conversations
listlengths 3
3
|
|---|
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Carry out subtraction problems involving two negative integers \nSubject: Adding and Subtracting Negative Numbers\nQuestion: What number belongs in the box?\n\\(\n(-8)-(-5)=\n\\square\\)\nIncorrect Answer: \\( 3 \\)\nCorrect Answer: \\( -3 \\)\n",
"role": "user"
},
{
"content": "When subtracting from a negative thinks the answer must be positive",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Prove statements involving multiples\nSubject: Algebraic Proof\nQuestion: On what line is the first mistake when proving \\( (n+1)^{2}-(n-1)^{2} \\) is divisible by \\( 4 \\) ? \\( n^{2}+2 n+1-\\left(n^{2}-2 n+1\\right) \\quad \\) Line \\( 1 \\) \\( n^{2}+2 n+1-n^{2}-2 n+1 \\quad \\) Line \\( 2 \\) \\[\n2\n\\]\n\nLine \\( 3 \\)\nIncorrect Answer: Line \\( 1 \\)\nCorrect Answer: Line \\( 2 \\)\n",
"role": "user"
},
{
"content": "Ignores negative sign when expanding bracket",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units\nSubject: Compound Area\nQuestion: What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]()\nIncorrect Answer: \\( 48 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 42 \\mathrm{~cm}^{2} \\)\n",
"role": "user"
},
{
"content": "Uses an incorrect side length when splitting a composite shape into parts",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units\nSubject: Compound Area\nQuestion: What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]()\nIncorrect Answer: \\( 104 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 42 \\mathrm{~cm}^{2} \\)\n",
"role": "user"
},
{
"content": "Uses an incorrect side length when splitting a composite shape into parts",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units\nSubject: Compound Area\nQuestion: What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]()\nIncorrect Answer: \\( 56 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 42 \\mathrm{~cm}^{2} \\)\n",
"role": "user"
},
{
"content": "Uses an incorrect side length when splitting a composite shape into parts",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Find the gradient of a line written in the form ax + by = c\nSubject: Finding the Gradient and Intercept of a Line from the Equation\nQuestion: In which region would \\( x+y=1 \\) belong? ![A Venn diagram with two intersecting sets. The set on the right is 'Crosses the y-axis at (0,1)' and the set of the right is 'Has a positive gradient'. A is in the 'Crosses the y-axis at (0,1)' set only, B is in the intersection, C is in the 'Has a positive gradient' only and D is outside both sets.]()\nIncorrect Answer: B\nCorrect Answer: A\n",
"role": "user"
},
{
"content": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use brackets to write function machines as calculations\nSubject: Writing Expressions\nQuestion: Jo and Paul are arguing about the result of this Function Machine:\nJo says the output is: \\( \\frac{n}{5}+3 \\)\nPaul says the output is: \\( \\frac{n+3}{5} \\)\nWho is correct? ![A function machine showing an input of n and operations divide by 5 and add 3]()\nIncorrect Answer: Only\nPaul\nCorrect Answer: Only\nJo\n",
"role": "user"
},
{
"content": "Does not follow the arrows through a function machine, changes the order of the operations asked.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use brackets to write function machines as calculations\nSubject: Writing Expressions\nQuestion: Jo and Paul are arguing about the result of this Function Machine:\nJo says the output is: \\( \\frac{n}{5}+3 \\)\nPaul says the output is: \\( \\frac{n+3}{5} \\)\nWho is correct? ![A function machine showing an input of n and operations divide by 5 and add 3]()\nIncorrect Answer: Both Jo and Paul\nCorrect Answer: Only\nJo\n",
"role": "user"
},
{
"content": "Does not follow the arrows through a function machine, changes the order of the operations asked.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Substitute positive integer values into expressions involving no powers or roots\nSubject: Substitution into Formula\nQuestion: When \\( h=10 \\)\n\\(\n\\frac{h}{2}=\n\\)\nIncorrect Answer: \\( 8 \\)\nCorrect Answer: \\( 5 \\)\n",
"role": "user"
},
{
"content": "Thinks the fraction bar means subtract rather than divide",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Substitute positive integer values into expressions involving no powers or roots\nSubject: Substitution into Formula\nQuestion: When \\( h=10 \\)\n\\(\n\\frac{h}{2}=\n\\)\nIncorrect Answer: \\( -5 \\)\nCorrect Answer: \\( 5 \\)\n",
"role": "user"
},
{
"content": "Believes dividing two positives will give a negative answer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Find the nth term rule for ascending quadratic sequences in the form ax² + bx + c\nSubject: Quadratic Sequences\nQuestion: \\(\n6,14,28,48,74, \\ldots\n\\)\n\nWhen calculating the nth-term rule of this sequence, what should replace the triangle?\n\nnth-term rule: \\( 3 n^{2} \\)\\( \\color{red}\\triangle \\) \\(n\\) \\( \\color{purple}\\square \\)\n\nIncorrect Answer: \\[\n+1\n\\]\n(or just a + sign)\nCorrect Answer: \\( -1 \\)\n(or just a - sign)\n",
"role": "user"
},
{
"content": "When finding the differences between terms in a sequence, believes they can do so from right to left ",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Find the nth term rule for ascending quadratic sequences in the form ax² + bx + c\nSubject: Quadratic Sequences\nQuestion: \\(\n6,14,28,48,74, \\ldots\n\\)\n\nWhen calculating the nth-term rule of this sequence, what should replace the triangle?\n\nnth-term rule: \\( 3 n^{2} \\)\\( \\color{red}\\triangle \\) \\(n\\) \\( \\color{purple}\\square \\)\n\nIncorrect Answer: \\( +3 \\)\nCorrect Answer: \\( -1 \\)\n(or just a - sign)\n",
"role": "user"
},
{
"content": "When finding the nth term rule for a quadratic sequence, believes they only need to use the first term to calculate the coefficient of n ",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve one-step linear equations requiring addition or subtraction, involving positive fractions\nSubject: Linear Equations\nQuestion: Solve the equation:\n\\(\np-5=\\frac{1}{10}\n\\)\nIncorrect Answer: \\( p=\\frac{6}{10} \\)\nCorrect Answer: \\( p=\\frac{51}{10} \\)\n",
"role": "user"
},
{
"content": "When adding an integer to a fraction, thinks you add the integer to the numerator",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve one-step linear equations requiring addition or subtraction, involving positive fractions\nSubject: Linear Equations\nQuestion: Solve the equation:\n\\(\np-5=\\frac{1}{10}\n\\)\nIncorrect Answer: \\( p=\\frac{5}{50} \\)\nCorrect Answer: \\( p=\\frac{51}{10} \\)\n",
"role": "user"
},
{
"content": "When solving an equation, multiplies instead of adding",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve one-step linear inequalities in one variable where the variable appears on one side of the equation\nSubject: Solving Linear Inequalities\nQuestion: Tom and Katie are arguing about solving inequalities.\nTom says \\( -2 m>12 \\) gives \\( m>-6 \\)\nKatie says \\( -2+m>12 \\) gives \\( m>14 \\)\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Katie\n",
"role": "user"
},
{
"content": "Believes they can multiply/divide through by a negative number without changing the direction of the inequality",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Work out the size of each interior angle in a regular polygon\nSubject: Angles in Polygons\nQuestion: Tom and Katie are discussing how to calculate the size of each interior angle in a regular \\( 20 \\) sided shape\n\nTom says you can do \\( \\frac{18 \\times 180}{20} \\)\n\nKatie says you can do \\( 180-\\frac{360}{20} \\)\n\nWho is correct?\nIncorrect Answer: Only Tom\nCorrect Answer: Both Tom and Katie\n",
"role": "user"
},
{
"content": "Does not recognise that interior and exterior angles are supplementary",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Work out the size of each interior angle in a regular polygon\nSubject: Angles in Polygons\nQuestion: Tom and Katie are discussing how to calculate the size of each interior angle in a regular \\( 20 \\) sided shape\n\nTom says you can do \\( \\frac{18 \\times 180}{20} \\)\n\nKatie says you can do \\( 180-\\frac{360}{20} \\)\n\nWho is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Both Tom and Katie\n",
"role": "user"
},
{
"content": "Believes the only way to find the interior angle of a regular polygon is to subtract the exterior angle from 180.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round numbers between 0 and 1 to one significant figure\nSubject: Rounding to Significant Figures\nQuestion: \\(\n0.095643\n\\)\n\nWhat is this number rounded to \\( 1 \\) significant figure?\nIncorrect Answer: \\( 0 \\)\nCorrect Answer: \\( 0.1 \\)\n",
"role": "user"
},
{
"content": "Counts leading zero as a significant figure",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round numbers between 0 and 1 to one significant figure\nSubject: Rounding to Significant Figures\nQuestion: \\(\n0.095643\n\\)\n\nWhat is this number rounded to \\( 1 \\) significant figure?\nIncorrect Answer: \\( 0.09 \\)\nCorrect Answer: \\( 0.1 \\)\n",
"role": "user"
},
{
"content": "Rounds down instead of up when next digit is 5",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round numbers between 0 and 1 to one significant figure\nSubject: Rounding to Significant Figures\nQuestion: \\(\n0.095643\n\\)\n\nWhat is this number rounded to \\( 1 \\) significant figure?\nIncorrect Answer: \\( 0.01 \\)\nCorrect Answer: \\( 0.1 \\)\n",
"role": "user"
},
{
"content": "When rounding up from a 9, does not add one on to the digit to the left",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve problems involving converting between fractions, decimals and percentages\nSubject: Converting between Fractions and Decimals\nQuestion: Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]()\nIncorrect Answer: \\( 100 \\% \\)\nCorrect Answer: \\( \\frac{2}{10} \\)\n",
"role": "user"
},
{
"content": "Identifies the wrong part of a fraction model as the whole",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve problems involving converting between fractions, decimals and percentages\nSubject: Converting between Fractions and Decimals\nQuestion: Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]()\nIncorrect Answer: \\( 60 \\% \\)\nCorrect Answer: \\( \\frac{2}{10} \\)\n",
"role": "user"
},
{
"content": "Believes to complete a part whole model you select a value already given in the model",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve problems involving converting between fractions, decimals and percentages\nSubject: Converting between Fractions and Decimals\nQuestion: Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]()\nIncorrect Answer: \\( 0.4 \\)\nCorrect Answer: \\( \\frac{2}{10} \\)\n",
"role": "user"
},
{
"content": "Believes to complete a part whole model you select a value already given in the model",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Carry out multiplication problems involving one negative integer\nSubject: Multiplying and Dividing Negative Numbers\nQuestion: The product of two numbers is \\( -24 \\).\nWhat could the two numbers be?\nIncorrect Answer: \\( -3 \\) and \\( -8 \\)\nCorrect Answer: \\( -4 \\) and \\( 6 \\)\n",
"role": "user"
},
{
"content": "Believes multiplying two negatives gives a negative answer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Carry out multiplication problems involving one negative integer\nSubject: Multiplying and Dividing Negative Numbers\nQuestion: The product of two numbers is \\( -24 \\).\nWhat could the two numbers be?\nIncorrect Answer: \\( -10 \\) and \\( -14 \\)\nCorrect Answer: \\( -4 \\) and \\( 6 \\)\n",
"role": "user"
},
{
"content": "Believes that product means add rather than multiply",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read values from piecewise functions\nSubject: Other Graphs-Others\nQuestion: Tom is has correctly drawn the graph of the following function:\n\\(\ny=\\left\\{\\begin{array}{c}\n3 \\text { for } 0 \\leq x<Q \\\\\nP \\text { for } 1.5 \\leq x<4 \\\\\n2.5 \\text { for } 4 \\leq x<7\n\\end{array}\\right.\n\\)\n\nWhat are the values of \\( P \\) and \\( Q \\) ? ![The graph is three separate horizontal lines. It goes from (0,3) to (1.5, 3), then (1.5, 2) to (4, 2) and the last section is from (4, 2.5) to (7, 2.5)]()\nIncorrect Answer: \\( \\begin{array}{c}P=1.5 \\\\ Q=2\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}P=2 \\\\ Q=1.5\\end{array} \\)\n",
"role": "user"
},
{
"content": "When reading value from graph, reads from the wrong axes.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read values from piecewise functions\nSubject: Other Graphs-Others\nQuestion: Tom is has correctly drawn the graph of the following function:\n\\(\ny=\\left\\{\\begin{array}{c}\n3 \\text { for } 0 \\leq x<Q \\\\\nP \\text { for } 1.5 \\leq x<4 \\\\\n2.5 \\text { for } 4 \\leq x<7\n\\end{array}\\right.\n\\)\n\nWhat are the values of \\( P \\) and \\( Q \\) ? ![The graph is three separate horizontal lines. It goes from (0,3) to (1.5, 3), then (1.5, 2) to (4, 2) and the last section is from (4, 2.5) to (7, 2.5)]()\nIncorrect Answer: \\( \\begin{array}{l}P=2 \\\\ Q=1\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}P=2 \\\\ Q=1.5\\end{array} \\)\n",
"role": "user"
},
{
"content": "When reading graph, chooses nearest marked value on axis instead of reading accurately",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify the net of a non-prism\nSubject: Nets\nQuestion: This is the net of a... ![An image with an equilateral triangle in the centre. Connected to each of the three sides of the equilateral triangle are 3 more identical, equilateral triangles forming a larger triangle shape.]()\nIncorrect Answer: Triangle\nCorrect Answer: Triangularbased pyramid\n",
"role": "user"
},
{
"content": "Names one of the faces of a 3D shape rather than the 3D shape name",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify the net of a non-prism\nSubject: Nets\nQuestion: This is the net of a... ![An image with an equilateral triangle in the centre. Connected to each of the three sides of the equilateral triangle are 3 more identical, equilateral triangles forming a larger triangle shape.]()\nIncorrect Answer: Triangular prism\nCorrect Answer: Triangularbased pyramid\n",
"role": "user"
},
{
"content": "Confuses pyramid with prism",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Expand two brackets with linear terms in the form (ax + b)(cx + d)\nSubject: Expanding Double Brackets\nQuestion: 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.]()\nIncorrect Answer: \\( -12 \\)\nCorrect Answer: \\( +12 \\)\n",
"role": "user"
},
{
"content": "Believes multiplying two negatives gives a negative answer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Expand two brackets with linear terms in the form (ax + b)(cx + d)\nSubject: Expanding Double Brackets\nQuestion: 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.]()\nIncorrect Answer: \\( -7 \\)\nCorrect Answer: \\( +12 \\)\n",
"role": "user"
},
{
"content": "Adds instead of multiplies",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a)\nSubject: Factorising into a Single Bracket\nQuestion: Factorise this expression, if possible:\n\\(\np^{2}-99p\n\\)\nIncorrect Answer: \\( (p+9)(p-9) \\)\nCorrect Answer: \\( p(p-99) \\)\n",
"role": "user"
},
{
"content": "When factorising a quadratic without a non variable term, tries to double bracket factorise",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a)\nSubject: Factorising into a Single Bracket\nQuestion: Factorise this expression, if possible:\n\\(\np^{2}-99p\n\\)\nIncorrect Answer: \\( (p+3 \\sqrt{11})(p-3 \\sqrt{11}) \\)\nCorrect Answer: \\( p(p-99) \\)\n",
"role": "user"
},
{
"content": "When factorising a quadratic without a non variable term, tries to double bracket factorise",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Given a negative x value, find the corresponding y value for curves in the form y = x² + c\nSubject: Plotting Quadratics from Tables of Values\nQuestion: Tom and Katie are discussing the table of values for \\( y=x^{2}-1 \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( \\bigstar \\) \\\\\n\\hline\\( y \\) & \\( 15 \\) \\\\\n\\hline\n\\end{tabular} Tom says the star could be \\( 4 \\)\n\nKatie says the star could be \\( -4 \\)\n\nWho is correct?\nIncorrect Answer: Only\nTom\nCorrect Answer: Both Tom and Katie\n",
"role": "user"
},
{
"content": "Believes the square of a negative will also be negative",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a protractor to measure angles between 270° and 360°\nSubject: Measuring Angles\nQuestion: What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).\n]()\nIncorrect Answer: \\( 345^{\\circ} \\)\nCorrect Answer: \\( 335^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Correct scale but wrong value on protractor reading.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a protractor to measure angles between 270° and 360°\nSubject: Measuring Angles\nQuestion: What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).\n]()\nIncorrect Answer: \\( 215^{\\circ} \\)\nCorrect Answer: \\( 335^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Reads the wrong scale on the protractor when measuring reflex angles",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a protractor to measure angles between 270° and 360°\nSubject: Measuring Angles\nQuestion: What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).\n]()\nIncorrect Answer: \\( 205^{\\circ} \\)\nCorrect Answer: \\( 335^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Reads the wrong scale on the protractor when measuring reflex angles",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Complete the square for expressions that end up in the form a(x + b)² + c\nSubject: Completing the Square\nQuestion: When Sarah completes the square, what should replace the star? \\( 2 g^{2}-6 g-5 \\equiv 2(g \\bigstar)^{2} \\triangle \\)\nIncorrect Answer: \\( \\bigstar=-6 \\)\nCorrect Answer: \\( \\bigstar=-1.5 \\)\n",
"role": "user"
},
{
"content": "When completing the square, believes the constant in the bracket is the coefficient of x",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Complete the square for expressions that end up in the form a(x + b)² + c\nSubject: Completing the Square\nQuestion: When Sarah completes the square, what should replace the star? \\( 2 g^{2}-6 g-5 \\equiv 2(g \\bigstar)^{2} \\triangle \\)\nIncorrect Answer: \\( \\bigstar=-3 \\)\nCorrect Answer: \\( \\bigstar=-1.5 \\)\n",
"role": "user"
},
{
"content": "When completing the square, believes that a is always half the x-coefficient. ",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Complete the square for expressions that end up in the form a(x + b)² + c\nSubject: Completing the Square\nQuestion: When Sarah completes the square, what should replace the star? \\( 2 g^{2}-6 g-5 \\equiv 2(g \\bigstar)^{2} \\triangle \\)\nIncorrect Answer: \\( \\bigstar=-\\sqrt{6} \\)\nCorrect Answer: \\( \\bigstar=-1.5 \\)\n",
"role": "user"
},
{
"content": "When completing the square, believes the constant in the bracket is the square root of the coefficient of x",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Continue a sequence involving triangle numbers\nSubject: Other Sequences\nQuestion: If you add together consecutive triangle numbers you get...\nIncorrect Answer: another triangle number\nCorrect Answer: a square number\n",
"role": "user"
},
{
"content": "Believes triangle numbers are formed differently to the correct way",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Multiply mixed number fraction in the form: Fraction × Fraction\nSubject: Multiplying Fractions\nQuestion: \\( 1 \\frac{1}{2} \\times 3 \\frac{2}{3}=\\bigstar\\frac{3}{6} \\) What should replace the star?\nIncorrect Answer: \\( 3 \\)\nCorrect Answer: \\( 5 \\)\n",
"role": "user"
},
{
"content": "When multiplying mixed numbers, forgets to multiply the fraction",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Multiply mixed number fraction in the form: Fraction × Fraction\nSubject: Multiplying Fractions\nQuestion: \\( 1 \\frac{1}{2} \\times 3 \\frac{2}{3}=\\bigstar\\frac{3}{6} \\) What should replace the star?\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: \\( 5 \\)\n",
"role": "user"
},
{
"content": "When multiplying mixed numbers thinks they add the integers",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read fractions\nSubject: Fractions of an Amount\nQuestion: How do you say this fraction?\n\\(\n\\frac{3}{5}\n\\)\nIncorrect Answer: Three point five\nCorrect Answer: Three fifths\n",
"role": "user"
},
{
"content": "Has used the decimal point to separate numerator and denominator",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read fractions\nSubject: Fractions of an Amount\nQuestion: How do you say this fraction?\n\\(\n\\frac{3}{5}\n\\)\nIncorrect Answer: Three fives\nCorrect Answer: Three fifths\n",
"role": "user"
},
{
"content": "Does not know how to say a fraction",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read fractions\nSubject: Fractions of an Amount\nQuestion: How do you say this fraction?\n\\(\n\\frac{3}{5}\n\\)\nIncorrect Answer: Third fifths\nCorrect Answer: Three fifths\n",
"role": "user"
},
{
"content": "Does not know how to say a fraction",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use inequality notation to order decimals with the same number of digits \nSubject: Ordering Decimals\nQuestion: Which signs belong in the boxes to make the statement correct?\n\n\\( 0.705 \\)\\[ {\\color{blue}\\square} \\]\\( 0.750 \\)\\[ {\\color{orange}\\square} \\]\\( 0.570 \\)\nIncorrect Answer: ![A blue box containing a \"greater than\" symbol and an orange box containing a \"less than\" symbol]()\nCorrect Answer: ![A blue box containing a \"less than\" symbol and an orange box containing a \"greater than\" symbol]()\n",
"role": "user"
},
{
"content": "Mixes up greater than and less than symbols",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Convert terminating decimals greater than 1 to fractions\nSubject: Converting between Fractions and Decimals\nQuestion: Convert this to a fraction:\n\\( 1.4 \\)\nIncorrect Answer: \\( \\frac{1}{4} \\)\nCorrect Answer: \\( \\frac{7}{5} \\)\n",
"role": "user"
},
{
"content": "Converts a fraction to a decimal by using the denominator after the decimal point",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Convert terminating decimals greater than 1 to fractions\nSubject: Converting between Fractions and Decimals\nQuestion: Convert this to a fraction:\n\\( 1.4 \\)\nIncorrect Answer: Not possible as it is greater than \\( 1 \\)\nCorrect Answer: \\( \\frac{7}{5} \\)\n",
"role": "user"
},
{
"content": "Thinks numbers greater than 1 cannot be converted into fractions",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Range and Interquartile Range from a List of Data\nQuestion: What is the range of the following numbers?\n\\[\n0.31,0.30,0.331\n\\]\nIncorrect Answer: \\( 0.021 \\)\nCorrect Answer: \\( 0.031 \\)\n",
"role": "user"
},
{
"content": "When calculating the range does not reorder the data to find the largest number minus the smallest number",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Range and Interquartile Range from a List of Data\nQuestion: What is the range of the following numbers?\n\\[\n0.31,0.30,0.331\n\\]\nIncorrect Answer: \\( 0.301 \\)\nCorrect Answer: \\( 0.031 \\)\n",
"role": "user"
},
{
"content": "When subtracting decimals with a different number of decimal places, lines up the digits incorrectly",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Range and Interquartile Range from a List of Data\nQuestion: What is the range of the following numbers?\n\\[\n0.31,0.30,0.331\n\\]\nIncorrect Answer: \\( 0.21 \\)\nCorrect Answer: \\( 0.031 \\)\n",
"role": "user"
},
{
"content": "When calculating the range does not reorder the data to find the largest number minus the smallest number",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify a unit of volume or capacity\nSubject: Volume of Prisms\nQuestion: Which of the following is not a measure of volume?\nIncorrect Answer: Cubic metres\nCorrect Answer: Metres\n",
"role": "user"
},
{
"content": "Does not know that cubic means the same as cubed in units",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify a unit of volume or capacity\nSubject: Volume of Prisms\nQuestion: Which of the following is not a measure of volume?\nIncorrect Answer: Centimetres cubed\nCorrect Answer: Metres\n",
"role": "user"
},
{
"content": "Does not know that units of volume are usually cubed",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify a unit of volume or capacity\nSubject: Volume of Prisms\nQuestion: Which of the following is not a measure of volume?\nIncorrect Answer: Litres\nCorrect Answer: Metres\n",
"role": "user"
},
{
"content": "Does not recognise litres as a unit of volume",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Describe a term-to-term sequence\nSubject: Other Sequences\nQuestion: Which of the following term-to-term rule describes this sequence? \\( 4, \\quad 10, \\quad 14, \\quad 24, \\quad \\ldots \\)\nIncorrect Answer: To get the next term you add \\( 6 \\) to the previous term\nCorrect Answer: To get the next term you add the previous two terms together\n",
"role": "user"
},
{
"content": "Uses only the first two terms of a sequence to work out a term-to-term rule",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Describe a term-to-term sequence\nSubject: Other Sequences\nQuestion: Which of the following term-to-term rule describes this sequence? \\( 4, \\quad 10, \\quad 14, \\quad 24, \\quad \\ldots \\)\nIncorrect Answer: To get the next term you double the previous term and add \\( 2 \\)\nCorrect Answer: To get the next term you add the previous two terms together\n",
"role": "user"
},
{
"content": "Uses only the first two terms of a sequence to work out a term-to-term rule",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Describe a term-to-term sequence\nSubject: Other Sequences\nQuestion: Which of the following term-to-term rule describes this sequence? \\( 4, \\quad 10, \\quad 14, \\quad 24, \\quad \\ldots \\)\nIncorrect Answer: To get the next term you multiply the previous term by \\( 3 \\) and subtract \\( 2 \\)\nCorrect Answer: To get the next term you add the previous two terms together\n",
"role": "user"
},
{
"content": "Uses only the first two terms of a sequence to work out a term-to-term rule",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round integers to the nearest 10\nSubject: Written Division\nQuestion: What is \\( 5050 \\) rounded to the nearest \\( 10 \\) ?\nIncorrect Answer: \\( 5100 \\)\nCorrect Answer: \\( 5050 \\)\n",
"role": "user"
},
{
"content": "Rounds to the wrong degree of accuracy (rounds too much)",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round integers to the nearest 10\nSubject: Written Division\nQuestion: What is \\( 5050 \\) rounded to the nearest \\( 10 \\) ?\nIncorrect Answer: \\( 5000 \\)\nCorrect Answer: \\( 5050 \\)\n",
"role": "user"
},
{
"content": "Rounds to the wrong degree of accuracy (rounds too much)",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round integers to the nearest 10\nSubject: Written Division\nQuestion: What is \\( 5050 \\) rounded to the nearest \\( 10 \\) ?\nIncorrect Answer: \\( 5010 \\)\nCorrect Answer: \\( 5050 \\)\n",
"role": "user"
},
{
"content": "Believes that rounding must change the number",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve two-step linear equations, with the variable on one side, involving positive fractions\nSubject: Linear Equations\nQuestion: Solve the equation:\n\\(12 d-3=0\\)\nIncorrect Answer: \\( d=-\\frac{1}{4} \\)\nCorrect Answer: \\( d=\\frac{1}{4} \\)\n",
"role": "user"
},
{
"content": "When solving an equation, uses the same operation rather than the inverse.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve two-step linear equations, with the variable on one side, involving positive fractions\nSubject: Linear Equations\nQuestion: Solve the equation:\n\\(12 d-3=0\\)\nIncorrect Answer: \\( d=4 \\)\nCorrect Answer: \\( d=\\frac{1}{4} \\)\n",
"role": "user"
},
{
"content": "Swaps the dividend and divisor in order to get an integer answer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate time where speed and distance are in the appropriate units\nSubject: Real Life Graphs\nQuestion: This displacement-time graph shows the start of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 4 \\mathrm{~m} / \\mathrm{s} \\).\nWhat are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).\nThe marked point is one square in on the Time axis and at 40 on the Distance axis.]()\nIncorrect Answer: \\( (1,40) \\)\nCorrect Answer: \\( (5,40) \\)\n",
"role": "user"
},
{
"content": "Makes an assumption about the squares on a scale representing either 1 or 10",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate time where speed and distance are in the appropriate units\nSubject: Real Life Graphs\nQuestion: This displacement-time graph shows the start of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 4 \\mathrm{~m} / \\mathrm{s} \\).\nWhat are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).\nThe marked point is one square in on the Time axis and at 40 on the Distance axis.]()\nIncorrect Answer: \\( (10,40) \\)\nCorrect Answer: \\( (5,40) \\)\n",
"role": "user"
},
{
"content": "Makes an assumption about the squares on a scale representing either 1 or 10",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate time where speed and distance are in the appropriate units\nSubject: Real Life Graphs\nQuestion: This displacement-time graph shows the start of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 4 \\mathrm{~m} / \\mathrm{s} \\).\nWhat are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).\nThe marked point is one square in on the Time axis and at 40 on the Distance axis.]()\nIncorrect Answer: \\( (20,40) \\)\nCorrect Answer: \\( (5,40) \\)\n",
"role": "user"
},
{
"content": "Believes scales on graphs must match on both axes",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a trapezium where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: When calculating the area of this trapezium, what are the values of \\( a \\) and \\( b \\) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \\( =\\left(\\frac{a+b}{2}\\right) h \\)\nIncorrect Answer: \\( 7+7.5 \\)\nCorrect Answer: \\( 9+10 \\)\n",
"role": "user"
},
{
"content": "Uses slant heights instead of parallel sides to find area of a trapezium",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a trapezium where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: When calculating the area of this trapezium, what are the values of \\( a \\) and \\( b \\) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \\( =\\left(\\frac{a+b}{2}\\right) h \\)\nIncorrect Answer: \\( 7+6 \\)\nCorrect Answer: \\( 9+10 \\)\n",
"role": "user"
},
{
"content": "Uses slant heights instead of parallel sides to find area of a trapezium",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a trapezium where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: When calculating the area of this trapezium, what are the values of \\( a \\) and \\( b \\) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \\( =\\left(\\frac{a+b}{2}\\right) h \\)\nIncorrect Answer: \\( 6+7.5 \\)\nCorrect Answer: \\( 9+10 \\)\n",
"role": "user"
},
{
"content": "Uses slant heights instead of parallel sides to find area of a trapezium",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify fractions that simplify to a unit fraction\nSubject: Converting Mixed Number and Improper Fractions\nQuestion: Write the following fraction in its simplest form: \\( 6 \\frac{3}{18} \\)\nIncorrect Answer: \\( 3 \\frac{1}{2} \\)\nCorrect Answer: \\( 6 \\frac{1}{6} \\)\n",
"role": "user"
},
{
"content": "Simplifies integers when simplifying a mixed number",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify fractions that simplify to a unit fraction\nSubject: Converting Mixed Number and Improper Fractions\nQuestion: Write the following fraction in its simplest form: \\( 6 \\frac{3}{18} \\)\nIncorrect Answer: Cannot be simplified\nCorrect Answer: \\( 6 \\frac{1}{6} \\)\n",
"role": "user"
},
{
"content": "Does not understand how to simplify fractions",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable\nSubject: Simplifying Expressions by Collecting Like Terms\nQuestion: Simplify the following by collecting like terms.\n\\[\n5 s-6 s+12 s-11 s\n\\]\nIncorrect Answer: \\( 0 s \\)\nCorrect Answer: \\( 0 \\)\n",
"role": "user"
},
{
"content": "In algebra, thinks it's ok to write (for example) 0x rather than just 0",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: When finding the range of a data set, what is the first step?\nIncorrect Answer: Write the numbers in ascending order.\nCorrect Answer: Subtract the smallest number from the largest number.\n",
"role": "user"
},
{
"content": "Finds the median instead of the range",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: When finding the range of a data set, what is the first step?\nIncorrect Answer: Add all the numbers together.\nCorrect Answer: Subtract the smallest number from the largest number.\n",
"role": "user"
},
{
"content": "Finds the mean instead of the range",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: When finding the range of a data set, what is the first step?\nIncorrect Answer: Write the numbers in ascending or descending order.\nCorrect Answer: Subtract the smallest number from the largest number.\n",
"role": "user"
},
{
"content": "Finds the median instead of the range",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic equations using factorisation in the form (x + a)(x + b) \nSubject: Quadratic Equations\nQuestion: This is the final stage of Lucy's solution to a quadratic equation.\nWhat should replace the star?\n\\[\n(h+4)(h-3)=0\n\\] \\( h=\\bigstar \\) or \\( h=3 \\)\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: \\( -4 \\)\n",
"role": "user"
},
{
"content": "Believes the solutions of a quadratic equation are the absolute values of the constants in the factorised form",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic equations using factorisation in the form (x + a)(x + b) \nSubject: Quadratic Equations\nQuestion: This is the final stage of Lucy's solution to a quadratic equation.\nWhat should replace the star?\n\\[\n(h+4)(h-3)=0\n\\] \\( h=\\bigstar \\) or \\( h=3 \\)\nIncorrect Answer: \\( 0 \\)\nCorrect Answer: \\( -4 \\)\n",
"role": "user"
},
{
"content": "Believes all quadratic equations have a solution of 0",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic equations using factorisation in the form (x + a)(x + b) \nSubject: Quadratic Equations\nQuestion: The area of the trapezium on the right is \\( 40 \\mathrm{~cm}^{2} \\). ![A trapezium with the parallel sides a and b labelled with x+2 and x+4 and the perpendicular height x.]() Based on the information given, Adam writes this formula:\n\\(x^{2}+3 x=40\\)\n\nWhat are the two solutions to this equation?\nIncorrect Answer: \\( \\begin{array}{c}x=8 \\\\ \\text { and } \\\\ x=-5\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}x=-8 \\\\ \\text { and } \\\\ x=5\\end{array} \\)\n",
"role": "user"
},
{
"content": "Believes the solutions of a quadratic equation are the constants in the factorised form",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one\nSubject: Linear Sequences (nth term)\nQuestion: Without drawing any more terms, how many circles do you predict will be in the \\( 7 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()\nIncorrect Answer: \\( 42 \\)\nCorrect Answer: \\( 30 \\)\n",
"role": "user"
},
{
"content": "Has multiplied the value of the first term by the the term being asked",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one\nSubject: Linear Sequences (nth term)\nQuestion: Without drawing any more terms, how many circles do you predict will be in the \\( 7 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()\nIncorrect Answer: \\( 26 \\)\nCorrect Answer: \\( 30 \\)\n",
"role": "user"
},
{
"content": "When asked for a specific term in a sequence gives the term before",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one\nSubject: Linear Sequences (nth term)\nQuestion: Without drawing any more terms, how many circles do you predict will be in the \\( 7 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()\nIncorrect Answer: \\( 34 \\)\nCorrect Answer: \\( 30 \\)\n",
"role": "user"
},
{
"content": "When asked for a specific term in a sequence gives the term after",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the median as an average from an even numbered list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: What is the median of the following numbers?\n\\[\n3,5,6,18,18,-4\n\\]\nIncorrect Answer: \\( 12 \\)\nCorrect Answer: \\( 5.5 \\)\n",
"role": "user"
},
{
"content": "Believes you don't need to numerically order the data before calculating the median",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the median as an average from an even numbered list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: What is the median of the following numbers?\n\\[\n3,5,6,18,18,-4\n\\]\nIncorrect Answer: \\( 6 \\)\nCorrect Answer: \\( 5.5 \\)\n",
"role": "user"
},
{
"content": "When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the median as an average from an even numbered list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: What is the median of the following numbers?\n\\[\n3,5,6,18,18,-4\n\\]\nIncorrect Answer: \\( 18 \\)\nCorrect Answer: \\( 5.5 \\)\n",
"role": "user"
},
{
"content": "Finds the mode instead of the median",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Factorise a quadratic expression in the form x² + bx + c\nSubject: Factorising into a Double Bracket\nQuestion: When factorising \\( x^{2}+5 x+6 \\) we need two numbers that:\nIncorrect Answer: Add to give \\( 6 \\) and multiply to give \\( 5 \\)\nCorrect Answer: Add to give \\( 5 \\) and multiply to give \\( 6 \\)\n",
"role": "user"
},
{
"content": "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",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Factorise a quadratic expression in the form x² + bx + c\nSubject: Factorising into a Double Bracket\nQuestion: When factorising \\( x^{2}+5 x+6 \\) we need two numbers that:\nIncorrect Answer: Add to give \\( 6 x \\) and multiply to give \\( 5 \\)\nCorrect Answer: Add to give \\( 5 \\) and multiply to give \\( 6 \\)\n",
"role": "user"
},
{
"content": "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",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Factorise a quadratic expression in the form x² + bx + c\nSubject: Factorising into a Double Bracket\nQuestion: When factorising \\( x^{2}+5 x+6 \\) we need two numbers that:\nIncorrect Answer: Add to give \\( 5 x \\) and multiply to give \\( 6 \\)\nCorrect Answer: Add to give \\( 5 \\) and multiply to give \\( 6 \\)\n",
"role": "user"
},
{
"content": "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",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a right-angled triangle where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]()\nIncorrect Answer: \\( 88 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 44 \\mathrm{~cm}^{2} \\)\n",
"role": "user"
},
{
"content": "Does not divide by 2 when calculating the area of a triangle",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a right-angled triangle where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]()\nIncorrect Answer: \\( 71.5 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 44 \\mathrm{~cm}^{2} \\)\n",
"role": "user"
},
{
"content": "Has used slant height and base to find area of a triangle rather than perpendicular height and base",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a right-angled triangle where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]()\nIncorrect Answer: \\( 1144 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 44 \\mathrm{~cm}^{2} \\)\n",
"role": "user"
},
{
"content": "Multiplies all given dimensions when calculating an area",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Triple numbers\nSubject: Mental Multiplication and Division\nQuestion: If you triple \\( 8 \\) you get...\nIncorrect Answer: \\( 38 \\)\nCorrect Answer: \\( 24 \\)\n",
"role": "user"
},
{
"content": "When multiplying just writes the numbers next to each other",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Triple numbers\nSubject: Mental Multiplication and Division\nQuestion: If you triple \\( 8 \\) you get...\nIncorrect Answer: \\( 11 \\)\nCorrect Answer: \\( 24 \\)\n",
"role": "user"
},
{
"content": "Adds instead of multiples",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Triple numbers\nSubject: Mental Multiplication and Division\nQuestion: If you triple \\( 8 \\) you get...\nIncorrect Answer: \\( 888 \\)\nCorrect Answer: \\( 24 \\)\n",
"role": "user"
},
{
"content": "When asked to triple, writes the digit out three times",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide algebraic fractions involving non-linear expressions\nSubject: Multiplying and Dividing Algebraic Fractions\nQuestion: STEP \\( 2 \\)\nWhich of the options is a correct second step to express the following as a single fraction?\n\n\\(\n\\begin{aligned}\n& \\frac{x-1}{6} \\div \\frac{x^{2}-1}{9} \\\\\n= & \\frac{x-1}{6} \\times \\frac{9}{x^{2}-1}\n\\end{aligned}\n\\)\nIncorrect Answer: \\( \\frac{9 x-1}{6 x^{2}-1} \\)\nCorrect Answer: \\( \\frac{x-1}{6} \\times \\frac{9}{(x+1)(x-1)} \\)\n",
"role": "user"
},
{
"content": "Answers order of operations questions with brackets as if the brackets are not there",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide algebraic fractions involving non-linear expressions\nSubject: Multiplying and Dividing Algebraic Fractions\nQuestion: STEP \\( 2 \\)\nWhich of the options is a correct second step to express the following as a single fraction?\n\n\\(\n\\begin{aligned}\n& \\frac{x-1}{6} \\div \\frac{x^{2}-1}{9} \\\\\n= & \\frac{x-1}{6} \\times \\frac{9}{x^{2}-1}\n\\end{aligned}\n\\)\nIncorrect Answer: \\( \\frac{-1}{6} \\times \\frac{9}{x-1} \\)\nCorrect Answer: \\( \\frac{x-1}{6} \\times \\frac{9}{(x+1)(x-1)} \\)\n",
"role": "user"
},
{
"content": "Incorrectly cancels what they believe is a factor in algebraic fractions",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide algebraic fractions involving non-linear expressions\nSubject: Multiplying and Dividing Algebraic Fractions\nQuestion: STEP \\( 2 \\)\nWhich of the options is a correct second step to express the following as a single fraction?\n\n\\(\n\\begin{aligned}\n& \\frac{x-1}{6} \\div \\frac{x^{2}-1}{9} \\\\\n= & \\frac{x-1}{6} \\times \\frac{9}{x^{2}-1}\n\\end{aligned}\n\\)\nIncorrect Answer: \\( \\frac{x-1}{6} \\times \\frac{9}{(x-1)(x-1)} \\)\nCorrect Answer: \\( \\frac{x-1}{6} \\times \\frac{9}{(x+1)(x-1)} \\)\n",
"role": "user"
},
{
"content": "Factorises difference of two squares with the same sign in both brackets",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read an integer on a scale where the required measurement is marked by a dash between two numbers\nSubject: Ordering Negative Numbers\nQuestion: What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-10\" next to the bottom dash and \"2\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the middle dash. ]()\nIncorrect Answer: \\( -7 \\)\nCorrect Answer: \\( -4 \\)\n",
"role": "user"
},
{
"content": "When reading integers on a number line, assumes each dash is 1",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read an integer on a scale where the required measurement is marked by a dash between two numbers\nSubject: Ordering Negative Numbers\nQuestion: What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-10\" next to the bottom dash and \"2\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the middle dash. ]()\nIncorrect Answer: \\( -1 \\)\nCorrect Answer: \\( -4 \\)\n",
"role": "user"
},
{
"content": "When reading integers on a number line, assumes each dash is 1",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read an integer on a scale where the required measurement is marked by a dash between two numbers\nSubject: Ordering Negative Numbers\nQuestion: What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-10\" next to the bottom dash and \"2\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the middle dash. ]()\nIncorrect Answer: \\( 8 \\)\nCorrect Answer: \\( -4 \\)\n",
"role": "user"
},
{
"content": "Counts on in the wrong direction on a number line",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Interpret a pictogram involving full symbols\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: The pictogram shows how many people came to watch a netball match.\nWhat is the mean number of people at each game? ![A pictogram with a key showing a smiley face represents 12 people. Game 1 has 4 smiley faces, Game 2 has 2 smiley faces, Game 3 has 3 smiley faces and Game 4 has 1 smiley face.]()\nIncorrect Answer: \\( 12 \\)\nCorrect Answer: \\( 30 \\)\n",
"role": "user"
},
{
"content": "Does not know you can find the mean from a pictogram",
"role": "assistant"
}
] |