messages
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| misconception
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[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise the equations of horizontal lines from a diagram\nSubject: Horizontal and Vertical Lines\nQuestion: What is the equation of this line? ![A graph of a horizontal line going through 3 on the y axis. ]()\nIncorrect Answer: \\( x=3 \\)\nCorrect Answer: \\( y=3 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks x = ? is a horizontal line through ? |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise the equations of horizontal lines from a diagram\nSubject: Horizontal and Vertical Lines\nQuestion: What is the equation of this line? ![A graph of a horizontal line going through 3 on the y axis. ]()\nIncorrect Answer: \\( x=3 y \\)\nCorrect Answer: \\( y=3 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes the equation of a horizontal line is in the form x = ay, where a is the y intercept |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Generate a descending integer linear sequence from the nth term rule\nSubject: Linear Sequences (nth term)\nQuestion: What is the first term of the sequence given by this rule:\n\\[\n2-7 n\n\\]\nIncorrect Answer: \\( 1 \\)\nCorrect Answer: \\( -5 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks the first term of a sequence must be 1 |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Generate a descending integer linear sequence from the nth term rule\nSubject: Linear Sequences (nth term)\nQuestion: What is the first term of the sequence given by this rule:\n\\[\n2-7 n\n\\]\nIncorrect Answer: \\( -7 \\)\nCorrect Answer: \\( -5 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n. |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Add proper fractions with the same denominator\nSubject: Adding and Subtracting Fractions\nQuestion: Work out:\n\\(\n\\frac{4}{11}+\\frac{7}{11}\n\\)\nWrite your answer in its simplest form.\nIncorrect Answer: \\( \\frac{11}{22} \\)\nCorrect Answer: \\( 1 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When adding fractions, adds the numerators and denominators |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Add proper fractions with the same denominator\nSubject: Adding and Subtracting Fractions\nQuestion: Work out:\n\\(\n\\frac{4}{11}+\\frac{7}{11}\n\\)\nWrite your answer in its simplest form.\nIncorrect Answer: \\( \\frac{1}{2} \\)\nCorrect Answer: \\( 1 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When adding fractions, adds the numerators and denominators |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Add proper fractions with the same denominator\nSubject: Adding and Subtracting Fractions\nQuestion: Work out:\n\\(\n\\frac{4}{11}+\\frac{7}{11}\n\\)\nWrite your answer in its simplest form.\nIncorrect Answer: \\( \\frac{11}{11} \\)\nCorrect Answer: \\( 1 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Forgot to simplify the fraction |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given a sketch of a quadratic graph, f(x), write down the solutions to f(x) = a\nSubject: Quadratic Equations\nQuestion: According to the graph, what is the approximate solution to\n\\(x^{2}+4 x-1=-6\\) ![A set of axes with the quadratic graph y=x^2+4x-1 drawn on.]()\nIncorrect Answer: \\( x=-4.25, \\quad x=0.25 \\)\nCorrect Answer: No real solutions\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Solves for y=0 instead of given y-value when reading from a quadratic graph |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given a sketch of a quadratic graph, f(x), write down the solutions to f(x) = a\nSubject: Quadratic Equations\nQuestion: According to the graph, what is the approximate solution to\n\\(x^{2}+4 x-1=-6\\) ![A set of axes with the quadratic graph y=x^2+4x-1 drawn on.]()\nIncorrect Answer: \\( x=-1 \\)\nCorrect Answer: No real solutions\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Finds the y intercept when asked to read the solution to a quadratic equation from a graph |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the volume of other prisms when the dimensions are given in the same units\nSubject: Volume of Prisms\nQuestion: ![A triangular based prism]() Tom likes to remember:\n\nVolume of a prism = Area of cross section \\( X \\) depth\n\nIn this shape, what length is the \"depth\"?\nIncorrect Answer: \\( 5 \\mathrm{~mm} \\)\nCorrect Answer: \\( 15 \\mathrm{~mm} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks depth always goes front to back in a diagram of a 3D shape |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Generate a descending integer linear sequence from the nth term rule\nSubject: Linear Sequences (nth term)\nQuestion: What is the first term of the sequence given by this rule:\n\\[\n1-5 n\n\\]\nIncorrect Answer: \\( 1 \\)\nCorrect Answer: \\( -4 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks the first term of a sequence must be 1 |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Generate a descending integer linear sequence from the nth term rule\nSubject: Linear Sequences (nth term)\nQuestion: What is the first term of the sequence given by this rule:\n\\[\n1-5 n\n\\]\nIncorrect Answer: \\( -5 \\)\nCorrect Answer: \\( -4 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n. |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Find missing angles in a non-special quadrilateral\nSubject: Angles in Polygons\nQuestion: What is the size of angle \\( p \\) in this quadrilateral? ![Not drawn to scale]()\nIncorrect Answer: \\( 120^{\\circ} \\)\nCorrect Answer: Not enough information to work it out\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Assumes that opposite angles are equal in a quadrilateral |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Find missing angles in a non-special quadrilateral\nSubject: Angles in Polygons\nQuestion: What is the size of angle \\( p \\) in this quadrilateral? ![Not drawn to scale]()\nIncorrect Answer: \\( 50^{\\circ} \\)\nCorrect Answer: Not enough information to work it out\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know what dashes on the sides of shapes mean |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Find missing angles in a non-special quadrilateral\nSubject: Angles in Polygons\nQuestion: What is the size of angle \\( p \\) in this quadrilateral? ![Not drawn to scale]()\nIncorrect Answer: \\( 70^{\\circ} \\)\nCorrect Answer: Not enough information to work it out\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know what dashes on the sides of shapes mean |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Rearrange a quadratic equation so that it is in the correct form to be factorised\nSubject: Quadratic Equations\nQuestion: What would be the most useful first step if we wanted to solve the following quadratic equation? \\( x^{2}+7 x=8 \\)\nIncorrect Answer: Divide by \\( x \\)\nCorrect Answer: Subtract \\( 8 \\) from both sides of the equation\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not realise a quadratic must be in the form ax^2+bx+c=0 to be factorised |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Rearrange a quadratic equation so that it is in the correct form to be factorised\nSubject: Quadratic Equations\nQuestion: What would be the most useful first step if we wanted to solve the following quadratic equation? \\( x^{2}+7 x=8 \\)\nIncorrect Answer: Square root both sides of the equation\nCorrect Answer: Subtract \\( 8 \\) from both sides of the equation\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not realise a quadratic must be in the form ax^2+bx+c=0 to be factorised |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Rearrange a quadratic equation so that it is in the correct form to be factorised\nSubject: Quadratic Equations\nQuestion: What would be the most useful first step if we wanted to solve the following quadratic equation? \\( x^{2}+7 x=8 \\)\nIncorrect Answer: Subtract \\( 7 x \\) from both sides of the equation\nCorrect Answer: Subtract \\( 8 \\) from both sides of the equation\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not realise a quadratic must be in the form ax^2+bx+c=0 to be factorised |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Reduce a ratio involving two numbers to its simplest form\nSubject: Writing Ratios\nQuestion: Write the following ratio in its simplest form so both sides of the ratio are integers:\n\\(\n\\frac{1}{4}: \\frac{1}{2}\n\\)\nIncorrect Answer: \\( 2: 4 \\)\nCorrect Answer: \\( 1: 2 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not fully simplify ratio |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given the sketch of a curve in the form (x + a)², work out its factorised form\nSubject: Sketching from Factorised Form\nQuestion: What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]()\nIncorrect Answer: \\( y=(x+1)^{2} \\)\nCorrect Answer: \\( y=(x-1)^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Forgets to swap the sign of roots when placing into brackets |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given the sketch of a curve in the form (x + a)², work out its factorised form\nSubject: Sketching from Factorised Form\nQuestion: What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]()\nIncorrect Answer: \\( y=x^{2}-1 \\)\nCorrect Answer: \\( y=(x-1)^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes the graph of x squared + c has the turning point of (-c, 0) |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given the sketch of a curve in the form (x + a)², work out its factorised form\nSubject: Sketching from Factorised Form\nQuestion: What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]()\nIncorrect Answer: \\( y=x^{2}+1 \\)\nCorrect Answer: \\( y=(x-1)^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes the graph of x squared + c has the turning point of (c, 0) |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise when a descending sequence is quadratic\nSubject: Quadratic Sequences\nQuestion: Tom and Katie are discussing quadratic sequences.\n\nTom says this is a quadratic sequence: \\( 24,15,8,3,0 \\ldots \\)\n\nKatie says this is a quadratic sequence: \\( 124,63,26,7,3,0, \\ldots \\)\n\nWho is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Only Tom\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not understand the term quadratic |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise when a descending sequence is quadratic\nSubject: Quadratic Sequences\nQuestion: Tom and Katie are discussing quadratic sequences.\n\nTom says this is a quadratic sequence: \\( 24,15,8,3,0 \\ldots \\)\n\nKatie says this is a quadratic sequence: \\( 124,63,26,7,3,0, \\ldots \\)\n\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Tom\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not understand the term quadratic |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise when a descending sequence is quadratic\nSubject: Quadratic Sequences\nQuestion: Tom and Katie are discussing quadratic sequences.\n\nTom says this is a quadratic sequence: \\( 24,15,8,3,0 \\ldots \\)\n\nKatie says this is a quadratic sequence: \\( 124,63,26,7,3,0, \\ldots \\)\n\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only Tom\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks a decreasing sequence cannot be quadratic |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given information about the relationship between two parts (e.g. one part is worth 5 more than another), work out other parts\nSubject: Sharing in a Ratio\nQuestion: Percy, Quentin and Robbie share gold coins in the ratio of\n\\[\n3: 7: 8\n\\]\nPercy gets \\( 36 \\) fewer coins than Quentin.\nHow many gold coins did Robbie get?\nIncorrect Answer: \\( 96 \\)\nCorrect Answer: \\( 72 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | In ratio question where the difference between the sides is given, uses that as the total for one side instead |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given information about the relationship between two parts (e.g. one part is worth 5 more than another), work out other parts\nSubject: Sharing in a Ratio\nQuestion: Percy, Quentin and Robbie share gold coins in the ratio of\n\\[\n3: 7: 8\n\\]\nPercy gets \\( 36 \\) fewer coins than Quentin.\nHow many gold coins did Robbie get?\nIncorrect Answer: \\( 12 \\)\nCorrect Answer: \\( 72 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | In ratio question where the difference between the sides is given, uses that as the total |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given information about the relationship between two parts (e.g. one part is worth 5 more than another), work out other parts\nSubject: Sharing in a Ratio\nQuestion: Percy, Quentin and Robbie share gold coins in the ratio of\n\\[\n3: 7: 8\n\\]\nPercy gets \\( 36 \\) fewer coins than Quentin.\nHow many gold coins did Robbie get?\nIncorrect Answer: \\( 63 \\)\nCorrect Answer: \\( 72 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Mixes up sides of a ratio |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Solve linear equations with the variable appearing on both sides, with all positive integers\nSubject: Linear Equations\nQuestion: Tom and Katie are arguing about a first step to solve this equation:\n\\(4 v+1=9 v-3\\)\n\nTom says you can write: \\( 5 v+1=-3 \\)\n\nKatie says you can write: \\( 4 v+4=9 v \\)\n\nWho is correct?\nIncorrect Answer: Only\nTom\nCorrect Answer: Only Katie\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Subtracts the smallest digit from the largest digit |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Solve linear equations with the variable appearing on both sides, with all positive integers\nSubject: Linear Equations\nQuestion: Tom and Katie are arguing about a first step to solve this equation:\n\\(4 v+1=9 v-3\\)\n\nTom says you can write: \\( 5 v+1=-3 \\)\n\nKatie says you can write: \\( 4 v+4=9 v \\)\n\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Katie\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Subtracts the smallest digit from the largest digit |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise the vertically opposite angles relationship\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]()\nIncorrect Answer: Alternate angles\nCorrect Answer: Vertically opposite angles\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Confuses alternate and opposite angles |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise the vertically opposite angles relationship\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]()\nIncorrect Answer: Corresponding angles\nCorrect Answer: Vertically opposite angles\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Confuses corresponding and vertically opposite angles |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise the vertically opposite angles relationship\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]()\nIncorrect Answer: Angles on a straight line\nCorrect Answer: Vertically opposite angles\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Confuses vertically opposite angles with angles on a straight line |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given a sketch of a linear graph solve f(x) = n\nSubject: Graphical Solution of Simultaneous Equations\nQuestion: This is a graph of\n\\(y=0.4 x-3\\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve\n\\(0.4 x-3=-1\\)\nIncorrect Answer: \\( x=-3.3 \\)\nCorrect Answer: \\( x=5 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Mixes up the value of two terms when substituting |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given a sketch of a linear graph solve f(x) = n\nSubject: Graphical Solution of Simultaneous Equations\nQuestion: This is a graph of\n\\(y=0.4 x-3\\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve\n\\(0.4 x-3=-1\\)\nIncorrect Answer: \\( x=7.5 \\)\nCorrect Answer: \\( x=5 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes the solution to mx + c = a is the x intercept of y = mx +c |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given a sketch of a linear graph solve f(x) = n\nSubject: Graphical Solution of Simultaneous Equations\nQuestion: This is a graph of\n\\(y=0.4 x-3\\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve\n\\(0.4 x-3=-1\\)\nIncorrect Answer: \\( x=-1 \\)\nCorrect Answer: \\( x=5 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes the solution of mx + c = a is x =a |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape\nSubject: Volume and Capacity Units\nQuestion: A regular pentagon has a total perimeter of \\( 17 \\mathrm{~cm} \\).\nWhat is the length of each of its sides?\nIncorrect Answer: \\( 85 \\mathrm{~cm} \\)\nCorrect Answer: \\( 3.4 \\mathrm{~cm} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When given the perimeter of a regular polygon, multiplies instead of divides to find each side length |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape\nSubject: Volume and Capacity Units\nQuestion: A regular pentagon has a total perimeter of \\( 17 \\mathrm{~cm} \\).\nWhat is the length of each of its sides?\nIncorrect Answer: \\( 12 \\mathrm{~cm} \\)\nCorrect Answer: \\( 3.4 \\mathrm{~cm} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When given the perimeter of a regular polygon, subtracts instead of divides to find each side length |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape\nSubject: Volume and Capacity Units\nQuestion: A regular pentagon has a total perimeter of \\( 17 \\mathrm{~cm} \\).\nWhat is the length of each of its sides?\nIncorrect Answer: Not enough information\nCorrect Answer: \\( 3.4 \\mathrm{~cm} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know the meaning of the word regular |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Interpret a pie chart\nSubject: Pie Chart\nQuestion: This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue?\nIncorrect Answer: \\( \\frac{1}{4} \\)\nCorrect Answer: \\( \\frac{3}{4} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Reads the complement of what is required from a pie chart |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Interpret a pie chart\nSubject: Pie Chart\nQuestion: This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue?\nIncorrect Answer: \\( 75 \\)\nCorrect Answer: \\( \\frac{3}{4} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Finds a percentage when asked for a fraction |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Interpret a pie chart\nSubject: Pie Chart\nQuestion: This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue?\nIncorrect Answer: Impossible to say\nCorrect Answer: \\( \\frac{3}{4} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know the meaning of square sign for right angle |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Express one quantity as a percentage of another mentally\nSubject: Percentages of an Amount\nQuestion: What is \\( 8 \\) out of \\( 40 \\) as a percentage?\nIncorrect Answer: \\( 8.4 \\% \\)\nCorrect Answer: \\( 20 \\% \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Converts a fraction to a percentage by writing the numerator followed by the denominator |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Express one quantity as a percentage of another mentally\nSubject: Percentages of an Amount\nQuestion: What is \\( 8 \\) out of \\( 40 \\) as a percentage?\nIncorrect Answer: \\( 16 \\% \\)\nCorrect Answer: \\( 20 \\% \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks they double the numerator to turn a fraction into a percentage |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units\nSubject: Missing Lengths\nQuestion: What is value of \\( p \\) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]()\nIncorrect Answer: \\( 6 \\mathrm{~cm} \\)\nCorrect Answer: \\( 5 \\mathrm{~cm} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Makes an assumption about line segments being equal within a shape |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units\nSubject: Missing Lengths\nQuestion: What is value of \\( p \\) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]()\nIncorrect Answer: \\( 7 \\mathrm{~cm} \\)\nCorrect Answer: \\( 5 \\mathrm{~cm} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Makes an assumption about line segments being equal within a shape |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units\nSubject: Missing Lengths\nQuestion: What is value of \\( p \\) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]()\nIncorrect Answer: Not enough information\nCorrect Answer: \\( 5 \\mathrm{~cm} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know that we can use the conservation of perimeter to find missing lengths |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a parallelogram where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]()\nIncorrect Answer: \\( 120 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 30 \\mathrm{~cm}^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When finding the area of a parallelogram does not understand which lengths to use |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a parallelogram where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]()\nIncorrect Answer: \\( 40 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 30 \\mathrm{~cm}^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Has used slant height and base to find area of a parallelogram rather than perpendicular height and base |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a parallelogram where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]()\nIncorrect Answer: \\( 15 \\mathrm{~cm}^{2} \\)\nCorrect Answer: \\( 30 \\mathrm{~cm}^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Has found the area of a triangle rather than an area of a parallelogram |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic equations using balancing\nSubject: Quadratic Equations\nQuestion: A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d-6)^{2}-16=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d-6)^{2}=16\n\\)\nIncorrect Answer: \\( d^{2}=22 \\)\nCorrect Answer: \\( d-6= \\pm 4 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes you can subtract from inside brackets without expanding when solving an equation |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic equations using balancing\nSubject: Quadratic Equations\nQuestion: A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d-6)^{2}-16=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d-6)^{2}=16\n\\)\nIncorrect Answer: \\( d-6=4 \\)\nCorrect Answer: \\( d-6= \\pm 4 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Only considers the positive solution when calculating a square root |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Find missing angles using vertically opposite angles\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: What is the size of angle \\( p \\) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]()\nIncorrect Answer: \\( 53^{\\circ} \\)\nCorrect Answer: \\( 42^{\\circ} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Mistakes lines as parallel |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Find missing angles using vertically opposite angles\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: What is the size of angle \\( p \\) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]()\nIncorrect Answer: \\( 138^{\\circ} \\)\nCorrect Answer: \\( 42^{\\circ} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Student thinks that any two angles along a straight line are equal |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Find missing angles using vertically opposite angles\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: What is the size of angle \\( p \\) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]()\nIncorrect Answer: Not enough information\nCorrect Answer: \\( 42^{\\circ} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know that vertically opposite angles are equal |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the sector angle on a pie chart for a given group\nSubject: Pie Chart\nQuestion: A class of students were surveyed about how many siblings they have.\n\nA selection of results are shown in the table. \\begin{tabular}{|c|c|c|}\n\\hline Number of siblings & Frequency & Angle on a pie chart \\\\\n\\hline 0 & \\( 7 \\) & \\( \\) \\\\\n\\hline 1 & \\( \\) & \\( 144 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 4 \\) & \\( \\bigstar \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 30 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\nWhat should replace the star?\nIncorrect Answer: \\( 40^{\\circ} \\)\nCorrect Answer: \\( 48^{\\circ} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes that the angle on a pie chart is the frequency multiplied by 10 |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the sector angle on a pie chart for a given group\nSubject: Pie Chart\nQuestion: A class of students were surveyed about how many siblings they have.\n\nA selection of results are shown in the table. \\begin{tabular}{|c|c|c|}\n\\hline Number of siblings & Frequency & Angle on a pie chart \\\\\n\\hline 0 & \\( 7 \\) & \\( \\) \\\\\n\\hline 1 & \\( \\) & \\( 144 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 4 \\) & \\( \\bigstar \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 30 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\nWhat should replace the star?\nIncorrect Answer: \\( 120^{\\circ} \\)\nCorrect Answer: \\( 48^{\\circ} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes you find the angle for a pie chart sector by doing its frequency multiplied by total frequency |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Divide proper fractions in the form: Integer ÷ Fraction\nSubject: Dividing Fractions\nQuestion: How many times does \\( \\frac{3}{5} \\) go into \\( 15 \\) ?\nIncorrect Answer: \\( \\frac{45}{75} \\)\nCorrect Answer: \\( 25 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When dividing an integer by a fraction, thinks they multiply numerator and denominator by the integer |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Divide proper fractions in the form: Integer ÷ Fraction\nSubject: Dividing Fractions\nQuestion: How many times does \\( \\frac{3}{5} \\) go into \\( 15 \\) ?\nIncorrect Answer: \\( 75 \\)\nCorrect Answer: \\( 25 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When dividing by a non unit fraction, thinks you multiply by the reciprocal of the corresponding unit fraction rather than the fraction given. |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Divide proper fractions in the form: Integer ÷ Fraction\nSubject: Dividing Fractions\nQuestion: How many times does \\( \\frac{3}{5} \\) go into \\( 15 \\) ?\nIncorrect Answer: \\( 9 \\)\nCorrect Answer: \\( 25 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | when dividing a fraction by an integer, multiplies the numerator by the integer |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Carry out multiplication problems involving one negative integer\nSubject: Expanding Double Brackets\nQuestion: John is expanding these two brackets.\n\nWhat should he get when he multiplies the two terms indicated by the arrows? ![The two brackets are (x+5)(x-3). The arrows are pointing at the +5 in the first bracket and the -3 in the second bracket.]()\nIncorrect Answer: \\( +2 \\)\nCorrect Answer: \\( -15 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Adds instead of multiplying when expanding bracket |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Carry out multiplication problems involving one negative integer\nSubject: Expanding Double Brackets\nQuestion: John is expanding these two brackets.\n\nWhat should he get when he multiplies the two terms indicated by the arrows? ![The two brackets are (x+5)(x-3). The arrows are pointing at the +5 in the first bracket and the -3 in the second bracket.]()\nIncorrect Answer: \\( +15 \\)\nCorrect Answer: \\( -15 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Ignores negative sign when expanding bracket |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis\nSubject: Sketching from Factorised Form\nQuestion: Tom and Katie are discussing quadratic graphs.\n\nTom says a quadratic expression that cannot be factorised will not intercept the \\( x \\) axis.\n\nKatie says a graph of a quadratic that does not intercept the \\( x \\) axis cannot be factorised.\nWho is correct?\nIncorrect Answer: Only Tom\nCorrect Answer: Only Katie\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When solving simultaneous equations graphically, they think the solutions are the x-intercepts |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis\nSubject: Sketching from Factorised Form\nQuestion: Tom and Katie are discussing quadratic graphs.\n\nTom says a quadratic expression that cannot be factorised will not intercept the \\( x \\) axis.\n\nKatie says a graph of a quadratic that does not intercept the \\( x \\) axis cannot be factorised.\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Katie\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When solving simultaneous equations graphically, they think the solutions are the x-intercepts |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Read values off a real life graph\nSubject: Direct Proportion\nQuestion: This is a conversion graph between kilograms and pounds.\n\nWhich of the following is the best estimate for the number of kilograms equivalent to \\( 20 \\) pounds? ![A graph on gridded paper with pounds (lb) on the y axis from 0 to 80 and kilograms (kg) on the x axis from 0 to 80. Both axis are labelled in increments of 20, with each increment split by gridlines into another 4 squares. A straight line goes from the origin and sloped upwards going through (25, 55) (not labelled - just a coordinate that it goes through) ]()\nIncorrect Answer: \\( 44 \\) kilograms\nCorrect Answer: \\( 9 \\) kilograms\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When reading value from graph, reads from the wrong axes. |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Understand the terms equilateral and regular, and recognise the notation for regular polygons\nSubject: Angles in Polygons\nQuestion: Which quadrilateral below is a regular polygon?\nIncorrect Answer: ![Trapezium]()\nCorrect Answer: ![Square]()\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know the meaning of the word regular |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Understand the terms equilateral and regular, and recognise the notation for regular polygons\nSubject: Angles in Polygons\nQuestion: Which quadrilateral below is a regular polygon?\nIncorrect Answer: ![Rhombus]()\nCorrect Answer: ![Square]()\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know the meaning of the word regular |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Understand the terms equilateral and regular, and recognise the notation for regular polygons\nSubject: Angles in Polygons\nQuestion: Which quadrilateral below is a regular polygon?\nIncorrect Answer: ![Rectangle]()\nCorrect Answer: ![Square]()\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not know the meaning of the word regular |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Express a division as a fraction\nSubject: Mental Multiplication and Division\nQuestion: Which calculation is equivalent to the fraction \\( \\frac{3}{4} \\) ?\nIncorrect Answer: \\( 3-4 \\)\nCorrect Answer: \\( 3 \\div 4 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks the fraction bar means subtract rather than divide |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Express a division as a fraction\nSubject: Mental Multiplication and Division\nQuestion: Which calculation is equivalent to the fraction \\( \\frac{3}{4} \\) ?\nIncorrect Answer: \\( 4-3 \\)\nCorrect Answer: \\( 3 \\div 4 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks the fraction bar means subtract rather than divide |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Express a division as a fraction\nSubject: Mental Multiplication and Division\nQuestion: Which calculation is equivalent to the fraction \\( \\frac{3}{4} \\) ?\nIncorrect Answer: \\( 4 \\div 3 \\)\nCorrect Answer: \\( 3 \\div 4 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes that a fraction means dividing the denominator by the numerator |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression\nSubject: Expanding Single Brackets\nQuestion: Expand and simplify:\n\\[\n4(2 x+1)-(5 x-9)\n\\]\nIncorrect Answer: \\( 3 x-5 \\)\nCorrect Answer: \\( 3 x+13 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not realise that subtracting a negative is the same as adding it's additive inverse |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression\nSubject: Expanding Single Brackets\nQuestion: Expand and simplify:\n\\[\n4(2 x+1)-(5 x-9)\n\\]\nIncorrect Answer: \\( 13 x-5 \\)\nCorrect Answer: \\( 3 x+13 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Adds instead of subtracts |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Expand double brackets with an extra variable outside\nSubject: Expanding Double Brackets\nQuestion: When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+5)(m-5) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\)\nIncorrect Answer: \\( \\triangle=+25 \\)\nCorrect Answer: \\( \\triangle=-25 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes multiplying a positive by a negative gives a positive answer |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Expand double brackets with an extra variable outside\nSubject: Expanding Double Brackets\nQuestion: When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+5)(m-5) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\)\nIncorrect Answer: \\( \\triangle=+5 \\)\nCorrect Answer: \\( \\triangle=-25 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When multiplying out 2 or more brackets, does not multiply all the combinations of terms |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Expand double brackets with an extra variable outside\nSubject: Expanding Double Brackets\nQuestion: When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+5)(m-5) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\)\nIncorrect Answer: \\(\n\\triangle=+0\n\\)\n(no \\( m \\) term)\nCorrect Answer: \\( \\triangle=-25 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Write a given translation in vector notation\nSubject: Translation and Vectors\nQuestion: Three left and five down in vector notation is... \\( \\left(\\begin{array}{c}\\triangle \\\\ \\bigcirc\\end{array}\\right) \\) What should replace the \\( \\triangle \\) ?\nIncorrect Answer: \\( 3 \\)\nCorrect Answer: \\( -3 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks a negative x value in a column vector means to move right rather than left |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Write a given translation in vector notation\nSubject: Translation and Vectors\nQuestion: Three left and five down in vector notation is... \\( \\left(\\begin{array}{c}\\triangle \\\\ \\bigcirc\\end{array}\\right) \\) What should replace the \\( \\triangle \\) ?\nIncorrect Answer: \\( -5 \\)\nCorrect Answer: \\( -3 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Find missing numbers in a fraction multiplication\nSubject: Multiplying Fractions\nQuestion: \\( \\frac{3}{5} \\times ?=\\frac{1}{2} \\)\nIncorrect Answer: \\( \\frac{3}{10} \\)\nCorrect Answer: \\( \\frac{5}{6} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Find missing numbers in a fraction multiplication\nSubject: Multiplying Fractions\nQuestion: \\( \\frac{3}{5} \\times ?=\\frac{1}{2} \\)\nIncorrect Answer: There are no values that make this calculation work\nCorrect Answer: \\( \\frac{5}{6} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not realise that division can be used to find the missing value in a multiplication problem |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given information about one part, work out other parts\nSubject: Sharing in a Ratio\nQuestion: To make pink paint, you mix red paint with white paint in the ratio \\( 3: 4 \\).\nWhat should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]()\nIncorrect Answer: \\( 1201 \\ \\mathrm{ml} \\)\nCorrect Answer: \\( 1600 \\ \\mathrm{ml} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks a difference of one part in a ratio means the quantities will differ by one unit |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given information about one part, work out other parts\nSubject: Sharing in a Ratio\nQuestion: To make pink paint, you mix red paint with white paint in the ratio \\( 3: 4 \\).\nWhat should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]()\nIncorrect Answer: \\( 900 \\ \\mathrm{ml} \\)\nCorrect Answer: \\( 1600 \\ \\mathrm{ml} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Mixes up sides of a ratio |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Given information about one part, work out other parts\nSubject: Sharing in a Ratio\nQuestion: To make pink paint, you mix red paint with white paint in the ratio \\( 3: 4 \\).\nWhat should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]()\nIncorrect Answer: \\( 4800 \\ \\mathrm{ml} \\)\nCorrect Answer: \\( 1600 \\ \\mathrm{ml} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | In ratio question where one side of ratio is given, uses that as one part in ratio without dividing |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a trapezium where the dimensions are given in different units\nSubject: Area of Simple Shapes\nQuestion: What should replace the star to calculate the area of this trapezium?\n Area \\( =\\frac{90+40}{2} \\times \\) \\(\\color{gold}\\bigstar\\)\n ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]()\nIncorrect Answer: \\( 5 \\)\nCorrect Answer: \\( 50 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not convert measurements to have the same units before calculating area or volume |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a trapezium where the dimensions are given in different units\nSubject: Area of Simple Shapes\nQuestion: What should replace the star to calculate the area of this trapezium?\n Area \\( =\\frac{90+40}{2} \\times \\) \\(\\color{gold}\\bigstar\\)\n ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]()\nIncorrect Answer: \\( 6 \\)\nCorrect Answer: \\( 50 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Uses slant height instead of perpendicular height to find area of a trapezium |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of a trapezium where the dimensions are given in different units\nSubject: Area of Simple Shapes\nQuestion: What should replace the star to calculate the area of this trapezium?\n Area \\( =\\frac{90+40}{2} \\times \\) \\(\\color{gold}\\bigstar\\)\n ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]()\nIncorrect Answer: \\( 60 \\)\nCorrect Answer: \\( 50 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Uses slant height instead of perpendicular height to find area of a trapezium |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Carry out division problems involving one negative integer\nSubject: Multiplying and Dividing Negative Numbers\nQuestion: Tom and Katie are trying to write different calculations for the diagram on the left.\nTom writes: \\( -3 \\times(-8)=-24 \\)\nKatie writes: \\( \\frac{(-24)}{-3}=-8 \\)\nWho is correct? ![A diagram showing an arrow to the left, marked with a value of -24. Underneath this arrow there is a smaller arrow, still pointing to the left, that is a third of the length of the larger arrow]()\nIncorrect Answer: Only\nTom\nCorrect Answer: Neither is correct\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes multiplying two negatives gives a negative answer |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Carry out division problems involving one negative integer\nSubject: Multiplying and Dividing Negative Numbers\nQuestion: Tom and Katie are trying to write different calculations for the diagram on the left.\nTom writes: \\( -3 \\times(-8)=-24 \\)\nKatie writes: \\( \\frac{(-24)}{-3}=-8 \\)\nWho is correct? ![A diagram showing an arrow to the left, marked with a value of -24. Underneath this arrow there is a smaller arrow, still pointing to the left, that is a third of the length of the larger arrow]()\nIncorrect Answer: Only\nKatie\nCorrect Answer: Neither is correct\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes dividing a negative by a negative gives a negative answer |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Perform calculations with areas when given in different units\nSubject: Area Units\nQuestion: Square \\( \\mathrm{P} \\) has an area of \\( 4 \\mathrm{~cm}^{2} \\)\nSquare \\( Q \\) has an area of \\( 4 \\mathrm{~mm}^{2} \\)\nWhat is the total area of squares \\( P \\) and \\( Q \\) in \\( \\mathrm{mm}^{2} \\) ?\nIncorrect Answer: \\( 8 \\mathrm{~mm}^{2} \\)\nCorrect Answer: \\( 404 \\mathrm{~mm}^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not convert measurements to have the same units before calculating area or volume |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Perform calculations with areas when given in different units\nSubject: Area Units\nQuestion: Square \\( \\mathrm{P} \\) has an area of \\( 4 \\mathrm{~cm}^{2} \\)\nSquare \\( Q \\) has an area of \\( 4 \\mathrm{~mm}^{2} \\)\nWhat is the total area of squares \\( P \\) and \\( Q \\) in \\( \\mathrm{mm}^{2} \\) ?\nIncorrect Answer: \\( 44 \\mathrm{~mm}^{2} \\)\nCorrect Answer: \\( 404 \\mathrm{~mm}^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Does not square the conversion factor when converting squared units |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Perform calculations with areas when given in different units\nSubject: Area Units\nQuestion: Square \\( \\mathrm{P} \\) has an area of \\( 4 \\mathrm{~cm}^{2} \\)\nSquare \\( Q \\) has an area of \\( 4 \\mathrm{~mm}^{2} \\)\nWhat is the total area of squares \\( P \\) and \\( Q \\) in \\( \\mathrm{mm}^{2} \\) ?\nIncorrect Answer: \\( 40004 \\mathrm{~mm}^{2} \\)\nCorrect Answer: \\( 404 \\mathrm{~mm}^{2} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks there are 100mm in a centimetre |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"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: What is the gradient of this line?\n\\(5 x+3 y=15\\)\nIncorrect Answer: \\( 5 \\)\nCorrect Answer: \\( -\\frac{5}{3} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"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: What is the gradient of this line?\n\\(5 x+3 y=15\\)\nIncorrect Answer: \\( -5 \\)\nCorrect Answer: \\( -\\frac{5}{3} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When solving an equation, believes that when they get to ax = b, b is the solution |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"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: What is the gradient of this line?\n\\(5 x+3 y=15\\)\nIncorrect Answer: \\( \\frac{5}{3} \\)\nCorrect Answer: \\( -\\frac{5}{3} \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When solving an equation, uses the same operation rather than the inverse. |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Compare sets of data using the range\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: The table shows the summary statistics from some girls and boys who took a test.\nWho performed the most consistently? ![\\begin{tabular}{|c|c|c|}\n\\hline Gender & Mean & Range \\\\\n\\hline Girls & \\( 75 \\) & \\( 20 \\) \\\\\n\\hline Boys & \\( 60 \\) & \\( 40 \\) \\\\\n\\hline\n\\end{tabular}]()\nIncorrect Answer: The boys because their mean is lower\nCorrect Answer: The girls because their range is lower\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks a lower average means the data is more consistent |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Compare sets of data using the range\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: The table shows the summary statistics from some girls and boys who took a test.\nWho performed the most consistently? ![\\begin{tabular}{|c|c|c|}\n\\hline Gender & Mean & Range \\\\\n\\hline Girls & \\( 75 \\) & \\( 20 \\) \\\\\n\\hline Boys & \\( 60 \\) & \\( 40 \\) \\\\\n\\hline\n\\end{tabular}]()\nIncorrect Answer: The boys because their range is higher\nCorrect Answer: The girls because their range is lower\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks a greater range means more consistent data |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Compare sets of data using the range\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: The table shows the summary statistics from some girls and boys who took a test.\nWho performed the most consistently? ![\\begin{tabular}{|c|c|c|}\n\\hline Gender & Mean & Range \\\\\n\\hline Girls & \\( 75 \\) & \\( 20 \\) \\\\\n\\hline Boys & \\( 60 \\) & \\( 40 \\) \\\\\n\\hline\n\\end{tabular}]()\nIncorrect Answer: The girls because their mean is higher\nCorrect Answer: The girls because their range is lower\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Thinks a higher average means more consistent data |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"role": "system"
},
{
"content": "\nConstruct: Recognise the notation for parallel lines\nSubject: Parallel Lines\nQuestion: Tom and Katie are discussing parallel lines. Tom says these two lines are parallel ![Image of a grid of squares with 2 lines on it. One line goes two squares to the right and one square up. The second line goes four squares to the right and two squares up.]() Katie says these two lines are parallel ![Image of a grid of squares with 2 lines on it. One line goes two squares to the right and one square up. The second line goes two squares to the right and one square down.]() Who is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Tom\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | Believes two lines of the same length are parallel |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"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: \\( -13 \\)\nCorrect Answer: \\( -3 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When subtracting a negative thinks the answer must be negative |
[
{
"content": "You are an assistant trying to identify the misconception that led a student to the incorrect answer instead of the correct one on a specific context",
"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: \\( 13 \\)\nCorrect Answer: \\( -3 \\)\n \n Identify the general misconception that led to the incorrect answer. Avoid using question-specific details such as exact numbers or variables. Focus on the overall reasoning error. Answer with a simple and concise sentence",
"role": "user"
}
] | When subtracting from a negative thinks the answer must be positive |