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: Use the order of operations to carry out calculations involving powers\nSubject: BIDMAS\nQuestion: \\[\n3 \\times 2+4-5\n\\]\nWhere do the brackets need to go to make the answer equal \\( 13 \\) ?\nIncorrect Answer: Does not need brackets\nCorrect Answer: \\( 3 \\times(2+4)-5 \\)\n",
"role": "user"
},
{
"content": "Confuses the order of operations, believes addition comes before 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: Simplify an algebraic fraction by factorising the numerator\nSubject: Simplifying Algebraic Fractions\nQuestion: Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\)\nIncorrect Answer: \\( m+1 \\)\nCorrect Answer: Does not simplify\n",
"role": "user"
},
{
"content": "Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term\n",
"role": "assistant"
}
] |
[
{
"content": "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 an algebraic fraction by factorising the numerator\nSubject: Simplifying Algebraic Fractions\nQuestion: Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\)\nIncorrect Answer: \\( m+2 \\)\nCorrect Answer: Does not simplify\n",
"role": "user"
},
{
"content": "Thinks that when you cancel identical terms from the numerator and denominator, they just disappear",
"role": "assistant"
}
] |
[
{
"content": "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 an algebraic fraction by factorising the numerator\nSubject: Simplifying Algebraic Fractions\nQuestion: Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\)\nIncorrect Answer: \\( m-1 \\)\nCorrect Answer: Does not simplify\n",
"role": "user"
},
{
"content": "Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term\n",
"role": "assistant"
}
] |
[
{
"content": "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: Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\( 24 \\mathrm{~cm}, 17 \\mathrm{~cm}, 42 \\mathrm{~cm}, 26 \\mathrm{~cm}, 13 \\mathrm{~cm} \\)\nTom says if all the plants were cut in half, the range wouldn't change.\nKatie says if all the plants grew by \\( 3 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with?\nIncorrect Answer: Only\nTom\nCorrect Answer: Only\nKatie\n",
"role": "user"
},
{
"content": "Believes if you changed all values by the same proportion the range would not change",
"role": "assistant"
}
] |
[
{
"content": "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: Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\( 24 \\mathrm{~cm}, 17 \\mathrm{~cm}, 42 \\mathrm{~cm}, 26 \\mathrm{~cm}, 13 \\mathrm{~cm} \\)\nTom says if all the plants were cut in half, the range wouldn't change.\nKatie says if all the plants grew by \\( 3 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only\nKatie\n",
"role": "user"
},
{
"content": "Believes if you changed all values by the same proportion the range would not change",
"role": "assistant"
}
] |
[
{
"content": "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: Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\( 24 \\mathrm{~cm}, 17 \\mathrm{~cm}, 42 \\mathrm{~cm}, 26 \\mathrm{~cm}, 13 \\mathrm{~cm} \\)\nTom says if all the plants were cut in half, the range wouldn't change.\nKatie says if all the plants grew by \\( 3 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with?\nIncorrect Answer: Neither is correct\nCorrect Answer: Only\nKatie\n",
"role": "user"
},
{
"content": "Believes if you add the same value to all numbers in the dataset the range will change",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Recall and use the intersecting diagonals properties of a rectangle\nSubject: Properties of Quadrilaterals\nQuestion: The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle at the bottom at the centre is highlighted in yellow.]()\nIncorrect Answer: acute\nCorrect Answer: \\( 90^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Does not know the properties of a rectangle",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Recall and use the intersecting diagonals properties of a rectangle\nSubject: Properties of Quadrilaterals\nQuestion: The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle at the bottom at the centre is highlighted in yellow.]()\nIncorrect Answer: obtuse\nCorrect Answer: \\( 90^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Does not know the properties of a rectangle",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Recall and use the intersecting diagonals properties of a rectangle\nSubject: Properties of Quadrilaterals\nQuestion: The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle at the bottom at the centre is highlighted in yellow.]()\nIncorrect Answer: Not enough information\nCorrect Answer: \\( 90^{\\circ} \\)\n",
"role": "user"
},
{
"content": "Does not know the properties of a rectangle",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Substitute positive integer values into formulae involving powers or roots\nSubject: Substitution into Formula\nQuestion: The equation \\( f=3 r^{2}+3 \\) is used to find values in the table below. What is the value covered by the star? \\begin{tabular}{|c|c|c|c|c|}\n\\hline\\( r \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( f \\) & \\( 6 \\) & \\( 15 \\) & \\( \\color{gold}\\bigstar \\) & \\\\\n\\hline\n\\end{tabular}\nIncorrect Answer: \\( 24 \\)\nCorrect Answer: \\( 30 \\)\n",
"role": "user"
},
{
"content": "Thinks you can find missing values in a given table by treating the row as linear and adding on the difference between the first two values given.",
"role": "assistant"
}
] |
[
{
"content": "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 area\nSubject: Area of Simple Shapes\nQuestion: James has answered a question on the area of a trapezium and got an answer of \\( 54 \\).\n\nBehind the star he has written the units that he used.\n\n\\(\n54 \\, \\bigstar \n\\)\n\nWhich of the following units could be correct?\nIncorrect Answer: \\( m \\)\nCorrect Answer: \\( \\mathrm{mm}^{2} \\)\n",
"role": "user"
},
{
"content": "Does not know units of area should be squared",
"role": "assistant"
}
] |
[
{
"content": "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 area\nSubject: Area of Simple Shapes\nQuestion: James has answered a question on the area of a trapezium and got an answer of \\( 54 \\).\n\nBehind the star he has written the units that he used.\n\n\\(\n54 \\, \\bigstar \n\\)\n\nWhich of the following units could be correct?\nIncorrect Answer: \\( \\mathrm{cm} \\)\nCorrect Answer: \\( \\mathrm{mm}^{2} \\)\n",
"role": "user"
},
{
"content": "Does not know units of area should be squared",
"role": "assistant"
}
] |
[
{
"content": "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 area\nSubject: Area of Simple Shapes\nQuestion: James has answered a question on the area of a trapezium and got an answer of \\( 54 \\).\n\nBehind the star he has written the units that he used.\n\n\\(\n54 \\, \\bigstar \n\\)\n\nWhich of the following units could be correct?\nIncorrect Answer: \\( \\mathrm{km}^{3} \\)\nCorrect Answer: \\( \\mathrm{mm}^{2} \\)\n",
"role": "user"
},
{
"content": "Does not know units of area should be squared",
"role": "assistant"
}
] |
[
{
"content": "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 two digit integer percentages to fractions\nSubject: Converting between Fractions and Percentages\nQuestion: Convert this percentage to a fraction\n\\( 62 \\% \\)\nIncorrect Answer: \\( \\frac{62}{10} \\)\nCorrect Answer: \\( \\frac{31}{50} \\)\n",
"role": "user"
},
{
"content": "Does not understand a percentage is out of 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: Convert two digit integer percentages to fractions\nSubject: Converting between Fractions and Percentages\nQuestion: Convert this percentage to a fraction\n\\( 62 \\% \\)\nIncorrect Answer: \\( \\frac{6}{2} \\)\nCorrect Answer: \\( \\frac{31}{50} \\)\n",
"role": "user"
},
{
"content": "Thinks they can convert a 2 digit percentage to a fraction by writing one number over the other.",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Convert two digit integer percentages to fractions\nSubject: Converting between Fractions and Percentages\nQuestion: Convert this percentage to a fraction\n\\( 62 \\% \\)\nIncorrect Answer: None of these\nCorrect Answer: \\( \\frac{31}{50} \\)\n",
"role": "user"
},
{
"content": "Does not understand a percentage is out of 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: Divide decimals by 10\nSubject: Multiplying and Dividing with Decimals\nQuestion: \\( 43.2 \\div 10= \\)\nIncorrect Answer: \\( 0.432 \\)\nCorrect Answer: \\( 4.32 \\)\n",
"role": "user"
},
{
"content": "Divided by 100 rather than 10",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide decimals by 10\nSubject: Multiplying and Dividing with Decimals\nQuestion: \\( 43.2 \\div 10= \\)\nIncorrect Answer: \\( 33.2 \\)\nCorrect Answer: \\( 4.32 \\)\n",
"role": "user"
},
{
"content": "Subtracts instead of divides",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide decimals by 10\nSubject: Multiplying and Dividing with Decimals\nQuestion: \\( 43.2 \\div 10= \\)\nIncorrect Answer: \\( 43.02 \\)\nCorrect Answer: \\( 4.32 \\)\n",
"role": "user"
},
{
"content": "When dividing a decimal by a multiple of 10, just divides the fractional place values ",
"role": "assistant"
}
] |
[
{
"content": "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{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star?\nIncorrect Answer: \\( 5 \\)\nCorrect Answer: \\( 7 \\)\n",
"role": "user"
},
{
"content": "Does not find a common denominator when adding/subtracting 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{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star?\nIncorrect Answer: \\( 17 \\)\nCorrect Answer: \\( 7 \\)\n",
"role": "user"
},
{
"content": "Adds instead of subtracts",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Subtract proper fractions with different denominators which do not share a common factor\nSubject: Adding and Subtracting Fractions\nQuestion: \\(\n\\frac{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star?\nIncorrect Answer: \\( 3 \\)\nCorrect Answer: \\( 7 \\)\n",
"role": "user"
},
{
"content": "Does not find a common denominator when adding/subtracting fractions",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Identify horizontal translations 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)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\)\nIncorrect Answer: Translation by vector\n\\(\n\\left[\\begin{array}{l}\n0 \\\\\n3\n\\end{array}\\right]\n\\)\nCorrect Answer: Translation by vector\n\\(\n\\left[\\begin{array}{l}\n3 \\\\\n0\n\\end{array}\\right]\n\\)\n",
"role": "user"
},
{
"content": "Believes f(x - a) translates the function up a 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: Identify horizontal translations 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)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\)\nIncorrect Answer: Translation by vector\n\\(\n\\left[\\begin{array}{c}\n0 \\\\\n-3\n\\end{array}\\right]\n\\)\nCorrect Answer: Translation by vector\n\\(\n\\left[\\begin{array}{l}\n3 \\\\\n0\n\\end{array}\\right]\n\\)\n",
"role": "user"
},
{
"content": "Believes f(x + a) translates the function up a 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: Identify horizontal translations 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)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\)\nIncorrect Answer: Translation by vector\n\\(\n\\left[\\begin{array}{r}\n-3 \\\\\n0\n\\end{array}\\right]\n\\)\nCorrect Answer: Translation by vector\n\\(\n\\left[\\begin{array}{l}\n3 \\\\\n0\n\\end{array}\\right]\n\\)\n",
"role": "user"
},
{
"content": "Believes f(x) + a translates the function right a 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: Expand products of three binomials in the form (x + a)(x + b)(x + c)\nSubject: Expanding Triple Brackets and more\nQuestion: John is expanding these three brackets:\n\\(\n(x+5)(x-3)(x+6)\n\\)\n\nHe finds it helpful to split the first bracket and view the problem as follows:\n\\(\nx(x-3)(x+6)+5(x-3)(x+6)\n\\)\n\nHe expands the brackets further. Before he simplifies, what are the terms than contain an \\( \\boldsymbol{x}^{2} \\) ?\nIncorrect Answer: \\( \\begin{array}{l}+6 x^{2} \\\\ +3 x^{2} \\\\ +5 x^{2}\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{l}+6 x^{2} \\\\ -3 x^{2} \\\\ +5 x^{2}\\end{array} \\)\n",
"role": "user"
},
{
"content": "Ignores negative sign when expanding 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: Identify the net of a non-prism\nSubject: Nets\nQuestion: This is the net of a... ![A circle touching a sector]()\nIncorrect Answer: Triangle\nCorrect Answer: Cone\n",
"role": "user"
},
{
"content": "Struggles to visualise nets of 3D shapes",
"role": "assistant"
}
] |
[
{
"content": "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 net of a non-prism\nSubject: Nets\nQuestion: This is the net of a... ![A circle touching a sector]()\nIncorrect Answer: Triangular prism\nCorrect Answer: Cone\n",
"role": "user"
},
{
"content": "Struggles to visualise nets of 3D shapes",
"role": "assistant"
}
] |
[
{
"content": "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 net of a non-prism\nSubject: Nets\nQuestion: This is the net of a... ![A circle touching a sector]()\nIncorrect Answer: Triangularbased pyramid\nCorrect Answer: Cone\n",
"role": "user"
},
{
"content": "Struggles to visualise nets of 3D shapes",
"role": "assistant"
}
] |
[
{
"content": "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 alternate angles\nSubject: Angle Facts with Parallel Lines\nQuestion: Tom and Katie are arguing about alternate angles.\nTom says angles \\( p \\) and \\( q \\) are alternate.\n\nKatie says angles \\( p \\) and \\( q \\) are equal.\nWho is correct? ![Shows two non parallel lines that are intersected by another line. Angles P and Q are both on the outside of the lines and on opposite sides of the transversal.]()\nIncorrect Answer: Only\nKatie\nCorrect Answer: Only\nTom\n",
"role": "user"
},
{
"content": "Thinks alternate angles are always 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: Identify alternate angles\nSubject: Angle Facts with Parallel Lines\nQuestion: Tom and Katie are arguing about alternate angles.\nTom says angles \\( p \\) and \\( q \\) are alternate.\n\nKatie says angles \\( p \\) and \\( q \\) are equal.\nWho is correct? ![Shows two non parallel lines that are intersected by another line. Angles P and Q are both on the outside of the lines and on opposite sides of the transversal.]()\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only\nTom\n",
"role": "user"
},
{
"content": "Thinks alternate angles are always 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: Identify alternate angles\nSubject: Angle Facts with Parallel Lines\nQuestion: Tom and Katie are arguing about alternate angles.\nTom says angles \\( p \\) and \\( q \\) are alternate.\n\nKatie says angles \\( p \\) and \\( q \\) are equal.\nWho is correct? ![Shows two non parallel lines that are intersected by another line. Angles P and Q are both on the outside of the lines and on opposite sides of the transversal.]()\nIncorrect Answer: Neither is correct\nCorrect Answer: Only\nTom\n",
"role": "user"
},
{
"content": "Thinks only angles on parallel lines can be alternate",
"role": "assistant"
}
] |
[
{
"content": "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: Hannah's journey to camp is \\( 3 \\) hours and \\( 16 \\) minutes.\nTori's journey to camp is \\( 214 \\) minutes.\nWhat is the difference in their journeys in minutes?\nIncorrect Answer: \\( 102 \\) minutes\nCorrect Answer: \\( 18 \\) minutes\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: Select the correct answer to an iteration question to the required degree of accuracy\nSubject: Trial and Improvement and Iterative Methods\nQuestion: \\(\nx_{n+1}=5-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=2 \\), what is the solution to \\( x=5-\\frac{1}{x} \\) to \\( 2 \\) decimal places?\nIncorrect Answer: \\( 4.78 \\)\nCorrect Answer: \\( 4.79 \\)\n",
"role": "user"
},
{
"content": "Stops iteration too early when solving equations",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Select the correct answer to an iteration question to the required degree of accuracy\nSubject: Trial and Improvement and Iterative Methods\nQuestion: \\(\nx_{n+1}=5-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=2 \\), what is the solution to \\( x=5-\\frac{1}{x} \\) to \\( 2 \\) decimal places?\nIncorrect Answer: \\( 4.79128 \\ldots \\)\nCorrect Answer: \\( 4.79 \\)\n",
"role": "user"
},
{
"content": "Rounds to the wrong degree of accuracy (rounds too little)",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Select the correct answer to an iteration question to the required degree of accuracy\nSubject: Trial and Improvement and Iterative Methods\nQuestion: \\(\nx_{n+1}=5-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=2 \\), what is the solution to \\( x=5-\\frac{1}{x} \\) to \\( 2 \\) decimal places?\nIncorrect Answer: \\( 4.8 \\)\nCorrect Answer: \\( 4.79 \\)\n",
"role": "user"
},
{
"content": "Rounds to the wrong degree of accuracy (significant figures rather than decimal places)",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of an equilateral triangle where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: How would you calculate the area of this triangle? ![A triangle, base 12m. All three sides are equal.]()\nIncorrect Answer: \\( \\frac{12 \\times 12}{2} \\)\nCorrect Answer: None of these\n",
"role": "user"
},
{
"content": "Has used slant height and base to find area of a triangle rather than perpendicular height and base",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Calculate the area of an equilateral triangle where the dimensions are given in the same units\nSubject: Area of Simple Shapes\nQuestion: How would you calculate the area of this triangle? ![A triangle, base 12m. All three sides are equal.]()\nIncorrect Answer: \\( \\frac{12 \\times 12 \\times 12}{2} \\)\nCorrect Answer: None of these\n",
"role": "user"
},
{
"content": "Multiplies all given dimensions when calculating an 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: Divide a quantity into two parts for a given a ratio, where each part is an integer\nSubject: Sharing in a Ratio\nQuestion: In the diagram, AN : NB \\( =3: 5 \\) \nWhat is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]()\nIncorrect Answer: \\( 16 \\mathrm{~m} \\)\nCorrect Answer: \\( 18 \\mathrm{~m} \\)\n",
"role": "user"
},
{
"content": "Divides total amount by each side of the ratio instead of dividing by the sum of the parts",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Divide a quantity into two parts for a given a ratio, where each part is an integer\nSubject: Sharing in a Ratio\nQuestion: In the diagram, AN : NB \\( =3: 5 \\) \nWhat is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]()\nIncorrect Answer: \\( 30 \\mathrm{~m} \\)\nCorrect Answer: \\( 18 \\mathrm{~m} \\)\n",
"role": "user"
},
{
"content": "Mixes up sides of a ratio",
"role": "assistant"
}
] |
[
{
"content": "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 a quantity into two parts for a given a ratio, where each part is an integer\nSubject: Sharing in a Ratio\nQuestion: In the diagram, AN : NB \\( =3: 5 \\) \nWhat is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]()\nIncorrect Answer: \\( 6 \\mathrm{~m} \\)\nCorrect Answer: \\( 18 \\mathrm{~m} \\)\n",
"role": "user"
},
{
"content": "Finds one part of a ratio but doesn't multiply that by the number of parts needed",
"role": "assistant"
}
] |
[
{
"content": "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 odd and even numbers\nSubject: Ordering Negative Numbers\nQuestion: Which of these shows part of the proof that the sum of two odd numbers is even?\nIncorrect Answer: \\( \\begin{array}{l}2 n+(2 m+1) \\\\ =2(n+m)+1\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{l}(2 n-1)+(2 m+1) \\\\ =2 n+2 m \\\\ =2(n+m)\\end{array} \\)\n",
"role": "user"
},
{
"content": "Does not understand that 2n represents an even 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: Prove statements involving odd and even numbers\nSubject: Ordering Negative Numbers\nQuestion: Which of these shows part of the proof that the sum of two odd numbers is even?\nIncorrect Answer: \\( \\begin{array}{l}(2 n-1)(2 m+1) \\\\ =4 m n+2 n-2 m-1 \\\\ =2(2 m n-n-m)+1\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{l}(2 n-1)+(2 m+1) \\\\ =2 n+2 m \\\\ =2(n+m)\\end{array} \\)\n",
"role": "user"
},
{
"content": "Does not know the meaning of the word \"sum\"",
"role": "assistant"
}
] |
[
{
"content": "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 odd and even numbers\nSubject: Ordering Negative Numbers\nQuestion: Which of these shows part of the proof that the sum of two odd numbers is even?\nIncorrect Answer: \\( \\begin{array}{l}\\text { Odd + Odd } \\\\ =\\text { even }\\end{array} \\)\nCorrect Answer: \\( \\begin{array}{l}(2 n-1)+(2 m+1) \\\\ =2 n+2 m \\\\ =2(n+m)\\end{array} \\)\n",
"role": "user"
},
{
"content": "Does not understand that 2n represents an even 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: Carry out missing number subtraction problems involving negative integers\nSubject: Adding and Subtracting Negative Numbers\nQuestion: ![Number line with -12 and -7 marked. Starting at -12, follow an arrow pointing to the right labelled +10. Then there is an arrow labelled b pointing to the left, which ends at -7 on the number line.]() What is the value of \\( b \\) ?\nIncorrect Answer: \\( -7 \\)\nCorrect Answer: \\( -5 \\)\n",
"role": "user"
},
{
"content": "Assumes that an arrow on a number line starts at zero",
"role": "assistant"
}
] |
[
{
"content": "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 missing number subtraction problems involving negative integers\nSubject: Adding and Subtracting Negative Numbers\nQuestion: ![Number line with -12 and -7 marked. Starting at -12, follow an arrow pointing to the right labelled +10. Then there is an arrow labelled b pointing to the left, which ends at -7 on the number line.]() What is the value of \\( b \\) ?\nIncorrect Answer: \\( -6 \\)\nCorrect Answer: \\( -5 \\)\n",
"role": "user"
},
{
"content": "Counts the starting number when counting backwards",
"role": "assistant"
}
] |
[
{
"content": "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 algebraic fractions where the denominators are single terms and are not multiples of each other\nSubject: Adding and Subtracting Algebraic Fractions\nQuestion: Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\)\nIncorrect Answer: \\( \\frac{1-t}{3 s} \\)\nCorrect Answer: \\( \\frac{3-s t}{3 s} \\)\n",
"role": "user"
},
{
"content": "When subtracting fractions, subtracts the numerators and multiplies the 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: Subtract algebraic fractions where the denominators are single terms and are not multiples of each other\nSubject: Adding and Subtracting Algebraic Fractions\nQuestion: Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\)\nIncorrect Answer: \\( \\frac{s-3 t}{3 s} \\)\nCorrect Answer: \\( \\frac{3-s t}{3 s} \\)\n",
"role": "user"
},
{
"content": "Believes they should multiply each numerator by its original denominator when adding/subtracting 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 algebraic fractions where the denominators are single terms and are not multiples of each other\nSubject: Adding and Subtracting Algebraic Fractions\nQuestion: Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\)\nIncorrect Answer: \\( \\frac{1-t}{s-3} \\)\nCorrect Answer: \\( \\frac{3-s t}{3 s} \\)\n",
"role": "user"
},
{
"content": "Does not find a common denominator when adding/subtracting fractions",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Given the volume of a cuboid, work out missing information\nSubject: Volume of Prisms\nQuestion: The volume of this cuboid is \\( 30 \\mathrm{~cm}^{3} \\)\n\nWhat length should replace the star? ![A cuboid, depth 2cm and height 3cm. The width is labelled with a star.]()\nIncorrect Answer: \\( 25 \\mathrm{~cm} \\)\nCorrect Answer: \\( 5 \\mathrm{~cm} \\)\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: Factorise a quadratic expression in the form ax² + bx + c where a is prime\nSubject: Factorising into a Double Bracket\nQuestion: Step 1: Factorise the following expression\n\n\\(\n3 x^{2}+5 x+2\n\\)\nIncorrect Answer: \\( (3 x+2)(3 x+1) \\)\nCorrect Answer: \\( (3 x+2)(x+1) \\)\n",
"role": "user"
},
{
"content": "When factorising a quadratic with a non-unit coefficient of x squared, believes that coefficient will be in front of both x terms 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: Given the solution to one problem, deduce the answer to a related problem using the same operation\nSubject: Mental Addition and Subtraction\nQuestion: Tom and Katie are discussing related calculations\nTom says if you know that \\( 3748+426=4174 \\), then \\( 3748+427 \\) must equal \\( \\mathbf{4 1 7 5} \\)\n\nKatie says if you know that \\( 3748-426=3322 \\), then \\( 3748 \\) - \\( 427 \\) must equal \\( \\mathbf{3 3 2 3} \\)\nWho is correct?\nIncorrect Answer: Only Katie\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Does not realise that adding a larger number gives a larger 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: Given the solution to one problem, deduce the answer to a related problem using the same operation\nSubject: Mental Addition and Subtraction\nQuestion: Tom and Katie are discussing related calculations\nTom says if you know that \\( 3748+426=4174 \\), then \\( 3748+427 \\) must equal \\( \\mathbf{4 1 7 5} \\)\n\nKatie says if you know that \\( 3748-426=3322 \\), then \\( 3748 \\) - \\( 427 \\) must equal \\( \\mathbf{3 3 2 3} \\)\nWho is correct?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only Tom\n",
"role": "user"
},
{
"content": "Does not realise that subtracting a larger number will give a smaller 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: Interpret sloping linear sections of a displacement-time graph\nSubject: Real Life Graphs\nQuestion: This graph shows how far Fido the dog is from his home.\nWhat might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis. ]()\nIncorrect Answer: Fido has fallen asleep\nCorrect Answer: Fido is walking home\n",
"role": "user"
},
{
"content": "Confuses rest and movement on a distance time 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: Interpret sloping linear sections of a displacement-time graph\nSubject: Real Life Graphs\nQuestion: This graph shows how far Fido the dog is from his home.\nWhat might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis. ]()\nIncorrect Answer: Fido is accelerating\nCorrect Answer: Fido is walking home\n",
"role": "user"
},
{
"content": "Believes the gradient of a distance-time graph is the acceleration",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Interpret sloping linear sections of a displacement-time graph\nSubject: Real Life Graphs\nQuestion: This graph shows how far Fido the dog is from his home.\nWhat might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis. ]()\nIncorrect Answer: Fido is walking away from home\nCorrect Answer: Fido is walking home\n",
"role": "user"
},
{
"content": "Believes a downward slope on a distance-time graph means travelling away",
"role": "assistant"
}
] |
[
{
"content": "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 missing number mental multiplication questions\nSubject: Mental Multiplication and Division\nQuestion: What should replace the star?\n\\[\n\\bigstar \\times 4=108\n\\]\nIncorrect Answer: \\( 432 \\)\nCorrect Answer: \\( 27 \\)\n",
"role": "user"
},
{
"content": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve missing number mental multiplication questions\nSubject: Mental Multiplication and Division\nQuestion: What should replace the star?\n\\[\n\\bigstar \\times 4=108\n\\]\nIncorrect Answer: \\( 104 \\)\nCorrect Answer: \\( 27 \\)\n",
"role": "user"
},
{
"content": "Adds instead of multiples",
"role": "assistant"
}
] |
[
{
"content": "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 speed where distance and time are in the appropriate units\nSubject: Substitution into Formula\nQuestion: The formula for speed is\n\\(\n\\text { Speed }=\\frac{\\text { Distance }}{\\text { Time }}\n\\)\nA snail travels \\( 4 \\mathrm{~m} \\) in \\( 10 \\) hours. What was its speed?\nIncorrect Answer: \\( 40 \\) metres per hour\nCorrect Answer: \\( 0.4 \\) metres per hour\n",
"role": "user"
},
{
"content": "Believes speed is distance multiplied by 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: Calculate speed where distance and time are in the appropriate units\nSubject: Substitution into Formula\nQuestion: The formula for speed is\n\\(\n\\text { Speed }=\\frac{\\text { Distance }}{\\text { Time }}\n\\)\nA snail travels \\( 4 \\mathrm{~m} \\) in \\( 10 \\) hours. What was its speed?\nIncorrect Answer: \\( 2.5 \\) metres per hour\nCorrect Answer: \\( 0.4 \\) metres per hour\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 sketch of a circle with centre at the origin, write its equation in the form x² + y² = r²\nSubject: Equation of a Circle\nQuestion: What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]()\nIncorrect Answer: \\( x^{2}+y^{2}=\\sqrt{4} \\)\nCorrect Answer: \\( x^{2}+y^{2}=16 \\)\n",
"role": "user"
},
{
"content": "Confuses the square root of the radius with the radius squared in the equation of a circle",
"role": "assistant"
}
] |
[
{
"content": "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 circle with centre at the origin, write its equation in the form x² + y² = r²\nSubject: Equation of a Circle\nQuestion: What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]()\nIncorrect Answer: \\( x^{2}+y^{2}=8 \\)\nCorrect Answer: \\( x^{2}+y^{2}=16 \\)\n",
"role": "user"
},
{
"content": "Mixes up squaring and multiplying by 2 or doubling",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Given a sketch of a circle with centre at the origin, write its equation in the form x² + y² = r²\nSubject: Equation of a Circle\nQuestion: What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]()\nIncorrect Answer: \\( x^{2}+y^{2}=4 \\)\nCorrect Answer: \\( x^{2}+y^{2}=16 \\)\n",
"role": "user"
},
{
"content": "Confuses the radius with the radius squared in the equation of a circle",
"role": "assistant"
}
] |
[
{
"content": "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 expressions involving no powers or roots\nSubject: Substitution into Formula\nQuestion: If \\( d=-2 \\) what is the value of \\( 10-2 d \\) ?\nIncorrect Answer: \\( 6 \\)\nCorrect Answer: \\( 14 \\)\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: Count backwards in steps of of something other than one\nSubject: Counting\nQuestion: George is counting backwards in steps of \\( 5 \\).\nHe starts at the number \\( 19,103 \\) what is the next number he will say?\nIncorrect Answer: \\( 19,102 \\)\nCorrect Answer: \\( 19,098 \\)\n",
"role": "user"
},
{
"content": "Counts on by 1, when asked to count forward/backwards in a step other than 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: Count backwards in steps of of something other than one\nSubject: Counting\nQuestion: George is counting backwards in steps of \\( 5 \\).\nHe starts at the number \\( 19,103 \\) what is the next number he will say?\nIncorrect Answer: \\( 19,099 \\)\nCorrect Answer: \\( 19,098 \\)\n",
"role": "user"
},
{
"content": "Counts the starting number when counting backwards",
"role": "assistant"
}
] |
[
{
"content": "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\\[\n2 n+3 \\leq 3 n-7\n\\]\nIncorrect Answer: \\( 2 \\leq n \\)\nCorrect Answer: \\( 10 \\leq 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\\[\n2 n+3 \\leq 3 n-7\n\\]\nIncorrect Answer: \\( n \\leq 10 \\)\nCorrect Answer: \\( 10 \\leq 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: Solve linear inequalities in one variable where the unknown appears on boths sides of the equation\nSubject: Solving Linear Inequalities\nQuestion: Solve\n\\[\n2 n+3 \\leq 3 n-7\n\\]\nIncorrect Answer: \\( -4 \\leq n \\)\nCorrect Answer: \\( 10 \\leq 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: Determine the function of a single function machine used to create an algebraic expression\nSubject: Function Machines\nQuestion: Tom and Katie are discussing this function machine ![A function machine with an input of m+2, no function labelled and an output of 3m+2]() Tom says the function could be \\( +2 m \\)\nKatie says the function could be \\( \\times 3 \\)\nWho do you agree with?\nIncorrect Answer: Both Tom and Katie\nCorrect Answer: Only\nTom\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: Convert between cm and m\nSubject: Length Units\nQuestion: \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \nIncorrect Answer: \\( 45 \\)\nCorrect Answer: \\( 4.5 \\)\n",
"role": "user"
},
{
"content": "Thinks there are 10cm in a metre",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Convert between cm and m\nSubject: Length Units\nQuestion: \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \nIncorrect Answer: \\( 5 \\)\nCorrect Answer: \\( 4.5 \\)\n",
"role": "user"
},
{
"content": "Gives a rounded whole number instead of a decimal",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Convert between cm and m\nSubject: Length Units\nQuestion: \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \nIncorrect Answer: \\( 45000 \\)\nCorrect Answer: \\( 4.5 \\)\n",
"role": "user"
},
{
"content": "Multiplies when converting to a larger unit",
"role": "assistant"
}
] |
[
{
"content": "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 equations with the variable appearing on both sides, involving positive fractions\nSubject: Linear Equations\nQuestion: Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\)\nIncorrect Answer: \\( \\frac{2 r}{5}=5+r \\)\nCorrect Answer: \\( 2 r-3=10+5 r \\)\n",
"role": "user"
},
{
"content": "Adds or subtracts from numerator first when solving an equation with a fraction",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Solve linear equations with the variable appearing on both sides, involving positive fractions\nSubject: Linear Equations\nQuestion: Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\)\nIncorrect Answer: \\( 10 r-15=10+5 r \\)\nCorrect Answer: \\( 2 r-3=10+5 r \\)\n",
"role": "user"
},
{
"content": "Incorrectly clears fractions from 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: Solve linear equations with the variable appearing on both sides, involving positive fractions\nSubject: Linear Equations\nQuestion: Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\)\nIncorrect Answer: \\( 2 r-3=10+r \\)\nCorrect Answer: \\( 2 r-3=10+5 r \\)\n",
"role": "user"
},
{
"content": "When solving an equation with a fraction, thinks you don't need to multiply every term on both sides when multiplying by the denominator ",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Given a situation sketch an appropriate real life graph\nSubject: Real Life Graphs\nQuestion: Water is poured into a glass at a constant rate.\n\nThis graph shows how the depth \\( (d) \\) of water in a glass changes over time \\( (t) \\).\n\nWhich of the following glasses is this most likely to be the graph of? ![A depth-time graph which is a curve starting at (0, 0), with a steep gradient to begin with but then the gradient decreases and the graph levels off to almost horizontal.]()\nIncorrect Answer: ![A cylinder sitting on one of its circular faces.]()\nCorrect Answer: ![A shape that looks like a beaker. It has a circular base, with sloped edges up to a larger circular face at the top.]()\n",
"role": "user"
},
{
"content": "Does not interpret a sloping gradient as a change in rate",
"role": "assistant"
}
] |
[
{
"content": "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 real life graph\nSubject: Real Life Graphs\nQuestion: Water is poured into a glass at a constant rate.\n\nThis graph shows how the depth \\( (d) \\) of water in a glass changes over time \\( (t) \\).\n\nWhich of the following glasses is this most likely to be the graph of? ![A depth-time graph which is a curve starting at (0, 0), with a steep gradient to begin with but then the gradient decreases and the graph levels off to almost horizontal.]()\nIncorrect Answer: ![A narrow cylinder with a wide cylinder on top.]()\nCorrect Answer: ![A shape that looks like a beaker. It has a circular base, with sloped edges up to a larger circular face at the top.]()\n",
"role": "user"
},
{
"content": "Does not spot the difference between a gradual change of gradient and 2 distinct line segments with different constant gradients",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Find another power of 10 less than a given number\nSubject: Place Value\nQuestion: What number is \\( 10,000 \\) less than \\( 901,426 \\) ?\nIncorrect Answer: \\( 801,426 \\)\nCorrect Answer: \\( 891,426 \\)\n",
"role": "user"
},
{
"content": "When subtracting a power of 10, subtracts from the wrong column",
"role": "assistant"
}
] |
[
{
"content": "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 another power of 10 less than a given number\nSubject: Place Value\nQuestion: What number is \\( 10,000 \\) less than \\( 901,426 \\) ?\nIncorrect Answer: \\( 911,426 \\)\nCorrect Answer: \\( 891,426 \\)\n",
"role": "user"
},
{
"content": "Adds rather than subtracts when answering worded 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: Find another power of 10 less than a given number\nSubject: Place Value\nQuestion: What number is \\( 10,000 \\) less than \\( 901,426 \\) ?\nIncorrect Answer: \\( 90.1426 \\)\nCorrect Answer: \\( 891,426 \\)\n",
"role": "user"
},
{
"content": "Divides rather than subtracts when given the command 'less than'",
"role": "assistant"
}
] |
[
{
"content": "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 1 decimal place to percentages\nSubject: Converting between Decimals and Percentages\nQuestion: Convert this decimal to a percentage\n\\[\n0.6\n\\]\nIncorrect Answer: \\( 6 \\% \\)\nCorrect Answer: \\( 60 \\% \\)\n",
"role": "user"
},
{
"content": "Multiplies by 10 instead of 100 when converting decimal to 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: Convert decimals less than 1 with 1 decimal place to percentages\nSubject: Converting between Decimals and Percentages\nQuestion: Convert this decimal to a percentage\n\\[\n0.6\n\\]\nIncorrect Answer: \\( 0.6 \\% \\)\nCorrect Answer: \\( 60 \\% \\)\n",
"role": "user"
},
{
"content": "Thinks you need to just add a % sign to a decimal to convert 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: Convert decimals less than 1 with 1 decimal place to percentages\nSubject: Converting between Decimals and Percentages\nQuestion: Convert this decimal to a percentage\n\\[\n0.6\n\\]\nIncorrect Answer: \\( 0.006 \\% \\)\nCorrect Answer: \\( 60 \\% \\)\n",
"role": "user"
},
{
"content": "Divides instead of multiplies 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: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable\nSubject: Simplifying Expressions by Collecting Like Terms\nQuestion: Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\]\nIncorrect Answer: \\( 4 \\times d \\)\nCorrect Answer: \\( 4 d \\)\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: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable\nSubject: Simplifying Expressions by Collecting Like Terms\nQuestion: Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\]\nIncorrect Answer: \\( d 4 \\)\nCorrect Answer: \\( 4 d \\)\n",
"role": "user"
},
{
"content": "Writes the variable before the coefficient in an algebraic 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: Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable\nSubject: Simplifying Expressions by Collecting Like Terms\nQuestion: Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\]\nIncorrect Answer: \\( d^{4} \\)\nCorrect Answer: \\( 4 d \\)\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: Simplify fractions that simplify to a unit fraction\nSubject: Simplifying Fractions\nQuestion: Write this fraction as simply as possible:\n\\(\n\\frac{9}{12}\n\\)\nIncorrect Answer: \\( \\frac{3}{6} \\)\nCorrect Answer: \\( \\frac{3}{4} \\)\n",
"role": "user"
},
{
"content": "Believes when simplifying a fraction you can divide the numerator and denominator by different values",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Simplify fractions that simplify to a unit fraction\nSubject: Simplifying Fractions\nQuestion: Write this fraction as simply as possible:\n\\(\n\\frac{9}{12}\n\\)\nIncorrect Answer: \\( \\frac{9}{12} \\)\nCorrect Answer: \\( \\frac{3}{4} \\)\n",
"role": "user"
},
{
"content": "Does not recognise when a fraction can be simplified",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Add algebraic fractions where one denominator is a multiple of the other\nSubject: Adding and Subtracting Algebraic Fractions\nQuestion: Write this as a single fraction as simply as possible:\n\\(\n\\frac{3}{2 x}+\\frac{4}{x}\n\\)\nIncorrect Answer: \\( \\frac{7}{3 x} \\)\nCorrect Answer: \\( \\frac{11}{2 x} \\)\n",
"role": "user"
},
{
"content": "When adding fractions, adds 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: Add algebraic fractions where one denominator is a multiple of the other\nSubject: Adding and Subtracting Algebraic Fractions\nQuestion: Write this as a single fraction as simply as possible:\n\\(\n\\frac{3}{2 x}+\\frac{4}{x}\n\\)\nIncorrect Answer: \\( \\frac{7}{2 x} \\)\nCorrect Answer: \\( \\frac{11}{2 x} \\)\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: Carry out a subtraction problem with positive integers where the answer is less than 0\nSubject: Place Value\nQuestion: \\( 598-1000= \\)\nIncorrect Answer: \\( 402 \\)\nCorrect Answer: \\( -402 \\)\n",
"role": "user"
},
{
"content": "Believes the smaller number is always subtracted from the larger, regardless of the order of the calculation",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Carry out a subtraction problem with positive integers where the answer is less than 0\nSubject: Place Value\nQuestion: \\( 598-1000= \\)\nIncorrect Answer: \\( -412 \\)\nCorrect Answer: \\( -402 \\)\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: Carry out a subtraction problem with positive integers where the answer is less than 0\nSubject: Place Value\nQuestion: \\( 598-1000= \\)\nIncorrect Answer: This problem cannot be solved\nCorrect Answer: \\( -402 \\)\n",
"role": "user"
},
{
"content": "Believes it is impossible to subtract a bigger number from a smaller 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: Read values off a real life graph\nSubject: Real Life Graphs\nQuestion: Lethna pays at one rate for the first \\( 100 \\) units of electricity she uses. She pays at a different rate for all the other units of electricity she uses.\n\nHow much must she pay for using a total of \\( 1000 \\) units of electricity? ![A graph showing how the cost changes for different numbers of units. The first 100 units cost £0.25 per unit. Then the rate changes to £0.10 per unit.]()\nIncorrect Answer: \\( £ 130 \\)\nCorrect Answer: \\( £ 115 \\)\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: Write a missing term of an ascending integer linear sequence\nSubject: Linear Sequences (nth term)\nQuestion: The \\( 1^{\\text {st }} \\) term in a linear sequence is \\( 7 \\).\n\nThe \\( 4^{\\text {th }} \\) term of the sequence is \\( 25 \\).\n\nWhat is the \\( 8^{\\text {th }} \\) term of the sequence?\nIncorrect Answer: \\( 50 \\)\nCorrect Answer: \\( 49 \\)\n",
"role": "user"
},
{
"content": "Believes there is a multiplicative relationship between values of terms in a linear sequence e.g. 10th term is double 5th 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 a missing term of an ascending integer linear sequence\nSubject: Linear Sequences (nth term)\nQuestion: The \\( 1^{\\text {st }} \\) term in a linear sequence is \\( 7 \\).\n\nThe \\( 4^{\\text {th }} \\) term of the sequence is \\( 25 \\).\n\nWhat is the \\( 8^{\\text {th }} \\) term of the sequence?\nIncorrect Answer: \\( 56 \\)\nCorrect Answer: \\( 49 \\)\n",
"role": "user"
},
{
"content": "Believes you multiply the constant difference by the term number to get the term 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: Given a gradient, state the gradient of a line parallel to it\nSubject: Parallel Lines\nQuestion: A line has a gradient of \\( 5 \\)\n\nA line parallel to this line would have a gradient of...\nIncorrect Answer: \\( -5 \\)\nCorrect Answer: \\( 5 \\)\n",
"role": "user"
},
{
"content": "Believes parallel lines have gradients of opposite signs",
"role": "assistant"
}
] |
[
{
"content": "You are an assistant trying to identify the misconception that led to the incorrect answer instead of the correct one",
"role": "system"
},
{
"content": "\nConstruct: Given a gradient, state the gradient of a line parallel to it\nSubject: Parallel Lines\nQuestion: A line has a gradient of \\( 5 \\)\n\nA line parallel to this line would have a gradient of...\nIncorrect Answer: \\( -\\frac{1}{5} \\)\nCorrect Answer: \\( 5 \\)\n",
"role": "user"
},
{
"content": "Believes parallel lines have gradients that multiply to give -1",
"role": "assistant"
}
] |