bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Change decimals of hours into minutes \\( 1.5 \\) hours \\( = _______\\) minutes \\( 105 \\)" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]
[ { "from": "human", "value": "Change decimals of hours into minutes \\( 1.5 \\) hours \\( = _______\\) minutes \\( 65 \\)" }, { "from": "gpt", "value": "Thinks there are 10 minutes in an hour" } ]
[ { "from": "human", "value": "Use the nth term rule for ascending integer linear sequences to find another term in the sequence If you know the first term of a linear sequence and you multiply it by \\( 10 \\), you get the \\( 10^{\\text {th }} \\) term of that sequence.\nIs this statement... always true" }, { "from": "gpt", "value": "Thinks terms in linear sequence are in direct proportion" } ]
[ { "from": "human", "value": "Use the nth term rule for ascending integer linear sequences to find another term in the sequence If you know the first term of a linear sequence and you multiply it by \\( 10 \\), you get the \\( 10^{\\text {th }} \\) term of that sequence.\nIs this statement... never true" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Given the speed, calculate missing values from a displacement-time graph This displacement-time graph shows the first \\( 10 \\) seconds of Mo's journey.\n\nDuring that time he travelled at a speed of \\( 6 \\mathrm{~m} / \\mathrm{s.} \\)\n\nWhat distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \\(\\bigstar \\))]() \\( 30 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Believes distance is the area under the graph on a displacement time graph" } ]
[ { "from": "human", "value": "Given the speed, calculate missing values from a displacement-time graph This displacement-time graph shows the first \\( 10 \\) seconds of Mo's journey.\n\nDuring that time he travelled at a speed of \\( 6 \\mathrm{~m} / \\mathrm{s.} \\)\n\nWhat distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \\(\\bigstar \\))]() \\( 6 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Believes scales on graphs must match on both axes" } ]
[ { "from": "human", "value": "Given the speed, calculate missing values from a displacement-time graph This displacement-time graph shows the first \\( 10 \\) seconds of Mo's journey.\n\nDuring that time he travelled at a speed of \\( 6 \\mathrm{~m} / \\mathrm{s.} \\)\n\nWhat distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \\(\\bigstar \\))]() \\( 16 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Believes distance = speed + time" } ]
[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram 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.]() Kate picks a yellow ball out and then replaces it.\n\nShe then has a second pick.\nWhat is the probability the second pick is also a yellow ball? \\( \\frac{3}{6} \\)" }, { "from": "gpt", "value": "Assumes the item has not been replaced in a probability question where it has actually been replaced" } ]
[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram 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.]() Kate picks a yellow ball out and then replaces it.\n\nShe then has a second pick.\nWhat is the probability the second pick is also a yellow ball? \\( \\frac{2}{6} \\)" }, { "from": "gpt", "value": "Assumes the item has not been replaced in a probability question where it has actually been replaced" } ]
[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. \"0\" above the 1st dash and \"2\" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to? \\( 1.8 \\)" }, { "from": "gpt", "value": "When reading decimals on a number line, assumes each dash is 0.1" } ]
[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. \"0\" above the 1st dash and \"2\" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to? \\( 1 \\)" }, { "from": "gpt", "value": "Believes the arrow on a number line points to the middle value" } ]
[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. \"0\" above the 1st dash and \"2\" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to? \\( 1.6 \\)" }, { "from": "gpt", "value": "Estimates a measurement on a diagram rather than working it out" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 \\( 20 \\% \\) of \\( \\pounds 140= \\) \\( £ 20 \\)" }, { "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 \\( 20 \\% \\) of \\( \\pounds 140= \\) \\( £ 120 \\)" }, { "from": "gpt", "value": "Has taken the percentage from the original " } ]
[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition This is how Dora calculates the answer to \\( 12.3+4.5 \\) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \\( 3.5+21.8 \\). Which of the following shows how she would do this? \\( \\begin{array}{c}3+21=24 \\\\ 0.5+0.8=0.13 \\\\ 24+0.13=24.13\\end{array} \\)" }, { "from": "gpt", "value": "When adding decimals, just adds the digits and ignores place value" } ]
[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition This is how Dora calculates the answer to \\( 12.3+4.5 \\) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \\( 3.5+21.8 \\). Which of the following shows how she would do this? \\( \\begin{array}{c}3.5+21=24.5 \\\\ 24.5+0.8=25.3\\end{array} \\)" }, { "from": "gpt", "value": "Does not interpret the correct order of operations from a worded problem" } ]
[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition This is how Dora calculates the answer to \\( 12.3+4.5 \\) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \\( 3.5+21.8 \\). Which of the following shows how she would do this? \\( \\begin{array}{c}3+21=24 \\\\ 0.5+0.8=1.3 \\\\ 24+1.3=24.13\\end{array} \\)" }, { "from": "gpt", "value": "Ignores place value when adding a whole number and a decimal" } ]
[ { "from": "human", "value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 63 \\mathrm{~cm}^{2} \\).\n\nWhat is the value of \\( a \\) ? ![A trapezium with the parallel sides labelled with 3cm and a and the height labelled with 9cm]() \\( 4 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Does not divide by 2 when calculating the area of a trapezium" } ]
[ { "from": "human", "value": "Calculate unit fractions of an amount \\( \\frac{1}{20} \\) of \\( 7=? \\times 7 \\) \\( 0.2 \\)" }, { "from": "gpt", "value": "Converts a fraction to a decimal by using the denominator after the decimal point" } ]
[ { "from": "human", "value": "Calculate unit fractions of an amount \\( \\frac{1}{20} \\) of \\( 7=? \\times 7 \\) \\( 20 \\)" }, { "from": "gpt", "value": "Multiplies by the denominator instead of dividing when finding a fraction of an amount" } ]
[ { "from": "human", "value": "Carry out subtraction problems involving one negative integer \\( 6-(-8)= \\) \\( -14 \\)" }, { "from": "gpt", "value": "When subtracting a negative thinks the answer must be negative " } ]
[ { "from": "human", "value": "Carry out subtraction problems involving one negative integer \\( 6-(-8)= \\) \\( -2 \\)" }, { "from": "gpt", "value": "Does not realise that subtracting a negative is the same as adding it's additive inverse" } ]
[ { "from": "human", "value": "Round integers to the nearest 1000 A distance has been rounded to the nearest \\( \\mathrm{km} \\), giving \\( 106 \\) \\( \\mathrm{km} \\).\nWhich of these values could the distance \\( \\underline{not} \\) be? \\( 106220 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]
[ { "from": "human", "value": "Round integers to the nearest 1000 A distance has been rounded to the nearest \\( \\mathrm{km} \\), giving \\( 106 \\) \\( \\mathrm{km} \\).\nWhich of these values could the distance \\( \\underline{not} \\) be? \\( 105605 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round integers to the nearest 1000 A distance has been rounded to the nearest \\( \\mathrm{km} \\), giving \\( 106 \\) \\( \\mathrm{km} \\).\nWhich of these values could the distance \\( \\underline{not} \\) be? \\( 105698 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Multiply algebraic fractions involving non-linear expressions Write this as a single fraction as simply as possible\n\\(\n\\frac{2}{m^{2}-4 m+3} \\times \\frac{m-3}{4}\n\\) \\( \\frac{2 m-6}{4 m^{2}-16 m+12} \\)" }, { "from": "gpt", "value": "Expands when asked to simplify" } ]
[ { "from": "human", "value": "Recognise an exponential graph from its shape Which of the following is most likely to be the graph of a exponential function? ![A graph with two curves, in the top right and bottom left quadrants. The top right curves starts up and right of the origin and travels steeply down and right, it then levels off to travel alongside the x-axis without touching it. The bottom left curve starts down and left of the origin, travels steeply up and left, it then levels off just below the x-axis without touching it.]()" }, { "from": "gpt", "value": "Confuses reciprocal and exponential graphs" } ]
[ { "from": "human", "value": "Recognise an exponential graph from its shape Which of the following is most likely to be the graph of a exponential 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 exponential graphs" } ]
[ { "from": "human", "value": "Recognise an exponential graph from its shape Which of the following is most likely to be the graph of a exponential 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 quadratic and exponential graphs" } ]
[ { "from": "human", "value": "Identify the regions on a double Venn diagram given in words \\( 60 \\) people completed an online survey about the car they own.\nThe results are shown in the Venn Diagram.\n\nHow many people own a black car? ![A Venn diagram with two circles labelled Owns a 4x4 and Owns a Black Car. The number 27 is in the Owns a 4x4 only region, 15 is in the intersection, and 8 is in the Owns a Black Car only region.]() \\( 15 \\)" }, { "from": "gpt", "value": "Believes the intersection on a Venn diagram represents the total of one set" } ]
[ { "from": "human", "value": "Identify the regions on a double Venn diagram given in words \\( 60 \\) people completed an online survey about the car they own.\nThe results are shown in the Venn Diagram.\n\nHow many people own a black car? ![A Venn diagram with two circles labelled Owns a 4x4 and Owns a Black Car. The number 27 is in the Owns a 4x4 only region, 15 is in the intersection, and 8 is in the Owns a Black Car only region.]() \\( 8 \\)" }, { "from": "gpt", "value": "Forgets to include the intersection value when asked for total value of a set in a Venn diagram" } ]
[ { "from": "human", "value": "Count backwards in steps of of something other than one Amelie is counting backwards in steps of \\( 4 \\).\nShe starts at the number \\( 24,993 \\)\nwhat is the next number she will say? \\( 24,992 \\)" }, { "from": "gpt", "value": "Counts on by 1, when asked to count forward/backwards in a step other than 1" } ]
[ { "from": "human", "value": "Count backwards in steps of of something other than one Amelie is counting backwards in steps of \\( 4 \\).\nShe starts at the number \\( 24,993 \\)\nwhat is the next number she will say? \\( 24,990 \\)" }, { "from": "gpt", "value": "Counts the starting number when counting backwards" } ]
[ { "from": "human", "value": "Understand the relationship between different factors of a number If \\( 12 \\) is a factor of a number, then another factor of that number must be... \\( 5 \\) and \\( 7 \\)" }, { "from": "gpt", "value": "Believes numbers are divisible by numbers which sum to their factors" } ]
[ { "from": "human", "value": "Understand the relationship between different factors of a number If \\( 12 \\) is a factor of a number, then another factor of that number must be... \\( 24 \\)" }, { "from": "gpt", "value": "Thinks numbers are divisible by all multiples of their factors" } ]
[ { "from": "human", "value": "Multiply a decimal by an integer \\( 9.4 \\times 50= \\) \\( 4700 \\)" }, { "from": "gpt", "value": "When multiplying a decimal by an integer, ignores decimal point and just multiplies the digits" } ]
[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Jo and Paul are arguing about simplifying fractions.\n\nJo says you can never simplify a fraction if either the numerator or denominator is a prime number.\n\nPaul says you will always be able to simplify a fraction if neither the numerator or denominator is prime.\n\nWho is correct? Only\nJo" }, { "from": "gpt", "value": "Assumes fractions with prime numerators cannot be simplified" } ]
[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Jo and Paul are arguing about simplifying fractions.\n\nJo says you can never simplify a fraction if either the numerator or denominator is a prime number.\n\nPaul says you will always be able to simplify a fraction if neither the numerator or denominator is prime.\n\nWho is correct? Only\nPaul" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 \\( 30 \\% \\) of \\( £ 120= \\) \\( £ 30 \\)" }, { "from": "gpt", "value": "Does not understand a percentage can be applied to something not out of 100" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) Multiply out the brackets:\n\\[\n(m-3)(m-2)\n\\] \\( m^{2}+5 m+6 \\)" }, { "from": "gpt", "value": "Believes adding two negatives gives a positive answer" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) Multiply out the brackets:\n\\[\n(m-3)(m-2)\n\\] \\( m^{2}-5 m-6 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]
[ { "from": "human", "value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c This is a part of the table of values for the equation\n\\[\n2 x+3 y=12\n\\] \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 4.2 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 p^{2}+11 p \\) \\( 6 \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 p^{2}+11 p \\) \\( 11 \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 p^{2}+11 p \\) \\( p^{2} \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]
[ { "from": "human", "value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one edge labelled 5cm]() \\( 15 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Adds when calculating volume instead of multiplying" } ]
[ { "from": "human", "value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one edge labelled 5cm]() \\( 25 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Finds area of one face when asked for volume" } ]
[ { "from": "human", "value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one edge labelled 5cm]() Not enough information" }, { "from": "gpt", "value": "Does not recognise that all lengths on a cube are equal" } ]
[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]() \\( (2,2) \\)" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]
[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]() \\( (2,0) \\)" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]
[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]() \\( (0,1) \\)" }, { "from": "gpt", "value": "Reflects horizontally or vertically instead of across a diagonal line of symmetry" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+12 x+32 \\) is factorised, what will appear in the box below? ![\\( (x+4) \\square \\)]() \\( (x+28) \\)" }, { "from": "gpt", "value": "When factorising into double brackets, finds the sum of two values which give the non variable term in the expression rather than the product" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+12 x+32 \\) is factorised, what will appear in the box below? ![\\( (x+4) \\square \\)]() \\( (x-8) \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]
[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 3 \\mathrm{~km} \\approx \\square \\) miles \\( 3.6 \\)" }, { "from": "gpt", "value": "Added rather than multiplied by a scale factor" } ]
[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 3 \\mathrm{~km} \\approx \\square \\) miles \\( 0.18 \\)" }, { "from": "gpt", "value": "When multiplying decimals, ignores place value and just multiplies the digits" } ]
[ { "from": "human", "value": "Interpret a pie chart \\( 24 \\) people went to an local ice hockey match.\nThe pie chart shows the colours of their shirts.\nHow many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]() \\( \\frac{1}{4} \\)" }, { "from": "gpt", "value": "Writes fraction rather than fraction of amount" } ]
[ { "from": "human", "value": "Interpret a pie chart \\( 24 \\) people went to an local ice hockey match.\nThe pie chart shows the colours of their shirts.\nHow many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]() \\( 3 \\)" }, { "from": "gpt", "value": "Finds the unit fraction when asked to find a non-unit fraction of an amount" } ]
[ { "from": "human", "value": "Interpret a pie chart \\( 24 \\) people went to an local ice hockey match.\nThe pie chart shows the colours of their shirts.\nHow many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]() \\( 2 \\)" }, { "from": "gpt", "value": "Gives number of sections of pie chart rather than the amount it represents" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots \\[\n\\text { When } h=10 \\text { and } j=4\n\\]\n\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=60 \\\\ h(2+j)=-60\\end{array} \\)" }, { "from": "gpt", "value": "Does not realise addition is commutative" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots \\[\n\\text { When } h=10 \\text { and } j=4\n\\]\n\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=42 \\\\ h(2+j)=24\\end{array} \\)" }, { "from": "gpt", "value": "Does not realise addition is commutative" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots \\[\n\\text { When } h=10 \\text { and } j=4\n\\]\n\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=24 \\\\ h(2+j)=42\\end{array} \\)" }, { "from": "gpt", "value": "Does not realise addition is commutative" } ]
[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]() \\( 48 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Uses an incorrect side length when splitting a composite shape into parts" } ]
[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]() \\( 15 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Uses an incorrect side length when splitting a composite shape into parts" } ]
[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]() \\( 10 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Believes the area of a rectangle is calculated by length add width" } ]
[ { "from": "human", "value": "Use inequality notation to order integers with the same number of digits Which signs belong in the boxes to make the statement correct?\n\\( 76426 \\)\\[ {\\color{blue}\\square} \\]\\( 76462 \\)\\[ {\\color{orange}\\square} \\]\\( 74662 \\) ![A blue box containing a \"greater than\" symbol and an orange box containing a \"less than\" symbol]()" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]
[ { "from": "human", "value": "Use inequality notation to order integers with the same number of digits Which signs belong in the boxes to make the statement correct?\n\\( 76426 \\)\\[ {\\color{blue}\\square} \\]\\( 76462 \\)\\[ {\\color{orange}\\square} \\]\\( 74662 \\) ![A blue box containing a \"less than\" symbol and an orange box containing a \"less than\" symbol]()" }, { "from": "gpt", "value": "Assumes that a list is given in size order" } ]
[ { "from": "human", "value": "Use inequality notation to order integers with the same number of digits Which signs belong in the boxes to make the statement correct?\n\\( 76426 \\)\\[ {\\color{blue}\\square} \\]\\( 76462 \\)\\[ {\\color{orange}\\square} \\]\\( 74662 \\) ![A blue box containing a \"greater than\" symbol and an orange box containing a \"greater than\" symbol]()" }, { "from": "gpt", "value": "Assumes that a list is given in size order" } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Tom and Katie are discussing how to solve:\n\\(\n\\frac{8 x}{5}=40\n\\)\n\nTom says a correct next line of working could be: \\( 8 x=8 \\)\nKatie says a correct next line of working could be: \\( \\frac{x}{5}=5 \\)\nWho is correct? Only\nTom" }, { "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 Tom and Katie are discussing how to solve:\n\\(\n\\frac{8 x}{5}=40\n\\)\n\nTom says a correct next line of working could be: \\( 8 x=8 \\)\nKatie says a correct next line of working could be: \\( \\frac{x}{5}=5 \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "When dividing a fraction by an integer, divides both the numerator and denominator by the integer" } ]
[ { "from": "human", "value": "Complete a sample space diagram These spinners are spun and the two scores are added together.\n\nBob records the results in a sample space diagram.\nHow many cells would contain a score of \\( 4 \\) ? ![Two 6-sided spinners. Both spinners are split into 6 equal sections with the numbers 1, 3, 3, 5, 5, and 5 in them.]() \\begin{tabular}{\|l\|l\|l\|l\|l\|l\|l\|}\n\\hline & \\( 1 \\) & \\( 3 \\) & \\( 3 \\) & \\( 5 \\) & \\( 5 \\) & \\( 5 \\) \\\\\n\\hline \\( 1 \\) \\\\\n\\hline \\( 3 \\) \\\\\n\\hline \\( 3 \\) \\\\\n\\hline \\( 5 \\)\\\\\n\\hline \\( 5 \\) \\\\\n\\hline \\( 5 \\) \\\\\n\\hline\n\\end{tabular} \\( 2 \\)" }, { "from": "gpt", "value": "Fails to consider all possible outcomes" } ]
[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 1 decimal place Convert \\( \\frac{4}{20} \\) into a decimal \\( 5.0 \\)" }, { "from": "gpt", "value": "Believes that a fraction means dividing the denominator by the numerator" } ]
[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 1 decimal place Convert \\( \\frac{4}{20} \\) into a decimal \\( 0.4 \\)" }, { "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 1 decimal place Convert \\( \\frac{4}{20} \\) into a decimal \\( 4.20 \\)" }, { "from": "gpt", "value": "Converts a fraction to a decimal by placing a decimal point between the numerator and denominator" } ]
[ { "from": "human", "value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]() Only\nKatie" }, { "from": "gpt", "value": "Thinks congruent shapes are the same shape but can be different sizes" } ]
[ { "from": "human", "value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]() Both Tom and Katie" }, { "from": "gpt", "value": "Thinks congruent shapes are the same shape but can be different sizes" } ]
[ { "from": "human", "value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]() Neither is correct" }, { "from": "gpt", "value": "Does not understand that shapes are congruent if they have the same size and shape" } ]
[ { "from": "human", "value": "Use the properties of an isosceles triangle to find missing lengths What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]() \\( 4 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When calculating perimeter, only adds the marked lengths" } ]
[ { "from": "human", "value": "Use the properties of an isosceles triangle to find missing lengths What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]() \\( 48 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When calculating perimeter, only adds the marked lengths" } ]
[ { "from": "human", "value": "Use the properties of an isosceles triangle to find missing lengths What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]() \\( 72 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Adds instead of subtracts when asked to find the difference" } ]
[ { "from": "human", "value": "Identify a right-angled triangle from a description of the properties A triangle has the following angles: \\( 90\\degree, 50\\degree, 40\\degree \\)\nTom says the triangle is right-angled\nKatie says the triangle is isosceles\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Does not understand that base angles in an isosceles are equal" } ]
[ { "from": "human", "value": "Identify a right-angled triangle from a description of the properties A triangle has the following angles: \\( 90\\degree, 50\\degree, 40\\degree \\)\nTom says the triangle is right-angled\nKatie says the triangle is isosceles\nWho is correct? Neither are correct" }, { "from": "gpt", "value": "Does not know that a right angle is 90 degrees" } ]
[ { "from": "human", "value": "Recognise and use efficient methods for mental multiplication Tom and Katie are trying to calculate the answer to \\( 19 \\times 8 \\)\nTom does this: \\( 20 \\times 8-1 \\times 8 \\)\nKatie does this: \\( 10 \\times 8+9 \\times 8 \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not correctly apply the distributive property of multiplication" } ]
[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}+4 p\n\\) \\( (p-2)(p+2) \\)" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]
[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}+4 p\n\\) \\( (p+2)(p+2) \\)" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]
[ { "from": "human", "value": "Use prime factor decomposition to find the Lowest Common Multiple of two numbers Here is the completed Venn diagram from earlier in the quiz.\nWhat calculation works out the lowest common multiple of \\( 36 \\) and \\( 90 \\) ? ![A Venn diagram showing the Prime factors of 36 set and the Prime factors of 90 set. There is a 2 in the prime factors of 36 set, there is 2, 3, 3 in the intersection and there is a 5 in the prime factors of 50 set.]() \\( 2 \\times 3 \\times 3 \\)" }, { "from": "gpt", "value": "Confuses the calculations for HCF and LCM" } ]
[ { "from": "human", "value": "Use prime factor decomposition to find the Lowest Common Multiple of two numbers Here is the completed Venn diagram from earlier in the quiz.\nWhat calculation works out the lowest common multiple of \\( 36 \\) and \\( 90 \\) ? ![A Venn diagram showing the Prime factors of 36 set and the Prime factors of 90 set. There is a 2 in the prime factors of 36 set, there is 2, 3, 3 in the intersection and there is a 5 in the prime factors of 50 set.]() \\( 2 \\times 5 \\)" }, { "from": "gpt", "value": "forgets to include the common factors when calculating the lowest common multiple" } ]
[ { "from": "human", "value": "Can read Roman numerals between 100 and 1000 What number is this CCXLIX? \\( 271 \\)" }, { "from": "gpt", "value": "When finding the value of a number given in roman numerals, adds the value of all letters together without considering the position of the letter." } ]
[ { "from": "human", "value": "Can read Roman numerals between 100 and 1000 What number is this CCXLIX? \\( 269 \\)" }, { "from": "gpt", "value": "When finding the value of a number given in roman numerals, adds the value of all letters together without considering the position of the letter." } ]
[ { "from": "human", "value": "Calculate the square root of a number Jo and Paul are discussing the table of values for \\( \\boldsymbol{y}=\\boldsymbol{x}^{2} \\) \\begin{tabular}{\|l\|c\|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 4 \\) \\\\\n\\hline\n\\end{tabular} Jo says the star could be \\( 16 \\).\nPaul says the star could be \\( -2 \\).\nWho is correct? Only\nJo" }, { "from": "gpt", "value": "Squares when asked to find the square root" } ]
[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages Write \\( 0.07 \\) as a percentage. \\( 70 \\% \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]
[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages Write \\( 0.07 \\) as a percentage. \\( 0.07 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a decimal to convert to a percentage" } ]
[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=3 x\n\\] ![A table with two rows and two columns. The top left box has 'x', top right has a star, the bottom left box has 'y', bottom right has '-1'. ]() What should replace the star? \\( -3 \\)" }, { "from": "gpt", "value": "Mixes up the value of two terms when substituting" } ]
[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=3 x\n\\] ![A table with two rows and two columns. The top left box has 'x', top right has a star, the bottom left box has 'y', bottom right has '-1'. ]() What should replace the star? \\( -0.3 \\)" }, { "from": "gpt", "value": "Rounds too early in calculation " } ]
[ { "from": "human", "value": "Calculate unit fractions of an amount \\( \\frac{1}{5} \\) of \\( 35= \\) \\( 30 \\)" }, { "from": "gpt", "value": "Thinks finding a fraction of an amount means subtracting from that amount" } ]
[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 100 ? \\) \\( 103 \\)" }, { "from": "gpt", "value": "Does not know what a cube number is" } ]
[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 100 ? \\) \\( 121 \\)" }, { "from": "gpt", "value": "Mixes up square numbers and cube numbers" } ]
[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 100 ? \\) \\( 102 \\)" }, { "from": "gpt", "value": "Believes cube numbers are just multiples of 3" } ]
[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators involve linear expressions Write this as a single fraction as simply as possible: \\( \\frac{5}{x-3} \\times \\frac{x^{2}}{2 y} \\) \\( \\frac{10 y}{x^{2}(x-3)} \\)" }, { "from": "gpt", "value": "when multiplying fractions multiplies by the reciprocal of the 2nd fraction instead" } ]
[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators involve linear expressions Write this as a single fraction as simply as possible: \\( \\frac{5}{x-3} \\times \\frac{x^{2}}{2 y} \\) \\( \\frac{5 x^{2}}{x-6 y} \\)" }, { "from": "gpt", "value": "Only multiplies second term in the expansion of a bracket" } ]
[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators involve linear expressions Write this as a single fraction as simply as possible: \\( \\frac{5}{x-3} \\times \\frac{x^{2}}{2 y} \\) \\( \\frac{5 x^{2}}{2 x y-3} \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]

[ { "from": "human", "value": "Change decimals of hours into minutes \\( 1.5 \\) hours \\( = _______\\) minutes \\( 105 \\)" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes" } ]

[ { "from": "human", "value": "Change decimals of hours into minutes \\( 1.5 \\) hours \\( = _______\\) minutes \\( 65 \\)" }, { "from": "gpt", "value": "Thinks there are 10 minutes in an hour" } ]

[ { "from": "human", "value": "Use the nth term rule for ascending integer linear sequences to find another term in the sequence If you know the first term of a linear sequence and you multiply it by \\( 10 \\), you get the \\( 10^{\\text {th }} \\) term of that sequence.\nIs this statement... always true" }, { "from": "gpt", "value": "Thinks terms in linear sequence are in direct proportion" } ]

[ { "from": "human", "value": "Use the nth term rule for ascending integer linear sequences to find another term in the sequence If you know the first term of a linear sequence and you multiply it by \\( 10 \\), you get the \\( 10^{\\text {th }} \\) term of that sequence.\nIs this statement... never true" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Given the speed, calculate missing values from a displacement-time graph This displacement-time graph shows the first \\( 10 \\) seconds of Mo's journey.\n\nDuring that time he travelled at a speed of \\( 6 \\mathrm{~m} / \\mathrm{s.} \\)\n\nWhat distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \\(\\bigstar \\))]() \\( 30 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Believes distance is the area under the graph on a displacement time graph" } ]

[ { "from": "human", "value": "Given the speed, calculate missing values from a displacement-time graph This displacement-time graph shows the first \\( 10 \\) seconds of Mo's journey.\n\nDuring that time he travelled at a speed of \\( 6 \\mathrm{~m} / \\mathrm{s.} \\)\n\nWhat distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \\(\\bigstar \\))]() \\( 6 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Believes scales on graphs must match on both axes" } ]

[ { "from": "human", "value": "Given the speed, calculate missing values from a displacement-time graph This displacement-time graph shows the first \\( 10 \\) seconds of Mo's journey.\n\nDuring that time he travelled at a speed of \\( 6 \\mathrm{~m} / \\mathrm{s.} \\)\n\nWhat distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \\(\\bigstar \\))]() \\( 16 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Believes distance = speed + time" } ]

[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram 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.]() Kate picks a yellow ball out and then replaces it.\n\nShe then has a second pick.\nWhat is the probability the second pick is also a yellow ball? \\( \\frac{3}{6} \\)" }, { "from": "gpt", "value": "Assumes the item has not been replaced in a probability question where it has actually been replaced" } ]

[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram 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.]() Kate picks a yellow ball out and then replaces it.\n\nShe then has a second pick.\nWhat is the probability the second pick is also a yellow ball? \\( \\frac{2}{6} \\)" }, { "from": "gpt", "value": "Assumes the item has not been replaced in a probability question where it has actually been replaced" } ]

[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. \"0\" above the 1st dash and \"2\" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to? \\( 1.8 \\)" }, { "from": "gpt", "value": "When reading decimals on a number line, assumes each dash is 0.1" } ]

[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. \"0\" above the 1st dash and \"2\" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to? \\( 1 \\)" }, { "from": "gpt", "value": "Believes the arrow on a number line points to the middle value" } ]

[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. \"0\" above the 1st dash and \"2\" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to? \\( 1.6 \\)" }, { "from": "gpt", "value": "Estimates a measurement on a diagram rather than working it out" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 \\( 20 \\% \\) of \\( \\pounds 140= \\) \\( £ 20 \\)" }, { "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 \\( 20 \\% \\) of \\( \\pounds 140= \\) \\( £ 120 \\)" }, { "from": "gpt", "value": "Has taken the percentage from the original " } ]

[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition This is how Dora calculates the answer to \\( 12.3+4.5 \\) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \\( 3.5+21.8 \\). Which of the following shows how she would do this? \\( \\begin{array}{c}3+21=24 \\\\ 0.5+0.8=0.13 \\\\ 24+0.13=24.13\\end{array} \\)" }, { "from": "gpt", "value": "When adding decimals, just adds the digits and ignores place value" } ]

[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition This is how Dora calculates the answer to \\( 12.3+4.5 \\) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \\( 3.5+21.8 \\). Which of the following shows how she would do this? \\( \\begin{array}{c}3.5+21=24.5 \\\\ 24.5+0.8=25.3\\end{array} \\)" }, { "from": "gpt", "value": "Does not interpret the correct order of operations from a worded problem" } ]

[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition This is how Dora calculates the answer to \\( 12.3+4.5 \\) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \\( 3.5+21.8 \\). Which of the following shows how she would do this? \\( \\begin{array}{c}3+21=24 \\\\ 0.5+0.8=1.3 \\\\ 24+1.3=24.13\\end{array} \\)" }, { "from": "gpt", "value": "Ignores place value when adding a whole number and a decimal" } ]

[ { "from": "human", "value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 63 \\mathrm{~cm}^{2} \\).\n\nWhat is the value of \\( a \\) ? ![A trapezium with the parallel sides labelled with 3cm and a and the height labelled with 9cm]() \\( 4 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Does not divide by 2 when calculating the area of a trapezium" } ]

[ { "from": "human", "value": "Calculate unit fractions of an amount \\( \\frac{1}{20} \\) of \\( 7=? \\times 7 \\) \\( 0.2 \\)" }, { "from": "gpt", "value": "Converts a fraction to a decimal by using the denominator after the decimal point" } ]

[ { "from": "human", "value": "Calculate unit fractions of an amount \\( \\frac{1}{20} \\) of \\( 7=? \\times 7 \\) \\( 20 \\)" }, { "from": "gpt", "value": "Multiplies by the denominator instead of dividing when finding a fraction of an amount" } ]

[ { "from": "human", "value": "Carry out subtraction problems involving one negative integer \\( 6-(-8)= \\) \\( -14 \\)" }, { "from": "gpt", "value": "When subtracting a negative thinks the answer must be negative " } ]

[ { "from": "human", "value": "Carry out subtraction problems involving one negative integer \\( 6-(-8)= \\) \\( -2 \\)" }, { "from": "gpt", "value": "Does not realise that subtracting a negative is the same as adding it's additive inverse" } ]

[ { "from": "human", "value": "Round integers to the nearest 1000 A distance has been rounded to the nearest \\( \\mathrm{km} \\), giving \\( 106 \\) \\( \\mathrm{km} \\).\nWhich of these values could the distance \\( \\underline{not} \\) be? \\( 106220 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]

[ { "from": "human", "value": "Round integers to the nearest 1000 A distance has been rounded to the nearest \\( \\mathrm{km} \\), giving \\( 106 \\) \\( \\mathrm{km} \\).\nWhich of these values could the distance \\( \\underline{not} \\) be? \\( 105605 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round integers to the nearest 1000 A distance has been rounded to the nearest \\( \\mathrm{km} \\), giving \\( 106 \\) \\( \\mathrm{km} \\).\nWhich of these values could the distance \\( \\underline{not} \\) be? \\( 105698 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Multiply algebraic fractions involving non-linear expressions Write this as a single fraction as simply as possible\n\\(\n\\frac{2}{m^{2}-4 m+3} \\times \\frac{m-3}{4}\n\\) \\( \\frac{2 m-6}{4 m^{2}-16 m+12} \\)" }, { "from": "gpt", "value": "Expands when asked to simplify" } ]

[ { "from": "human", "value": "Recognise an exponential graph from its shape Which of the following is most likely to be the graph of a exponential function? ![A graph with two curves, in the top right and bottom left quadrants. The top right curves starts up and right of the origin and travels steeply down and right, it then levels off to travel alongside the x-axis without touching it. The bottom left curve starts down and left of the origin, travels steeply up and left, it then levels off just below the x-axis without touching it.]()" }, { "from": "gpt", "value": "Confuses reciprocal and exponential graphs" } ]

[ { "from": "human", "value": "Recognise an exponential graph from its shape Which of the following is most likely to be the graph of a exponential 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 exponential graphs" } ]

[ { "from": "human", "value": "Recognise an exponential graph from its shape Which of the following is most likely to be the graph of a exponential 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 quadratic and exponential graphs" } ]

[ { "from": "human", "value": "Identify the regions on a double Venn diagram given in words \\( 60 \\) people completed an online survey about the car they own.\nThe results are shown in the Venn Diagram.\n\nHow many people own a black car? ![A Venn diagram with two circles labelled Owns a 4x4 and Owns a Black Car. The number 27 is in the Owns a 4x4 only region, 15 is in the intersection, and 8 is in the Owns a Black Car only region.]() \\( 15 \\)" }, { "from": "gpt", "value": "Believes the intersection on a Venn diagram represents the total of one set" } ]

[ { "from": "human", "value": "Identify the regions on a double Venn diagram given in words \\( 60 \\) people completed an online survey about the car they own.\nThe results are shown in the Venn Diagram.\n\nHow many people own a black car? ![A Venn diagram with two circles labelled Owns a 4x4 and Owns a Black Car. The number 27 is in the Owns a 4x4 only region, 15 is in the intersection, and 8 is in the Owns a Black Car only region.]() \\( 8 \\)" }, { "from": "gpt", "value": "Forgets to include the intersection value when asked for total value of a set in a Venn diagram" } ]

[ { "from": "human", "value": "Count backwards in steps of of something other than one Amelie is counting backwards in steps of \\( 4 \\).\nShe starts at the number \\( 24,993 \\)\nwhat is the next number she will say? \\( 24,992 \\)" }, { "from": "gpt", "value": "Counts on by 1, when asked to count forward/backwards in a step other than 1" } ]

[ { "from": "human", "value": "Count backwards in steps of of something other than one Amelie is counting backwards in steps of \\( 4 \\).\nShe starts at the number \\( 24,993 \\)\nwhat is the next number she will say? \\( 24,990 \\)" }, { "from": "gpt", "value": "Counts the starting number when counting backwards" } ]

[ { "from": "human", "value": "Understand the relationship between different factors of a number If \\( 12 \\) is a factor of a number, then another factor of that number must be... \\( 5 \\) and \\( 7 \\)" }, { "from": "gpt", "value": "Believes numbers are divisible by numbers which sum to their factors" } ]

[ { "from": "human", "value": "Understand the relationship between different factors of a number If \\( 12 \\) is a factor of a number, then another factor of that number must be... \\( 24 \\)" }, { "from": "gpt", "value": "Thinks numbers are divisible by all multiples of their factors" } ]

[ { "from": "human", "value": "Multiply a decimal by an integer \\( 9.4 \\times 50= \\) \\( 4700 \\)" }, { "from": "gpt", "value": "When multiplying a decimal by an integer, ignores decimal point and just multiplies the digits" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Jo and Paul are arguing about simplifying fractions.\n\nJo says you can never simplify a fraction if either the numerator or denominator is a prime number.\n\nPaul says you will always be able to simplify a fraction if neither the numerator or denominator is prime.\n\nWho is correct? Only\nJo" }, { "from": "gpt", "value": "Assumes fractions with prime numerators cannot be simplified" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Jo and Paul are arguing about simplifying fractions.\n\nJo says you can never simplify a fraction if either the numerator or denominator is a prime number.\n\nPaul says you will always be able to simplify a fraction if neither the numerator or denominator is prime.\n\nWho is correct? Only\nPaul" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 \\( 30 \\% \\) of \\( £ 120= \\) \\( £ 30 \\)" }, { "from": "gpt", "value": "Does not understand a percentage can be applied to something not out of 100" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) Multiply out the brackets:\n\\[\n(m-3)(m-2)\n\\] \\( m^{2}+5 m+6 \\)" }, { "from": "gpt", "value": "Believes adding two negatives gives a positive answer" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) Multiply out the brackets:\n\\[\n(m-3)(m-2)\n\\] \\( m^{2}-5 m-6 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]

[ { "from": "human", "value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c This is a part of the table of values for the equation\n\\[\n2 x+3 y=12\n\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 4.2 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 p^{2}+11 p \\) \\( 6 \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 p^{2}+11 p \\) \\( 11 \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Which of the following is a factor of: \\( 6 p^{2}+11 p \\) \\( p^{2} \\)" }, { "from": "gpt", "value": "When asked for factors of an algebraic expression, thinks any part of a term will be a factor" } ]

[ { "from": "human", "value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one edge labelled 5cm]() \\( 15 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Adds when calculating volume instead of multiplying" } ]

[ { "from": "human", "value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one edge labelled 5cm]() \\( 25 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Finds area of one face when asked for volume" } ]

[ { "from": "human", "value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one edge labelled 5cm]() Not enough information" }, { "from": "gpt", "value": "Does not recognise that all lengths on a cube are equal" } ]

[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]() \\( (2,2) \\)" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]

[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]() \\( (2,0) \\)" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]

[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( P \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]() \\( (0,1) \\)" }, { "from": "gpt", "value": "Reflects horizontally or vertically instead of across a diagonal line of symmetry" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+12 x+32 \\) is factorised, what will appear in the box below? ![\\( (x+4) \\square \\)]() \\( (x+28) \\)" }, { "from": "gpt", "value": "When factorising into double brackets, finds the sum of two values which give the non variable term in the expression rather than the product" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When \\( x^{2}+12 x+32 \\) is factorised, what will appear in the box below? ![\\( (x+4) \\square \\)]() \\( (x-8) \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]

[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 3 \\mathrm{~km} \\approx \\square \\) miles \\( 3.6 \\)" }, { "from": "gpt", "value": "Added rather than multiplied by a scale factor" } ]

[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 3 \\mathrm{~km} \\approx \\square \\) miles \\( 0.18 \\)" }, { "from": "gpt", "value": "When multiplying decimals, ignores place value and just multiplies the digits" } ]

[ { "from": "human", "value": "Interpret a pie chart \\( 24 \\) people went to an local ice hockey match.\nThe pie chart shows the colours of their shirts.\nHow many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]() \\( \\frac{1}{4} \\)" }, { "from": "gpt", "value": "Writes fraction rather than fraction of amount" } ]

[ { "from": "human", "value": "Interpret a pie chart \\( 24 \\) people went to an local ice hockey match.\nThe pie chart shows the colours of their shirts.\nHow many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]() \\( 3 \\)" }, { "from": "gpt", "value": "Finds the unit fraction when asked to find a non-unit fraction of an amount" } ]

[ { "from": "human", "value": "Interpret a pie chart \\( 24 \\) people went to an local ice hockey match.\nThe pie chart shows the colours of their shirts.\nHow many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]() \\( 2 \\)" }, { "from": "gpt", "value": "Gives number of sections of pie chart rather than the amount it represents" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots \\[\n\\text { When } h=10 \\text { and } j=4\n\\]\n\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=60 \\\\ h(2+j)=-60\\end{array} \\)" }, { "from": "gpt", "value": "Does not realise addition is commutative" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots \\[\n\\text { When } h=10 \\text { and } j=4\n\\]\n\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=42 \\\\ h(2+j)=24\\end{array} \\)" }, { "from": "gpt", "value": "Does not realise addition is commutative" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots \\[\n\\text { When } h=10 \\text { and } j=4\n\\]\n\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=24 \\\\ h(2+j)=42\\end{array} \\)" }, { "from": "gpt", "value": "Does not realise addition is commutative" } ]

[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]() \\( 48 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Uses an incorrect side length when splitting a composite shape into parts" } ]

[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]() \\( 15 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Uses an incorrect side length when splitting a composite shape into parts" } ]

[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]() \\( 10 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Believes the area of a rectangle is calculated by length add width" } ]

[ { "from": "human", "value": "Use inequality notation to order integers with the same number of digits Which signs belong in the boxes to make the statement correct?\n\\( 76426 \\)\\[ {\\color{blue}\\square} \\]\\( 76462 \\)\\[ {\\color{orange}\\square} \\]\\( 74662 \\) ![A blue box containing a \"greater than\" symbol and an orange box containing a \"less than\" symbol]()" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Use inequality notation to order integers with the same number of digits Which signs belong in the boxes to make the statement correct?\n\\( 76426 \\)\\[ {\\color{blue}\\square} \\]\\( 76462 \\)\\[ {\\color{orange}\\square} \\]\\( 74662 \\) ![A blue box containing a \"less than\" symbol and an orange box containing a \"less than\" symbol]()" }, { "from": "gpt", "value": "Assumes that a list is given in size order" } ]

[ { "from": "human", "value": "Use inequality notation to order integers with the same number of digits Which signs belong in the boxes to make the statement correct?\n\\( 76426 \\)\\[ {\\color{blue}\\square} \\]\\( 76462 \\)\\[ {\\color{orange}\\square} \\]\\( 74662 \\) ![A blue box containing a \"greater than\" symbol and an orange box containing a \"greater than\" symbol]()" }, { "from": "gpt", "value": "Assumes that a list is given in size order" } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Tom and Katie are discussing how to solve:\n\\(\n\\frac{8 x}{5}=40\n\\)\n\nTom says a correct next line of working could be: \\( 8 x=8 \\)\nKatie says a correct next line of working could be: \\( \\frac{x}{5}=5 \\)\nWho is correct? Only\nTom" }, { "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 Tom and Katie are discussing how to solve:\n\\(\n\\frac{8 x}{5}=40\n\\)\n\nTom says a correct next line of working could be: \\( 8 x=8 \\)\nKatie says a correct next line of working could be: \\( \\frac{x}{5}=5 \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "When dividing a fraction by an integer, divides both the numerator and denominator by the integer" } ]

[ { "from": "human", "value": "Complete a sample space diagram These spinners are spun and the two scores are added together.\n\nBob records the results in a sample space diagram.\nHow many cells would contain a score of \\( 4 \\) ? ![Two 6-sided spinners. Both spinners are split into 6 equal sections with the numbers 1, 3, 3, 5, 5, and 5 in them.]() \\begin{tabular}{|l|l|l|l|l|l|l|}\n\\hline & \\( 1 \\) & \\( 3 \\) & \\( 3 \\) & \\( 5 \\) & \\( 5 \\) & \\( 5 \\) \\\\\n\\hline \\( 1 \\) \\\\\n\\hline \\( 3 \\) \\\\\n\\hline \\( 3 \\) \\\\\n\\hline \\( 5 \\)\\\\\n\\hline \\( 5 \\) \\\\\n\\hline \\( 5 \\) \\\\\n\\hline\n\\end{tabular} \\( 2 \\)" }, { "from": "gpt", "value": "Fails to consider all possible outcomes" } ]

[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 1 decimal place Convert \\( \\frac{4}{20} \\) into a decimal \\( 5.0 \\)" }, { "from": "gpt", "value": "Believes that a fraction means dividing the denominator by the numerator" } ]

[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 1 decimal place Convert \\( \\frac{4}{20} \\) into a decimal \\( 0.4 \\)" }, { "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 1 decimal place Convert \\( \\frac{4}{20} \\) into a decimal \\( 4.20 \\)" }, { "from": "gpt", "value": "Converts a fraction to a decimal by placing a decimal point between the numerator and denominator" } ]

[ { "from": "human", "value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]() Only\nKatie" }, { "from": "gpt", "value": "Thinks congruent shapes are the same shape but can be different sizes" } ]

[ { "from": "human", "value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]() Both Tom and Katie" }, { "from": "gpt", "value": "Thinks congruent shapes are the same shape but can be different sizes" } ]

[ { "from": "human", "value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]() Neither is correct" }, { "from": "gpt", "value": "Does not understand that shapes are congruent if they have the same size and shape" } ]

[ { "from": "human", "value": "Use the properties of an isosceles triangle to find missing lengths What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]() \\( 4 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When calculating perimeter, only adds the marked lengths" } ]

[ { "from": "human", "value": "Use the properties of an isosceles triangle to find missing lengths What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]() \\( 48 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When calculating perimeter, only adds the marked lengths" } ]

[ { "from": "human", "value": "Use the properties of an isosceles triangle to find missing lengths What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]() \\( 72 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Adds instead of subtracts when asked to find the difference" } ]

[ { "from": "human", "value": "Identify a right-angled triangle from a description of the properties A triangle has the following angles: \\( 90\\degree, 50\\degree, 40\\degree \\)\nTom says the triangle is right-angled\nKatie says the triangle is isosceles\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Does not understand that base angles in an isosceles are equal" } ]

[ { "from": "human", "value": "Identify a right-angled triangle from a description of the properties A triangle has the following angles: \\( 90\\degree, 50\\degree, 40\\degree \\)\nTom says the triangle is right-angled\nKatie says the triangle is isosceles\nWho is correct? Neither are correct" }, { "from": "gpt", "value": "Does not know that a right angle is 90 degrees" } ]

[ { "from": "human", "value": "Recognise and use efficient methods for mental multiplication Tom and Katie are trying to calculate the answer to \\( 19 \\times 8 \\)\nTom does this: \\( 20 \\times 8-1 \\times 8 \\)\nKatie does this: \\( 10 \\times 8+9 \\times 8 \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not correctly apply the distributive property of multiplication" } ]

[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}+4 p\n\\) \\( (p-2)(p+2) \\)" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]

[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}+4 p\n\\) \\( (p+2)(p+2) \\)" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]

[ { "from": "human", "value": "Use prime factor decomposition to find the Lowest Common Multiple of two numbers Here is the completed Venn diagram from earlier in the quiz.\nWhat calculation works out the lowest common multiple of \\( 36 \\) and \\( 90 \\) ? ![A Venn diagram showing the Prime factors of 36 set and the Prime factors of 90 set. There is a 2 in the prime factors of 36 set, there is 2, 3, 3 in the intersection and there is a 5 in the prime factors of 50 set.]() \\( 2 \\times 3 \\times 3 \\)" }, { "from": "gpt", "value": "Confuses the calculations for HCF and LCM" } ]

[ { "from": "human", "value": "Use prime factor decomposition to find the Lowest Common Multiple of two numbers Here is the completed Venn diagram from earlier in the quiz.\nWhat calculation works out the lowest common multiple of \\( 36 \\) and \\( 90 \\) ? ![A Venn diagram showing the Prime factors of 36 set and the Prime factors of 90 set. There is a 2 in the prime factors of 36 set, there is 2, 3, 3 in the intersection and there is a 5 in the prime factors of 50 set.]() \\( 2 \\times 5 \\)" }, { "from": "gpt", "value": "forgets to include the common factors when calculating the lowest common multiple" } ]

[ { "from": "human", "value": "Can read Roman numerals between 100 and 1000 What number is this CCXLIX? \\( 271 \\)" }, { "from": "gpt", "value": "When finding the value of a number given in roman numerals, adds the value of all letters together without considering the position of the letter." } ]

[ { "from": "human", "value": "Can read Roman numerals between 100 and 1000 What number is this CCXLIX? \\( 269 \\)" }, { "from": "gpt", "value": "When finding the value of a number given in roman numerals, adds the value of all letters together without considering the position of the letter." } ]

[ { "from": "human", "value": "Calculate the square root of a number Jo and Paul are discussing the table of values for \\( \\boldsymbol{y}=\\boldsymbol{x}^{2} \\) \\begin{tabular}{|l|c|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( 4 \\) \\\\\n\\hline\n\\end{tabular} Jo says the star could be \\( 16 \\).\nPaul says the star could be \\( -2 \\).\nWho is correct? Only\nJo" }, { "from": "gpt", "value": "Squares when asked to find the square root" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages Write \\( 0.07 \\) as a percentage. \\( 70 \\% \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages Write \\( 0.07 \\) as a percentage. \\( 0.07 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a decimal to convert to a percentage" } ]

[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=3 x\n\\] ![A table with two rows and two columns. The top left box has 'x', top right has a star, the bottom left box has 'y', bottom right has '-1'. ]() What should replace the star? \\( -3 \\)" }, { "from": "gpt", "value": "Mixes up the value of two terms when substituting" } ]

[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation\n\\[\ny=3 x\n\\] ![A table with two rows and two columns. The top left box has 'x', top right has a star, the bottom left box has 'y', bottom right has '-1'. ]() What should replace the star? \\( -0.3 \\)" }, { "from": "gpt", "value": "Rounds too early in calculation " } ]

[ { "from": "human", "value": "Calculate unit fractions of an amount \\( \\frac{1}{5} \\) of \\( 35= \\) \\( 30 \\)" }, { "from": "gpt", "value": "Thinks finding a fraction of an amount means subtracting from that amount" } ]

[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 100 ? \\) \\( 103 \\)" }, { "from": "gpt", "value": "Does not know what a cube number is" } ]

[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 100 ? \\) \\( 121 \\)" }, { "from": "gpt", "value": "Mixes up square numbers and cube numbers" } ]

[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 100 ? \\) \\( 102 \\)" }, { "from": "gpt", "value": "Believes cube numbers are just multiples of 3" } ]

[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators involve linear expressions Write this as a single fraction as simply as possible: \\( \\frac{5}{x-3} \\times \\frac{x^{2}}{2 y} \\) \\( \\frac{10 y}{x^{2}(x-3)} \\)" }, { "from": "gpt", "value": "when multiplying fractions multiplies by the reciprocal of the 2nd fraction instead" } ]

[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators involve linear expressions Write this as a single fraction as simply as possible: \\( \\frac{5}{x-3} \\times \\frac{x^{2}}{2 y} \\) \\( \\frac{5 x^{2}}{x-6 y} \\)" }, { "from": "gpt", "value": "Only multiplies second term in the expansion of a bracket" } ]

[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators involve linear expressions Write this as a single fraction as simply as possible: \\( \\frac{5}{x-3} \\times \\frac{x^{2}}{2 y} \\) \\( \\frac{5 x^{2}}{2 x y-3} \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]