bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Given a term in an ascending integer linear sequence, use the nth term rule to find its position in that sequence Here are the first \\( 4 \\) terms of a sequence ![\\( \\begin{array}{lllll}11 & 15 & 19 & 23 & \\ldots\\end{array} \\)]() What position in the sequence is the number \\( 87 ? \\) \\( 21.75 \\)" }, { "from": "gpt", "value": "Believes you multiply the constant difference by the term number to get the term value" } ]
[ { "from": "human", "value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... An octagon" }, { "from": "gpt", "value": "Does not understand the naming structure of polygons" } ]
[ { "from": "human", "value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... A hexagon" }, { "from": "gpt", "value": "Does not understand the naming structure of polygons" } ]
[ { "from": "human", "value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... A dodecagon" }, { "from": "gpt", "value": "Does not understand the naming structure of polygons" } ]
[ { "from": "human", "value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Commutativity" }, { "from": "gpt", "value": "Does not recognise the distributive property" } ]
[ { "from": "human", "value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Factors" }, { "from": "gpt", "value": "Believes splitting a multiplication using the distributive property is the same as splitting it into factors" } ]
[ { "from": "human", "value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Associativity" }, { "from": "gpt", "value": "Does not recognise the distributive property" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+9 x+14 \\) is factorised, what will appear in the box below? ![Bracket (x+2) and a rectangular box beside it where the second bracket should be.]() \\( (x+12) \\)" }, { "from": "gpt", "value": "When factorising into double brackets, finds the sum of two values which give the non variable term in the expression rather than the product" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+9 x+14 \\) is factorised, what will appear in the box below? ![Bracket (x+2) and a rectangular box beside it where the second bracket should be.]() \\( (x-7) \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]
[ { "from": "human", "value": "Convert between kg and g A \\( 0.5 \\) kilogram weight has \\( 10 \\) grams shaved off it.\n\nWhat is the mass of the weight that remains?\nGive your answer in grams. \\( 40 \\mathrm{~g} \\)" }, { "from": "gpt", "value": "Thinks there are 100g in a kilogram" } ]
[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.1 \\div 4= \\) \\( 0.4 \\)" }, { "from": "gpt", "value": "Multiplies rather than divides" } ]
[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.1 \\div 4= \\) \\( 0.25 \\)" }, { "from": "gpt", "value": "When dividing a decimal by a whole number, ignores decimal point and just divides the digits" } ]
[ { "from": "human", "value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( -6 n+92 \\)" }, { "from": "gpt", "value": "Believes that in the nth term of a descending sequence, b is the difference between the term and the positive multiple of n" } ]
[ { "from": "human", "value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( -6 n \\)" }, { "from": "gpt", "value": "Thinks terms in linear sequence are in direct proportion" } ]
[ { "from": "human", "value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( 6 n+92 \\)" }, { "from": "gpt", "value": "Believes the nth term of a descending sequence will have a positive coefficient of n" } ]
[ { "from": "human", "value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\sqrt[3]{\\frac{4 V \\pi}{3}} \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\sqrt[3]{\\frac{4 V}{3 \\pi}} \\mathrm{cm} \\)" }, { "from": "gpt", "value": "When dividing by a fraction, switches to multiplication without also using the reciprocal" } ]
[ { "from": "human", "value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\frac{3 \\sqrt[3]{V}}{4 \\pi} \\mathrm{cm} \\)" }, { "from": "gpt", "value": "Does not reverse the order of operations when solving an equation" } ]
[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, with all positive integers Alisha is using cups and counters to help her solve an equation. Which would be the correct start to work it out? ![Three diagrams of equations shown with cups and counters. \nStep 1 is one cup plus four counters equals two cups and two counters.\nStep 2 is four counters equals one cup plus two counters.\nStep 3 is two counters equals one cup.]() \\( 3 x=6 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, with all positive integers Alisha is using cups and counters to help her solve an equation. Which would be the correct start to work it out? ![Three diagrams of equations shown with cups and counters. \nStep 1 is one cup plus four counters equals two cups and two counters.\nStep 2 is four counters equals one cup plus two counters.\nStep 3 is two counters equals one cup.]() \\( \\begin{array}{c}x+4=2 x+2 \\\\ 3 x=6\\end{array} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Solve linear simultaneous equations requiring no scaling of expressions Which of the following pairs of simultaneous equations would have no solutions?\n\\begin{array}{ccc} \nPair \\( 1 \\) & Pair \\( 2 \\) \\\\\n\\( 2 y-2 x=7 \\) & & \\( 2 x+2 y=7 \\) \\\\\n\\( 2 x-2 y=7 \\) & & \\( 2 x-2 y=7 \\)\n\\end{array} Both Pair \\( 1 \\) and Pair \\( 2 \\)" }, { "from": "gpt", "value": "Believes 0 is not a real solution to an equation" } ]
[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Fraction \\( \\frac{6}{7} \\times \\frac{2}{3}=? \\) \\( \\frac{9}{7} \\)" }, { "from": "gpt", "value": "Uses dividing fractions method for multiplying fractions" } ]
[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Fraction \\( \\frac{6}{7} \\times \\frac{2}{3}=? \\) \\( \\frac{8}{21} \\)" }, { "from": "gpt", "value": "When multiplying fractions, adds the numerators and multiplies the denominators" } ]
[ { "from": "human", "value": "Substitute positive non-integer values into expressions involving powers or roots Jo and Paul are discussing quadratic equations.\n\nJo says there is no value of \\( x \\) that can make \\( (1-x)^{2} \\) negative.\n\nPaul says there is no value of \\( x \\) that can make \\( 1-x^{2} \\) positive.\nWho is correct? Both Jo and Paul" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Substitute positive non-integer values into expressions involving powers or roots Jo and Paul are discussing quadratic equations.\n\nJo says there is no value of \\( x \\) that can make \\( (1-x)^{2} \\) negative.\n\nPaul says there is no value of \\( x \\) that can make \\( 1-x^{2} \\) positive.\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Believes the square of a negative will also be negative" } ]
[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) What should replace the circle when this expression is fully factorised? \\( 9 y^{2}+4 y \\equiv \\bigstar(\\triangle y+\\bigcirc) \\) \\( \\bigcirc=4 y \\)" }, { "from": "gpt", "value": "When factorising into single brackets, only factors out the numerical values and forgets to factorise possible variables" } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 60 \\)" }, { "from": "gpt", "value": "Believes that addition should be used when finding the difference between two values on a time series graph" } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 50 \\)" }, { "from": "gpt", "value": "When finding the difference between two points on a time series graph, only uses one of the points. " } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 30 \\)" }, { "from": "gpt", "value": "When finding the difference between two points on a time series graph, only uses one of the points. " } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c Which of the following answers shows a correct factorisation of the expression below? \\( 2 x^{2}-50 \\) \\( 2\\left(x^{2}-25\\right) \\)" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c Which of the following answers shows a correct factorisation of the expression below? \\( 2 x^{2}-50 \\) \\( 2(x-5)(x-5) \\)" }, { "from": "gpt", "value": "Factorises difference of two squares with the same sign in both brackets" } ]
[ { "from": "human", "value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( 14 \\)" }, { "from": "gpt", "value": "Ignores the negative signs when adding positive and negative numbers" } ]
[ { "from": "human", "value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( -14 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]
[ { "from": "human", "value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( -2 \\)" }, { "from": "gpt", "value": "When subtracting a negative thinks the answer must be negative " } ]
[ { "from": "human", "value": "Express one quantity as a percentage of another mentally I increase \\( £ 200 \\) by \\( 50 \\% \\).\nThen, I increase the new amount by \\( 10 \\% \\).\nWhat percentage of the original amount do I have now? \\( 155 \\% \\)" }, { "from": "gpt", "value": "In repeated percentage change, believes the second change is only a percentage of the first change, without including the original" } ]
[ { "from": "human", "value": "Recognise cube numbers Which of these is a cube number? \\( 15 \\)" }, { "from": "gpt", "value": "Thinks numbers are a multiple of their index" } ]
[ { "from": "human", "value": "Recognise cube numbers Which of these is a cube number? \\( 100 \\)" }, { "from": "gpt", "value": "Mixes up square numbers and cube numbers" } ]
[ { "from": "human", "value": "Recognise cube numbers Which of these is a cube number? \\( 3 \\)" }, { "from": "gpt", "value": "Thinks numbers are a multiple of their index" } ]
[ { "from": "human", "value": "Identify and count the faces, vertices and edges of a 3D shape ![An orange cube]() How many faces does this cube have? \\( 12 \\)" }, { "from": "gpt", "value": "Confuses the terms faces and edges" } ]
[ { "from": "human", "value": "Identify and count the faces, vertices and edges of a 3D shape ![An orange cube]() How many faces does this cube have? \\( 8 \\)" }, { "from": "gpt", "value": "Confuses the terms faces and vertices" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first term? \\( 10 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the term after" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first term? \\( -10 \\)" }, { "from": "gpt", "value": "Does not know the definition of term or term-to-term rule" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first term? \\( 1 \\)" }, { "from": "gpt", "value": "Thinks the first term of a sequence must be 1" } ]
[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place Convert this fraction to a percentage\n\\(\n\\frac{27}{200}\n\\) \\( 27 \\% \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]
[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place Convert this fraction to a percentage\n\\(\n\\frac{27}{200}\n\\) \\( 54 \\% \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]
[ { "from": "human", "value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 1 \\) day? \\( 24 \\times 60 \\)" }, { "from": "gpt", "value": "Converted hours to minutes instead of hours to seconds" } ]
[ { "from": "human", "value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 1 \\) day? \\( 12 \\times 60 \\times 60 \\)" }, { "from": "gpt", "value": "Thinks there are 12 hours in 1 day" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 2.507 \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 2.50 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 3.00 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{\|c\|c\|c\|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline Conger Eel & \\( 12 \\) & \\( \\mathrm{~F} \\) \\\\\n\\hline\n\\end{tabular} Which one of these is a correct method for finding F? \\( 360-180+45 \\)" }, { "from": "gpt", "value": "Does not include brackets when required" } ]
[ { "from": "human", "value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{\|c\|c\|c\|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline Conger Eel & \\( 12 \\) & \\( \\mathrm{~F} \\) \\\\\n\\hline\n\\end{tabular} Which one of these is a correct method for finding F? \\( \\frac{12}{20} \\times 360 \\)" }, { "from": "gpt", "value": "Believes to find the proportion of a pie chart sector you do frequency/sum of other frequencies rather than frequency/overall total" } ]
[ { "from": "human", "value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{\|c\|c\|c\|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline Conger Eel & \\( 12 \\) & \\( \\mathrm{~F} \\) \\\\\n\\hline\n\\end{tabular} Which one of these is a correct method for finding F? \\( \\frac{360}{32} \\)" }, { "from": "gpt", "value": "Finds the degrees for 1 person rather than the required number of people for a pie chart sector" } ]
[ { "from": "human", "value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... no equal side lengths." }, { "from": "gpt", "value": "Confuses isosceles and scalene triangles" } ]
[ { "from": "human", "value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... one pair of parallel sides." }, { "from": "gpt", "value": "Does not know the meaning of the word parallel" } ]
[ { "from": "human", "value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... three equal angles." }, { "from": "gpt", "value": "Confuses isosceles and equilateral triangles" } ]
[ { "from": "human", "value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter \"P\". The line y=4 is shown with a blue dashed line.]() \\( (2,3) \\)" }, { "from": "gpt", "value": "Does not understand that a point on the line of reflection will stay the same when reflected " } ]
[ { "from": "human", "value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter \"P\". The line y=4 is shown with a blue dashed line.]() \\( (2,2) \\)" }, { "from": "gpt", "value": "Does not understand that a point on the line of reflection will stay the same when reflected " } ]
[ { "from": "human", "value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter \"P\". The line y=4 is shown with a blue dashed line.]() \\( (2,-4) \\)" }, { "from": "gpt", "value": "Reflects in an axis, instead of the given mirror line" } ]
[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=6 x\n\\] \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 0 \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( -6 \\)" }, { "from": "gpt", "value": "Thinks the inverse of subtraction is multiplication" } ]
[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=6 x\n\\] \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 0 \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? There is no possible solution" }, { "from": "gpt", "value": "Doesn't believe that when you divide by 0 the answer will always be 0" } ]
[ { "from": "human", "value": "Given a midpoint and a coordinate work out the position of the other coordinate, where at least one value is negative and at least one is a non-integer Here are two points and their midpoint.\nWhat should replace the triangle? ![The image is a set of axes with three points marked. One point is (1,7). The midpoint is (-1, 0.5). The third point is given as (star, triangle), so the triangle is the y value of the point.]() \\( \\Delta=-7 \\)" }, { "from": "gpt", "value": "Given a line segment with a midpoint that is not the origin, assumes that the two end points will still have the same absolute value" } ]
[ { "from": "human", "value": "Given a midpoint and a coordinate work out the position of the other coordinate, where at least one value is negative and at least one is a non-integer Here are two points and their midpoint.\nWhat should replace the triangle? ![The image is a set of axes with three points marked. One point is (1,7). The midpoint is (-1, 0.5). The third point is given as (star, triangle), so the triangle is the y value of the point.]() \\( \\Delta=-6.5 \\)" }, { "from": "gpt", "value": "Believes midpoint calculation is just half of the difference" } ]
[ { "from": "human", "value": "Expand products of three binomials in the form (x + a)(x + b)(x + c) Ori is expanding these three brackets:\n\\(\n(x+2)(x-4)(x-7)\n\\)\n\nHe finds it helpful to split the first bracket and view the problem as follows:\n\\(\nx(x-4)(x-7)+2(x-4)(x-7)\n\\)\n\nHe expands the brackets further. Before he simplifies, what are the terms than contain an \\( x^{2} \\) ? \\( \\begin{array}{l}+7 x^{2} \\\\ +4 x^{2} \\\\ +2 x^{2}\\end{array} \\)" }, { "from": "gpt", "value": "Ignores negative sign when expanding bracket" } ]
[ { "from": "human", "value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in total? \\( 35 \\div 7 \\)" }, { "from": "gpt", "value": "Divides rather than multiplies when answering worded problems" } ]
[ { "from": "human", "value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in total? \\( 35-7 \\)" }, { "from": "gpt", "value": "Subtracts rather than multiplies when answering worded problems" } ]
[ { "from": "human", "value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in total? \\( 35+7 \\)" }, { "from": "gpt", "value": "Adds rather than multiplies when asked for a total" } ]
[ { "from": "human", "value": "Divide proper fractions in the form: Fraction ÷ Integer What fraction replaces the question mark? ![A bar split into 5 equal parts, with two shaded. One of the shaded parts is labelled with a question mark.]() \\( \\frac{1}{2} \\)" }, { "from": "gpt", "value": "Identifies the wrong part of a fraction model as the whole" } ]
[ { "from": "human", "value": "Answer decimal problems that require the use of BIDMAS Which calculation should you do first?\n\\(\n((0.5 \\div(0.2+0.4)-0.3) \\times 0.6)\n\\) \\( 0.5 \\div 0.2 \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]
[ { "from": "human", "value": "Answer decimal problems that require the use of BIDMAS Which calculation should you do first?\n\\(\n((0.5 \\div(0.2+0.4)-0.3) \\times 0.6)\n\\) \\( 0.3 \\times 0.6 \\)" }, { "from": "gpt", "value": "Carries out operations from right to left regardless of priority order" } ]
[ { "from": "human", "value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? \\( 12 \\times 6-(1+2) \\)" }, { "from": "gpt", "value": "Performs subtraction in wrong order" } ]
[ { "from": "human", "value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? \\( 12 \\times(6-1+2) \\)" }, { "from": "gpt", "value": "Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)" } ]
[ { "from": "human", "value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? Does not need brackets" }, { "from": "gpt", "value": "Carries out operations from right to left regardless of priority order" } ]
[ { "from": "human", "value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.\n\nShe wants to work out the probability all the balls are red.\n\nWhat is the denominator of the final unsimplified answer? \\( 7 \\)" }, { "from": "gpt", "value": "Adds rather than multiplies for combined probabilities" } ]
[ { "from": "human", "value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.\n\nShe wants to work out the probability all the balls are red.\n\nWhat is the denominator of the final unsimplified answer? \\( 343 \\)" }, { "from": "gpt", "value": "Does not recognise that choosing 2 items at once means the first item does not get replaced in a probability question" } ]
[ { "from": "human", "value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.\n\nShe wants to work out the probability all the balls are red.\n\nWhat is the denominator of the final unsimplified answer? \\( 18 \\)" }, { "from": "gpt", "value": "Adds rather than multiplies for combined probabilities" } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow\\times 3\\rightarrow+4\\rightarrow4+3 a \\\\ a\\rightarrow \\times 3\\rightarrow+4\\rightarrow3(4+a)\\end{array} \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow+4 \\rightarrow\\times 3\\rightarrow4+3 a \\\\ a \\rightarrow\\times 3\\rightarrow+4\\rightarrow-3(4+a)\\end{array} \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow4 \\rightarrow\\times 3\\rightarrow4+3 a \\\\ a\\rightarrow+4\\rightarrow\\times 3\\rightarrow3(4+a)\\end{array} \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 2 \\)" }, { "from": "gpt", "value": "Confuses factors and multiples" } ]
[ { "from": "human", "value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 18 \\)" }, { "from": "gpt", "value": "Identifies a common multiple of two numbers when asked to consider a common multiple of three numbers" } ]
[ { "from": "human", "value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 20 \\)" }, { "from": "gpt", "value": "Identifies a multiple of a number but not a common multiple of a group of numbers" } ]
[ { "from": "human", "value": "Carry out missing number subtraction problems involving negative integers \\( \\fbox{-5} \\) x\\( \\hspace{0.2cm} \\fbox{4} = \\hspace{0.2cm} \\fbox{-12} - \\hspace{0.2cm}\\fbox{ ? } \\) \\( -8 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]
[ { "from": "human", "value": "Carry out missing number subtraction problems involving negative integers \\( \\fbox{-5} \\) x\\( \\hspace{0.2cm} \\fbox{4} = \\hspace{0.2cm} \\fbox{-12} - \\hspace{0.2cm}\\fbox{ ? } \\) \\( -32 \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]
[ { "from": "human", "value": "Multiplication, division and power law of indices with positive integer powers \\(\\frac{\\left(5^{6}\\right)^{4}}{5^{2}} \\equiv 5^{n}\\)\n\nWhat is the value of \\( n \\) ? \\( 8 \\)" }, { "from": "gpt", "value": "Thinks a power raised to a power leads to addition of the powers" } ]
[ { "from": "human", "value": "Multiplication, division and power law of indices with positive integer powers \\(\\frac{\\left(5^{6}\\right)^{4}}{5^{2}} \\equiv 5^{n}\\)\n\nWhat is the value of \\( n \\) ? \\( 12 \\)" }, { "from": "gpt", "value": "Believes when dividing numbers with the same base you divide the powers, rather than subtracting" } ]
[ { "from": "human", "value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.8989 \\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}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.75 \\)" }, { "from": "gpt", "value": "Believes substituting the starting value into an iteration formula immediately gives the solution" } ]
[ { "from": "human", "value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.9 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (significant figures rather than decimal places)" } ]
[ { "from": "human", "value": "Identify factors of a number \\begin{tabular}{\|c\|c\|c\|}\n & Multiple of \\( 4 \\) & Not a multiple of \\( 4 \\) \\\\\n\\hline Factor of \\( 60 \\) & A & B \\\\\n\\hline Not a factor of \\( 60 \\) & C & D \\\\\n\\hline\n\\end{tabular} In which box should you place \\( \\mathbf{3 0} \\) ? D" }, { "from": "gpt", "value": "Does not understand the term factor" } ]
[ { "from": "human", "value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( n, 2 n, 3 n \\)" }, { "from": "gpt", "value": "Does not know the meaning of consecutive" } ]
[ { "from": "human", "value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( 3 n, 2 n, n \\)" }, { "from": "gpt", "value": "Does not know the meaning of consecutive" } ]
[ { "from": "human", "value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( n, n+2, n+4 \\)" }, { "from": "gpt", "value": "Does not know the meaning of consecutive" } ]
[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 18 \\)" }, { "from": "gpt", "value": "Halves when asked to find the square root" } ]
[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 1296 \\)" }, { "from": "gpt", "value": "Squares when asked to find the square root" } ]
[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 72 \\)" }, { "from": "gpt", "value": "Mixes up square rooting and multiplying by 2 or doubling" } ]
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 0.4 \\)" }, { "from": "gpt", "value": "Adds instead of multiplies" } ]
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 0.0256 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 2.56 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]
[ { "from": "human", "value": "Given the sector angle on a pie chart, calculate the frequency of a group The pie chart shows the favourite subjects of children at a school.\n\nIf \\( 12 \\) students chose Science, how many chose French? ![A pie chart split into four parts, labelled with school subjects. The part for Mathematics is 144 degrees, Science is 36 degrees, English is 72 degrees and French is 108 degrees.]() \\( 108 \\)" }, { "from": "gpt", "value": "Believes the angle in a pie chart sector is equal to the frequency" } ]

[ { "from": "human", "value": "Given a term in an ascending integer linear sequence, use the nth term rule to find its position in that sequence Here are the first \\( 4 \\) terms of a sequence ![\\( \\begin{array}{lllll}11 & 15 & 19 & 23 & \\ldots\\end{array} \\)]() What position in the sequence is the number \\( 87 ? \\) \\( 21.75 \\)" }, { "from": "gpt", "value": "Believes you multiply the constant difference by the term number to get the term value" } ]

[ { "from": "human", "value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... An octagon" }, { "from": "gpt", "value": "Does not understand the naming structure of polygons" } ]

[ { "from": "human", "value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... A hexagon" }, { "from": "gpt", "value": "Does not understand the naming structure of polygons" } ]

[ { "from": "human", "value": "Given the number of sides of a polygon identify the name A ten sided polygon is also known as... A dodecagon" }, { "from": "gpt", "value": "Does not understand the naming structure of polygons" } ]

[ { "from": "human", "value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Commutativity" }, { "from": "gpt", "value": "Does not recognise the distributive property" } ]

[ { "from": "human", "value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Factors" }, { "from": "gpt", "value": "Believes splitting a multiplication using the distributive property is the same as splitting it into factors" } ]

[ { "from": "human", "value": "Recognise and use the law of distributivity What word do we use to describe the relationship:\n\\(\n7 \\times 9=5 \\times 9+2 \\times 9\n\\) Associativity" }, { "from": "gpt", "value": "Does not recognise the distributive property" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+9 x+14 \\) is factorised, what will appear in the box below? ![Bracket (x+2) and a rectangular box beside it where the second bracket should be.]() \\( (x+12) \\)" }, { "from": "gpt", "value": "When factorising into double brackets, finds the sum of two values which give the non variable term in the expression rather than the product" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+9 x+14 \\) is factorised, what will appear in the box below? ![Bracket (x+2) and a rectangular box beside it where the second bracket should be.]() \\( (x-7) \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]

[ { "from": "human", "value": "Convert between kg and g A \\( 0.5 \\) kilogram weight has \\( 10 \\) grams shaved off it.\n\nWhat is the mass of the weight that remains?\nGive your answer in grams. \\( 40 \\mathrm{~g} \\)" }, { "from": "gpt", "value": "Thinks there are 100g in a kilogram" } ]

[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.1 \\div 4= \\) \\( 0.4 \\)" }, { "from": "gpt", "value": "Multiplies rather than divides" } ]

[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.1 \\div 4= \\) \\( 0.25 \\)" }, { "from": "gpt", "value": "When dividing a decimal by a whole number, ignores decimal point and just divides the digits" } ]

[ { "from": "human", "value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( -6 n+92 \\)" }, { "from": "gpt", "value": "Believes that in the nth term of a descending sequence, b is the difference between the term and the positive multiple of n" } ]

[ { "from": "human", "value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( -6 n \\)" }, { "from": "gpt", "value": "Thinks terms in linear sequence are in direct proportion" } ]

[ { "from": "human", "value": "Find the nth term rule for a descending integer linear sequence Here are the first three terms of a sequence ![\\( \\begin{array}{llll}98 & 92 & 86 & \\ldots\\end{array} \\)]() Find an expression for the nth term of this sequence. \\( 6 n+92 \\)" }, { "from": "gpt", "value": "Believes the nth term of a descending sequence will have a positive coefficient of n" } ]

[ { "from": "human", "value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\sqrt[3]{\\frac{4 V \\pi}{3}} \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\sqrt[3]{\\frac{4 V}{3 \\pi}} \\mathrm{cm} \\)" }, { "from": "gpt", "value": "When dividing by a fraction, switches to multiplication without also using the reciprocal" } ]

[ { "from": "human", "value": "Given the volume of a sphere, work out missing information A sphere has a volume of\n\\[\nV \\mathrm{~cm}^{3} \\text {. }\n\\] ![A sphere with the radius labelled '?']() What is its radius? \\( \\frac{3 \\sqrt[3]{V}}{4 \\pi} \\mathrm{cm} \\)" }, { "from": "gpt", "value": "Does not reverse the order of operations when solving an equation" } ]

[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, with all positive integers Alisha is using cups and counters to help her solve an equation. Which would be the correct start to work it out? ![Three diagrams of equations shown with cups and counters. \nStep 1 is one cup plus four counters equals two cups and two counters.\nStep 2 is four counters equals one cup plus two counters.\nStep 3 is two counters equals one cup.]() \\( 3 x=6 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, with all positive integers Alisha is using cups and counters to help her solve an equation. Which would be the correct start to work it out? ![Three diagrams of equations shown with cups and counters. \nStep 1 is one cup plus four counters equals two cups and two counters.\nStep 2 is four counters equals one cup plus two counters.\nStep 3 is two counters equals one cup.]() \\( \\begin{array}{c}x+4=2 x+2 \\\\ 3 x=6\\end{array} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Solve linear simultaneous equations requiring no scaling of expressions Which of the following pairs of simultaneous equations would have no solutions?\n\\begin{array}{ccc} \nPair \\( 1 \\) & Pair \\( 2 \\) \\\\\n\\( 2 y-2 x=7 \\) & & \\( 2 x+2 y=7 \\) \\\\\n\\( 2 x-2 y=7 \\) & & \\( 2 x-2 y=7 \\)\n\\end{array} Both Pair \\( 1 \\) and Pair \\( 2 \\)" }, { "from": "gpt", "value": "Believes 0 is not a real solution to an equation" } ]

[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Fraction \\( \\frac{6}{7} \\times \\frac{2}{3}=? \\) \\( \\frac{9}{7} \\)" }, { "from": "gpt", "value": "Uses dividing fractions method for multiplying fractions" } ]

[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Fraction \\( \\frac{6}{7} \\times \\frac{2}{3}=? \\) \\( \\frac{8}{21} \\)" }, { "from": "gpt", "value": "When multiplying fractions, adds the numerators and multiplies the denominators" } ]

[ { "from": "human", "value": "Substitute positive non-integer values into expressions involving powers or roots Jo and Paul are discussing quadratic equations.\n\nJo says there is no value of \\( x \\) that can make \\( (1-x)^{2} \\) negative.\n\nPaul says there is no value of \\( x \\) that can make \\( 1-x^{2} \\) positive.\nWho is correct? Both Jo and Paul" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Substitute positive non-integer values into expressions involving powers or roots Jo and Paul are discussing quadratic equations.\n\nJo says there is no value of \\( x \\) that can make \\( (1-x)^{2} \\) negative.\n\nPaul says there is no value of \\( x \\) that can make \\( 1-x^{2} \\) positive.\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Believes the square of a negative will also be negative" } ]

[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) What should replace the circle when this expression is fully factorised? \\( 9 y^{2}+4 y \\equiv \\bigstar(\\triangle y+\\bigcirc) \\) \\( \\bigcirc=4 y \\)" }, { "from": "gpt", "value": "When factorising into single brackets, only factors out the numerical values and forgets to factorise possible variables" } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 60 \\)" }, { "from": "gpt", "value": "Believes that addition should be used when finding the difference between two values on a time series graph" } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 50 \\)" }, { "from": "gpt", "value": "When finding the difference between two points on a time series graph, only uses one of the points. " } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph ![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \\( 10 \\) and \\( 40 \\) seconds? \\( 30 \\)" }, { "from": "gpt", "value": "When finding the difference between two points on a time series graph, only uses one of the points. " } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c Which of the following answers shows a correct factorisation of the expression below? \\( 2 x^{2}-50 \\) \\( 2\\left(x^{2}-25\\right) \\)" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c Which of the following answers shows a correct factorisation of the expression below? \\( 2 x^{2}-50 \\) \\( 2(x-5)(x-5) \\)" }, { "from": "gpt", "value": "Factorises difference of two squares with the same sign in both brackets" } ]

[ { "from": "human", "value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( 14 \\)" }, { "from": "gpt", "value": "Ignores the negative signs when adding positive and negative numbers" } ]

[ { "from": "human", "value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( -14 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]

[ { "from": "human", "value": "Carry out subtraction problems involving two negative integers \\( (-6)-(-8)= \\) \\( -2 \\)" }, { "from": "gpt", "value": "When subtracting a negative thinks the answer must be negative " } ]

[ { "from": "human", "value": "Express one quantity as a percentage of another mentally I increase \\( £ 200 \\) by \\( 50 \\% \\).\nThen, I increase the new amount by \\( 10 \\% \\).\nWhat percentage of the original amount do I have now? \\( 155 \\% \\)" }, { "from": "gpt", "value": "In repeated percentage change, believes the second change is only a percentage of the first change, without including the original" } ]

[ { "from": "human", "value": "Recognise cube numbers Which of these is a cube number? \\( 15 \\)" }, { "from": "gpt", "value": "Thinks numbers are a multiple of their index" } ]

[ { "from": "human", "value": "Recognise cube numbers Which of these is a cube number? \\( 100 \\)" }, { "from": "gpt", "value": "Mixes up square numbers and cube numbers" } ]

[ { "from": "human", "value": "Recognise cube numbers Which of these is a cube number? \\( 3 \\)" }, { "from": "gpt", "value": "Thinks numbers are a multiple of their index" } ]

[ { "from": "human", "value": "Identify and count the faces, vertices and edges of a 3D shape ![An orange cube]() How many faces does this cube have? \\( 12 \\)" }, { "from": "gpt", "value": "Confuses the terms faces and edges" } ]

[ { "from": "human", "value": "Identify and count the faces, vertices and edges of a 3D shape ![An orange cube]() How many faces does this cube have? \\( 8 \\)" }, { "from": "gpt", "value": "Confuses the terms faces and vertices" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first term? \\( 10 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the term after" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first term? \\( -10 \\)" }, { "from": "gpt", "value": "Does not know the definition of term or term-to-term rule" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.\nIf the third term is \\( 35 \\), what is the first term? \\( 1 \\)" }, { "from": "gpt", "value": "Thinks the first term of a sequence must be 1" } ]

[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place Convert this fraction to a percentage\n\\(\n\\frac{27}{200}\n\\) \\( 27 \\% \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]

[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place Convert this fraction to a percentage\n\\(\n\\frac{27}{200}\n\\) \\( 54 \\% \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]

[ { "from": "human", "value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 1 \\) day? \\( 24 \\times 60 \\)" }, { "from": "gpt", "value": "Converted hours to minutes instead of hours to seconds" } ]

[ { "from": "human", "value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 1 \\) day? \\( 12 \\times 60 \\times 60 \\)" }, { "from": "gpt", "value": "Thinks there are 12 hours in 1 day" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 2.507 \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 2.50 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to three or more significant figures What is \\( \\mathbf{2 . 5 0 6 7 1 0} \\) rounded to three significant figures? \\( 3.00 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{|c|c|c|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline Conger Eel & \\( 12 \\) & \\( \\mathrm{~F} \\) \\\\\n\\hline\n\\end{tabular} Which one of these is a correct method for finding F? \\( 360-180+45 \\)" }, { "from": "gpt", "value": "Does not include brackets when required" } ]

[ { "from": "human", "value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{|c|c|c|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline Conger Eel & \\( 12 \\) & \\( \\mathrm{~F} \\) \\\\\n\\hline\n\\end{tabular} Which one of these is a correct method for finding F? \\( \\frac{12}{20} \\times 360 \\)" }, { "from": "gpt", "value": "Believes to find the proportion of a pie chart sector you do frequency/sum of other frequencies rather than frequency/overall total" } ]

[ { "from": "human", "value": "Calculate the sector angle on a pie chart for a given group A diver wants to make a pie chart of his trip. \\begin{tabular}{|c|c|c|}\n\\hline & Frequency & Degrees \\\\\n\\hline Manta Ray & \\( 16 \\) & \\( 180 \\) \\\\\n\\hline Hammerhead & \\( 4 \\) & \\( 45 \\) \\\\\n\\hline Conger Eel & \\( 12 \\) & \\( \\mathrm{~F} \\) \\\\\n\\hline\n\\end{tabular} Which one of these is a correct method for finding F? \\( \\frac{360}{32} \\)" }, { "from": "gpt", "value": "Finds the degrees for 1 person rather than the required number of people for a pie chart sector" } ]

[ { "from": "human", "value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... no equal side lengths." }, { "from": "gpt", "value": "Confuses isosceles and scalene triangles" } ]

[ { "from": "human", "value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... one pair of parallel sides." }, { "from": "gpt", "value": "Does not know the meaning of the word parallel" } ]

[ { "from": "human", "value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... three equal angles." }, { "from": "gpt", "value": "Confuses isosceles and equilateral triangles" } ]

[ { "from": "human", "value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter \"P\". The line y=4 is shown with a blue dashed line.]() \\( (2,3) \\)" }, { "from": "gpt", "value": "Does not understand that a point on the line of reflection will stay the same when reflected " } ]

[ { "from": "human", "value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter \"P\". The line y=4 is shown with a blue dashed line.]() \\( (2,2) \\)" }, { "from": "gpt", "value": "Does not understand that a point on the line of reflection will stay the same when reflected " } ]

[ { "from": "human", "value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter \"P\". The line y=4 is shown with a blue dashed line.]() \\( (2,-4) \\)" }, { "from": "gpt", "value": "Reflects in an axis, instead of the given mirror line" } ]

[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=6 x\n\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 0 \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( -6 \\)" }, { "from": "gpt", "value": "Thinks the inverse of subtraction is multiplication" } ]

[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=6 x\n\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 0 \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? There is no possible solution" }, { "from": "gpt", "value": "Doesn't believe that when you divide by 0 the answer will always be 0" } ]

[ { "from": "human", "value": "Given a midpoint and a coordinate work out the position of the other coordinate, where at least one value is negative and at least one is a non-integer Here are two points and their midpoint.\nWhat should replace the triangle? ![The image is a set of axes with three points marked. One point is (1,7). The midpoint is (-1, 0.5). The third point is given as (star, triangle), so the triangle is the y value of the point.]() \\( \\Delta=-7 \\)" }, { "from": "gpt", "value": "Given a line segment with a midpoint that is not the origin, assumes that the two end points will still have the same absolute value" } ]

[ { "from": "human", "value": "Given a midpoint and a coordinate work out the position of the other coordinate, where at least one value is negative and at least one is a non-integer Here are two points and their midpoint.\nWhat should replace the triangle? ![The image is a set of axes with three points marked. One point is (1,7). The midpoint is (-1, 0.5). The third point is given as (star, triangle), so the triangle is the y value of the point.]() \\( \\Delta=-6.5 \\)" }, { "from": "gpt", "value": "Believes midpoint calculation is just half of the difference" } ]

[ { "from": "human", "value": "Expand products of three binomials in the form (x + a)(x + b)(x + c) Ori is expanding these three brackets:\n\\(\n(x+2)(x-4)(x-7)\n\\)\n\nHe finds it helpful to split the first bracket and view the problem as follows:\n\\(\nx(x-4)(x-7)+2(x-4)(x-7)\n\\)\n\nHe expands the brackets further. Before he simplifies, what are the terms than contain an \\( x^{2} \\) ? \\( \\begin{array}{l}+7 x^{2} \\\\ +4 x^{2} \\\\ +2 x^{2}\\end{array} \\)" }, { "from": "gpt", "value": "Ignores negative sign when expanding bracket" } ]

[ { "from": "human", "value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in total? \\( 35 \\div 7 \\)" }, { "from": "gpt", "value": "Divides rather than multiplies when answering worded problems" } ]

[ { "from": "human", "value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in total? \\( 35-7 \\)" }, { "from": "gpt", "value": "Subtracts rather than multiplies when answering worded problems" } ]

[ { "from": "human", "value": "Identify that a problem needs to be solved using multiplication Which of the following calculations would solve this problem?\nFred is monitoring the growth of his plant. The plant grew \\( 7 \\mathrm{~cm} \\) every week for \\( 35 \\) weeks.\nBy how much did the plant grow in total? \\( 35+7 \\)" }, { "from": "gpt", "value": "Adds rather than multiplies when asked for a total" } ]

[ { "from": "human", "value": "Divide proper fractions in the form: Fraction ÷ Integer What fraction replaces the question mark? ![A bar split into 5 equal parts, with two shaded. One of the shaded parts is labelled with a question mark.]() \\( \\frac{1}{2} \\)" }, { "from": "gpt", "value": "Identifies the wrong part of a fraction model as the whole" } ]

[ { "from": "human", "value": "Answer decimal problems that require the use of BIDMAS Which calculation should you do first?\n\\(\n((0.5 \\div(0.2+0.4)-0.3) \\times 0.6)\n\\) \\( 0.5 \\div 0.2 \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]

[ { "from": "human", "value": "Answer decimal problems that require the use of BIDMAS Which calculation should you do first?\n\\(\n((0.5 \\div(0.2+0.4)-0.3) \\times 0.6)\n\\) \\( 0.3 \\times 0.6 \\)" }, { "from": "gpt", "value": "Carries out operations from right to left regardless of priority order" } ]

[ { "from": "human", "value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? \\( 12 \\times 6-(1+2) \\)" }, { "from": "gpt", "value": "Performs subtraction in wrong order" } ]

[ { "from": "human", "value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? \\( 12 \\times(6-1+2) \\)" }, { "from": "gpt", "value": "Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)" } ]

[ { "from": "human", "value": "Insert brackets to make a calculation correct \\[\n12 \\times 6-1+2\n\\]\nWhere do the brackets need to go to make the answer equal \\( 36 \\) ? Does not need brackets" }, { "from": "gpt", "value": "Carries out operations from right to left regardless of priority order" } ]

[ { "from": "human", "value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.\n\nShe wants to work out the probability all the balls are red.\n\nWhat is the denominator of the final unsimplified answer? \\( 7 \\)" }, { "from": "gpt", "value": "Adds rather than multiplies for combined probabilities" } ]

[ { "from": "human", "value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.\n\nShe wants to work out the probability all the balls are red.\n\nWhat is the denominator of the final unsimplified answer? \\( 343 \\)" }, { "from": "gpt", "value": "Does not recognise that choosing 2 items at once means the first item does not get replaced in a probability question" } ]

[ { "from": "human", "value": "Calculate the probability of three or more dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.\n\nShe wants to work out the probability all the balls are red.\n\nWhat is the denominator of the final unsimplified answer? \\( 18 \\)" }, { "from": "gpt", "value": "Adds rather than multiplies for combined probabilities" } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow\\times 3\\rightarrow+4\\rightarrow4+3 a \\\\ a\\rightarrow \\times 3\\rightarrow+4\\rightarrow3(4+a)\\end{array} \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow+4 \\rightarrow\\times 3\\rightarrow4+3 a \\\\ a \\rightarrow\\times 3\\rightarrow+4\\rightarrow-3(4+a)\\end{array} \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? \\( \\begin{array}{l}a\\rightarrow4 \\rightarrow\\times 3\\rightarrow4+3 a \\\\ a\\rightarrow+4\\rightarrow\\times 3\\rightarrow3(4+a)\\end{array} \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 2 \\)" }, { "from": "gpt", "value": "Confuses factors and multiples" } ]

[ { "from": "human", "value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 18 \\)" }, { "from": "gpt", "value": "Identifies a common multiple of two numbers when asked to consider a common multiple of three numbers" } ]

[ { "from": "human", "value": "Identify common multiples of three or more numbers Which of the following numbers is a common multiple of \\( 4,6 \\) and \\( 12 \\) ? \\( 20 \\)" }, { "from": "gpt", "value": "Identifies a multiple of a number but not a common multiple of a group of numbers" } ]

[ { "from": "human", "value": "Carry out missing number subtraction problems involving negative integers \\( \\fbox{-5} \\) x\\( \\hspace{0.2cm} \\fbox{4} = \\hspace{0.2cm} \\fbox{-12} - \\hspace{0.2cm}\\fbox{ ? } \\) \\( -8 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]

[ { "from": "human", "value": "Carry out missing number subtraction problems involving negative integers \\( \\fbox{-5} \\) x\\( \\hspace{0.2cm} \\fbox{4} = \\hspace{0.2cm} \\fbox{-12} - \\hspace{0.2cm}\\fbox{ ? } \\) \\( -32 \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]

[ { "from": "human", "value": "Multiplication, division and power law of indices with positive integer powers \\(\\frac{\\left(5^{6}\\right)^{4}}{5^{2}} \\equiv 5^{n}\\)\n\nWhat is the value of \\( n \\) ? \\( 8 \\)" }, { "from": "gpt", "value": "Thinks a power raised to a power leads to addition of the powers" } ]

[ { "from": "human", "value": "Multiplication, division and power law of indices with positive integer powers \\(\\frac{\\left(5^{6}\\right)^{4}}{5^{2}} \\equiv 5^{n}\\)\n\nWhat is the value of \\( n \\) ? \\( 12 \\)" }, { "from": "gpt", "value": "Believes when dividing numbers with the same base you divide the powers, rather than subtracting" } ]

[ { "from": "human", "value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.8989 \\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}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.75 \\)" }, { "from": "gpt", "value": "Believes substituting the starting value into an iteration formula immediately gives the solution" } ]

[ { "from": "human", "value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=10-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=4 \\), what is the solution to \\( x=10-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 9.9 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (significant figures rather than decimal places)" } ]

[ { "from": "human", "value": "Identify factors of a number \\begin{tabular}{|c|c|c|}\n & Multiple of \\( 4 \\) & Not a multiple of \\( 4 \\) \\\\\n\\hline Factor of \\( 60 \\) & A & B \\\\\n\\hline Not a factor of \\( 60 \\) & C & D \\\\\n\\hline\n\\end{tabular} In which box should you place \\( \\mathbf{3 0} \\) ? D" }, { "from": "gpt", "value": "Does not understand the term factor" } ]

[ { "from": "human", "value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( n, 2 n, 3 n \\)" }, { "from": "gpt", "value": "Does not know the meaning of consecutive" } ]

[ { "from": "human", "value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( 3 n, 2 n, n \\)" }, { "from": "gpt", "value": "Does not know the meaning of consecutive" } ]

[ { "from": "human", "value": "Form expressions from situations described in words Which of these always produces consecutive numbers if \\( n \\) is a positive integer? \\( n, n+2, n+4 \\)" }, { "from": "gpt", "value": "Does not know the meaning of consecutive" } ]

[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 18 \\)" }, { "from": "gpt", "value": "Halves when asked to find the square root" } ]

[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 1296 \\)" }, { "from": "gpt", "value": "Squares when asked to find the square root" } ]

[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 36 \\) ? \\( 72 \\)" }, { "from": "gpt", "value": "Mixes up square rooting and multiplying by 2 or doubling" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 0.4 \\)" }, { "from": "gpt", "value": "Adds instead of multiplies" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 0.0256 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.32 \\times 0.8= \\) \\( 2.56 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]

[ { "from": "human", "value": "Given the sector angle on a pie chart, calculate the frequency of a group The pie chart shows the favourite subjects of children at a school.\n\nIf \\( 12 \\) students chose Science, how many chose French? ![A pie chart split into four parts, labelled with school subjects. The part for Mathematics is 144 degrees, Science is 36 degrees, English is 72 degrees and French is 108 degrees.]() \\( 108 \\)" }, { "from": "gpt", "value": "Believes the angle in a pie chart sector is equal to the frequency" } ]