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Fernandosr85
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adaption-math-misconception-match

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Decide whether the misconception explains the student's wrong answer. Question context: Order fractions whose denominators are multiples of the same number Averages (mean, median, mode) from a List of Data \begin{tabular}{llllll} $ \frac{2}{10} $ & $ \frac{9}{50} $ & $ \frac{9}{20} $ & $ 0.21 $ & \( \frac{1}{...	NO_MATCH	null	To determine if the candidate misconception explains the student's wrong answer, we first need to analyze the data set and identify the correct outlier. 1. Convert all values to decimals: - $ \frac{2}{10} = 0.2 $ - $ \frac{9}{50} = 0.18 $ - $ \frac{9}{20} = 0.45 $ - $ 0.21 = 0.21 $ - \( \fra...
Decide whether the misconception explains the student's wrong answer. Question context: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplifying Expressions by Collecting Like Terms Simplify, if possible: \[ c+a \] Student's wrong answer: \( c a \...	NO_MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Perform calculations with temperature when given in the same units Adding and Subtracting Negative Numbers Which statement about the temperatures $ -7^{\circ} \mathrm{C} $ and $ 5^{\circ} \mathrm{C} $ is true? Student's wrong ...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Recognise and name a formula Writing Formula Which of the following is the most appropriate word to describe: $ A=\frac{b h}{2} $ ![A triangle with base labelled b and height labelled h.]() Student's wrong answer: Expression Ca...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Factorise a quadratic expression in the form x² - c Difference of Two Squares Factorise this expression, if possible: $ p^{2}-16 $ Student's wrong answer: $ p(p-16) $ Candidate misconception: Believes that they can fully fact...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Divide a decimal by an integer Multiplying and Dividing with Decimals $ 0.1 \div 4= $ Student's wrong answer: $ 0.4 $ Candidate misconception: Multiplies rather than divides when answering worded problems Does this misconcep...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Identify questions involving a 2D right-angled triangle that require the use of the Cosine (cos) ratio Right-angled Triangles (SOHCAHTOA) Which ratio would you use to find the value of $ \theta $ ? ![A right angled triangle with ...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Identify a kite from a description of the properties Properties of Polygons Which of the following quadrilaterals could not be classified as a kite? Student's wrong answer: Square Candidate misconception: Does not recognise the p...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Change decimals of hours into minutes Time $ 0.2 $ hours $ = _______ $ minutes Student's wrong answer: $ 2 $ Candidate misconception: Thinks there are 10 minutes in an hour Does this misconception explain the wrong answer?...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Convert between kg and tonne Weight Units $ 3000 \mathrm{~kg} $ is the same as $ ___ $ tonnes Student's wrong answer: $ 3000000 $ Candidate misconception: Multiplies rather than divides Does this misconception explain the ...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Convert from improper fractions to mixed number fractions Converting Mixed Number and Improper Fractions Write $ \textbf{nineteen fifths} $ as a mixed number fraction. Student's wrong answer: $ 19 \frac{1}{5} $ Candidate misc...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Multiply a decimal by an integer Multiplying and Dividing with Decimals Work out: \[ 0.3 \times 12 \] Student's wrong answer: $ 0.036 $ Candidate misconception: When multiplying a decimal less than 1 by an integer, gives an ans...	NO_MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Recognise the equations of horizontal lines from a diagram Horizontal and Vertical Lines What is the equation of this line? ![A set of axes with a line drawn on. The lines passes through the points: (0,2) (1,2) (2,2) (3,2) and (4,2...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Calculate the length of horizontal and vertical line segments Distance Between Two Co-ordinates ![A rectangle drawn on a coordinate grid. Three of the vertices are labelled (3,12) (10,12) and (10,7). There is a red arrow between (3...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Use the order of operations to carry out calculations involving brackets BIDMAS \[ 1+2 \times(3-4)= \] Which calculation should you do first? Student's wrong answer: $ 1+2 $ Candidate misconception: Carries out operations from...	NO_MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Convert between cm and mm Length Units How many millimetres are there in $ 1 $ centimetre? Student's wrong answer: $ 1000 $ Candidate misconception: Thinks there are 100mm in a metre Does this misconception explain the wrong...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Expanding Single Brackets $ 3(4 x+6)-2(x-9) \equiv A x+B $ What is the value of $ A $ ? Student's wrong answer...	NO_MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Round the elements of a calculation to one significant figure to perform an estimation Estimation Julie wants to estimate the answer to this calculation by rounding each number to $ 1 $ significant figure. \[ 87.4 \times 0.3727 ...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Divide proper fractions in the form: Fraction ÷ Integer Dividing Fractions Calculate: $ \frac{2}{5} \div 2 $ Student's wrong answer: $ \frac{4}{5} $ Candidate misconception: when dividing a fraction by an integer, multiplies ...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Draw the net of a prism Nets This is an incomplete net for a triangular prism. What shapes do you add to complete this net? ![An incomplete net of a triangular prism comprising a rectangle (landscape) and an equilateral triangle. ...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Identify the total number of combinations in a given scenario by using the product rule for counting where duplicates are considered different Systematic Listing Strategies Jumbo Restaurant has $ 34 $ choices of starters, \( 92 \...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Represent a linear inequality with a single tail on a numberline Inequalities on Number Lines Which of the following diagrams represents $ x>-1 $ ? Student's wrong answer: ![Image of a number line. At -1 there is a red, filled c...	NO_MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Calculate the length of horizontal and vertical line segments Distance Between Two Co-ordinates ![A rectangle drawn on a coordinate grid. Three of the vertices are labelled (3,12) (10,12) and (10,7). There is a red arrow between (3...	NO_MATCH	null	NO_MATCH Reasoning: 1. Correct Answer: The width is the horizontal distance between $x = 3$ and $x = 10$. The calculation is $10 - 3 = 7$. 2. Student's Answer: The student answered $13$. 3. Analysis of Student's Error: The number $13$ is the sum of the x-coordinates ($3 + 10 = 13$). This indicates t...
Decide whether the misconception explains the student's wrong answer. Question context: Solve linear inequalities involving two inequality signs Solving Linear Inequalities What is the solution to the following inequality? $ -5<2 x+1<5 $ Student's wrong answer: $ -2<x<2 $ Candidate misconception: Believes that a...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Calculate the area of an isosceles triangle where the dimensions are given in the same units Area of Simple Shapes Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 4...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Solve length problems involving similar shapes where the missing length is the shorter one Length Scale Factors in Similar Shapes These two shapes are similar. What is the value of $ y $ ? ![The diagram is of two trapeziums. The...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Triple numbers Mental Multiplication and Division If you triple $ 8 $ you get... Student's wrong answer: $ 888 $ Candidate misconception: Repeats the digits twice when squaring a number Does this misconception explain the wr...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Factorise a quadratic expression in the form x² - bx - c Factorising into a Double Bracket Which answer shows the correct factorisation of: $ x^{2}-x-6 $ Student's wrong answer: $ (x+3)(x-2) $ Candidate misconception: When fa...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Recognise the notation for parallel lines Parallel Lines This notation means that these two lines are: ![Pair of parallel lines]() Student's wrong answer: Horizontal Candidate misconception: Does not recognise a parallelogram Do...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Given the sketch of a negative quadratic, work out its factorised form Sketching from Factorised Form Which of the following could be the equation of the curve? ![A negative quadratic graph that crosses the x-axis at (-5,0) and (1...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Understand inequality notation Inequalities on Number Lines Which of these statements show that $ \mathrm{j} $ is smaller than $ 5 $ ? Student's wrong answer: $ j=5 $ Candidate misconception: Confuses inequality symbols wit...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Complete missing number mental subtraction problems up to 100 Mental Addition and Subtraction What should replace the star? \[ \bigstar-26=28 \] Student's wrong answer: $ -2 $ Candidate misconception: When solving a problem tha...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Substitute positive integer values into formulae involving powers or roots Substitution into Formula The equation $ f=3 r^{2}+3 $ is used to find values in the table below. What is the value covered by the star? \begin{tabular}{\|...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Continue a sequence involving triangle numbers Other Sequences Here are two consecutive triangle numbers: $ 120,136, \ldots $ What is the next triangle number in the sequence? Student's wrong answer: $ 151 $ Candidate misconc...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Round integers to the nearest 10 Written Division What is $ 4296 $ rounded to the nearest $ 10 $ ? Student's wrong answer: $ 4310 $ Candidate misconception: Rounded to nearest 100 instead of 1sf Does this misconception exp...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Factorise a quadratic expression in the form x² - c Difference of Two Squares Factorise this expression, if possible: $ p^{2}-16 $ Student's wrong answer: Does not factorise Candidate misconception: Does not recognise differenc...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Expand two brackets with linear terms in the form (ax + b)(cx + d) Expanding Double Brackets Molly is expanding these two brackets. What should she get when she multiplies the two terms indicated by the arrows? ![The brackets show...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Solve positive quadratic inequalities by balancing e.g x² ≤ a Solving Quadratic Inequalities Which of the following is the correct solution to the inequality? $ x^{2}<64 $ Student's wrong answer: $ \{-32<x<32\} $ Candidate mi...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Factorise a single bracket containing a linear expression by taking out a single numeric common factor (e.g. 6) Factorising into a Single Bracket What should replace the star and triangle when this expression is fully factorised? \...	NO_MATCH	null	The problem asks to factorise the expression $ 8m - 10 $. The correct factorisation involves finding the Highest Common Factor (HCF) of 8 and 10, which is 2. So, $ 8m - 10 = 2(4m - 5) $. Here, $ \bigstar = 2 $ and $ \triangle = 4 $. The student's answer is $ \bigstar = 5 $ and $ \triangle = 3 $. This impli...
Decide whether the misconception explains the student's wrong answer. Question context: Calculate the range from a list of data Range and Interquartile Range from a List of Data Tom and Katie are discussing the $ 5 $ plants with these heights: \( 24 \mathrm{~cm}, 17 \mathrm{~cm}, 42 \mathrm{~cm}, 26 \mathrm{~cm}, 13...	NO_MATCH	null	MATCH Explanation: 1. Correct Mathematical Analysis: * Original Range: $\text{Max} - \text{Min} = 42 - 13 = 29$. * Tom's Claim (Divide by 2): New Max = 21, New Min = 6.5. New Range = $14.5$. The range changes. Tom is incorrect. * Katie's Claim (Add 3): New Max = 45, New Min =...
Decide whether the misconception explains the student's wrong answer. Question context: Given a negative x value, find the corresponding y value for curves in the form y = x² + c Plotting Quadratics from Tables of Values This is a part of the table of values for the equation $ y=x^{2} $ \begin{tabular}{\|l\|l\|} \hline...	NO_MATCH	null	NO_MATCH Explanation: The student's answer is -81, which indicates they calculated $-(9^2)$ instead of $(-9)^2$, effectively believing that squaring a negative number results in a negative answer. The candidate misconception states: "Believes the negative of a positive squared (where there are no brackets) gi...
Decide whether the misconception explains the student's wrong answer. Question context: Recall and use the intersecting diagonals properties of a rectangle Properties of Quadrilaterals The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The an...	NO_MATCH	null	The correct answer to the question is that the highlighted angles can never be 90° (right angles). Here is the geometric reasoning: 1. In any rectangle, the diagonals are equal in length and bisect each other. 2. The diagonals of a parallelogram are perpendicular (intersect at 90°) if and only if the figure is a rho...
Decide whether the misconception explains the student's wrong answer. Question context: Calculate distance where speed and time are in the appropriate units Real Life Graphs This displacement-time graph shows $ 10 $ seconds of Mo's journey home. During that time he travelled at a speed of \( 15 \mathrm{~m} / \mathr...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Solve one-step linear inequalities in one variable where the variable appears on one side of the equation Solving Linear Inequalities Tom and Katie are arguing about the solution to this inequality: \[ 20 \geq 8 m \] Tom says \( m...	NO_MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Understand the relationship between parts of a ratio Writing Ratios Tom and Katie are arguing about the information on the right. Tom says there are $ 9 $ times as many students as teachers. Katie says one in ten people are tea...	NO_MATCH	null	MATCH Explanation: 1. Correct Interpretation: The ratio is teachers : students = 1 : 9. - Tom's statement ("9 times as many students as teachers") is correct. - Katie's statement ("one in ten people are teachers") is correct (1 teacher + 9 students = 10 total people). - Therefore, the cor...
Decide whether the misconception explains the student's wrong answer. Question context: Understand the term mutually exclusive Probability of Single Events Percy is playing a game where all $ 26 $ letters of the alphabet at placed into a bag and Percy has to pick one out at random. Picking a $ \mathrm{P} $ and a v...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Solve quadratic equations using balancing Quadratic Equations One of these equations has no real solutions. Which is it? Student's wrong answer: $ t^{3}=-27 $ Candidate misconception: Believes raising a negative number to an od...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Multiply algebraic fractions where the numerators and denominators involve linear expressions Multiplying and Dividing Algebraic Fractions Write this as a single fraction as simply as possible: \( \frac{5}{x-3} \times \frac{x^{2}}{...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Calculate the distance between two coordinates in 2D, where all the values are positive integers Distance Between Two Co-ordinates Mark is working out the distance between these two points. What type of triangle would help him? ![A...	MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Find the gradient of a line written in the form ax + by = c Finding the Gradient and Intercept of a Line from the Equation In which region would $ x+y=1 $ belong? ![A Venn diagram with two intersecting sets. The set on the right ...	NO_MATCH	null	Step 1 — Compare - Content accuracy & completeness: Responses 0 and 1 correctly conclude NO_MATCH. Response 1 provides the most rigorous analysis: it shows that if a student swaps m and c in y = -x + 1, they would get gradient = 1 (positive) but intercept = -1, placing the line in region C, not B. The st...
Decide whether the misconception explains the student's wrong answer. Question context: Represent an equation using a bar model Writing Expressions ![Tom and Katie are discussing bar models.]() Tom says this bar model represents $ 2 x $ \begin{tabular}{\|l\|l\|} \hline $ 2 $ & $ x $ \\ \hline \end{tabular} Katie sa...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Calculate a positive fractional gradient between two coordinates where all values are positive Gradient Between Two Co-ordinates Max is working out the gradient between these two points. He has worked out the lengths of the triangl...	NO_MATCH	null	NO_MATCH Reasoning: The correct gradient is calculated as the change in $y$ divided by the change in $x$, which is $\frac{3}{6} = 0.5$. The student's answer is $2$. Given the problem context explicitly states that the student has worked out the lengths of the triangle (base = 6, height = 3), the most direct expl...
Decide whether the misconception explains the student's wrong answer. Question context: Recognise and use efficient strategies for mental subtraction Mental Addition and Subtraction Nick wants to subtract $ 199 $ from a number. Which one of the following methods would give him the correct answer? Student's wrong an...	MATCH	null	NO_MATCH The student's error involves the mental math strategy known as compensation. To subtract 199, the efficient strategy is to subtract 200 and then add 1 (because 199 is 1 less than 200). The student chose to subtract 200 and then subtract 1, treating 199 as "200 plus 1" instead of "200 minus 1". The ca...
Decide whether the misconception explains the student's wrong answer. Question context: Multiply an integer and an algebraic term Expanding Double Brackets John is expanding these two brackets. What should he get when he multiplies the two terms indicated by the arrows? ![$ (x+5)(x-3) $]() Student's wrong answer:...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Round numbers between 0 and 1 to one significant figure Rounding to Significant Figures Round this number to $ 1 $ significant figure: $ 0.00809 $ Student's wrong answer: $ 0.01 $ Candidate misconception: Rounds to the wron...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Add two equations together to remove a variable Simultaneous Equations Eliza is trying to solve the pair of simultaneous equations below. $ \begin{aligned} -6 g-2 h & = & -2 \\ g-2h & = & 10 \\ \end{aligned} $ She decides to a...	MATCH	null	MATCH Reasoning: 1. Analyze the Student's Action: The student's answer has a constant term of $8$. The constants in the equations are $-2$ and $10$. Since $-2 + 10 = 8$, the student added the two equations. 2. Analyze the Elimination: The student's answer ($5g = 8$) does not contain the variable $h$. T...
Decide whether the misconception explains the student's wrong answer. Question context: Convert between l and m³ Volume and Capacity Units $ 10 $ litres $ =\square $ cubic metres Student's wrong answer: $ 10 $ Candidate misconception: Thinks 1l = 1 cubic metre Does this misconception explain the wrong answer...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units Compound Area What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape ...	MATCH	null	MATCH Reasoning: 1. Identify the Target Shape: The problem asks for the area of the "shaded section," which is the top rectangle. 2. Identify Dimensions: The dimensions of this top rectangle are a width of $6\text{ cm}$ and a height of $8\text{ cm}$. 3. Calculate Correct Area: The area of a rectangl...
Decide whether the misconception explains the student's wrong answer. Question context: Solve quadratic equations using completing the square in the form (x + q)² + r Quadratic Equations One of these equations has no real solutions Which is it? Student's wrong answer: $ (w+5)^{2}=0 $ Candidate misconception: Beli...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Recognise when an ascending sequence is quadratic Quadratic Sequences Tom and Katie are discussing quadratic sequences. Tom says this is a quadratic sequence: $ 3,5,10,17,26, \ldots $ Katie says this is a quadratic sequence: \(...	MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Rearrange formulae to change the subject where the subject appears once and three or more steps are needed Rearranging Formula and Equations Tom and Katie are discussing rearranging $ t=\sqrt{u+9} $ to make $ u $ the subject To...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Identify corresponding angles Angle Facts with Parallel Lines These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above th...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Rotate an object or point 180° about a point, where the point lies on the edge or outside of the object Rotation ![A pair of axes: x-axis is from -3 to 4; y-axis is from -4 to 4. A quadrilateral, labelled "P", is made by joining t...	NO_MATCH	null	The correct answer for a 180° rotation of the point (-1, 3) about the origin is (1, -3), which corresponds to point D. The rule for a 180° rotation is (x, y) → (-x, -y). The student selected point A, which is at (3, 1). The transformation that maps (-1, 3) to (3, 1) follows the rule (x, y) → (y, -x), which is a 90° cl...
Decide whether the misconception explains the student's wrong answer. Question context: Identify a transversal Angle Facts with Parallel Lines What is the name given to the red line that intersects the two dashed lines? ![Shows two straight horizontal dashed lines that are converging and are both intersected by a soli...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Interpret discrete data using a line graph Time Series and Line Graphs This graph shows the amount of potatoes consumed by a restaurant in a week. How many potatoes were consumed on Friday? ![Graph of potatoes consumed with kilos ...	MATCH	null	MATCH The student's answer is $ 3 \mathrm{~kg} $. In line graph questions where the answer is an integer corresponding to the number of grid units (squares) from the axis, but the answer is marked wrong, it typically implies the scale of the axis is not 1 unit per square (e.g., each square might represent 2 kg or 5 ...
Decide whether the misconception explains the student's wrong answer. Question context: Identify and distinguish between polygons and non-polygons Properties of Polygons Tom and Katie are discussing polygons Tom says this is a polygon: ![Triangle]() Katie says this is a polygon: ![Semi-circle]() Who is correct? Stude...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Express pictorial representations of objects as a ratio Pie Chart What is the ratio of tables to chairs? ![tables chairs]() Student's wrong answer: $ \frac{270}{360} $ Candidate misconception: Does not understand parts must be ...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Find missing angles in an isosceles triangle Basic Angle Facts (straight line, opposite, around a point, etc) What is the size of angle $ w $ ? ![An isosceles triangle with one of the base angles labelled with a w and the angle v...	NO_MATCH	null	NO_MATCH The correct calculation for angle $ w $ is as follows: 1. The angle vertically opposite the vertex angle is $ 27^\circ $, so the vertex angle inside the triangle is also $ 27^\circ $ (vertically opposite angles are equal). 2. The triangle is isosceles, so the two base angles are equal. Let the base angl...
Decide whether the misconception explains the student's wrong answer. Question context: Find missing angles in a scalene triangle Angles in Triangles What is the size of angle $ p $ ? ![A triangle with angles labelled 49 degrees, 51 degrees and p [not to scale]]() Student's wrong answer: $ 51^{\circ} $ Candidate...	NO_MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Round decimals to the nearest whole number Estimation Jane measures the length and width of her rectangular classroom as $ 8.3 \mathrm{~m} $ and $ 12.9 \mathrm{~m} $. Which calculation will give the best estimate of the area? ...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Work out the sum of the interior angles in polygons Angles in Polygons What do all the interior angles of this shape add up to? ![Image of an irregular pentagon]() Student's wrong answer: $ 360^{\degree} $ Candidate misconcepti...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Calculate percentage of an amount mentally where the percent is a multiple of 10 Percentages of an Amount $ 30 \% $ of $ £ 120= $ Student's wrong answer: $ £ 30 $ Candidate misconception: Does not understand a percentage ca...	MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Solve one-step linear equations requiring addition or subtraction, with all positive integers Linear Equations Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Simplify an algebraic fraction by factorising the numerator Simplifying Algebraic Fractions Simplify the following, if possible: $ \frac{t^{2}+t-2}{t-1} $ Student's wrong answer: Does not simplify Candidate misconception: Incor...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Solve quadratic equations using balancing Quadratic Equations One of these equations has no real solutions. Which is it? Student's wrong answer: $ t^{3}=-27 $ Candidate misconception: Believes a number raised to a power will al...	MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Recall the formulae for the trigonometric ratios Right-angled Triangles (SOHCAHTOA) $ \bigstar=\frac{\text { Hypotenuse }}{\text { Opposite }} $ What should replace the star? Student's wrong answer: $ \sin (\theta) $ Candida...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Divide two decimals with a different number of decimal places Multiplying and Dividing with Decimals $ 70.04 \div 0.1= $ Student's wrong answer: $ 70.004 $ Candidate misconception: When dividing decimals, divides rather than ...	NO_MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Convert between l and cm³ Volume and Capacity Units Complete this statement: $ 5 $ litres $ = $ ________$ \mathrm{cm}^{3} $ Student's wrong answer: $ 5 $ Candidate misconception: Thinks 1l = 10 cubic centimetres Does th...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Multiply algebraic terms, where both are linear versions of different letters (e.g. 4a x 2b) Multiplying Terms Simplify, if possible: \[ 6 a \times 4 b \] Student's wrong answer: $ 10 a b $ Candidate misconception: Adds instead...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Solve linear inequalities in one variable that require three or more steps where the variable appears on one side of the equation Solving Linear Inequalities Solve \[ 42 \geq 6(2 n+1) \] Student's wrong answer: \( \frac{35}{12} \...	NO_MATCH	null	The correct solution to the inequality $ 42 \geq 6(2n + 1) $ is: 1. Expand the bracket: $ 42 \geq 12n + 6 $ 2. Subtract 6 from both sides: $ 36 \geq 12n $ 3. Divide by 12: $ 3 \geq n $ The student's answer is $ \frac{35}{12} \geq n $. Working backwards from this answer: 1. Multiply by 12: $ 35 \geq 12n $ 2...
Decide whether the misconception explains the student's wrong answer. Question context: Insert brackets to make a calculation correct BIDMAS \[ 12 \times 6-1+2 \] Where do the brackets need to go to make the answer equal $ 36 $ ? Student's wrong answer: $ 12 \times(6-1+2) $ Candidate misconception: Applies BIDMA...	MATCH	null	MATCH Reasoning: 1. Analyze the Goal: The student needs to insert brackets into $12 \times 6 - 1 + 2$ to make the result equal to $36$. 2. Analyze the Student's Answer: The student proposed $12 \times (6 - 1 + 2)$. 3. Evaluate Correctly: Using standard BIDMAS rules, addition and subtraction have equ...
Decide whether the misconception explains the student's wrong answer. Question context: Given a situation sketch an appropriate real life graph Real Life Graphs Johan wants to plot a graph to show the distance a ball travels over time. After $ 2 $ seconds the ball has travelled $ 3 $ metres. Where on the graph s...	NO_MATCH	null	To determine if the misconception "Confuses x and y axes" explains the student's wrong answer, let's analyze the given information: 1. Correct Answer: Time = 2 seconds is on the horizontal (x) axis, and Distance = 3 metres is on the vertical (y) axis. The correct point to plot is (2, 3). 2. **Student's Wrong A...
Decide whether the misconception explains the student's wrong answer. Question context: Calculate the area of a rectangle where the dimensions are given in the same units Mental Multiplication and Division ![A rectangle with one part shaded, labelled with dimensions 20, 8 and 6]() Which of the following calculations w...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Given a sketch of a quadratic graph, f(x), write down the solutions to f(x) = a Quadratic Equations According to the graph, what is the approximate solution to $x^{2}+4 x-1=-6$ ![A set of axes with the quadratic graph y=x^2+4x-1 ...	NO_MATCH	null	NO_MATCH Explanation: 1. Analyze the Student's Error: The question asks for the solutions to the equation $x^{2}+4 x-1=-6$, which corresponds to finding the $x$-coordinates where the graph of $y = x^2 + 4x - 1$ intersects the horizontal line $y = -6$. The student provided the values $x = -4.25$ and \...
Decide whether the misconception explains the student's wrong answer. Question context: Substitute negative integer values into formulae involving powers or roots Substitution into Formula $ F=3^{a} $ What is the value of $ F $ when $ a=-5 $ ? Student's wrong answer: $ -243 $ Candidate misconception: Believ...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Divide algebraic fractions involving non-linear expressions Multiplying and Dividing Algebraic Fractions STEP $ 2 $ Which of the options is a correct second step to express the following as a single fraction? \( \begin{aligned} ...	NO_MATCH	null	NO_MATCH Reasoning: 1. Analyze the Student's Error: The student incorrectly factorized the denominator $x^2 - 1$ as $(x-1)(x-1)$. The correct factorization of the difference of two squares is $(x-1)(x+1)$. The student's error stems from confusing $a^2 - b^2$ with $(a-b)^2$, resulting in two minus signs instead...
Decide whether the misconception explains the student's wrong answer. Question context: Understand the non-commutativity of division Mental Multiplication and Division Jacob makes a conjecture: If you have two different numbers, $ P $ and $ Q $, the order you divide does not matter. $ P \div Q=Q \div P $ Is Jaco...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Calculate the volume of a cuboid when the dimensions are given in different units Volume of Prisms Which of the following calculations would give the volume of this cuboid? ![A cuboid with dimensions 60mm, 7cm and 5cm]() Student's...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Multiply two decimals together with the same number of decimal places Multiplying and Dividing with Decimals $ 0.01^{3}= $ Student's wrong answer: $ 0.03 $ Candidate misconception: Believes cubing a number means you multiply ...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Interpret continuous data using a line graph Time Series and Line Graphs This graph shows the amount of potatoes consumed by a restaurant in a week. How many more potatoes were consumed on Sunday compared to Saturday? ![Chart of p...	NO_MATCH	null	NO_MATCH To determine if the candidate misconception explains the student's wrong answer, let's analyze the graph and the question. 1. Analyze the Question and Graph: * The question asks for the difference in potato consumption between Sunday and Saturday. * Based on the graph, Sunday's consumption is 45 kg...
Decide whether the misconception explains the student's wrong answer. Question context: Shade percentages of a shape where the percent is a multiple of 10 Percentages of an Amount How many rectangles would you need to shade so that $ 60 \% $ of this shape is shaded? ![A rectangle split into 20 equal parts]() Studen...	NO_MATCH	null	The correct calculation is to find 60% of 20, which is 0.60 × 20 = 12. The student answered 3. The candidate misconception states that the student "Subtracts rather than divides when scaling down in direct proportion problems." However, the student's answer of 3 is most likely derived from division (60 ÷ 20 = 3) or b...
Decide whether the misconception explains the student's wrong answer. Question context: Calculate the area of a trapezium where the dimensions are given in the same units Area of Simple Shapes When calculating the area of this trapezium, what is the value of $ h $ in the formula? Area \( =\left(\frac{a+b}{2}\right) ...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Understand the relationship between parts of a ratio Writing Ratios Tom and Katie are arguing about the information on the right. Tom says there are $ 9 $ times as many students as teachers. Katie says one in ten people are tea...	NO_MATCH	null	The correct answer is that both Tom and Katie are correct. The ratio of teachers to students is 1:9, which means there are 9 times as many students as teachers (Tom's claim) and 1 in every 10 people is a teacher (Katie's claim, since 1 + 9 = 10). The student answered "Only Katie," meaning they believe Katie is cor...
Decide whether the misconception explains the student's wrong answer. Question context: Find the gradient of a line written in the form ax + by = c Finding the Gradient and Intercept of a Line from the Equation A line has equation $ 5 x+3 y=7 $ What is its gradient? Student's wrong answer: $ \frac{3}{5} $ Candid...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Round non-integers to the nearest 10 Rounding to the Nearest Whole (10, 100, etc) What is $ \mathbf{9 9 9 . 9 9 9} $ rounded to the nearest ten? Student's wrong answer: $ 990 $ Candidate misconception: Rounds to the nearest i...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Multiply two decimals together with the same number of decimal places Multiplying and Dividing with Decimals $ 0.2 \times 0.8= $ Student's wrong answer: $ 1.6 $ Candidate misconception: When multiplying decimals, divides by t...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Express pictorial representations of objects as a ratio Pie Chart What is the ratio of tables to chairs? ![tables chairs]() Student's wrong answer: $ \frac{3}{4} $ Candidate misconception: When writing fraction from diagram, wr...	MATCH	null	MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object Reflection The triangle is reflected in the dashed line. What are the new coor...	MATCH	null	MATCH The correct answer is $(2, 4)$ because point $ P $ lies exactly on the line of reflection ($ y = 4 $). Any point on the line of reflection remains unchanged (invariant) after the reflection. The student answered $(2, 3)$, moving the point down by 1 unit. This indicates that the student believed the poin...
Decide whether the misconception explains the student's wrong answer. Question context: Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Expanding Single Brackets Expand: $ -(2-3 p) $ Student's wrong answer: $ 2-3 p $ Candidate misconcept...	NO_MATCH	null	NO_MATCH
Decide whether the misconception explains the student's wrong answer. Question context: Solve linear inequalities involving two inequality signs Solving Linear Inequalities What is the solution to the following inequality? $ -5<2 x+1<5 $ Student's wrong answer: $ -2<x<2 $ Candidate misconception: Believes subtra...	MATCH	null	MATCH Explanation: To solve the inequality $-5 < 2x + 1 < 5$, the first step is to subtract 1 from all parts. The correct calculation is $-5 - 1 = -6$, which results in $-6 < 2x < 4$. Dividing by 2 gives the correct solution: $-3 < x < 2$. The student's answer is $-2 < x < 2$. Working backward, this implies they ...

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This dataset is a remastered version prepared using Adaption's Adaptive Data platform.

adaption-math_misconception_match

This dataset contains pairs of math problems, student wrong answers, and candidate misconceptions. The task is to determine if the specific misconception logically explains the student's error. Each sample provides the question context, the incorrect response, and a labeled classification of 'MATCH' or 'NO_MATCH'.