bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Solve quadratic equations using factorisation in the form (x + a)(x + b) This is the final stage of Beth's solution to a quadratic equation.\nWhat should replace the star?\n\n\\[\n(h-8)(h+3)=0\n\\] \\( h=\\bigstar \\) or \\( h=-3 \\) \\( 0 \\)" }, { "from": "gpt", "value": "Believes all quadratic equations have a solution of 0" } ]
[ { "from": "human", "value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]() \\( \\operatorname{Sin} \\)" }, { "from": "gpt", "value": "Uses sin when tan is required" } ]
[ { "from": "human", "value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]() Cos" }, { "from": "gpt", "value": "Uses cos when tan is required" } ]
[ { "from": "human", "value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]() None of these" }, { "from": "gpt", "value": "Does not understand how to apply sohcahtoa" } ]
[ { "from": "human", "value": "Add 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{t}{s}+\\frac{2 s}{t} \\) \\( \\frac{t^{2}+4 s^{2}}{s t} \\)" }, { "from": "gpt", "value": "When squaring a variable, believes they also need to square the coefficient" } ]
[ { "from": "human", "value": "Add 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{t}{s}+\\frac{2 s}{t} \\) \\( \\frac{t+2 s}{s+t} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]
[ { "from": "human", "value": "Add 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{t}{s}+\\frac{2 s}{t} \\) \\( \\frac{2 s t}{s+t} \\)" }, { "from": "gpt", "value": "When adding/subtracting fractions, adds/subtracts the denominators and multiplies the numerators" } ]
[ { "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? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"+ 3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"3 + 2p\" written inside it.\n The second function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"+ 3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(3 + p)\" written inside it.]()" }, { "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? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"+ 3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"3 + 2p\" written inside it.\n The second function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"+ 3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(3 + p)\" written inside it.]()" }, { "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? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"+ 3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"3 + 2p\" written inside it.\n The second function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"+ 3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(3 + p)\" written inside it.]()" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation below.\n\nHere are his steps.\n\nWhich steps, if any, are correct? ![An equation 15 = 2p - 4 on the first line. \nOn the second line, Step 1 : 11 = 2p. \nOn the third line, Step 2: 22 = p]() Only step \\( 1 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation below.\n\nHere are his steps.\n\nWhich steps, if any, are correct? ![An equation 15 = 2p - 4 on the first line. \nOn the second line, Step 1 : 11 = 2p. \nOn the third line, Step 2: 22 = p]() Only step \\( 2 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation below.\n\nHere are his steps.\n\nWhich steps, if any, are correct? ![An equation 15 = 2p - 4 on the first line. \nOn the second line, Step 1 : 11 = 2p. \nOn the third line, Step 2: 22 = p]() Both steps are correct" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Calculate the area of an isosceles triangle where the dimensions are given in the same units Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]() \\( \\frac{40 \\times 25}{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 isosceles triangle where the dimensions are given in the same units Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]() \\( \\frac{40 \\times 25 \\times 15}{2} \\)" }, { "from": "gpt", "value": "Has multiplied base by slant height and perpendicular height to find area of a triangle" } ]
[ { "from": "human", "value": "Calculate the area of an isosceles triangle where the dimensions are given in the same units Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]() \\( \\frac{20 \\times 15}{2} \\)" }, { "from": "gpt", "value": "Halves base but still divides product by 2 when finding area of a triangle" } ]
[ { "from": "human", "value": "Describe a translation using vector notation where at least one value is negative Which vector correctly describes the translation that maps object \\( Q \\) onto object \\(P \\)? ![The image shows a set of axes and two congruent trapezia P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (4, 2), (5, 4), (7, 4), (8, 2).]() \\( \\left(\\begin{array}{c}5 \\\\ -3\\end{array}\\right) \\)" }, { "from": "gpt", "value": "Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round" } ]
[ { "from": "human", "value": "Describe a translation using vector notation where at least one value is negative Which vector correctly describes the translation that maps object \\( Q \\) onto object \\(P \\)? ![The image shows a set of axes and two congruent trapezia P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (4, 2), (5, 4), (7, 4), (8, 2).]() \\( \\left(\\begin{array}{c}3 \\\\ -5\\end{array}\\right) \\)" }, { "from": "gpt", "value": "When describing a translation, goes from the image to the original" } ]
[ { "from": "human", "value": "Work out the equation of a line when given a positive gradient and a point on the line A line has a gradient of \\( 2 \\) and passes through the point \\( (1,1) \\) \nThe equation of this line could be... \\( y=2 x+1 \\)" }, { "from": "gpt", "value": "Believes c, in y=mx+c, will be the y value of the coordinate given despite the x coordinate not being 0." } ]
[ { "from": "human", "value": "Add amounts of money together to make a total between £1 and £10 Sunita wants to buy a sandwich and a tea.\n\nHow much money will she need? Joe's Café\nSandwich \\( £3.25 \\)\nPasty \\( £ 2.99 \\)\nCake \\( £ 2.25 \\)\nSoup \\( £ 3.19 \\)\nTea \\( £ 1.55 \\)\nCoffee \\( £ 1.95 \\)\nOrange \\( 89\\)p £5.70" }, { "from": "gpt", "value": "When adding powers of 10 adds onto the wrong column" } ]
[ { "from": "human", "value": "Add amounts of money together to make a total between £1 and £10 Sunita wants to buy a sandwich and a tea.\n\nHow much money will she need? Joe's Café\nSandwich \\( £3.25 \\)\nPasty \\( £ 2.99 \\)\nCake \\( £ 2.25 \\)\nSoup \\( £ 3.19 \\)\nTea \\( £ 1.55 \\)\nCoffee \\( £ 1.95 \\)\nOrange \\( 89\\)p £4.70" }, { "from": "gpt", "value": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit" } ]
[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon The octagon below is regular. Find angle \\( x \\). ![A regular octagon (8 sided polygon). Each side is marked with a single dash to show that all sides are equal in length. One of the interior angles of the octagon is labelled with the letter \"x\".]() \\( 22.5^{\\circ} \\)" }, { "from": "gpt", "value": "Thinks the interior angles of any polygon add up to 180 degrees" } ]
[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon The octagon below is regular. Find angle \\( x \\). ![A regular octagon (8 sided polygon). Each side is marked with a single dash to show that all sides are equal in length. One of the interior angles of the octagon is labelled with the letter \"x\".]() \\( 45^{\\circ} \\)" }, { "from": "gpt", "value": "Thinks the interior angles of any polygon add up to 360" } ]
[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a common factor involving numeric and algebraic components (e.g. 5a) When this expression is fully factorised, what is left inside the brackets? \\( 24 a b c^{2}-16 b^{2} c \\equiv 8 b c(\\square) \\) \\( 3 a c \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]
[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a common factor involving numeric and algebraic components (e.g. 5a) When this expression is fully factorised, what is left inside the brackets? \\( 24 a b c^{2}-16 b^{2} c \\equiv 8 b c(\\square) \\) \\( 3 a-2 \\)" }, { "from": "gpt", "value": "Does not realise multiplying a variable by itself results in a power of that variable" } ]
[ { "from": "human", "value": "Add decimals where the numbers involved have a different number of decimal places \\( 0.15+0.2= \\) \\( 0.17 \\)" }, { "from": "gpt", "value": "When adding decimals with a different number of decimal places, lines up the digits incorrectly" } ]
[ { "from": "human", "value": "Add decimals where the numbers involved have a different number of decimal places \\( 0.15+0.2= \\) \\( 0.152 \\)" }, { "from": "gpt", "value": "When adding decimals with a different number of decimal places, lines up the digits incorrectly" } ]
[ { "from": "human", "value": "Identify triangular numbers ![\\begin{tabular}{\|lll\|}\n\\hline\\( \\bullet \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular}]() How many circles will the next term in this sequence have? \\( 8 \\)" }, { "from": "gpt", "value": "Uses only the first two terms of a sequence to work out a term-to-term rule" } ]
[ { "from": "human", "value": "Identify triangular numbers ![\\begin{tabular}{\|lll\|}\n\\hline\\( \\bullet \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular}]() How many circles will the next term in this sequence have? \\( 9 \\)" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]
[ { "from": "human", "value": "Identify triangular numbers ![\\begin{tabular}{\|lll\|}\n\\hline\\( \\bullet \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular}]() How many circles will the next term in this sequence have? \\( 12 \\)" }, { "from": "gpt", "value": "Only looks at the difference between one pair of terms when discerning the pattern" } ]
[ { "from": "human", "value": "Convert from minutes to hours \\( 5 \\) hours \\( +500 \\) minutes \\( = \\) \\( 10 \\) hours" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]
[ { "from": "human", "value": "Convert from minutes to hours \\( 5 \\) hours \\( +500 \\) minutes \\( = \\) \\( 13 \\) hours and \\( 33 \\) minutes" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]
[ { "from": "human", "value": "Express a linear equation as a function machine Which function matches the equation\n\\[\ny=5(x+1) ?\n\\] ![A function machine which has 4 parts joined by arrows pointing from left to right. \"𝑥\" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has \"✕ 5\" written inside it, followed by a horizontal arrow pointing to a rectangle that has \"+ 1\" written inside it, followed by a horizontal arrow pointing to \"y\"]()" }, { "from": "gpt", "value": "Answers order of operations questions with brackets as if the brackets are not there" } ]
[ { "from": "human", "value": "Express a linear equation as a function machine Which function matches the equation\n\\[\ny=5(x+1) ?\n\\] ![A function machine which has 4 parts joined by arrows pointing from left to right. \"y\" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has \"+ 1\" written inside it, followed by a horizontal arrow pointing to a rectangle that has \"✕ 5\" written inside it, followed by a horizontal arrow pointing to \"𝑥\"]()" }, { "from": "gpt", "value": "When writing a function as a function machine confuses the input and the output." } ]
[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\( x+y=20 \\) Which pair of numbers fits the equation? \\( \\begin{array}{c}x=10 \\\\ y=2\\end{array} \\)" }, { "from": "gpt", "value": "Changes the given operation when substituting" } ]
[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\( x+y=20 \\) Which pair of numbers fits the equation? \\( \\begin{array}{l}x=10 \\\\ y=-2\\end{array} \\)" }, { "from": "gpt", "value": "substitutes incorrectly" } ]
[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\( x+y=20 \\) Which pair of numbers fits the equation? \\( \\begin{array}{l}x=-8 \\\\ y=12\\end{array} \\)" }, { "from": "gpt", "value": "substitutes incorrectly" } ]
[ { "from": "human", "value": "Add fractions involving mixed number fractions with different denominators \\( 2 \\frac{7}{10}+2 \\frac{1}{4}= \\) Leave your answer as a mixed number \\( \\frac{99}{20} \\)" }, { "from": "gpt", "value": "Confused mixed numbers with improper fractions" } ]
[ { "from": "human", "value": "Add fractions involving mixed number fractions with different denominators \\( 2 \\frac{7}{10}+2 \\frac{1}{4}= \\) Leave your answer as a mixed number \\( \\frac{99}{40} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]
[ { "from": "human", "value": "Add fractions involving mixed number fractions with different denominators \\( 2 \\frac{7}{10}+2 \\frac{1}{4}= \\) Leave your answer as a mixed number \\( 4 \\frac{8}{14} \\)" }, { "from": "gpt", "value": "Does not find a common denominator when adding/subtracting fractions" } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph How many months have an average temperature below 25⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 3 \\)" }, { "from": "gpt", "value": "When asked to find data points below a certain value, gives the number of data points above this value" } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph How many months have an average temperature below 25⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 4 \\)" }, { "from": "gpt", "value": "When asked to find data points below a certain value, gives the number of data points above this value" } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph How many months have an average temperature below 25⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 9 \\)" }, { "from": "gpt", "value": "Includes a data point with the value, when asked to find the number of data points below a value" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and EG.]() \\( E \\)" }, { "from": "gpt", "value": "Gives the vertex instead of the 3-letter angle notation" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and EG.]() FEC" }, { "from": "gpt", "value": "In 3 letter angle notation, gives a wider angle that contains the shaded angle" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and EG.]() CGE" }, { "from": "gpt", "value": "Gives 3-letter angle notation in the wrong order" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Which multiplication will help factorise \\( x^{2}+13 x+30 \\) ? \\( 1 \\times 30 \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Which multiplication will help factorise \\( x^{2}+13 x+30 \\) ? \\( 2 \\times 15 \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Which multiplication will help factorise \\( x^{2}+13 x+30 \\) ? \\( 5 \\times 6 \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]
[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number Which option shows the fractions in order from smallest to largest? \\( \\begin{array}{llll}\\frac{3}{4} & \\frac{1}{2} & \\frac{2}{6} & \\frac{1}{12}\\end{array} \\)" }, { "from": "gpt", "value": "Mixes up smallest and largest when ordering fractions" } ]
[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number Which option shows the fractions in order from smallest to largest? \\( \\begin{array}{llll}\\frac{1}{2} & \\frac{3}{4} & \\frac{2}{6} & \\frac{1}{12}\\end{array} \\)" }, { "from": "gpt", "value": "Ordered fractions by comparing denominators rather than using equivalent fractions." } ]
[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number Which option shows the fractions in order from smallest to largest? \\( \\begin{array}{llll}\\frac{1}{2} & \\frac{1}{12} & \\frac{2}{6} & \\frac{3}{4}\\end{array} \\)" }, { "from": "gpt", "value": "When comparing unit fractions believes that fractions with larger denominators are greater in size." } ]
[ { "from": "human", "value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18\n\\] \\( 10 \\)" }, { "from": "gpt", "value": "Finds the mean instead of the median" } ]
[ { "from": "human", "value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18\n\\] \\( 12 \\)" }, { "from": "gpt", "value": "When finding the median for an odd numbered data set, find the midpoint of two values rather than giving the middle value" } ]
[ { "from": "human", "value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18\n\\] \\( 18 \\)" }, { "from": "gpt", "value": "Finds the mode instead of the median" } ]
[ { "from": "human", "value": "Identify multiples of a number If you list the multiples of \\( 15 \\) in ascending order, what is the \\( 5^{\\text {th }} \\) number in the list? \\( 90 \\)" }, { "from": "gpt", "value": "Believes the first multiple of a is 2a" } ]
[ { "from": "human", "value": "Can calculate missing coordinates in a geometric shape Here are \\( 3 \\) vertices of a rectangle:\n\\((0,3),(4,-1),(2,-3),\\)\n\nWhat are the coordinates of the \\( 4^{\\text {th }} \\) vertex? \\( (0,1) \\)" }, { "from": "gpt", "value": "Believes the sides of a rectangle must be horizontal and vertical, not diagonal" } ]
[ { "from": "human", "value": "Can calculate missing coordinates in a geometric shape Here are \\( 3 \\) vertices of a rectangle:\n\\((0,3),(4,-1),(2,-3),\\)\n\nWhat are the coordinates of the \\( 4^{\\text {th }} \\) vertex? \\( (4,1) \\)" }, { "from": "gpt", "value": "Believes the sides of a rectangle must be horizontal and vertical, not diagonal" } ]
[ { "from": "human", "value": "Can calculate missing coordinates in a geometric shape Here are \\( 3 \\) vertices of a rectangle:\n\\((0,3),(4,-1),(2,-3),\\)\n\nWhat are the coordinates of the \\( 4^{\\text {th }} \\) vertex? \\( (-2,-3) \\)" }, { "from": "gpt", "value": "Believes the sides of a rectangle must be horizontal and vertical, not diagonal" } ]
[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators are all single terms Write this as a single fraction as simply as possible:\n\n\\(\n\\frac{5}{x} \\times \\frac{2 y}{x^{2}}\n\\) \\( \\frac{5 x+10 y}{x^{2}} \\)" }, { "from": "gpt", "value": "When asked to multiply fractions, uses the method for adding instead" } ]
[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators are all single terms Write this as a single fraction as simply as possible:\n\n\\(\n\\frac{5}{x} \\times \\frac{2 y}{x^{2}}\n\\) \\( \\frac{10 y}{3 x} \\)" }, { "from": "gpt", "value": "Believes cubing a number means you multiply it by 3" } ]
[ { "from": "human", "value": "Subtract two equations together to remove a variable Isaac is trying to solve the pair of simultaneous equations on the right.\n\n\\[\n6 g+h=12\n\\]\n\\[\n6 g-3 h=-3\n\\]\n\nHe decides to subtract the bottom equation from the top equation.\nWhat will he end up with? \\( -2 h=9 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]
[ { "from": "human", "value": "Subtract two equations together to remove a variable Isaac is trying to solve the pair of simultaneous equations on the right.\n\n\\[\n6 g+h=12\n\\]\n\\[\n6 g-3 h=-3\n\\]\n\nHe decides to subtract the bottom equation from the top equation.\nWhat will he end up with? \\( -2 h=15 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]
[ { "from": "human", "value": "Subtract two equations together to remove a variable Isaac is trying to solve the pair of simultaneous equations on the right.\n\n\\[\n6 g+h=12\n\\]\n\\[\n6 g-3 h=-3\n\\]\n\nHe decides to subtract the bottom equation from the top equation.\nWhat will he end up with? \\( 4 h=9 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]
[ { "from": "human", "value": "Subtract fractions involving mixed number fractions with different denominators \\( 3 \\frac{4}{7}-1 \\frac{3}{4}= \\) Leave your answer as a mixed number \\( 2 \\frac{5}{28} \\)" }, { "from": "gpt", "value": "Ignores the negative sign" } ]
[ { "from": "human", "value": "Subtract fractions involving mixed number fractions with different denominators \\( 3 \\frac{4}{7}-1 \\frac{3}{4}= \\) Leave your answer as a mixed number \\( \\frac{51}{28} \\)" }, { "from": "gpt", "value": "Confused mixed numbers with improper fractions" } ]
[ { "from": "human", "value": "Compare the lengths of diagonal line segments without calculating the exact length Tom and Katie are arguing about distance and coordinates. \n\nTom says \\( (3,-2) \\) and \\( (2,-3) \\) are equidistant from the origin. \nKatie says \\( (4,1) \\) and \\( (7,-2) \\) are equidistant from the origin. \n\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Believes the sum of change in x and change in y gives the distance between points" } ]
[ { "from": "human", "value": "Compare the lengths of diagonal line segments without calculating the exact length Tom and Katie are arguing about distance and coordinates. \n\nTom says \\( (3,-2) \\) and \\( (2,-3) \\) are equidistant from the origin. \nKatie says \\( (4,1) \\) and \\( (7,-2) \\) are equidistant from the origin. \n\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Confuses negative and positive coordinates when working with graphs in four quadrants" } ]
[ { "from": "human", "value": "Round numbers to an appropriate degree to estimate the answer to a calculation Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \\( 505 \\div 198 \\) \\( 2.243 \\ldots \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Round numbers to an appropriate degree to estimate the answer to a calculation Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \\( 505 \\div 198 \\) \\( 5.136 \\ldots \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Round numbers to an appropriate degree to estimate the answer to a calculation Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \\( 505 \\div 198 \\) \\( 3.1101 \\ldots \\)" }, { "from": "gpt", "value": "Rounds every number up when estimating" } ]
[ { "from": "human", "value": "Given the area of a square, calculate a missing dimension A shape is made up a square and regular pentagon.\nThe area of the square is \\( 196 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![A regular pentagon with a square joined along one edge]() \\( 343 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Thinks that square root is found by dividing by 4" } ]
[ { "from": "human", "value": "Given the area of a square, calculate a missing dimension A shape is made up a square and regular pentagon.\nThe area of the square is \\( 196 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![A regular pentagon with a square joined along one edge]() \\( 112 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Believes lines inside the shape are included when finding perimeter" } ]
[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular octagon has a total perimeter of \\( 12 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? \\( 4 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When given the perimeter of a regular polygon, subtracts instead of divides to find each side length" } ]
[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular octagon has a total perimeter of \\( 12 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? \\( 96 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When given the perimeter of a regular polygon, multiplies instead of divides to find each side length" } ]
[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular octagon has a total perimeter of \\( 12 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? Not enough information" }, { "from": "gpt", "value": "Does not know the meaning of the word regular " } ]
[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Estimate the value of\n\\(\n\\frac{3.24 \\times 17.6}{0.224}\n\\) \\( 10.8 \\)" }, { "from": "gpt", "value": "Rounds too little when estimating" } ]
[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Estimate the value of\n\\(\n\\frac{3.24 \\times 17.6}{0.224}\n\\) \\( 12 \\)" }, { "from": "gpt", "value": "Believes that dividing by a decimal is the same as dividing by its reciprocal" } ]
[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Estimate the value of\n\\(\n\\frac{3.24 \\times 17.6}{0.224}\n\\) \\( 270 \\)" }, { "from": "gpt", "value": "Rounds to the nearest integer when estimating" } ]
[ { "from": "human", "value": "Use inequality notation to order fractions whose denominators are not multiples of the same number What sign would make this statement true?\n\\(\n\\frac{5}{9} ? \\frac{7}{12}\n\\) \\( > \\)" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]
[ { "from": "human", "value": "Recognise and name an expression Which of the following is the most appropriate word to describe: \\( 6-3 g \\) Variable" }, { "from": "gpt", "value": "Confuses an expression with a variable" } ]
[ { "from": "human", "value": "Recognise and name an expression Which of the following is the most appropriate word to describe: \\( 6-3 g \\) Equation" }, { "from": "gpt", "value": "Confuses an equation with an expression" } ]
[ { "from": "human", "value": "Recognise and name an expression Which of the following is the most appropriate word to describe: \\( 6-3 g \\) Term" }, { "from": "gpt", "value": "Confuses an expression with a term" } ]
[ { "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 ![Squared paper with a horizontal line of reflection and a triangle. The horizontal base of the triangle is two squares above the line of reflection.]() Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![Tom does this: his reflected triangle is sitting upright the same as the original object. The base is 3 squares below the line of reflection.]() ![Katie does this: her reflected triangle is upside down compared to the original object. The base of the reflected triangle is on the line of reflection.]() Only Tom" }, { "from": "gpt", "value": "Translates rather than reflects across a line of symmetry" } ]
[ { "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 ![Squared paper with a horizontal line of reflection and a triangle. The horizontal base of the triangle is two squares above the line of reflection.]() Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![Tom does this: his reflected triangle is sitting upright the same as the original object. The base is 3 squares below the line of reflection.]() ![Katie does this: her reflected triangle is upside down compared to the original object. The base of the reflected triangle is on the line of reflection.]() Only Katie" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]
[ { "from": "human", "value": "Identify or mark lines of symmetry on a shape ![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have? \\( 0 \\)" }, { "from": "gpt", "value": "Cannot identify a line of symmetry in a simple shape" } ]
[ { "from": "human", "value": "Identify or mark lines of symmetry on a shape ![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have? \\( 2 \\)" }, { "from": "gpt", "value": "Ignores colours or design on shape when looking for symmetry" } ]
[ { "from": "human", "value": "Identify or mark lines of symmetry on a shape ![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have? \\( 4 \\)" }, { "from": "gpt", "value": "Thinks rectangles have line symmetry in the diagonals " } ]
[ { "from": "human", "value": "Tell the time from a 24 hour digital clock with times after half past the hour Which clock shows ten to twelve at night? 10:12" }, { "from": "gpt", "value": "Gets the minutes and hours the wrong way around" } ]
[ { "from": "human", "value": "Tell the time from a 24 hour digital clock with times after half past the hour Which clock shows ten to twelve at night? \\( 12: 50 \\)" }, { "from": "gpt", "value": "Does not adjust the hour for “to” times" } ]
[ { "from": "human", "value": "Tell the time from a 24 hour digital clock with times after half past the hour Which clock shows ten to twelve at night? 00:50" }, { "from": "gpt", "value": "Does not adjust the hour for “to” times" } ]
[ { "from": "human", "value": "Interpret numbers in a frequency table Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\\begin{tabular}{\|c\|c\|}\n\\hline Goals scored & Frequency \\\\\n\\hline \\( 0 \\) & \\( 6 \\) \\\\\n\\hline \\( 1 \\) & \\( 7 \\) \\\\\n\\hline \\( 2 \\) & \\( 4 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 5 \\)" }, { "from": "gpt", "value": "Believes total frequency in a table is found by counting rows" } ]
[ { "from": "human", "value": "Interpret numbers in a frequency table Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\\begin{tabular}{\|c\|c\|}\n\\hline Goals scored & Frequency \\\\\n\\hline \\( 0 \\) & \\( 6 \\) \\\\\n\\hline \\( 1 \\) & \\( 7 \\) \\\\\n\\hline \\( 2 \\) & \\( 4 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 28 \\)" }, { "from": "gpt", "value": "Believes the total frequency is the overall total in a grouped table" } ]
[ { "from": "human", "value": "Interpret numbers in a frequency table Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\\begin{tabular}{\|c\|c\|}\n\\hline Goals scored & Frequency \\\\\n\\hline \\( 0 \\) & \\( 6 \\) \\\\\n\\hline \\( 1 \\) & \\( 7 \\) \\\\\n\\hline \\( 2 \\) & \\( 4 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 10 \\)" }, { "from": "gpt", "value": "Believes total frequency in a table is given by the sum of the categories given" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx - c If\n\\(\nm^{2}+5 m-14 \\equiv(m+a)(m+b)\n\\)\nthen \\( a \\times b= \\) \\( 5 \\)" }, { "from": "gpt", "value": "Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx - c If\n\\(\nm^{2}+5 m-14 \\equiv(m+a)(m+b)\n\\)\nthen \\( a \\times b= \\) \\( 14 \\)" }, { "from": "gpt", "value": "When factorising into double brackets, believes the product of the constants in the brackets is of the opposite sign to the constant in the expanded equation." } ]
[ { "from": "human", "value": "Express one quantity as a percentage of another mentally What is \\( 60 \\mathrm{~m} \\) as a percentage of \\( 2 \\mathrm{~km} \\) ? \\( 333 \\% \\)" }, { "from": "gpt", "value": "When writing a number as a percentage of another number gets them the wrong way around" } ]
[ { "from": "human", "value": "Express one quantity as a percentage of another mentally What is \\( 60 \\mathrm{~m} \\) as a percentage of \\( 2 \\mathrm{~km} \\) ? \\( 30 \\% \\)" }, { "from": "gpt", "value": "Thinks there are 100m and a km" } ]
[ { "from": "human", "value": "Express one quantity as a percentage of another mentally What is \\( 60 \\mathrm{~m} \\) as a percentage of \\( 2 \\mathrm{~km} \\) ? \\( 60 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a number to make it a percentage" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio ![A group of 8 squares and 5 circles]() What is the ratio of squares to circles? \\( 5: 13 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]

[ { "from": "human", "value": "Solve quadratic equations using factorisation in the form (x + a)(x + b) This is the final stage of Beth's solution to a quadratic equation.\nWhat should replace the star?\n\n\\[\n(h-8)(h+3)=0\n\\] \\( h=\\bigstar \\) or \\( h=-3 \\) \\( 0 \\)" }, { "from": "gpt", "value": "Believes all quadratic equations have a solution of 0" } ]

[ { "from": "human", "value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]() \\( \\operatorname{Sin} \\)" }, { "from": "gpt", "value": "Uses sin when tan is required" } ]

[ { "from": "human", "value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]() Cos" }, { "from": "gpt", "value": "Uses cos when tan is required" } ]

[ { "from": "human", "value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]() None of these" }, { "from": "gpt", "value": "Does not understand how to apply sohcahtoa" } ]

[ { "from": "human", "value": "Add 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{t}{s}+\\frac{2 s}{t} \\) \\( \\frac{t^{2}+4 s^{2}}{s t} \\)" }, { "from": "gpt", "value": "When squaring a variable, believes they also need to square the coefficient" } ]

[ { "from": "human", "value": "Add 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{t}{s}+\\frac{2 s}{t} \\) \\( \\frac{t+2 s}{s+t} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]

[ { "from": "human", "value": "Add 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{t}{s}+\\frac{2 s}{t} \\) \\( \\frac{2 s t}{s+t} \\)" }, { "from": "gpt", "value": "When adding/subtracting fractions, adds/subtracts the denominators and multiplies the numerators" } ]

[ { "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? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"+ 3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"3 + 2p\" written inside it.\n The second function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"+ 3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(3 + p)\" written inside it.]()" }, { "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? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"+ 3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"3 + 2p\" written inside it.\n The second function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"+ 3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(3 + p)\" written inside it.]()" }, { "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? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"+ 3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"3 + 2p\" written inside it.\n The second function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"+ 3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(3 + p)\" written inside it.]()" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation below.\n\nHere are his steps.\n\nWhich steps, if any, are correct? ![An equation 15 = 2p - 4 on the first line. \nOn the second line, Step 1 : 11 = 2p. \nOn the third line, Step 2: 22 = p]() Only step \\( 1 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation below.\n\nHere are his steps.\n\nWhich steps, if any, are correct? ![An equation 15 = 2p - 4 on the first line. \nOn the second line, Step 1 : 11 = 2p. \nOn the third line, Step 2: 22 = p]() Only step \\( 2 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation below.\n\nHere are his steps.\n\nWhich steps, if any, are correct? ![An equation 15 = 2p - 4 on the first line. \nOn the second line, Step 1 : 11 = 2p. \nOn the third line, Step 2: 22 = p]() Both steps are correct" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Calculate the area of an isosceles triangle where the dimensions are given in the same units Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]() \\( \\frac{40 \\times 25}{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 isosceles triangle where the dimensions are given in the same units Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]() \\( \\frac{40 \\times 25 \\times 15}{2} \\)" }, { "from": "gpt", "value": "Has multiplied base by slant height and perpendicular height to find area of a triangle" } ]

[ { "from": "human", "value": "Calculate the area of an isosceles triangle where the dimensions are given in the same units Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]() \\( \\frac{20 \\times 15}{2} \\)" }, { "from": "gpt", "value": "Halves base but still divides product by 2 when finding area of a triangle" } ]

[ { "from": "human", "value": "Describe a translation using vector notation where at least one value is negative Which vector correctly describes the translation that maps object \\( Q \\) onto object \\(P \\)? ![The image shows a set of axes and two congruent trapezia P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (4, 2), (5, 4), (7, 4), (8, 2).]() \\( \\left(\\begin{array}{c}5 \\\\ -3\\end{array}\\right) \\)" }, { "from": "gpt", "value": "Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round" } ]

[ { "from": "human", "value": "Describe a translation using vector notation where at least one value is negative Which vector correctly describes the translation that maps object \\( Q \\) onto object \\(P \\)? ![The image shows a set of axes and two congruent trapezia P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (4, 2), (5, 4), (7, 4), (8, 2).]() \\( \\left(\\begin{array}{c}3 \\\\ -5\\end{array}\\right) \\)" }, { "from": "gpt", "value": "When describing a translation, goes from the image to the original" } ]

[ { "from": "human", "value": "Work out the equation of a line when given a positive gradient and a point on the line A line has a gradient of \\( 2 \\) and passes through the point \\( (1,1) \\) \nThe equation of this line could be... \\( y=2 x+1 \\)" }, { "from": "gpt", "value": "Believes c, in y=mx+c, will be the y value of the coordinate given despite the x coordinate not being 0." } ]

[ { "from": "human", "value": "Add amounts of money together to make a total between £1 and £10 Sunita wants to buy a sandwich and a tea.\n\nHow much money will she need? Joe's Café\nSandwich \\( £3.25 \\)\nPasty \\( £ 2.99 \\)\nCake \\( £ 2.25 \\)\nSoup \\( £ 3.19 \\)\nTea \\( £ 1.55 \\)\nCoffee \\( £ 1.95 \\)\nOrange \\( 89\\)p £5.70" }, { "from": "gpt", "value": "When adding powers of 10 adds onto the wrong column" } ]

[ { "from": "human", "value": "Add amounts of money together to make a total between £1 and £10 Sunita wants to buy a sandwich and a tea.\n\nHow much money will she need? Joe's Café\nSandwich \\( £3.25 \\)\nPasty \\( £ 2.99 \\)\nCake \\( £ 2.25 \\)\nSoup \\( £ 3.19 \\)\nTea \\( £ 1.55 \\)\nCoffee \\( £ 1.95 \\)\nOrange \\( 89\\)p £4.70" }, { "from": "gpt", "value": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit" } ]

[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon The octagon below is regular. Find angle \\( x \\). ![A regular octagon (8 sided polygon). Each side is marked with a single dash to show that all sides are equal in length. One of the interior angles of the octagon is labelled with the letter \"x\".]() \\( 22.5^{\\circ} \\)" }, { "from": "gpt", "value": "Thinks the interior angles of any polygon add up to 180 degrees" } ]

[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon The octagon below is regular. Find angle \\( x \\). ![A regular octagon (8 sided polygon). Each side is marked with a single dash to show that all sides are equal in length. One of the interior angles of the octagon is labelled with the letter \"x\".]() \\( 45^{\\circ} \\)" }, { "from": "gpt", "value": "Thinks the interior angles of any polygon add up to 360" } ]

[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a common factor involving numeric and algebraic components (e.g. 5a) When this expression is fully factorised, what is left inside the brackets? \\( 24 a b c^{2}-16 b^{2} c \\equiv 8 b c(\\square) \\) \\( 3 a c \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]

[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a common factor involving numeric and algebraic components (e.g. 5a) When this expression is fully factorised, what is left inside the brackets? \\( 24 a b c^{2}-16 b^{2} c \\equiv 8 b c(\\square) \\) \\( 3 a-2 \\)" }, { "from": "gpt", "value": "Does not realise multiplying a variable by itself results in a power of that variable" } ]

[ { "from": "human", "value": "Add decimals where the numbers involved have a different number of decimal places \\( 0.15+0.2= \\) \\( 0.17 \\)" }, { "from": "gpt", "value": "When adding decimals with a different number of decimal places, lines up the digits incorrectly" } ]

[ { "from": "human", "value": "Add decimals where the numbers involved have a different number of decimal places \\( 0.15+0.2= \\) \\( 0.152 \\)" }, { "from": "gpt", "value": "When adding decimals with a different number of decimal places, lines up the digits incorrectly" } ]

[ { "from": "human", "value": "Identify triangular numbers ![\\begin{tabular}{|lll|}\n\\hline\\( \\bullet \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular}]() How many circles will the next term in this sequence have? \\( 8 \\)" }, { "from": "gpt", "value": "Uses only the first two terms of a sequence to work out a term-to-term rule" } ]

[ { "from": "human", "value": "Identify triangular numbers ![\\begin{tabular}{|lll|}\n\\hline\\( \\bullet \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular}]() How many circles will the next term in this sequence have? \\( 9 \\)" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]

[ { "from": "human", "value": "Identify triangular numbers ![\\begin{tabular}{|lll|}\n\\hline\\( \\bullet \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular}]() How many circles will the next term in this sequence have? \\( 12 \\)" }, { "from": "gpt", "value": "Only looks at the difference between one pair of terms when discerning the pattern" } ]

[ { "from": "human", "value": "Convert from minutes to hours \\( 5 \\) hours \\( +500 \\) minutes \\( = \\) \\( 10 \\) hours" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]

[ { "from": "human", "value": "Convert from minutes to hours \\( 5 \\) hours \\( +500 \\) minutes \\( = \\) \\( 13 \\) hours and \\( 33 \\) minutes" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]

[ { "from": "human", "value": "Express a linear equation as a function machine Which function matches the equation\n\\[\ny=5(x+1) ?\n\\] ![A function machine which has 4 parts joined by arrows pointing from left to right. \"𝑥\" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has \"✕ 5\" written inside it, followed by a horizontal arrow pointing to a rectangle that has \"+ 1\" written inside it, followed by a horizontal arrow pointing to \"y\"]()" }, { "from": "gpt", "value": "Answers order of operations questions with brackets as if the brackets are not there" } ]

[ { "from": "human", "value": "Express a linear equation as a function machine Which function matches the equation\n\\[\ny=5(x+1) ?\n\\] ![A function machine which has 4 parts joined by arrows pointing from left to right. \"y\" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has \"+ 1\" written inside it, followed by a horizontal arrow pointing to a rectangle that has \"✕ 5\" written inside it, followed by a horizontal arrow pointing to \"𝑥\"]()" }, { "from": "gpt", "value": "When writing a function as a function machine confuses the input and the output." } ]

[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\( x+y=20 \\) Which pair of numbers fits the equation? \\( \\begin{array}{c}x=10 \\\\ y=2\\end{array} \\)" }, { "from": "gpt", "value": "Changes the given operation when substituting" } ]

[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\( x+y=20 \\) Which pair of numbers fits the equation? \\( \\begin{array}{l}x=10 \\\\ y=-2\\end{array} \\)" }, { "from": "gpt", "value": "substitutes incorrectly" } ]

[ { "from": "human", "value": "Identify pairs of numbers that satisfy an equation with two unknowns \\( x+y=20 \\) Which pair of numbers fits the equation? \\( \\begin{array}{l}x=-8 \\\\ y=12\\end{array} \\)" }, { "from": "gpt", "value": "substitutes incorrectly" } ]

[ { "from": "human", "value": "Add fractions involving mixed number fractions with different denominators \\( 2 \\frac{7}{10}+2 \\frac{1}{4}= \\) Leave your answer as a mixed number \\( \\frac{99}{20} \\)" }, { "from": "gpt", "value": "Confused mixed numbers with improper fractions" } ]

[ { "from": "human", "value": "Add fractions involving mixed number fractions with different denominators \\( 2 \\frac{7}{10}+2 \\frac{1}{4}= \\) Leave your answer as a mixed number \\( \\frac{99}{40} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]

[ { "from": "human", "value": "Add fractions involving mixed number fractions with different denominators \\( 2 \\frac{7}{10}+2 \\frac{1}{4}= \\) Leave your answer as a mixed number \\( 4 \\frac{8}{14} \\)" }, { "from": "gpt", "value": "Does not find a common denominator when adding/subtracting fractions" } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph How many months have an average temperature below 25⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 3 \\)" }, { "from": "gpt", "value": "When asked to find data points below a certain value, gives the number of data points above this value" } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph How many months have an average temperature below 25⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 4 \\)" }, { "from": "gpt", "value": "When asked to find data points below a certain value, gives the number of data points above this value" } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph How many months have an average temperature below 25⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 9 \\)" }, { "from": "gpt", "value": "Includes a data point with the value, when asked to find the number of data points below a value" } ]

[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and EG.]() \\( E \\)" }, { "from": "gpt", "value": "Gives the vertex instead of the 3-letter angle notation" } ]

[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and EG.]() FEC" }, { "from": "gpt", "value": "In 3 letter angle notation, gives a wider angle that contains the shaded angle" } ]

[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and EG.]() CGE" }, { "from": "gpt", "value": "Gives 3-letter angle notation in the wrong order" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Which multiplication will help factorise \\( x^{2}+13 x+30 \\) ? \\( 1 \\times 30 \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Which multiplication will help factorise \\( x^{2}+13 x+30 \\) ? \\( 2 \\times 15 \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c Which multiplication will help factorise \\( x^{2}+13 x+30 \\) ? \\( 5 \\times 6 \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]

[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number Which option shows the fractions in order from smallest to largest? \\( \\begin{array}{llll}\\frac{3}{4} & \\frac{1}{2} & \\frac{2}{6} & \\frac{1}{12}\\end{array} \\)" }, { "from": "gpt", "value": "Mixes up smallest and largest when ordering fractions" } ]

[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number Which option shows the fractions in order from smallest to largest? \\( \\begin{array}{llll}\\frac{1}{2} & \\frac{3}{4} & \\frac{2}{6} & \\frac{1}{12}\\end{array} \\)" }, { "from": "gpt", "value": "Ordered fractions by comparing denominators rather than using equivalent fractions." } ]

[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number Which option shows the fractions in order from smallest to largest? \\( \\begin{array}{llll}\\frac{1}{2} & \\frac{1}{12} & \\frac{2}{6} & \\frac{3}{4}\\end{array} \\)" }, { "from": "gpt", "value": "When comparing unit fractions believes that fractions with larger denominators are greater in size." } ]

[ { "from": "human", "value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18\n\\] \\( 10 \\)" }, { "from": "gpt", "value": "Finds the mean instead of the median" } ]

[ { "from": "human", "value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18\n\\] \\( 12 \\)" }, { "from": "gpt", "value": "When finding the median for an odd numbered data set, find the midpoint of two values rather than giving the middle value" } ]

[ { "from": "human", "value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18\n\\] \\( 18 \\)" }, { "from": "gpt", "value": "Finds the mode instead of the median" } ]

[ { "from": "human", "value": "Identify multiples of a number If you list the multiples of \\( 15 \\) in ascending order, what is the \\( 5^{\\text {th }} \\) number in the list? \\( 90 \\)" }, { "from": "gpt", "value": "Believes the first multiple of a is 2a" } ]

[ { "from": "human", "value": "Can calculate missing coordinates in a geometric shape Here are \\( 3 \\) vertices of a rectangle:\n\\((0,3),(4,-1),(2,-3),\\)\n\nWhat are the coordinates of the \\( 4^{\\text {th }} \\) vertex? \\( (0,1) \\)" }, { "from": "gpt", "value": "Believes the sides of a rectangle must be horizontal and vertical, not diagonal" } ]

[ { "from": "human", "value": "Can calculate missing coordinates in a geometric shape Here are \\( 3 \\) vertices of a rectangle:\n\\((0,3),(4,-1),(2,-3),\\)\n\nWhat are the coordinates of the \\( 4^{\\text {th }} \\) vertex? \\( (4,1) \\)" }, { "from": "gpt", "value": "Believes the sides of a rectangle must be horizontal and vertical, not diagonal" } ]

[ { "from": "human", "value": "Can calculate missing coordinates in a geometric shape Here are \\( 3 \\) vertices of a rectangle:\n\\((0,3),(4,-1),(2,-3),\\)\n\nWhat are the coordinates of the \\( 4^{\\text {th }} \\) vertex? \\( (-2,-3) \\)" }, { "from": "gpt", "value": "Believes the sides of a rectangle must be horizontal and vertical, not diagonal" } ]

[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators are all single terms Write this as a single fraction as simply as possible:\n\n\\(\n\\frac{5}{x} \\times \\frac{2 y}{x^{2}}\n\\) \\( \\frac{5 x+10 y}{x^{2}} \\)" }, { "from": "gpt", "value": "When asked to multiply fractions, uses the method for adding instead" } ]

[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators are all single terms Write this as a single fraction as simply as possible:\n\n\\(\n\\frac{5}{x} \\times \\frac{2 y}{x^{2}}\n\\) \\( \\frac{10 y}{3 x} \\)" }, { "from": "gpt", "value": "Believes cubing a number means you multiply it by 3" } ]

[ { "from": "human", "value": "Subtract two equations together to remove a variable Isaac is trying to solve the pair of simultaneous equations on the right.\n\n\\[\n6 g+h=12\n\\]\n\\[\n6 g-3 h=-3\n\\]\n\nHe decides to subtract the bottom equation from the top equation.\nWhat will he end up with? \\( -2 h=9 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]

[ { "from": "human", "value": "Subtract two equations together to remove a variable Isaac is trying to solve the pair of simultaneous equations on the right.\n\n\\[\n6 g+h=12\n\\]\n\\[\n6 g-3 h=-3\n\\]\n\nHe decides to subtract the bottom equation from the top equation.\nWhat will he end up with? \\( -2 h=15 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]

[ { "from": "human", "value": "Subtract two equations together to remove a variable Isaac is trying to solve the pair of simultaneous equations on the right.\n\n\\[\n6 g+h=12\n\\]\n\\[\n6 g-3 h=-3\n\\]\n\nHe decides to subtract the bottom equation from the top equation.\nWhat will he end up with? \\( 4 h=9 \\)" }, { "from": "gpt", "value": "When subtracting a negative number, subtracts the absolute value rather than adding it" } ]

[ { "from": "human", "value": "Subtract fractions involving mixed number fractions with different denominators \\( 3 \\frac{4}{7}-1 \\frac{3}{4}= \\) Leave your answer as a mixed number \\( 2 \\frac{5}{28} \\)" }, { "from": "gpt", "value": "Ignores the negative sign" } ]

[ { "from": "human", "value": "Subtract fractions involving mixed number fractions with different denominators \\( 3 \\frac{4}{7}-1 \\frac{3}{4}= \\) Leave your answer as a mixed number \\( \\frac{51}{28} \\)" }, { "from": "gpt", "value": "Confused mixed numbers with improper fractions" } ]

[ { "from": "human", "value": "Compare the lengths of diagonal line segments without calculating the exact length Tom and Katie are arguing about distance and coordinates. \n\nTom says \\( (3,-2) \\) and \\( (2,-3) \\) are equidistant from the origin. \nKatie says \\( (4,1) \\) and \\( (7,-2) \\) are equidistant from the origin. \n\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Believes the sum of change in x and change in y gives the distance between points" } ]

[ { "from": "human", "value": "Compare the lengths of diagonal line segments without calculating the exact length Tom and Katie are arguing about distance and coordinates. \n\nTom says \\( (3,-2) \\) and \\( (2,-3) \\) are equidistant from the origin. \nKatie says \\( (4,1) \\) and \\( (7,-2) \\) are equidistant from the origin. \n\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Confuses negative and positive coordinates when working with graphs in four quadrants" } ]

[ { "from": "human", "value": "Round numbers to an appropriate degree to estimate the answer to a calculation Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \\( 505 \\div 198 \\) \\( 2.243 \\ldots \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Round numbers to an appropriate degree to estimate the answer to a calculation Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \\( 505 \\div 198 \\) \\( 5.136 \\ldots \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Round numbers to an appropriate degree to estimate the answer to a calculation Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \\( 505 \\div 198 \\) \\( 3.1101 \\ldots \\)" }, { "from": "gpt", "value": "Rounds every number up when estimating" } ]

[ { "from": "human", "value": "Given the area of a square, calculate a missing dimension A shape is made up a square and regular pentagon.\nThe area of the square is \\( 196 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![A regular pentagon with a square joined along one edge]() \\( 343 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Thinks that square root is found by dividing by 4" } ]

[ { "from": "human", "value": "Given the area of a square, calculate a missing dimension A shape is made up a square and regular pentagon.\nThe area of the square is \\( 196 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![A regular pentagon with a square joined along one edge]() \\( 112 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Believes lines inside the shape are included when finding perimeter" } ]

[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular octagon has a total perimeter of \\( 12 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? \\( 4 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When given the perimeter of a regular polygon, subtracts instead of divides to find each side length" } ]

[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular octagon has a total perimeter of \\( 12 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? \\( 96 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When given the perimeter of a regular polygon, multiplies instead of divides to find each side length" } ]

[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular octagon has a total perimeter of \\( 12 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? Not enough information" }, { "from": "gpt", "value": "Does not know the meaning of the word regular " } ]

[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Estimate the value of\n\\(\n\\frac{3.24 \\times 17.6}{0.224}\n\\) \\( 10.8 \\)" }, { "from": "gpt", "value": "Rounds too little when estimating" } ]

[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Estimate the value of\n\\(\n\\frac{3.24 \\times 17.6}{0.224}\n\\) \\( 12 \\)" }, { "from": "gpt", "value": "Believes that dividing by a decimal is the same as dividing by its reciprocal" } ]

[ { "from": "human", "value": "Round the elements of a calculation to one significant figure to perform an estimation Estimate the value of\n\\(\n\\frac{3.24 \\times 17.6}{0.224}\n\\) \\( 270 \\)" }, { "from": "gpt", "value": "Rounds to the nearest integer when estimating" } ]

[ { "from": "human", "value": "Use inequality notation to order fractions whose denominators are not multiples of the same number What sign would make this statement true?\n\\(\n\\frac{5}{9} ? \\frac{7}{12}\n\\) \\( > \\)" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Recognise and name an expression Which of the following is the most appropriate word to describe: \\( 6-3 g \\) Variable" }, { "from": "gpt", "value": "Confuses an expression with a variable" } ]

[ { "from": "human", "value": "Recognise and name an expression Which of the following is the most appropriate word to describe: \\( 6-3 g \\) Equation" }, { "from": "gpt", "value": "Confuses an equation with an expression" } ]

[ { "from": "human", "value": "Recognise and name an expression Which of the following is the most appropriate word to describe: \\( 6-3 g \\) Term" }, { "from": "gpt", "value": "Confuses an expression with a term" } ]

[ { "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 ![Squared paper with a horizontal line of reflection and a triangle. The horizontal base of the triangle is two squares above the line of reflection.]() Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![Tom does this: his reflected triangle is sitting upright the same as the original object. The base is 3 squares below the line of reflection.]() ![Katie does this: her reflected triangle is upside down compared to the original object. The base of the reflected triangle is on the line of reflection.]() Only Tom" }, { "from": "gpt", "value": "Translates rather than reflects across a line of symmetry" } ]

[ { "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 ![Squared paper with a horizontal line of reflection and a triangle. The horizontal base of the triangle is two squares above the line of reflection.]() Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![Tom does this: his reflected triangle is sitting upright the same as the original object. The base is 3 squares below the line of reflection.]() ![Katie does this: her reflected triangle is upside down compared to the original object. The base of the reflected triangle is on the line of reflection.]() Only Katie" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]

[ { "from": "human", "value": "Identify or mark lines of symmetry on a shape ![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have? \\( 0 \\)" }, { "from": "gpt", "value": "Cannot identify a line of symmetry in a simple shape" } ]

[ { "from": "human", "value": "Identify or mark lines of symmetry on a shape ![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have? \\( 2 \\)" }, { "from": "gpt", "value": "Ignores colours or design on shape when looking for symmetry" } ]

[ { "from": "human", "value": "Identify or mark lines of symmetry on a shape ![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have? \\( 4 \\)" }, { "from": "gpt", "value": "Thinks rectangles have line symmetry in the diagonals " } ]

[ { "from": "human", "value": "Tell the time from a 24 hour digital clock with times after half past the hour Which clock shows ten to twelve at night? 10:12" }, { "from": "gpt", "value": "Gets the minutes and hours the wrong way around" } ]

[ { "from": "human", "value": "Tell the time from a 24 hour digital clock with times after half past the hour Which clock shows ten to twelve at night? \\( 12: 50 \\)" }, { "from": "gpt", "value": "Does not adjust the hour for “to” times" } ]

[ { "from": "human", "value": "Tell the time from a 24 hour digital clock with times after half past the hour Which clock shows ten to twelve at night? 00:50" }, { "from": "gpt", "value": "Does not adjust the hour for “to” times" } ]

[ { "from": "human", "value": "Interpret numbers in a frequency table Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\\begin{tabular}{|c|c|}\n\\hline Goals scored & Frequency \\\\\n\\hline \\( 0 \\) & \\( 6 \\) \\\\\n\\hline \\( 1 \\) & \\( 7 \\) \\\\\n\\hline \\( 2 \\) & \\( 4 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 5 \\)" }, { "from": "gpt", "value": "Believes total frequency in a table is found by counting rows" } ]

[ { "from": "human", "value": "Interpret numbers in a frequency table Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\\begin{tabular}{|c|c|}\n\\hline Goals scored & Frequency \\\\\n\\hline \\( 0 \\) & \\( 6 \\) \\\\\n\\hline \\( 1 \\) & \\( 7 \\) \\\\\n\\hline \\( 2 \\) & \\( 4 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 28 \\)" }, { "from": "gpt", "value": "Believes the total frequency is the overall total in a grouped table" } ]

[ { "from": "human", "value": "Interpret numbers in a frequency table Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\\begin{tabular}{|c|c|}\n\\hline Goals scored & Frequency \\\\\n\\hline \\( 0 \\) & \\( 6 \\) \\\\\n\\hline \\( 1 \\) & \\( 7 \\) \\\\\n\\hline \\( 2 \\) & \\( 4 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 10 \\)" }, { "from": "gpt", "value": "Believes total frequency in a table is given by the sum of the categories given" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx - c If\n\\(\nm^{2}+5 m-14 \\equiv(m+a)(m+b)\n\\)\nthen \\( a \\times b= \\) \\( 5 \\)" }, { "from": "gpt", "value": "Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx - c If\n\\(\nm^{2}+5 m-14 \\equiv(m+a)(m+b)\n\\)\nthen \\( a \\times b= \\) \\( 14 \\)" }, { "from": "gpt", "value": "When factorising into double brackets, believes the product of the constants in the brackets is of the opposite sign to the constant in the expanded equation." } ]

[ { "from": "human", "value": "Express one quantity as a percentage of another mentally What is \\( 60 \\mathrm{~m} \\) as a percentage of \\( 2 \\mathrm{~km} \\) ? \\( 333 \\% \\)" }, { "from": "gpt", "value": "When writing a number as a percentage of another number gets them the wrong way around" } ]

[ { "from": "human", "value": "Express one quantity as a percentage of another mentally What is \\( 60 \\mathrm{~m} \\) as a percentage of \\( 2 \\mathrm{~km} \\) ? \\( 30 \\% \\)" }, { "from": "gpt", "value": "Thinks there are 100m and a km" } ]

[ { "from": "human", "value": "Express one quantity as a percentage of another mentally What is \\( 60 \\mathrm{~m} \\) as a percentage of \\( 2 \\mathrm{~km} \\) ? \\( 60 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a number to make it a percentage" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio ![A group of 8 squares and 5 circles]() What is the ratio of squares to circles? \\( 5: 13 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]