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: Given a gradient, state the gradient of a line parallel to it\nSubject: Parallel Lines\nQuestion: A line has a gradient of \\( 5 \\)\n\nA line parallel to this line would have a gradient of...\nIncorrect Answer: Not enough information\nCorrect Answer: \\( 5 \\)\n",
"role": "user"
},
{
"content": "Does not know parallel lines have equal gradients ",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide proper fractions in the form: Fraction ÷ Integer\nSubject: Dividing Fractions\nQuestion: Calculate: \\( \\frac{4}{8} \\div 2 \\)\nIncorrect Answer: \\( \\frac{2}{4} \\)\nCorrect Answer: \\( \\frac{2}{8} \\)\n",
"role": "user"
},
{
"content": "When dividing a fraction by an integer, divides both the numerator and denominator by the integer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide proper fractions in the form: Fraction ÷ Integer\nSubject: Dividing Fractions\nQuestion: Calculate: \\( \\frac{4}{8} \\div 2 \\)\nIncorrect Answer: \\( \\frac{4}{4} \\)\nCorrect Answer: \\( \\frac{2}{8} \\)\n",
"role": "user"
},
{
"content": "When dividing a fraction by an integer, divides the denominator by the integer",
"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 right-angled triangle when presented non-conventionally\nSubject: Properties of Triangles\nQuestion: \\( A B C D \\) is a rectangle.\nWhat type of triangle is triangle \\( \\mathrm{BCD} \\) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]()\nIncorrect Answer: Scalene\nCorrect Answer: Right-angled\n",
"role": "user"
},
{
"content": "Confuses scalene and right angle triangles",
"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 right-angled triangle when presented non-conventionally\nSubject: Properties of Triangles\nQuestion: \\( A B C D \\) is a rectangle.\nWhat type of triangle is triangle \\( \\mathrm{BCD} \\) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]()\nIncorrect Answer: Isosceles\nCorrect Answer: Right-angled\n",
"role": "user"
},
{
"content": "Confuses isosceles and right angle triangles",
"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 right-angled triangle when presented non-conventionally\nSubject: Properties of Triangles\nQuestion: \\( A B C D \\) is a rectangle.\nWhat type of triangle is triangle \\( \\mathrm{BCD} \\) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]()\nIncorrect Answer: Equilateral\nCorrect Answer: Right-angled\n",
"role": "user"
},
{
"content": "Confuses isosceles and right angle triangles",
"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: For a given algebraic input, find the output of a function machine\nSubject: Function Machines\nQuestion: ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"5a + 2\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine?\nIncorrect Answer: \\( 10 a+2 \\)\nCorrect Answer: \\( 10 a+4 \\)\n",
"role": "user"
},
{
"content": "Only multiplies the first term in the expansion of a bracket",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: For a given algebraic input, find the output of a function machine\nSubject: Function Machines\nQuestion: ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"5a + 2\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine?\nIncorrect Answer: \\( 5 a+4 \\)\nCorrect Answer: \\( 10 a+4 \\)\n",
"role": "user"
},
{
"content": "Only multiplies second term in the expansion of a bracket",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: For a given algebraic input, find the output of a function machine\nSubject: Function Machines\nQuestion: ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"5a + 2\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine?\nIncorrect Answer: \\( 7 a+4 \\)\nCorrect Answer: \\( 10 a+4 \\)\n",
"role": "user"
},
{
"content": "Adds instead of multiplies when multiplying algebraic terms",
"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 an equation using a bar model\nSubject: Writing Expressions\nQuestion: ![Tom and Katie are discussing bar models.]() Tom says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline \\( 2 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Who do you agree with?\nIncorrect Answer: Only Tom\nCorrect Answer: Only Katie\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: Represent an equation using a bar model\nSubject: Writing Expressions\nQuestion: ![Tom and Katie are discussing bar models.]() Tom says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline \\( 2 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Who do you agree with?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Katie\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: Represent an equation using a bar model\nSubject: Writing Expressions\nQuestion: ![Tom and Katie are discussing bar models.]() Tom says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline \\( 2 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Who do you agree with?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only Katie\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: Calculate the whole amount, given a fraction of the amount\nSubject: Fractions of an Amount\nQuestion: What should replace the star?\n\\(\n\\frac{1}{3} \\text { of } \\color{yellow}\\bigstar\\)\\(=27\n\\)\nIncorrect Answer: \\( 61 \\)\nCorrect Answer: \\( 81 \\)\n",
"role": "user"
},
{
"content": "When two digits multiply to 10 or more during a multiplication problem, does not add carried value to the preceding digit",
"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 whole amount, given a fraction of the amount\nSubject: Fractions of an Amount\nQuestion: What should replace the star?\n\\(\n\\frac{1}{3} \\text { of } \\color{yellow}\\bigstar\\)\\(=27\n\\)\nIncorrect Answer: \\( 9 \\)\nCorrect Answer: \\( 81 \\)\n",
"role": "user"
},
{
"content": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original 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: Determine the input of a double function machine used to create an algebraic expression\nSubject: Function Machines\nQuestion: input \\(\\Rightarrow-3 \\Rightarrow \\times 3 \\Rightarrow 9a-21 \\) What is the input of this function machine?\nIncorrect Answer: \\( 3 a-18 \\)\nCorrect Answer: \\( 3 a-4 \\)\n",
"role": "user"
},
{
"content": "Does not apply the inverse function to every term in an expression",
"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: Determine the input of a double function machine used to create an algebraic expression\nSubject: Function Machines\nQuestion: input \\(\\Rightarrow-3 \\Rightarrow \\times 3 \\Rightarrow 9a-21 \\) What is the input of this function machine?\nIncorrect Answer: \\( 3 a-21 \\)\nCorrect Answer: \\( 3 a-4 \\)\n",
"role": "user"
},
{
"content": "Has completed only one of the two 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: Determine the input of a double function machine used to create an algebraic expression\nSubject: Function Machines\nQuestion: input \\(\\Rightarrow-3 \\Rightarrow \\times 3 \\Rightarrow 9a-21 \\) What is the input of this function machine?\nIncorrect Answer: \\( 3 a-7 \\)\nCorrect Answer: \\( 3 a-4 \\)\n",
"role": "user"
},
{
"content": "Has completed only one of the two 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: Convert from years to days\nSubject: Time\nQuestion: \\( 2 \\) leap years \\( =\\square \\) days\nIncorrect Answer: \\( 728 \\)\nCorrect Answer: \\( 732 \\)\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: Convert from years to days\nSubject: Time\nQuestion: \\( 2 \\) leap years \\( =\\square \\) days\nIncorrect Answer: \\( 730 \\)\nCorrect Answer: \\( 732 \\)\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: Divide decimals by 1000\nSubject: Place Value\nQuestion: What is the value of:\n\\[\n23.04 \\div 1000\n\\]\nIncorrect Answer: \\( 0.2304 \\)\nCorrect Answer: \\( 0.02304 \\)\n",
"role": "user"
},
{
"content": "When dividing involving a power of 10, gives an answer 10 times bigger than it should be",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide decimals by 1000\nSubject: Place Value\nQuestion: What is the value of:\n\\[\n23.04 \\div 1000\n\\]\nIncorrect Answer: \\( 0.0002304 \\)\nCorrect Answer: \\( 0.02304 \\)\n",
"role": "user"
},
{
"content": "When dividing a decimal by a power of 10 adds zeroes to start of the number ignoring the placement of the initial 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: Divide decimals by 1000\nSubject: Place Value\nQuestion: What is the value of:\n\\[\n23.04 \\div 1000\n\\]\nIncorrect Answer: \\( 0.002304 \\)\nCorrect Answer: \\( 0.02304 \\)\n",
"role": "user"
},
{
"content": "When dividing involving a power of 10, gives an answer 10 times smaller than it should be",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Multiply 3 digit integers by 1 digit integers using the grid method\nSubject: Mental Multiplication and Division\nQuestion: \\( 427 \\times 6= \\)\nIncorrect Answer: \\( 240+120+42 \\)\nCorrect Answer: \\( 2400+120+42 \\)\n",
"role": "user"
},
{
"content": "When multiplying multiples of ten and the answer requires an extra digit, leaves off that extra digit",
"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 answer shows the following calculation using the correct algebraic convention?\n\\(\nb \\div a\n\\)\nIncorrect Answer: \\( a \\div b \\)\nCorrect Answer: \\( \\frac{b}{a} \\)\n",
"role": "user"
},
{
"content": "Believes division 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: Write algebraic expressions with correct algebraic convention\nSubject: Writing Expressions\nQuestion: Which answer shows the following calculation using the correct algebraic convention?\n\\(\nb \\div a\n\\)\nIncorrect Answer: \\( \\frac{a}{b} \\)\nCorrect Answer: \\( \\frac{b}{a} \\)\n",
"role": "user"
},
{
"content": "Believes that a fraction means dividing the denominator by 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: Write algebraic expressions with correct algebraic convention\nSubject: Writing Expressions\nQuestion: Which answer shows the following calculation using the correct algebraic convention?\n\\(\nb \\div a\n\\)\nIncorrect Answer: \\( a b \\)\nCorrect Answer: \\( \\frac{b}{a} \\)\n",
"role": "user"
},
{
"content": "Thinks that we can remove a division symbol and just write the variables next to each other",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify the order of rotational symmetry of a shape\nSubject: Properties of Quadrilaterals\nQuestion: In which region would a rectangle belong? ![Venn diagram with two circles labelled with 'exactly two lines of symmetry' and 'rotational symmetry of order 2'. A is in the only exactly two lines of symmetry region, B is in the intersection, C is in the only rotational symmetry of order 2 region and D is outside the two circles.]()\nIncorrect Answer: A\nCorrect Answer: B\n",
"role": "user"
},
{
"content": "Thinks rectangles have rotational symmetry or order 4",
"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: Properties of Quadrilaterals\nQuestion: In which region would a rectangle belong? ![Venn diagram with two circles labelled with 'exactly two lines of symmetry' and 'rotational symmetry of order 2'. A is in the only exactly two lines of symmetry region, B is in the intersection, C is in the only rotational symmetry of order 2 region and D is outside the two circles.]()\nIncorrect Answer: C\nCorrect Answer: B\n",
"role": "user"
},
{
"content": "Thinks rectangles have line symmetry in the diagonals ",
"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 non-unit fractions when part of a shape\nSubject: Fractions of an Amount\nQuestion: What fraction of the rectangle is shaded? ![A rectangle split into 10 equal parts with 3 parts shaded in yellow]()\nIncorrect Answer: \\( 3 \\)\nCorrect Answer: \\( \\frac{3}{10} \\)\n",
"role": "user"
},
{
"content": "Does not know how to write a fraction - just given an integer answer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify non-unit fractions when part of a shape\nSubject: Fractions of an Amount\nQuestion: What fraction of the rectangle is shaded? ![A rectangle split into 10 equal parts with 3 parts shaded in yellow]()\nIncorrect Answer: \\( \\frac{3}{7} \\)\nCorrect Answer: \\( \\frac{3}{10} \\)\n",
"role": "user"
},
{
"content": "Denominator used for other parts rather than total parts",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Complete missing number mental subtraction problems up to 100\nSubject: Mental Addition and Subtraction\nQuestion: What should replace the star? \\( \\bigstar-37=38 \\)\nIncorrect Answer: \\( 1 \\)\nCorrect Answer: \\( 75 \\)\n",
"role": "user"
},
{
"content": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original 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: Complete missing number mental subtraction problems up to 100\nSubject: Mental Addition and Subtraction\nQuestion: What should replace the star? \\( \\bigstar-37=38 \\)\nIncorrect Answer: \\( -1 \\)\nCorrect Answer: \\( 75 \\)\n",
"role": "user"
},
{
"content": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original 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: Complete missing number mental subtraction problems up to 100\nSubject: Mental Addition and Subtraction\nQuestion: What should replace the star? \\( \\bigstar-37=38 \\)\nIncorrect Answer: \\( 65 \\)\nCorrect Answer: \\( 75 \\)\n",
"role": "user"
},
{
"content": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit",
"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 written scenarios as ratios\nSubject: Writing Ratios\nQuestion: For every \\( 5 \\) marbles Karen has, Marty has three times as many.\n\nWrite the number of marbles Karen and Marty have as a ratio, with Karen's part first.\nIncorrect Answer: None of these\nCorrect Answer: \\( 1: 3 \\)\n",
"role": "user"
},
{
"content": "Does not realise ratio in worded problem can be simplified",
"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 questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio\nSubject: Right-angled Triangles (SOHCAHTOA)\nQuestion: Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]()\nIncorrect Answer: \\( \\operatorname{Sin} \\)\nCorrect Answer: Tan\n",
"role": "user"
},
{
"content": "Uses sin when tan is required",
"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 questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio\nSubject: Right-angled Triangles (SOHCAHTOA)\nQuestion: Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]()\nIncorrect Answer: Cos\nCorrect Answer: Tan\n",
"role": "user"
},
{
"content": "Uses cos when tan is required",
"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 questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio\nSubject: Right-angled Triangles (SOHCAHTOA)\nQuestion: Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]()\nIncorrect Answer: None of these\nCorrect Answer: Tan\n",
"role": "user"
},
{
"content": "Does not understand how to apply sohcahtoa",
"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 a linear inequality with a single tail on a numberline\nSubject: Inequalities on Number Lines\nQuestion: Which of the following diagrams represents \\( x>-1 \\) ?\nIncorrect Answer: ![Image of a number line. At -1 there is an open, unfilled circle drawn, with a arrow pointing to the left, towards the negative numbers in the number line.]()\nCorrect Answer: ![Image of a number line. At -1 there is an open, unfilled circle drawn, with a arrow pointing to the right, towards the higher positive numbers in the number line.]()\n",
"role": "user"
},
{
"content": "Mixes up greater than and less than symbols",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Represent a linear inequality with a single tail on a numberline\nSubject: Inequalities on Number Lines\nQuestion: Which of the following diagrams represents \\( x>-1 \\) ?\nIncorrect Answer: ![Image of a number line. At -1 there is a red, filled circle drawn, with a arrow pointing to the right, towards the higher positive numbers in the number line.]()\nCorrect Answer: ![Image of a number line. At -1 there is an open, unfilled circle drawn, with a arrow pointing to the right, towards the higher positive numbers in the number line.]()\n",
"role": "user"
},
{
"content": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning.",
"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 percentage of an amount mentally where the percent is greater than 100\nSubject: Percentages of an Amount\nQuestion: \\( 130 \\% \\) of \\( 40= \\)\nIncorrect Answer: \\( 12 \\)\nCorrect Answer: \\( 52 \\)\n",
"role": "user"
},
{
"content": "Found the percentage but forgot to add to 100%",
"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 percentage of an amount mentally where the percent is greater than 100\nSubject: Percentages of an Amount\nQuestion: \\( 130 \\% \\) of \\( 40= \\)\nIncorrect Answer: \\( 170 \\)\nCorrect Answer: \\( 52 \\)\n",
"role": "user"
},
{
"content": "Added the values together instead of finding the percentage",
"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 percentage of an amount mentally where the percent is greater than 100\nSubject: Percentages of an Amount\nQuestion: \\( 130 \\% \\) of \\( 40= \\)\nIncorrect Answer: Impossible as you cannot have a percentage greater than \\( 100 \\)\nCorrect Answer: \\( 52 \\)\n",
"role": "user"
},
{
"content": "Does not understand that you can have percentages greater than 100%",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify fractions that simplify to a unit fraction\nSubject: Converting Mixed Number and Improper Fractions\nQuestion: Write the following fraction in its simplest form: \\( 3 \\frac{7}{21} \\)\nIncorrect Answer: \\( 1 \\frac{1}{3} \\)\nCorrect Answer: \\( 3 \\frac{1}{3} \\)\n",
"role": "user"
},
{
"content": "Simplifies integers when simplifying a mixed number",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify fractions that simplify to a unit fraction\nSubject: Converting Mixed Number and Improper Fractions\nQuestion: Write the following fraction in its simplest form: \\( 3 \\frac{7}{21} \\)\nIncorrect Answer: Cannot be simplified\nCorrect Answer: \\( 3 \\frac{1}{3} \\)\n",
"role": "user"
},
{
"content": "Believes mixed numbers cannot be simplified",
"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 a fraction on a scale where the required number is marked by a dash between two numbers\nSubject: Ordering Fractions\nQuestion: What fraction should replace the star? ![A number line marked with 1/4, 2/4, 3/4, 4/4, 5/4. The star is halfway between 2/4 and 3/4.]()\nIncorrect Answer: None of these\nCorrect Answer: \\( \\frac{5}{8} \\)\n",
"role": "user"
},
{
"content": "Does not realise you can use equivalent fractions to break fractions up into smaller divisions",
"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 mean from a frequency table\nSubject: Averages and Range from Frequency Table\nQuestion: This table shows the number of pets a group of students owns.\nIf calculating the mean number of pets owned, what would replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Number of pets & Frequency & \\\\\n\\hline \\( 0 \\) & \\( 9 \\) & \\\\\n\\hline \\( 1 \\) & \\( 5 \\) & \\\\\n\\hline \\( 2 \\) & \\( 4 \\) & \\( \\color{gold}\\bigstar \\)\n\\hline \\( 3 \\) & \\( 2 \\) & \\\\\n\\hline \\( 4 \\) & \\( 3 \\) & \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 2+4=6 \\)\nCorrect Answer: \\( 2 \\times 4=8 \\)\n",
"role": "user"
},
{
"content": "Believes the fx column for calculating mean is value + frequency",
"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 mean from a frequency table\nSubject: Averages and Range from Frequency Table\nQuestion: This table shows the number of pets a group of students owns.\nIf calculating the mean number of pets owned, what would replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Number of pets & Frequency & \\\\\n\\hline \\( 0 \\) & \\( 9 \\) & \\\\\n\\hline \\( 1 \\) & \\( 5 \\) & \\\\\n\\hline \\( 2 \\) & \\( 4 \\) & \\( \\color{gold}\\bigstar \\)\n\\hline \\( 3 \\) & \\( 2 \\) & \\\\\n\\hline \\( 4 \\) & \\( 3 \\) & \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 2-4=(-2) \\)\nCorrect Answer: \\( 2 \\times 4=8 \\)\n",
"role": "user"
},
{
"content": "Believes the fx column for calculating mean is value - frequency",
"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 mean from a frequency table\nSubject: Averages and Range from Frequency Table\nQuestion: This table shows the number of pets a group of students owns.\nIf calculating the mean number of pets owned, what would replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Number of pets & Frequency & \\\\\n\\hline \\( 0 \\) & \\( 9 \\) & \\\\\n\\hline \\( 1 \\) & \\( 5 \\) & \\\\\n\\hline \\( 2 \\) & \\( 4 \\) & \\( \\color{gold}\\bigstar \\)\n\\hline \\( 3 \\) & \\( 2 \\) & \\\\\n\\hline \\( 4 \\) & \\( 3 \\) & \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 2 \\div 4=0.5 \\)\nCorrect Answer: \\( 2 \\times 4=8 \\)\n",
"role": "user"
},
{
"content": "Believes the fx column for calculating mean is value/frequency",
"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 integers up to 4 digits using a written method where carrying is needed\nSubject: Written Subtraction\nQuestion: What number should replace the star? \\begin{tabular}{cccc}\n\\(\\space\\) & \\( 9 \\) & \\( 3 \\) & \\( 5 \\) & \\( 2 \\) \\\\\n\\(-\\) & \\(4\\) & \\(5\\) & \\(7\\) & \\(\\bigstar\\)\\\\\n\\(\\space\\) & \\(4\\) & \\(7\\) & \\(7\\) & \\(3\\)\\\\\n\\end{tabular}\nIncorrect Answer: \\( 1 \\)\nCorrect Answer: \\( 9 \\)\n",
"role": "user"
},
{
"content": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original 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: Subtract integers up to 4 digits using a written method where carrying is needed\nSubject: Written Subtraction\nQuestion: What number should replace the star? \\begin{tabular}{cccc}\n\\(\\space\\) & \\( 9 \\) & \\( 3 \\) & \\( 5 \\) & \\( 2 \\) \\\\\n\\(-\\) & \\(4\\) & \\(5\\) & \\(7\\) & \\(\\bigstar\\)\\\\\n\\(\\space\\) & \\(4\\) & \\(7\\) & \\(7\\) & \\(3\\)\\\\\n\\end{tabular}\nIncorrect Answer: \\( 5 \\)\nCorrect Answer: \\( 9 \\)\n",
"role": "user"
},
{
"content": "Confuses the part and the whole in missing number subtraction problems",
"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 integers up to 4 digits using a written method where carrying is needed\nSubject: Written Subtraction\nQuestion: What number should replace the star? \\begin{tabular}{cccc}\n\\(\\space\\) & \\( 9 \\) & \\( 3 \\) & \\( 5 \\) & \\( 2 \\) \\\\\n\\(-\\) & \\(4\\) & \\(5\\) & \\(7\\) & \\(\\bigstar\\)\\\\\n\\(\\space\\) & \\(4\\) & \\(7\\) & \\(7\\) & \\(3\\)\\\\\n\\end{tabular}\nIncorrect Answer: It is not possible\nCorrect Answer: \\( 9 \\)\n",
"role": "user"
},
{
"content": "Does not realise we can borrow from the preceding digit in a subtraction problem",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve one-step linear equations requiring multiplication or division, involving positive decimals\nSubject: Linear Equations\nQuestion: Solve the equation:\n\\[\n0.45=0.3 p\n\\]\nIncorrect Answer: \\( p=\\frac{2}{3} \\)\nCorrect Answer: \\( p=1.5 \\)\n",
"role": "user"
},
{
"content": "Believes division 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: Solve one-step linear equations requiring multiplication or division, involving positive decimals\nSubject: Linear Equations\nQuestion: Solve the equation:\n\\[\n0.45=0.3 p\n\\]\nIncorrect Answer: \\( p=0.135 \\)\nCorrect Answer: \\( p=1.5 \\)\n",
"role": "user"
},
{
"content": "When solving an equation, multiplies instead of dividing ",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic equations using the quadratic formula where the coefficient of x² is 1 \nSubject: Quadratic Equations\nQuestion: Vera wants to solve this equation using the quadratic formula.\n\\(\nh^{2}+4=5 h\n\\)\n\nWhat should replace the triangle? ![The image shows the structure of the quadratic formula. It says plus or minus the square root, and the triangle is the first thing after the square root sign, with a minus sign after it.]()\nIncorrect Answer: \\( -10 \\)\nCorrect Answer: \\( 25 \\)\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: Solve quadratic equations using the quadratic formula where the coefficient of x² is 1 \nSubject: Quadratic Equations\nQuestion: Vera wants to solve this equation using the quadratic formula.\n\\(\nh^{2}+4=5 h\n\\)\n\nWhat should replace the triangle? ![The image shows the structure of the quadratic formula. It says plus or minus the square root, and the triangle is the first thing after the square root sign, with a minus sign after it.]()\nIncorrect Answer: \\( 16 \\)\nCorrect Answer: \\( 25 \\)\n",
"role": "user"
},
{
"content": "When using the formula to solve a quadratic equation, believes that a, b and c are always taken from the 1st, 2nd and 3rd terms, respectively, of the quadratic. ",
"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: \\( 4.72-3.1 \\) What should replace the star?\nIncorrect Answer: \\( 4.41 \\)\nCorrect Answer: \\( 1.62 \\)\n",
"role": "user"
},
{
"content": "Hasn't lined up the place value columns when writing out the calculation",
"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: \\( 4.72-3.1 \\) What should replace the star?\nIncorrect Answer: \\( 1.71 \\)\nCorrect Answer: \\( 1.62 \\)\n",
"role": "user"
},
{
"content": "Hasn't lined up the place value columns when writing out the calculation",
"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: \\( 4.72-3.1 \\) What should replace the star?\nIncorrect Answer: \\( 7.82 \\)\nCorrect Answer: \\( 1.62 \\)\n",
"role": "user"
},
{
"content": "Adds instead of subtracts",
"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 root of a number\nSubject: Square Roots, Cube Roots, etc\nQuestion: What is the square root of nine?\nIncorrect Answer: \\( 4.5 \\)\nCorrect Answer: \\( 3 \\)\n",
"role": "user"
},
{
"content": "Halves when asked to find the square root",
"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 root of a number\nSubject: Square Roots, Cube Roots, etc\nQuestion: What is the square root of nine?\nIncorrect Answer: \\( 81 \\)\nCorrect Answer: \\( 3 \\)\n",
"role": "user"
},
{
"content": "Squares when asked to find the square root",
"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 root of a number\nSubject: Square Roots, Cube Roots, etc\nQuestion: What is the square root of nine?\nIncorrect Answer: \\( 18 \\)\nCorrect Answer: \\( 3 \\)\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: Solve quadratic equations using completing the square in the form (x + q)² + r \nSubject: Quadratic Equations\nQuestion: One of these equations has no real solutions\nWhich is it?\nIncorrect Answer: \\( (w-4)^{2}=0 \\)\nCorrect Answer: \\( (w-4)^{2}+16=0 \\)\n",
"role": "user"
},
{
"content": "Believes 0 has no square root",
"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: Compare relative frequencies in order to determine which prediction is likely to be more reliable\nSubject: Experimental Probability and Relative Frequency\nQuestion: A vegetarian restaurant wants to know people's eating habits\n\\( 50 \\) people in Town \\( A \\) are asked if they eat meat. \\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{ Town A } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 39 \\) \\\\\n\\hline No & \\( 11 \\) \\\\\n\\hline\n\\end{tabular} \\( 200 \\) people in Town B are asked if they eat meat. \\begin{tabular}{|cc|}\n\\hline \\multicolumn{2}{|c|}{ Town B } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 143 \\) \\\\\n\\hline No & \\( 57 \\) \\\\\n\\hline\n\\end{tabular} Which results are more reliable?\nIncorrect Answer: Town A\nCorrect Answer: Town B\n",
"role": "user"
},
{
"content": "Does not know that sample size affects reliability",
"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: Compare relative frequencies in order to determine which prediction is likely to be more reliable\nSubject: Experimental Probability and Relative Frequency\nQuestion: A vegetarian restaurant wants to know people's eating habits\n\\( 50 \\) people in Town \\( A \\) are asked if they eat meat. \\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{ Town A } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 39 \\) \\\\\n\\hline No & \\( 11 \\) \\\\\n\\hline\n\\end{tabular} \\( 200 \\) people in Town B are asked if they eat meat. \\begin{tabular}{|cc|}\n\\hline \\multicolumn{2}{|c|}{ Town B } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 143 \\) \\\\\n\\hline No & \\( 57 \\) \\\\\n\\hline\n\\end{tabular} Which results are more reliable?\nIncorrect Answer: They are the same\nCorrect Answer: Town B\n",
"role": "user"
},
{
"content": "Does not know that sample size affects reliability",
"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: Compare relative frequencies in order to determine which prediction is likely to be more reliable\nSubject: Experimental Probability and Relative Frequency\nQuestion: A vegetarian restaurant wants to know people's eating habits\n\\( 50 \\) people in Town \\( A \\) are asked if they eat meat. \\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{ Town A } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 39 \\) \\\\\n\\hline No & \\( 11 \\) \\\\\n\\hline\n\\end{tabular} \\( 200 \\) people in Town B are asked if they eat meat. \\begin{tabular}{|cc|}\n\\hline \\multicolumn{2}{|c|}{ Town B } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 143 \\) \\\\\n\\hline No & \\( 57 \\) \\\\\n\\hline\n\\end{tabular} Which results are more reliable?\nIncorrect Answer: Impossible to say\nCorrect Answer: Town B\n",
"role": "user"
},
{
"content": "Does not know that sample size affects reliability",
"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 percentage of an amount using a calculator where the percent is an integer\nSubject: Percentages of an Amount\nQuestion: What should replace the star? ![A percentage number line representing the value 630 with a star above the 84% mark]() Use your calculator, if needed, and give your answer to \\( 1 \\) decimal place.\nIncorrect Answer: \\( 750 \\)\nCorrect Answer: \\( 529.2 \\)\n",
"role": "user"
},
{
"content": "Thinks when finding a percentage you divide by the percentage being asked",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Interpret continuous data using a line graph\nSubject: Time Series and Line Graphs\nQuestion: ![A line graph with title \"Height of rocket\". \nThe x-axis is titled \"Time in seconds\" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.\nThe y-axis is titled \"Height in metres\" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).\n]() How many metres did the rocket travel between \\( 20 \\) and \\( 50 \\) seconds?\nIncorrect Answer: \\( 85 \\)\nCorrect Answer: \\( 25 \\)\n",
"role": "user"
},
{
"content": "Adds instead of subtracts when asked to find the difference",
"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 continuous data using a line graph\nSubject: Time Series and Line Graphs\nQuestion: ![A line graph with title \"Height of rocket\". \nThe x-axis is titled \"Time in seconds\" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.\nThe y-axis is titled \"Height in metres\" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).\n]() How many metres did the rocket travel between \\( 20 \\) and \\( 50 \\) seconds?\nIncorrect Answer: \\( 30 \\)\nCorrect Answer: \\( 25 \\)\n",
"role": "user"
},
{
"content": "When finding the difference between two points on a time series graph, only uses one of the points. ",
"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 continuous data using a line graph\nSubject: Time Series and Line Graphs\nQuestion: ![A line graph with title \"Height of rocket\". \nThe x-axis is titled \"Time in seconds\" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.\nThe y-axis is titled \"Height in metres\" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).\n]() How many metres did the rocket travel between \\( 20 \\) and \\( 50 \\) seconds?\nIncorrect Answer: \\( 55 \\)\nCorrect Answer: \\( 25 \\)\n",
"role": "user"
},
{
"content": "When finding the difference between two points on a time series graph, only uses one of the points. ",
"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 the equation of the axes\nSubject: Horizontal and Vertical Lines\nQuestion: What is the equation of the \\( y \\) axis?\nIncorrect Answer: \\( y=1 \\)\nCorrect Answer: \\( x=0 \\)\n",
"role": "user"
},
{
"content": "Thinks y =1 is the y axis",
"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 the equation of the axes\nSubject: Horizontal and Vertical Lines\nQuestion: What is the equation of the \\( y \\) axis?\nIncorrect Answer: \\( y=0 \\)\nCorrect Answer: \\( x=0 \\)\n",
"role": "user"
},
{
"content": "Confuses the equations of vertical and horizontal lines",
"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 the equation of the axes\nSubject: Horizontal and Vertical Lines\nQuestion: What is the equation of the \\( y \\) axis?\nIncorrect Answer: \\( y=x \\)\nCorrect Answer: \\( x=0 \\)\n",
"role": "user"
},
{
"content": "Thinks x = y is an axis",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round integers to the nearest 1000\nSubject: Rounding to the Nearest Whole (10, 100, etc)\nQuestion: What is \\( 326 \\) rounded to the nearest \\( 1000 \\) ?\nIncorrect Answer: \\( 1000 \\)\nCorrect Answer: \\( 0 \\)\n",
"role": "user"
},
{
"content": "Rounds up instead of down",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round integers to the nearest 1000\nSubject: Rounding to the Nearest Whole (10, 100, etc)\nQuestion: What is \\( 326 \\) rounded to the nearest \\( 1000 \\) ?\nIncorrect Answer: \\( 500 \\)\nCorrect Answer: \\( 0 \\)\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: Solve quadratic equations using balancing\nSubject: Quadratic Equations\nQuestion: One of these equations has no real solutions.\nWhich is it?\nIncorrect Answer: \\( t^{2}-45=-45 \\)\nCorrect Answer: \\( t^{2}=-45 \\)\n",
"role": "user"
},
{
"content": "Believes 0 is not a real solution to 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: Solve quadratic equations using balancing\nSubject: Quadratic Equations\nQuestion: One of these equations has no real solutions.\nWhich is it?\nIncorrect Answer: \\( t^{3}=-45 \\)\nCorrect Answer: \\( t^{2}=-45 \\)\n",
"role": "user"
},
{
"content": "Believes a number raised to a power will always give 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: Select the correct answer to an iteration question to the required degree of accuracy\nSubject: Trial and Improvement and Iterative Methods\nQuestion: The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nTo find the value of \\( x \\), Sally uses:\n\\(x_{n+1}=\\frac{8}{9}-\\frac{x^{3}{ }_{n}}{9}\\)\n\nIf \\( x_{0}=0 \\), what is the value of \\( x \\) to \\( 3 \\) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]()\nIncorrect Answer: \\( 0.830 \\)\nCorrect Answer: \\( 0.826 \\)\n",
"role": "user"
},
{
"content": "Stops iteration too early when solving equations",
"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: Select the correct answer to an iteration question to the required degree of accuracy\nSubject: Trial and Improvement and Iterative Methods\nQuestion: The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nTo find the value of \\( x \\), Sally uses:\n\\(x_{n+1}=\\frac{8}{9}-\\frac{x^{3}{ }_{n}}{9}\\)\n\nIf \\( x_{0}=0 \\), what is the value of \\( x \\) to \\( 3 \\) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]()\nIncorrect Answer: \\( 0.825 \\)\nCorrect Answer: \\( 0.826 \\)\n",
"role": "user"
},
{
"content": "Stops iteration too early when solving equations",
"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: Select the correct answer to an iteration question to the required degree of accuracy\nSubject: Trial and Improvement and Iterative Methods\nQuestion: The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nTo find the value of \\( x \\), Sally uses:\n\\(x_{n+1}=\\frac{8}{9}-\\frac{x^{3}{ }_{n}}{9}\\)\n\nIf \\( x_{0}=0 \\), what is the value of \\( x \\) to \\( 3 \\) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]()\nIncorrect Answer: \\( 0.8101 \\)\nCorrect Answer: \\( 0.826 \\)\n",
"role": "user"
},
{
"content": "Stops iteration too early when solving equations",
"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: Recall and use the intersecting diagonals properties of a rectangle\nSubject: Properties of Quadrilaterals\nQuestion: The diagonals of a rectangle with different length sides \\(_____________\\) intersect at right-angles ![A rectangle]()\nIncorrect Answer: always\nCorrect Answer: never\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: Recall and use the intersecting diagonals properties of a rectangle\nSubject: Properties of Quadrilaterals\nQuestion: The diagonals of a rectangle with different length sides \\(_____________\\) intersect at right-angles ![A rectangle]()\nIncorrect Answer: sometimes\nCorrect Answer: never\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: Recall and use the intersecting diagonals properties of a rectangle\nSubject: Properties of Quadrilaterals\nQuestion: The diagonals of a rectangle with different length sides \\(_____________\\) intersect at right-angles ![A rectangle]()\nIncorrect Answer: I don't know\nCorrect Answer: never\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: Identify perpendicular lines written in the form y = mx + c\nSubject: Perpendicular Lines\nQuestion: Which of the following lines is perpendicular to\n\\[\ny=3 x-2 ?\n\\]\nIncorrect Answer: \\( y=\\frac{1}{3} x+1 \\)\nCorrect Answer: \\( y=5-\\frac{1}{3} x \\)\n",
"role": "user"
},
{
"content": "Believes the gradients of perpendicular lines are reciprocals of the same sign",
"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 perpendicular lines written in the form y = mx + c\nSubject: Perpendicular Lines\nQuestion: Which of the following lines is perpendicular to\n\\[\ny=3 x-2 ?\n\\]\nIncorrect Answer: \\( y=3 x+7 \\)\nCorrect Answer: \\( y=5-\\frac{1}{3} x \\)\n",
"role": "user"
},
{
"content": "Confuses the meaning of parallel and 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: Given the area of a parallelogram, calculate a missing dimension\nSubject: Area of Simple Shapes\nQuestion: The area of this parallelogram is \\( 24 \\mathrm{~cm}^{2} \\)\n\nWhat measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]()\nIncorrect Answer: \\( 2 \\mathrm{~cm} \\)\nCorrect Answer: \\( 4 \\mathrm{~cm} \\)\n",
"role": "user"
},
{
"content": "When finding a missing side of a parallelogram given the area completes an extra step of 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: Given the area of a parallelogram, calculate a missing dimension\nSubject: Area of Simple Shapes\nQuestion: The area of this parallelogram is \\( 24 \\mathrm{~cm}^{2} \\)\n\nWhat measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]()\nIncorrect Answer: \\( 8 \\mathrm{~cm} \\)\nCorrect Answer: \\( 4 \\mathrm{~cm} \\)\n",
"role": "user"
},
{
"content": "When finding the area of a parallelogram finds base x perpendicular height but divides the answer 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: Given the area of a parallelogram, calculate a missing dimension\nSubject: Area of Simple Shapes\nQuestion: The area of this parallelogram is \\( 24 \\mathrm{~cm}^{2} \\)\n\nWhat measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]()\nIncorrect Answer: Not enough information\nCorrect Answer: \\( 4 \\mathrm{~cm} \\)\n",
"role": "user"
},
{
"content": "Does not realise we can find a missing length if we know the base of a parallelogram and its area. ",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic inequalities from the graph of the quadratic\nSubject: Solving Quadratic Inequalities\nQuestion: Using the graph of\n\\(\ny=x^{2}-x-6\n\\)\n\nWhat is the correct way to write the solution to\n\\(\ny=x^{2}-x-6 \\geq 0 ?\n\\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]()\nIncorrect Answer: \\( \\{-2 \\leq x \\leq 3\\} \\)\nCorrect Answer: \\( \\{x \\leq-2\\} \\cup\\{x \\geq 3\\} \\)\n",
"role": "user"
},
{
"content": "Believes the solution of a quadratic inequality is always the interval between the roots",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic inequalities from the graph of the quadratic\nSubject: Solving Quadratic Inequalities\nQuestion: Using the graph of\n\\(\ny=x^{2}-x-6\n\\)\n\nWhat is the correct way to write the solution to\n\\(\ny=x^{2}-x-6 \\geq 0 ?\n\\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]()\nIncorrect Answer: \\( \\{-2 \\geq x \\geq 3\\} \\)\nCorrect Answer: \\( \\{x \\leq-2\\} \\cup\\{x \\geq 3\\} \\)\n",
"role": "user"
},
{
"content": "Believes any two inequalities can be combined into a double inequality",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve quadratic inequalities from the graph of the quadratic\nSubject: Solving Quadratic Inequalities\nQuestion: Using the graph of\n\\(\ny=x^{2}-x-6\n\\)\n\nWhat is the correct way to write the solution to\n\\(\ny=x^{2}-x-6 \\geq 0 ?\n\\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]()\nIncorrect Answer: \\( \\{x \\geq-2\\} \\cup\\{x \\leq 3\\} \\)\nCorrect Answer: \\( \\{x \\leq-2\\} \\cup\\{x \\geq 3\\} \\)\n",
"role": "user"
},
{
"content": "Mixes up greater than and less than symbols",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Fill in regions of a double Venn diagram with numbers from given information\nSubject: Venn Diagrams\nQuestion: In which region would \\( \\mathbf{1 5} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()\nIncorrect Answer: A\nCorrect Answer: C\n",
"role": "user"
},
{
"content": "Does not know what a square number is",
"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: Fill in regions of a double Venn diagram with numbers from given information\nSubject: Venn Diagrams\nQuestion: In which region would \\( \\mathbf{1 5} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()\nIncorrect Answer: B\nCorrect Answer: C\n",
"role": "user"
},
{
"content": "Does not know what a square number is",
"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: Fill in regions of a double Venn diagram with numbers from given information\nSubject: Venn Diagrams\nQuestion: In which region would \\( \\mathbf{1 5} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()\nIncorrect Answer: D\nCorrect Answer: C\n",
"role": "user"
},
{
"content": "Mixes up odd and even numbers",
"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: Order integers with a different number of digits\nSubject: Place Value\nQuestion: Which of these options show the numbers\n650,312 \n3,506,212\n3,652\n605,321\nin order from smallest to largest?\nIncorrect Answer: \\( \\begin{array}{l}3,506,212 \\\\ 3,652 \\\\ 605,321 \\\\ 650,312\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{l}3,652 \\\\ 605,321 \\\\ 650,312 \\\\ 3,506,212\\end{array} \\)\n",
"role": "user"
},
{
"content": "Orders integers based on first digits without taking into account place value",
"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: Order integers with a different number of digits\nSubject: Place Value\nQuestion: Which of these options show the numbers\n650,312 \n3,506,212\n3,652\n605,321\nin order from smallest to largest?\nIncorrect Answer: \\( \\begin{array}{l}605,321 \\\\ 3,506,212 \\\\ 650,312 \\\\ 3,652\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{l}3,652 \\\\ 605,321 \\\\ 650,312 \\\\ 3,506,212\\end{array} \\)\n",
"role": "user"
},
{
"content": "When ordering integers, orders from the digits at the end of the number instead of the digits at the start",
"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 inequality notation\nSubject: Inequalities on Number Lines\nQuestion: Which of the following shows \" \\( x \\) is greater than \\( 9 \\) \"?\nIncorrect Answer: \\( x<9 \\)\nCorrect Answer: \\( x>9 \\)\n",
"role": "user"
},
{
"content": "Mixes up greater than and less than symbols",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Understand inequality notation\nSubject: Inequalities on Number Lines\nQuestion: Which of the following shows \" \\( x \\) is greater than \\( 9 \\) \"?\nIncorrect Answer: \\( x \\geq 9 \\)\nCorrect Answer: \\( x>9 \\)\n",
"role": "user"
},
{
"content": "When using inequality notation, thinks \"greater than/less than or equal to\" symbols are instead the \"greater than/less than\" symbols and vice versa",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round numbers greater than 1 to one significant figure\nSubject: Rounding to Significant Figures\nQuestion: Round this number to \\( 1 \\) significant figure:\n\\( 400099 \\)\nIncorrect Answer: \\( 500000 \\)\nCorrect Answer: \\( 400000 \\)\n",
"role": "user"
},
{
"content": "Rounds up instead of down",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round numbers greater than 1 to one significant figure\nSubject: Rounding to Significant Figures\nQuestion: Round this number to \\( 1 \\) significant figure:\n\\( 400099 \\)\nIncorrect Answer: \\( 400100 \\)\nCorrect Answer: \\( 400000 \\)\n",
"role": "user"
},
{
"content": "Rounded to nearest 100 instead of 1sf",
"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 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: \\( y=3 x \\)\nCorrect Answer: \\( y=3 \\)\n",
"role": "user"
},
{
"content": "Includes the x variable when giving the equation of a horizontal line",
"role": "assistant"
}
] |