bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object John rotates hexagon \\( \\mathrm{ABCDEF} 90^{\\degree} \\) clockwise from the centre \\( (5,4) \\). What error has he made? ![A positive, coordinate grid with two L-shaped hexagons drawn on it. The hexagon labelled ABCDEF has the coordinates: A(2,4) B(2,1) C(4,1) D(4,2) E(3,2) and F (3,4). The other hexagon has the coordinates: (6,7) (3,7) (3,5) (4,5) (4,6) and (6,6)]() He has translated by the vector \\( \\left(\\begin{array}{l}5 \\\\ 4\\end{array}\\right) \\)" }, { "from": "gpt", "value": "Mistakes rotations for translations" } ]
[ { "from": "human", "value": "Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object John rotates hexagon \\( \\mathrm{ABCDEF} 90^{\\degree} \\) clockwise from the centre \\( (5,4) \\). What error has he made? ![A positive, coordinate grid with two L-shaped hexagons drawn on it. The hexagon labelled ABCDEF has the coordinates: A(2,4) B(2,1) C(4,1) D(4,2) E(3,2) and F (3,4). The other hexagon has the coordinates: (6,7) (3,7) (3,5) (4,5) (4,6) and (6,6)]() He has rotated \\( 90^{\\circ} \\) anticlockwise" }, { "from": "gpt", "value": "Mixes up clockwise and anticlockwise" } ]
[ { "from": "human", "value": "Solve coordinate geometry questions involving ratio Given that \\( A C=3 A B \\), what are the coordinates of \\( C \\) ? ![A straight line labelled y=2x-1 is drawn on a set of axes. Points A, B and C are all on the line. Point A is (2,3) and B is (5,9).]() \\( (14,27) \\)" }, { "from": "gpt", "value": "Assumes a ratio is part to part instead of part to whole" } ]
[ { "from": "human", "value": "Solve coordinate geometry questions involving ratio Given that \\( A C=3 A B \\), what are the coordinates of \\( C \\) ? ![A straight line labelled y=2x-1 is drawn on a set of axes. Points A, B and C are all on the line. Point A is (2,3) and B is (5,9).]() \\( (21,36) \\)" }, { "from": "gpt", "value": "Does not know how to find the length of a line segment from coordinates" } ]
[ { "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 Expand:\n\\[\n6(2-3 p)\n\\] \\( 8-18 p \\)" }, { "from": "gpt", "value": "Adds instead of multiplying when expanding bracket" } ]
[ { "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 Expand:\n\\[\n6(2-3 p)\n\\] \\( 2-18 p \\)" }, { "from": "gpt", "value": "Only multiplies second term in the expansion of a bracket" } ]
[ { "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 Expand:\n\\[\n6(2-3 p)\n\\] \\( 18 p-6 \\)" }, { "from": "gpt", "value": "Believes subtraction is commutative " } ]
[ { "from": "human", "value": "Express one quantity as a percentage of another mentally What is \\( 16 \\) out of \\( 25 \\) as a percentage? \\( 16 \\% \\)" }, { "from": "gpt", "value": "Thinks you just add a % sign to the numerator to make a fraction into a percentage" } ]
[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 1 decimal place What is the mode of the following numbers?\n\\(\n0.4, \\quad \\frac{1}{4}, \\quad 2.5, \\quad \\frac{2}{5}\n\\) \\( 0.4 \\) and \\( 2.5 \\)" }, { "from": "gpt", "value": "Converts a fraction to a percentage by placing a decimal point between the numerator and denominator" } ]
[ { "from": "human", "value": "Given an equation, form or identify related equations Jo and Paul are talking about statements that can be made about the equation on the right. \\( 2 x=y \\) Jo says this is always true: \\( 2 x+1>y \\) \nPaul says this is always true: \\( -2 x<y \\)\nWho is correct? Both Jo and Paul" }, { "from": "gpt", "value": "Believes -a is always smaller than a, ignoring the possibility that a is negative" } ]
[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages \\( 0.01+57 \\%= \\) \\( 57.1 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]
[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages \\( 0.01+57 \\%= \\) \\( 67 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 1000 instead of 100 when converting a decimal to a percentage" } ]
[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for the area of a triangle, \\( A \\), is\n\\(A=\\frac{1}{2}(b \\times h)\\)\n\nRearrange this to make the height, \\( h \\), the subject. ![An image of a triangle with the base labelled b and the perpendicular height h.]() \\( h=\\frac{1}{2}(b \\times A) \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for the area of a triangle, \\( A \\), is\n\\(A=\\frac{1}{2}(b \\times h)\\)\n\nRearrange this to make the height, \\( h \\), the subject. ![An image of a triangle with the base labelled b and the perpendicular height h.]() \\( h=\\frac{A}{2 b} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation on the right.\nHere are his steps.\n\nWhich steps, if any, are correct? ![\\[\n27=9(1+k)\n\\]\n\nStep \\( 1 \\quad 3=1+k \\)\n\nStep \\( 2 \\)\n\\[\n2=k\n\\]]() Only step \\( 2 \\)" }, { "from": "gpt", "value": "Believes they must expand brackets before solving an equation" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=15 \\)\n\n\\(\n\\frac{h}{3}=\n\\)\n \\( 12 \\)" }, { "from": "gpt", "value": "Thinks the fraction bar means subtract rather than divide" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=15 \\)\n\n\\(\n\\frac{h}{3}=\n\\)\n \\( -5 \\)" }, { "from": "gpt", "value": "Believes dividing two positives will give a negative answer" } ]
[ { "from": "human", "value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\[\ny=-2 x+7 \\text { ? }\n\\] \\( 3 y=-6 x-8 \\)" }, { "from": "gpt", "value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c" } ]
[ { "from": "human", "value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\[\ny=-2 x+7 \\text { ? }\n\\] \\( y=2-2 x \\)" }, { "from": "gpt", "value": "When given the equation of a straight line, believes the first term always gives the gradient, even when the first term is actually c" } ]
[ { "from": "human", "value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\[\ny=-2 x+7 \\text { ? }\n\\] \\( y=2(1-x) \\)" }, { "from": "gpt", "value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]() \\( P \\)" }, { "from": "gpt", "value": "Gives the vertex instead of the 3-letter angle notation" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]() \\( Q P \\)" }, { "from": "gpt", "value": "Uses 2 letters to describe an angle" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]() QPRS" }, { "from": "gpt", "value": "Uses more than 3 letters to describe an angle" } ]
[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms Express the following as a single fraction, writing your answer as simply as possible:\n\\(\n\\frac{1}{s+1}-\\frac{t}{2}\n\\) \\( \\frac{1-t}{2(s+1)} \\)" }, { "from": "gpt", "value": "Does not understand equivalent fractions" } ]
[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms Express the following as a single fraction, writing your answer as simply as possible:\n\\(\n\\frac{1}{s+1}-\\frac{t}{2}\n\\) \\( \\frac{1-s t}{2(s+1)} \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]
[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms Express the following as a single fraction, writing your answer as simply as possible:\n\\(\n\\frac{1}{s+1}-\\frac{t}{2}\n\\) \\( \\frac{1-t}{s-1} \\)" }, { "from": "gpt", "value": "When subtracting fractions, subtracts the numerators and denominators" } ]
[ { "from": "human", "value": "Reduce a ratio involving two numbers to its simplest form Write the following ratio in its simplest form so both sides of the ratio are integers:\n\\(\n\\frac{1}{8}: \\frac{1}{2}\n\\) \\( 4: 1 \\)" }, { "from": "gpt", "value": "Does not realise that the order is important in a ratio" } ]
[ { "from": "human", "value": "Reduce a ratio involving two numbers to its simplest form Write the following ratio in its simplest form so both sides of the ratio are integers:\n\\(\n\\frac{1}{8}: \\frac{1}{2}\n\\) \\( 2: 8 \\)" }, { "from": "gpt", "value": "Does not fully simplify ratio" } ]
[ { "from": "human", "value": "Find the lower bound of a number rounded to 2 decimal places A number, \\( n \\), has been rounded to \\( 2 \\) decimal places to give \\( \\mathbf{3 . 7 2} \\)\nWhat is the smallest \\( n \\) can be? \\( 3.7 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Find the lower bound of a number rounded to 2 decimal places A number, \\( n \\), has been rounded to \\( 2 \\) decimal places to give \\( \\mathbf{3 . 7 2} \\)\nWhat is the smallest \\( n \\) can be? \\( 3.71 \\)" }, { "from": "gpt", "value": "Does not understand which place value is the one that determines if a number rounds up or down" } ]
[ { "from": "human", "value": "Find the lower bound of a number rounded to 2 decimal places A number, \\( n \\), has been rounded to \\( 2 \\) decimal places to give \\( \\mathbf{3 . 7 2} \\)\nWhat is the smallest \\( n \\) can be? \\( 3.719 \\)" }, { "from": "gpt", "value": "Does not understand which place value is the one that determines if a number rounds up or down" } ]
[ { "from": "human", "value": "Match linear sequences to other representations, such as tables and graphs ![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \\begin{tabular}{\|l\|c\|c\|c\|}\n\\hline Position & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline Term & \\( \\) & \\( \\bigstar \\) & \\( \\) \\\\\n\\hline\n\\end{tabular} What value should replace the star? \\( 2 \\)" }, { "from": "gpt", "value": "Mixes up term in a sequence and position of a term" } ]
[ { "from": "human", "value": "Match linear sequences to other representations, such as tables and graphs ![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \\begin{tabular}{\|l\|c\|c\|c\|}\n\\hline Position & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline Term & \\( \\) & \\( \\bigstar \\) & \\( \\) \\\\\n\\hline\n\\end{tabular} What value should replace the star? \\( 4 \\)" }, { "from": "gpt", "value": "Thinks the term in a sequence is double the position value" } ]
[ { "from": "human", "value": "Match linear sequences to other representations, such as tables and graphs ![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \\begin{tabular}{\|l\|c\|c\|c\|}\n\\hline Position & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline Term & \\( \\) & \\( \\bigstar \\) & \\( \\) \\\\\n\\hline\n\\end{tabular} What value should replace the star? \\( 7 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the term after" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a decimal What is \\( 5.5 \\% \\) of \\( 400 \\) ? \\( 5.5 \\)" }, { "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 decimal What is \\( 5.5 \\% \\) of \\( 400 \\) ? \\( 220 \\)" }, { "from": "gpt", "value": "Believes that dividing by 10 gives 1%" } ]
[ { "from": "human", "value": "Follow simple directions to translate a shape or object using words not vectors If you translate the star \\( 3 \\) squares left and \\( 2 \\) squares down, which letter do you land on? ![Positive coordinate grid from 0 to 8 in the x and y directions with a gold star at (4,4), A at (7,2), B at (2,1), C at (2,2) and D at (1,2)]() A" }, { "from": "gpt", "value": "Confuses left and right" } ]
[ { "from": "human", "value": "Follow simple directions to translate a shape or object using words not vectors If you translate the star \\( 3 \\) squares left and \\( 2 \\) squares down, which letter do you land on? ![Positive coordinate grid from 0 to 8 in the x and y directions with a gold star at (4,4), A at (7,2), B at (2,1), C at (2,2) and D at (1,2)]() C" }, { "from": "gpt", "value": "When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares." } ]
[ { "from": "human", "value": "Recognise the angles on a straight line relationship Which of the following cannot represent a straight line? ![A straight line, separated into an angle of 53 degrees and an angle of 127 degrees]()" }, { "from": "gpt", "value": "Does not know that angles on a straight line sum to 180 degrees" } ]
[ { "from": "human", "value": "Recognise the angles on a straight line relationship Which of the following cannot represent a straight line? ![A straight line, separated into three angles. One is unmarked, one is 90 degrees and one is 45 degrees]()" }, { "from": "gpt", "value": "Misinterprets the meaning of angles on a straight line angle fact" } ]
[ { "from": "human", "value": "Recognise the angles on a straight line relationship Which of the following cannot represent a straight line? ![A straight line, separated into two angles of 90 degrees]()" }, { "from": "gpt", "value": "Does not know that angles on a straight line sum to 180 degrees" } ]
[ { "from": "human", "value": "Solve length problems involving similar shapes where the missing length is the longer one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]() \\( 8 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Doubles side length for similar shape instead of using correct scale factor" } ]
[ { "from": "human", "value": "Solve length problems involving similar shapes where the missing length is the longer one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]() \\( 14 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Thinks adding the same value to each side makes shapes similar" } ]
[ { "from": "human", "value": "Solve length problems involving similar shapes where the missing length is the longer one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]() Not enough information" }, { "from": "gpt", "value": "Does not understand how to find a scale factor" } ]
[ { "from": "human", "value": "Calculate the volume of a cuboid when the dimensions are given in the same units What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]() \\( 19 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Adds when calculating volume instead of multiplying" } ]
[ { "from": "human", "value": "Calculate the volume of a cuboid when the dimensions are given in the same units What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]() \\( 50 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Finds area of one face when asked for volume" } ]
[ { "from": "human", "value": "Calculate the volume of a cuboid when the dimensions are given in the same units What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]() \\( 220 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Finds surface area when asked for volume" } ]
[ { "from": "human", "value": "Carry out division problems involving one negative integer ![Arrow pointing to the left showing -18 and 3 arrows pointing to the left showing -18 in 3 equal parts]() Tom and Katie are trying to write different calculations for the diagram shown.\nTom writes: \\( 3 \\times(-6)=-18 \\)\nKatie writes: \\( \\frac{(-18)}{3}=-6 \\)\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Believes dividing a negative by a positive gives a positive answer" } ]
[ { "from": "human", "value": "Carry out division problems involving one negative integer ![Arrow pointing to the left showing -18 and 3 arrows pointing to the left showing -18 in 3 equal parts]() Tom and Katie are trying to write different calculations for the diagram shown.\nTom writes: \\( 3 \\times(-6)=-18 \\)\nKatie writes: \\( \\frac{(-18)}{3}=-6 \\)\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]
[ { "from": "human", "value": "Add two equations together to remove a variable Eliza is trying to solve the pair of simultaneous equations below.\n\n\\( \\begin{aligned} -6 g-2 h & = & -2 \\\\ g-2h & = & 10 \\\\ \\end{aligned} \\)\n\nShe decides to add them together.\nWhat will she end up with? \\( 5 g=8 \\)" }, { "from": "gpt", "value": "Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations." } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\nWhat was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]() \\( 4^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "Misreads scale" } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\nWhat was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]() \\( 4.5^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "Misreads scale" } ]
[ { "from": "human", "value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\nWhat was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]() \\( 2.5^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "Misreads scale" } ]
[ { "from": "human", "value": "Count backwards through zero starting from a positive integer John's flat is on floor \\( 4 \\).\n\nThe gym is on floor \\( -1 \\).\n\nHow many floors does John need to go down to get from his flat to the gym? ![A vertical number line from -8 to 7 increasing in 1 digit increments]() \\( 6 \\)" }, { "from": "gpt", "value": "Counts the starting number when counting backwards" } ]
[ { "from": "human", "value": "Count backwards through zero starting from a positive integer John's flat is on floor \\( 4 \\).\n\nThe gym is on floor \\( -1 \\).\n\nHow many floors does John need to go down to get from his flat to the gym? ![A vertical number line from -8 to 7 increasing in 1 digit increments]() \\( 4 \\)" }, { "from": "gpt", "value": "Does not count end number when counting" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=10 \\)\nWhich of the following pairs of statements is true? \\( 3 h^{2}=300 \\)\n\\( (3 h)^{2}=300 \\)" }, { "from": "gpt", "value": "Answers order of operations questions with brackets as if the brackets are not there" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=10 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}3 h^{2}=900 \\\\ (3 h)^{2}=900\\end{array} \\)" }, { "from": "gpt", "value": "Multiplies before applying a power " } ]
[ { "from": "human", "value": "Round numbers to one decimal place \\( 58.2684 \\) to \\( 1 \\) decimal place is.... \\( 58.2 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round numbers to one decimal place \\( 58.2684 \\) to \\( 1 \\) decimal place is.... \\( 59.3 \\)" }, { "from": "gpt", "value": "Rounds incorrectly by changing multiple place values" } ]
[ { "from": "human", "value": "Round numbers to one decimal place \\( 58.2684 \\) to \\( 1 \\) decimal place is.... \\( 59.2 \\)" }, { "from": "gpt", "value": "Rounds incorrectly by changing multiple place values" } ]
[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information \\( \\begin{array}{c}\\xi=\\{\\text { integers between } 1 \\\\ \\text { and } 10 \\text { inclusive }\\} \\\\ P=\\{\\text { odd numbers }\\} \\\\ Q=\\{\\text { factors of } 30\\}\\end{array} \\) ![A Venn diagram with two circles labelled P and Q. P without the intersection is labelled A, Q without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() In which region does \\( \\mathbf{5} \\) belong? A" }, { "from": "gpt", "value": "Does not recognise that the intersection of a Venn diagram represents those belonging to both sets" } ]
[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information \\( \\begin{array}{c}\\xi=\\{\\text { integers between } 1 \\\\ \\text { and } 10 \\text { inclusive }\\} \\\\ P=\\{\\text { odd numbers }\\} \\\\ Q=\\{\\text { factors of } 30\\}\\end{array} \\) ![A Venn diagram with two circles labelled P and Q. P without the intersection is labelled A, Q without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() In which region does \\( \\mathbf{5} \\) belong? C" }, { "from": "gpt", "value": "Does not recognise that the intersection of a Venn diagram represents those belonging to both sets" } ]
[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\\(\n\\frac{13}{78}\n\\) Simplify fully (if possible): \\( \\frac{13}{78} \\) \\( \\frac{1}{66} \\) \\( \\frac{1}{66} \\)" }, { "from": "gpt", "value": "Simplifies a fraction by adding or subtracting the same amount from the numerator and denominator" } ]
[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\\(\n\\frac{13}{78}\n\\) Simplify fully (if possible): \\( \\frac{13}{78} \\) Cannot be simplified Cannot be simplified" }, { "from": "gpt", "value": "Assumes fractions with prime numerators cannot be simplified" } ]
[ { "from": "human", "value": "Plot two straight lines to find the solution to a pair of simultaneous equations Which diagram shows the graphical solution to: \\( \\begin{array}{c}3 x+2 y=12 \\\\ y=3-x\\end{array} \\) ![A four quadrant plane. Y axis -15 to 30 and x axis -15 to 25. A blue line goes from bottom left to top right sloping upwards. It goes through (-10, -7) and (10, 12). A red line goes from bottom left to top right sloping upwards. It goes through (0, -6) and (10, 9) ]()" }, { "from": "gpt", "value": "Believes an upward line has a negative gradient" } ]
[ { "from": "human", "value": "Plot two straight lines to find the solution to a pair of simultaneous equations Which diagram shows the graphical solution to: \\( \\begin{array}{c}3 x+2 y=12 \\\\ y=3-x\\end{array} \\) ![A four quadrant plane. Y axis --3 to 6 and x axis -4 to 7. A blue line goes from bottom left to top right sloping upwards. It goes through (-3, 0) and (0, 3). A red line goes from top left to bottom right sloping downwards. It goes through (0, 6) and (4, 0) ]()" }, { "from": "gpt", "value": "Believes an upward line has a negative gradient" } ]
[ { "from": "human", "value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences\nTom says \\( (\\boldsymbol{n}+\\mathbf{1})^{3} \\) would produce a linear sequence.\nKatie says \\( 3-\\frac{n}{3} \\) would produce a linear sequence\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]
[ { "from": "human", "value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences\nTom says \\( (\\boldsymbol{n}+\\mathbf{1})^{3} \\) would produce a linear sequence.\nKatie says \\( 3-\\frac{n}{3} \\) would produce a linear sequence\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]
[ { "from": "human", "value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences\nTom says \\( (\\boldsymbol{n}+\\mathbf{1})^{3} \\) would produce a linear sequence.\nKatie says \\( 3-\\frac{n}{3} \\) would produce a linear sequence\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Believes linear sequences cannot include fractions" } ]
[ { "from": "human", "value": "Given information about one part, work out other parts To make green paint, you mix blue paint with yellow paint in the ratio \\( 5: 3 \\).\nWhat should replace the star? \\begin{tabular}{\|c\|c\|c\|}\n\\hline Blue & Yellow & Total \\\\\n\\hline \\( \\mathrm{1500 ml} \\) & \\( \\bigstar \\) \n\\hline\n\\end{tabular} \\( 2500 \\mathrm{ml} \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]
[ { "from": "human", "value": "Given information about one part, work out other parts To make green paint, you mix blue paint with yellow paint in the ratio \\( 5: 3 \\).\nWhat should replace the star? \\begin{tabular}{\|c\|c\|c\|}\n\\hline Blue & Yellow & Total \\\\\n\\hline \\( \\mathrm{1500 ml} \\) & \\( \\bigstar \\) \n\\hline\n\\end{tabular} \\( 1502 \\mathrm{ml} \\)" }, { "from": "gpt", "value": "Thinks a difference of one part in a ratio means the quantities will differ by one unit" } ]
[ { "from": "human", "value": "Given information about one part, work out other parts To make green paint, you mix blue paint with yellow paint in the ratio \\( 5: 3 \\).\nWhat should replace the star? \\begin{tabular}{\|c\|c\|c\|}\n\\hline Blue & Yellow & Total \\\\\n\\hline \\( \\mathrm{1500 ml} \\) & \\( \\bigstar \\) \n\\hline\n\\end{tabular} \\( 4500 \\mathrm{ml} \\)" }, { "from": "gpt", "value": "In ratio question where one side of ratio is given, uses that as one part in ratio without dividing" } ]
[ { "from": "human", "value": "Calculate the sector angle on a pie chart for a given group Which calculation is correct to find the number of degrees representing comedy in a pie chart showing the following information? \\begin{tabular}{\|c\|c\|c\|c\|}\n\\hline Film Genre & Comedy & Romance & Action \\\\\n\\hline Number of teachers & \\( 9 \\) & \\( 4 \\) & \\( 7 \\) \\\\\n\\hline\n\\end{tabular} \\( 360 \\div 9 \\)" }, { "from": "gpt", "value": "Believes to find the angle for a pie chart sector you calculate 360 divided by the frequency of that sector" } ]
[ { "from": "human", "value": "Calculate the distance travelled using a speed-time graph ![A speed-time graph. At 6 seconds, the car is travelling at a speed of 8 metres per second. After 8 seconds, the car is travelling at a speed of 15 metres per second. ]() Here is a speed-time graph for a car.\n\nWhich of the following gives the best estimate for the distance travelled between \\( 6 \\) and \\( 8 \\) seconds? \\( 30 m \\)" }, { "from": "gpt", "value": "Believes that when finding area under graph you can use the upper y value rather than average of upper and lower" } ]
[ { "from": "human", "value": "Add decimals where the numbers involved have a different number of decimal places \\( 0.32+0.8= \\) \\( 0.4 \\)" }, { "from": "gpt", "value": "When adding decimals with a different number of decimal places, lines up the digits incorrectly" } ]
[ { "from": "human", "value": "Add decimals where the numbers involved have a different number of decimal places \\( 0.32+0.8= \\) \\( 0.328 \\)" }, { "from": "gpt", "value": "When adding decimals with a different number of decimal places, lines up the digits incorrectly" } ]
[ { "from": "human", "value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]() \\( 37^{\\circ} \\)" }, { "from": "gpt", "value": "Thinks angles which look the same on diagram will be equal" } ]
[ { "from": "human", "value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]() \\( 17^{\\circ} \\)" }, { "from": "gpt", "value": "Misinterprets the meaning of angles on a straight line angle fact" } ]
[ { "from": "human", "value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]() \\( 64^{\\circ} \\)" }, { "from": "gpt", "value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit" } ]
[ { "from": "human", "value": "Complete missing number mental subtraction problems with numbers over 1000 A \\( 4 \\) digit number belongs in this box to make the calculation true\n\\(\n\\square-6027=1253\n\\)\nWhat is the \\( 4^{\\text {th }} \\) digit of the number that belongs in the box? \\( 4 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]
[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition Nick wants to add \\( 97 \\) to a number.\nWhich one of the following methods would give him the correct answer? \\( +100 \\) then \\( +3 \\)" }, { "from": "gpt", "value": "Does not understand the effect of consecutive operations" } ]
[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition Nick wants to add \\( 97 \\) to a number.\nWhich one of the following methods would give him the correct answer? \\( -100 \\) then \\( +3 \\)" }, { "from": "gpt", "value": "Subtracts instead of adds when answering worded problems " } ]
[ { "from": "human", "value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0.9 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Certain" }, { "from": "gpt", "value": "Does not understand that a probability of 1 represents something that is certain" } ]
[ { "from": "human", "value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0.9 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Unlikely" }, { "from": "gpt", "value": "Does not understand that a probability of 1 represents something that is certain" } ]
[ { "from": "human", "value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0.9 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Impossible" }, { "from": "gpt", "value": "Does not understand that a probability of 0 represents something that is impossible" } ]
[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]() \\( 67.5 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Has used slant height and base to find area of a triangle rather than perpendicular height and base" } ]
[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]() \\( 810 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Multiplies all given dimensions when calculating an area" } ]
[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]() \\( 108 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Does not divide by 2 when calculating the area of a triangle" } ]
[ { "from": "human", "value": "Calculate the change from purchases between £10 and £100 Sunita wants to buy a soup and a coffee.\nHow much change should she get from f20? \\begin{tabular}{\|c\|}\n\\hline Joe's Café \\\\\nSandwich \\( £ 3.25 \\) \\\\\nPasty \\( £ 2.99 \\) \\\\\nCake \\( £ 2.25 \\) \\\\\nSoup \\( £ 3.19 \\) \\\\\nTea \\( £ 1.55 \\) \\\\\nCoffee \\( £ 1.95 \\) \\\\\nOrange \\( 89 p \\) \\\\\n\\hline\n\\end{tabular} \\( £ 5.14 \\)" }, { "from": "gpt", "value": "In a worded problem, does not complete all calculations" } ]
[ { "from": "human", "value": "Use the nth term rule of an ascending integer linear sequence to test whether a term belongs in the sequence or not Jo and Paul are discussing the sequence \\( \\mathbf{7 n}+\\mathbf{5} \\)\n\nJo says \\( \\mathbf{1 4 9} \\) is a term in the sequence.\n\nPaul says \\( \\mathbf{1 5 0} \\) is a term in the sequence.\n\nWho is correct? Only Jo" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio Tom says for every one circle there are two squares \n\\(\\bigcirc\\bigcirc\\bigcirc\\)\n\\(\\square\\;\\square\\;\\square\\;\\square\\;\\square\\;\\square\\) Katie says for every one circle there are two squares\n\\(\\square\\quad\\square\\quad\\square\\quad\\square\\quad\\square\\)\n\\(\\bigcirc\\bigcirc\\bigcirc\\bigcirc\\bigcirc\\)\n\\(\\square\\quad\\square\\quad\\square\\quad\\square\\quad\\square\\) Who is correct? Only Katie" }, { "from": "gpt", "value": "Is not able to spot a proportional relationship pictorially unless they are laid out in groups" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio Tom says for every one circle there are two squares \n\\(\\bigcirc\\bigcirc\\bigcirc\\)\n\\(\\square\\;\\square\\;\\square\\;\\square\\;\\square\\;\\square\\) Katie says for every one circle there are two squares\n\\(\\square\\quad\\square\\quad\\square\\quad\\square\\quad\\square\\)\n\\(\\bigcirc\\bigcirc\\bigcirc\\bigcirc\\bigcirc\\)\n\\(\\square\\quad\\square\\quad\\square\\quad\\square\\quad\\square\\) Who is correct? Neither is correct" }, { "from": "gpt", "value": "Does not believe you can scale up a proportional statement" } ]
[ { "from": "human", "value": "Multiplication law of indices with positive integer powers and a different base number Jo and Paul are discussing \\( 3^{2} \\times 4^{2} \\)\nJo says \\( 3^{2} \\times 4^{2}=12^{4} \\)\nPaul says \\( 3^{2} \\times 4^{2}=12^{2} \\)\nWho is correct? Only\nJo" }, { "from": "gpt", "value": "When multiplying numbers with different bases, multiplies the powers and multiplies the base numbers." } ]
[ { "from": "human", "value": "Multiplication law of indices with positive integer powers and a different base number Jo and Paul are discussing \\( 3^{2} \\times 4^{2} \\)\nJo says \\( 3^{2} \\times 4^{2}=12^{4} \\)\nPaul says \\( 3^{2} \\times 4^{2}=12^{2} \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not realise that multiplication can be broken down into factors" } ]
[ { "from": "human", "value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n32, \\quad 28, \\quad 24, \\quad \\ldots\n\\] \\( 4 \\)" }, { "from": "gpt", "value": "Identifies the term-to-term rule rather than the next term in a sequence" } ]
[ { "from": "human", "value": "Identify cross sections of 3D shapes This is the uniform cross-section of solid \\( Q \\).\n\nWhich of the following could shape \\( Q \\) be? ![A rectangle.]() Rectangle" }, { "from": "gpt", "value": "Does not know that a solid is a 3D shape" } ]
[ { "from": "human", "value": "Identify cross sections of 3D shapes This is the uniform cross-section of solid \\( Q \\).\n\nWhich of the following could shape \\( Q \\) be? ![A rectangle.]() Cube" }, { "from": "gpt", "value": "Mixes up cubes and cuboids" } ]
[ { "from": "human", "value": "Identify cross sections of 3D shapes This is the uniform cross-section of solid \\( Q \\).\n\nWhich of the following could shape \\( Q \\) be? ![A rectangle.]() Cylinder" }, { "from": "gpt", "value": "Does not know the meaning of uniform cross section" } ]
[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number \\( \\begin{array}{llllll}\\frac{8}{10} & \\frac{41}{50} & \\frac{7}{20} & 0.77 & \\frac{4}{5} & \\frac{79}{100}\\end{array} \\) Which value is the outlier in this set of data? \\( \\frac{41}{50} \\)" }, { "from": "gpt", "value": "Believes an outlier is a value that does not fit the same characteristics as the other values" } ]
[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number \\( \\begin{array}{llllll}\\frac{8}{10} & \\frac{41}{50} & \\frac{7}{20} & 0.77 & \\frac{4}{5} & \\frac{79}{100}\\end{array} \\) Which value is the outlier in this set of data? \\( 0.77 \\)" }, { "from": "gpt", "value": "Believes an outlier is a value that does not fit the same characteristics as the other values" } ]

[ { "from": "human", "value": "Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object John rotates hexagon \\( \\mathrm{ABCDEF} 90^{\\degree} \\) clockwise from the centre \\( (5,4) \\). What error has he made? ![A positive, coordinate grid with two L-shaped hexagons drawn on it. The hexagon labelled ABCDEF has the coordinates: A(2,4) B(2,1) C(4,1) D(4,2) E(3,2) and F (3,4). The other hexagon has the coordinates: (6,7) (3,7) (3,5) (4,5) (4,6) and (6,6)]() He has translated by the vector \\( \\left(\\begin{array}{l}5 \\\\ 4\\end{array}\\right) \\)" }, { "from": "gpt", "value": "Mistakes rotations for translations" } ]

[ { "from": "human", "value": "Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object John rotates hexagon \\( \\mathrm{ABCDEF} 90^{\\degree} \\) clockwise from the centre \\( (5,4) \\). What error has he made? ![A positive, coordinate grid with two L-shaped hexagons drawn on it. The hexagon labelled ABCDEF has the coordinates: A(2,4) B(2,1) C(4,1) D(4,2) E(3,2) and F (3,4). The other hexagon has the coordinates: (6,7) (3,7) (3,5) (4,5) (4,6) and (6,6)]() He has rotated \\( 90^{\\circ} \\) anticlockwise" }, { "from": "gpt", "value": "Mixes up clockwise and anticlockwise" } ]

[ { "from": "human", "value": "Solve coordinate geometry questions involving ratio Given that \\( A C=3 A B \\), what are the coordinates of \\( C \\) ? ![A straight line labelled y=2x-1 is drawn on a set of axes. Points A, B and C are all on the line. Point A is (2,3) and B is (5,9).]() \\( (14,27) \\)" }, { "from": "gpt", "value": "Assumes a ratio is part to part instead of part to whole" } ]

[ { "from": "human", "value": "Solve coordinate geometry questions involving ratio Given that \\( A C=3 A B \\), what are the coordinates of \\( C \\) ? ![A straight line labelled y=2x-1 is drawn on a set of axes. Points A, B and C are all on the line. Point A is (2,3) and B is (5,9).]() \\( (21,36) \\)" }, { "from": "gpt", "value": "Does not know how to find the length of a line segment from coordinates" } ]

[ { "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 Expand:\n\\[\n6(2-3 p)\n\\] \\( 8-18 p \\)" }, { "from": "gpt", "value": "Adds instead of multiplying when expanding bracket" } ]

[ { "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 Expand:\n\\[\n6(2-3 p)\n\\] \\( 2-18 p \\)" }, { "from": "gpt", "value": "Only multiplies second term in the expansion of a bracket" } ]

[ { "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 Expand:\n\\[\n6(2-3 p)\n\\] \\( 18 p-6 \\)" }, { "from": "gpt", "value": "Believes subtraction is commutative " } ]

[ { "from": "human", "value": "Express one quantity as a percentage of another mentally What is \\( 16 \\) out of \\( 25 \\) as a percentage? \\( 16 \\% \\)" }, { "from": "gpt", "value": "Thinks you just add a % sign to the numerator to make a fraction into a percentage" } ]

[ { "from": "human", "value": "Convert fractions less than 1 to terminating decimals of 1 decimal place What is the mode of the following numbers?\n\\(\n0.4, \\quad \\frac{1}{4}, \\quad 2.5, \\quad \\frac{2}{5}\n\\) \\( 0.4 \\) and \\( 2.5 \\)" }, { "from": "gpt", "value": "Converts a fraction to a percentage by placing a decimal point between the numerator and denominator" } ]

[ { "from": "human", "value": "Given an equation, form or identify related equations Jo and Paul are talking about statements that can be made about the equation on the right. \\( 2 x=y \\) Jo says this is always true: \\( 2 x+1>y \\) \nPaul says this is always true: \\( -2 x<y \\)\nWho is correct? Both Jo and Paul" }, { "from": "gpt", "value": "Believes -a is always smaller than a, ignoring the possibility that a is negative" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages \\( 0.01+57 \\%= \\) \\( 57.1 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages \\( 0.01+57 \\%= \\) \\( 67 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 1000 instead of 100 when converting a decimal to a percentage" } ]

[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for the area of a triangle, \\( A \\), is\n\\(A=\\frac{1}{2}(b \\times h)\\)\n\nRearrange this to make the height, \\( h \\), the subject. ![An image of a triangle with the base labelled b and the perpendicular height h.]() \\( h=\\frac{1}{2}(b \\times A) \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for the area of a triangle, \\( A \\), is\n\\(A=\\frac{1}{2}(b \\times h)\\)\n\nRearrange this to make the height, \\( h \\), the subject. ![An image of a triangle with the base labelled b and the perpendicular height h.]() \\( h=\\frac{A}{2 b} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation on the right.\nHere are his steps.\n\nWhich steps, if any, are correct? ![\\[\n27=9(1+k)\n\\]\n\nStep \\( 1 \\quad 3=1+k \\)\n\nStep \\( 2 \\)\n\\[\n2=k\n\\]]() Only step \\( 2 \\)" }, { "from": "gpt", "value": "Believes they must expand brackets before solving an equation" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=15 \\)\n\n\\(\n\\frac{h}{3}=\n\\)\n \\( 12 \\)" }, { "from": "gpt", "value": "Thinks the fraction bar means subtract rather than divide" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=15 \\)\n\n\\(\n\\frac{h}{3}=\n\\)\n \\( -5 \\)" }, { "from": "gpt", "value": "Believes dividing two positives will give a negative answer" } ]

[ { "from": "human", "value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\[\ny=-2 x+7 \\text { ? }\n\\] \\( 3 y=-6 x-8 \\)" }, { "from": "gpt", "value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c" } ]

[ { "from": "human", "value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\[\ny=-2 x+7 \\text { ? }\n\\] \\( y=2-2 x \\)" }, { "from": "gpt", "value": "When given the equation of a straight line, believes the first term always gives the gradient, even when the first term is actually c" } ]

[ { "from": "human", "value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\[\ny=-2 x+7 \\text { ? }\n\\] \\( y=2(1-x) \\)" }, { "from": "gpt", "value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c" } ]

[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]() \\( P \\)" }, { "from": "gpt", "value": "Gives the vertex instead of the 3-letter angle notation" } ]

[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]() \\( Q P \\)" }, { "from": "gpt", "value": "Uses 2 letters to describe an angle" } ]

[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]() QPRS" }, { "from": "gpt", "value": "Uses more than 3 letters to describe an angle" } ]

[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms Express the following as a single fraction, writing your answer as simply as possible:\n\\(\n\\frac{1}{s+1}-\\frac{t}{2}\n\\) \\( \\frac{1-t}{2(s+1)} \\)" }, { "from": "gpt", "value": "Does not understand equivalent fractions" } ]

[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms Express the following as a single fraction, writing your answer as simply as possible:\n\\(\n\\frac{1}{s+1}-\\frac{t}{2}\n\\) \\( \\frac{1-s t}{2(s+1)} \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]

[ { "from": "human", "value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms Express the following as a single fraction, writing your answer as simply as possible:\n\\(\n\\frac{1}{s+1}-\\frac{t}{2}\n\\) \\( \\frac{1-t}{s-1} \\)" }, { "from": "gpt", "value": "When subtracting fractions, subtracts the numerators and denominators" } ]

[ { "from": "human", "value": "Reduce a ratio involving two numbers to its simplest form Write the following ratio in its simplest form so both sides of the ratio are integers:\n\\(\n\\frac{1}{8}: \\frac{1}{2}\n\\) \\( 4: 1 \\)" }, { "from": "gpt", "value": "Does not realise that the order is important in a ratio" } ]

[ { "from": "human", "value": "Reduce a ratio involving two numbers to its simplest form Write the following ratio in its simplest form so both sides of the ratio are integers:\n\\(\n\\frac{1}{8}: \\frac{1}{2}\n\\) \\( 2: 8 \\)" }, { "from": "gpt", "value": "Does not fully simplify ratio" } ]

[ { "from": "human", "value": "Find the lower bound of a number rounded to 2 decimal places A number, \\( n \\), has been rounded to \\( 2 \\) decimal places to give \\( \\mathbf{3 . 7 2} \\)\nWhat is the smallest \\( n \\) can be? \\( 3.7 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Find the lower bound of a number rounded to 2 decimal places A number, \\( n \\), has been rounded to \\( 2 \\) decimal places to give \\( \\mathbf{3 . 7 2} \\)\nWhat is the smallest \\( n \\) can be? \\( 3.71 \\)" }, { "from": "gpt", "value": "Does not understand which place value is the one that determines if a number rounds up or down" } ]

[ { "from": "human", "value": "Find the lower bound of a number rounded to 2 decimal places A number, \\( n \\), has been rounded to \\( 2 \\) decimal places to give \\( \\mathbf{3 . 7 2} \\)\nWhat is the smallest \\( n \\) can be? \\( 3.719 \\)" }, { "from": "gpt", "value": "Does not understand which place value is the one that determines if a number rounds up or down" } ]

[ { "from": "human", "value": "Match linear sequences to other representations, such as tables and graphs ![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \\begin{tabular}{|l|c|c|c|}\n\\hline Position & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline Term & \\( \\) & \\( \\bigstar \\) & \\( \\) \\\\\n\\hline\n\\end{tabular} What value should replace the star? \\( 2 \\)" }, { "from": "gpt", "value": "Mixes up term in a sequence and position of a term" } ]

[ { "from": "human", "value": "Match linear sequences to other representations, such as tables and graphs ![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \\begin{tabular}{|l|c|c|c|}\n\\hline Position & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline Term & \\( \\) & \\( \\bigstar \\) & \\( \\) \\\\\n\\hline\n\\end{tabular} What value should replace the star? \\( 4 \\)" }, { "from": "gpt", "value": "Thinks the term in a sequence is double the position value" } ]

[ { "from": "human", "value": "Match linear sequences to other representations, such as tables and graphs ![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \\begin{tabular}{|l|c|c|c|}\n\\hline Position & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline Term & \\( \\) & \\( \\bigstar \\) & \\( \\) \\\\\n\\hline\n\\end{tabular} What value should replace the star? \\( 7 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the term after" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a decimal What is \\( 5.5 \\% \\) of \\( 400 \\) ? \\( 5.5 \\)" }, { "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 decimal What is \\( 5.5 \\% \\) of \\( 400 \\) ? \\( 220 \\)" }, { "from": "gpt", "value": "Believes that dividing by 10 gives 1%" } ]

[ { "from": "human", "value": "Follow simple directions to translate a shape or object using words not vectors If you translate the star \\( 3 \\) squares left and \\( 2 \\) squares down, which letter do you land on? ![Positive coordinate grid from 0 to 8 in the x and y directions with a gold star at (4,4), A at (7,2), B at (2,1), C at (2,2) and D at (1,2)]() A" }, { "from": "gpt", "value": "Confuses left and right" } ]

[ { "from": "human", "value": "Follow simple directions to translate a shape or object using words not vectors If you translate the star \\( 3 \\) squares left and \\( 2 \\) squares down, which letter do you land on? ![Positive coordinate grid from 0 to 8 in the x and y directions with a gold star at (4,4), A at (7,2), B at (2,1), C at (2,2) and D at (1,2)]() C" }, { "from": "gpt", "value": "When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares." } ]

[ { "from": "human", "value": "Recognise the angles on a straight line relationship Which of the following cannot represent a straight line? ![A straight line, separated into an angle of 53 degrees and an angle of 127 degrees]()" }, { "from": "gpt", "value": "Does not know that angles on a straight line sum to 180 degrees" } ]

[ { "from": "human", "value": "Recognise the angles on a straight line relationship Which of the following cannot represent a straight line? ![A straight line, separated into three angles. One is unmarked, one is 90 degrees and one is 45 degrees]()" }, { "from": "gpt", "value": "Misinterprets the meaning of angles on a straight line angle fact" } ]

[ { "from": "human", "value": "Recognise the angles on a straight line relationship Which of the following cannot represent a straight line? ![A straight line, separated into two angles of 90 degrees]()" }, { "from": "gpt", "value": "Does not know that angles on a straight line sum to 180 degrees" } ]

[ { "from": "human", "value": "Solve length problems involving similar shapes where the missing length is the longer one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]() \\( 8 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Doubles side length for similar shape instead of using correct scale factor" } ]

[ { "from": "human", "value": "Solve length problems involving similar shapes where the missing length is the longer one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]() \\( 14 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Thinks adding the same value to each side makes shapes similar" } ]

[ { "from": "human", "value": "Solve length problems involving similar shapes where the missing length is the longer one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]() Not enough information" }, { "from": "gpt", "value": "Does not understand how to find a scale factor" } ]

[ { "from": "human", "value": "Calculate the volume of a cuboid when the dimensions are given in the same units What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]() \\( 19 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Adds when calculating volume instead of multiplying" } ]

[ { "from": "human", "value": "Calculate the volume of a cuboid when the dimensions are given in the same units What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]() \\( 50 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Finds area of one face when asked for volume" } ]

[ { "from": "human", "value": "Calculate the volume of a cuboid when the dimensions are given in the same units What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]() \\( 220 \\mathrm{~cm}^{3} \\)" }, { "from": "gpt", "value": "Finds surface area when asked for volume" } ]

[ { "from": "human", "value": "Carry out division problems involving one negative integer ![Arrow pointing to the left showing -18 and 3 arrows pointing to the left showing -18 in 3 equal parts]() Tom and Katie are trying to write different calculations for the diagram shown.\nTom writes: \\( 3 \\times(-6)=-18 \\)\nKatie writes: \\( \\frac{(-18)}{3}=-6 \\)\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Believes dividing a negative by a positive gives a positive answer" } ]

[ { "from": "human", "value": "Carry out division problems involving one negative integer ![Arrow pointing to the left showing -18 and 3 arrows pointing to the left showing -18 in 3 equal parts]() Tom and Katie are trying to write different calculations for the diagram shown.\nTom writes: \\( 3 \\times(-6)=-18 \\)\nKatie writes: \\( \\frac{(-18)}{3}=-6 \\)\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]

[ { "from": "human", "value": "Add two equations together to remove a variable Eliza is trying to solve the pair of simultaneous equations below.\n\n\\( \\begin{aligned} -6 g-2 h & = & -2 \\\\ g-2h & = & 10 \\\\ \\end{aligned} \\)\n\nShe decides to add them together.\nWhat will she end up with? \\( 5 g=8 \\)" }, { "from": "gpt", "value": "Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations." } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\nWhat was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]() \\( 4^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "Misreads scale" } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\nWhat was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]() \\( 4.5^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "Misreads scale" } ]

[ { "from": "human", "value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\nWhat was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]() \\( 2.5^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "Misreads scale" } ]

[ { "from": "human", "value": "Count backwards through zero starting from a positive integer John's flat is on floor \\( 4 \\).\n\nThe gym is on floor \\( -1 \\).\n\nHow many floors does John need to go down to get from his flat to the gym? ![A vertical number line from -8 to 7 increasing in 1 digit increments]() \\( 6 \\)" }, { "from": "gpt", "value": "Counts the starting number when counting backwards" } ]

[ { "from": "human", "value": "Count backwards through zero starting from a positive integer John's flat is on floor \\( 4 \\).\n\nThe gym is on floor \\( -1 \\).\n\nHow many floors does John need to go down to get from his flat to the gym? ![A vertical number line from -8 to 7 increasing in 1 digit increments]() \\( 4 \\)" }, { "from": "gpt", "value": "Does not count end number when counting" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=10 \\)\nWhich of the following pairs of statements is true? \\( 3 h^{2}=300 \\)\n\\( (3 h)^{2}=300 \\)" }, { "from": "gpt", "value": "Answers order of operations questions with brackets as if the brackets are not there" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=10 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}3 h^{2}=900 \\\\ (3 h)^{2}=900\\end{array} \\)" }, { "from": "gpt", "value": "Multiplies before applying a power " } ]

[ { "from": "human", "value": "Round numbers to one decimal place \\( 58.2684 \\) to \\( 1 \\) decimal place is.... \\( 58.2 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round numbers to one decimal place \\( 58.2684 \\) to \\( 1 \\) decimal place is.... \\( 59.3 \\)" }, { "from": "gpt", "value": "Rounds incorrectly by changing multiple place values" } ]

[ { "from": "human", "value": "Round numbers to one decimal place \\( 58.2684 \\) to \\( 1 \\) decimal place is.... \\( 59.2 \\)" }, { "from": "gpt", "value": "Rounds incorrectly by changing multiple place values" } ]

[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information \\( \\begin{array}{c}\\xi=\\{\\text { integers between } 1 \\\\ \\text { and } 10 \\text { inclusive }\\} \\\\ P=\\{\\text { odd numbers }\\} \\\\ Q=\\{\\text { factors of } 30\\}\\end{array} \\) ![A Venn diagram with two circles labelled P and Q. P without the intersection is labelled A, Q without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() In which region does \\( \\mathbf{5} \\) belong? A" }, { "from": "gpt", "value": "Does not recognise that the intersection of a Venn diagram represents those belonging to both sets" } ]

[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information \\( \\begin{array}{c}\\xi=\\{\\text { integers between } 1 \\\\ \\text { and } 10 \\text { inclusive }\\} \\\\ P=\\{\\text { odd numbers }\\} \\\\ Q=\\{\\text { factors of } 30\\}\\end{array} \\) ![A Venn diagram with two circles labelled P and Q. P without the intersection is labelled A, Q without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() In which region does \\( \\mathbf{5} \\) belong? C" }, { "from": "gpt", "value": "Does not recognise that the intersection of a Venn diagram represents those belonging to both sets" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\\(\n\\frac{13}{78}\n\\) Simplify fully (if possible): \\( \\frac{13}{78} \\) \\( \\frac{1}{66} \\) \\( \\frac{1}{66} \\)" }, { "from": "gpt", "value": "Simplifies a fraction by adding or subtracting the same amount from the numerator and denominator" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\\(\n\\frac{13}{78}\n\\) Simplify fully (if possible): \\( \\frac{13}{78} \\) Cannot be simplified Cannot be simplified" }, { "from": "gpt", "value": "Assumes fractions with prime numerators cannot be simplified" } ]

[ { "from": "human", "value": "Plot two straight lines to find the solution to a pair of simultaneous equations Which diagram shows the graphical solution to: \\( \\begin{array}{c}3 x+2 y=12 \\\\ y=3-x\\end{array} \\) ![A four quadrant plane. Y axis -15 to 30 and x axis -15 to 25. A blue line goes from bottom left to top right sloping upwards. It goes through (-10, -7) and (10, 12). A red line goes from bottom left to top right sloping upwards. It goes through (0, -6) and (10, 9) ]()" }, { "from": "gpt", "value": "Believes an upward line has a negative gradient" } ]

[ { "from": "human", "value": "Plot two straight lines to find the solution to a pair of simultaneous equations Which diagram shows the graphical solution to: \\( \\begin{array}{c}3 x+2 y=12 \\\\ y=3-x\\end{array} \\) ![A four quadrant plane. Y axis --3 to 6 and x axis -4 to 7. A blue line goes from bottom left to top right sloping upwards. It goes through (-3, 0) and (0, 3). A red line goes from top left to bottom right sloping downwards. It goes through (0, 6) and (4, 0) ]()" }, { "from": "gpt", "value": "Believes an upward line has a negative gradient" } ]

[ { "from": "human", "value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences\nTom says \\( (\\boldsymbol{n}+\\mathbf{1})^{3} \\) would produce a linear sequence.\nKatie says \\( 3-\\frac{n}{3} \\) would produce a linear sequence\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]

[ { "from": "human", "value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences\nTom says \\( (\\boldsymbol{n}+\\mathbf{1})^{3} \\) would produce a linear sequence.\nKatie says \\( 3-\\frac{n}{3} \\) would produce a linear sequence\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]

[ { "from": "human", "value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences\nTom says \\( (\\boldsymbol{n}+\\mathbf{1})^{3} \\) would produce a linear sequence.\nKatie says \\( 3-\\frac{n}{3} \\) would produce a linear sequence\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Believes linear sequences cannot include fractions" } ]

[ { "from": "human", "value": "Given information about one part, work out other parts To make green paint, you mix blue paint with yellow paint in the ratio \\( 5: 3 \\).\nWhat should replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Blue & Yellow & Total \\\\\n\\hline \\( \\mathrm{1500 ml} \\) & \\( \\bigstar \\) \n\\hline\n\\end{tabular} \\( 2500 \\mathrm{ml} \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]

[ { "from": "human", "value": "Given information about one part, work out other parts To make green paint, you mix blue paint with yellow paint in the ratio \\( 5: 3 \\).\nWhat should replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Blue & Yellow & Total \\\\\n\\hline \\( \\mathrm{1500 ml} \\) & \\( \\bigstar \\) \n\\hline\n\\end{tabular} \\( 1502 \\mathrm{ml} \\)" }, { "from": "gpt", "value": "Thinks a difference of one part in a ratio means the quantities will differ by one unit" } ]

[ { "from": "human", "value": "Given information about one part, work out other parts To make green paint, you mix blue paint with yellow paint in the ratio \\( 5: 3 \\).\nWhat should replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Blue & Yellow & Total \\\\\n\\hline \\( \\mathrm{1500 ml} \\) & \\( \\bigstar \\) \n\\hline\n\\end{tabular} \\( 4500 \\mathrm{ml} \\)" }, { "from": "gpt", "value": "In ratio question where one side of ratio is given, uses that as one part in ratio without dividing" } ]

[ { "from": "human", "value": "Calculate the sector angle on a pie chart for a given group Which calculation is correct to find the number of degrees representing comedy in a pie chart showing the following information? \\begin{tabular}{|c|c|c|c|}\n\\hline Film Genre & Comedy & Romance & Action \\\\\n\\hline Number of teachers & \\( 9 \\) & \\( 4 \\) & \\( 7 \\) \\\\\n\\hline\n\\end{tabular} \\( 360 \\div 9 \\)" }, { "from": "gpt", "value": "Believes to find the angle for a pie chart sector you calculate 360 divided by the frequency of that sector" } ]

[ { "from": "human", "value": "Calculate the distance travelled using a speed-time graph ![A speed-time graph. At 6 seconds, the car is travelling at a speed of 8 metres per second. After 8 seconds, the car is travelling at a speed of 15 metres per second. ]() Here is a speed-time graph for a car.\n\nWhich of the following gives the best estimate for the distance travelled between \\( 6 \\) and \\( 8 \\) seconds? \\( 30 m \\)" }, { "from": "gpt", "value": "Believes that when finding area under graph you can use the upper y value rather than average of upper and lower" } ]

[ { "from": "human", "value": "Add decimals where the numbers involved have a different number of decimal places \\( 0.32+0.8= \\) \\( 0.4 \\)" }, { "from": "gpt", "value": "When adding decimals with a different number of decimal places, lines up the digits incorrectly" } ]

[ { "from": "human", "value": "Add decimals where the numbers involved have a different number of decimal places \\( 0.32+0.8= \\) \\( 0.328 \\)" }, { "from": "gpt", "value": "When adding decimals with a different number of decimal places, lines up the digits incorrectly" } ]

[ { "from": "human", "value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]() \\( 37^{\\circ} \\)" }, { "from": "gpt", "value": "Thinks angles which look the same on diagram will be equal" } ]

[ { "from": "human", "value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]() \\( 17^{\\circ} \\)" }, { "from": "gpt", "value": "Misinterprets the meaning of angles on a straight line angle fact" } ]

[ { "from": "human", "value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]() \\( 64^{\\circ} \\)" }, { "from": "gpt", "value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit" } ]

[ { "from": "human", "value": "Complete missing number mental subtraction problems with numbers over 1000 A \\( 4 \\) digit number belongs in this box to make the calculation true\n\\(\n\\square-6027=1253\n\\)\nWhat is the \\( 4^{\\text {th }} \\) digit of the number that belongs in the box? \\( 4 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]

[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition Nick wants to add \\( 97 \\) to a number.\nWhich one of the following methods would give him the correct answer? \\( +100 \\) then \\( +3 \\)" }, { "from": "gpt", "value": "Does not understand the effect of consecutive operations" } ]

[ { "from": "human", "value": "Recognise and use efficient strategies for mental addition Nick wants to add \\( 97 \\) to a number.\nWhich one of the following methods would give him the correct answer? \\( -100 \\) then \\( +3 \\)" }, { "from": "gpt", "value": "Subtracts instead of adds when answering worded problems " } ]

[ { "from": "human", "value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0.9 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Certain" }, { "from": "gpt", "value": "Does not understand that a probability of 1 represents something that is certain" } ]

[ { "from": "human", "value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0.9 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Unlikely" }, { "from": "gpt", "value": "Does not understand that a probability of 1 represents something that is certain" } ]

[ { "from": "human", "value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0.9 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Impossible" }, { "from": "gpt", "value": "Does not understand that a probability of 0 represents something that is impossible" } ]

[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]() \\( 67.5 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Has used slant height and base to find area of a triangle rather than perpendicular height and base" } ]

[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]() \\( 810 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Multiplies all given dimensions when calculating an area" } ]

[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]() \\( 108 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Does not divide by 2 when calculating the area of a triangle" } ]

[ { "from": "human", "value": "Calculate the change from purchases between £10 and £100 Sunita wants to buy a soup and a coffee.\nHow much change should she get from f20? \\begin{tabular}{|c|}\n\\hline Joe's Café \\\\\nSandwich \\( £ 3.25 \\) \\\\\nPasty \\( £ 2.99 \\) \\\\\nCake \\( £ 2.25 \\) \\\\\nSoup \\( £ 3.19 \\) \\\\\nTea \\( £ 1.55 \\) \\\\\nCoffee \\( £ 1.95 \\) \\\\\nOrange \\( 89 p \\) \\\\\n\\hline\n\\end{tabular} \\( £ 5.14 \\)" }, { "from": "gpt", "value": "In a worded problem, does not complete all calculations" } ]

[ { "from": "human", "value": "Use the nth term rule of an ascending integer linear sequence to test whether a term belongs in the sequence or not Jo and Paul are discussing the sequence \\( \\mathbf{7 n}+\\mathbf{5} \\)\n\nJo says \\( \\mathbf{1 4 9} \\) is a term in the sequence.\n\nPaul says \\( \\mathbf{1 5 0} \\) is a term in the sequence.\n\nWho is correct? Only Jo" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio Tom says for every one circle there are two squares \n\\(\\bigcirc\\bigcirc\\bigcirc\\)\n\\(\\square\\;\\square\\;\\square\\;\\square\\;\\square\\;\\square\\) Katie says for every one circle there are two squares\n\\(\\square\\quad\\square\\quad\\square\\quad\\square\\quad\\square\\)\n\\(\\bigcirc\\bigcirc\\bigcirc\\bigcirc\\bigcirc\\)\n\\(\\square\\quad\\square\\quad\\square\\quad\\square\\quad\\square\\) Who is correct? Only Katie" }, { "from": "gpt", "value": "Is not able to spot a proportional relationship pictorially unless they are laid out in groups" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio Tom says for every one circle there are two squares \n\\(\\bigcirc\\bigcirc\\bigcirc\\)\n\\(\\square\\;\\square\\;\\square\\;\\square\\;\\square\\;\\square\\) Katie says for every one circle there are two squares\n\\(\\square\\quad\\square\\quad\\square\\quad\\square\\quad\\square\\)\n\\(\\bigcirc\\bigcirc\\bigcirc\\bigcirc\\bigcirc\\)\n\\(\\square\\quad\\square\\quad\\square\\quad\\square\\quad\\square\\) Who is correct? Neither is correct" }, { "from": "gpt", "value": "Does not believe you can scale up a proportional statement" } ]

[ { "from": "human", "value": "Multiplication law of indices with positive integer powers and a different base number Jo and Paul are discussing \\( 3^{2} \\times 4^{2} \\)\nJo says \\( 3^{2} \\times 4^{2}=12^{4} \\)\nPaul says \\( 3^{2} \\times 4^{2}=12^{2} \\)\nWho is correct? Only\nJo" }, { "from": "gpt", "value": "When multiplying numbers with different bases, multiplies the powers and multiplies the base numbers." } ]

[ { "from": "human", "value": "Multiplication law of indices with positive integer powers and a different base number Jo and Paul are discussing \\( 3^{2} \\times 4^{2} \\)\nJo says \\( 3^{2} \\times 4^{2}=12^{4} \\)\nPaul says \\( 3^{2} \\times 4^{2}=12^{2} \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not realise that multiplication can be broken down into factors" } ]

[ { "from": "human", "value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n32, \\quad 28, \\quad 24, \\quad \\ldots\n\\] \\( 4 \\)" }, { "from": "gpt", "value": "Identifies the term-to-term rule rather than the next term in a sequence" } ]

[ { "from": "human", "value": "Identify cross sections of 3D shapes This is the uniform cross-section of solid \\( Q \\).\n\nWhich of the following could shape \\( Q \\) be? ![A rectangle.]() Rectangle" }, { "from": "gpt", "value": "Does not know that a solid is a 3D shape" } ]

[ { "from": "human", "value": "Identify cross sections of 3D shapes This is the uniform cross-section of solid \\( Q \\).\n\nWhich of the following could shape \\( Q \\) be? ![A rectangle.]() Cube" }, { "from": "gpt", "value": "Mixes up cubes and cuboids" } ]

[ { "from": "human", "value": "Identify cross sections of 3D shapes This is the uniform cross-section of solid \\( Q \\).\n\nWhich of the following could shape \\( Q \\) be? ![A rectangle.]() Cylinder" }, { "from": "gpt", "value": "Does not know the meaning of uniform cross section" } ]

[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number \\( \\begin{array}{llllll}\\frac{8}{10} & \\frac{41}{50} & \\frac{7}{20} & 0.77 & \\frac{4}{5} & \\frac{79}{100}\\end{array} \\) Which value is the outlier in this set of data? \\( \\frac{41}{50} \\)" }, { "from": "gpt", "value": "Believes an outlier is a value that does not fit the same characteristics as the other values" } ]

[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number \\( \\begin{array}{llllll}\\frac{8}{10} & \\frac{41}{50} & \\frac{7}{20} & 0.77 & \\frac{4}{5} & \\frac{79}{100}\\end{array} \\) Which value is the outlier in this set of data? \\( 0.77 \\)" }, { "from": "gpt", "value": "Believes an outlier is a value that does not fit the same characteristics as the other values" } ]