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: Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables\nSubject: Expanding Single Brackets\nQuestion: \\(\nx(3 x-5)+6(2 x-3) \\equiv P x^{2}+Q x+R\n\\)\n\nWhat is the value of \\( R \\) ?\nIncorrect Answer: \\( -3 \\)\nCorrect Answer: \\( -18 \\)\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 direct proportion to solve non-unitary missing amounts in problems (e.g. recipes)\nSubject: Direct Proportion\nQuestion: Twelve rulers cost \\( 96 p \\).\nHow much do five rulers cost?\nIncorrect Answer: \\( 89 p \\)\nCorrect Answer: \\( 40 p \\)\n",
"role": "user"
},
{
"content": "Subtracts rather than divides when scaling down in direct proportion 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: Use direct proportion to solve non-unitary missing amounts in problems (e.g. recipes)\nSubject: Direct Proportion\nQuestion: Twelve rulers cost \\( 96 p \\).\nHow much do five rulers cost?\nIncorrect Answer: \\( 8 p \\)\nCorrect Answer: \\( 40 p \\)\n",
"role": "user"
},
{
"content": "Finds unit price but doesn't multiply up for number in question",
"role": "assistant"
}
] |
[
{
"content": "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 direct proportion to solve non-unitary missing amounts in problems (e.g. recipes)\nSubject: Direct Proportion\nQuestion: Twelve rulers cost \\( 96 p \\).\nHow much do five rulers cost?\nIncorrect Answer: \\( £ 4.80 \\)\nCorrect Answer: \\( 40 p \\)\n",
"role": "user"
},
{
"content": "Multiplies up without finding unit price in proportion question",
"role": "assistant"
}
] |
[
{
"content": "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 minutes to seconds\nSubject: Time\nQuestion: Order the times from shortest to longest.\nA: 8 minutes\nB: 8 minutes 40 seconds\nC: 8 \\(\n\\frac{1}{2}\n\\) minutes\nD: 500 seconds \nIncorrect Answer: \\( B, D, C, A \\)\nCorrect Answer: \\( A, D, C, B \\)\n",
"role": "user"
},
{
"content": "Mixes up shortest and longest when ordering times",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round numbers between 0 and 1 to one significant figure\nSubject: Rounding to Significant Figures\nQuestion: Round this number to \\( 1 \\) significant figure:\n\\( 0.8532 \\)\nIncorrect Answer: \\( 1 \\)\nCorrect Answer: \\( 0.9 \\)\n",
"role": "user"
},
{
"content": "Rounds to the wrong degree of accuracy (rounds too much)",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Round numbers between 0 and 1 to one significant figure\nSubject: Rounding to Significant Figures\nQuestion: Round this number to \\( 1 \\) significant figure:\n\\( 0.8532 \\)\nIncorrect Answer: \\( 0.8 \\)\nCorrect Answer: \\( 0.9 \\)\n",
"role": "user"
},
{
"content": "Rounds down instead of up",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve problems involving converting between fractions, decimals and percentages\nSubject: Converting between Fractions and Percentages\nQuestion: \\( 0.6=\\frac{3}{5}=? \\% \\)\nIncorrect Answer: \\( 35 \\% \\)\nCorrect Answer: \\( 60 \\% \\)\n",
"role": "user"
},
{
"content": "Converts a fraction to a percentage by writing the numerator followed by the denominator",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve problems involving converting between fractions, decimals and percentages\nSubject: Converting between Fractions and Percentages\nQuestion: \\( 0.6=\\frac{3}{5}=? \\% \\)\nIncorrect Answer: \\( 6 \\% \\)\nCorrect Answer: \\( 60 \\% \\)\n",
"role": "user"
},
{
"content": "Believes a decimal with one significant figure is a multiple of 10 when converted to a percentage, regardless of 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: Represent a linear inequality in the form x ≤ a or x ≥ b (and other sign arrangements) on a numberline\nSubject: Inequalities on Number Lines\nQuestion: Which of the following diagrams represents \\( x<-1 \\) or \\( x \\geq 2 \\) ?\nIncorrect Answer: ![Number line from -5 to 5. Closed circle at -1 with arrow to the left. Open circle at 2 with arrow to the right. ]()\nCorrect Answer: ![Number line from -5 to 5. Open circle at -1 with arrow to the left. Closed circle at 2 with arrow to the right. ]()\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: Find the reciprocal of a fraction\nSubject: Laws of Indices\nQuestion: What is the reciprocal of \\( -\\frac{1}{3} \\) ?\nIncorrect Answer: \\( -0.333 \\ldots \\)\nCorrect Answer: \\( -3 \\)\n",
"role": "user"
},
{
"content": "Has an incorrect assumption about the definition of a reciprocal",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Find the reciprocal of a fraction\nSubject: Laws of Indices\nQuestion: What is the reciprocal of \\( -\\frac{1}{3} \\) ?\nIncorrect Answer: \\( 3 \\)\nCorrect Answer: \\( -3 \\)\n",
"role": "user"
},
{
"content": "Correctly finds the reciprocal of a number, but believes it should be opposite in sign to the original 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: Find the reciprocal of a fraction\nSubject: Laws of Indices\nQuestion: What is the reciprocal of \\( -\\frac{1}{3} \\) ?\nIncorrect Answer: \\( \\frac{1}{3} \\)\nCorrect Answer: \\( -3 \\)\n",
"role": "user"
},
{
"content": "Makes the number negative when asked to find the reciprocal",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables\nSubject: Simplifying Expressions by Collecting Like Terms\nQuestion: Which answer shows the following calculation using the correct algebraic convention?\n\n\\(\na+6+a+j+5+j+j\n\\)\nIncorrect Answer: \\( 6+5+2 a+3 j \\)\nCorrect Answer: \\( 11+2 a+3 j \\)\n",
"role": "user"
},
{
"content": "Does not understand when like terms can be collected",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables\nSubject: Simplifying Expressions by Collecting Like Terms\nQuestion: Which answer shows the following calculation using the correct algebraic convention?\n\n\\(\na+6+a+j+5+j+j\n\\)\nIncorrect Answer: \\( 6+2 a+5+3 j \\)\nCorrect Answer: \\( 11+2 a+3 j \\)\n",
"role": "user"
},
{
"content": "Does not understand when like terms can be collected",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables\nSubject: Simplifying Expressions by Collecting Like Terms\nQuestion: Which answer shows the following calculation using the correct algebraic convention?\n\n\\(\na+6+a+j+5+j+j\n\\)\nIncorrect Answer: \\( 11+a^{2}+j^{3} \\)\nCorrect Answer: \\( 11+2 a+3 j \\)\n",
"role": "user"
},
{
"content": "Confuses collecting like terms with 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: Read an integer on a scale where the required measurement is marked by a dash between two numbers\nSubject: Ordering Negative Numbers\nQuestion: What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-8\" next to the bottom dash and \"4\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the dash that is 2 below the \"4\" label and 4 above the \"-8\" label. ]()\nIncorrect Answer: \\( 2 \\)\nCorrect Answer: \\( 0 \\)\n",
"role": "user"
},
{
"content": "When reading integers on a number line, assumes each dash is 1",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Read an integer on a scale where the required measurement is marked by a dash between two numbers\nSubject: Ordering Negative Numbers\nQuestion: What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-8\" next to the bottom dash and \"4\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the dash that is 2 below the \"4\" label and 4 above the \"-8\" label. ]()\nIncorrect Answer: \\( -4 \\)\nCorrect Answer: \\( 0 \\)\n",
"role": "user"
},
{
"content": "When reading integers on a number line, assumes each dash is 1",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify parallel lines written in the form y = mx + c\nSubject: Parallel Lines\nQuestion: Tom and Katie are arguing about parallel lines.\n\nTom says \\( \\boldsymbol{y}=\\mathbf{2 x}+\\mathbf{3} \\) and \\( \\boldsymbol{y}=\\mathbf{3 x}+\\mathbf{2} \\) are parallel. \n\nKatie says \\( \\boldsymbol{y}=\\mathbf{2 x}+\\mathbf{3} \\) and \\( \\boldsymbol{y}=\\mathbf{2 x}-\\mathbf{3} \\) are parallel.\n\nWho is correct?\nIncorrect Answer: Only\nTom\nCorrect Answer: Only\nKatie\n",
"role": "user"
},
{
"content": "Believes switching the gradient and y-intercept gives a parallel 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: Identify parallel lines written in the form y = mx + c\nSubject: Parallel Lines\nQuestion: Tom and Katie are arguing about parallel lines.\n\nTom says \\( \\boldsymbol{y}=\\mathbf{2 x}+\\mathbf{3} \\) and \\( \\boldsymbol{y}=\\mathbf{3 x}+\\mathbf{2} \\) are parallel. \n\nKatie says \\( \\boldsymbol{y}=\\mathbf{2 x}+\\mathbf{3} \\) and \\( \\boldsymbol{y}=\\mathbf{2 x}-\\mathbf{3} \\) are parallel.\n\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only\nKatie\n",
"role": "user"
},
{
"content": "Believes switching the gradient and y-intercept gives a parallel 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: Solve one-step linear equations requiring multiplication or division, involving positive decimals\nSubject: Linear Equations\nQuestion: Solve the equation:\n\\(\n0.15=0.5 p\n\\)\nIncorrect Answer: \\( p=-0.35 \\)\nCorrect Answer: \\( p=0.3 \\)\n",
"role": "user"
},
{
"content": "When solving an equation, subtracts 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 one-step linear equations requiring multiplication or division, involving positive decimals\nSubject: Linear Equations\nQuestion: Solve the equation:\n\\(\n0.15=0.5 p\n\\)\nIncorrect Answer: \\( p=\\frac{10}{3} \\)\nCorrect Answer: \\( p=0.3 \\)\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: Given a situation sketch an appropriate non linear real life graph\nSubject: Indirect (Inverse) Proportion\nQuestion: Which of the following graphs is most likely to represent the change in journey time against average speed?\nIncorrect Answer: ![A straight line graph starting at the origin and travelling right with a positive gradient.]()\nCorrect Answer: ![A curved graph that starts up and right of the origin. As you move right it travels steeply down, then levels off. but never reaches the x-axis.]()\n",
"role": "user"
},
{
"content": "Thinks the faster you travel the longer the time it will take",
"role": "assistant"
}
] |
[
{
"content": "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 situation sketch an appropriate non linear real life graph\nSubject: Indirect (Inverse) Proportion\nQuestion: Which of the following graphs is most likely to represent the change in journey time against average speed?\nIncorrect Answer: ![A curved graph that starts at the origin. As you move right it travels steeply up, then levels off]()\nCorrect Answer: ![A curved graph that starts up and right of the origin. As you move right it travels steeply down, then levels off. but never reaches the x-axis.]()\n",
"role": "user"
},
{
"content": "Thinks the faster you travel the longer the time it will take",
"role": "assistant"
}
] |
[
{
"content": "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 situation sketch an appropriate non linear real life graph\nSubject: Indirect (Inverse) Proportion\nQuestion: Which of the following graphs is most likely to represent the change in journey time against average speed?\nIncorrect Answer: ![A straight line graph starting partway up the y-axis and travelling right with a negative gradient until it hits the x-axis.]()\nCorrect Answer: ![A curved graph that starts up and right of the origin. As you move right it travels steeply down, then levels off. but never reaches the x-axis.]()\n",
"role": "user"
},
{
"content": "Believes a reciprocal graph can be 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: Identify the mode from a frequency table\nSubject: Averages and Range from Frequency Table\nQuestion: This table shows the number of pets a group of students owns.\n\nWhat is the modal number of pets owned? \\begin{tabular}{|c|c|}\n\\hline Number of pets & Frequency \\\\\n\\hline \\( 0 \\) & \\( 9 \\) \\\\\n\\hline \\( 1 \\) & \\( 6 \\) \\\\\n\\hline \\( 2 \\) & \\( 3 \\) \\\\\n\\hline \\( 3 \\) & \\( 2 \\) \\\\\n\\hline \\( 4 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 2 \\)\nCorrect Answer: \\( 0 \\)\n",
"role": "user"
},
{
"content": "Finds the median instead of the mode",
"role": "assistant"
}
] |
[
{
"content": "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 mode from a frequency table\nSubject: Averages and Range from Frequency Table\nQuestion: This table shows the number of pets a group of students owns.\n\nWhat is the modal number of pets owned? \\begin{tabular}{|c|c|}\n\\hline Number of pets & Frequency \\\\\n\\hline \\( 0 \\) & \\( 9 \\) \\\\\n\\hline \\( 1 \\) & \\( 6 \\) \\\\\n\\hline \\( 2 \\) & \\( 3 \\) \\\\\n\\hline \\( 3 \\) & \\( 2 \\) \\\\\n\\hline \\( 4 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 3 \\)\nCorrect Answer: \\( 0 \\)\n",
"role": "user"
},
{
"content": "Believes the mode is the frequency rather than the value/group",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify the mode from a frequency table\nSubject: Averages and Range from Frequency Table\nQuestion: This table shows the number of pets a group of students owns.\n\nWhat is the modal number of pets owned? \\begin{tabular}{|c|c|}\n\\hline Number of pets & Frequency \\\\\n\\hline \\( 0 \\) & \\( 9 \\) \\\\\n\\hline \\( 1 \\) & \\( 6 \\) \\\\\n\\hline \\( 2 \\) & \\( 3 \\) \\\\\n\\hline \\( 3 \\) & \\( 2 \\) \\\\\n\\hline \\( 4 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: \\( 0 \\)\n",
"role": "user"
},
{
"content": "Believes when identifying the mode you look at all values, not just frequencies, for the highest 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: Enlarge a shape, with a centre of enlargement given, by a positive scale factor bigger than 1, where the centre of enlargement lies on the edge or outside of the object\nSubject: Enlargement\nQuestion: The triangle is enlarged by scale factor \\( 3 \\), with the centre of enlargement at \\( (1,0) \\).\nWhat are the new coordinates of the point marked \\( T \\) ? ![A coordinate grid with the x-axis going from -1 to 10 and the y-axis going from -1 to 7.\n3 points are plotted and joined with straight lines to form a triangle. The points are (1,1), (1,4) and (3,1). Point (3,1) is labelled as T.\nPoint (1,0) is also plotted.]()\nIncorrect Answer: \\( (6,4) \\)\nCorrect Answer: \\( (7,3) \\)\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: Enlarge a shape, with a centre of enlargement given, by a positive scale factor bigger than 1, where the centre of enlargement lies on the edge or outside of the object\nSubject: Enlargement\nQuestion: The triangle is enlarged by scale factor \\( 3 \\), with the centre of enlargement at \\( (1,0) \\).\nWhat are the new coordinates of the point marked \\( T \\) ? ![A coordinate grid with the x-axis going from -1 to 10 and the y-axis going from -1 to 7.\n3 points are plotted and joined with straight lines to form a triangle. The points are (1,1), (1,4) and (3,1). Point (3,1) is labelled as T.\nPoint (1,0) is also plotted.]()\nIncorrect Answer: \\( (9,3) \\)\nCorrect Answer: \\( (7,3) \\)\n",
"role": "user"
},
{
"content": "Enlarges by the wrong centre of enlargement",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Range and Interquartile Range from a List of Data\nQuestion: What is the range of this set of data?\n\\[\n5 \\mathrm{~cm}, 19 \\mathrm{~cm}, 6 \\mathrm{~cm}, 2 \\mathrm{~cm}\n\\]\nIncorrect Answer: \\( 19 \\mathrm{~cm} \\)\nCorrect Answer: \\( 17 \\mathrm{~cm} \\)\n",
"role": "user"
},
{
"content": "Identifies the biggest value for the range",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Range and Interquartile Range from a List of Data\nQuestion: What is the range of this set of data?\n\\[\n5 \\mathrm{~cm}, 19 \\mathrm{~cm}, 6 \\mathrm{~cm}, 2 \\mathrm{~cm}\n\\]\nIncorrect Answer: \\( 3 \\mathrm{~cm} \\)\nCorrect Answer: \\( 17 \\mathrm{~cm} \\)\n",
"role": "user"
},
{
"content": "Thinks the range is just the first value subtracted from the last value, without ordering",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Range and Interquartile Range from a List of Data\nQuestion: What is the range of this set of data?\n\\[\n5 \\mathrm{~cm}, 19 \\mathrm{~cm}, 6 \\mathrm{~cm}, 2 \\mathrm{~cm}\n\\]\nIncorrect Answer: \\( 21 \\mathrm{~cm} \\)\nCorrect Answer: \\( 17 \\mathrm{~cm} \\)\n",
"role": "user"
},
{
"content": "To find the range adds the biggest and smallest number rather than subtract",
"role": "assistant"
}
] |
[
{
"content": "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 solution to a graphical inequality involving a single diagonal line\nSubject: Graphing Linear Inequalities (Shading Regions)\nQuestion: Which inequality is represented by the shaded region? ![Graph showing four quadrants with a straight line going from the top left to the bottom right. The line goes through (-4, 4) (-3, 3) (-2, 2) and so on]()\nIncorrect Answer: \\( y>x \\)\nCorrect Answer: \\( y>-x \\)\n",
"role": "user"
},
{
"content": "Confuses the lines y=x and 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: Describe the solution to a graphical inequality involving a single diagonal line\nSubject: Graphing Linear Inequalities (Shading Regions)\nQuestion: Which inequality is represented by the shaded region? ![Graph showing four quadrants with a straight line going from the top left to the bottom right. The line goes through (-4, 4) (-3, 3) (-2, 2) and so on]()\nIncorrect Answer: \\( y<-x \\)\nCorrect Answer: \\( y>-x \\)\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: Use brackets to write function machines as calculations\nSubject: BIDMAS\nQuestion: Here is a function machine\n\\( input\\Rightarrow +2 \\Rightarrow \\times 3 \\Rightarrow output\\)\nThe input is \\( 5 \\).\nWhich calculation gives the correct output?\nIncorrect Answer: \\( 5 \\times 3+2 \\)\nCorrect Answer: \\( 3(5+2) \\)\n",
"role": "user"
},
{
"content": "Does not follow the arrows through a function machine, changes the order of the operations asked.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use brackets to write function machines as calculations\nSubject: BIDMAS\nQuestion: Here is a function machine\n\\( input\\Rightarrow +2 \\Rightarrow \\times 3 \\Rightarrow output\\)\nThe input is \\( 5 \\).\nWhich calculation gives the correct output?\nIncorrect Answer: \\( 5(3+2) \\)\nCorrect Answer: \\( 3(5+2) \\)\n",
"role": "user"
},
{
"content": "In a function machine, confuses an operation with the input",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use brackets to write function machines as calculations\nSubject: BIDMAS\nQuestion: Here is a function machine\n\\( input\\Rightarrow +2 \\Rightarrow \\times 3 \\Rightarrow output\\)\nThe input is \\( 5 \\).\nWhich calculation gives the correct output?\nIncorrect Answer: \\( 5+2 \\times 3 \\)\nCorrect Answer: \\( 3(5+2) \\)\n",
"role": "user"
},
{
"content": "Believes order of operations does not affect the answer to a 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: Given the area of a square, calculate a missing dimension\nSubject: Square Roots, Cube Roots, etc\nQuestion: A square has an area \\( 64 \\mathrm{~mm}^{2} \\)\n\nWhat is the length of one side of the square?\nIncorrect Answer: \\( 16 \\mathrm{~mm} \\)\nCorrect Answer: \\( 8 \\mathrm{~mm} \\)\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: Given the area of a square, calculate a missing dimension\nSubject: Square Roots, Cube Roots, etc\nQuestion: A square has an area \\( 64 \\mathrm{~mm}^{2} \\)\n\nWhat is the length of one side of the square?\nIncorrect Answer: \\( 32 \\mathrm{~mm} \\)\nCorrect Answer: \\( 8 \\mathrm{~mm} \\)\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: Given information about one part, work out the whole\nSubject: Sharing in a Ratio\nQuestion: The ratio of cars to bikes in a housing estate is \\( 5: 2 \\)\nIf there are \\( \\mathbf{7 0} \\) cars, how many vehicles (cars and bikes) are there in total?\nIncorrect Answer: \\( 72 \\)\nCorrect Answer: \\( 98 \\)\n",
"role": "user"
},
{
"content": "Thinks the number in the ratio is the total",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Given a sketch of a linear graph solve f(x) = n\nSubject: Linear Equations\nQuestion: This is the graph of\n\\[\ny=0.5 x-2\n\\]\n\nAccording to the graph, what is the solution to:\n\\[\n0.5 x-2=1\n\\] ![Graph showing straight line with y intercept (0,-2) and x intercept (4,0)]()\nIncorrect Answer: \\( x=-1.5 \\)\nCorrect Answer: \\( x=6 \\)\n",
"role": "user"
},
{
"content": "Thinks they solve mx + c = a, by substituting in the value of a for x and therefore calculating ma + c",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Given a sketch of a linear graph solve f(x) = n\nSubject: Linear Equations\nQuestion: This is the graph of\n\\[\ny=0.5 x-2\n\\]\n\nAccording to the graph, what is the solution to:\n\\[\n0.5 x-2=1\n\\] ![Graph showing straight line with y intercept (0,-2) and x intercept (4,0)]()\nIncorrect Answer: \\( x=4 \\)\nCorrect Answer: \\( x=6 \\)\n",
"role": "user"
},
{
"content": "Believes the solution to mx + c = a is the x intercept of y = mx +c",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use inequality notation to order a negative and a positive integer\nSubject: Inequalities on Number Lines\nQuestion: One of these pairs of numbers does not fit \nthe inequality \\( d \\leq h \\)\n\nCan you find which pair?\nIncorrect Answer: \\( \\begin{array}{l}d=4 \\\\ h=4\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}d=2 \\\\ h=-4\\end{array} \\)\n",
"role": "user"
},
{
"content": "Does not understand inequality notation",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use inequality notation to order a negative and a positive integer\nSubject: Inequalities on Number Lines\nQuestion: One of these pairs of numbers does not fit \nthe inequality \\( d \\leq h \\)\n\nCan you find which pair?\nIncorrect Answer: \\( \\begin{array}{c}d=-4\\\\h=4\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}d=2 \\\\ h=-4\\end{array} \\)\n",
"role": "user"
},
{
"content": "Does not understand inequality notation",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Use inequality notation to order a negative and a positive integer\nSubject: Inequalities on Number Lines\nQuestion: One of these pairs of numbers does not fit \nthe inequality \\( d \\leq h \\)\n\nCan you find which pair?\nIncorrect Answer: \\( \\begin{array}{c}d=-2 \\\\ h=2\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{c}d=2 \\\\ h=-4\\end{array} \\)\n",
"role": "user"
},
{
"content": "Does not understand inequality notation",
"role": "assistant"
}
] |
[
{
"content": "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 midpoint and a coordinate work out the position of the other coordinate, where all the values are integers but at least one is negative\nSubject: Midpoint Between Two Co-ordinates\nQuestion: Tom and Katie are arguing about midpoints.\n\\( M \\) is the midpoint between points \\( P \\) and \\( Q \\).\n\nTom says if you know the location of \\( M \\) only, then there is more than one possible location for \\( \\mathrm{P} \\) and \\( \\mathrm{Q} \\).\n\nKatie says if you only know the locations of \\( M \\) and \\( Q \\), then there is more than one possible location for \\( \\mathrm{P} \\).\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Believes there is more than one line which passes through a given pair of 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: Given a midpoint and a coordinate work out the position of the other coordinate, where all the values are integers but at least one is negative\nSubject: Midpoint Between Two Co-ordinates\nQuestion: Tom and Katie are arguing about midpoints.\n\\( M \\) is the midpoint between points \\( P \\) and \\( Q \\).\n\nTom says if you know the location of \\( M \\) only, then there is more than one possible location for \\( \\mathrm{P} \\) and \\( \\mathrm{Q} \\).\n\nKatie says if you only know the locations of \\( M \\) and \\( Q \\), then there is more than one possible location for \\( \\mathrm{P} \\).\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Believes that one point is enough to specify a 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: Continue linear sequences expressed as patterns by drawing the next pattern\nSubject: Linear Sequences (nth term)\nQuestion: How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequence. \nPattern 1 contains 3 squares in this arrangement :. \nPattern 2 contains 5 squares in this arrangement ::.\nPattern 3 contains 7 squares in this arrangement :::.]()\nIncorrect Answer: \\( 8 \\)\nCorrect Answer: \\( 9 \\)\n",
"role": "user"
},
{
"content": "When asked for the next term in the sequence adds one to the last term given, despite the sequence not going up in ones.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Continue linear sequences expressed as patterns by drawing the next pattern\nSubject: Linear Sequences (nth term)\nQuestion: How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequence. \nPattern 1 contains 3 squares in this arrangement :. \nPattern 2 contains 5 squares in this arrangement ::.\nPattern 3 contains 7 squares in this arrangement :::.]()\nIncorrect Answer: \\( 10 \\)\nCorrect Answer: \\( 9 \\)\n",
"role": "user"
},
{
"content": "Does not notice all changes in a sequence of visual patterns",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Continue linear sequences expressed as patterns by drawing the next pattern\nSubject: Linear Sequences (nth term)\nQuestion: How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequence. \nPattern 1 contains 3 squares in this arrangement :. \nPattern 2 contains 5 squares in this arrangement ::.\nPattern 3 contains 7 squares in this arrangement :::.]()\nIncorrect Answer: \\( 14 \\)\nCorrect Answer: \\( 9 \\)\n",
"role": "user"
},
{
"content": "Does not notice all changes in a sequence of visual patterns",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Express one quantity as a percentage of another mentally\nSubject: Percentages of an Amount\nQuestion: What is \\( 50 \\mathrm{~m} \\) as a percentage of \\( 5 \\mathrm{~km} \\) ?\nIncorrect Answer: \\( 100 \\% \\)\nCorrect Answer: \\( 1 \\% \\)\n",
"role": "user"
},
{
"content": "Has found the total as a percentage of the amount 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: Express one quantity as a percentage of another mentally\nSubject: Percentages of an Amount\nQuestion: What is \\( 50 \\mathrm{~m} \\) as a percentage of \\( 5 \\mathrm{~km} \\) ?\nIncorrect Answer: \\( 50 \\% \\)\nCorrect Answer: \\( 1 \\% \\)\n",
"role": "user"
},
{
"content": "Thinks you need to just add a % sign to a number to make it 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: Express one quantity as a percentage of another mentally\nSubject: Percentages of an Amount\nQuestion: What is \\( 50 \\mathrm{~m} \\) as a percentage of \\( 5 \\mathrm{~km} \\) ?\nIncorrect Answer: \\( 10 \\% \\)\nCorrect Answer: \\( 1 \\% \\)\n",
"role": "user"
},
{
"content": "Thinks there are 100m and a km",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative\nSubject: Finding the Equation of a Line\nQuestion: Which of the following sketches could represent \\( y=4-2 x \\) ?\nIncorrect Answer: ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis below the origin.]()\nCorrect Answer: ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis above the origin.]()\n",
"role": "user"
},
{
"content": "Believes that in y=mx+c, m is the y-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: Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative\nSubject: Finding the Equation of a Line\nQuestion: Which of the following sketches could represent \\( y=4-2 x \\) ?\nIncorrect Answer: ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis above the origin.]()\nCorrect Answer: ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis above the origin.]()\n",
"role": "user"
},
{
"content": "Believes that in y = mx+c, c is the gradient",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative\nSubject: Finding the Equation of a Line\nQuestion: Which of the following sketches could represent \\( y=4-2 x \\) ?\nIncorrect Answer: ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis below the origin.]()\nCorrect Answer: ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis above the origin.]()\n",
"role": "user"
},
{
"content": "Believes that in y = mx+c, c is the gradient",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify factors of algebraic expressions\nSubject: Factors and Highest Common Factor\nQuestion: Tom and Katie are discussing factors\n\nTom says \\( 3 \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nKatie says \\( x \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nWho is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Only\nTom\n",
"role": "user"
},
{
"content": "Does not know how to identify common factors from 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: Identify factors of algebraic expressions\nSubject: Factors and Highest Common Factor\nQuestion: Tom and Katie are discussing factors\n\nTom says \\( 3 \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nKatie says \\( x \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only\nTom\n",
"role": "user"
},
{
"content": "Does not know how to identify common factors from 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: Identify factors of algebraic expressions\nSubject: Factors and Highest Common Factor\nQuestion: Tom and Katie are discussing factors\n\nTom says \\( 3 \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nKatie says \\( x \\) is a common factor of \\( 6 x \\) and \\( 9 y \\)\n\nWho is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only\nTom\n",
"role": "user"
},
{
"content": "Does not know how to identify common factors from 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: Write algebraic expressions with correct algebraic convention\nSubject: Writing Expressions\nQuestion: Which answer shows the following calculation using the correct algebraic convention?\n\\(\n2 \\div(3+a \\times b)\n\\)\nIncorrect Answer: \\( \\frac{2}{3}+a b \\)\nCorrect Answer: \\( \\frac{2}{a b+3} \\)\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: Write algebraic expressions with correct algebraic convention\nSubject: Writing Expressions\nQuestion: Which answer shows the following calculation using the correct algebraic convention?\n\\(\n2 \\div(3+a \\times b)\n\\)\nIncorrect Answer: \\( \\frac{2}{b(a+3)} \\)\nCorrect Answer: \\( \\frac{2}{a b+3} \\)\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: Write algebraic expressions with correct algebraic convention\nSubject: Writing Expressions\nQuestion: Which answer shows the following calculation using the correct algebraic convention?\n\\(\n2 \\div(3+a \\times b)\n\\)\nIncorrect Answer: \\( \\frac{2}{a \\times b+3} \\)\nCorrect Answer: \\( \\frac{2}{a b+3} \\)\n",
"role": "user"
},
{
"content": "Does not realize we can omit the multiplication symbol in algebraic expressions",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Range and Interquartile Range from a List of Data\nQuestion: When finding the range of a data set, which step is never needed\nIncorrect Answer: Check the units of your answer\nCorrect Answer: Add all the numbers together.\n",
"role": "user"
},
{
"content": "Believes range does not need units",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the range from a list of data\nSubject: Range and Interquartile Range from a List of Data\nQuestion: When finding the range of a data set, which step is never needed\nIncorrect Answer: Write the numbers in ascending or descending order.\nCorrect Answer: Add all the numbers together.\n",
"role": "user"
},
{
"content": "When calculating the range does not reorder the data to find the largest number minus the smallest number",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Assign probabilities to single events using fractions\nSubject: Probability of Single Events\nQuestion: A box contains \\( 10 \\) coloured counters.\n\n\\( 3 \\) of the counters are pink\n\n\\( 3 \\) of the counters are blue\n\nThe rest of the counters are green\n\nWhat is the probability of choosing a green counter?\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: \\( \\frac{4}{10} \\)\n",
"role": "user"
},
{
"content": "Forgets the denominator in probability",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Assign probabilities to single events using fractions\nSubject: Probability of Single Events\nQuestion: A box contains \\( 10 \\) coloured counters.\n\n\\( 3 \\) of the counters are pink\n\n\\( 3 \\) of the counters are blue\n\nThe rest of the counters are green\n\nWhat is the probability of choosing a green counter?\nIncorrect Answer: \\( \\frac{1}{3} \\)\nCorrect Answer: \\( \\frac{4}{10} \\)\n",
"role": "user"
},
{
"content": "Thinks that probabilities of an event occurring or not occurring must be equal",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the volume of a cuboid when the dimensions are given in different units\nSubject: Volume of Prisms\nQuestion: Which of the following calculations would give the volume of this cuboid? ![A cuboid with dimensions 60mm, 7cm and 5cm]()\nIncorrect Answer: \\( 7 \\times 5 \\times 60 \\)\nCorrect Answer: \\( 7 \\times 5 \\times 6 \\)\n",
"role": "user"
},
{
"content": "Does not convert measurements to have the same units before calculating area or volume",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the volume of a cuboid when the dimensions are given in different units\nSubject: Volume of Prisms\nQuestion: Which of the following calculations would give the volume of this cuboid? ![A cuboid with dimensions 60mm, 7cm and 5cm]()\nIncorrect Answer: \\( 7+5+6 \\)\nCorrect Answer: \\( 7 \\times 5 \\times 6 \\)\n",
"role": "user"
},
{
"content": "Adds when calculating volume 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: Expand two brackets with linear terms in the form (x + a)(x + b)\nSubject: Expanding Double Brackets\nQuestion: What should replace the circle when these two brackets are\nexpanded and simplified?\n\n\\(\n(p-3)(p+3) \\equiv p^{2} \\color{purple}\\triangle\\) \\(p\\)\\(\\color{green}\\bigcirc\n\\)\n\nIncorrect Answer: \\(\\color{green}\\bigcirc\\) = +0 \n(no number term)\nCorrect Answer: \\(\\color{green}\\bigcirc\\) = -9\n",
"role": "user"
},
{
"content": "Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Expand two brackets with linear terms in the form (x + a)(x + b)\nSubject: Expanding Double Brackets\nQuestion: What should replace the circle when these two brackets are\nexpanded and simplified?\n\n\\(\n(p-3)(p+3) \\equiv p^{2} \\color{purple}\\triangle\\) \\(p\\)\\(\\color{green}\\bigcirc\n\\)\n\nIncorrect Answer: \\(\\color{green}\\bigcirc\\) = +9\nCorrect Answer: \\(\\color{green}\\bigcirc\\) = -9\n",
"role": "user"
},
{
"content": "Believes multiplying a positive by a negative gives a positive answer",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Add column vectors each containing two elements\nSubject: Translation and Vectors\nQuestion: \\( \\left(\\begin{array}{l}2 \\\\ 3\\end{array}\\right)+\\left(\\begin{array}{c}-1 \\\\ 0\\end{array}\\right)= \\)\nIncorrect Answer: \\( \\left(\\begin{array}{c}-2 \\\\ 0\\end{array}\\right) \\)\nCorrect Answer: \\( \\left(\\begin{array}{l}1 \\\\ 3\\end{array}\\right) \\)\n",
"role": "user"
},
{
"content": "When adding column vectors, multiplies rather than adds",
"role": "assistant"
}
] |
[
{
"content": "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 a quadratic graph from its shape\nSubject: Quadratic Graphs-Others\nQuestion: Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() Who is correct?\nIncorrect Answer: Only Tom\nCorrect Answer: Both Tom and Katie\n",
"role": "user"
},
{
"content": "Only recognises the positive form of a quadratic graph",
"role": "assistant"
}
] |
[
{
"content": "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 a quadratic graph from its shape\nSubject: Quadratic Graphs-Others\nQuestion: Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() Who is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Both Tom and Katie\n",
"role": "user"
},
{
"content": "Only recognises the negative form of a quadratic graph",
"role": "assistant"
}
] |
[
{
"content": "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 a quadratic graph from its shape\nSubject: Quadratic Graphs-Others\nQuestion: Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() Who is correct?\nIncorrect Answer: Neither is correct\nCorrect Answer: Both Tom and Katie\n",
"role": "user"
},
{
"content": "Does not recognise a quadratic graph",
"role": "assistant"
}
] |
[
{
"content": "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 trapezium, calculate a missing dimension\nSubject: Area of Simple Shapes\nQuestion: The area of this trapezium is \\( 40 \\mathrm{~cm}^{2} \\).\n\nWhat is the value of \\( a \\) ? ![A trapezium with the parallel sides labelled with 2cm and a and the height labelled with 8cm]()\nIncorrect Answer: \\( 3 \\mathrm{~cm} \\)\nCorrect Answer: \\( 8 \\mathrm{~cm} \\)\n",
"role": "user"
},
{
"content": "Does not divide by 2 when calculating the area of a trapezium",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the square root of a number\nSubject: Square Roots, Cube Roots, etc\nQuestion: \\( \\sqrt{-16}=? \\)\nIncorrect Answer: \\( -4 \\)\nCorrect Answer: No real solutions\n",
"role": "user"
},
{
"content": "Can not square root a negative number",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the square root of a number\nSubject: Square Roots, Cube Roots, etc\nQuestion: \\( \\sqrt{-16}=? \\)\nIncorrect Answer: \\( 4 \\)\nCorrect Answer: No real solutions\n",
"role": "user"
},
{
"content": "Can not square root a negative 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: Multiply amounts of money up to £10\nSubject: Basic Money\nQuestion: Alicia wants to buy some bottles of water.\nEach bottle of water costs \\( £ 1.65 \\)\nAlicia has \\( £ 10 \\) to spend.\nWhat is the greatest number of bottles can she buy?\nIncorrect Answer: \\( 7 \\)\nCorrect Answer: \\( 6 \\)\n",
"role": "user"
},
{
"content": "Believes you can go above an amount of money when finding how much of something you can buy",
"role": "assistant"
}
] |
[
{
"content": "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 inequalities in one variable where the unknown appears on boths sides of the equation\nSubject: Solving Linear Inequalities\nQuestion: Solve\n\\[\n3 n+2 \\geq 4 n-5\n\\]\nIncorrect Answer: \\( -3 \\geq n \\)\nCorrect Answer: \\( 7 \\geq n \\)\n",
"role": "user"
},
{
"content": "When solving an equation, uses the same operation rather than the inverse.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve linear inequalities in one variable where the unknown appears on boths sides of the equation\nSubject: Solving Linear Inequalities\nQuestion: Solve\n\\[\n3 n+2 \\geq 4 n-5\n\\]\nIncorrect Answer: \\( 1 \\geq n \\)\nCorrect Answer: \\( 7 \\geq n \\)\n",
"role": "user"
},
{
"content": "When solving an equation, uses the same operation rather than the inverse.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve linear inequalities in one variable where the unknown appears on boths sides of the equation\nSubject: Solving Linear Inequalities\nQuestion: Solve\n\\[\n3 n+2 \\geq 4 n-5\n\\]\nIncorrect Answer: \\( n \\geq 7 \\)\nCorrect Answer: \\( 7 \\geq n \\)\n",
"role": "user"
},
{
"content": "Believes they can multiply/divide through by a negative number without changing the direction of the inequality",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Substitute into simple formulae given in words\nSubject: Substitution into Formula\nQuestion: A theme park charges \\( £ 8 \\) entry fee and then \\( £ 3 \\) for every ride you go on.\nHeena goes on \\( 5 \\) rides.\nHow much does she pay in total?\nIncorrect Answer: \\( £ 55 \\)\nCorrect Answer: \\( £ 23 \\)\n",
"role": "user"
},
{
"content": "Combines variables with constants when writing a formula from a given situation",
"role": "assistant"
}
] |
[
{
"content": "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 into simple formulae given in words\nSubject: Substitution into Formula\nQuestion: A theme park charges \\( £ 8 \\) entry fee and then \\( £ 3 \\) for every ride you go on.\nHeena goes on \\( 5 \\) rides.\nHow much does she pay in total?\nIncorrect Answer: \\( £ 15 \\)\nCorrect Answer: \\( £ 23 \\)\n",
"role": "user"
},
{
"content": "Does not add on the constant in a worded substitution 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: Substitute into simple formulae given in words\nSubject: Substitution into Formula\nQuestion: A theme park charges \\( £ 8 \\) entry fee and then \\( £ 3 \\) for every ride you go on.\nHeena goes on \\( 5 \\) rides.\nHow much does she pay in total?\nIncorrect Answer: \\( £ 11 \\)\nCorrect Answer: \\( £ 23 \\)\n",
"role": "user"
},
{
"content": "Does not consider the variable when evaluating an expression that requires substitution.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Increase a number by a given percentage mentally where the percent is a multiple of 10\nSubject: Percentage Increase and Decrease\nQuestion: Increase \\( 160 \\) by \\( 30 \\% \\)\nIncorrect Answer: \\( 190 \\)\nCorrect Answer: \\( 208 \\)\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: Increase a number by a given percentage mentally where the percent is a multiple of 10\nSubject: Percentage Increase and Decrease\nQuestion: Increase \\( 160 \\) by \\( 30 \\% \\)\nIncorrect Answer: \\( 48 \\)\nCorrect Answer: \\( 208 \\)\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: Increase a number by a given percentage mentally where the percent is a multiple of 10\nSubject: Percentage Increase and Decrease\nQuestion: Increase \\( 160 \\) by \\( 30 \\% \\)\nIncorrect Answer: \\( 4800 \\)\nCorrect Answer: \\( 208 \\)\n",
"role": "user"
},
{
"content": "Thinks when finding a percentage you multiply 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: Continue a sequence involving triangle numbers\nSubject: Other Sequences\nQuestion: Here are two consecutive triangle numbers: \\( 153,171, \\ldots \\) What is the next triangle number in the sequence?\nIncorrect Answer: \\( 188 \\)\nCorrect Answer: \\( 190 \\)\n",
"role": "user"
},
{
"content": "Believes the difference between triangle numbers decreases by 1 each 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: Continue a sequence involving triangle numbers\nSubject: Other Sequences\nQuestion: Here are two consecutive triangle numbers: \\( 153,171, \\ldots \\) What is the next triangle number in the sequence?\nIncorrect Answer: \\( 189 \\)\nCorrect Answer: \\( 190 \\)\n",
"role": "user"
},
{
"content": "Believes the difference between triangle numbers remains the same",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Continue a sequence involving triangle numbers\nSubject: Other Sequences\nQuestion: Here are two consecutive triangle numbers: \\( 153,171, \\ldots \\) What is the next triangle number in the sequence?\nIncorrect Answer: \\( 324 \\)\nCorrect Answer: \\( 190 \\)\n",
"role": "user"
},
{
"content": "Believes to find the next traingle number you add the previous two numbers together i.e. Fibonacci",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve problems that combine addition and subtraction\nSubject: Written Subtraction\nQuestion: At the start of the day, there was \\( £ 1,456 \\) in the till. \\( £ 7,347 \\) was taken and \\( £ 4,377 \\) was handed out. How much money was left?\nIncorrect Answer: \\( £ 13,180 \\)\nCorrect Answer: \\( £ 4,426 \\)\n",
"role": "user"
},
{
"content": "Assumes they add all values in a worded problem, thereby not interpreting the problem correctly",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve problems that combine addition and subtraction\nSubject: Written Subtraction\nQuestion: At the start of the day, there was \\( £ 1,456 \\) in the till. \\( £ 7,347 \\) was taken and \\( £ 4,377 \\) was handed out. How much money was left?\nIncorrect Answer: \\( £ 2,970 \\)\nCorrect Answer: \\( £ 4,426 \\)\n",
"role": "user"
},
{
"content": "In a worded problem, does not complete all calculations",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve problems that combine addition and subtraction\nSubject: Written Subtraction\nQuestion: At the start of the day, there was \\( £ 1,456 \\) in the till. \\( £ 7,347 \\) was taken and \\( £ 4,377 \\) was handed out. How much money was left?\nIncorrect Answer: \\( £ 10,268 \\)\nCorrect Answer: \\( £ 4,426 \\)\n",
"role": "user"
},
{
"content": "When talking about money \"taken\" in a retail context, thinks that means take-away rather than add",
"role": "assistant"
}
] |
[
{
"content": "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 a quadratic graph from its shape\nSubject: Quadratic Graphs-Others\nQuestion: Which of the following is an example of a quadratic graph?\nIncorrect Answer: ![A graph showing a straight line from top left to bottom right.]()\nCorrect Answer: ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape.]()\n",
"role": "user"
},
{
"content": "Does not recognise a quadratic graph",
"role": "assistant"
}
] |
[
{
"content": "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 a quadratic graph from its shape\nSubject: Quadratic Graphs-Others\nQuestion: Which of the following is an example of a quadratic graph?\nIncorrect Answer: ![A graph showing a curve that starts in the bottom left, moves steeply up and right, levels off briefly, then continues steeply up and right.]()\nCorrect Answer: ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape.]()\n",
"role": "user"
},
{
"content": "Confuses cubic and quadratic graphs",
"role": "assistant"
}
] |
[
{
"content": "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 a quadratic graph from its shape\nSubject: Quadratic Graphs-Others\nQuestion: Which of the following is an example of a quadratic graph?\nIncorrect Answer: ![A graph with two curves. One curve is in the positive x, positive y quadrant. It starts at the top close to the y axis, as we move right it drops very quickly towards the x axis then levels off to travel almost parallel to the x axis.\nThe other curve is in the negative x, negative y quadrant. It starts at the top left close to the x axis, as we move right it drops very quickly towards the y axis then becomes almost vertical to travel almost parallel to the y axis. ]()\nCorrect Answer: ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape.]()\n",
"role": "user"
},
{
"content": "Confuses reciprocal and quadratic graphs",
"role": "assistant"
}
] |
[
{
"content": "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: Tom and Katie are discussing this pair of simultaneous equations: \\( \\begin{array}{l}3 x-2 y=8 \\\\ 3 x+y=14\\end{array} \\) Tom says if you add the two equations together you will eliminate a variable\n\nKatie says if you subtract the two equations together you will eliminate a variable\n\nWho is correct?\nIncorrect Answer: Only\nTom\nCorrect Answer: Only\nKatie\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: Tom and Katie are discussing this pair of simultaneous equations: \\( \\begin{array}{l}3 x-2 y=8 \\\\ 3 x+y=14\\end{array} \\) Tom says if you add the two equations together you will eliminate a variable\n\nKatie says if you subtract the two equations together you will eliminate a variable\n\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only\nKatie\n",
"role": "user"
},
{
"content": "When solving simultaneous equations thinks that identical terms in given equations can be eliminated by either adding or subtracting.",
"role": "assistant"
}
] |
[
{
"content": "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: \\( 7 \\)\nCorrect Answer: \\( 8 \\)\n",
"role": "user"
},
{
"content": "Does not understand the first significant value is the first non-zero digit number",
"role": "assistant"
}
] |