the original constant","When completing the square, believes a coefficient of x^2 does not affect the value of the constant inside the bracket","When completing the square, believes the constant in the bracket is the square root of the coefficient of x","When completing the square, believes that a is always half the x-coefficient. ","When completing the square in the form (x - a)^2 + b, believes b = a^2 + the original constant","When completing the square in the form (x - a)^2 + b, believes b = -a^2 regardless of the original constant","In completed square form, confuses the x and y coordinates of the turning point","Believes that when factorising a quadratic with a coefficient of x squared, the two constants in the brackets still add to give the coefficient of x","When factorising into double brackets, believes the sum of the two values in the brackets equals bx rather than b","Believes that in completed square form, the x co-ordinate of the turning point has the same sign as the constant in the brackets.","When factorising into double brackets, finds the two values which sum to give the constant rather than the coefficient of x","Believes the second term in a 2 term quadratic equation is always a coefficient and the variable","Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets","Believes that in completed square form, they need to change the sign of the constant to get the turning point","Mixes up squaring and multiplying by 2 or doubling","Believes that in completed square form, they need to change the signs of both values to get the turning point","Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets","Thinks factorising a quadratic means factorising the variable terms into a single bracket, and leaving out the constant","Only multiplies the first term in the expansion of a bracket","Misremembers the quadratic formula","When factorising a quadratic with a non-unit coefficient of x squared, believes that coefficient will be in front of both x terms in the factorised form","Adds instead of multiplies","Believes the numbers in factorising should multiply to give the coefficient of x and add to give the constant","When multiplying out 2 or more brackets, does not multiply all the combinations of terms","Adds instead of multiples","Adds instead of multiplying when expanding bracket","Only multiplies second term in the expansion of a bracket","When solving an equation thinks they add when in fact they need to multiply","When factorising into single brackets, factorises the first term correctly but subtracts the number outside the bracket with the second term in the expression to find the second term in the bracket","Believes the inverse of square rooting is doubling","Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant","Multiplies by the index","Thinks that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression","When squaring a variable, believes they also need to square the coefficient","Does not include brackets when attempting to multiply an expression","Believes they can factorise a difference of two squares by placing the constant in both brackets without square rooting","Believes we can only take the square root of a perfect square","Writes a repeated root once, rather than in a squared bracket","When factorising, finds a factor that goes into only the first term of the expression","Squares when asked to find the square root","Thinks converting an integer to a fraction means both the numerator and denominator are equal","Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x","Believes a power of 2 has no impact on its value","When solving an equation, uses the same operation rather than the inverse.","Believes expanding a squared expression means writing it as a set of double brackets","When solving an equation forgets to eliminate the coefficient in front of the variable in the last step","Does not think that a variable with no coefficient has a coefficient of 1."],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Mental Multiplication and Division ### ConstructName: Recognise and use efficient methods for mental multiplication ### Question: Tom and Katie are discussing ways to calculate \\( 49 \\times 9 \\) mentally\nTom multiplies \\( 49 \\) by \\( 10 \\) and then subtracts \\( 49 \\) from the answer.\nKatie does \\( 50 \\times 9 \\) and then subtracts \\( 9 \\) from the answer\nWho would get the correct answer?","positive":["Believes that the compensation strategy for the multiplication of 2 numbers can only be used one way round."],"negative":["When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal","When multiplying a decimal less than 1 by an integer, gives an answer 10 times bigger than it should be","When multiplying decimals, ignores place value and just multiplies the digits","When multiplying decimals, multiplies rather than divides when reinserting the decimal.","When multiplying a decimal by an integer, ignores decimal point and just multiplies the digits","When multiplying decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.","When multiplying a decimal less than 1 by an integer, gives an answer 100 times smaller than it should be","When multiplying a decimal less than 1 by an integer, gives an answer 10 times smaller than it should be","Does not understand place value within a number","When multiplying a decimal by a power of 10, just adds a zero to the end of the number, not changing the place value of the digits","When multiplying just writes the numbers next to each other","Thinks that when multiplying decimals (less than 1), the number will get bigger","When adding decimals, just adds the digits and ignores place value","Mixes up squaring and multiplying by 2 or doubling","Adds instead of multiplies","Multiplies by the index","When multiplying, treats digits in other columns as if they are units","Believes multiplying by 0.1 is the same as multiplying by 10","Believes you write the carried value in the number rather than adding it to the next place value column","When multiplying by 1 gives an answer of 1 (for a number other than 1)","Ignores place value when adding a whole number and a decimal","Divides instead of multiplies when multiplying by a decimal","Has multiplied the base number and the power","When dividing a decimal by a whole number, ignores decimal point and just divides the digits","When dividing decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.","When finding the square root of a decimal, ignores place value","Reads a power as a normal digit","When doing operations with decimals, ignores significant zeros after the decimal point","Believes a power of 2 has no impact on its value","Adds instead of multiples","Believes multiplying two negatives gives a negative answer","Multiplied by 10 rather than 100","Has written something to the power of 1 as 0.1","Multiplies rather than divides","When dividing decimals, divides rather than multiplies when reinserting the decimal.","Believes that when multiplying an integer by a decimal greater than 1, you multiply by the integer component of the decimal but add on the decimal component multiplied by 10.","When multiplying with negative numbers, assumes any negative sign can be ignored","Thinks any 2 values multiplied together can be denoted with a squared symbol","When dividing a decimal by an integer, divides by the wrong power of 10 when reinserting the decimal.","When dividing a decimal by a power of 10 adds zeroes to start of the number ignoring the placement of the initial decimal point","When adding, just writes the digit to the right of the number without considering place value","Does not understand place value after the decimal point","Believes that when multiplying by a power of 10 you add zeroes after the decimal point","Does not realise that in standard form the decimal we use must be between 1 and 10","When multiplying out 2 or more brackets, does not multiply all the combinations of terms","Does not understand the value of zeros as placeholders","Added rather than multiplied by a scale factor","When adding decimals, does not keep place value the same as the original digits","Believes dividing by 0.1 is the same as dividing by 10","When two digits sum to 10 or more during addition of decimals, does not carry across decimal point to preceding digit."],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Ordering Decimals ### ConstructName: Read a decimal on a scale where the required measurement is marked by a dash between two numbers ### Question: ![A number line from 0 to 1 split into 5 parts with a red arrow pointing to the marker for the value 0.4]() What number is the arrow pointing to?","positive":["When reading decimals on a number line, assumes each dash is 0.1"],"negative":["Thinks the number in the ratio is the total","Shares equally instead of in given ratio","Thinks a difference of one part in a ratio means the quantities will differ by one unit","Mixes up sides of a ratio","In ratio question where one side of ratio is given, treats that as the total","Finds one part of a ratio but doesn't multiply that by the number of parts needed","Does not believe you can scale up a proportional statement","In ratio question where the difference between the sides is given, uses that as the total","Gets order of ratio wrong","Estimates shares of a ratio instead of calculating","When answering questions regarding adding items to get a new ratio, looks at the difference between the numbers in the original and new ratio rather than finding the size of a part","In ratio question where the difference between the sides is given, uses that as the total for one side instead","Thinks adding same amount to each side of a ratio gives an equivalent ratio","In ratio question where the difference between the sides is given, uses that as one part without dividing","Mixes up total and part in ratio","In ratio question where one side of ratio is given, uses that as one part in ratio without dividing","When writing ratio from diagram, writes total as one side","Does not scale up a ratio to find an equivalent value","Finds unit amount but doesn't multiply up","When converting fractions to ratios, puts the other side of the ratio as the total of the numerator and denominator","When writing ratio, writes total as one side","Multiplies up without finding unit amount","In ratio where total is given, treats that as one part without dividing","Believes they can change only one side of a ratio and it will remain equivalent","Thinks you need to include the total as well as the individual parts when asked to write a ratio","Does not understand equivalent ratios","Difficulty with translating a mathematical answer into a real world context","Assumes a ratio is part to part instead of part to whole","Does not understand that in the ratio 1:n the total number of parts would be 1+n ","Does not realise that the order is important in a ratio","Does not round up when an answer is non-sensical in a real-life context","Ignores numbers written as words in worded questions, and just calculates using those written in digits","Mixes up sides of a ratio, when working with vectors for line segments.","Divides total amount by each side of the ratio instead of dividing by the sum of the parts","May have estimated when using ratios with geometry","Only counts visible vertices","Does not fully simplify ratio","When converting ratio to fractions, puts the other side of the ratio as the denominator rather than the total","Believes that when converting ratio to fractions, the denominator is the difference between the parts of the ratio","Forgets to include values outside of the Venn diagram when finding the total","Attempts to simplify ratio by subtracting from both sides","Finds total instead of difference when asked 'How many more'","Does not realise ratio in worded problem can be simplified","When asked for more, find the total","Adds rather than multiplies when scaling up in direct proportion problems","Believes ratios can be combined without equalizing common terms","Uses the denominator when converting from fractions to ratio, rather than numerator.","Believes you do not include an \"other\" category when finding a total frequency","Does not know the meaning of consecutive","Only counts visible edges"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Volume and Capacity Units ### ConstructName: Convert between l and  cm\u00b3 ### Question: Complete this statement:\n\\( 5 \\) litres \\( = \\) ________\\( \\mathrm{cm}^{3} \\)","positive":["Thinks 1l = 1 cubic centimetre"],"negative":["Thinks the interior angles of any polygon add up to 180 degrees","Thinks the interior angle of a regular polygon is 10n","Thinks the interior angles of any polygon add up to 360","Thinks the interior angles of a polygon add up to 100n","Does not know how to calculate the sum of interior angles","Does not understand to find each interior angle of a regular polygon you divide the sum by the number of sides","Believes an interior angle in a regular polygon can be found using 180(n+2)\/n","Believes an interior angle in a regular polygon can be found using 360 subtract (180 over number of sides)","Believes interior angles are outside a shape","Does not subtract 2 from the number of sides when finding the sum of interior angles","Finds interior angle rather than given angle","Confuses interior angles with exterior angles","Believes that you are unable to calculate the sum of the interior angles of an irregular polygon given the number of sides","Believes you add 2 instead of subtracting 2 to the numbers of sides when finding total interior angles","Believes the only way to find the interior angle of a regular polygon is to subtract the exterior angle from 180.","Identified the interior not exterior angle at a point","Divides by (n-2) rather than n when finding an interior angle","Subtracts 1 rather than 2 from the number of sides when finding the sum of interior angles","Thinks rule for calculating interior angles only applies to regular polygons","Does not understand what an interior angle is","Does not recognise that interior and exterior angles are supplementary","When given the perimeter of a regular polygon, subtracts instead of divides to find each side length","When given the perimeter of a regular polygon, multiplies instead of divides to find each side length","Assumes an angle has been split into equal parts","Thinks that only the sides need to be equal for a polygon to be regular","Does not understand that all angles and sides must be equal for regular shapes","Thinks that only the angles need to be the same for a polygon to be regular","Believes lines inside the shape are included when finding perimeter","Does not know the meaning of the word regular ","Does not know what an exterior angle is ","Thinks co-interior angles sum to 90 degrees","Believes angles around a point sum to 180","Believes a quarter of 2 is 0.25","Believes a polygon can have curved sides","Thinks the value of an exterior angle is 360 degrees","Calculates perimeter when asked for area","Ignores unlabelled angles when applying angle sum rules","Believes angles in a quadrilateral sum to 450 degrees","Finds the degrees for 1 person rather than the required number of people for a pie chart sector","Believes if a circle is divided into n equal sectors, the angles at the centre will each be n degrees","Does not understand the naming structure of polygons","Calculates area when asked for perimeter","Confuses octagon and pentagon","Believes alternate angles sum to 180 degrees","Mixes up squaring and multiplying by 2 or doubling","Confuses obtuse and acute angles","Divides 360 degrees by sum of sides rather than given amount of angles","Believes that an exterior angle can have a value of 360 degrees","Thinks there are 180 degrees in a full turn","Does not recognise parallel lines angle rules applied inside a shape"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Solving Linear Inequalities ### ConstructName: Solve one-step linear inequalities in one variable where the variable appears on one side of the equation ### Question: Solve the inequality:\n\\(-\\frac{1}{3} y \\leq-6\\)","positive":["Believes they can multiply\/divide through by a negative number without changing the direction of the inequality"],"negative":["When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.","Confuses left and right","When describing a translation, miscounts when crossing an axis","When describing a translation, identifies the correct number of jumps but mixes up the directions .","When describing a translation, goes from the image to the original","Struggles to visualise the new position of an object after transformations","Reflects instead of rotates","Rotates by the wrong center of rotation (not including the origin)","Mistakes rotations for translations","Reflects horizontally or vertically instead of across a diagonal line of symmetry","Counts the squares rather than the diagonals when reflecting in y=x or y=-x ","Confuses negative and positive coordinates when working with graphs in four quadrants","Fails to reflect across mirror line","Translates rather than reflects across a line of symmetry","When finding the distance between coordinates, includes the starting number","Mixes up clockwise and anticlockwise","Does not recognise that a shape translated would not change orientation","Rotates instead of reflects","Thinks a positive x value in a column vector means to move left rather than right","Counts the starting number when counting backwards","Counts squares instead of the correct scale when plotting coordinates","Counts on by 1, when asked to count forward\/backwards in a step other than 1","Forgets to add starting value when calculating new coordinates","When asked to rotate by 180 degrees rotates by 90 degrees","Mixes up squaring and multiplying by 2 or doubling","When asked for a specific term in a sequence gives the term after","Has completed only one of the two operations.","Believes f(x - a) translates the function down a units","Believes displacement continues to increase even when returning to starting point","Rounds down instead of up","Believes the centre of rotation is always the origin","Believes a coordinate cannot be placed beyond the bounds of the grid shown","Does not notice all changes in a sequence of visual patterns","Reflects in an axis, instead of the given mirror line","Chooses an incorrect point in between the shapes when describing a 90 or 270 degree rotation","Chooses an incorrect point on the object when describing a 90 or 270 degree rotation","Counts the starting number when counting on","Does not recognise the origin as the starting point for coordinates","Does not know the meaning of square sign for right angle","Has used the wrong data point on the graph","Does not know how to find area by counting squares on a grid","Thinks positive values in a column vector denote movement left and down (and vice-versa for negative values).","Does not follow the arrows through a function machine, changes the order of the operations asked.","Does not count end number when counting","Does not count from the centre of enlargement to find the image","Makes an assumption about the squares on a scale representing either 1 or 10","Adds instead of subtracts","Counts a side length more than once when counting perimeter due to not marking a starting point","Believes the square of a negative will also be negative","Carries out operations from left to right regardless of priority order"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Combined Events ### ConstructName: Calculate the probability of two independent events occurring without drawing a tree diagram ### Question: ![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners\nWhat is the probability of getting a \\( 1 \\) on both spinners?","positive":["When multiplying fractions, multiplies the numerator and adds the denominator"],"negative":["Does not know how to identify common factors from algebraic terms","Identifies a number as a common factor but doesn't identify a letter as a common factor","Misunderstands the concept of common factors in algebra","Does not know the meaning of common, eg. common factor","Identifies a letter as a common factor but doesn't identify a number as a common factor","Cannot identify a common factor when simplifying algebraic fractions","Believes factors of algebraic terms\/expressions will only be numbers","Does not understand the term factor","Does not know the 6 timestable","When asked for factors of an algebraic expression, thinks a term will be a factor","When asked for factors of an algebraic expression, thinks any part of a term will be a factor","Does not recognise difference of two squares","Thinks a factor of the final digit is also a factor of the whole number","Does not know the 9 timestable","Does not understand how to divide algebraic terms","Does not understand how to multiply algebraic terms","Does not know how to simplify algebraic fractions","Identifies a common factor but not the highest common factor","Does not recognise when to find a factor from a worded question","Does not understand when like terms can be collected","Thinks they can simplify algebraic fractions by cancelling unlike variables","When factorising into single brackets, only factors out the numerical values and forgets to factorise possible variables","Does not recognise factorising a quadratic","Does not understand how to subtract algebraic fractions","Does not realise that two letters together, or a number and letter together, are multiplying","Identifies a multiple of a number but not a common multiple of a group of numbers","Believes only the first term needs to be divided when factorising an expression","Does not use the associative property of multiplication to find other factors of a number","Thinks only like terms can be multiplied","Incorrectly cancels what they believe is a factor in algebraic fractions","Thinks you can divide terms by different factors when simplifying an algebraic fraction","Does not know the meaning of the identity symbol","Does not understand that a number is divisible by the factors of its factors","When simplifying an algebraic fraction, only looks for number factors","Does not realise that two letters together are multiplying","Does not understand the term multiple","Can not recognise all factor pairs of numbers","When factorising, finds a factor that goes into only the first term of the expression","Thinks you can ignore the variable when simplifying algebraic fractions","Does not know the meaning of the word identity ","Believes a factor pair doesn't have to be 2 integers","Identifies a common multiple of two numbers when asked to consider a common multiple of three numbers","Does not realize we can omit the multiplication symbol in algebraic expressions","Believes that they can fully factorise an expression by taking out any common factor, not just the HCF","Does not think a number can be a factor of itself","Believes multiplication is not commutative","Does not realise similar has a specific mathematical meaning","Believes you need to know the value of all algebraic variables before any general conclusions can be made","When factorising, thinks the smallest coefficient will be the numerical factor, regardless of whether it divides into all terms","Believes sets are the same if the elements within them have a shared property"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Length Scale Factors in Similar Shapes ### ConstructName: Solve length problems involving similar shapes where the missing length is the longer one ### Question: What is the ratio of \\( x \\) to \\( y \\) ? ![A triangle. The bottom width is marked '15cm'. One side is split into two parts, one part is called 'x', the other is marked 'y'. A second line goes across the triangle from where the side is split into two parts. It is marked '5cm'. ]()","positive":["Does not understand that in the ratio 1:n the total number of parts would be 1+n "],"negative":["When writing a number as a percentage of another number gets them the wrong way around","When the change in value is greater than the original amount, thinks percentage change = original\/change x 100","Does not understand that you can have percentages greater than 100%","Found the percentage but added it to 100%","Multiplied by 100 rather than divided by 100","Thinks when finding a percentage you divide by the percentage being asked","Finds 10% of an amount rather than the percentage being asked","Believes that a greater percentage represents a greater quantity","Believes a proportion of a whole is whole\/part not part\/whole","Does not understand a percentage is out of 100","Thinks they had to give the new amount rather than the total percentage that the original has been increased by.","Has considered the percentage rather than the percentage of the amount","Increases by the given percentage rather than finding the percentage of an amount","Found the percentage but forgot to add to 100%","Thinks when finding a percentage you multiply by the percentage being asked","Has found the total as a percentage of the amount being asked","Multiplied by 1000 instead of 100","Gives the change in value when asked for the percentage change","Thinks they double the numerator to turn a fraction into a percentage","Converts a fraction to a percentage by writing the numerator followed by the denominator","Believes a pie chart makes 360% not 360 degrees","Added the values together instead of finding the percentage","Finds a percentage when asked for a fraction","Error finding percentage value after finding 1%","When calculating a scale factor, thinks the division is the other way around.","Converts fraction to percentage by putting % sign after the denominator","Thinks you just add a % sign to the numerator to make a fraction into a percentage","Multiplies instead of divides by 100 when converting a percentage to a decimal","Multiplies by 1000 instead of 100 when converting a decimal to a percentage","Believes a fraction out of a number other than 100 represents a percentage","Thinks you need to just add a % sign to a number to make it a percentage","Multiplies rather than divides","Gets order of ratio wrong","Believes that any percentage of a larger number will be greater than any percentage of a smaller number","Believes that dividing by 100 gives 10%","Believes division is commutative ","Believes that a fraction means dividing the denominator by the numerator","Does not know that you can have a decimal percentage","Believes you can divide the change by 100 to find the percentage change ","When finding a percentage of an amount, assumes they divide the percentage by 10, but not the amount, before multiplying","Does not understand how to find percentages of an amount","Believes 30% is equivalent to 1\/3","Does not understand a percentage can be applied to something not out of 100","Multiplied by the scale factor rather than divided in direct proportion problems","Believes a percentage of a number will be a multiple of the percentage","Divides length of original by length of image rather finding length of image divided by length of original to find an enlargement scale factor.","Divided by 100 rather than multiplied by 100","Multiplies rather than divides when answering worded problems","Multiplies by the denominator instead of dividing when finding a fraction of an amount","Thinks that to decrease by a percentage you multiply by 1+ the decimal equivalent to that percentage"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Converting between Decimals and Percentages ### ConstructName: Convert integer percentages with 1 digit to decimals  ### Question: How do you write \\( 2 \\% \\) as a decimal?","positive":["Does not understand a percentage is out of 100"],"negative":["Forgets to change the numerators when finding equivalent fractions","Does not find a common denominator when adding\/subtracting fractions","Does not understand how to maintain equivalence in fractions","When subtracting fractions, subtracts the numerators and denominators","Does not understand equivalent fractions","Uses the numerator of an improper fraction as the denominator of the equivalent mixed number","When adding fractions, changes to common denominator but leaves numerators the same","Does not find a common denominator when comparing fractions","When subtracting a fraction from a mixed number, assumes they subtract the numerator from the integer and the numerator of the mixed number","Removes the common denominator when making equivalent algebraic fractions","Believes they should multiply each numerator by its original denominator when adding\/subtracting fractions","Confused mixed numbers with improper fractions","Believes that if the numerators of 2 fractions are equal then the fractions are equal, regardless of the denominator","Believes a mixed number can contain an improper fraction","Finds an equivalent improper fraction when asked for a mixed number","When subtracting a fraction from a mixed number, assumes they just subtract the numerator from the integer of the mixed number","When subtracting fractions, subtracts the numerators and multiplies the denominators","Believes that fractions with the same denominator are equal","Does not consider the denominator when adding\/ subtracting fractions. Adds\/subtracts the numerator and makes the denominator the one with the highest value.","When subtracting fractions, divides the numerators","When adding fractions, adds the numerators and denominators","Does not understand how to subtract algebraic fractions","Adds or subtracts from numerator first when solving an equation with a fraction","When adding fractions with identical numerators, leaves the numerator and adds the denominators","Subtracts numerators when dividing fractions with a common denominator","Can identify the multiplier used to form an equivalent fraction but does not apply to the numerator","After multiplying to get a common denominator, simplifies back to the original fractions","Believes equivalent fractions are formed with addition not multiplication","Incorrectly cancels what they believe is a factor in algebraic fractions","Adds instead of subtracts","Mixes up the terms for the parts of a fraction","Uses numerators to convert fractions to ratio despite different denominators","When converting from an improper fraction to a mixed number, adds on the part left to make the whole, rather than subtracting it","Thinks you multiply by the numerator and add the denominator when converting a mixed number to an improper fraction","Believes you add the whole to the numerators, ignoring denominators, when adding a mixed number to a proper fraction with the same denominator.","Is not familiar with the names of the different parts of a fraction","Does not know the term numerator","When adding\/subtracting fractions, adds\/subtracts the denominators and multiplies the numerators","Believes when changing an improper fraction to a mixed number you divide the numerator by 10, regardless of the denominator","When subtracting mixed numbers, does not realise that a negative fractional answer needs to be taken away from their integer answer","Believes a common denominator must always be the two denominators multiplied together","When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation","Cannot identify a fraction on a number line","Does not see fraction diagrams as equivalent if the shading is in a different pattern","Believes a common denominator can only be the lowest common multiple","Mixes up the numerator and denominator","Believes the whole and remainder are the other way when changing an improper fraction to a mixed number","When asked to subtract a fraction from a unit, removes the unit value from the denominator","Does not know how to solve linear equations involving fractions","Uses numerator as whole part of a fraction"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Writing Expressions ### ConstructName: Use brackets to write function machines as calculations ### Question: Tom and Katie are arguing about the result of this Function Machine:\nTom says the output is: \\( 3 n-12 \\)\nKatie says the output is: \\( 3(n-4) \\)\nWho is correct? ![A function machine with input n and operations subtract 4, multiply by 3]()","positive":["Does not think a factorised expression is equivalent to its multiplied out form"],"negative":["When solving an equation, subtracts instead of dividing","When solving an equation, uses the same operation rather than the inverse.","When solving an equation, adds instead of dividing","When solving an equation,  subtracts instead of multiplying","When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value","When solving an equation, multiplies instead of dividing ","When solving an equation thinks they divide when in fact they need to multiply","Subtracts instead of adds when using inverse operations to solve an equation","When solving an equation, thinks the divisor and dividend are the opposite way around","When solving an equation forgets to eliminate the coefficient in front of the variable in the last step","When solving an equation thinks they add when in fact they need to multiply","When solving an equation, multiplies instead of adding","Confusion over whether multiplication or division is the correct way to solve the problem.","Does not reverse the order of operations when solving an equation","Thinks the inverse of subtraction is division","Swaps the dividend and divisor in order to get an integer answer","Thinks the inverse of multiplication is addition","Thinks they solve mx + c = a, by substituting in the value of a for x and therefore calculating ma + c","Adds or subtracts from numerator first when solving an equation with a fraction","Subtracts instead of divides","When solving a problem that requires an inverse operation (e.g. missing number problems), does subtraction when division is required","Thinks the inverse of subtraction is multiplication","Misunderstands the process of making a variable the subject of an equation","When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation","Thinks the inverse of addition is division","Multiplies rather than divides","Believes that a number divided by itself equals 0","Believes dividing by 0.1 is the same as dividing by 10","Believes that the solution to ax + b = 0 is x = -a\/b","Assumes the denominator is divided by the numerator","substitutes incorrectly","Divides rather than multiplies ","Stops iteration too early when solving equations","Believes dividing by a unit fraction is equivalent to dividing by its reciprocal","Thinks the inverse of addition is multiplication","Believes you can subtract from inside brackets without expanding when solving an equation","Believes they must change the direction of the inequality when dividing through by a positive number.","Believes you can add or subtract from inside brackets without expanding when solving an equation","Believes the solution of mx + c = 0 is x = m","Thinks the subtraction sign means divide","Believes they can multiply\/divide through by a negative number without changing the direction of the inequality","Believes 0 multiplied by a number gives the number","Incorrectly clears fractions from equations","Believes you keep the divisor unchanged when dividing by a fraction","Believes the solution to mx + c = a is the x intercept of y = mx +c","Believes that dividing by a decimal is the same as dividing by its reciprocal","Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount","Believes that a number divided by itself equals the original number","Believes dividing two positives will give a negative answer","Heads towards zero when subtracting from a negative"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Place Value ### ConstructName: Write 3 digit numbers as words  ### Question: How do you write this number in words?\n\\( 107 \\)","positive":["The student does not understand the place value of 3-digit numbers"],"negative":["Finds volume when asked for surface area","When calculating surface area, only includes visible faces","Finds surface area when asked for volume","Multiplies all given dimensions when calculating an area","Cannot identify the correct side lengths to use when asked to find the area of a face","Believes you find the surface area of a prism by finding the total area of the unique faces","Calculates perimeter when asked for area","Thinks all dimensions given must be used when calculating the area","Believes volume of a cuboid is the area of the three unique faces multiplied together","adds all given dimensions when calculating area","Includes all faces when finding surface area of a compound shape, including those which are stuck together","Calculates area when asked for perimeter","Adds when calculating volume instead of multiplying","Calculates circumference when asked for area","Finds area of one face when asked for volume","When calculating perimeter, only adds two sides","Adds when calculating area instead of multiplying","Does not know how to calculate volume","Does not know how to find missing lengths in a composite shape","Does not know how to calculate the volume of a prism","When calculating perimeter, multiplies instead of adds","Has used slant height and base to find area rather than perpendicular height and base","Finds the circumference instead of the area","Uses an incorrect side length when splitting a composite shape into parts","When calculating the area of a rectilinear compound shape, calculates the are of the surrounding rectangle","Thinks area of a circle = radius x pi ","Has multiplied base by slant height and perpendicular height to find area of a triangle","Does not recognise that all lengths on a cube are equal","Multiplies all terms together when simplifying an expression","Confuses the terms faces and edges","Does not convert measurements to have the same units before calculating area or volume","Multiplies by the index","Does not divide by 2 when calculating the area of a triangle","Believes the area of a rectangle is calculated by length add width","When calculating volume expressed in cubes, counts the faces of all the cubes","Believes the number of edges on a 3D shape match those of the 2D cross section","Thinks measures of area must end in squared","Thinks only labelled dimensions need to be included when calculating the perimeter","Multiplies all given dimensions when calculating the length of the hypotenuse in a right angled triangle","Mixes up squaring and multiplying by 2 or doubling","When calculating volume expressed in cubes, counts only the squares on one face","Does not have when calculating the area of a triangle","Adds instead of multiples","When multiplying out 2 or more brackets, does not multiply all the combinations of terms","Struggles to visualise nets of 3D shapes","Believes you multiply all of the values given when using the capture-recapture sampling method","Only counts visible faces","Adds instead of subtracts when using an area model for multiplication","When calculating perimeter, only adds the marked lengths","Mixes up cubes and cuboids"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}
+{"query":"### SubjectName: Averages and Range from Frequency Table ### ConstructName: Calculate the mean from a frequency table ### Question: This table shows the ages of people on a university running team.\nTo calculate the mean age, what is the most sensible heading for the third column? \\begin{tabular}{|c|c|l|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular}","positive":["Adds instead of multiplies"],"negative":["Added rather than multiplied by a scale factor","Adds instead of multiples","Subtracted rather than divided by a scale factor","Thinks a variable next to a number means addition rather than multiplication","Believes distance = speed + time","When multiplying just writes the numbers next to each other","Thinks the multiplication sign means to add","Believes they add the conversion factor when converting between units","Thinks two variables next to each other represent addition","Multiplies rather than adds ","Adds when calculating area instead of multiplying","Adds the index to the number","Thinks a variable next to a number means write the digits together","Writes the index as a digit on the end of a number","Adds when calculating volume instead of multiplying","Adds instead of multiplying when expanding bracket","Believes the area of a rectangle is calculated by length add width","Think 1km = 1 mile","When adding, just writes the digit to the right of the number without considering place value","When calculating perimeter, multiplies instead of adds","Subtracts instead of multiplies","Forgets to add starting value when calculating new coordinates","When multiplying fractions, multiplies the numerator and adds the denominator","Adds rather than multiplies for combined probabilities","Multiplies rather than adds when given the command word 'more'","Adds rather than multiplies when asked for a product","Added the values together instead of finding the percentage","Adds rather than multiplies when scaling up in direct proportion problems","Calculates perimeter when asked for area","Confuses additive and multiplicative relationships","Multiplied by the scale factor rather than divided in direct proportion problems","Multiplies rather than divides","Adds instead of subtracts","Thinks multiplication and addition are the same","Adds instead of multiplies when using grid method","When calculating a scale factor, multiplies instead of dividing.","Believes the fx column for calculating mean is value + frequency","Multiplies by the index","Adds instead of multiplies when multiplying algebraic terms","When adding column vectors, multiplies rather than adds","Subtracts instead of adds","Thinks the subtraction sign means multiply","When solving an equation thinks they add when in fact they need to multiply","Adds instead of multiplies when calculating total frequency","Believes they write the digits next to each other instead of multiplying, when multiplying a vector by an integer.","When asked to multiply fractions, uses the method for adding instead","Adds rather than multiplies when asked for a total","When solving an equation, multiplies instead of adding","When scaling the perimeter multiplies the number of sides by the scale factor"],"prompt":"A math problem, its correct answer, and an incorrect answer are given. Retrieve the reasoning behind how the incorrect answer was derived."}