bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Recognise integers expressed visually What number is represented below? ![An image showing four rods, each cut into ten squares, three individual squares and one large square cut into ten rows and ten columns. ]() \\( 431 \\)" }, { "from": "gpt", "value": "Writes digits in the order of the pictorial representation rather than using place value columns" } ]
[ { "from": "human", "value": "Recognise integers expressed visually What number is represented below? ![An image showing four rods, each cut into ten squares, three individual squares and one large square cut into ten rows and ten columns. ]() \\( 134 \\)" }, { "from": "gpt", "value": "Writes digits in the order of the pictorial representation rather than using place value columns" } ]
[ { "from": "human", "value": "Given a y value, find the corresponding x value from a non -linear graph What is the value of \\( x \\) when \\( y=1 \\) ?\n\nGive your answer(s) to \\( 1 \\) decimal place ![A curved U shaped graph. There are 5 boxes between 0 and 1 on both axes. The graph goes through (-2, 1), (0,0), (2,1) and (4,4).]() \\( x=2 \\)" }, { "from": "gpt", "value": "Only gives 1 value of x for a given value of y, when reading from a parabolic graph" } ]
[ { "from": "human", "value": "Assign probabilities to single events using fractions There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() What is the probability of picking a red ball? \\( \\frac{4}{3} \\)" }, { "from": "gpt", "value": "Gives the probability out of the number of non-successes rather than the total" } ]
[ { "from": "human", "value": "Assign probabilities to single events using fractions There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() What is the probability of picking a red ball? \\( \\frac{7}{4} \\)" }, { "from": "gpt", "value": "Writes the numerator and the denominator the wrong way round in a probability" } ]
[ { "from": "human", "value": "Recognise a linear graph from its shape Which of the following is most likely to be the graph of a linear function? ![A graph showing a curve that starts in the bottom left, moves steeply up and right, drops half way back down, then continues steeply up and right.]()" }, { "from": "gpt", "value": "Believes linear graphs can be curved" } ]
[ { "from": "human", "value": "Recognise a linear graph from its shape Which of the following is most likely to be the graph of a linear function? ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape.]()" }, { "from": "gpt", "value": "Believes linear graphs can be curved" } ]
[ { "from": "human", "value": "Recognise a linear graph from its shape Which of the following is most likely to be the graph of a linear function? ![A graph with two curves. One curve is in the negative x, positive y quadrant. It starts at the bottom left close to the x axis, as we move right it rises very quickly towards the y axis then levels off to travel almost parallel to the y axis.\nThe other curve is in the negative y, positive x quadrant. It starts at the bottom left close to the y axis, as we move right it rises very quickly towards the x axis then becomes almost horizontal to travel almost parallel to the x axis. ]()" }, { "from": "gpt", "value": "Confuses linear and reciprocal graphs" } ]
[ { "from": "human", "value": "Order negative decimals with a different number of digits Tom and Katie are discussing negative numbers.\n\nTom says \\( -12>-9 \\)\n\nKatie says \\( -0.401>-0.41 \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Believes negative numbers with a larger absolute value are greater" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 What is \\( 80 \\% \\) of \\( 300 \\) ? \\( 380 \\)" }, { "from": "gpt", "value": "Added the values together instead of finding the percentage" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 What is \\( 80 \\% \\) of \\( 300 \\) ? \\( 80 \\)" }, { "from": "gpt", "value": "Does not understand a percentage can be applied to something not out of 100" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 What is \\( 80 \\% \\) of \\( 300 \\) ? \\( 24 \\)" }, { "from": "gpt", "value": "Believes that dividing by 100 gives 10%" } ]
[ { "from": "human", "value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Multiply out the brackets: \\( -3(m-2) \\) \\( 3 m+6 \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]
[ { "from": "human", "value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Multiply out the brackets: \\( -3(m-2) \\) \\( -3 m-6 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]
[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b \\[\nx^{2}-5 x+8 \\equiv(x-b)^{2}+1.75\n\\]\nWhat is the value of \\( b \\) ? \\( 5 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is the coefficient of x" } ]
[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b \\[\nx^{2}-5 x+8 \\equiv(x-b)^{2}+1.75\n\\]\nWhat is the value of \\( b \\) ? \\( 6.25 \\)" }, { "from": "gpt", "value": "When completing the square in the form (x - a)^2 + b, believes b is the difference between a and the constant of the original quadratic" } ]
[ { "from": "human", "value": "Round decimals to the nearest whole number Jane measures the length and width of her rectangular classroom as \\( 9.1 \\mathrm{~m} \\) and \\( 11.7 \\mathrm{~m} \\).\nWhich calculation will give the best estimate of the area? \\( 10 \\times 12 \\)" }, { "from": "gpt", "value": "Rounds every number up when estimating" } ]
[ { "from": "human", "value": "Round decimals to the nearest whole number Jane measures the length and width of her rectangular classroom as \\( 9.1 \\mathrm{~m} \\) and \\( 11.7 \\mathrm{~m} \\).\nWhich calculation will give the best estimate of the area? \\( 9 \\times 11 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Identify percentages of a shape where the percent is a multiple of 10 What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]() \\( 30 \\% \\)" }, { "from": "gpt", "value": "Assumed each part of a fraction diagram is worth 10%" } ]
[ { "from": "human", "value": "Identify percentages of a shape where the percent is a multiple of 10 What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]() \\( 3 \\% \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]
[ { "from": "human", "value": "Identify percentages of a shape where the percent is a multiple of 10 What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]() \\( 55 \\% \\)" }, { "from": "gpt", "value": "Estimated when not appropriate" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]() \\( 5: 4: 9 \\)" }, { "from": "gpt", "value": "Thinks you need to include the total as well as the individual parts when asked to write a ratio" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]() \\( 4: 5 \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]() \\( 5: 9 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]
[ { "from": "human", "value": "Understand inequality notation Which of these statements show that \\( \\mathrm{j} \\) is smaller than \\( 5 \\) ? \\( j=5 \\)" }, { "from": "gpt", "value": "Confuses inequality symbols with equality" } ]
[ { "from": "human", "value": "Understand inequality notation Which of these statements show that \\( \\mathrm{j} \\) is smaller than \\( 5 \\) ? \\( \\mathrm{j}>5 \\)" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]
[ { "from": "human", "value": "Substitute positive non-integer values into formulae involving powers or roots Calculate the time taken \\( (t) \\) for a a particle to travel with acceleration \\( (a)=4.1 \\mathrm{~ms}^{-2} \\), initial velocity \\( (u)=2.8 \\mathrm{~ms}^{-1} \\) and final velocity \\( (v)=8.7 \\mathrm{~ms}^{-1} \\) \\( t=\\frac{1}{a}(v-u) \\) \\( \\begin{array}{c}t=\\frac{1}{4.1}+(8.7-2.8) \\\\ t=6.14\\end{array} \\)" }, { "from": "gpt", "value": "Thinks a variable next to a number means addition rather than multiplication" } ]
[ { "from": "human", "value": "Substitute positive non-integer values into formulae involving powers or roots Calculate the time taken \\( (t) \\) for a a particle to travel with acceleration \\( (a)=4.1 \\mathrm{~ms}^{-2} \\), initial velocity \\( (u)=2.8 \\mathrm{~ms}^{-1} \\) and final velocity \\( (v)=8.7 \\mathrm{~ms}^{-1} \\) \\( t=\\frac{1}{a}(v-u) \\) \\( \\begin{array}{c}t=4.1 \\times(8.7-2.8) \\\\ t=24.19\\end{array} \\)" }, { "from": "gpt", "value": "When multiplying fractions, multiplies the denominator" } ]
[ { "from": "human", "value": "Recognise perpendicular lines ![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a diagonal line, with a positive gradient of 1.5. EF is a vertical line measuring 3 units. GH is a diagonal line with a negative gradient of -4/6. IJ is a diagonal line with a negative gradient of -3. KL is a diagonal line with a positive gradient of 1/3. MN is a vertical line measuring 6 units. OP is a diagonal line with a positive gradient of 6/4.]() Which line segment is perpendicular to IJ? EF" }, { "from": "gpt", "value": "Confuses the meaning of perpendicular and vertical " } ]
[ { "from": "human", "value": "Recognise perpendicular lines ![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a diagonal line, with a positive gradient of 1.5. EF is a vertical line measuring 3 units. GH is a diagonal line with a negative gradient of -4/6. IJ is a diagonal line with a negative gradient of -3. KL is a diagonal line with a positive gradient of 1/3. MN is a vertical line measuring 6 units. OP is a diagonal line with a positive gradient of 6/4.]() Which line segment is perpendicular to IJ? \\( \\mathrm{MN} \\)" }, { "from": "gpt", "value": "Confuses the meaning of perpendicular and vertical " } ]
[ { "from": "human", "value": "Substitute numbers into a SUVAT equation to work out distance \\( s=u t+\\frac{1}{2} a t^{2} \\) What is the value of \\( S \\) when\n\\[\\begin{array}{l} a=4 \\\\ u=3 \\\\ t=5\\end{array}\\] \\( 625 \\)" }, { "from": "gpt", "value": "When a variable in an expression has a power, thinks the power applies to the whole expression" } ]
[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{7}-\\frac{1}{4} \\) Give your answer in the simplest form. \\( \\frac{27}{28} \\)" }, { "from": "gpt", "value": "Adds instead of subtracts" } ]
[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{7}-\\frac{1}{4} \\) Give your answer in the simplest form. \\( \\frac{4}{3} \\)" }, { "from": "gpt", "value": "When subtracting fractions, subtracts the numerators and denominators" } ]
[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{7}-\\frac{1}{4} \\) Give your answer in the simplest form. \\( \\frac{1}{7} \\)" }, { "from": "gpt", "value": "Forgets to change the numerators when finding equivalent fractions" } ]
[ { "from": "human", "value": "Substitute negative integer values into formulae involving powers or roots \\(\nT=k^{4}\n\\)\n\nWhat is the value of \\( T \\) when \\( k=-3 \\) ? \\( -81 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]
[ { "from": "human", "value": "Substitute negative integer values into formulae involving powers or roots \\(\nT=k^{4}\n\\)\n\nWhat is the value of \\( T \\) when \\( k=-3 \\) ? \\( -12 \\)" }, { "from": "gpt", "value": "Has multiplied the base number and the power" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Which of the following answers shows a correct factorisation of the expression below? \\( x^{2}-9 \\) \\( x(x-9) \\)" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Which of the following answers shows a correct factorisation of the expression below? \\( x^{2}-9 \\) \\( (x-3)^{2} \\)" }, { "from": "gpt", "value": "Confuses the factorised form of repeated roots and the difference of 2 squares" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Which of the following answers shows a correct factorisation of the expression below? \\( x^{2}-9 \\) Cannot be factorised" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]
[ { "from": "human", "value": "Add proper fractions with different denominators which do not share a common factor \\( \\frac{1}{3}+\\frac{1}{4}+\\frac{2}{3}+\\frac{3}{4}= \\) \\( \\frac{7}{12} \\)" }, { "from": "gpt", "value": "Forgets to change the numerators when finding equivalent fractions" } ]
[ { "from": "human", "value": "Add proper fractions with different denominators which do not share a common factor \\( \\frac{1}{3}+\\frac{1}{4}+\\frac{2}{3}+\\frac{3}{4}= \\) \\( \\frac{7}{14} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]
[ { "from": "human", "value": "Add algebraic fractions with the same denominator Write this as a single fraction as simply as possible\n\\(\n\\frac{2}{x}+\\frac{3}{x}\n\\) \\( \\frac{5 x}{x^{2}} \\)" }, { "from": "gpt", "value": "Does not fully simplify fraction" } ]
[ { "from": "human", "value": "Add algebraic fractions with the same denominator Write this as a single fraction as simply as possible\n\\(\n\\frac{2}{x}+\\frac{3}{x}\n\\) \\( \\frac{5}{2 x} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]
[ { "from": "human", "value": "Add algebraic fractions with the same denominator Write this as a single fraction as simply as possible\n\\(\n\\frac{2}{x}+\\frac{3}{x}\n\\) \\( \\frac{6}{x^{2}} \\)" }, { "from": "gpt", "value": "When asked to add fractions uses the method for multiplying fractions instead." } ]
[ { "from": "human", "value": "Find the reciprocal of an integer What is the reciprocal of \\( 7 \\) ? \\( -\\frac{1}{7} \\)" }, { "from": "gpt", "value": "Correctly finds the reciprocal of a number, but believes it should be opposite in sign to the original number." } ]
[ { "from": "human", "value": "Find the reciprocal of an integer What is the reciprocal of \\( 7 \\) ? \\( -7 \\)" }, { "from": "gpt", "value": "Makes the number negative when asked to find the reciprocal" } ]
[ { "from": "human", "value": "Identify the line of symmetry of curves in the form (x + a)(x + b) This is the graph of \\( y=(x+4)(x-2) \\) ![\\( W \\)]() What is the equation of the line of symmetry? \\( y=-1 \\)" }, { "from": "gpt", "value": "Confuses the equations of vertical and horizontal lines" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as simply as possible: \\( \\frac{6 p-9}{6 p-3} \\) \\( \\frac{p-3}{p-1} \\)" }, { "from": "gpt", "value": "Thinks you can divide the variables and the numerical values by different numbers when simplifying an algebraic fraction" } ]
[ { "from": "human", "value": "Answer fraction problems that require the use of BIDMAS \\( \\frac{1}{3}+\\frac{1}{2} \\times \\frac{1}{3}= \\) \\( \\frac{5}{18} \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]
[ { "from": "human", "value": "Answer fraction problems that require the use of BIDMAS \\( \\frac{1}{3}+\\frac{1}{2} \\times \\frac{1}{3}= \\) \\( \\frac{2}{9} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]
[ { "from": "human", "value": "Solve quadratic equations using factorisation in the form x(x + b) Solve this equation, giving all solutions:\n\\(\nk^{2}-8 k=0\n\\) \\( \\begin{array}{c}k=-8 \\\\ \\text { or } \\\\ k=8\\end{array} \\)" }, { "from": "gpt", "value": "Thinks x^2 - a^2x is a valid form of difference of two squares" } ]
[ { "from": "human", "value": "Solve quadratic equations using factorisation in the form x(x + b) Solve this equation, giving all solutions:\n\\(\nk^{2}-8 k=0\n\\) \\( k=8 \\)" }, { "from": "gpt", "value": "Believes they can divide by a variable without checking whether it could equal zero" } ]
[ { "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 \\( 18 \\) 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.]() \\( 36 \\)" }, { "from": "gpt", "value": "Believes the angle in a pie chart sector is equal to the frequency" } ]
[ { "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 \\( 18 \\) 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": "Perform subtraction calculations using standard form \\( \\left(3 \\times 10^{4}\\right)-\\left(2 \\times 10^{5}\\right)= \\) \\( 1.7 \\times 10^{-5} \\)" }, { "from": "gpt", "value": "Believes a negative power results in a negative answer" } ]
[ { "from": "human", "value": "Perform subtraction calculations using standard form \\( \\left(3 \\times 10^{4}\\right)-\\left(2 \\times 10^{5}\\right)= \\) \\( 1 \\times 10^{-1} \\)" }, { "from": "gpt", "value": "When calculating with numbers in standard form, just applies the operation to the number and the power separately" } ]
[ { "from": "human", "value": "Identify the net of a prism This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]() Rectangle" }, { "from": "gpt", "value": "Names one of the faces of a 3D shape rather than the 3D shape name" } ]
[ { "from": "human", "value": "Identify the net of a prism This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]() Cube" }, { "from": "gpt", "value": "Mixes up cubes and cuboids" } ]
[ { "from": "human", "value": "Identify the net of a prism This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]() Rectanglebased pyramid" }, { "from": "gpt", "value": "Confuses pyramid with prism" } ]
[ { "from": "human", "value": "Identify parallel lines written in the form y = mx + c Tom and Katie are arguing about parallel lines. \nTom says \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}+\\mathbf{7} \\) and \\( \\boldsymbol{y}=\\mathbf{3 x + 7} \\) are parallel. \nKatie says \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}+\\mathbf{7} \\) and \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}-\\mathbf{2 2} \\) are parallel. \nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Believes lines are parallel if they have the same y intercept " } ]
[ { "from": "human", "value": "Identify parallel lines written in the form y = mx + c Tom and Katie are arguing about parallel lines. \nTom says \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}+\\mathbf{7} \\) and \\( \\boldsymbol{y}=\\mathbf{3 x + 7} \\) are parallel. \nKatie says \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}+\\mathbf{7} \\) and \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}-\\mathbf{2 2} \\) are parallel. \nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes lines can be parallel by having the same y intercept OR gradient" } ]
[ { "from": "human", "value": "Convert fractions to two digit integer percentages Complete the missing blank as a percentage:\n\\(\n0.4=\\frac{2}{5}< \\_\\_\\_\\_\n\\) \\( 40 \\% \\)" }, { "from": "gpt", "value": "Does not understand inequality notation" } ]
[ { "from": "human", "value": "Convert fractions to two digit integer percentages Complete the missing blank as a percentage:\n\\(\n0.4=\\frac{2}{5}< \\_\\_\\_\\_\n\\) \\( 20 \\% \\)" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]
[ { "from": "human", "value": "Multiply a decimal by an integer \\( 0.4 \\times 5= \\) \\( 0.9 \\)" }, { "from": "gpt", "value": "Adds instead of multiplies" } ]
[ { "from": "human", "value": "Multiply a decimal by an integer \\( 0.4 \\times 5= \\) \\( 0.20 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]
[ { "from": "human", "value": "Multiply a decimal by an integer \\( 0.4 \\times 5= \\) \\( 0.45 \\)" }, { "from": "gpt", "value": "When multiplying just writes the numbers next to each other" } ]
[ { "from": "human", "value": "Recognise a reciprocal graph from its shape Which of the following is most likely to be the graph of a reciprocal function? ![A curved graph that starts just above the x-axis on the left and travels right and very gradually up. Just before it reaches the y-axis it travels more steeply up and right, going through a point on the y-axis above the origin and continually steeply rising up and right. ]()" }, { "from": "gpt", "value": "Confuses reciprocal and exponential graphs" } ]
[ { "from": "human", "value": "Recognise a reciprocal graph from its shape Which of the following is most likely to be the graph of a reciprocal function? ![A curved graph that starts in the top left, travels steeply down and right, turns to travel steeply up and right, to the origin, where it turns around to travel down and right again.]()" }, { "from": "gpt", "value": "confuses cubic and reciprocal graphs" } ]
[ { "from": "human", "value": "Recognise a reciprocal graph from its shape Which of the following is most likely to be the graph of a reciprocal function? ![A curved graph, an upside down symmetrical U shape. It starts in the bottom left, travels steeply up and right, turns at a point on the y-axis above the origin and travels steeply right and down.]()" }, { "from": "gpt", "value": "Confuses reciprocal and quadratic graphs" } ]
[ { "from": "human", "value": "Recognise the angles around a point relationship What is the relationship between these two angles? ![\\( \\theta \\)]() They are equal" }, { "from": "gpt", "value": "Confuses vertically opposite angles and angles around a point" } ]
[ { "from": "human", "value": "Recognise the angles around a point relationship What is the relationship between these two angles? ![\\( \\theta \\)]() They are parallel" }, { "from": "gpt", "value": "Does not know the meaning of the word parallel" } ]
[ { "from": "human", "value": "Recognise the angles around a point relationship What is the relationship between these two angles? ![\\( \\theta \\)]() They add together to make \\[180\\degree\\]" }, { "from": "gpt", "value": "Believes angles around a point sum to 180" } ]
[ { "from": "human", "value": "Order fractions whose denominators are not multiples of the same number Which of the following fractions would lie between \\( \\frac{1}{5} \\) and \\( \\frac{1}{4} \\) on a number line? There are no fractions between these two" }, { "from": "gpt", "value": "Believes unit fractions with a difference of 1 in the denominator have no other fractions between them" } ]
[ { "from": "human", "value": "Write algebraic expressions with correct algebraic convention \\( a, b \\) and \\( c \\) are different numbers\n\\(\n\\frac{a+b}{c}=(a+b) \\div c\n\\)\nIs the above relationship... never true" }, { "from": "gpt", "value": "Does not realize we can write a division as a fraction" } ]
[ { "from": "human", "value": "Write algebraic expressions with correct algebraic convention \\( a, b \\) and \\( c \\) are different numbers\n\\(\n\\frac{a+b}{c}=(a+b) \\div c\n\\)\nIs the above relationship... Need more information" }, { "from": "gpt", "value": "Does not realize we can write a division as a fraction" } ]
[ { "from": "human", "value": "Describe the meaning algebraic terms with no powers Which statement correctly describes the following algebraic expression?\n\\(\n3+a b\n\\) \"Add \\( \\mathrm{a} \\) and \\( \\mathrm{b} \\) then add three.\"" }, { "from": "gpt", "value": "Thinks two variables next to each other represent addition" } ]
[ { "from": "human", "value": "Describe the meaning algebraic terms with no powers Which statement correctly describes the following algebraic expression?\n\\(\n3+a b\n\\) \"Add three to a and then multiply by b.\"" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]
[ { "from": "human", "value": "Describe the meaning algebraic terms with no powers Which statement correctly describes the following algebraic expression?\n\\(\n3+a b\n\\) \"Add three to \\( \\mathrm{b} \\) and then multiply by a.\"" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]
[ { "from": "human", "value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 45 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]() \\( h=4.5 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Uses only the base and perpendicular height when calculating the area of a trapezium" } ]
[ { "from": "human", "value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 45 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]() \\( h=3 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Does not divide by 2 when calculating the area of a trapezium" } ]
[ { "from": "human", "value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 45 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]() \\( h=9 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Uses only the base and perpendicular height when calculating the area of a trapezium" } ]
[ { "from": "human", "value": "Calculate the cube of a number \\( 3^{3}=? \\) \\( 6 \\)" }, { "from": "gpt", "value": "Adds the index to the number" } ]
[ { "from": "human", "value": "Calculate the cube of a number \\( 3^{3}=? \\) \\( 9 \\)" }, { "from": "gpt", "value": "Multiplies by the index" } ]
[ { "from": "human", "value": "Calculate the cube of a number \\( 3^{3}=? \\) \\( 33 \\)" }, { "from": "gpt", "value": "Writes the index as a digit on the end of a number" } ]
[ { "from": "human", "value": "Recognise the equations of vertical lines from a diagram What is the equation of this line? ![A graph showing a vertical line going through a number on the x axis. The number is one box to the right of -10, where there are 5 boxes between 0 and -10.]() \\( x=-9 \\)" }, { "from": "gpt", "value": "Assumes every dash on a scale represents an increase of 1" } ]
[ { "from": "human", "value": "Recognise the equations of vertical lines from a diagram What is the equation of this line? ![A graph showing a vertical line going through a number on the x axis. The number is one box to the right of -10, where there are 5 boxes between 0 and -10.]() \\( y=-8 \\)" }, { "from": "gpt", "value": "Confuses the equations of vertical and horizontal lines" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)(cx + d) Molly is expanding these two brackets.\n\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The brackets shown are (2p-1)(3p-4). The arrows are pointing at the 2p in the first bracket and the -4 in the second bracket.]() \\( +8 p \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]
[ { "from": "human", "value": "Divide two decimals with the same number of decimal places \\( 0.4 \\div 0.6= \\) \\( 0.6 \\)" }, { "from": "gpt", "value": "When dividing, ignores any remainders" } ]
[ { "from": "human", "value": "Divide two decimals with the same number of decimal places \\( 0.4 \\div 0.6= \\) \\( 1.5 \\)" }, { "from": "gpt", "value": "Believes division is commutative " } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio ![A group of six squares and three circles]() What is the ratio of squares to circles? \\( 2: 3 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio ![A group of six squares and three circles]() What is the ratio of squares to circles? \\( 6: 9 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio ![A group of six squares and three circles]() What is the ratio of squares to circles? \\( 3: 6 \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]
[ { "from": "human", "value": "Understand the relationship between parts of a ratio Kate and Isaac share some biscuits in the ratio \\( 1: 4 \\). Isaac has \\( _____ \\) times as many biscuits as Kate.\nWhat number completes the sentence? \\( 5 \\)" }, { "from": "gpt", "value": "Does not understand that in a ratio 1:n that one part of the ratio would be n times bigger than the one part" } ]
[ { "from": "human", "value": "Understand the relationship between parts of a ratio Kate and Isaac share some biscuits in the ratio \\( 1: 4 \\). Isaac has \\( _____ \\) times as many biscuits as Kate.\nWhat number completes the sentence? \\( 3 \\)" }, { "from": "gpt", "value": "Does not understand that in a ratio 1:n that one part of the ratio would be n times bigger than the one part" } ]
[ { "from": "human", "value": "Solve missing number problems involving the median The median of these four numbers is \\( 5 \\).\n\\(\n\\begin{array}{cccc}\n3&12&1&?\n\\end{array}\n\\)\nFind the value of the missing number. \\( 4 \\)" }, { "from": "gpt", "value": "Finds the mean instead of the median" } ]
[ { "from": "human", "value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one What is the \\( 6 \\) th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is one orange square. The second pattern is 3 orange squares arranged in an incomplete 2 by 2 square shape with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle with base 3 and height 2, with the top left orange square missing.]() ![6 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left and top right orange squares missing.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]
[ { "from": "human", "value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one What is the \\( 6 \\) th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is one orange square. The second pattern is 3 orange squares arranged in an incomplete 2 by 2 square shape with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle with base 3 and height 2, with the top left orange square missing.]() ![10 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left and top right orange squares missing.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]
[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 3 or more decimal places Convert \\( \\frac{97}{250} \\) into a decimal \\( 0.97 \\)" }, { "from": "gpt", "value": "Converts a fraction to a decimal by using only the numerator after the decimal point" } ]
[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 3 or more decimal places Convert \\( \\frac{97}{250} \\) into a decimal \\( 97.25 \\)" }, { "from": "gpt", "value": "Converts a fraction to a decimal by placing a decimal point between the numerator and denominator" } ]
[ { "from": "human", "value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The top rectangle is shaded red.]() \\( 14 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]

[ { "from": "human", "value": "Recognise integers expressed visually What number is represented below? ![An image showing four rods, each cut into ten squares, three individual squares and one large square cut into ten rows and ten columns. ]() \\( 431 \\)" }, { "from": "gpt", "value": "Writes digits in the order of the pictorial representation rather than using place value columns" } ]

[ { "from": "human", "value": "Recognise integers expressed visually What number is represented below? ![An image showing four rods, each cut into ten squares, three individual squares and one large square cut into ten rows and ten columns. ]() \\( 134 \\)" }, { "from": "gpt", "value": "Writes digits in the order of the pictorial representation rather than using place value columns" } ]

[ { "from": "human", "value": "Given a y value, find the corresponding x value from a non -linear graph What is the value of \\( x \\) when \\( y=1 \\) ?\n\nGive your answer(s) to \\( 1 \\) decimal place ![A curved U shaped graph. There are 5 boxes between 0 and 1 on both axes. The graph goes through (-2, 1), (0,0), (2,1) and (4,4).]() \\( x=2 \\)" }, { "from": "gpt", "value": "Only gives 1 value of x for a given value of y, when reading from a parabolic graph" } ]

[ { "from": "human", "value": "Assign probabilities to single events using fractions There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() What is the probability of picking a red ball? \\( \\frac{4}{3} \\)" }, { "from": "gpt", "value": "Gives the probability out of the number of non-successes rather than the total" } ]

[ { "from": "human", "value": "Assign probabilities to single events using fractions There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() What is the probability of picking a red ball? \\( \\frac{7}{4} \\)" }, { "from": "gpt", "value": "Writes the numerator and the denominator the wrong way round in a probability" } ]

[ { "from": "human", "value": "Recognise a linear graph from its shape Which of the following is most likely to be the graph of a linear function? ![A graph showing a curve that starts in the bottom left, moves steeply up and right, drops half way back down, then continues steeply up and right.]()" }, { "from": "gpt", "value": "Believes linear graphs can be curved" } ]

[ { "from": "human", "value": "Recognise a linear graph from its shape Which of the following is most likely to be the graph of a linear function? ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape.]()" }, { "from": "gpt", "value": "Believes linear graphs can be curved" } ]

[ { "from": "human", "value": "Recognise a linear graph from its shape Which of the following is most likely to be the graph of a linear function? ![A graph with two curves. One curve is in the negative x, positive y quadrant. It starts at the bottom left close to the x axis, as we move right it rises very quickly towards the y axis then levels off to travel almost parallel to the y axis.\nThe other curve is in the negative y, positive x quadrant. It starts at the bottom left close to the y axis, as we move right it rises very quickly towards the x axis then becomes almost horizontal to travel almost parallel to the x axis. ]()" }, { "from": "gpt", "value": "Confuses linear and reciprocal graphs" } ]

[ { "from": "human", "value": "Order negative decimals with a different number of digits Tom and Katie are discussing negative numbers.\n\nTom says \\( -12>-9 \\)\n\nKatie says \\( -0.401>-0.41 \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Believes negative numbers with a larger absolute value are greater" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 What is \\( 80 \\% \\) of \\( 300 \\) ? \\( 380 \\)" }, { "from": "gpt", "value": "Added the values together instead of finding the percentage" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 What is \\( 80 \\% \\) of \\( 300 \\) ? \\( 80 \\)" }, { "from": "gpt", "value": "Does not understand a percentage can be applied to something not out of 100" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 What is \\( 80 \\% \\) of \\( 300 \\) ? \\( 24 \\)" }, { "from": "gpt", "value": "Believes that dividing by 100 gives 10%" } ]

[ { "from": "human", "value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Multiply out the brackets: \\( -3(m-2) \\) \\( 3 m+6 \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]

[ { "from": "human", "value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Multiply out the brackets: \\( -3(m-2) \\) \\( -3 m-6 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]

[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b \\[\nx^{2}-5 x+8 \\equiv(x-b)^{2}+1.75\n\\]\nWhat is the value of \\( b \\) ? \\( 5 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is the coefficient of x" } ]

[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b \\[\nx^{2}-5 x+8 \\equiv(x-b)^{2}+1.75\n\\]\nWhat is the value of \\( b \\) ? \\( 6.25 \\)" }, { "from": "gpt", "value": "When completing the square in the form (x - a)^2 + b, believes b is the difference between a and the constant of the original quadratic" } ]

[ { "from": "human", "value": "Round decimals to the nearest whole number Jane measures the length and width of her rectangular classroom as \\( 9.1 \\mathrm{~m} \\) and \\( 11.7 \\mathrm{~m} \\).\nWhich calculation will give the best estimate of the area? \\( 10 \\times 12 \\)" }, { "from": "gpt", "value": "Rounds every number up when estimating" } ]

[ { "from": "human", "value": "Round decimals to the nearest whole number Jane measures the length and width of her rectangular classroom as \\( 9.1 \\mathrm{~m} \\) and \\( 11.7 \\mathrm{~m} \\).\nWhich calculation will give the best estimate of the area? \\( 9 \\times 11 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Identify percentages of a shape where the percent is a multiple of 10 What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]() \\( 30 \\% \\)" }, { "from": "gpt", "value": "Assumed each part of a fraction diagram is worth 10%" } ]

[ { "from": "human", "value": "Identify percentages of a shape where the percent is a multiple of 10 What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]() \\( 3 \\% \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]

[ { "from": "human", "value": "Identify percentages of a shape where the percent is a multiple of 10 What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]() \\( 55 \\% \\)" }, { "from": "gpt", "value": "Estimated when not appropriate" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]() \\( 5: 4: 9 \\)" }, { "from": "gpt", "value": "Thinks you need to include the total as well as the individual parts when asked to write a ratio" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]() \\( 4: 5 \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]() \\( 5: 9 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]

[ { "from": "human", "value": "Understand inequality notation Which of these statements show that \\( \\mathrm{j} \\) is smaller than \\( 5 \\) ? \\( j=5 \\)" }, { "from": "gpt", "value": "Confuses inequality symbols with equality" } ]

[ { "from": "human", "value": "Understand inequality notation Which of these statements show that \\( \\mathrm{j} \\) is smaller than \\( 5 \\) ? \\( \\mathrm{j}>5 \\)" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Substitute positive non-integer values into formulae involving powers or roots Calculate the time taken \\( (t) \\) for a a particle to travel with acceleration \\( (a)=4.1 \\mathrm{~ms}^{-2} \\), initial velocity \\( (u)=2.8 \\mathrm{~ms}^{-1} \\) and final velocity \\( (v)=8.7 \\mathrm{~ms}^{-1} \\) \\( t=\\frac{1}{a}(v-u) \\) \\( \\begin{array}{c}t=\\frac{1}{4.1}+(8.7-2.8) \\\\ t=6.14\\end{array} \\)" }, { "from": "gpt", "value": "Thinks a variable next to a number means addition rather than multiplication" } ]

[ { "from": "human", "value": "Substitute positive non-integer values into formulae involving powers or roots Calculate the time taken \\( (t) \\) for a a particle to travel with acceleration \\( (a)=4.1 \\mathrm{~ms}^{-2} \\), initial velocity \\( (u)=2.8 \\mathrm{~ms}^{-1} \\) and final velocity \\( (v)=8.7 \\mathrm{~ms}^{-1} \\) \\( t=\\frac{1}{a}(v-u) \\) \\( \\begin{array}{c}t=4.1 \\times(8.7-2.8) \\\\ t=24.19\\end{array} \\)" }, { "from": "gpt", "value": "When multiplying fractions, multiplies the denominator" } ]

[ { "from": "human", "value": "Recognise perpendicular lines ![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a diagonal line, with a positive gradient of 1.5. EF is a vertical line measuring 3 units. GH is a diagonal line with a negative gradient of -4/6. IJ is a diagonal line with a negative gradient of -3. KL is a diagonal line with a positive gradient of 1/3. MN is a vertical line measuring 6 units. OP is a diagonal line with a positive gradient of 6/4.]() Which line segment is perpendicular to IJ? EF" }, { "from": "gpt", "value": "Confuses the meaning of perpendicular and vertical " } ]

[ { "from": "human", "value": "Recognise perpendicular lines ![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a diagonal line, with a positive gradient of 1.5. EF is a vertical line measuring 3 units. GH is a diagonal line with a negative gradient of -4/6. IJ is a diagonal line with a negative gradient of -3. KL is a diagonal line with a positive gradient of 1/3. MN is a vertical line measuring 6 units. OP is a diagonal line with a positive gradient of 6/4.]() Which line segment is perpendicular to IJ? \\( \\mathrm{MN} \\)" }, { "from": "gpt", "value": "Confuses the meaning of perpendicular and vertical " } ]

[ { "from": "human", "value": "Substitute numbers into a SUVAT equation to work out distance \\( s=u t+\\frac{1}{2} a t^{2} \\) What is the value of \\( S \\) when\n\\[\\begin{array}{l} a=4 \\\\ u=3 \\\\ t=5\\end{array}\\] \\( 625 \\)" }, { "from": "gpt", "value": "When a variable in an expression has a power, thinks the power applies to the whole expression" } ]

[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{7}-\\frac{1}{4} \\) Give your answer in the simplest form. \\( \\frac{27}{28} \\)" }, { "from": "gpt", "value": "Adds instead of subtracts" } ]

[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{7}-\\frac{1}{4} \\) Give your answer in the simplest form. \\( \\frac{4}{3} \\)" }, { "from": "gpt", "value": "When subtracting fractions, subtracts the numerators and denominators" } ]

[ { "from": "human", "value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{7}-\\frac{1}{4} \\) Give your answer in the simplest form. \\( \\frac{1}{7} \\)" }, { "from": "gpt", "value": "Forgets to change the numerators when finding equivalent fractions" } ]

[ { "from": "human", "value": "Substitute negative integer values into formulae involving powers or roots \\(\nT=k^{4}\n\\)\n\nWhat is the value of \\( T \\) when \\( k=-3 \\) ? \\( -81 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]

[ { "from": "human", "value": "Substitute negative integer values into formulae involving powers or roots \\(\nT=k^{4}\n\\)\n\nWhat is the value of \\( T \\) when \\( k=-3 \\) ? \\( -12 \\)" }, { "from": "gpt", "value": "Has multiplied the base number and the power" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Which of the following answers shows a correct factorisation of the expression below? \\( x^{2}-9 \\) \\( x(x-9) \\)" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Which of the following answers shows a correct factorisation of the expression below? \\( x^{2}-9 \\) \\( (x-3)^{2} \\)" }, { "from": "gpt", "value": "Confuses the factorised form of repeated roots and the difference of 2 squares" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Which of the following answers shows a correct factorisation of the expression below? \\( x^{2}-9 \\) Cannot be factorised" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]

[ { "from": "human", "value": "Add proper fractions with different denominators which do not share a common factor \\( \\frac{1}{3}+\\frac{1}{4}+\\frac{2}{3}+\\frac{3}{4}= \\) \\( \\frac{7}{12} \\)" }, { "from": "gpt", "value": "Forgets to change the numerators when finding equivalent fractions" } ]

[ { "from": "human", "value": "Add proper fractions with different denominators which do not share a common factor \\( \\frac{1}{3}+\\frac{1}{4}+\\frac{2}{3}+\\frac{3}{4}= \\) \\( \\frac{7}{14} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]

[ { "from": "human", "value": "Add algebraic fractions with the same denominator Write this as a single fraction as simply as possible\n\\(\n\\frac{2}{x}+\\frac{3}{x}\n\\) \\( \\frac{5 x}{x^{2}} \\)" }, { "from": "gpt", "value": "Does not fully simplify fraction" } ]

[ { "from": "human", "value": "Add algebraic fractions with the same denominator Write this as a single fraction as simply as possible\n\\(\n\\frac{2}{x}+\\frac{3}{x}\n\\) \\( \\frac{5}{2 x} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]

[ { "from": "human", "value": "Add algebraic fractions with the same denominator Write this as a single fraction as simply as possible\n\\(\n\\frac{2}{x}+\\frac{3}{x}\n\\) \\( \\frac{6}{x^{2}} \\)" }, { "from": "gpt", "value": "When asked to add fractions uses the method for multiplying fractions instead." } ]

[ { "from": "human", "value": "Find the reciprocal of an integer What is the reciprocal of \\( 7 \\) ? \\( -\\frac{1}{7} \\)" }, { "from": "gpt", "value": "Correctly finds the reciprocal of a number, but believes it should be opposite in sign to the original number." } ]

[ { "from": "human", "value": "Find the reciprocal of an integer What is the reciprocal of \\( 7 \\) ? \\( -7 \\)" }, { "from": "gpt", "value": "Makes the number negative when asked to find the reciprocal" } ]

[ { "from": "human", "value": "Identify the line of symmetry of curves in the form (x + a)(x + b) This is the graph of \\( y=(x+4)(x-2) \\) ![\\( W \\)]() What is the equation of the line of symmetry? \\( y=-1 \\)" }, { "from": "gpt", "value": "Confuses the equations of vertical and horizontal lines" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as simply as possible: \\( \\frac{6 p-9}{6 p-3} \\) \\( \\frac{p-3}{p-1} \\)" }, { "from": "gpt", "value": "Thinks you can divide the variables and the numerical values by different numbers when simplifying an algebraic fraction" } ]

[ { "from": "human", "value": "Answer fraction problems that require the use of BIDMAS \\( \\frac{1}{3}+\\frac{1}{2} \\times \\frac{1}{3}= \\) \\( \\frac{5}{18} \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]

[ { "from": "human", "value": "Answer fraction problems that require the use of BIDMAS \\( \\frac{1}{3}+\\frac{1}{2} \\times \\frac{1}{3}= \\) \\( \\frac{2}{9} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]

[ { "from": "human", "value": "Solve quadratic equations using factorisation in the form x(x + b) Solve this equation, giving all solutions:\n\\(\nk^{2}-8 k=0\n\\) \\( \\begin{array}{c}k=-8 \\\\ \\text { or } \\\\ k=8\\end{array} \\)" }, { "from": "gpt", "value": "Thinks x^2 - a^2x is a valid form of difference of two squares" } ]

[ { "from": "human", "value": "Solve quadratic equations using factorisation in the form x(x + b) Solve this equation, giving all solutions:\n\\(\nk^{2}-8 k=0\n\\) \\( k=8 \\)" }, { "from": "gpt", "value": "Believes they can divide by a variable without checking whether it could equal zero" } ]

[ { "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 \\( 18 \\) 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.]() \\( 36 \\)" }, { "from": "gpt", "value": "Believes the angle in a pie chart sector is equal to the frequency" } ]

[ { "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 \\( 18 \\) 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": "Perform subtraction calculations using standard form \\( \\left(3 \\times 10^{4}\\right)-\\left(2 \\times 10^{5}\\right)= \\) \\( 1.7 \\times 10^{-5} \\)" }, { "from": "gpt", "value": "Believes a negative power results in a negative answer" } ]

[ { "from": "human", "value": "Perform subtraction calculations using standard form \\( \\left(3 \\times 10^{4}\\right)-\\left(2 \\times 10^{5}\\right)= \\) \\( 1 \\times 10^{-1} \\)" }, { "from": "gpt", "value": "When calculating with numbers in standard form, just applies the operation to the number and the power separately" } ]

[ { "from": "human", "value": "Identify the net of a prism This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]() Rectangle" }, { "from": "gpt", "value": "Names one of the faces of a 3D shape rather than the 3D shape name" } ]

[ { "from": "human", "value": "Identify the net of a prism This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]() Cube" }, { "from": "gpt", "value": "Mixes up cubes and cuboids" } ]

[ { "from": "human", "value": "Identify the net of a prism This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]() Rectanglebased pyramid" }, { "from": "gpt", "value": "Confuses pyramid with prism" } ]

[ { "from": "human", "value": "Identify parallel lines written in the form y = mx + c Tom and Katie are arguing about parallel lines. \nTom says \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}+\\mathbf{7} \\) and \\( \\boldsymbol{y}=\\mathbf{3 x + 7} \\) are parallel. \nKatie says \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}+\\mathbf{7} \\) and \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}-\\mathbf{2 2} \\) are parallel. \nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Believes lines are parallel if they have the same y intercept " } ]

[ { "from": "human", "value": "Identify parallel lines written in the form y = mx + c Tom and Katie are arguing about parallel lines. \nTom says \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}+\\mathbf{7} \\) and \\( \\boldsymbol{y}=\\mathbf{3 x + 7} \\) are parallel. \nKatie says \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}+\\mathbf{7} \\) and \\( \\boldsymbol{y}=\\mathbf{5} \\boldsymbol{x}-\\mathbf{2 2} \\) are parallel. \nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes lines can be parallel by having the same y intercept OR gradient" } ]

[ { "from": "human", "value": "Convert fractions to two digit integer percentages Complete the missing blank as a percentage:\n\\(\n0.4=\\frac{2}{5}< \\_\\_\\_\\_\n\\) \\( 40 \\% \\)" }, { "from": "gpt", "value": "Does not understand inequality notation" } ]

[ { "from": "human", "value": "Convert fractions to two digit integer percentages Complete the missing blank as a percentage:\n\\(\n0.4=\\frac{2}{5}< \\_\\_\\_\\_\n\\) \\( 20 \\% \\)" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Multiply a decimal by an integer \\( 0.4 \\times 5= \\) \\( 0.9 \\)" }, { "from": "gpt", "value": "Adds instead of multiplies" } ]

[ { "from": "human", "value": "Multiply a decimal by an integer \\( 0.4 \\times 5= \\) \\( 0.20 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]

[ { "from": "human", "value": "Multiply a decimal by an integer \\( 0.4 \\times 5= \\) \\( 0.45 \\)" }, { "from": "gpt", "value": "When multiplying just writes the numbers next to each other" } ]

[ { "from": "human", "value": "Recognise a reciprocal graph from its shape Which of the following is most likely to be the graph of a reciprocal function? ![A curved graph that starts just above the x-axis on the left and travels right and very gradually up. Just before it reaches the y-axis it travels more steeply up and right, going through a point on the y-axis above the origin and continually steeply rising up and right. ]()" }, { "from": "gpt", "value": "Confuses reciprocal and exponential graphs" } ]

[ { "from": "human", "value": "Recognise a reciprocal graph from its shape Which of the following is most likely to be the graph of a reciprocal function? ![A curved graph that starts in the top left, travels steeply down and right, turns to travel steeply up and right, to the origin, where it turns around to travel down and right again.]()" }, { "from": "gpt", "value": "confuses cubic and reciprocal graphs" } ]

[ { "from": "human", "value": "Recognise a reciprocal graph from its shape Which of the following is most likely to be the graph of a reciprocal function? ![A curved graph, an upside down symmetrical U shape. It starts in the bottom left, travels steeply up and right, turns at a point on the y-axis above the origin and travels steeply right and down.]()" }, { "from": "gpt", "value": "Confuses reciprocal and quadratic graphs" } ]

[ { "from": "human", "value": "Recognise the angles around a point relationship What is the relationship between these two angles? ![\\( \\theta \\)]() They are equal" }, { "from": "gpt", "value": "Confuses vertically opposite angles and angles around a point" } ]

[ { "from": "human", "value": "Recognise the angles around a point relationship What is the relationship between these two angles? ![\\( \\theta \\)]() They are parallel" }, { "from": "gpt", "value": "Does not know the meaning of the word parallel" } ]

[ { "from": "human", "value": "Recognise the angles around a point relationship What is the relationship between these two angles? ![\\( \\theta \\)]() They add together to make \\[180\\degree\\]" }, { "from": "gpt", "value": "Believes angles around a point sum to 180" } ]

[ { "from": "human", "value": "Order fractions whose denominators are not multiples of the same number Which of the following fractions would lie between \\( \\frac{1}{5} \\) and \\( \\frac{1}{4} \\) on a number line? There are no fractions between these two" }, { "from": "gpt", "value": "Believes unit fractions with a difference of 1 in the denominator have no other fractions between them" } ]

[ { "from": "human", "value": "Write algebraic expressions with correct algebraic convention \\( a, b \\) and \\( c \\) are different numbers\n\\(\n\\frac{a+b}{c}=(a+b) \\div c\n\\)\nIs the above relationship... never true" }, { "from": "gpt", "value": "Does not realize we can write a division as a fraction" } ]

[ { "from": "human", "value": "Write algebraic expressions with correct algebraic convention \\( a, b \\) and \\( c \\) are different numbers\n\\(\n\\frac{a+b}{c}=(a+b) \\div c\n\\)\nIs the above relationship... Need more information" }, { "from": "gpt", "value": "Does not realize we can write a division as a fraction" } ]

[ { "from": "human", "value": "Describe the meaning algebraic terms with no powers Which statement correctly describes the following algebraic expression?\n\\(\n3+a b\n\\) \"Add \\( \\mathrm{a} \\) and \\( \\mathrm{b} \\) then add three.\"" }, { "from": "gpt", "value": "Thinks two variables next to each other represent addition" } ]

[ { "from": "human", "value": "Describe the meaning algebraic terms with no powers Which statement correctly describes the following algebraic expression?\n\\(\n3+a b\n\\) \"Add three to a and then multiply by b.\"" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]

[ { "from": "human", "value": "Describe the meaning algebraic terms with no powers Which statement correctly describes the following algebraic expression?\n\\(\n3+a b\n\\) \"Add three to \\( \\mathrm{b} \\) and then multiply by a.\"" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]

[ { "from": "human", "value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 45 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]() \\( h=4.5 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Uses only the base and perpendicular height when calculating the area of a trapezium" } ]

[ { "from": "human", "value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 45 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]() \\( h=3 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Does not divide by 2 when calculating the area of a trapezium" } ]

[ { "from": "human", "value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 45 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]() \\( h=9 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Uses only the base and perpendicular height when calculating the area of a trapezium" } ]

[ { "from": "human", "value": "Calculate the cube of a number \\( 3^{3}=? \\) \\( 6 \\)" }, { "from": "gpt", "value": "Adds the index to the number" } ]

[ { "from": "human", "value": "Calculate the cube of a number \\( 3^{3}=? \\) \\( 9 \\)" }, { "from": "gpt", "value": "Multiplies by the index" } ]

[ { "from": "human", "value": "Calculate the cube of a number \\( 3^{3}=? \\) \\( 33 \\)" }, { "from": "gpt", "value": "Writes the index as a digit on the end of a number" } ]

[ { "from": "human", "value": "Recognise the equations of vertical lines from a diagram What is the equation of this line? ![A graph showing a vertical line going through a number on the x axis. The number is one box to the right of -10, where there are 5 boxes between 0 and -10.]() \\( x=-9 \\)" }, { "from": "gpt", "value": "Assumes every dash on a scale represents an increase of 1" } ]

[ { "from": "human", "value": "Recognise the equations of vertical lines from a diagram What is the equation of this line? ![A graph showing a vertical line going through a number on the x axis. The number is one box to the right of -10, where there are 5 boxes between 0 and -10.]() \\( y=-8 \\)" }, { "from": "gpt", "value": "Confuses the equations of vertical and horizontal lines" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)(cx + d) Molly is expanding these two brackets.\n\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The brackets shown are (2p-1)(3p-4). The arrows are pointing at the 2p in the first bracket and the -4 in the second bracket.]() \\( +8 p \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]

[ { "from": "human", "value": "Divide two decimals with the same number of decimal places \\( 0.4 \\div 0.6= \\) \\( 0.6 \\)" }, { "from": "gpt", "value": "When dividing, ignores any remainders" } ]

[ { "from": "human", "value": "Divide two decimals with the same number of decimal places \\( 0.4 \\div 0.6= \\) \\( 1.5 \\)" }, { "from": "gpt", "value": "Believes division is commutative " } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio ![A group of six squares and three circles]() What is the ratio of squares to circles? \\( 2: 3 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio ![A group of six squares and three circles]() What is the ratio of squares to circles? \\( 6: 9 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio ![A group of six squares and three circles]() What is the ratio of squares to circles? \\( 3: 6 \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]

[ { "from": "human", "value": "Understand the relationship between parts of a ratio Kate and Isaac share some biscuits in the ratio \\( 1: 4 \\). Isaac has \\( _____ \\) times as many biscuits as Kate.\nWhat number completes the sentence? \\( 5 \\)" }, { "from": "gpt", "value": "Does not understand that in a ratio 1:n that one part of the ratio would be n times bigger than the one part" } ]

[ { "from": "human", "value": "Understand the relationship between parts of a ratio Kate and Isaac share some biscuits in the ratio \\( 1: 4 \\). Isaac has \\( _____ \\) times as many biscuits as Kate.\nWhat number completes the sentence? \\( 3 \\)" }, { "from": "gpt", "value": "Does not understand that in a ratio 1:n that one part of the ratio would be n times bigger than the one part" } ]

[ { "from": "human", "value": "Solve missing number problems involving the median The median of these four numbers is \\( 5 \\).\n\\(\n\\begin{array}{cccc}\n3&12&1&?\n\\end{array}\n\\)\nFind the value of the missing number. \\( 4 \\)" }, { "from": "gpt", "value": "Finds the mean instead of the median" } ]

[ { "from": "human", "value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one What is the \\( 6 \\) th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is one orange square. The second pattern is 3 orange squares arranged in an incomplete 2 by 2 square shape with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle with base 3 and height 2, with the top left orange square missing.]() ![6 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left and top right orange squares missing.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]

[ { "from": "human", "value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one What is the \\( 6 \\) th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is one orange square. The second pattern is 3 orange squares arranged in an incomplete 2 by 2 square shape with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle with base 3 and height 2, with the top left orange square missing.]() ![10 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left and top right orange squares missing.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]

[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 3 or more decimal places Convert \\( \\frac{97}{250} \\) into a decimal \\( 0.97 \\)" }, { "from": "gpt", "value": "Converts a fraction to a decimal by using only the numerator after the decimal point" } ]

[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 3 or more decimal places Convert \\( \\frac{97}{250} \\) into a decimal \\( 97.25 \\)" }, { "from": "gpt", "value": "Converts a fraction to a decimal by placing a decimal point between the numerator and denominator" } ]

[ { "from": "human", "value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The top rectangle is shaded red.]() \\( 14 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]