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bwowe

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mis_conv

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[ { "from": "human", "value": "Use the order of operations to carry out calculations involving powers \\[\n3 \\times 2+4-5\n\\]\nWhere do the brackets need to go to make the answer equal \\( 13 \\) ? Does not need brackets" }, { "from": "gpt", "value": "Confuses the order of operations, believes addition comes before multiplication " } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\) \\( m+1 \\)" }, { "from": "gpt", "value": "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" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\) \\( m+2 \\)" }, { "from": "gpt", "value": "Thinks that when you cancel identical terms from the numerator and denominator, they just disappear" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\) \\( m-1 \\)" }, { "from": "gpt", "value": "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" } ]

[ { "from": "human", "value": "Calculate the range from a list of data 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? Only\nTom" }, { "from": "gpt", "value": "Believes if you changed all values by the same proportion the range would not change" } ]

[ { "from": "human", "value": "Calculate the range from a list of data 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? Both Tom and Katie" }, { "from": "gpt", "value": "Believes if you changed all values by the same proportion the range would not change" } ]

[ { "from": "human", "value": "Calculate the range from a list of data 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? Neither is correct" }, { "from": "gpt", "value": "Believes if you add the same value to all numbers in the dataset the range will change" } ]

[ { "from": "human", "value": "Recall and use the intersecting diagonals properties of a rectangle 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.]() acute" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]

[ { "from": "human", "value": "Recall and use the intersecting diagonals properties of a rectangle 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.]() obtuse" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]

[ { "from": "human", "value": "Recall and use the intersecting diagonals properties of a rectangle 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.]() Not enough information" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]

[ { "from": "human", "value": "Substitute positive integer values into formulae involving powers or roots 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} \\( 24 \\)" }, { "from": "gpt", "value": "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." } ]

[ { "from": "human", "value": "Identify a unit of area 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? \\( m \\)" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]

[ { "from": "human", "value": "Identify a unit of area 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? \\( \\mathrm{cm} \\)" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]

[ { "from": "human", "value": "Identify a unit of area 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? \\( \\mathrm{km}^{3} \\)" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]

[ { "from": "human", "value": "Convert two digit integer percentages to fractions Convert this percentage to a fraction\n\\( 62 \\% \\) \\( \\frac{62}{10} \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]

[ { "from": "human", "value": "Convert two digit integer percentages to fractions Convert this percentage to a fraction\n\\( 62 \\% \\) \\( \\frac{6}{2} \\)" }, { "from": "gpt", "value": "Thinks they can convert a 2 digit percentage to a fraction by writing one number over the other." } ]

[ { "from": "human", "value": "Convert two digit integer percentages to fractions Convert this percentage to a fraction\n\\( 62 \\% \\) None of these" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]

[ { "from": "human", "value": "Divide decimals by 10 \\( 43.2 \\div 10= \\) \\( 0.432 \\)" }, { "from": "gpt", "value": "Divided by 100 rather than 10" } ]

[ { "from": "human", "value": "Divide decimals by 10 \\( 43.2 \\div 10= \\) \\( 33.2 \\)" }, { "from": "gpt", "value": "Subtracts instead of divides" } ]

[ { "from": "human", "value": "Divide decimals by 10 \\( 43.2 \\div 10= \\) \\( 43.02 \\)" }, { "from": "gpt", "value": "When dividing a decimal by a multiple of 10, just divides the fractional place values " } ]

[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star? \\( 5 \\)" }, { "from": "gpt", "value": "Does not find a common denominator when adding/subtracting fractions" } ]

[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star? \\( 17 \\)" }, { "from": "gpt", "value": "Adds instead of subtracts" } ]

[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star? \\( 3 \\)" }, { "from": "gpt", "value": "Does not find a common denominator when adding/subtracting fractions" } ]

[ { "from": "human", "value": "Identify horizontal translations in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\) Translation by vector\n\\(\n\\left[\\begin{array}{l}\n0 \\\\\n3\n\\end{array}\\right]\n\\)" }, { "from": "gpt", "value": "Believes f(x - a) translates the function up a units" } ]

[ { "from": "human", "value": "Identify horizontal translations in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\) Translation by vector\n\\(\n\\left[\\begin{array}{c}\n0 \\\\\n-3\n\\end{array}\\right]\n\\)" }, { "from": "gpt", "value": "Believes f(x + a) translates the function up a units" } ]

[ { "from": "human", "value": "Identify horizontal translations in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\) Translation by vector\n\\(\n\\left[\\begin{array}{r}\n-3 \\\\\n0\n\\end{array}\\right]\n\\)" }, { "from": "gpt", "value": "Believes f(x) + a translates the function right a units" } ]

[ { "from": "human", "value": "Expand products of three binomials in the form (x + a)(x + b)(x + c) 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} \\) ? \\( \\begin{array}{l}+6 x^{2} \\\\ +3 x^{2} \\\\ +5 x^{2}\\end{array} \\)" }, { "from": "gpt", "value": "Ignores negative sign when expanding bracket" } ]

[ { "from": "human", "value": "Identify the net of a non-prism This is the net of a... ![A circle touching a sector]() Triangle" }, { "from": "gpt", "value": "Struggles to visualise nets of 3D shapes" } ]

[ { "from": "human", "value": "Identify the net of a non-prism This is the net of a... ![A circle touching a sector]() Triangular prism" }, { "from": "gpt", "value": "Struggles to visualise nets of 3D shapes" } ]

[ { "from": "human", "value": "Identify the net of a non-prism This is the net of a... ![A circle touching a sector]() Triangularbased pyramid" }, { "from": "gpt", "value": "Struggles to visualise nets of 3D shapes" } ]

[ { "from": "human", "value": "Identify alternate angles 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.]() Only\nKatie" }, { "from": "gpt", "value": "Thinks alternate angles are always equal" } ]

[ { "from": "human", "value": "Identify alternate angles 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.]() Both Tom and Katie" }, { "from": "gpt", "value": "Thinks alternate angles are always equal" } ]

[ { "from": "human", "value": "Identify alternate angles 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.]() Neither is correct" }, { "from": "gpt", "value": "Thinks only angles on parallel lines can be alternate" } ]

[ { "from": "human", "value": "Convert from hours to minutes 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? \\( 102 \\) minutes" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]

[ { "from": "human", "value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\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? \\( 4.78 \\)" }, { "from": "gpt", "value": "Stops iteration too early when solving equations" } ]

[ { "from": "human", "value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\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? \\( 4.79128 \\ldots \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\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? \\( 4.8 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (significant figures rather than decimal places)" } ]

[ { "from": "human", "value": "Calculate the area of an equilateral triangle where the dimensions are given in the same units How would you calculate the area of this triangle? ![A triangle, base 12m. All three sides are equal.]() \\( \\frac{12 \\times 12}{2} \\)" }, { "from": "gpt", "value": "Has used slant height and base to find area of a triangle rather than perpendicular height and base" } ]

[ { "from": "human", "value": "Calculate the area of an equilateral triangle where the dimensions are given in the same units How would you calculate the area of this triangle? ![A triangle, base 12m. All three sides are equal.]() \\( \\frac{12 \\times 12 \\times 12}{2} \\)" }, { "from": "gpt", "value": "Multiplies all given dimensions when calculating an area" } ]

[ { "from": "human", "value": "Divide a quantity into two parts for a given a ratio, where each part is an integer 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.]() \\( 16 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Divides total amount by each side of the ratio instead of dividing by the sum of the parts" } ]

[ { "from": "human", "value": "Divide a quantity into two parts for a given a ratio, where each part is an integer 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.]() \\( 30 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]

[ { "from": "human", "value": "Divide a quantity into two parts for a given a ratio, where each part is an integer 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.]() \\( 6 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Finds one part of a ratio but doesn't multiply that by the number of parts needed" } ]

[ { "from": "human", "value": "Prove statements involving odd and even numbers Which of these shows part of the proof that the sum of two odd numbers is even? \\( \\begin{array}{l}2 n+(2 m+1) \\\\ =2(n+m)+1\\end{array} \\)" }, { "from": "gpt", "value": "Does not understand that 2n represents an even number" } ]

[ { "from": "human", "value": "Prove statements involving odd and even numbers Which of these shows part of the proof that the sum of two odd numbers is even? \\( \\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} \\)" }, { "from": "gpt", "value": "Does not know the meaning of the word \"sum\"" } ]

[ { "from": "human", "value": "Prove statements involving odd and even numbers Which of these shows part of the proof that the sum of two odd numbers is even? \\( \\begin{array}{l}\\text { Odd + Odd } \\\\ =\\text { even }\\end{array} \\)" }, { "from": "gpt", "value": "Does not understand that 2n represents an even number" } ]

[ { "from": "human", "value": "Carry out missing number subtraction problems involving negative integers ![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 \\) ? \\( -7 \\)" }, { "from": "gpt", "value": "Assumes that an arrow on a number line starts at zero" } ]

[ { "from": "human", "value": "Carry out missing number subtraction problems involving negative integers ![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 \\) ? \\( -6 \\)" }, { "from": "gpt", "value": "Counts the starting number when counting backwards" } ]

[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are single terms and are not multiples of each other Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\) \\( \\frac{1-t}{3 s} \\)" }, { "from": "gpt", "value": "When subtracting fractions, subtracts the numerators and multiplies the denominators" } ]

[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are single terms and are not multiples of each other Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\) \\( \\frac{s-3 t}{3 s} \\)" }, { "from": "gpt", "value": "Believes they should multiply each numerator by its original denominator when adding/subtracting fractions" } ]

[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are single terms and are not multiples of each other Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\) \\( \\frac{1-t}{s-3} \\)" }, { "from": "gpt", "value": "Does not find a common denominator when adding/subtracting fractions" } ]

[ { "from": "human", "value": "Given the volume of a cuboid, work out missing information 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.]() \\( 25 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Adds when calculating volume instead of multiplying" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² + bx + c where a is prime Step 1: Factorise the following expression\n\n\\(\n3 x^{2}+5 x+2\n\\) \\( (3 x+2)(3 x+1) \\)" }, { "from": "gpt", "value": "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" } ]

[ { "from": "human", "value": "Given the solution to one problem, deduce the answer to a related problem using the same operation 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? Only Katie" }, { "from": "gpt", "value": "Does not realise that adding a larger number gives a larger answer" } ]

[ { "from": "human", "value": "Given the solution to one problem, deduce the answer to a related problem using the same operation 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? Both Tom and Katie" }, { "from": "gpt", "value": "Does not realise that subtracting a larger number will give a smaller answer" } ]

[ { "from": "human", "value": "Interpret sloping linear sections of a displacement-time graph 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. ]() Fido has fallen asleep" }, { "from": "gpt", "value": "Confuses rest and movement on a distance time graph" } ]

[ { "from": "human", "value": "Interpret sloping linear sections of a displacement-time graph 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. ]() Fido is accelerating" }, { "from": "gpt", "value": "Believes the gradient of a distance-time graph is the acceleration" } ]

[ { "from": "human", "value": "Interpret sloping linear sections of a displacement-time graph 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. ]() Fido is walking away from home" }, { "from": "gpt", "value": "Believes a downward slope on a distance-time graph means travelling away" } ]

[ { "from": "human", "value": "Solve missing number mental multiplication questions What should replace the star?\n\\[\n\\bigstar \\times 4=108\n\\] \\( 432 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]

[ { "from": "human", "value": "Solve missing number mental multiplication questions What should replace the star?\n\\[\n\\bigstar \\times 4=108\n\\] \\( 104 \\)" }, { "from": "gpt", "value": "Adds instead of multiples" } ]

[ { "from": "human", "value": "Calculate speed where distance and time are in the appropriate units 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? \\( 40 \\) metres per hour" }, { "from": "gpt", "value": "Believes speed is distance multiplied by time" } ]

[ { "from": "human", "value": "Calculate speed where distance and time are in the appropriate units 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? \\( 2.5 \\) metres per hour" }, { "from": "gpt", "value": "Believes division is commutative " } ]

[ { "from": "human", "value": "Given a sketch of a circle with centre at the origin, write its equation in the form x² + y² = r² 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). ]() \\( x^{2}+y^{2}=\\sqrt{4} \\)" }, { "from": "gpt", "value": "Confuses the square root of the radius with the radius squared in the equation of a circle" } ]

[ { "from": "human", "value": "Given a sketch of a circle with centre at the origin, write its equation in the form x² + y² = r² 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). ]() \\( x^{2}+y^{2}=8 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]

[ { "from": "human", "value": "Given a sketch of a circle with centre at the origin, write its equation in the form x² + y² = r² 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). ]() \\( x^{2}+y^{2}=4 \\)" }, { "from": "gpt", "value": "Confuses the radius with the radius squared in the equation of a circle" } ]

[ { "from": "human", "value": "Substitute negative integer values into expressions involving no powers or roots If \\( d=-2 \\) what is the value of \\( 10-2 d \\) ? \\( 6 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]

[ { "from": "human", "value": "Count backwards in steps of of something other than one George is counting backwards in steps of \\( 5 \\).\nHe starts at the number \\( 19,103 \\) what is the next number he will say? \\( 19,102 \\)" }, { "from": "gpt", "value": "Counts on by 1, when asked to count forward/backwards in a step other than 1" } ]

[ { "from": "human", "value": "Count backwards in steps of of something other than one George is counting backwards in steps of \\( 5 \\).\nHe starts at the number \\( 19,103 \\) what is the next number he will say? \\( 19,099 \\)" }, { "from": "gpt", "value": "Counts the starting number when counting backwards" } ]

[ { "from": "human", "value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n2 n+3 \\leq 3 n-7\n\\] \\( 2 \\leq n \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n2 n+3 \\leq 3 n-7\n\\] \\( n \\leq 10 \\)" }, { "from": "gpt", "value": "Believes they can multiply/divide through by a negative number without changing the direction of the inequality" } ]

[ { "from": "human", "value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n2 n+3 \\leq 3 n-7\n\\] \\( -4 \\leq n \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Determine the function of a single function machine used to create an algebraic expression 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? Both Tom and Katie" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]

[ { "from": "human", "value": "Convert between cm and m \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \\( 45 \\)" }, { "from": "gpt", "value": "Thinks there are 10cm in a metre" } ]

[ { "from": "human", "value": "Convert between cm and m \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \\( 5 \\)" }, { "from": "gpt", "value": "Gives a rounded whole number instead of a decimal" } ]

[ { "from": "human", "value": "Convert between cm and m \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \\( 45000 \\)" }, { "from": "gpt", "value": "Multiplies when converting to a larger unit" } ]

[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\) \\( \\frac{2 r}{5}=5+r \\)" }, { "from": "gpt", "value": "Adds or subtracts from numerator first when solving an equation with a fraction" } ]

[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\) \\( 10 r-15=10+5 r \\)" }, { "from": "gpt", "value": "Incorrectly clears fractions from equations" } ]

[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\) \\( 2 r-3=10+r \\)" }, { "from": "gpt", "value": "When solving an equation with a fraction, thinks you don't need to multiply every term on both sides when multiplying by the denominator " } ]

[ { "from": "human", "value": "Given a situation sketch an appropriate real life graph 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.]() ![A cylinder sitting on one of its circular faces.]()" }, { "from": "gpt", "value": "Does not interpret a sloping gradient as a change in rate" } ]

[ { "from": "human", "value": "Given a situation sketch an appropriate real life graph 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.]() ![A narrow cylinder with a wide cylinder on top.]()" }, { "from": "gpt", "value": "Does not spot the difference between a gradual change of gradient and 2 distinct line segments with different constant gradients" } ]

[ { "from": "human", "value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 901,426 \\) ? \\( 801,426 \\)" }, { "from": "gpt", "value": "When subtracting a power of 10, subtracts from the wrong column" } ]

[ { "from": "human", "value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 901,426 \\) ? \\( 911,426 \\)" }, { "from": "gpt", "value": "Adds rather than subtracts when answering worded problems" } ]

[ { "from": "human", "value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 901,426 \\) ? \\( 90.1426 \\)" }, { "from": "gpt", "value": "Divides rather than subtracts when given the command 'less than'" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 1 decimal place to percentages Convert this decimal to a percentage\n\\[\n0.6\n\\] \\( 6 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 1 decimal place to percentages Convert this decimal to a percentage\n\\[\n0.6\n\\] \\( 0.6 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a decimal to convert to a percentage" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 1 decimal place to percentages Convert this decimal to a percentage\n\\[\n0.6\n\\] \\( 0.006 \\% \\)" }, { "from": "gpt", "value": "Divides instead of multiplies when converting a decimal to a percentage" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\] \\( 4 \\times d \\)" }, { "from": "gpt", "value": "Does not realize we can omit the multiplication symbol in algebraic expressions" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\] \\( d 4 \\)" }, { "from": "gpt", "value": "Writes the variable before the coefficient in an algebraic term" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\] \\( d^{4} \\)" }, { "from": "gpt", "value": "Confuses collecting like terms with multiplication" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a unit fraction Write this fraction as simply as possible:\n\\(\n\\frac{9}{12}\n\\) \\( \\frac{3}{6} \\)" }, { "from": "gpt", "value": "Believes when simplifying a fraction you can divide the numerator and denominator by different values" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a unit fraction Write this fraction as simply as possible:\n\\(\n\\frac{9}{12}\n\\) \\( \\frac{9}{12} \\)" }, { "from": "gpt", "value": "Does not recognise when a fraction can be simplified" } ]

[ { "from": "human", "value": "Add algebraic fractions where one denominator is a multiple of the other Write this as a single fraction as simply as possible:\n\\(\n\\frac{3}{2 x}+\\frac{4}{x}\n\\) \\( \\frac{7}{3 x} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]

[ { "from": "human", "value": "Add algebraic fractions where one denominator is a multiple of the other Write this as a single fraction as simply as possible:\n\\(\n\\frac{3}{2 x}+\\frac{4}{x}\n\\) \\( \\frac{7}{2 x} \\)" }, { "from": "gpt", "value": "Forgets to change the numerators when finding equivalent fractions" } ]

[ { "from": "human", "value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 598-1000= \\) \\( 402 \\)" }, { "from": "gpt", "value": "Believes the smaller number is always subtracted from the larger, regardless of the order of the calculation" } ]

[ { "from": "human", "value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 598-1000= \\) \\( -412 \\)" }, { "from": "gpt", "value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit" } ]

[ { "from": "human", "value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 598-1000= \\) This problem cannot be solved" }, { "from": "gpt", "value": "Believes it is impossible to subtract a bigger number from a smaller number" } ]

[ { "from": "human", "value": "Read values off a real life graph 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.]() \\( £ 130 \\)" }, { "from": "gpt", "value": "Thinks terms in linear sequence are in direct proportion" } ]

[ { "from": "human", "value": "Write a missing term of an ascending integer linear sequence 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? \\( 50 \\)" }, { "from": "gpt", "value": "Believes there is a multiplicative relationship between values of terms in a linear sequence e.g. 10th term is double 5th term" } ]

[ { "from": "human", "value": "Write a missing term of an ascending integer linear sequence 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? \\( 56 \\)" }, { "from": "gpt", "value": "Believes you multiply the constant difference by the term number to get the term value" } ]

[ { "from": "human", "value": "Given a gradient, state the gradient of a line parallel to it A line has a gradient of \\( 5 \\)\n\nA line parallel to this line would have a gradient of... \\( -5 \\)" }, { "from": "gpt", "value": "Believes parallel lines have gradients of opposite signs" } ]

[ { "from": "human", "value": "Given a gradient, state the gradient of a line parallel to it A line has a gradient of \\( 5 \\)\n\nA line parallel to this line would have a gradient of... \\( -\\frac{1}{5} \\)" }, { "from": "gpt", "value": "Believes parallel lines have gradients that multiply to give -1" } ]