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: Round numbers greater than 1 to two significant figures\nSubject: Rounding to Significant Figures\nQuestion: \\(\n180.5672\n\\)\n\nWhat is the second significant figure in the number above?\nIncorrect Answer: \\( 2 \\)\nCorrect Answer: \\( 8 \\)\n",
"role": "user"
},
{
"content": "Does not understand the first significant value is the first non-zero digit 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: Round numbers greater than 1 to two significant figures\nSubject: Rounding to Significant Figures\nQuestion: \\(\n180.5672\n\\)\n\nWhat is the second significant figure in the number above?\nIncorrect Answer: \\( 6 \\)\nCorrect Answer: \\( 8 \\)\n",
"role": "user"
},
{
"content": "Identifies second decimal place value when asked for the second significant figure",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Recognise whether you need to add or subtract linear equations in order to eliminate a variable\nSubject: Simultaneous Equations\nQuestion: What do you need to do to eliminate the \\( q \\)s in each of these pairs of simultaneous equations?\n\\begin{array}{cc}\n Pair 1 & Pair 2 \\\\\n\\( 2p-4q=6 \\) & \\( 2p-4q=6 \\)\\\\\n\\( 7p+4q=9 \\) & \\( 7p-4q=9 \\)\n\\end{array}\n\nIncorrect Answer: Add Pair \\( 1 \\)\nAdd Pair \\( 2 \\)\nCorrect Answer: Add Pair \\( 1 \\)\nSubtract Pair \\( 2 \\)\n",
"role": "user"
},
{
"content": "Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the 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: Recognise whether you need to add or subtract linear equations in order to eliminate a variable\nSubject: Simultaneous Equations\nQuestion: What do you need to do to eliminate the \\( q \\)s in each of these pairs of simultaneous equations?\n\\begin{array}{cc}\n Pair 1 & Pair 2 \\\\\n\\( 2p-4q=6 \\) & \\( 2p-4q=6 \\)\\\\\n\\( 7p+4q=9 \\) & \\( 7p-4q=9 \\)\n\\end{array}\n\nIncorrect Answer: Subtract Pair \\( 1 \\)\nSubtract Pair \\( 2 \\)\nCorrect Answer: Add Pair \\( 1 \\)\nSubtract Pair \\( 2 \\)\n",
"role": "user"
},
{
"content": "Believes that when eliminating a variable, regardless of the signs of the terms with matching coefficients, we subtract the 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: Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis\nSubject: Sketching from Factorised Form\nQuestion: \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis?\nIncorrect Answer: \\( (3,5) \\)\nCorrect Answer: \\( \\begin{array}{c}(3,0) \\\\ \\text { and } \\\\ (5,0)\\end{array} \\)\n",
"role": "user"
},
{
"content": "Believes both the x and y co-ordinates of the x-intercept of a quadratic are derived from the constants in the factorised form.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis\nSubject: Sketching from Factorised Form\nQuestion: \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis?\nIncorrect Answer: \\( \\begin{array}{c}(-3,0) \\\\ \\text { and } \\\\ (-5,0)\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}(3,0) \\\\ \\text { and } \\\\ (5,0)\\end{array} \\)\n",
"role": "user"
},
{
"content": "Believes the solutions of a quadratic equation are the constants in the factorised form",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis\nSubject: Sketching from Factorised Form\nQuestion: \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis?\nIncorrect Answer: \\( \\begin{array}{c}(3,5) \\\\ \\text { and } \\\\ (-3,-5)\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}(3,0) \\\\ \\text { and } \\\\ (5,0)\\end{array} \\)\n",
"role": "user"
},
{
"content": "Believes both the x and y co-ordinates of the x-intercept of a quadratic are derived from the constants in the factorised form.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Find missing angles using angles on a straight line\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]()\nIncorrect Answer: \\( 46^{\\circ} \\)\nCorrect Answer: \\( 19^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Confuses vertically opposite angles with angles on a straight 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: Find missing angles using angles on a straight line\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]()\nIncorrect Answer: \\( 65^{\\circ} \\)\nCorrect Answer: \\( 19^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Misinterprets the meaning of angles on a straight line angle fact",
"role": "assistant"
}
] |
[
{
"content": "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 missing angles using angles on a straight line\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]()\nIncorrect Answer: Not enough information\nCorrect Answer: \\( 19^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Does not know that angles on a straight line sum to 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: Calculate the mean as an average from a list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\]\nIncorrect Answer: \\( 0+1+3+4+7 \\div 5 \\)\nCorrect Answer: \\( \\frac{1+3+4+7}{5} \\)\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: Calculate the mean as an average from a list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\]\nIncorrect Answer: \\( \\frac{1+3+4+7}{4} \\)\nCorrect Answer: \\( \\frac{1+3+4+7}{5} \\)\n",
"role": "user"
},
{
"content": "When asked for the mean of a list of data, does not count any zeros in the data when working out what to divide by",
"role": "assistant"
}
] |
[
{
"content": "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 as an average from a list of data\nSubject: Averages (mean, median, mode) from a List of Data\nQuestion: When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\]\nIncorrect Answer: None of them\nCorrect Answer: \\( \\frac{1+3+4+7}{5} \\)\n",
"role": "user"
},
{
"content": "Does not know how to calculate the mean",
"role": "assistant"
}
] |
[
{
"content": "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 improper fractions to mixed number fractions\nSubject: Converting Mixed Number and Improper Fractions\nQuestion: Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\)\nIncorrect Answer: \\( 1 \\frac{3}{5} \\)\nCorrect Answer: \\( 2 \\frac{3}{5} \\)\n",
"role": "user"
},
{
"content": "Believes when changing an improper fraction to a mixed number you divide the numerator by 10, regardless of 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: Convert from improper fractions to mixed number fractions\nSubject: Converting Mixed Number and Improper Fractions\nQuestion: Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\)\nIncorrect Answer: \\( 3 \\frac{2}{5} \\)\nCorrect Answer: \\( 2 \\frac{3}{5} \\)\n",
"role": "user"
},
{
"content": "Believes the whole and remainder are the other way when changing an improper fraction to 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: Convert from improper fractions to mixed number fractions\nSubject: Converting Mixed Number and Improper Fractions\nQuestion: Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\)\nIncorrect Answer: \\( 13 \\frac{1}{5} \\)\nCorrect Answer: \\( 2 \\frac{3}{5} \\)\n",
"role": "user"
},
{
"content": "Believes the number of wholes in a mixed number multiplies by the fraction part",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use area to write algebraic expressions\nSubject: Expanding Single Brackets\nQuestion: The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]()\nIncorrect Answer: \\( 12 x-2=10 x+2 \\)\nCorrect Answer: \\( 12 x-8=10 x+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: Use area to write algebraic expressions\nSubject: Expanding Single Brackets\nQuestion: The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]()\nIncorrect Answer: \\( 8+6 x-4=4+10 x+4 \\)\nCorrect Answer: \\( 12 x-8=10 x+4 \\)\n",
"role": "user"
},
{
"content": "Calculates perimeter when asked for 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: Use area to write algebraic expressions\nSubject: Expanding Single Brackets\nQuestion: The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]()\nIncorrect Answer: \\( 4+3 x-2=2+5 x+2 \\)\nCorrect Answer: \\( 12 x-8=10 x+4 \\)\n",
"role": "user"
},
{
"content": "Adds when calculating area instead of multiplying",
"role": "assistant"
}
] |
[
{
"content": "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 kilometers to miles\nSubject: Length Units\nQuestion: \\( 3 \\) miles \\( \\approx 5 \\mathrm{~km} \\) \\( 30 \\mathrm{~km} \\approx \\square \\) miles\nIncorrect Answer: \\( 28 \\)\nCorrect Answer: \\( 18 \\)\n",
"role": "user"
},
{
"content": "Added rather than multiplied by a scale factor",
"role": "assistant"
}
] |
[
{
"content": "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 methods for mental multiplication\nSubject: Mental Multiplication and Division\nQuestion: Tom and Katie are discussing mental multiplication strategies.\nTom says \\( 15 \\times 42=154 \\times 2 \\)\nKatie says \\( 15 \\times 42=(15 \\times 4)+(15 \\times 2) \\)\nWho is correct?\nIncorrect Answer: Only Tom\nCorrect Answer: Neither is correct\n",
"role": "user"
},
{
"content": "Does not correctly apply the commutative property of 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 use efficient methods for mental multiplication\nSubject: Mental Multiplication and Division\nQuestion: Tom and Katie are discussing mental multiplication strategies.\nTom says \\( 15 \\times 42=154 \\times 2 \\)\nKatie says \\( 15 \\times 42=(15 \\times 4)+(15 \\times 2) \\)\nWho is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Neither is correct\n",
"role": "user"
},
{
"content": "Does not correctly apply the distributive property of 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: Convert from hours to minutes\nSubject: Time\nQuestion: \\( 3 \\) hours is the same as ___________ minutes\nIncorrect Answer: \\( 90 \\)\nCorrect Answer: \\( 180 \\)\n",
"role": "user"
},
{
"content": "Thinks there are 30 minutes in a hour",
"role": "assistant"
}
] |
[
{
"content": "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 hours to minutes\nSubject: Time\nQuestion: \\( 3 \\) hours is the same as ___________ minutes\nIncorrect Answer: \\( 30 \\)\nCorrect Answer: \\( 180 \\)\n",
"role": "user"
},
{
"content": "Thinks there are 10 minutes in an hour",
"role": "assistant"
}
] |
[
{
"content": "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 hours to minutes\nSubject: Time\nQuestion: \\( 3 \\) hours is the same as ___________ minutes\nIncorrect Answer: \\( 300 \\)\nCorrect Answer: \\( 180 \\)\n",
"role": "user"
},
{
"content": "Answers as if there are 100 minutes in an hour when changing from hours to minutes",
"role": "assistant"
}
] |
[
{
"content": "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 the next term of a descending integer linear sequence\nSubject: Sequences-Others\nQuestion: What is the next term in this sequence?\n\n\n\\[\n18, \\quad 11, \\quad 4, \\quad \\ldots\n\\]\nIncorrect Answer: \\( -7 \\)\nCorrect Answer: \\( -3 \\)\n",
"role": "user"
},
{
"content": "Identifies the term-to-term rule rather than the next 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: Write the next term of a descending integer linear sequence\nSubject: Sequences-Others\nQuestion: What is the next term in this sequence?\n\n\n\\[\n18, \\quad 11, \\quad 4, \\quad \\ldots\n\\]\nIncorrect Answer: Not enough information\nCorrect Answer: \\( -3 \\)\n",
"role": "user"
},
{
"content": "Does not know how to find the next term in a sequence",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Change minutes into decimals of hours (e.g. 90 minutes = 1.5 hours)\nSubject: Time\nQuestion: \\( 90 \\) minutes is the same as _________ hours\nIncorrect Answer: \\( 9 \\)\nCorrect Answer: \\( 1.5 \\)\n",
"role": "user"
},
{
"content": "Thinks there are 10 minutes in an hour",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Change minutes into decimals of hours (e.g. 90 minutes = 1.5 hours)\nSubject: Time\nQuestion: \\( 90 \\) minutes is the same as _________ hours\nIncorrect Answer: \\( 1.3 \\)\nCorrect Answer: \\( 1.5 \\)\n",
"role": "user"
},
{
"content": "Answers as if there are 100 minutes in an hour when writing minutes as decimals",
"role": "assistant"
}
] |
[
{
"content": "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 factors of a number\nSubject: Factors and Highest Common Factor\nQuestion: \\[\n1,2,4,8\n\\]\nThese are the only factors of...\nIncorrect Answer: \\( 16 \\)\nCorrect Answer: \\( 8 \\)\n",
"role": "user"
},
{
"content": "Does not think a number can be a factor of itself",
"role": "assistant"
}
] |
[
{
"content": "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 proper fractions with different denominators which do not share a common factor\nSubject: Adding and Subtracting Fractions\nQuestion: \\(\n\\frac{2}{3}-\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star?\nIncorrect Answer: \\( 19 \\)\nCorrect Answer: \\( 17 \\)\n",
"role": "user"
},
{
"content": "Forgets to change the numerators when finding 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: Subtract proper fractions with different denominators which do not share a common factor\nSubject: Adding and Subtracting Fractions\nQuestion: \\(\n\\frac{2}{3}-\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star?\nIncorrect Answer: \\( 1 \\)\nCorrect Answer: \\( 17 \\)\n",
"role": "user"
},
{
"content": "When subtracting fractions, subtracts the numerators and denominators",
"role": "assistant"
}
] |
[
{
"content": "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 or equal to \\( 6 \\) \"?\nIncorrect Answer: \\( x>6 \\)\nCorrect Answer: \\( x \\geq 6 \\)\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: Understand inequality notation\nSubject: Inequalities on Number Lines\nQuestion: Which of the following shows \" \\( x \\) is greater than or equal to \\( 6 \\) \"?\nIncorrect Answer: \\( x \\leq 6 \\)\nCorrect Answer: \\( x \\geq 6 \\)\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: Calculate the volume of a cone where the dimensions are all given in the same units\nSubject: Volume of Non-Prisms\nQuestion: STEP \\( 2 \\)\n\nJessica is trying to work out the volume of this cone. ![A cone with the slant height labelled 9cm, the perpendicular height labelled h and half the cone's base (forming a right angled triangle with the slant and perpendicular heights) is labelled 6cm.]() First she needs the perpendicular height.\n\nWhich of the following equations is true?\nIncorrect Answer: \\( h^{2}=9^{2}+6^{2} \\)\nCorrect Answer: \\( h^{2}=9^{2}-6^{2} \\)\n",
"role": "user"
},
{
"content": "Does not rearrange the Pythagoras' Theorem formula accurately",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the volume of a cone where the dimensions are all given in the same units\nSubject: Volume of Non-Prisms\nQuestion: STEP \\( 2 \\)\n\nJessica is trying to work out the volume of this cone. ![A cone with the slant height labelled 9cm, the perpendicular height labelled h and half the cone's base (forming a right angled triangle with the slant and perpendicular heights) is labelled 6cm.]() First she needs the perpendicular height.\n\nWhich of the following equations is true?\nIncorrect Answer: \\( h^{2}=12^{2}-9^{2} \\)\nCorrect Answer: \\( h^{2}=9^{2}-6^{2} \\)\n",
"role": "user"
},
{
"content": "When using Pythagoras to find the height of an isosceles triangle, uses the whole base instead of half",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Multiply mixed number fractions in the form: Fraction × Integer\nSubject: Multiplying Fractions\nQuestion: \\(\n1 \\frac{2}{3} \\times 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation?\nIncorrect Answer: \\( 2 \\frac{2}{3} \\)\nCorrect Answer: \\( 3 \\frac{1}{3} \\)\n",
"role": "user"
},
{
"content": "When multiplying mixed numbers, forgets to multiply the fraction",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Multiply mixed number fractions in the form: Fraction × Integer\nSubject: Multiplying Fractions\nQuestion: \\(\n1 \\frac{2}{3} \\times 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation?\nIncorrect Answer: \\( 2 \\frac{4}{6} \\)\nCorrect Answer: \\( 3 \\frac{1}{3} \\)\n",
"role": "user"
},
{
"content": "When multiplying a fraction by an integer, multiplies both 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: Calculate questions involving the power law of indices with positive integer powers\nSubject: Laws of Indices\nQuestion: \\( \\left(5^{4}\\right)^{3}= \\)\nIncorrect Answer: \\( 5^{7} \\)\nCorrect Answer: \\( 5^{12} \\)\n",
"role": "user"
},
{
"content": "Has added the powers rather than multiplying them",
"role": "assistant"
}
] |
[
{
"content": "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 questions involving the power law of indices with positive integer powers\nSubject: Laws of Indices\nQuestion: \\( \\left(5^{4}\\right)^{3}= \\)\nIncorrect Answer: \\( 125^{12} \\)\nCorrect Answer: \\( 5^{12} \\)\n",
"role": "user"
},
{
"content": "Has cubed the base number and the power",
"role": "assistant"
}
] |
[
{
"content": "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 questions involving the power law of indices with positive integer powers\nSubject: Laws of Indices\nQuestion: \\( \\left(5^{4}\\right)^{3}= \\)\nIncorrect Answer: None of these options\nCorrect Answer: \\( 5^{12} \\)\n",
"role": "user"
},
{
"content": "Does not understand laws of indices",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Follow simple directions to translate a shape or object using words not vectors\nSubject: Translation and Vectors\nQuestion: If you translate the star \\( 2 \\) squares left and \\( 3 \\) squares down, which letter do you land on? ![A set of axes: x-axis from 0 to 8, y-axis from 0 to 8. A yellow star is at point (4, 4). Point A is at (6, 1), Point B is at (2, 1), Point C is at (2, 2), Point D is at (1, 2). ]()\nIncorrect Answer: A\nCorrect Answer: B\n",
"role": "user"
},
{
"content": "Confuses left and right",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Follow simple directions to translate a shape or object using words not vectors\nSubject: Translation and Vectors\nQuestion: If you translate the star \\( 2 \\) squares left and \\( 3 \\) squares down, which letter do you land on? ![A set of axes: x-axis from 0 to 8, y-axis from 0 to 8. A yellow star is at point (4, 4). Point A is at (6, 1), Point B is at (2, 1), Point C is at (2, 2), Point D is at (1, 2). ]()\nIncorrect Answer: D\nCorrect Answer: B\n",
"role": "user"
},
{
"content": "Counts the squares rather than the diagonals when reflecting in y=x or y=-x ",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Convert decimals less than 1 with 3 or more decimal place to percentages\nSubject: Converting between Decimals and Percentages\nQuestion: How do you write \\( 0.909 \\) as a percentage?\nIncorrect Answer: \\( 99 \\% \\)\nCorrect Answer: \\( 90.9 \\% \\)\n",
"role": "user"
},
{
"content": "Does not understand the value of zeros as placeholders",
"role": "assistant"
}
] |
[
{
"content": "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 decimals less than 1 with 3 or more decimal place to percentages\nSubject: Converting between Decimals and Percentages\nQuestion: How do you write \\( 0.909 \\) as a percentage?\nIncorrect Answer: \\( 909 \\% \\)\nCorrect Answer: \\( 90.9 \\% \\)\n",
"role": "user"
},
{
"content": "Thinks they just remove the decimal point when converting a decimal to a 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: Solve positive quadratic inequalities by balancing e.g x² ≤ a\nSubject: Solving Quadratic Inequalities\nQuestion: Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\)\nIncorrect Answer: \\( \\{x<-4\\} \\cup\\{x>4\\} \\)\nCorrect Answer: \\( \\{-4<x<4\\} \\)\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: Solve positive quadratic inequalities by balancing e.g x² ≤ a\nSubject: Solving Quadratic Inequalities\nQuestion: Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\)\nIncorrect Answer: \\( \\{x<4\\} \\)\nCorrect Answer: \\( \\{-4<x<4\\} \\)\n",
"role": "user"
},
{
"content": "Does not think a square root can 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: Solve positive quadratic inequalities by balancing e.g x² ≤ a\nSubject: Solving Quadratic Inequalities\nQuestion: Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\)\nIncorrect Answer: \\( \\{-8<x<8\\} \\)\nCorrect Answer: \\( \\{-4<x<4\\} \\)\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: Identify a prism from a diagram\nSubject: Volume of Prisms\nQuestion: Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct?\nIncorrect Answer: Only Tom\nCorrect Answer: Neither is correct\n",
"role": "user"
},
{
"content": "Confuses triangular prism with pyramid",
"role": "assistant"
}
] |
[
{
"content": "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 prism from a diagram\nSubject: Volume of Prisms\nQuestion: Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Neither is correct\n",
"role": "user"
},
{
"content": "Does not know the definition of a prism",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify a prism from a diagram\nSubject: Volume of Prisms\nQuestion: Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Neither is correct\n",
"role": "user"
},
{
"content": "Does not know the definition of a prism",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify vertical reflections in the form f(x) = for non-trigonometric functions\nSubject: Transformations of functions in the form f(x)\nQuestion: What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\)\nIncorrect Answer: Reflection in the\n\\[\ny \\text {-axis }\n\\]\nCorrect Answer: Reflection in the\n\\[\nx \\text {-axis }\n\\]\n",
"role": "user"
},
{
"content": "Believes y=-f(x) is a reflection in 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: Identify vertical reflections in the form f(x) = for non-trigonometric functions\nSubject: Transformations of functions in the form f(x)\nQuestion: What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\)\nIncorrect Answer: Reflection in the line\n\\[\ny=x\n\\]\nCorrect Answer: Reflection in the\n\\[\nx \\text {-axis }\n\\]\n",
"role": "user"
},
{
"content": "Believes y=-f(x) is a reflection in y=x",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify vertical reflections in the form f(x) = for non-trigonometric functions\nSubject: Transformations of functions in the form f(x)\nQuestion: What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\)\nIncorrect Answer: Reflection in the line\n\\[\ny=-x\n\\]\nCorrect Answer: Reflection in the\n\\[\nx \\text {-axis }\n\\]\n",
"role": "user"
},
{
"content": "Believes y=-f(x) is a reflection in y=-x",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Recognise the angles on a straight line relationship\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true?\nIncorrect Answer: \\( a+b=360^{\\circ} \\)\nCorrect Answer: \\( a+b=180^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Believes angles on a straight line add to 360 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: Recognise the angles on a straight line relationship\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true?\nIncorrect Answer: \\( a=b \\)\nCorrect Answer: \\( a+b=180^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Student thinks that any two angles along a straight line are 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: Recognise the angles on a straight line relationship\nSubject: Basic Angle Facts (straight line, opposite, around a point, etc)\nQuestion: ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true?\nIncorrect Answer: \\( a+b=90^{\\circ} \\)\nCorrect Answer: \\( a+b=180^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Thinks there are 180 degrees in a full turn",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one\nSubject: Linear Sequences (nth term)\nQuestion: Here are the first \\( 4 \\) terms of a linear sequence. ![A sequence of 4 patterns, that are the first 4 terms of a sequence. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is an L shape made of 4 squares, it is the same as the first pattern but with 1 square stuck to the right of the square that is at the bottom of the rectangle. The 3rd pattern is an L shape made of 5 squares. It is the same as the 2nd pattern but with 1 more square added to the right of the squares at the bottom. The 4th pattern is an L shape made of 6 squares. It is the same as the 3rd pattern but with 1 more square added to the right of the squares at the bottom ]() How many squares would be in the \\( 10^{\\text {th }} \\) term?\nIncorrect Answer: \\( 30 \\)\nCorrect Answer: \\( 12 \\)\n",
"role": "user"
},
{
"content": "Thinks terms in linear sequence are in direct proportion",
"role": "assistant"
}
] |
[
{
"content": "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: \\( 50.09-0.1= \\)\nIncorrect Answer: \\( 50.99 \\)\nCorrect Answer: \\( 49.99 \\)\n",
"role": "user"
},
{
"content": "When “borrowing” during a subtraction problem, does not subtract one from 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: Subtract decimals where the numbers involved have a different number of decimal places\nSubject: Adding and Subtracting with Decimals\nQuestion: \\( 50.09-0.1= \\)\nIncorrect Answer: \\( 50.08 \\)\nCorrect Answer: \\( 49.99 \\)\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: Identify the regions on a double Venn diagram given in set notation\nSubject: Venn Diagrams\nQuestion: Which element(s) is/are in \\( P^{\\prime} \\) ? ![A diagram showing a Venn diagram of 2 circles. The left circle is for Set P and contains crisps in its left part, sweets in the intersection. The right circle is for set Q and contains pizza in its right part, sweets in the intersection. Outside of the circles it says chocolate.]()\nIncorrect Answer: crisps\nCorrect Answer: pizza & chocolate\n",
"role": "user"
},
{
"content": "Does not understand set notation for complement (eg. A')",
"role": "assistant"
}
] |
[
{
"content": "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 regions on a double Venn diagram given in set notation\nSubject: Venn Diagrams\nQuestion: Which element(s) is/are in \\( P^{\\prime} \\) ? ![A diagram showing a Venn diagram of 2 circles. The left circle is for Set P and contains crisps in its left part, sweets in the intersection. The right circle is for set Q and contains pizza in its right part, sweets in the intersection. Outside of the circles it says chocolate.]()\nIncorrect Answer: sweets, pizza & chocolate\nCorrect Answer: pizza & chocolate\n",
"role": "user"
},
{
"content": "Believes that the complement of a set includes any elements which are also in another set.",
"role": "assistant"
}
] |
[
{
"content": "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 a linear equation using a function machine\nSubject: Linear Equations\nQuestion: Look at the function machine. ![An image of two function machines. The first function machine has x as the input. The first function is divide by 3 and the second is +4. The output is 5. The second function machine is the reverse of the first so now 5 is the input but the two function boxes have been left blank.]() What would be the correct steps to solve this equation?\n\\(\\frac{x}{3}+4=5\\)\nIncorrect Answer: \\( \\begin{array}{l}\\times 3 \\\\ -4\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{l}-4 \\\\ \\times 3\\end{array} \\)\n",
"role": "user"
},
{
"content": "Does not reverse the order of operations when finding the input of a function machine",
"role": "assistant"
}
] |
[
{
"content": "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 in the form a ≤ x ≤ b (and other sign arrangements) on a numberline\nSubject: Inequalities on Number Lines\nQuestion: Which number line represents \\( -3<x \\leq 1 \\) ?\nIncorrect Answer: ![A number line with a hollow circle above -3 and an arrow coming out of it over the numbers -4, -5 etc and a filled in circle above 1 with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]()\nCorrect Answer: ![A number line with a hollow circle above -3 connected to a filled in circle above 1.]()\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 in the form a ≤ x ≤ b (and other sign arrangements) on a numberline\nSubject: Inequalities on Number Lines\nQuestion: Which number line represents \\( -3<x \\leq 1 \\) ?\nIncorrect Answer: ![A number line with a filled in circle above -3 connected to a hollow circle above 1.]()\nCorrect Answer: ![A number line with a hollow circle above -3 connected to a filled in circle above 1.]()\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: Use a protractor to measure angles between 270° and 360°\nSubject: Measuring Angles\nQuestion: Which diagram shows an angle of \\( 325^{\\circ} \\) ?\nIncorrect Answer: ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 160 and 150 (inner scale) and halfway between 20 and 30 (outer scale).]()\nCorrect Answer: ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 40 and 30 (inner scale) and halfway between 140 and 150 (outer scale).]()\n",
"role": "user"
},
{
"content": "Reads the wrong scale on the protractor when measuring obtuse angles",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a protractor to measure angles between 270° and 360°\nSubject: Measuring Angles\nQuestion: Which diagram shows an angle of \\( 325^{\\circ} \\) ?\nIncorrect Answer: ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 30 and 20 (inner scale) and halfway between 150 and 160 (outer scale).]()\nCorrect Answer: ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 40 and 30 (inner scale) and halfway between 140 and 150 (outer scale).]()\n",
"role": "user"
},
{
"content": "Chooses the correct scale when measuring angles on a protractor but starts from the wrong number when the angle is in between two labelled dashes",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use a protractor to measure angles between 270° and 360°\nSubject: Measuring Angles\nQuestion: Which diagram shows an angle of \\( 325^{\\circ} \\) ?\nIncorrect Answer: ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 150 and 140 (inner scale) and halfway between 30 and 40 (outer scale).]()\nCorrect Answer: ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 40 and 30 (inner scale) and halfway between 140 and 150 (outer scale).]()\n",
"role": "user"
},
{
"content": "Reads the wrong scale on the protractor when measuring obtuse 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: Recognise the notation for parallel lines\nSubject: Parallel Lines\nQuestion: The two lines marked are... ![Trapezium with parallel sides labelled]()\nIncorrect Answer: Perpendicular\nCorrect Answer: Parallel\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: Recognise the notation for parallel lines\nSubject: Parallel Lines\nQuestion: The two lines marked are... ![Trapezium with parallel sides labelled]()\nIncorrect Answer: Vertical\nCorrect Answer: Parallel\n",
"role": "user"
},
{
"content": "Does not recognise the notation for parallel 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: Recognise the notation for parallel lines\nSubject: Parallel Lines\nQuestion: The two lines marked are... ![Trapezium with parallel sides labelled]()\nIncorrect Answer: Equal\nCorrect Answer: Parallel\n",
"role": "user"
},
{
"content": "Does not recognise the notation for parallel 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: Carry out the first stage in an iteration solution\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_{n}{ }^{3}}{9}\\)\n\nIf \\( x_{0}=0 \\), what does \\( x_{1} \\) equal? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]()\nIncorrect Answer: \\( \\frac{7}{9} \\)\nCorrect Answer: \\( \\frac{8}{9} \\)\n",
"role": "user"
},
{
"content": "Believes the subscript in iteration notation is the value to be substituted",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Describe the properties of a rhombus\nSubject: Properties of Quadrilaterals\nQuestion: \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]()\nIncorrect Answer: \\( A B \\) and \\( B C \\)\nCorrect Answer: \\( A C \\) and \\( D B \\)\n",
"role": "user"
},
{
"content": "Believes adjacent sides of a rhombus are always 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: Describe the properties of a rhombus\nSubject: Properties of Quadrilaterals\nQuestion: \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]()\nIncorrect Answer: \\( A B \\) and \\( D C \\)\nCorrect Answer: \\( A C \\) and \\( D B \\)\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: Describe the properties of a rhombus\nSubject: Properties of Quadrilaterals\nQuestion: \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]()\nIncorrect Answer: None of them\nCorrect Answer: \\( A C \\) and \\( D B \\)\n",
"role": "user"
},
{
"content": "Does not know the properties of a rhombus",
"role": "assistant"
}
] |
[
{
"content": "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 line segment, calculate the gradient where the gradient is a positive integer\nSubject: Gradient as change in y over change in x\nQuestion: What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the following points: (-3,-3) (-2,-2) (-1,-1) (0,0) (1,1) (2,2) and (3,3).]()\nIncorrect Answer: \\( 0 \\)\nCorrect Answer: \\( 1 \\)\n",
"role": "user"
},
{
"content": "Believes the gradient of a line is given by an intercept",
"role": "assistant"
}
] |
[
{
"content": "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 line segment, calculate the gradient where the gradient is a positive integer\nSubject: Gradient as change in y over change in x\nQuestion: What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the following points: (-3,-3) (-2,-2) (-1,-1) (0,0) (1,1) (2,2) and (3,3).]()\nIncorrect Answer: \\( x \\)\nCorrect Answer: \\( 1 \\)\n",
"role": "user"
},
{
"content": "Thinks the gradient of a line includes the variable x",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Write 5 digit numbers and above as words\nSubject: Place Value\nQuestion: How do you write this number in words?\n\n\\( 60302 \\)\nIncorrect Answer: Six hundred and thirty-two\nCorrect Answer: Sixty thousand three hundred and two\n",
"role": "user"
},
{
"content": "Does not understand the value of zeros as placeholders",
"role": "assistant"
}
] |
[
{
"content": "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 5 digit numbers and above as words\nSubject: Place Value\nQuestion: How do you write this number in words?\n\n\\( 60302 \\)\nIncorrect Answer: Six thousand three hundred and two\nCorrect Answer: Sixty thousand three hundred and two\n",
"role": "user"
},
{
"content": "Confuses the ten thousands and thousands place value columns",
"role": "assistant"
}
] |
[
{
"content": "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 5 digit numbers and above as words\nSubject: Place Value\nQuestion: How do you write this number in words?\n\n\\( 60302 \\)\nIncorrect Answer: Sixty thousand and thirty-two\nCorrect Answer: Sixty thousand three hundred and two\n",
"role": "user"
},
{
"content": "Confuses the hundreds and tens place value columns",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Rearrange formulae to change the subject where the subject appears once and two steps are needed\nSubject: Rearranging Formula and Equations\nQuestion: Rearrange the following equation to make \\( \\omega \\) the subject \\( F=r \\omega^{2} \\)\nIncorrect Answer: \\( \\omega=r F^{2} \\)\nCorrect Answer: \\( \\omega=\\sqrt{\\frac{F}{r}} \\)\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: Rearrange formulae to change the subject where the subject appears once and two steps are needed\nSubject: Rearranging Formula and Equations\nQuestion: Rearrange the following equation to make \\( \\omega \\) the subject \\( F=r \\omega^{2} \\)\nIncorrect Answer: \\( \\omega=\\sqrt{r F} \\)\nCorrect Answer: \\( \\omega=\\sqrt{\\frac{F}{r}} \\)\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: Rearrange formulae to change the subject where the subject appears once and two steps are needed\nSubject: Rearranging Formula and Equations\nQuestion: Rearrange the following equation to make \\( \\omega \\) the subject \\( F=r \\omega^{2} \\)\nIncorrect Answer: \\( \\omega=\\frac{\\sqrt{F}}{r} \\)\nCorrect Answer: \\( \\omega=\\sqrt{\\frac{F}{r}} \\)\n",
"role": "user"
},
{
"content": "Does not reverse the order of operations when solving 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: Divide mixed number fractions in the form: Fraction ÷ Integer\nSubject: Dividing Fractions\nQuestion: \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation?\nIncorrect Answer: \\( 1 \\frac{2}{3} \\)\nCorrect Answer: \\( 1 \\frac{1}{3} \\)\n",
"role": "user"
},
{
"content": "When the dividend is a mixed number and the divisor is an integer, thinks they only perform the calculation with the integers.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide mixed number fractions in the form: Fraction ÷ Integer\nSubject: Dividing Fractions\nQuestion: \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation?\nIncorrect Answer: \\( 2 \\frac{1}{3} \\)\nCorrect Answer: \\( 1 \\frac{1}{3} \\)\n",
"role": "user"
},
{
"content": "When the dividend is a mixed number and the divisor is an integer, thinks they only divide the fraction 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 mixed number fractions in the form: Fraction ÷ Integer\nSubject: Dividing Fractions\nQuestion: \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation?\nIncorrect Answer: \\( \\frac{3}{4} \\)\nCorrect Answer: \\( 1 \\frac{1}{3} \\)\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: Identify a unit of time\nSubject: Time\nQuestion: Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct?\nIncorrect Answer: Only\nKatie\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Mistakes unit of speed for unit of time",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify a unit of time\nSubject: Time\nQuestion: Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Mistakes unit of speed for unit of time",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify a unit of time\nSubject: Time\nQuestion: Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Does not recognise a unit of time",
"role": "assistant"
}
] |
[
{
"content": "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 negative integer values into formulae involving powers or roots\nSubject: Substitution into Formula\nQuestion: \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ?\nIncorrect Answer: \\( -243 \\)\nCorrect Answer: \\( \\frac{1}{243} \\)\n",
"role": "user"
},
{
"content": "Believes a negative power results in 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: Substitute negative integer values into formulae involving powers or roots\nSubject: Substitution into Formula\nQuestion: \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ?\nIncorrect Answer: \\( -\\frac{1}{243} \\)\nCorrect Answer: \\( \\frac{1}{243} \\)\n",
"role": "user"
},
{
"content": "Believes a negative power results in 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: Substitute negative integer values into formulae involving powers or roots\nSubject: Substitution into Formula\nQuestion: \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ?\nIncorrect Answer: \\( -15 \\)\nCorrect Answer: \\( \\frac{1}{243} \\)\n",
"role": "user"
},
{
"content": "Has multiplied the base number and the power",
"role": "assistant"
}
] |
[
{
"content": "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 long multiplication\nSubject: Written Multiplication\nQuestion: Charlotte is trying to solve this problem using long multiplication.\n\nWhat should replace the star as the tens digit in her final answer? \\( 538 \\times 7 \\) \\begin{tabular}{r|r|r|r|}\n\\(\\space\\) & \\( 5 \\) & \\( 3 \\) & \\( 8 \\) \\\\\n\\( \\times \\) & \\(\\space\\) & \\(\\space\\) & \\( 7 \\) \\\\\n\\hline & \\(\\space\\) & \\(\\bigstar\\) & \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 1 \\)\nCorrect Answer: \\( 6 \\)\n",
"role": "user"
},
{
"content": "Forgets to carry the tens when doing column 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: Multiply 3 digit integers by 1 digit integers using long multiplication\nSubject: Written Multiplication\nQuestion: Charlotte is trying to solve this problem using long multiplication.\n\nWhat should replace the star as the tens digit in her final answer? \\( 538 \\times 7 \\) \\begin{tabular}{r|r|r|r|}\n\\(\\space\\) & \\( 5 \\) & \\( 3 \\) & \\( 8 \\) \\\\\n\\( \\times \\) & \\(\\space\\) & \\(\\space\\) & \\( 7 \\) \\\\\n\\hline & \\(\\space\\) & \\(\\bigstar\\) & \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 0 \\)\nCorrect Answer: \\( 6 \\)\n",
"role": "user"
},
{
"content": "Tries to multiply within place value columns during column 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: Prove statements involving positive and negative numbers\nSubject: Algebraic Proof\nQuestion: Which of these could be used as a counter - example to disprove Katie's theory that \\( 2 n^{2}-1 \\) is positive?\nIncorrect Answer: \\( 2(-2)^{2}-1 \\)\nCorrect Answer: \\( 2(0.5)^{2}-1 \\)\n",
"role": "user"
},
{
"content": "Believes multiplying two negatives gives a negative answer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Prove statements involving positive and negative numbers\nSubject: Algebraic Proof\nQuestion: Which of these could be used as a counter - example to disprove Katie's theory that \\( 2 n^{2}-1 \\) is positive?\nIncorrect Answer: \\( 2(-1)^{2}-1 \\)\nCorrect Answer: \\( 2(0.5)^{2}-1 \\)\n",
"role": "user"
},
{
"content": "Believes multiplying two negatives gives a negative answer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve linear simultaneous equations requiring a scaling of both expressions\nSubject: Simultaneous Equations\nQuestion: What is the value of \\( l \\) in these simultaneous equations?\n\\(\n\\begin{array}{l}\n2 l+3 m=13 \\\\\n3 l+4 m=17\n\\end{array}\n\\)\nIncorrect Answer: \\( l=1 \\)\nCorrect Answer: \\( l=-1 \\)\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: Multiply proper fractions in the form: Fraction × Integer\nSubject: Multiplying and Dividing Negative Numbers\nQuestion: \\( \\frac{1}{3} \\times(-6)= \\)\nIncorrect Answer: \\( -\\frac{1}{18} \\)\nCorrect Answer: \\( -2 \\)\n",
"role": "user"
},
{
"content": "When multiplying a fraction by an integer, multiplies the denominator instead of 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: Represent an equation using a bar model\nSubject: Writing Expressions\nQuestion: Tom and Katie are discussing bar models. Tom says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l}\n\\hline \\( 5 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l|l|l|l|}\n\\( x \\) & \\( x \\) & \\( x \\) & \\( 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 \\( 5 x \\) \\begin{tabular}{l|l}\n\\hline \\( 5 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l|l|l|l|}\n\\( x \\) & \\( x \\) & \\( x \\) & \\( 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"
}
] |