conversations
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[
{
"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, with all positive integers\nSubject: Linear Equations\nQuestion: Tom and Katie are discussing how to solve:\n\\(\n\\frac{x}{3}-5=12\n\\)\n\nTom says a correct next line of working could be: \\( \\frac{x}{3}=17 \\)\n\nKatie says a correct next line of working could be: \\( x-5=36 \\)\nWho is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Only\nTom\n",
"role": "user"
},
{
"content": "Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount",
"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, with all positive integers\nSubject: Linear Equations\nQuestion: Tom and Katie are discussing how to solve:\n\\(\n\\frac{x}{3}-5=12\n\\)\n\nTom says a correct next line of working could be: \\( \\frac{x}{3}=17 \\)\n\nKatie says a correct next line of working could be: \\( x-5=36 \\)\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only\nTom\n",
"role": "user"
},
{
"content": "Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount",
"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, with all positive integers\nSubject: Linear Equations\nQuestion: Tom and Katie are discussing how to solve:\n\\(\n\\frac{x}{3}-5=12\n\\)\n\nTom says a correct next line of working could be: \\( \\frac{x}{3}=17 \\)\n\nKatie says a correct next line of working could be: \\( x-5=36 \\)\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only\nTom\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: Subtract decimals where the numbers involved have a different number of decimal places\nSubject: Adding and Subtracting with Decimals\nQuestion: \\( 0.26-0.6= \\)\nIncorrect Answer: \\( 0.34 \\)\nCorrect Answer: \\( -0.34 \\)\n",
"role": "user"
},
{
"content": "Believes subtraction is commutative ",
"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: Subtract decimals where the numbers involved have a different number of decimal places\nSubject: Adding and Subtracting with Decimals\nQuestion: \\( 0.26-0.6= \\)\nIncorrect Answer: \\( -0.44 \\)\nCorrect Answer: \\( -0.34 \\)\n",
"role": "user"
},
{
"content": "Believes you subtract the smaller digit from the larger digit in column subtraction, regardless of position",
"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: Subtract decimals where the numbers involved have a different number of decimal places\nSubject: Adding and Subtracting with Decimals\nQuestion: \\( 0.26-0.6= \\)\nIncorrect Answer: \\( 0.2 \\)\nCorrect Answer: \\( -0.34 \\)\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: Represent positive unit fractions on a number line\nSubject: Probability of Single Events\nQuestion: The probability of picking a green ball is \\( \\frac{1}{5} \\) Where is this value on the probability scale? ![B\nc\nD]()\nIncorrect Answer: C\nCorrect Answer: B\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: Recognise and use efficient strategies for mental subtraction\nSubject: Mental Addition and Subtraction\nQuestion: Jo and Paul are discussing mental addition and subtraction strategies.\n\nJo says a good way to add \\( 19 \\) is to add \\( 10 \\), then another \\( 10 \\) and then subtract \\( 1 \\).\n\nPaul says a good way to subtract \\( 19 \\) is to subtract \\( 10 \\), then another \\( 10 \\) and then add \\( 1 \\).\n\nWho is correct?\nIncorrect Answer: Only\nJo\nCorrect Answer: Both Jo and Paul\n",
"role": "user"
},
{
"content": "Does not understand the effect of consecutive operations",
"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: Recognise and use efficient strategies for mental subtraction\nSubject: Mental Addition and Subtraction\nQuestion: Jo and Paul are discussing mental addition and subtraction strategies.\n\nJo says a good way to add \\( 19 \\) is to add \\( 10 \\), then another \\( 10 \\) and then subtract \\( 1 \\).\n\nPaul says a good way to subtract \\( 19 \\) is to subtract \\( 10 \\), then another \\( 10 \\) and then add \\( 1 \\).\n\nWho is correct?\nIncorrect Answer: Only\nPaul\nCorrect Answer: Both Jo and Paul\n",
"role": "user"
},
{
"content": "Does not understand the effect of consecutive operations",
"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: Recognise and use efficient strategies for mental subtraction\nSubject: Mental Addition and Subtraction\nQuestion: Jo and Paul are discussing mental addition and subtraction strategies.\n\nJo says a good way to add \\( 19 \\) is to add \\( 10 \\), then another \\( 10 \\) and then subtract \\( 1 \\).\n\nPaul says a good way to subtract \\( 19 \\) is to subtract \\( 10 \\), then another \\( 10 \\) and then add \\( 1 \\).\n\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Both Jo and Paul\n",
"role": "user"
},
{
"content": "Does not understand the effect of consecutive operations",
"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 fractions of symbols\nSubject: Pictogram\nQuestion: ![A pictogram where one smiley face =8 people. Game 1 has 4 faces. Game 2 has 3 faces. Game 3 has 2 faces. Game 4 has 2.75 faces.]() The pictogram shows the number of people who went to watch a netball match.\nHow many people went to game 4?\nIncorrect Answer: \\( 24 \\)\nCorrect Answer: \\( 22 \\)\n",
"role": "user"
},
{
"content": "Counts partial symbols as if they were whole on pictograms",
"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 fractions of symbols\nSubject: Pictogram\nQuestion: ![A pictogram where one smiley face =8 people. Game 1 has 4 faces. Game 2 has 3 faces. Game 3 has 2 faces. Game 4 has 2.75 faces.]() The pictogram shows the number of people who went to watch a netball match.\nHow many people went to game 4?\nIncorrect Answer: \\( 16 \\)\nCorrect Answer: \\( 22 \\)\n",
"role": "user"
},
{
"content": "Ignores partial symbols on pictograms",
"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 fractions of symbols\nSubject: Pictogram\nQuestion: ![A pictogram where one smiley face =8 people. Game 1 has 4 faces. Game 2 has 3 faces. Game 3 has 2 faces. Game 4 has 2.75 faces.]() The pictogram shows the number of people who went to watch a netball match.\nHow many people went to game 4?\nIncorrect Answer: \\( 2.75 \\)\nCorrect Answer: \\( 22 \\)\n",
"role": "user"
},
{
"content": "When interpreting a pictogram, thinks each symbol stands for 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: Solve problems involving converting between fractions, decimals and percentages\nSubject: Converting between Fractions and Percentages\nQuestion: Jo and Paul are arguing about percentages.\nJo says \\( 52 \\%=0.052 \\)\nPaul says \\( 52 \\%<\\frac{20}{41} \\)\nWho is correct?\nIncorrect Answer: Only\nJo\nCorrect Answer: Neither is correct\n",
"role": "user"
},
{
"content": "Divides by 1000 instead of 100 when converting a percentage to a decimal",
"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 equivalent fractions when presented as numbers\nSubject: Equivalent Fractions\nQuestion: Complete the statement \\( \\frac{4}{6}=\\frac{}{12} \\)\nIncorrect Answer: \\( \\frac{4}{6}=\\frac{2}{12} \\)\nCorrect Answer: \\( \\frac{4}{6}=\\frac{8}{12} \\)\n",
"role": "user"
},
{
"content": "Can identify the multiplier used to form an equivalent fraction but does not apply 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: Identify equivalent fractions when presented as numbers\nSubject: Equivalent Fractions\nQuestion: Complete the statement \\( \\frac{4}{6}=\\frac{}{12} \\)\nIncorrect Answer: \\( \\frac{4}{6}=\\frac{4}{12} \\)\nCorrect Answer: \\( \\frac{4}{6}=\\frac{8}{12} \\)\n",
"role": "user"
},
{
"content": "Does not understand equivalent 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: Identify equivalent fractions when presented as numbers\nSubject: Equivalent Fractions\nQuestion: Complete the statement \\( \\frac{4}{6}=\\frac{}{12} \\)\nIncorrect Answer: \\( \\frac{4}{6}=\\frac{10}{12} \\)\nCorrect Answer: \\( \\frac{4}{6}=\\frac{8}{12} \\)\n",
"role": "user"
},
{
"content": "Believes equivalent fractions are formed with addition not multiplication",
"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: Recognise and name a term\nSubject: Writing Expressions\nQuestion: Which of the following is the most appropriate word to describe \\( 3 g \\) in this: \\( 6-3 g \\)\nIncorrect Answer: Variable\nCorrect Answer: Term\n",
"role": "user"
},
{
"content": "Confuses a term with a variable",
"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: Recognise and name a term\nSubject: Writing Expressions\nQuestion: Which of the following is the most appropriate word to describe \\( 3 g \\) in this: \\( 6-3 g \\)\nIncorrect Answer: Expression\nCorrect Answer: Term\n",
"role": "user"
},
{
"content": "Confuses an expression with a term",
"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: Recognise and name a term\nSubject: Writing Expressions\nQuestion: Which of the following is the most appropriate word to describe \\( 3 g \\) in this: \\( 6-3 g \\)\nIncorrect Answer: Equation\nCorrect Answer: Term\n",
"role": "user"
},
{
"content": "Confuses a term with an equation",
"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: Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: The triangle is reflected in the \\( y \\)-axis\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -5 to 5, y-axis from -2 to 2. Three points are plotted and joined to make a triangle: (2, -2), (4, -2), (3, -1). Point (3, -1) is labelled with the letter \"P\". ]()\nIncorrect Answer: \\( (0,-1) \\)\nCorrect Answer: \\( (-3,-1) \\)\n",
"role": "user"
},
{
"content": "Fails to reflect across mirror 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: Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: The triangle is reflected in the \\( y \\)-axis\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -5 to 5, y-axis from -2 to 2. Three points are plotted and joined to make a triangle: (2, -2), (4, -2), (3, -1). Point (3, -1) is labelled with the letter \"P\". ]()\nIncorrect Answer: \\( (-2,-1) \\)\nCorrect Answer: \\( (-3,-1) \\)\n",
"role": "user"
},
{
"content": "Fails to reflect across mirror 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: Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: The triangle is reflected in the \\( y \\)-axis\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -5 to 5, y-axis from -2 to 2. Three points are plotted and joined to make a triangle: (2, -2), (4, -2), (3, -1). Point (3, -1) is labelled with the letter \"P\". ]()\nIncorrect Answer: \\( (3,-1) \\)\nCorrect Answer: \\( (-3,-1) \\)\n",
"role": "user"
},
{
"content": "Fails to reflect across mirror 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: Reflect an object or a point in a vertical line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: ![A grid of 7 squares across and 7 squares up. A red vertical line goes from the bottom to the top of the grid, it is 4 squares left from the edge of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn to the left of the red line, with its right-hand side on the red line. The bottom side of the rectangle is 3 squares up from the bottom of the grid. The top right corner of the rectangle is marked with the letter P, which is 5 squares up from the bottom of the grid on the red line. The bottom right corner of the rectangle is marked with the letter Q, which is 3 squares up from the bottom of the grid on the red line. ]() Tom and Katie are discussing reflections\n\nTom says if you reflect the rectangle in the vertical line, Point \\( P \\) stays in the same position\n\nKatie says if you reflect the rectangle in the vertical line, Point \\( Q \\) stays in the same position\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Both Tom and Katie\n",
"role": "user"
},
{
"content": "Does not understand that a point on the line of reflection will stay the same when reflected ",
"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 obtuse angles\nSubject: Types, Naming and Estimating\nQuestion: Which of the following is an obtuse angle?\nIncorrect Answer: \\( 85^{\\circ} \\)\nCorrect Answer: \\( 110^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Does not understand that an obtuse angle is between 90 and 180 degrees",
"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 obtuse angles\nSubject: Types, Naming and Estimating\nQuestion: Which of the following is an obtuse angle?\nIncorrect Answer: \\( 270^{\\circ} \\)\nCorrect Answer: \\( 110^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Does not understand that an obtuse angle is between 90 and 180 degrees",
"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 obtuse angles\nSubject: Types, Naming and Estimating\nQuestion: Which of the following is an obtuse angle?\nIncorrect Answer: \\( 180^{\\circ} \\)\nCorrect Answer: \\( 110^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Believes 180 degrees is an obtuse angle",
"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 rectangle when presented non-conventionally\nSubject: Naming Co-ordinates in 2D\nQuestion: What shape do you get if you join up the midpoints of the sides of this shape? ![An irregular quadrilateral drawn on a grid]()\nIncorrect Answer: Rhombus\nCorrect Answer: Parallelogram\n",
"role": "user"
},
{
"content": "Does not remember that a rhombus has equal sides",
"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 rectangle when presented non-conventionally\nSubject: Naming Co-ordinates in 2D\nQuestion: What shape do you get if you join up the midpoints of the sides of this shape? ![An irregular quadrilateral drawn on a grid]()\nIncorrect Answer: Kite\nCorrect Answer: Parallelogram\n",
"role": "user"
},
{
"content": "Does not recognise the properties of a kite",
"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 rectangle when presented non-conventionally\nSubject: Naming Co-ordinates in 2D\nQuestion: What shape do you get if you join up the midpoints of the sides of this shape? ![An irregular quadrilateral drawn on a grid]()\nIncorrect Answer: Rectangle\nCorrect Answer: Parallelogram\n",
"role": "user"
},
{
"content": "Does not know the properties of a rectangle",
"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 between m³ and cm³\nSubject: Volume and Capacity Units\nQuestion: \\(\n0.7 m^3 =\\bigstar \\,cm^3\n\\)\n\nWhat should replace the star?\nIncorrect Answer: \\( 70 \\)\nCorrect Answer: \\( 700000 \\)\n",
"role": "user"
},
{
"content": "Does not cube the conversion factor when converting cubed 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: Round non-integers to the nearest 10\nSubject: Rounding to the Nearest Whole (10, 100, etc)\nQuestion: What is \\( \\mathbf{1 2 6 . 0 5} \\) rounded to the nearest ten?\nIncorrect Answer: \\( 100 \\)\nCorrect Answer: \\( 130 \\)\n",
"role": "user"
},
{
"content": "Rounds to the wrong degree of accuracy (rounds too little)",
"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 non-integers to the nearest 10\nSubject: Rounding to the Nearest Whole (10, 100, etc)\nQuestion: What is \\( \\mathbf{1 2 6 . 0 5} \\) rounded to the nearest ten?\nIncorrect Answer: \\( 120 \\)\nCorrect Answer: \\( 130 \\)\n",
"role": "user"
},
{
"content": "Rounds down instead of up",
"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 non-integers to the nearest 10\nSubject: Rounding to the Nearest Whole (10, 100, etc)\nQuestion: What is \\( \\mathbf{1 2 6 . 0 5} \\) rounded to the nearest ten?\nIncorrect Answer: \\( 126 \\)\nCorrect Answer: \\( 130 \\)\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: Convert ratios to fractions\nSubject: Writing Ratios\nQuestion: Kate and Isaac share some yoghurt in the ratio \\( 2: 5 \\).\nKate has \\(_____\\) of the total yoghurt\nWhat fraction completes the sentence?\nIncorrect Answer: \\( \\frac{2}{5} \\)\nCorrect Answer: \\( \\frac{2}{7} \\)\n",
"role": "user"
},
{
"content": "When converting ratio to fractions, puts the other side of the ratio as the denominator rather than the total",
"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 non-integer values into formulae involving powers or roots\nSubject: Substitution into Formula\nQuestion: Calculate the displacement \\( (s) \\), of a particle when initial velocity \\( (u)=2.9 \\mathrm{~ms}^{-1} \\), final velocity \\( (v)=3.5 \\mathrm{~ms}^{-1} \\), and the time \\( (t) \\) taken is \\( 5.2 \\) seconds. \\( s=\\frac{1}{2}(u+v) t \\)\nIncorrect Answer: \\( \\begin{array}{c}s=\\frac{1}{2}(2.9+3.5)+5.2 \\\\ s=8.4\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}s=\\frac{1}{2}(2.9+3.5) \\times 5.2 \\\\ s=16.64\\end{array} \\)\n",
"role": "user"
},
{
"content": "Thinks two variables next to each other represent addition",
"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 non-integer values into formulae involving powers or roots\nSubject: Substitution into Formula\nQuestion: Calculate the displacement \\( (s) \\), of a particle when initial velocity \\( (u)=2.9 \\mathrm{~ms}^{-1} \\), final velocity \\( (v)=3.5 \\mathrm{~ms}^{-1} \\), and the time \\( (t) \\) taken is \\( 5.2 \\) seconds. \\( s=\\frac{1}{2}(u+v) t \\)\nIncorrect Answer: \\( \\begin{array}{c}s=\\frac{1}{2}(2.9+3.5+5.2) \\\\ s=5.8\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}s=\\frac{1}{2}(2.9+3.5) \\times 5.2 \\\\ s=16.64\\end{array} \\)\n",
"role": "user"
},
{
"content": "Thinks two variables next to each other represent addition",
"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 from years to days\nSubject: Time\nQuestion: How many days in a non-leap year?\nIncorrect Answer: \\( 350 \\)\nCorrect Answer: \\( 365 \\)\n",
"role": "user"
},
{
"content": "Thinks there are 50 weeks in a year",
"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 from years to days\nSubject: Time\nQuestion: How many days in a non-leap year?\nIncorrect Answer: \\( 100 \\)\nCorrect Answer: \\( 365 \\)\n",
"role": "user"
},
{
"content": "Does not know how many days are in a leap year",
"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 two negative integers\nSubject: Multiplying and Dividing Negative Numbers\nQuestion: Which calculation is incorrect?\nIncorrect Answer: \\( (-7) \\times 2=-14 \\)\nCorrect Answer: \\( (-7) \\times(-2)=-14 \\)\n",
"role": "user"
},
{
"content": "Believes multiplying a positive by a negative gives a positive 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 two negative integers\nSubject: Multiplying and Dividing Negative Numbers\nQuestion: Which calculation is incorrect?\nIncorrect Answer: \\( 7 \\times 2=14 \\)\nCorrect Answer: \\( (-7) \\times(-2)=-14 \\)\n",
"role": "user"
},
{
"content": "Believes multiplying two positives 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 two negative integers\nSubject: Multiplying and Dividing Negative Numbers\nQuestion: Which calculation is incorrect?\nIncorrect Answer: \\( 7 \\times(-2)=-14 \\)\nCorrect Answer: \\( (-7) \\times(-2)=-14 \\)\n",
"role": "user"
},
{
"content": "Believes multiplying a positive by a negative gives a positive 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: Know that the probabilities of exhaustive events must sum to 1\nSubject: Probability of Single Events\nQuestion: The probability of an event occurring is \\( \\frac{2}{7} \\).\n\nWhat is the probability of the event not occurring?\nIncorrect Answer: \\( \\frac{2}{7} \\)\nCorrect Answer: \\( \\frac{5}{7} \\)\n",
"role": "user"
},
{
"content": "Thinks that probabilities of an event occurring or not occurring must be equal",
"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: Know that the probabilities of exhaustive events must sum to 1\nSubject: Probability of Single Events\nQuestion: The probability of an event occurring is \\( \\frac{2}{7} \\).\n\nWhat is the probability of the event not occurring?\nIncorrect Answer: \\( 5 \\)\nCorrect Answer: \\( \\frac{5}{7} \\)\n",
"role": "user"
},
{
"content": "Gives probability as an integer instead of 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: Calculate the square of a number\nSubject: Squares, Cubes, etc\nQuestion: \\( (16)^{2}=? \\)\nIncorrect Answer: \\( 8 \\)\nCorrect Answer: \\( 256 \\)\n",
"role": "user"
},
{
"content": "Mixes up squaring with dividing by 2",
"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 square of a number\nSubject: Squares, Cubes, etc\nQuestion: \\( (16)^{2}=? \\)\nIncorrect Answer: \\( 32 \\)\nCorrect Answer: \\( 256 \\)\n",
"role": "user"
},
{
"content": "Mixes up squaring and multiplying by 2 or doubling",
"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: This is a part of the table of values for the equation\n\\(y=x^{2}+4\\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( -6 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star?\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: \\( 40 \\)\n",
"role": "user"
},
{
"content": "Believes addition comes before indices, in orders of operation",
"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: This is a part of the table of values for the equation\n\\(y=x^{2}+4\\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( -6 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star?\nIncorrect Answer: \\( -32 \\)\nCorrect Answer: \\( 40 \\)\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: 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 this shape? ![Parallelogram drawn on square grid with area of 6 squares]()\nIncorrect Answer: \\( 8 \\)\nCorrect Answer: \\( 6 \\)\n",
"role": "user"
},
{
"content": "Counts half-squares as full squares when calculating area on a square grid",
"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 parallelogram where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: What is the area of this shape? ![Parallelogram drawn on square grid with area of 6 squares]()\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: \\( 6 \\)\n",
"role": "user"
},
{
"content": "Underestimates the area of shapes when counting squares when some squares are neither wholes nor halves",
"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 parallelogram where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: What is the area of this shape? ![Parallelogram drawn on square grid with area of 6 squares]()\nIncorrect Answer: \\( 7 \\)\nCorrect Answer: \\( 6 \\)\n",
"role": "user"
},
{
"content": "Counts half-squares as full squares when calculating area on a square grid",
"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 square of a number\nSubject: Squares, Cubes, etc\nQuestion: \\( -(16)^{2}=? \\)\nIncorrect Answer: \\( -32 \\)\nCorrect Answer: \\( -256 \\)\n",
"role": "user"
},
{
"content": "Mixes up squaring and multiplying by 2 or doubling",
"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 square of a number\nSubject: Squares, Cubes, etc\nQuestion: \\( -(16)^{2}=? \\)\nIncorrect Answer: \\( 256 \\)\nCorrect Answer: \\( -256 \\)\n",
"role": "user"
},
{
"content": "Does not understand that the negative outside the bracket means answer will 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: Identify the order of rotational symmetry of a shape\nSubject: Rotational Symmetry\nQuestion: Which quadrilateral has the highest order of rotational symmetry?\nIncorrect Answer: ![Trapezium]()\nCorrect Answer: ![Parallelogram]()\n",
"role": "user"
},
{
"content": "Does not know how to find order of rotational symmetry",
"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 order of rotational symmetry of a shape\nSubject: Rotational Symmetry\nQuestion: Which quadrilateral has the highest order of rotational symmetry?\nIncorrect Answer: ![Irregular quadrilateral]()\nCorrect Answer: ![Parallelogram]()\n",
"role": "user"
},
{
"content": "Does not know how to find order of rotational symmetry",
"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 order of rotational symmetry of a shape\nSubject: Rotational Symmetry\nQuestion: Which quadrilateral has the highest order of rotational symmetry?\nIncorrect Answer: They each have the same order of rotational symmetry\nCorrect Answer: ![Parallelogram]()\n",
"role": "user"
},
{
"content": "Believes the number of sides gives the order of rotational symmetry",
"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: Place Value\nQuestion: What number is the arrow pointing to? ![A number line from 100 to 200 with an arrow pointing to the value 160]()\nIncorrect Answer: \\( 154 \\)\nCorrect Answer: \\( 160 \\)\n",
"role": "user"
},
{
"content": "When reading integers on a number line, assumes each dash is 2",
"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: Place Value\nQuestion: What number is the arrow pointing to? ![A number line from 100 to 200 with an arrow pointing to the value 160]()\nIncorrect Answer: \\( 170 \\)\nCorrect Answer: \\( 160 \\)\n",
"role": "user"
},
{
"content": "When reading integers on a number line, assumes each dash is 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: Read an integer on a scale where the required measurement is marked by a dash between two numbers\nSubject: Place Value\nQuestion: What number is the arrow pointing to? ![A number line from 100 to 200 with an arrow pointing to the value 160]()\nIncorrect Answer: \\( 152 \\)\nCorrect Answer: \\( 160 \\)\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: Write algebraic expressions with correct algebraic convention\nSubject: Writing Expressions\nQuestion: Which of the following is the correct way of writing:\n\n\\( m \\) multiplied by \\( n \\), then add \\( 5 \\)\n\nusing algebraic convention?\nIncorrect Answer: \\( m(n+5) \\)\nCorrect Answer: \\( m n+5 \\)\n",
"role": "user"
},
{
"content": "Does not account for grammar when writing algebra e.g. ,then making a group",
"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: Write algebraic expressions with correct algebraic convention\nSubject: Writing Expressions\nQuestion: Which of the following is the correct way of writing:\n\n\\( m \\) multiplied by \\( n \\), then add \\( 5 \\)\n\nusing algebraic convention?\nIncorrect Answer: \\( m \\times n+5 \\)\nCorrect Answer: \\( m n+5 \\)\n",
"role": "user"
},
{
"content": "Does not realize we can omit the multiplication symbol in algebraic expressions",
"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 transversal\nSubject: Angle Facts with Parallel Lines\nQuestion: Line \\( X Y \\) is... ![A pair of parallel lines are drawn with the arrows pointing up to the left.\nA straight red line, XY, is drawn so that it diagonally crosses the pair of parallel lines. The red line rises from X on the left up to Y.]()\nIncorrect Answer: Perpendicular\nCorrect Answer: A transversal\n",
"role": "user"
},
{
"content": "Believes any lines that cross are perpendicular",
"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 transversal\nSubject: Angle Facts with Parallel Lines\nQuestion: Line \\( X Y \\) is... ![A pair of parallel lines are drawn with the arrows pointing up to the left.\nA straight red line, XY, is drawn so that it diagonally crosses the pair of parallel lines. The red line rises from X on the left up to Y.]()\nIncorrect Answer: Skew\nCorrect Answer: A transversal\n",
"role": "user"
},
{
"content": "Does not know the term transversal",
"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: Write algebraic expressions with correct algebraic convention involving powers\nSubject: Writing Expressions\nQuestion: If we want to write\n\"\\( m \\) multiplied by \\( m \\) multiplied by \\( m \\)\"\nusing algebra, this would be:\nIncorrect Answer: \\( m \\times m \\times m \\)\nCorrect Answer: \\( m^{3} \\)\n",
"role": "user"
},
{
"content": "Does not realize we can omit the multiplication symbol in algebraic expressions",
"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: Write algebraic expressions with correct algebraic convention involving powers\nSubject: Writing Expressions\nQuestion: If we want to write\n\"\\( m \\) multiplied by \\( m \\) multiplied by \\( m \\)\"\nusing algebra, this would be:\nIncorrect Answer: \\( 3 m \\)\nCorrect Answer: \\( m^{3} \\)\n",
"role": "user"
},
{
"content": "Multiplies by the index",
"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: Write algebraic expressions with correct algebraic convention involving powers\nSubject: Writing Expressions\nQuestion: If we want to write\n\"\\( m \\) multiplied by \\( m \\) multiplied by \\( m \\)\"\nusing algebra, this would be:\nIncorrect Answer: \\( \\mathrm{mmm} \\)\nCorrect Answer: \\( m^{3} \\)\n",
"role": "user"
},
{
"content": "Writes repeated letters instead of using index form of a variable",
"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\\[\n2,2,4,7,10,-15\n\\]\nIncorrect Answer: \\( 7 \\)\nCorrect Answer: \\( 3 \\)\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\\[\n2,2,4,7,10,-15\n\\]\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: \\( 3 \\)\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\\[\n2,2,4,7,10,-15\n\\]\nIncorrect Answer: \\( 5.5 \\)\nCorrect Answer: \\( 3 \\)\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: Solve problems that combine addition and subtraction\nSubject: BIDMAS\nQuestion: ![Think of a number, then subtract \\( 5 \\), next divide by \\( 8 \\), next add 4, and finally multiply by \\( 7 \\).]() Jo says you can write this as:\n\\[\n7\\left(\\frac{(n-5)}{8}+4\\right)\n\\]\nPaul says you can write this as:\n\\[\n7((n-5) \\div 8)+4\n\\]\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only\nJo\n",
"role": "user"
},
{
"content": "Carries out operations from left to right regardless of priority order",
"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: A line has equation \\( 4 x+3 y=5 \\)\nWhat is it's gradient?\nIncorrect Answer: \\( -4 \\)\nCorrect Answer: \\( -\\frac{4}{3} \\)\n",
"role": "user"
},
{
"content": "When solving an equation forgets to eliminate the coefficient in front of the variable in the last step",
"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: A line has equation \\( 4 x+3 y=5 \\)\nWhat is it's gradient?\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: \\( -\\frac{4}{3} \\)\n",
"role": "user"
},
{
"content": "Believes that for a line written in the form ax + by = c, a is the gradient",
"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: A line has equation \\( 4 x+3 y=5 \\)\nWhat is it's gradient?\nIncorrect Answer: \\( \\frac{4}{3} \\)\nCorrect Answer: \\( -\\frac{4}{3} \\)\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: Create a situation to match an algebraic expression\nSubject: Writing Expressions\nQuestion: Which model does not correctly represent the following expression?\n\\(2(n+3)\\)\nIncorrect Answer: ![\\begin{tabular}{|c|c|}\n\\hline\\( n \\) & \\( 3 \\) \\\\\n\\hline\\( n \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}]()\nCorrect Answer: ![\\begin{tabular}{|c|c|}\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\n\\end{tabular}]()\n",
"role": "user"
},
{
"content": "Does not understand bar modelling in algebra",
"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: Create a situation to match an algebraic expression\nSubject: Writing Expressions\nQuestion: Which model does not correctly represent the following expression?\n\\(2(n+3)\\)\nIncorrect Answer: ![\\begin{tabular}{|l|l|l|l|}\n\\hline \\( \\mathrm{n} \\) & \\( 3 \\) & \\( \\mathrm{n} \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}]()\nCorrect Answer: ![\\begin{tabular}{|c|c|}\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\n\\end{tabular}]()\n",
"role": "user"
},
{
"content": "Does not understand bar modelling in algebra",
"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: Create a situation to match an algebraic expression\nSubject: Writing Expressions\nQuestion: Which model does not correctly represent the following expression?\n\\(2(n+3)\\)\nIncorrect Answer: ![\\begin{tabular}{|l|l|l|l|}\n\\hline \\( \\mathrm{n} \\) & \\( \\mathrm{n} \\) & \\( 3 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}]()\nCorrect Answer: ![\\begin{tabular}{|c|c|}\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\\( n \\) & \\( 2 \\) \\\\\n\\hline\n\\end{tabular}]()\n",
"role": "user"
},
{
"content": "Does not recognise the distributive property",
"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 an equation, form or identify related equations\nSubject: Substitution into Formula\nQuestion: \\[\n3 k+2<m+2\n\\]\nUsing the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()\nIncorrect Answer: always true\nCorrect Answer: never true\n",
"role": "user"
},
{
"content": "Does not understand bar modelling in algebra",
"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 an equation, form or identify related equations\nSubject: Substitution into Formula\nQuestion: \\[\n3 k+2<m+2\n\\]\nUsing the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()\nIncorrect Answer: sometimes true\nCorrect Answer: never true\n",
"role": "user"
},
{
"content": "Does not understand bar modelling in algebra",
"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 an equation, form or identify related equations\nSubject: Substitution into Formula\nQuestion: \\[\n3 k+2<m+2\n\\]\nUsing the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()\nIncorrect Answer: Need more information\nCorrect Answer: never true\n",
"role": "user"
},
{
"content": "Does not understand bar modelling in algebra",
"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: Understand the terms equilateral and regular, and recognise the notation for regular polygons\nSubject: 2D Names and Properties of Shapes-Others\nQuestion: Tom and Katie are discussing regular polygons. Tom says this is a regular polygon ![A triangle with 3 equal sides and 3 equal angles]() Katie says this is a regular polygon ![A parallelogram with 2 pairs of parallel sides marked]() Who is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Does not know the meaning of the word regular ",
"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: Understand the terms equilateral and regular, and recognise the notation for regular polygons\nSubject: 2D Names and Properties of Shapes-Others\nQuestion: Tom and Katie are discussing regular polygons. Tom says this is a regular polygon ![A triangle with 3 equal sides and 3 equal angles]() Katie says this is a regular polygon ![A parallelogram with 2 pairs of parallel sides marked]() Who is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Does not know the meaning of the word regular ",
"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: Understand the terms equilateral and regular, and recognise the notation for regular polygons\nSubject: 2D Names and Properties of Shapes-Others\nQuestion: Tom and Katie are discussing regular polygons. Tom says this is a regular polygon ![A triangle with 3 equal sides and 3 equal angles]() Katie says this is a regular polygon ![A parallelogram with 2 pairs of parallel sides marked]() Who is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Does not know the meaning of the word regular ",
"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 is the value of \\( h \\) in the formula? Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) ![Trapezium with the slanted sides labelled 8cm and 7.5cm. The parallel sides labelled 3cm and 8cm. The perpendicular height labelled 7cm.]()\nIncorrect Answer: \\( 8 \\)\nCorrect Answer: \\( 7 \\)\n",
"role": "user"
},
{
"content": "Uses slant height instead of perpendicular height 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 is the value of \\( h \\) in the formula? Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) ![Trapezium with the slanted sides labelled 8cm and 7.5cm. The parallel sides labelled 3cm and 8cm. The perpendicular height labelled 7cm.]()\nIncorrect Answer: \\( 7.5 \\)\nCorrect Answer: \\( 7 \\)\n",
"role": "user"
},
{
"content": "Uses slant height instead of perpendicular height 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 is the value of \\( h \\) in the formula? Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) ![Trapezium with the slanted sides labelled 8cm and 7.5cm. The parallel sides labelled 3cm and 8cm. The perpendicular height labelled 7cm.]()\nIncorrect Answer: \\( 3 \\)\nCorrect Answer: \\( 7 \\)\n",
"role": "user"
},
{
"content": "Uses base instead of height as h in area of a trapezium formula",
"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: Reflect an object or a point in a vertical line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: ![A grid of 7 squares across and 7 squares up. A red vertical line goes from the bottom to the top of the grid, it is 4 squares left from the edge of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn to the left of the red line, with its right-hand side on the red line. The bottom side of the rectangle is 3 squares up from the bottom of the grid. The bottom left corner of the rectangle is marked with the letter P, which is 3 squares up from the bottom of the grid and 3 squares to the left of the red line. The bottom right corner of the rectangle is marked with the letter Q, which is 3 squares up from the bottom of the grid on the red line. ]() Tom and Katie are discussing reflections\n\nTom says if you reflect the rectangle in the vertical line, Point \\( P \\) stays in the same position\n\nKatie says if you reflect the rectangle in the vertical line, Point \\( Q \\) stays in the same position\nWho is correct?\nIncorrect Answer: Only Tom\nCorrect Answer: Only Katie\n",
"role": "user"
},
{
"content": "Fails to reflect across mirror 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: Reflect an object or a point in a vertical line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: ![A grid of 7 squares across and 7 squares up. A red vertical line goes from the bottom to the top of the grid, it is 4 squares left from the edge of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn to the left of the red line, with its right-hand side on the red line. The bottom side of the rectangle is 3 squares up from the bottom of the grid. The bottom left corner of the rectangle is marked with the letter P, which is 3 squares up from the bottom of the grid and 3 squares to the left of the red line. The bottom right corner of the rectangle is marked with the letter Q, which is 3 squares up from the bottom of the grid on the red line. ]() Tom and Katie are discussing reflections\n\nTom says if you reflect the rectangle in the vertical line, Point \\( P \\) stays in the same position\n\nKatie says if you reflect the rectangle in the vertical line, Point \\( Q \\) stays in the same position\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Katie\n",
"role": "user"
},
{
"content": "Fails to reflect across mirror 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: Reflect an object or a point in a vertical line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: ![A grid of 7 squares across and 7 squares up. A red vertical line goes from the bottom to the top of the grid, it is 4 squares left from the edge of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn to the left of the red line, with its right-hand side on the red line. The bottom side of the rectangle is 3 squares up from the bottom of the grid. The bottom left corner of the rectangle is marked with the letter P, which is 3 squares up from the bottom of the grid and 3 squares to the left of the red line. The bottom right corner of the rectangle is marked with the letter Q, which is 3 squares up from the bottom of the grid on the red line. ]() Tom and Katie are discussing reflections\n\nTom says if you reflect the rectangle in the vertical line, Point \\( P \\) stays in the same position\n\nKatie says if you reflect the rectangle in the vertical line, Point \\( Q \\) stays in the same position\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only Katie\n",
"role": "user"
},
{
"content": "Fails to reflect across mirror 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: Calculate which two integer values the decimal equivalent of a square root must lie between\nSubject: Square Roots, Cube Roots, etc\nQuestion: Without using a calculator, which two integers must \\( \\sqrt{89} \\) lie between?\nIncorrect Answer: \\( 44 \\) and \\( 45 \\)\nCorrect Answer: \\( 9 \\) and \\( 10 \\)\n",
"role": "user"
},
{
"content": "Confuses square rooting and halving 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, with all positive integers\nSubject: Linear Equations\nQuestion: Jo and Paul are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{6}-4=24\n\\)\nJo says you can write: \\( \\frac{m}{6}=28 \\)\nPaul says you can write: \\( m-4=144 \\)\nWho is correct?\nIncorrect Answer: Both Jo and Paul\nCorrect Answer: Only Jo\n",
"role": "user"
},
{
"content": "When solving an equation with a fraction, thinks you don't need to multiply every term on both sides when multiplying by the 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: Solve two-step linear equations, with the variable on one side, with all positive integers\nSubject: Linear Equations\nQuestion: Jo and Paul are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{6}-4=24\n\\)\nJo says you can write: \\( \\frac{m}{6}=28 \\)\nPaul says you can write: \\( m-4=144 \\)\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only Jo\n",
"role": "user"
},
{
"content": "Does not know how to solve linear equations involving 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: Given a positive x value, find a y value in a table of values for lines in the form y = mx + c \nSubject: Plotting Lines from Tables of Values\nQuestion: \\begin{tabular}{l|l|l|l}\n\\( x \\) & \\( \\) & \\( 0 \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( -7 \\) & \\( -5 \\) & \\( \\color{gold}\\bigstar\\ \\) \\\\\n\\end{tabular}\n This is a table of values for \\( y=2 x+c \\)\nWhat should replace the star?\nIncorrect Answer: \\( 6 \\)\nCorrect Answer: \\( 1 \\)\n",
"role": "user"
},
{
"content": "Does not realise that a pair of coordinates can be used to find missing parts of an equation",
"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: Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object\nSubject: Rotation\nQuestion: John rotates rectangle \\( A B C D 90^{\\circ} \\) clockwise from the centre \\( (3,2) \\). What error has he made? ![A positive, coordinate grid with two rectangles drawn on it. The rectangle labelled ABCD has the coordinates: A(1,3) B(1,5) C(2,5) and D(2,3). The other rectangle has the coordinates: (4,3) (6,3) (6,2) and (4,2).]()\nIncorrect Answer: He has translated by the vector \\( \\left(\\begin{array}{l}3 \\\\ 2\\end{array}\\right) \\)\nCorrect Answer: He has used the wrong centre\n",
"role": "user"
},
{
"content": "Does not recognise that a shape translated would not change orientation",
"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: Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object\nSubject: Rotation\nQuestion: John rotates rectangle \\( A B C D 90^{\\circ} \\) clockwise from the centre \\( (3,2) \\). What error has he made? ![A positive, coordinate grid with two rectangles drawn on it. The rectangle labelled ABCD has the coordinates: A(1,3) B(1,5) C(2,5) and D(2,3). The other rectangle has the coordinates: (4,3) (6,3) (6,2) and (4,2).]()\nIncorrect Answer: He has rotated \\( 90^{\\circ} \\) anticlockwise\nCorrect Answer: He has used the wrong centre\n",
"role": "user"
},
{
"content": "Mixes up clockwise and anticlockwise",
"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: Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: The triangle is reflected in the dashed line.\nWhat are the new coordinates of point P? ![A set of axes: x-axis from -1 to 5, y-axis from -3 to 4. Three points are plotted and joined to make a triangle: (2, 2), (4, 2), (3, 3). Point (2, 2) is labelled with the letter \"P\". The line y=2 is shown with a purple dashed line.]()\nIncorrect Answer: \\( (2,1) \\)\nCorrect Answer: \\( (2,2) \\)\n",
"role": "user"
},
{
"content": "Does not understand that a point on the line of reflection will stay the same when reflected ",
"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: Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: The triangle is reflected in the dashed line.\nWhat are the new coordinates of point P? ![A set of axes: x-axis from -1 to 5, y-axis from -3 to 4. Three points are plotted and joined to make a triangle: (2, 2), (4, 2), (3, 3). Point (2, 2) is labelled with the letter \"P\". The line y=2 is shown with a purple dashed line.]()\nIncorrect Answer: \\( (2,0) \\)\nCorrect Answer: \\( (2,2) \\)\n",
"role": "user"
},
{
"content": "Does not understand that a point on the line of reflection will stay the same when reflected ",
"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: Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object\nSubject: Reflection\nQuestion: The triangle is reflected in the dashed line.\nWhat are the new coordinates of point P? ![A set of axes: x-axis from -1 to 5, y-axis from -3 to 4. Three points are plotted and joined to make a triangle: (2, 2), (4, 2), (3, 3). Point (2, 2) is labelled with the letter \"P\". The line y=2 is shown with a purple dashed line.]()\nIncorrect Answer: \\( (2,-2) \\)\nCorrect Answer: \\( (2,2) \\)\n",
"role": "user"
},
{
"content": "Does not understand that a point on the line of reflection will stay the same when reflected ",
"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 corresponding angles\nSubject: Angle Facts with Parallel Lines\nQuestion: Which angle is corresponding to angle \\( p \\) ? ![Image showing two parallel lines cut by a transversal creating two distinct angles around a point. On the left hand side the pink angle is labelled with A, vertically opposite this is the angle labelled p. On the right hand side, angle B is co-interior to p. Then lying on the same straight line as B is the angle labelled C. Vertically opposite angle C is the angle labelled D.]()\nIncorrect Answer: A\nCorrect Answer: C\n",
"role": "user"
},
{
"content": "Confuses corresponding and vertically opposite 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: Identify corresponding angles\nSubject: Angle Facts with Parallel Lines\nQuestion: Which angle is corresponding to angle \\( p \\) ? ![Image showing two parallel lines cut by a transversal creating two distinct angles around a point. On the left hand side the pink angle is labelled with A, vertically opposite this is the angle labelled p. On the right hand side, angle B is co-interior to p. Then lying on the same straight line as B is the angle labelled C. Vertically opposite angle C is the angle labelled D.]()\nIncorrect Answer: B\nCorrect Answer: C\n",
"role": "user"
},
{
"content": "Confuses co-interior and corresponding 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: Identify corresponding angles\nSubject: Angle Facts with Parallel Lines\nQuestion: Which angle is corresponding to angle \\( p \\) ? ![Image showing two parallel lines cut by a transversal creating two distinct angles around a point. On the left hand side the pink angle is labelled with A, vertically opposite this is the angle labelled p. On the right hand side, angle B is co-interior to p. Then lying on the same straight line as B is the angle labelled C. Vertically opposite angle C is the angle labelled D.]()\nIncorrect Answer: D\nCorrect Answer: C\n",
"role": "user"
},
{
"content": "Confuses corresponding and alternate angles",
"role": "assistant"
}
] |