bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Count a number of objects \\[\n1,3,6,10, \\ldots \\text { ? }\n\\]\n\nWhich pattern matches the sequence above? ![The square numbers represented by green circles arranged into squares.]()" }, { "from": "gpt", "value": "When given a linear sequence, cannot match it to a visual pattern" } ]
[ { "from": "human", "value": "Count a number of objects \\[\n1,3,6,10, \\ldots \\text { ? }\n\\]\n\nWhich pattern matches the sequence above? ![The cube numbers represented by small, pale, blue cubes arranged into larger cubes]()" }, { "from": "gpt", "value": "When given a linear sequence, cannot match it to a visual pattern" } ]
[ { "from": "human", "value": "Count a number of objects \\[\n1,3,6,10, \\ldots \\text { ? }\n\\]\n\nWhich pattern matches the sequence above? ![A sequence represented using red circles arranged in a pattern so that the first term has one red dot and then an additional two dots are added underneath this one red dot for the second term. For the third term another two red dots are added underneath and for the fourth term, two more added underneath the previous pattern.]()" }, { "from": "gpt", "value": "Uses only the first two terms of a sequence to work out a term-to-term rule" } ]
[ { "from": "human", "value": "Raise a positive integer to a positive integer power Tom and Katie are arguing about powers.\n\\( m \\) and \\( n \\) are integers\n\nTom says there is no value of \\( m \\) that means \\( 2^{m} \\) ends in \\( 0 \\).\nKatie says there is no value of \\( n \\) that means \\( 5^{n} \\) ends in \\( 0 \\).\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Raise a positive integer to a positive integer power Tom and Katie are arguing about powers.\n\\( m \\) and \\( n \\) are integers\n\nTom says there is no value of \\( m \\) that means \\( 2^{m} \\) ends in \\( 0 \\).\nKatie says there is no value of \\( n \\) that means \\( 5^{n} \\) ends in \\( 0 \\).\nWho is correct? Only\nKatie" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Raise a positive integer to a positive integer power Tom and Katie are arguing about powers.\n\\( m \\) and \\( n \\) are integers\n\nTom says there is no value of \\( m \\) that means \\( 2^{m} \\) ends in \\( 0 \\).\nKatie says there is no value of \\( n \\) that means \\( 5^{n} \\) ends in \\( 0 \\).\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Use direct proportion to solve unitary missing amounts in problems (e.g. recipes) Eight bottles of water cost \\( £ 3.60 \\).\n\nHow much does one bottle of water cost? \\( £ 28.80 \\)" }, { "from": "gpt", "value": "Multiplies up without finding unit price in proportion question" } ]
[ { "from": "human", "value": "Use direct proportion to solve unitary missing amounts in problems (e.g. recipes) Eight bottles of water cost \\( £ 3.60 \\).\n\nHow much does one bottle of water cost? \\( £ 3.53 \\)" }, { "from": "gpt", "value": "Subtracts rather than dividing to find unit price" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is greater than 100 What is \\( 120 \\% \\) of \\( 50 \\) ? \\( 10 \\)" }, { "from": "gpt", "value": "Found the percentage but forgot to add to 100%" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is greater than 100 What is \\( 120 \\% \\) of \\( 50 \\) ? \\( 70 \\)" }, { "from": "gpt", "value": "Added the values together instead of finding the percentage" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is greater than 100 What is \\( 120 \\% \\) of \\( 50 \\) ? You cannot have percentages greater than \\( 100 \\)" }, { "from": "gpt", "value": "Does not understand that you can have percentages greater than 100%" } ]
[ { "from": "human", "value": "Carry out division problems involving two negative integers \\( (-3) \\div(-5)= \\) \\( -0.6 \\)" }, { "from": "gpt", "value": "Believes dividing a negative by a negative gives a negative answer" } ]
[ { "from": "human", "value": "Calculate a positive fractional gradient between two coordinates where all values are positive Max is working out the gradient between these two points. He has worked out the lengths of the triangle.\nWhat is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]() \\( 3 \\)" }, { "from": "gpt", "value": "Believes gradient is the difference between the change in x and the change in y" } ]
[ { "from": "human", "value": "Calculate a positive fractional gradient between two coordinates where all values are positive Max is working out the gradient between these two points. He has worked out the lengths of the triangle.\nWhat is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]() \\( 2 \\)" }, { "from": "gpt", "value": "Believes gradient = change in x/change in y" } ]
[ { "from": "human", "value": "Calculate a positive fractional gradient between two coordinates where all values are positive Max is working out the gradient between these two points. He has worked out the lengths of the triangle.\nWhat is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]() \\( 18 \\)" }, { "from": "gpt", "value": "Believes gradient = change in y multiplied by change in x" } ]
[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give no real solutions.\nWhich one? \\( \\frac{-6 \\pm \\sqrt{12}}{-3} \\)" }, { "from": "gpt", "value": "Believes the discriminant must be a perfect square for an equation to have real solutions" } ]
[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give no real solutions.\nWhich one? \\( \\frac{-6 \\pm \\sqrt{1200}}{3} \\)" }, { "from": "gpt", "value": "Believes the discriminant must be a perfect square for an equation to have real solutions" } ]
[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give no real solutions.\nWhich one? \\( \\frac{-6 \\pm \\sqrt{0}}{3} \\)" }, { "from": "gpt", "value": "Believes that a discriminant of 0 means there are no real solutions" } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"−3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2p − 3\" written inside it.\nThe first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"−3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(p − 3)\" written inside it.\n]()" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"−3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2p − 3\" written inside it.\n The second function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"✕ 2\" written inside the next rectangle, \"−3\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(p − 3)\" written inside it.]()" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine Which of the following pairs of function machines are correct? ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"−3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2p − 3\" written inside it.\n The second function machine has \"p\" written inside the first rectangle on the left and \"input\" written above it; it has \"−3\" written inside the next rectangle, \"✕ 2\" written inside the next rectangle and the final rectangle on the right has \"output\" written above it and \"2(p − 3)\" written inside it.]()" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "Find the whole amount given a percentage of the amount mentally What should replace the star? ![A number line from 0% to 100% with 20% labelled with 90 and a star above the 100%]() \\( 18 \\)" }, { "from": "gpt", "value": "Identifies the wrong part of a fraction model as the whole" } ]
[ { "from": "human", "value": "Identify whether two shapes are similar or not Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]() Only Tom" }, { "from": "gpt", "value": "Does not understand that similar shapes sides must all have the same scale factor" } ]
[ { "from": "human", "value": "Identify whether two shapes are similar or not Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]() Only Katie" }, { "from": "gpt", "value": "Thinks adding the same value to each side makes shapes similar" } ]
[ { "from": "human", "value": "Identify whether two shapes are similar or not Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]() Both Tom and Katie" }, { "from": "gpt", "value": "Does not understand that similar shapes sides must all have the same scale factor" } ]
[ { "from": "human", "value": "Convert between cm and m How should you write \\( 5 \\) kilometres and \\( 7 \\) centimetres in metres? \\( 5070 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Incorrectly converted cm to m" } ]
[ { "from": "human", "value": "Convert between cm and m How should you write \\( 5 \\) kilometres and \\( 7 \\) centimetres in metres? \\( 5007 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Has forgotten to convert cm to m" } ]
[ { "from": "human", "value": "Convert between cm and m How should you write \\( 5 \\) kilometres and \\( 7 \\) centimetres in metres? \\( 5700 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Incorrectly converted cm to m" } ]
[ { "from": "human", "value": "Multiply a single term over a bracket where the term on the outside contains a letter and the inside contains a linear expression Multiply out the brackets: \\( m(2 m-7) \\) \\( 3 m-7 \\)" }, { "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 contains a letter and the inside contains a linear expression Multiply out the brackets: \\( m(2 m-7) \\) \\( 2 m^{2}-7 \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]
[ { "from": "human", "value": "Multiply a single term over a bracket where the term on the outside contains a letter and the inside contains a linear expression Multiply out the brackets: \\( m(2 m-7) \\) \\( 3 m-7 m \\)" }, { "from": "gpt", "value": "Believes you add the terms together when multiplying like terms." } ]
[ { "from": "human", "value": "Add decimals with the same number of decimals places \\( 0.8+0.2= \\) \\( 10 \\)" }, { "from": "gpt", "value": "When adding decimals, just adds the digits and ignores place value" } ]
[ { "from": "human", "value": "Add decimals with the same number of decimals places \\( 0.8+0.2= \\) \\( 0.10 \\)" }, { "from": "gpt", "value": "When adding, just writes the digit to the right of the number without considering place value" } ]
[ { "from": "human", "value": "Add decimals with the same number of decimals places \\( 0.8+0.2= \\) \\( 0.1 \\)" }, { "from": "gpt", "value": "When two digits sum to 10 or more during addition of decimals, does not carry across decimal point to preceding digit." } ]
[ { "from": "human", "value": "Identify and count the faces, vertices and edges of a 3D shape How many faces does this shape have? ![\\( \\theta \\)]() \\( 2 \\)" }, { "from": "gpt", "value": "Confuses the terms faces and edges" } ]
[ { "from": "human", "value": "Interpret a bar chart ![A bar chart with blue vertical bars. The x-axis is titled \"Fruits\" and the y-axis is titled \"Number of Children\" and its scale is from 0 to 50 in steps of 10. The bars represent the following numbers of children: Banana, 30; Apple, 20; Kiwi Fruits, 30; Orange, 35; Pineapple, 10.]() \\begin{tabular}{\|c\|c\|}\n\\hline\nType of Fruit & Number of Children\\\\\n\\hline Banana & \\( \\) \\\\\n\\hline Apple & \\( 20 \\) \\\\\n\\hline Kiwi & \\( 30 \\) \\\\\n\\hline Orange & \\( \\) \\\\\n\\hline Pineapple & \\( 10 \\) \\\\\n\\hline\n\\end{tabular} Using the bar chart, what two numbers are missing from the table? \\( 30 \\) and \\( 40 \\)" }, { "from": "gpt", "value": "When reading graph, chooses nearest marked value on axis instead of reading accurately" } ]
[ { "from": "human", "value": "For a given input find the output of a function machine Here is a function machine Input \\( \\longrightarrow \\times 5 \\longrightarrow-1 \\quad \\longrightarrow \\) Output What is the output when the input is \\( 9 ? \\) \\( 2 \\)" }, { "from": "gpt", "value": "When using a function machine, confuses the input and the output." } ]
[ { "from": "human", "value": "For a given input find the output of a function machine Here is a function machine Input \\( \\longrightarrow \\times 5 \\longrightarrow-1 \\quad \\longrightarrow \\) Output What is the output when the input is \\( 9 ? \\) \\( 40 \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "For a given input find the output of a function machine Here is a function machine Input \\( \\longrightarrow \\times 5 \\longrightarrow-1 \\quad \\longrightarrow \\) Output What is the output when the input is \\( 9 ? \\) \\( 36 \\)" }, { "from": "gpt", "value": "In a function machine, confuses the first operation and the input" } ]
[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using long multiplication What is a correct way to set up this problem to solve it using long multiplication?\n\\[\n128 \\times 26\n\\] ![128 multiplied by 26 set out to perform long multiplication. 26 is written under 128. The 2 of 26 is under the 1 of 128 and the 6 of 26 is under the 2 of 128.]()" }, { "from": "gpt", "value": "Hasn't lined up the place value columns when writing out the calculation" } ]
[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using long multiplication What is a correct way to set up this problem to solve it using long multiplication?\n\\[\n128 \\times 26\n\\] ![128 multiplied by 26 set out to perform long multiplication. 128 is written in 3 columns with 100 in the first column, 20 in the second column and 8 in the third column. 26 is written underneath this, with 20 under 20 and 6 under 8.]()" }, { "from": "gpt", "value": "Has partitioned the digits when doing long multiplication" } ]
[ { "from": "human", "value": "Find missing angles on parallel lines using more than one angle fact Jane is trying to find the angles \\( x \\) and \\( y \\). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]() \\[\nx=103\\degree\\]\nas alternate angles" }, { "from": "gpt", "value": "Does not know the meaning of alternate" } ]
[ { "from": "human", "value": "Find missing angles on parallel lines using more than one angle fact Jane is trying to find the angles \\( x \\) and \\( y \\). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]() \\[\ny=65\\degree\n\\]\nas alternate angles" }, { "from": "gpt", "value": "Does not know the meaning of alternate" } ]
[ { "from": "human", "value": "Find missing angles on parallel lines using more than one angle fact Jane is trying to find the angles \\( x \\) and \\( y \\). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]() Both steps are incorrect" }, { "from": "gpt", "value": "Does not know the meaning of alternate" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as a single fraction, giving your answer as simply as possible: \\( \\frac{4 t^{2}-4 t-48}{8} \\times \\frac{2}{t-4} \\) \\( \\frac{t^{2}-t-12}{t-4} \\)" }, { "from": "gpt", "value": "When simplifying an algebraic fraction, only looks for number factors" } ]
[ { "from": "human", "value": "Identify where negative non-integers lie on a number line Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with \"-6\", the 3rd dash is labelled \"-4\", the 5th dash is labelled \"-2\", the 7th dash is labelled \"0\", the 9th dash is labelled \"2\", the 11th dash is labelled \"4\" and the 13th dash is labelled \"6\" A red arrow, labelled with a question mark is pointing halfway between the 6th and 7th dashes. ]() Which of the following numbers could be indicated by the arrow? \\( -1.5 \\)" }, { "from": "gpt", "value": "Counts on in the wrong direction on a number line" } ]
[ { "from": "human", "value": "Identify where negative non-integers lie on a number line Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with \"-6\", the 3rd dash is labelled \"-4\", the 5th dash is labelled \"-2\", the 7th dash is labelled \"0\", the 9th dash is labelled \"2\", the 11th dash is labelled \"4\" and the 13th dash is labelled \"6\" A red arrow, labelled with a question mark is pointing halfway between the 6th and 7th dashes. ]() Which of the following numbers could be indicated by the arrow? \\( -0.25 \\)" }, { "from": "gpt", "value": "Believes a quarter of 2 is 0.25" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer? \\( 3+6=9 \\)" }, { "from": "gpt", "value": "Believes a negative number can be replaced with its positive equivalent when answering an addition problem from a numberline" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer? \\( 6+9=-3 \\)" }, { "from": "gpt", "value": "Believes we move down a number line when we add" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer? \\( -3+6=9 \\)" }, { "from": "gpt", "value": "Believes the number of jumps between two numbers on a numberline represents the sum of those 2 numbers " } ]
[ { "from": "human", "value": "Use facts about interior angles in triangles with algebra to solve equations Find the value of \\( x \\). ![A triangle with the angles labelled: 4x, 2x - 12 and 4x + 42]() \\( x=33^{\\circ} \\)" }, { "from": "gpt", "value": "Believes angles in a triangle sum to 360 degrees" } ]
[ { "from": "human", "value": "Use facts about interior angles in triangles with algebra to solve equations Find the value of \\( x \\). ![A triangle with the angles labelled: 4x, 2x - 12 and 4x + 42]() \\( x=21^{\\circ} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Understand the non-commutativity of division Miran says the following:\n\n\"It doesn't matter if you do \\( \\mathbf{7} \\div \\mathbf{1 4 0} \\) or \\( \\mathbf{1 4 0} \\div \\mathbf{7} \\), you get the same answer\"\n\nWhat do you think? Miran is correct because division is commutative" }, { "from": "gpt", "value": "Believes division is commutative " } ]
[ { "from": "human", "value": "Understand the non-commutativity of division Miran says the following:\n\n\"It doesn't matter if you do \\( \\mathbf{7} \\div \\mathbf{1 4 0} \\) or \\( \\mathbf{1 4 0} \\div \\mathbf{7} \\), you get the same answer\"\n\nWhat do you think? Miran is incorrect because division is commutative" }, { "from": "gpt", "value": "Does not understand the meaning of the word commutative " } ]
[ { "from": "human", "value": "Understand the non-commutativity of division Miran says the following:\n\n\"It doesn't matter if you do \\( \\mathbf{7} \\div \\mathbf{1 4 0} \\) or \\( \\mathbf{1 4 0} \\div \\mathbf{7} \\), you get the same answer\"\n\nWhat do you think? Miran is correct because division is not commutative" }, { "from": "gpt", "value": "Does not understand the meaning of the word commutative " } ]
[ { "from": "human", "value": "Identify a unit of area Tom and Katie are discussing units of area\nTom says centimetres is a unit of area\nKatie says \\( \\mathrm{mm}^{2} \\) is a unit of area\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]
[ { "from": "human", "value": "Identify a unit of area Tom and Katie are discussing units of area\nTom says centimetres is a unit of area\nKatie says \\( \\mathrm{mm}^{2} \\) is a unit of area\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]
[ { "from": "human", "value": "Identify a unit of area Tom and Katie are discussing units of area\nTom says centimetres is a unit of area\nKatie says \\( \\mathrm{mm}^{2} \\) is a unit of area\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]
[ { "from": "human", "value": "Solve comparison, sum and difference problems using information presented in pictograms This pictogram shows the different types of music Bob has in his music collection.\n\nHow many more Pop CDs does Bob have than Rock CDs? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]() \\( 4.5 \\)" }, { "from": "gpt", "value": "When counting partial symbols on pictogram, uses the fraction rather than the amount it represents" } ]
[ { "from": "human", "value": "Solve comparison, sum and difference problems using information presented in pictograms This pictogram shows the different types of music Bob has in his music collection.\n\nHow many more Pop CDs does Bob have than Rock CDs? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]() \\( 1.5 \\)" }, { "from": "gpt", "value": "When interpreting a pictogram, thinks each symbol stands for 1" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer What number belongs in the box?\n\\(\n(-11)+7=\n\\square\\) \\( -18 \\)" }, { "from": "gpt", "value": "Counts on in the wrong direction on a number line" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer What number belongs in the box?\n\\(\n(-11)+7=\n\\square\\) \\( -5 \\)" }, { "from": "gpt", "value": "Counts the starting number when counting on" } ]
[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = c - x This is a part of the table of values for the equation\n\\[\ny=6-x\n\\] \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\( \\bigstar \\) \\\\\n\\hline\\( y \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 14 \\)" }, { "from": "gpt", "value": "Believes subtraction is commutative " } ]
[ { "from": "human", "value": "Calculate unit fractions of an amount \\( \\frac{1}{8} \\) th of an hour \\( = _______ \\) minutes \\( 12.5 \\)" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and BC.]() BCA" }, { "from": "gpt", "value": "Chooses the wrong 3 letters to describe an angle" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and BC.]() CDB" }, { "from": "gpt", "value": "Gives 3-letter angle notation in the wrong order" } ]
[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and BC.]() None of these options" }, { "from": "gpt", "value": "Thinks 3-letter angle notation has to use the nearest vertex on each side of the angle" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the denominator Simplify the following: \\( \\frac{9 y^{3}}{6 y^{2}+3 y} \\) \\( \\frac{9 y^{2}}{6 y+3} \\)" }, { "from": "gpt", "value": "Does not fully simplify fraction" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the denominator Simplify the following: \\( \\frac{9 y^{3}}{6 y^{2}+3 y} \\) \\( \\frac{3 y}{2+y} \\)" }, { "from": "gpt", "value": "Thinks you can divide terms by different factors when simplifying an algebraic fraction" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the denominator Simplify the following: \\( \\frac{9 y^{3}}{6 y^{2}+3 y} \\) \\( \\frac{3 y^{3}}{2 y^{2}+3 y} \\)" }, { "from": "gpt", "value": "Thinks you can divide terms by different factors when simplifying an algebraic fraction" } ]
[ { "from": "human", "value": "Find the area of rectilinear shapes by counting squares What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]() The red square has a larger area" }, { "from": "gpt", "value": "Counts half-squares as full squares when calculating area on a square grid" } ]
[ { "from": "human", "value": "Find the area of rectilinear shapes by counting squares What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]() The areas are the same" }, { "from": "gpt", "value": "Thinks the diagonal of a square is the same length as the side of the square" } ]
[ { "from": "human", "value": "Find the area of rectilinear shapes by counting squares What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]() It is impossible to say without measuring" }, { "from": "gpt", "value": "Does not know how to find area by counting squares on a grid" } ]
[ { "from": "human", "value": "Calculate the area of a rectangle where the dimensions are given in the same units What is the area of this rectangle? ![A rectangle, 5cm by 12cm]() \\( 17 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]
[ { "from": "human", "value": "Calculate the area of a rectangle where the dimensions are given in the same units What is the area of this rectangle? ![A rectangle, 5cm by 12cm]() \\( 34 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Calculates perimeter when asked for area" } ]
[ { "from": "human", "value": "Calculate the area of a rectangle where the dimensions are given in the same units What is the area of this rectangle? ![A rectangle, 5cm by 12cm]() Not enough information" }, { "from": "gpt", "value": "Does not recall rectangle side length property" } ]
[ { "from": "human", "value": "Convert percentages containing 1 decimal place to fractions How do you write \\( 0.5 \\% \\) as a fraction? \\( \\frac{1}{2} \\)" }, { "from": "gpt", "value": "Assumes that converting a decimal percentage to a fraction, they can just convert the decimal to a fraction, instead of writing the decimal over 100." } ]
[ { "from": "human", "value": "Convert percentages containing 1 decimal place to fractions How do you write \\( 0.5 \\% \\) as a fraction? \\( \\frac{1}{20} \\)" }, { "from": "gpt", "value": "Assumes decimal point can be ignored when given a decimal percentage to convert to a fraction" } ]
[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b When Aaron completes the square, what should replace the star? \\( p^{2}-p-1 \\equiv(p \\bigstar )^{2} \\triangle \\) \\(\\bigstar =-2 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is double the coefficient of x" } ]
[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b When Aaron completes the square, what should replace the star? \\( p^{2}-p-1 \\equiv(p \\bigstar )^{2} \\triangle \\) \\(\\bigstar =-1 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is the coefficient of x" } ]
[ { "from": "human", "value": "Given the number of sides of a polygon identify the name If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]() An octagon" }, { "from": "gpt", "value": "Confuses octagon and pentagon" } ]
[ { "from": "human", "value": "Given the number of sides of a polygon identify the name If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]() A hexagon" }, { "from": "gpt", "value": "Confuses pentagon and hexagon" } ]
[ { "from": "human", "value": "Given the number of sides of a polygon identify the name If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]() A circle" }, { "from": "gpt", "value": "Does not know the meaning of the word regular " } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\n\\(\nh^{2}=\n\\) \\( 10 \\)" }, { "from": "gpt", "value": "Multiplies by the index" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\n\\(\nh^{2}=\n\\) \\( 7 \\)" }, { "from": "gpt", "value": "Believes squaring is the same as adding two" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\n\\(\nh^{2}=\n\\) \\( 52 \\)" }, { "from": "gpt", "value": "Writes the index as a digit on the end of a number" } ]
[ { "from": "human", "value": "Add surds in the form va + vb \\(\n\\sqrt{3}+\\sqrt{5}\n\\)\n\nSimplify, if possible. \\( 3 \\sqrt{5} \\)" }, { "from": "gpt", "value": "When adding or subtracting surds, simplifies the surds correctly but puts the digits in the answer the wrong way round" } ]
[ { "from": "human", "value": "Add surds in the form va + vb \\(\n\\sqrt{3}+\\sqrt{5}\n\\)\n\nSimplify, if possible. \\( \\sqrt{8} \\)" }, { "from": "gpt", "value": "When adding or subtracting surds, just adds or subtracts the numbers under the surd rather than first trying to simplifying to find like surds" } ]
[ { "from": "human", "value": "Add surds in the form va + vb \\(\n\\sqrt{3}+\\sqrt{5}\n\\)\n\nSimplify, if possible. \\( \\sqrt{15} \\)" }, { "from": "gpt", "value": "When adding surds, just multiplies the numbers under the surd rather than first trying to simplifying to find like surds" } ]
[ { "from": "human", "value": "Use area to write algebraic expressions The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nWhich of the following equations can we write from the information given? ![A rectangle with the short side labelled \\(x\\) and the opposite side labelled \\(x^2 + 9\\).]() \\( x^{3}+9=8 \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]
[ { "from": "human", "value": "Use area to write algebraic expressions The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nWhich of the following equations can we write from the information given? ![A rectangle with the short side labelled \\(x\\) and the opposite side labelled \\(x^2 + 9\\).]() \\( x^{2}+x+9=8 \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]
[ { "from": "human", "value": "Use area to write algebraic expressions The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nWhich of the following equations can we write from the information given? ![A rectangle with the short side labelled \\(x\\) and the opposite side labelled \\(x^2 + 9\\).]() \\( 2 x^{2}+2 x+18=8 \\)" }, { "from": "gpt", "value": "Calculates perimeter when asked for area" } ]
[ { "from": "human", "value": "Know the exact value of tan(30), tan(45) and tan(60) What is the exact value of \\( \\tan (30) \\) ? \\( \\sqrt{3} \\)" }, { "from": "gpt", "value": "Misremembers the exact values of trigonometric functions at standard angles" } ]
[ { "from": "human", "value": "Know the exact value of tan(30), tan(45) and tan(60) What is the exact value of \\( \\tan (30) \\) ? \\( \\frac{\\sqrt{3}}{2} \\)" }, { "from": "gpt", "value": "Misremembers the exact values of trigonometric functions at standard angles" } ]
[ { "from": "human", "value": "Know the exact value of tan(30), tan(45) and tan(60) What is the exact value of \\( \\tan (30) \\) ? \\( \\frac{1}{2} \\)" }, { "from": "gpt", "value": "Misremembers the exact values of trigonometric functions at standard angles" } ]
[ { "from": "human", "value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Amy is trying to work out the distance between these two points: \\( (2,-5) \\) and \\( (-7,1) \\) She labels them like this: \\( \\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (2, & -5) & (-7, & 1)\\end{array} \\) And then decides to use this formula: \\( \\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}} \\) \\( \\sqrt{(-9)^{2}+(6)^{2}} \\) What is the distance between the points? \\( -\\sqrt{45} \\)" }, { "from": "gpt", "value": "Believes the square of a negative will also be negative" } ]
[ { "from": "human", "value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( V=\\frac{1}{3} \\pi r^{2} h \\) ![A cone, with the dimensions labelled h and r]() Equation" }, { "from": "gpt", "value": "Confuses a formula with an equation" } ]
[ { "from": "human", "value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( V=\\frac{1}{3} \\pi r^{2} h \\) ![A cone, with the dimensions labelled h and r]() Variable" }, { "from": "gpt", "value": "Confuses a variable with a formula" } ]
[ { "from": "human", "value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( V=\\frac{1}{3} \\pi r^{2} h \\) ![A cone, with the dimensions labelled h and r]() Expression" }, { "from": "gpt", "value": "Confuses a formula with an expression" } ]
[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed Rearrange the following equation to make \\( v \\) the subject\n\\(F=\\frac{v^{2}}{r}\\) \\( v=r F^{2} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Count a number of objects \\[\n1,3,6,10, \\ldots \\text { ? }\n\\]\n\nWhich pattern matches the sequence above? ![The square numbers represented by green circles arranged into squares.]()" }, { "from": "gpt", "value": "When given a linear sequence, cannot match it to a visual pattern" } ]

[ { "from": "human", "value": "Count a number of objects \\[\n1,3,6,10, \\ldots \\text { ? }\n\\]\n\nWhich pattern matches the sequence above? ![The cube numbers represented by small, pale, blue cubes arranged into larger cubes]()" }, { "from": "gpt", "value": "When given a linear sequence, cannot match it to a visual pattern" } ]

[ { "from": "human", "value": "Count a number of objects \\[\n1,3,6,10, \\ldots \\text { ? }\n\\]\n\nWhich pattern matches the sequence above? ![A sequence represented using red circles arranged in a pattern so that the first term has one red dot and then an additional two dots are added underneath this one red dot for the second term. For the third term another two red dots are added underneath and for the fourth term, two more added underneath the previous pattern.]()" }, { "from": "gpt", "value": "Uses only the first two terms of a sequence to work out a term-to-term rule" } ]

[ { "from": "human", "value": "Raise a positive integer to a positive integer power Tom and Katie are arguing about powers.\n\\( m \\) and \\( n \\) are integers\n\nTom says there is no value of \\( m \\) that means \\( 2^{m} \\) ends in \\( 0 \\).\nKatie says there is no value of \\( n \\) that means \\( 5^{n} \\) ends in \\( 0 \\).\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Raise a positive integer to a positive integer power Tom and Katie are arguing about powers.\n\\( m \\) and \\( n \\) are integers\n\nTom says there is no value of \\( m \\) that means \\( 2^{m} \\) ends in \\( 0 \\).\nKatie says there is no value of \\( n \\) that means \\( 5^{n} \\) ends in \\( 0 \\).\nWho is correct? Only\nKatie" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Raise a positive integer to a positive integer power Tom and Katie are arguing about powers.\n\\( m \\) and \\( n \\) are integers\n\nTom says there is no value of \\( m \\) that means \\( 2^{m} \\) ends in \\( 0 \\).\nKatie says there is no value of \\( n \\) that means \\( 5^{n} \\) ends in \\( 0 \\).\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Use direct proportion to solve unitary missing amounts in problems (e.g. recipes) Eight bottles of water cost \\( £ 3.60 \\).\n\nHow much does one bottle of water cost? \\( £ 28.80 \\)" }, { "from": "gpt", "value": "Multiplies up without finding unit price in proportion question" } ]

[ { "from": "human", "value": "Use direct proportion to solve unitary missing amounts in problems (e.g. recipes) Eight bottles of water cost \\( £ 3.60 \\).\n\nHow much does one bottle of water cost? \\( £ 3.53 \\)" }, { "from": "gpt", "value": "Subtracts rather than dividing to find unit price" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is greater than 100 What is \\( 120 \\% \\) of \\( 50 \\) ? \\( 10 \\)" }, { "from": "gpt", "value": "Found the percentage but forgot to add to 100%" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is greater than 100 What is \\( 120 \\% \\) of \\( 50 \\) ? \\( 70 \\)" }, { "from": "gpt", "value": "Added the values together instead of finding the percentage" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is greater than 100 What is \\( 120 \\% \\) of \\( 50 \\) ? You cannot have percentages greater than \\( 100 \\)" }, { "from": "gpt", "value": "Does not understand that you can have percentages greater than 100%" } ]

[ { "from": "human", "value": "Carry out division problems involving two negative integers \\( (-3) \\div(-5)= \\) \\( -0.6 \\)" }, { "from": "gpt", "value": "Believes dividing a negative by a negative gives a negative answer" } ]

[ { "from": "human", "value": "Calculate a positive fractional gradient between two coordinates where all values are positive Max is working out the gradient between these two points. He has worked out the lengths of the triangle.\nWhat is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]() \\( 3 \\)" }, { "from": "gpt", "value": "Believes gradient is the difference between the change in x and the change in y" } ]

[ { "from": "human", "value": "Calculate a positive fractional gradient between two coordinates where all values are positive Max is working out the gradient between these two points. He has worked out the lengths of the triangle.\nWhat is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]() \\( 2 \\)" }, { "from": "gpt", "value": "Believes gradient = change in x/change in y" } ]

[ { "from": "human", "value": "Calculate a positive fractional gradient between two coordinates where all values are positive Max is working out the gradient between these two points. He has worked out the lengths of the triangle.\nWhat is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]() \\( 18 \\)" }, { "from": "gpt", "value": "Believes gradient = change in y multiplied by change in x" } ]

[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give no real solutions.\nWhich one? \\( \\frac{-6 \\pm \\sqrt{12}}{-3} \\)" }, { "from": "gpt", "value": "Believes the discriminant must be a perfect square for an equation to have real solutions" } ]

[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give no real solutions.\nWhich one? \\( \\frac{-6 \\pm \\sqrt{1200}}{3} \\)" }, { "from": "gpt", "value": "Believes the discriminant must be a perfect square for an equation to have real solutions" } ]

[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give no real solutions.\nWhich one? \\( \\frac{-6 \\pm \\sqrt{0}}{3} \\)" }, { "from": "gpt", "value": "Believes that a discriminant of 0 means there are no real solutions" } ]

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

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

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

[ { "from": "human", "value": "Find the whole amount given a percentage of the amount mentally What should replace the star? ![A number line from 0% to 100% with 20% labelled with 90 and a star above the 100%]() \\( 18 \\)" }, { "from": "gpt", "value": "Identifies the wrong part of a fraction model as the whole" } ]

[ { "from": "human", "value": "Identify whether two shapes are similar or not Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]() Only Tom" }, { "from": "gpt", "value": "Does not understand that similar shapes sides must all have the same scale factor" } ]

[ { "from": "human", "value": "Identify whether two shapes are similar or not Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]() Only Katie" }, { "from": "gpt", "value": "Thinks adding the same value to each side makes shapes similar" } ]

[ { "from": "human", "value": "Identify whether two shapes are similar or not Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]() Both Tom and Katie" }, { "from": "gpt", "value": "Does not understand that similar shapes sides must all have the same scale factor" } ]

[ { "from": "human", "value": "Convert between cm and m How should you write \\( 5 \\) kilometres and \\( 7 \\) centimetres in metres? \\( 5070 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Incorrectly converted cm to m" } ]

[ { "from": "human", "value": "Convert between cm and m How should you write \\( 5 \\) kilometres and \\( 7 \\) centimetres in metres? \\( 5007 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Has forgotten to convert cm to m" } ]

[ { "from": "human", "value": "Convert between cm and m How should you write \\( 5 \\) kilometres and \\( 7 \\) centimetres in metres? \\( 5700 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Incorrectly converted cm to m" } ]

[ { "from": "human", "value": "Multiply a single term over a bracket where the term on the outside contains a letter and the inside contains a linear expression Multiply out the brackets: \\( m(2 m-7) \\) \\( 3 m-7 \\)" }, { "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 contains a letter and the inside contains a linear expression Multiply out the brackets: \\( m(2 m-7) \\) \\( 2 m^{2}-7 \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]

[ { "from": "human", "value": "Multiply a single term over a bracket where the term on the outside contains a letter and the inside contains a linear expression Multiply out the brackets: \\( m(2 m-7) \\) \\( 3 m-7 m \\)" }, { "from": "gpt", "value": "Believes you add the terms together when multiplying like terms." } ]

[ { "from": "human", "value": "Add decimals with the same number of decimals places \\( 0.8+0.2= \\) \\( 10 \\)" }, { "from": "gpt", "value": "When adding decimals, just adds the digits and ignores place value" } ]

[ { "from": "human", "value": "Add decimals with the same number of decimals places \\( 0.8+0.2= \\) \\( 0.10 \\)" }, { "from": "gpt", "value": "When adding, just writes the digit to the right of the number without considering place value" } ]

[ { "from": "human", "value": "Add decimals with the same number of decimals places \\( 0.8+0.2= \\) \\( 0.1 \\)" }, { "from": "gpt", "value": "When two digits sum to 10 or more during addition of decimals, does not carry across decimal point to preceding digit." } ]

[ { "from": "human", "value": "Identify and count the faces, vertices and edges of a 3D shape How many faces does this shape have? ![\\( \\theta \\)]() \\( 2 \\)" }, { "from": "gpt", "value": "Confuses the terms faces and edges" } ]

[ { "from": "human", "value": "Interpret a bar chart ![A bar chart with blue vertical bars. The x-axis is titled \"Fruits\" and the y-axis is titled \"Number of Children\" and its scale is from 0 to 50 in steps of 10. The bars represent the following numbers of children: Banana, 30; Apple, 20; Kiwi Fruits, 30; Orange, 35; Pineapple, 10.]() \\begin{tabular}{|c|c|}\n\\hline\nType of Fruit & Number of Children\\\\\n\\hline Banana & \\( \\) \\\\\n\\hline Apple & \\( 20 \\) \\\\\n\\hline Kiwi & \\( 30 \\) \\\\\n\\hline Orange & \\( \\) \\\\\n\\hline Pineapple & \\( 10 \\) \\\\\n\\hline\n\\end{tabular} Using the bar chart, what two numbers are missing from the table? \\( 30 \\) and \\( 40 \\)" }, { "from": "gpt", "value": "When reading graph, chooses nearest marked value on axis instead of reading accurately" } ]

[ { "from": "human", "value": "For a given input find the output of a function machine Here is a function machine Input \\( \\longrightarrow \\times 5 \\longrightarrow-1 \\quad \\longrightarrow \\) Output What is the output when the input is \\( 9 ? \\) \\( 2 \\)" }, { "from": "gpt", "value": "When using a function machine, confuses the input and the output." } ]

[ { "from": "human", "value": "For a given input find the output of a function machine Here is a function machine Input \\( \\longrightarrow \\times 5 \\longrightarrow-1 \\quad \\longrightarrow \\) Output What is the output when the input is \\( 9 ? \\) \\( 40 \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "For a given input find the output of a function machine Here is a function machine Input \\( \\longrightarrow \\times 5 \\longrightarrow-1 \\quad \\longrightarrow \\) Output What is the output when the input is \\( 9 ? \\) \\( 36 \\)" }, { "from": "gpt", "value": "In a function machine, confuses the first operation and the input" } ]

[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using long multiplication What is a correct way to set up this problem to solve it using long multiplication?\n\\[\n128 \\times 26\n\\] ![128 multiplied by 26 set out to perform long multiplication. 26 is written under 128. The 2 of 26 is under the 1 of 128 and the 6 of 26 is under the 2 of 128.]()" }, { "from": "gpt", "value": "Hasn't lined up the place value columns when writing out the calculation" } ]

[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using long multiplication What is a correct way to set up this problem to solve it using long multiplication?\n\\[\n128 \\times 26\n\\] ![128 multiplied by 26 set out to perform long multiplication. 128 is written in 3 columns with 100 in the first column, 20 in the second column and 8 in the third column. 26 is written underneath this, with 20 under 20 and 6 under 8.]()" }, { "from": "gpt", "value": "Has partitioned the digits when doing long multiplication" } ]

[ { "from": "human", "value": "Find missing angles on parallel lines using more than one angle fact Jane is trying to find the angles \\( x \\) and \\( y \\). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]() \\[\nx=103\\degree\\]\nas alternate angles" }, { "from": "gpt", "value": "Does not know the meaning of alternate" } ]

[ { "from": "human", "value": "Find missing angles on parallel lines using more than one angle fact Jane is trying to find the angles \\( x \\) and \\( y \\). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]() \\[\ny=65\\degree\n\\]\nas alternate angles" }, { "from": "gpt", "value": "Does not know the meaning of alternate" } ]

[ { "from": "human", "value": "Find missing angles on parallel lines using more than one angle fact Jane is trying to find the angles \\( x \\) and \\( y \\). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]() Both steps are incorrect" }, { "from": "gpt", "value": "Does not know the meaning of alternate" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as a single fraction, giving your answer as simply as possible: \\( \\frac{4 t^{2}-4 t-48}{8} \\times \\frac{2}{t-4} \\) \\( \\frac{t^{2}-t-12}{t-4} \\)" }, { "from": "gpt", "value": "When simplifying an algebraic fraction, only looks for number factors" } ]

[ { "from": "human", "value": "Identify where negative non-integers lie on a number line Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with \"-6\", the 3rd dash is labelled \"-4\", the 5th dash is labelled \"-2\", the 7th dash is labelled \"0\", the 9th dash is labelled \"2\", the 11th dash is labelled \"4\" and the 13th dash is labelled \"6\" A red arrow, labelled with a question mark is pointing halfway between the 6th and 7th dashes. ]() Which of the following numbers could be indicated by the arrow? \\( -1.5 \\)" }, { "from": "gpt", "value": "Counts on in the wrong direction on a number line" } ]

[ { "from": "human", "value": "Identify where negative non-integers lie on a number line Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with \"-6\", the 3rd dash is labelled \"-4\", the 5th dash is labelled \"-2\", the 7th dash is labelled \"0\", the 9th dash is labelled \"2\", the 11th dash is labelled \"4\" and the 13th dash is labelled \"6\" A red arrow, labelled with a question mark is pointing halfway between the 6th and 7th dashes. ]() Which of the following numbers could be indicated by the arrow? \\( -0.25 \\)" }, { "from": "gpt", "value": "Believes a quarter of 2 is 0.25" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer? \\( 3+6=9 \\)" }, { "from": "gpt", "value": "Believes a negative number can be replaced with its positive equivalent when answering an addition problem from a numberline" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer? \\( 6+9=-3 \\)" }, { "from": "gpt", "value": "Believes we move down a number line when we add" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer? \\( -3+6=9 \\)" }, { "from": "gpt", "value": "Believes the number of jumps between two numbers on a numberline represents the sum of those 2 numbers " } ]

[ { "from": "human", "value": "Use facts about interior angles in triangles with algebra to solve equations Find the value of \\( x \\). ![A triangle with the angles labelled: 4x, 2x - 12 and 4x + 42]() \\( x=33^{\\circ} \\)" }, { "from": "gpt", "value": "Believes angles in a triangle sum to 360 degrees" } ]

[ { "from": "human", "value": "Use facts about interior angles in triangles with algebra to solve equations Find the value of \\( x \\). ![A triangle with the angles labelled: 4x, 2x - 12 and 4x + 42]() \\( x=21^{\\circ} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Understand the non-commutativity of division Miran says the following:\n\n\"It doesn't matter if you do \\( \\mathbf{7} \\div \\mathbf{1 4 0} \\) or \\( \\mathbf{1 4 0} \\div \\mathbf{7} \\), you get the same answer\"\n\nWhat do you think? Miran is correct because division is commutative" }, { "from": "gpt", "value": "Believes division is commutative " } ]

[ { "from": "human", "value": "Understand the non-commutativity of division Miran says the following:\n\n\"It doesn't matter if you do \\( \\mathbf{7} \\div \\mathbf{1 4 0} \\) or \\( \\mathbf{1 4 0} \\div \\mathbf{7} \\), you get the same answer\"\n\nWhat do you think? Miran is incorrect because division is commutative" }, { "from": "gpt", "value": "Does not understand the meaning of the word commutative " } ]

[ { "from": "human", "value": "Understand the non-commutativity of division Miran says the following:\n\n\"It doesn't matter if you do \\( \\mathbf{7} \\div \\mathbf{1 4 0} \\) or \\( \\mathbf{1 4 0} \\div \\mathbf{7} \\), you get the same answer\"\n\nWhat do you think? Miran is correct because division is not commutative" }, { "from": "gpt", "value": "Does not understand the meaning of the word commutative " } ]

[ { "from": "human", "value": "Identify a unit of area Tom and Katie are discussing units of area\nTom says centimetres is a unit of area\nKatie says \\( \\mathrm{mm}^{2} \\) is a unit of area\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]

[ { "from": "human", "value": "Identify a unit of area Tom and Katie are discussing units of area\nTom says centimetres is a unit of area\nKatie says \\( \\mathrm{mm}^{2} \\) is a unit of area\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]

[ { "from": "human", "value": "Identify a unit of area Tom and Katie are discussing units of area\nTom says centimetres is a unit of area\nKatie says \\( \\mathrm{mm}^{2} \\) is a unit of area\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not know units of area should be squared" } ]

[ { "from": "human", "value": "Solve comparison, sum and difference problems using information presented in pictograms This pictogram shows the different types of music Bob has in his music collection.\n\nHow many more Pop CDs does Bob have than Rock CDs? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]() \\( 4.5 \\)" }, { "from": "gpt", "value": "When counting partial symbols on pictogram, uses the fraction rather than the amount it represents" } ]

[ { "from": "human", "value": "Solve comparison, sum and difference problems using information presented in pictograms This pictogram shows the different types of music Bob has in his music collection.\n\nHow many more Pop CDs does Bob have than Rock CDs? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]() \\( 1.5 \\)" }, { "from": "gpt", "value": "When interpreting a pictogram, thinks each symbol stands for 1" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer What number belongs in the box?\n\\(\n(-11)+7=\n\\square\\) \\( -18 \\)" }, { "from": "gpt", "value": "Counts on in the wrong direction on a number line" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer What number belongs in the box?\n\\(\n(-11)+7=\n\\square\\) \\( -5 \\)" }, { "from": "gpt", "value": "Counts the starting number when counting on" } ]

[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = c - x This is a part of the table of values for the equation\n\\[\ny=6-x\n\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( \\bigstar \\) \\\\\n\\hline\\( y \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 14 \\)" }, { "from": "gpt", "value": "Believes subtraction is commutative " } ]

[ { "from": "human", "value": "Calculate unit fractions of an amount \\( \\frac{1}{8} \\) th of an hour \\( = _______ \\) minutes \\( 12.5 \\)" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour" } ]

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

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

[ { "from": "human", "value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it. The marked angle is between the lines CE and BC.]() None of these options" }, { "from": "gpt", "value": "Thinks 3-letter angle notation has to use the nearest vertex on each side of the angle" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the denominator Simplify the following: \\( \\frac{9 y^{3}}{6 y^{2}+3 y} \\) \\( \\frac{9 y^{2}}{6 y+3} \\)" }, { "from": "gpt", "value": "Does not fully simplify fraction" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the denominator Simplify the following: \\( \\frac{9 y^{3}}{6 y^{2}+3 y} \\) \\( \\frac{3 y}{2+y} \\)" }, { "from": "gpt", "value": "Thinks you can divide terms by different factors when simplifying an algebraic fraction" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the denominator Simplify the following: \\( \\frac{9 y^{3}}{6 y^{2}+3 y} \\) \\( \\frac{3 y^{3}}{2 y^{2}+3 y} \\)" }, { "from": "gpt", "value": "Thinks you can divide terms by different factors when simplifying an algebraic fraction" } ]

[ { "from": "human", "value": "Find the area of rectilinear shapes by counting squares What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]() The red square has a larger area" }, { "from": "gpt", "value": "Counts half-squares as full squares when calculating area on a square grid" } ]

[ { "from": "human", "value": "Find the area of rectilinear shapes by counting squares What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]() The areas are the same" }, { "from": "gpt", "value": "Thinks the diagonal of a square is the same length as the side of the square" } ]

[ { "from": "human", "value": "Find the area of rectilinear shapes by counting squares What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]() It is impossible to say without measuring" }, { "from": "gpt", "value": "Does not know how to find area by counting squares on a grid" } ]

[ { "from": "human", "value": "Calculate the area of a rectangle where the dimensions are given in the same units What is the area of this rectangle? ![A rectangle, 5cm by 12cm]() \\( 17 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]

[ { "from": "human", "value": "Calculate the area of a rectangle where the dimensions are given in the same units What is the area of this rectangle? ![A rectangle, 5cm by 12cm]() \\( 34 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Calculates perimeter when asked for area" } ]

[ { "from": "human", "value": "Calculate the area of a rectangle where the dimensions are given in the same units What is the area of this rectangle? ![A rectangle, 5cm by 12cm]() Not enough information" }, { "from": "gpt", "value": "Does not recall rectangle side length property" } ]

[ { "from": "human", "value": "Convert percentages containing 1 decimal place to fractions How do you write \\( 0.5 \\% \\) as a fraction? \\( \\frac{1}{2} \\)" }, { "from": "gpt", "value": "Assumes that converting a decimal percentage to a fraction, they can just convert the decimal to a fraction, instead of writing the decimal over 100." } ]

[ { "from": "human", "value": "Convert percentages containing 1 decimal place to fractions How do you write \\( 0.5 \\% \\) as a fraction? \\( \\frac{1}{20} \\)" }, { "from": "gpt", "value": "Assumes decimal point can be ignored when given a decimal percentage to convert to a fraction" } ]

[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b When Aaron completes the square, what should replace the star? \\( p^{2}-p-1 \\equiv(p \\bigstar )^{2} \\triangle \\) \\(\\bigstar =-2 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is double the coefficient of x" } ]

[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b When Aaron completes the square, what should replace the star? \\( p^{2}-p-1 \\equiv(p \\bigstar )^{2} \\triangle \\) \\(\\bigstar =-1 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is the coefficient of x" } ]

[ { "from": "human", "value": "Given the number of sides of a polygon identify the name If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]() An octagon" }, { "from": "gpt", "value": "Confuses octagon and pentagon" } ]

[ { "from": "human", "value": "Given the number of sides of a polygon identify the name If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]() A hexagon" }, { "from": "gpt", "value": "Confuses pentagon and hexagon" } ]

[ { "from": "human", "value": "Given the number of sides of a polygon identify the name If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]() A circle" }, { "from": "gpt", "value": "Does not know the meaning of the word regular " } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\n\\(\nh^{2}=\n\\) \\( 10 \\)" }, { "from": "gpt", "value": "Multiplies by the index" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\n\\(\nh^{2}=\n\\) \\( 7 \\)" }, { "from": "gpt", "value": "Believes squaring is the same as adding two" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\n\\(\nh^{2}=\n\\) \\( 52 \\)" }, { "from": "gpt", "value": "Writes the index as a digit on the end of a number" } ]

[ { "from": "human", "value": "Add surds in the form va + vb \\(\n\\sqrt{3}+\\sqrt{5}\n\\)\n\nSimplify, if possible. \\( 3 \\sqrt{5} \\)" }, { "from": "gpt", "value": "When adding or subtracting surds, simplifies the surds correctly but puts the digits in the answer the wrong way round" } ]

[ { "from": "human", "value": "Add surds in the form va + vb \\(\n\\sqrt{3}+\\sqrt{5}\n\\)\n\nSimplify, if possible. \\( \\sqrt{8} \\)" }, { "from": "gpt", "value": "When adding or subtracting surds, just adds or subtracts the numbers under the surd rather than first trying to simplifying to find like surds" } ]

[ { "from": "human", "value": "Add surds in the form va + vb \\(\n\\sqrt{3}+\\sqrt{5}\n\\)\n\nSimplify, if possible. \\( \\sqrt{15} \\)" }, { "from": "gpt", "value": "When adding surds, just multiplies the numbers under the surd rather than first trying to simplifying to find like surds" } ]

[ { "from": "human", "value": "Use area to write algebraic expressions The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nWhich of the following equations can we write from the information given? ![A rectangle with the short side labelled \\(x\\) and the opposite side labelled \\(x^2 + 9\\).]() \\( x^{3}+9=8 \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]

[ { "from": "human", "value": "Use area to write algebraic expressions The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nWhich of the following equations can we write from the information given? ![A rectangle with the short side labelled \\(x\\) and the opposite side labelled \\(x^2 + 9\\).]() \\( x^{2}+x+9=8 \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]

[ { "from": "human", "value": "Use area to write algebraic expressions The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nWhich of the following equations can we write from the information given? ![A rectangle with the short side labelled \\(x\\) and the opposite side labelled \\(x^2 + 9\\).]() \\( 2 x^{2}+2 x+18=8 \\)" }, { "from": "gpt", "value": "Calculates perimeter when asked for area" } ]

[ { "from": "human", "value": "Know the exact value of tan(30), tan(45) and tan(60) What is the exact value of \\( \\tan (30) \\) ? \\( \\sqrt{3} \\)" }, { "from": "gpt", "value": "Misremembers the exact values of trigonometric functions at standard angles" } ]

[ { "from": "human", "value": "Know the exact value of tan(30), tan(45) and tan(60) What is the exact value of \\( \\tan (30) \\) ? \\( \\frac{\\sqrt{3}}{2} \\)" }, { "from": "gpt", "value": "Misremembers the exact values of trigonometric functions at standard angles" } ]

[ { "from": "human", "value": "Know the exact value of tan(30), tan(45) and tan(60) What is the exact value of \\( \\tan (30) \\) ? \\( \\frac{1}{2} \\)" }, { "from": "gpt", "value": "Misremembers the exact values of trigonometric functions at standard angles" } ]

[ { "from": "human", "value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Amy is trying to work out the distance between these two points: \\( (2,-5) \\) and \\( (-7,1) \\) She labels them like this: \\( \\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (2, & -5) & (-7, & 1)\\end{array} \\) And then decides to use this formula: \\( \\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}} \\) \\( \\sqrt{(-9)^{2}+(6)^{2}} \\) What is the distance between the points? \\( -\\sqrt{45} \\)" }, { "from": "gpt", "value": "Believes the square of a negative will also be negative" } ]

[ { "from": "human", "value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( V=\\frac{1}{3} \\pi r^{2} h \\) ![A cone, with the dimensions labelled h and r]() Equation" }, { "from": "gpt", "value": "Confuses a formula with an equation" } ]

[ { "from": "human", "value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( V=\\frac{1}{3} \\pi r^{2} h \\) ![A cone, with the dimensions labelled h and r]() Variable" }, { "from": "gpt", "value": "Confuses a variable with a formula" } ]

[ { "from": "human", "value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( V=\\frac{1}{3} \\pi r^{2} h \\) ![A cone, with the dimensions labelled h and r]() Expression" }, { "from": "gpt", "value": "Confuses a formula with an expression" } ]

[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed Rearrange the following equation to make \\( v \\) the subject\n\\(F=\\frac{v^{2}}{r}\\) \\( v=r F^{2} \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]