bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Perform calculations with temperature when given in the same units Which statement about the temperatures \\( -5^{\\circ} \\mathrm{C} \\) and \\( 2^{\\circ} \\mathrm{C} \\) is true? \\( 2^{\\circ} \\mathrm{C} \\) is \\( 7^{\\circ} \\mathrm{C} \\) colder than\n\\[\n-5^{\\circ} \\mathrm{C}\n\\]" }, { "from": "gpt", "value": "Mixes up colder and hotter when comparing temperatures" } ]
[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? \\( 7+6 \\)" }, { "from": "gpt", "value": "Carries out operations from right to left regardless of priority order" } ]
[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? \\( 10-8 \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]
[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? It doesn't matter: you get the same answer" }, { "from": "gpt", "value": "Believes order of operations does not affect the answer to a calculation" } ]
[ { "from": "human", "value": "Convert between cm³ and l \\( 500000 \\mathrm{~cm}^{3} \\) is the same as ______ litres \\( 5 \\)" }, { "from": "gpt", "value": "Thinks 1l = 10 000 cubic centimetres" } ]
[ { "from": "human", "value": "Convert between cm³ and l \\( 500000 \\mathrm{~cm}^{3} \\) is the same as ______ litres \\( 5000 \\)" }, { "from": "gpt", "value": "Thinks 1l = 100 cubic centimetres" } ]
[ { "from": "human", "value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Equation" }, { "from": "gpt", "value": "Confuses a variable with an equation" } ]
[ { "from": "human", "value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Term" }, { "from": "gpt", "value": "Confuses a term with a variable" } ]
[ { "from": "human", "value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Expression" }, { "from": "gpt", "value": "Confuses an expression with a variable" } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\nz+5\n\\] \\( 5 z \\)" }, { "from": "gpt", "value": "Does not realise that two letters together, or a number and letter together, are multiplying" } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\nz+5\n\\] \\( z^{5} \\)" }, { "from": "gpt", "value": "Believes addition of terms and powers of terms are equivalent e.g. a + c = a^c" } ]
[ { "from": "human", "value": "Identify or mark lines of symmetry on a shape Which shape has a line of symmetry? ![A Trapezium above the label \"A\"; A shape which is a circle with a 90 degree sector removed above the label \"B\"; A crescent (moon) shape above the label \"C\"; the words \"All of them\" above the label \"D\".]() A" }, { "from": "gpt", "value": "Believes lines of symmetry must be vertical or horizontal" } ]
[ { "from": "human", "value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).\n]() \\( 255^{\\circ} \\)" }, { "from": "gpt", "value": "Reads the wrong scale on the protractor when measuring reflex angles" } ]
[ { "from": "human", "value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).\n]() \\( 180^{\\circ} \\)" }, { "from": "gpt", "value": "Reads the wrong scale on the protractor when measuring reflex angles" } ]
[ { "from": "human", "value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).\n]() \\( 295^{\\circ} \\)" }, { "from": "gpt", "value": "Correct scale but wrong value on protractor reading." } ]
[ { "from": "human", "value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() Acute" }, { "from": "gpt", "value": "Confuses obtuse and acute angles" } ]
[ { "from": "human", "value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() Reflex" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]
[ { "from": "human", "value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() A right angle" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]
[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (0,1) (0,3) and (-3,2). The point P is the coordinate (0,3)]() \\( (0,2) \\)" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]
[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (0,1) (0,3) and (-3,2). The point P is the coordinate (0,3)]() \\( (2,3) \\)" }, { "from": "gpt", "value": "Reflects horizontally or vertically instead of across a diagonal line of symmetry" } ]
[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (0,1) (0,3) and (-3,2). The point P is the coordinate (0,3)]() \\( (0,1) \\)" }, { "from": "gpt", "value": "Reflects horizontally or vertically instead of across a diagonal line of symmetry" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"-4\" written inside it and the final rectangle has \"output\" written above it and \"11\" written inside it.]() What is the input of this function machine? \\( -7 \\)" }, { "from": "gpt", "value": "Believes subtraction is commutative " } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"-4\" written inside it and the final rectangle has \"output\" written above it and \"11\" written inside it.]() What is the input of this function machine? \\( 44 \\)" }, { "from": "gpt", "value": "Thinks the inverse of subtraction is multiplication" } ]
[ { "from": "human", "value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=0 \\)" }, { "from": "gpt", "value": "Believes the solution of mx + c = 0 is x =0" } ]
[ { "from": "human", "value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=1 \\)" }, { "from": "gpt", "value": "Believes they solve mx + c = 0 by substituting in x = 0" } ]
[ { "from": "human", "value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=-0.4 \\)" }, { "from": "gpt", "value": "Believes the solution of mx + c = 0 is x = m" } ]
[ { "from": "human", "value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -1 \\leq x<3 \\) ? ![Number line with numbers from -5 to 5. Above the -1 is a blue, filled circle with an arrow to the left. Above the 3 is an open, unfilled circle with an arrow to the right.]()" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]
[ { "from": "human", "value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -1 \\leq x<3 \\) ? ![Number line with numbers from -5 to 5. Above the -1 is an open, unfilled circle and above the 3 is a green, filled circle. The two circles are joined by a horizontal line.]()" }, { "from": "gpt", "value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning." } ]
[ { "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\\[\n3(p-1)\n\\] \\( 3 p-1 \\)" }, { "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 is a number and the inside contains a linear expression Expand:\n\\[\n3(p-1)\n\\] \\( p-3 \\)" }, { "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\\[\n3(p-1)\n\\] \\( 3 p-2 \\)" }, { "from": "gpt", "value": "When expanding brackets, multiplies out the first term correctly but adds together the number outside the bracket with the second term inside the bracket." } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 3 m+2 \\)" }, { "from": "gpt", "value": "Only multiplies second term in the expansion of a bracket" } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 6 m+1 \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]
[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 6 m+3 \\)" }, { "from": "gpt", "value": "Adds instead of multiplies" } ]
[ { "from": "human", "value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( +200 \\) then \\( +1 \\)" }, { "from": "gpt", "value": "Does not understand the effect of consecutive operations" } ]
[ { "from": "human", "value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( -200 \\) then \\( -1 \\)" }, { "from": "gpt", "value": "Does not understand the effect of consecutive operations" } ]
[ { "from": "human", "value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( +200 \\) then \\( -1 \\)" }, { "from": "gpt", "value": "Does not understand the effect of consecutive operations" } ]
[ { "from": "human", "value": "Interpret numbers in a frequency table \\begin{tabular}{\|c\|c\|c\|}\n\\hline TVs & Frequency & TVs \\( \\times \\) Frequency \\\\\n\\hline \\( 0 \\) & \\( 3 \\) & \\( 0 \\) \\\\\n\\hline \\( 1 \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline \\( 2 \\) & \\( 8 \\) & \\( 16 \\) \\\\\n\\hline \\( 3 \\) & \\( 4 \\) & \\( 12 \\) \\\\\n\\hline \\( 4 \\) & \\( 2 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular} The table shows the numbers of TVs in the households of students in a class.\n\nWhat does the \"16\" represent? The mean number of TVs in the \\( 8 \\) households" }, { "from": "gpt", "value": "Does not understand the interpretation of the fx column in a frequency table" } ]
[ { "from": "human", "value": "Interpret numbers in a frequency table \\begin{tabular}{\|c\|c\|c\|}\n\\hline TVs & Frequency & TVs \\( \\times \\) Frequency \\\\\n\\hline \\( 0 \\) & \\( 3 \\) & \\( 0 \\) \\\\\n\\hline \\( 1 \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline \\( 2 \\) & \\( 8 \\) & \\( 16 \\) \\\\\n\\hline \\( 3 \\) & \\( 4 \\) & \\( 12 \\) \\\\\n\\hline \\( 4 \\) & \\( 2 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular} The table shows the numbers of TVs in the households of students in a class.\n\nWhat does the \"16\" represent? The total number of TVs in the \\( 2 \\) households" }, { "from": "gpt", "value": "Confuses the variable and frequency columns in a frequency table" } ]
[ { "from": "human", "value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Radius" }, { "from": "gpt", "value": "Confuses diameter and radius" } ]
[ { "from": "human", "value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Arc" }, { "from": "gpt", "value": "Confuses arc and diameter" } ]
[ { "from": "human", "value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Circumference" }, { "from": "gpt", "value": "Confuses circumference and diameter" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( 3: 4 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( \\frac{3}{4} \\)" }, { "from": "gpt", "value": "When writing fraction from diagram, writes total as denominator" } ]
[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( \\frac{270}{360} \\)" }, { "from": "gpt", "value": "When writing fraction from diagram, writes total as denominator" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Jo and Paul are arguing about rounding.\n\nJo says \\( \\mathbf{9 9 . 9 6} \\) rounded to \\( 1 \\) significant figure is \\( \\mathbf{1 0 0} \\)\n\nPaul says \\( \\mathbf{9 9 . 9 6} \\) rounded to \\( 1 \\) decimal place is \\( \\mathbf{1 0 0} \\)\nWho is correct? Both Jo and Paul" }, { "from": "gpt", "value": "When rounding to decimal places and the only digits after the decimal point will be zeros, just gives the integer as the answer." } ]
[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and three or more steps are needed Tom and Katie are discussing rearranging \\( t=\\sqrt{u+9} \\) to make \\( u \\) the subject\nTom says a correct first line of working could be: \\( t=\\sqrt{u}+3 \\)\nKatie says a correct first line of working could be: \\( t^{2}=u+9 \\)\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Thinks that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression" } ]
[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and three or more steps are needed Tom and Katie are discussing rearranging \\( t=\\sqrt{u+9} \\) to make \\( u \\) the subject\nTom says a correct first line of working could be: \\( t=\\sqrt{u}+3 \\)\nKatie says a correct first line of working could be: \\( t^{2}=u+9 \\)\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Thinks that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression" } ]
[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 0.3 \\)" }, { "from": "gpt", "value": "Subtracts instead of divides" } ]
[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 0.025 \\)" }, { "from": "gpt", "value": "When dividing a decimal by an integer, divides by the wrong power of 10 when reinserting the decimal." } ]
[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 1 \\)" }, { "from": "gpt", "value": "Multiplies rather than divides" } ]
[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 0.81 \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]
[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 1.8 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]
[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 2.7 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 95365 \\) \\( 10000 \\)" }, { "from": "gpt", "value": "When rounding up from a 9, does not add one on to the digit to the left" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 95365 \\) \\( 90000 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.15 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.154 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]
[ { "from": "human", "value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.253 \\)" }, { "from": "gpt", "value": "Rounds incorrectly by changing multiple place values" } ]
[ { "from": "human", "value": "Convert between cm³ and mm³ \\( 1 \\mathrm{~cm}^{3} \\) is the same as _______ \\( \\mathrm{mm}^{3} \\) \\( 10 \\)" }, { "from": "gpt", "value": "Does not cube the conversion factor when converting cubed units" } ]
[ { "from": "human", "value": "Convert between cm³ and mm³ \\( 1 \\mathrm{~cm}^{3} \\) is the same as _______ \\( \\mathrm{mm}^{3} \\) \\( 100 \\)" }, { "from": "gpt", "value": "Does not cube the conversion factor when converting cubed units" } ]
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 0.64 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 1.12 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Calculates perimeter when asked for area" } ]
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 0.56 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]
[ { "from": "human", "value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 1 \\) hexagon\n\\( 6 \\) triangles" }, { "from": "gpt", "value": "Confuses pyramid with prism" } ]
[ { "from": "human", "value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 1 \\) hexagon\n\\( 6 \\) rectangles" }, { "from": "gpt", "value": "Confuses pyramid with prism" } ]
[ { "from": "human", "value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 2 \\) hexagons\n\\( 6 \\) triangles" }, { "from": "gpt", "value": "Struggles to visualise nets of 3D shapes" } ]
[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 3 \\)" }, { "from": "gpt", "value": "Misremembers the quadratic formula" } ]
[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 5 \\)" }, { "from": "gpt", "value": "Thinks a variable next to a number means addition rather than multiplication" } ]
[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 9 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]
[ { "from": "human", "value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) digits" }, { "from": "gpt", "value": "Does not recognise when to find a factor from a worded question" } ]
[ { "from": "human", "value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) multiples" }, { "from": "gpt", "value": "Confuses factors and multiples" } ]
[ { "from": "human", "value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) reciprocal" }, { "from": "gpt", "value": "Does not recognise when to find a factor from a worded question" } ]
[ { "from": "human", "value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{\|c\|c\|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hline \\( 6 \\) & \\( 4 \\) \\\\\n\\hline \\( 7 \\) & \\( 12 \\) \\\\\n\\hline \\( 8 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 0.2(1 \\mathrm{dp}) \\)" }, { "from": "gpt", "value": "Believes the mean is total frequency divided by sum of categories given" } ]
[ { "from": "human", "value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{\|c\|c\|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hline \\( 6 \\) & \\( 4 \\) \\\\\n\\hline \\( 7 \\) & \\( 12 \\) \\\\\n\\hline \\( 8 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 32.75 \\)" }, { "from": "gpt", "value": "Believes mean is total divided by number of groups" } ]
[ { "from": "human", "value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{\|c\|c\|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hline \\( 6 \\) & \\( 4 \\) \\\\\n\\hline \\( 7 \\) & \\( 12 \\) \\\\\n\\hline \\( 8 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 6.5(1 \\mathrm{dp}) \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![Positive coordinate grid from 0 to 5 in the x and y directions with a gold star at (1,4) and a purple triangle at (4,3)]() \\( 4 \\) squares right,\n\\( 1 \\) square down" }, { "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": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![Positive coordinate grid from 0 to 5 in the x and y directions with a gold star at (1,4) and a purple triangle at (4,3)]() \\( 3 \\) squares down,\n\\( 1 \\) square right" }, { "from": "gpt", "value": "When describing a translation, identifies the correct number of jumps but mixes up the directions ." } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+6 x+8 \\) we need two numbers that: Add to give \\( 6 x \\) and multiply to give \\( 8 \\)" }, { "from": "gpt", "value": "When factorising into double brackets, believes the sum of the two values in the brackets equals bx rather than b" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+6 x+8 \\) we need two numbers that: Add to give \\( 8 \\) and multiply to give \\( 6 \\)" }, { "from": "gpt", "value": "Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term\n" } ]
[ { "from": "human", "value": "Identify and represent sets using set notation Tom and Katie are discussing the probability spinner\n\nTom says the sample space can be written as: \\( S=\\{1,2\\} \\)\n\nKatie says the sample space can be written as: \\( S=\\{1,1,2,2,2\\} \\)\nWho do you agree with? ![Circle divided into 5 equal sections. 2 sections labelled with a blue number 1. 3 sections labelled with a red number 2.]() Only\nKatie" }, { "from": "gpt", "value": "Believes a sample space should show repeated outcomes, not just unique possible outcomes." } ]
[ { "from": "human", "value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() 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: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() 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: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() Expression" }, { "from": "gpt", "value": "Confuses a formula with an expression" } ]
[ { "from": "human", "value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 650 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 600 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 630 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Determine if a given point lies on a line Tom and Katie are arguing about points on the line\n\\[\ny=2 x-3\n\\]\n\nTom says \\( (5,7) \\) lies on the line \\( \\boldsymbol{y}=\\mathbf{2} \\boldsymbol{x}-\\mathbf{3} \\)\n\nKatie says \\( (-5,-7) \\) lies on the line \\( \\boldsymbol{y}=\\mathbf{2 x}-\\mathbf{3} \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes subtracting a positive number from a negative number makes the answer less negative" } ]
[ { "from": "human", "value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{\|l\|l\|l\|l\|l\|l\|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabular} This is a table of values for \\( 4 x+2 y=10 \\) \nWhat should replace the star? \\( 20 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{\|l\|l\|l\|l\|l\|l\|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabular} This is a table of values for \\( 4 x+2 y=10 \\) \nWhat should replace the star? \\( 3 \\)" }, { "from": "gpt", "value": "Believes 0 multiplied by a number gives the number" } ]
[ { "from": "human", "value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{\|l\|l\|l\|l\|l\|l\|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabular} This is a table of values for \\( 4 x+2 y=10 \\) \nWhat should replace the star? \\( 2.5 \\)" }, { "from": "gpt", "value": "Mixes up the value of two terms when substituting" } ]
[ { "from": "human", "value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=1 \\)" }, { "from": "gpt", "value": "Believes dividing a negative by a positive gives a positive answer" } ]
[ { "from": "human", "value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=9 \\)" }, { "from": "gpt", "value": "Ignores the negative signs when adding positive and negative numbers" } ]
[ { "from": "human", "value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=-9 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - bx - c Tom and Katie are arguing about factorising. Tom says \\( x^{2}+5 x+6 \\equiv(x+3)(x+2) \\) \nKatie says \\( x^{2}-5 x-6 \\equiv(x-3)(x-2) \\) \nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]
[ { "from": "human", "value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 90 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 90.7 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 92 \\)" }, { "from": "gpt", "value": "Rounds incorrectly by changing multiple place values" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer Peter is counting up in threes. He starts at \\( -16 \\)\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -28 \\)" }, { "from": "gpt", "value": "Counts on in the wrong direction on a number line" } ]
[ { "from": "human", "value": "Carry out addition problems involving one negative integer Peter is counting up in threes. He starts at \\( -16 \\)\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -31 \\)" }, { "from": "gpt", "value": "Counts on in the wrong direction on a number line" } ]

[ { "from": "human", "value": "Perform calculations with temperature when given in the same units Which statement about the temperatures \\( -5^{\\circ} \\mathrm{C} \\) and \\( 2^{\\circ} \\mathrm{C} \\) is true? \\( 2^{\\circ} \\mathrm{C} \\) is \\( 7^{\\circ} \\mathrm{C} \\) colder than\n\\[\n-5^{\\circ} \\mathrm{C}\n\\]" }, { "from": "gpt", "value": "Mixes up colder and hotter when comparing temperatures" } ]

[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? \\( 7+6 \\)" }, { "from": "gpt", "value": "Carries out operations from right to left regardless of priority order" } ]

[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? \\( 10-8 \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]

[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\[\n10-8 \\times 7+6=\n\\]\n\nWhich calculation should you do first? It doesn't matter: you get the same answer" }, { "from": "gpt", "value": "Believes order of operations does not affect the answer to a calculation" } ]

[ { "from": "human", "value": "Convert between cm³ and l \\( 500000 \\mathrm{~cm}^{3} \\) is the same as ______ litres \\( 5 \\)" }, { "from": "gpt", "value": "Thinks 1l = 10 000 cubic centimetres" } ]

[ { "from": "human", "value": "Convert between cm³ and l \\( 500000 \\mathrm{~cm}^{3} \\) is the same as ______ litres \\( 5000 \\)" }, { "from": "gpt", "value": "Thinks 1l = 100 cubic centimetres" } ]

[ { "from": "human", "value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Equation" }, { "from": "gpt", "value": "Confuses a variable with an equation" } ]

[ { "from": "human", "value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Term" }, { "from": "gpt", "value": "Confuses a term with a variable" } ]

[ { "from": "human", "value": "Recognise and name a variable Which of the following is the most appropriate word to describe \\( p \\) in this:\n\\(\n3 p+7\n\\) Expression" }, { "from": "gpt", "value": "Confuses an expression with a variable" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\nz+5\n\\] \\( 5 z \\)" }, { "from": "gpt", "value": "Does not realise that two letters together, or a number and letter together, are multiplying" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\nz+5\n\\] \\( z^{5} \\)" }, { "from": "gpt", "value": "Believes addition of terms and powers of terms are equivalent e.g. a + c = a^c" } ]

[ { "from": "human", "value": "Identify or mark lines of symmetry on a shape Which shape has a line of symmetry? ![A Trapezium above the label \"A\"; A shape which is a circle with a 90 degree sector removed above the label \"B\"; A crescent (moon) shape above the label \"C\"; the words \"All of them\" above the label \"D\".]() A" }, { "from": "gpt", "value": "Believes lines of symmetry must be vertical or horizontal" } ]

[ { "from": "human", "value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).\n]() \\( 255^{\\circ} \\)" }, { "from": "gpt", "value": "Reads the wrong scale on the protractor when measuring reflex angles" } ]

[ { "from": "human", "value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).\n]() \\( 180^{\\circ} \\)" }, { "from": "gpt", "value": "Reads the wrong scale on the protractor when measuring reflex angles" } ]

[ { "from": "human", "value": "Use a protractor to measure angles between 270° and 360° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).\n]() \\( 295^{\\circ} \\)" }, { "from": "gpt", "value": "Correct scale but wrong value on protractor reading." } ]

[ { "from": "human", "value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() Acute" }, { "from": "gpt", "value": "Confuses obtuse and acute angles" } ]

[ { "from": "human", "value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() Reflex" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]

[ { "from": "human", "value": "Identify obtuse angles This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]() A right angle" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]

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

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

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

[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"-4\" written inside it and the final rectangle has \"output\" written above it and \"11\" written inside it.]() What is the input of this function machine? \\( -7 \\)" }, { "from": "gpt", "value": "Believes subtraction is commutative " } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"-4\" written inside it and the final rectangle has \"output\" written above it and \"11\" written inside it.]() What is the input of this function machine? \\( 44 \\)" }, { "from": "gpt", "value": "Thinks the inverse of subtraction is multiplication" } ]

[ { "from": "human", "value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=0 \\)" }, { "from": "gpt", "value": "Believes the solution of mx + c = 0 is x =0" } ]

[ { "from": "human", "value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=1 \\)" }, { "from": "gpt", "value": "Believes they solve mx + c = 0 by substituting in x = 0" } ]

[ { "from": "human", "value": "Given a sketch of a linear graph solve f(x) = 0 This is a graph of\n\\(y=1-0.4 x\\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve\n\\(1-0.4 x=0\\) \\( x=-0.4 \\)" }, { "from": "gpt", "value": "Believes the solution of mx + c = 0 is x = m" } ]

[ { "from": "human", "value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -1 \\leq x<3 \\) ? ![Number line with numbers from -5 to 5. Above the -1 is a blue, filled circle with an arrow to the left. Above the 3 is an open, unfilled circle with an arrow to the right.]()" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -1 \\leq x<3 \\) ? ![Number line with numbers from -5 to 5. Above the -1 is an open, unfilled circle and above the 3 is a green, filled circle. The two circles are joined by a horizontal line.]()" }, { "from": "gpt", "value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning." } ]

[ { "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\\[\n3(p-1)\n\\] \\( 3 p-1 \\)" }, { "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 is a number and the inside contains a linear expression Expand:\n\\[\n3(p-1)\n\\] \\( p-3 \\)" }, { "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\\[\n3(p-1)\n\\] \\( 3 p-2 \\)" }, { "from": "gpt", "value": "When expanding brackets, multiplies out the first term correctly but adds together the number outside the bracket with the second term inside the bracket." } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 3 m+2 \\)" }, { "from": "gpt", "value": "Only multiplies second term in the expansion of a bracket" } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 6 m+1 \\)" }, { "from": "gpt", "value": "Only multiplies the first term in the expansion of a bracket" } ]

[ { "from": "human", "value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"3m + 1\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 6 m+3 \\)" }, { "from": "gpt", "value": "Adds instead of multiplies" } ]

[ { "from": "human", "value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( +200 \\) then \\( +1 \\)" }, { "from": "gpt", "value": "Does not understand the effect of consecutive operations" } ]

[ { "from": "human", "value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( -200 \\) then \\( -1 \\)" }, { "from": "gpt", "value": "Does not understand the effect of consecutive operations" } ]

[ { "from": "human", "value": "Recognise and use efficient strategies for mental subtraction Nick wants to subtract \\( 199 \\) from a number.\nWhich one of the following methods would give him the correct answer? \\( +200 \\) then \\( -1 \\)" }, { "from": "gpt", "value": "Does not understand the effect of consecutive operations" } ]

[ { "from": "human", "value": "Interpret numbers in a frequency table \\begin{tabular}{|c|c|c|}\n\\hline TVs & Frequency & TVs \\( \\times \\) Frequency \\\\\n\\hline \\( 0 \\) & \\( 3 \\) & \\( 0 \\) \\\\\n\\hline \\( 1 \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline \\( 2 \\) & \\( 8 \\) & \\( 16 \\) \\\\\n\\hline \\( 3 \\) & \\( 4 \\) & \\( 12 \\) \\\\\n\\hline \\( 4 \\) & \\( 2 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular} The table shows the numbers of TVs in the households of students in a class.\n\nWhat does the \"16\" represent? The mean number of TVs in the \\( 8 \\) households" }, { "from": "gpt", "value": "Does not understand the interpretation of the fx column in a frequency table" } ]

[ { "from": "human", "value": "Interpret numbers in a frequency table \\begin{tabular}{|c|c|c|}\n\\hline TVs & Frequency & TVs \\( \\times \\) Frequency \\\\\n\\hline \\( 0 \\) & \\( 3 \\) & \\( 0 \\) \\\\\n\\hline \\( 1 \\) & \\( 8 \\) & \\( 8 \\) \\\\\n\\hline \\( 2 \\) & \\( 8 \\) & \\( 16 \\) \\\\\n\\hline \\( 3 \\) & \\( 4 \\) & \\( 12 \\) \\\\\n\\hline \\( 4 \\) & \\( 2 \\) & \\( 8 \\) \\\\\n\\hline\n\\end{tabular} The table shows the numbers of TVs in the households of students in a class.\n\nWhat does the \"16\" represent? The total number of TVs in the \\( 2 \\) households" }, { "from": "gpt", "value": "Confuses the variable and frequency columns in a frequency table" } ]

[ { "from": "human", "value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Radius" }, { "from": "gpt", "value": "Confuses diameter and radius" } ]

[ { "from": "human", "value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Arc" }, { "from": "gpt", "value": "Confuses arc and diameter" } ]

[ { "from": "human", "value": "Identify a diameter The straight line shown in this diagram is a ....? ![A circle with a line across from edge to edge, passing through the centre]() Circumference" }, { "from": "gpt", "value": "Confuses circumference and diameter" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( 3: 4 \\)" }, { "from": "gpt", "value": "When writing ratio from diagram, writes total as one side" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( \\frac{3}{4} \\)" }, { "from": "gpt", "value": "When writing fraction from diagram, writes total as denominator" } ]

[ { "from": "human", "value": "Express pictorial representations of objects as a ratio What is the ratio of tables to chairs? ![tables\nchairs]() \\( \\frac{270}{360} \\)" }, { "from": "gpt", "value": "When writing fraction from diagram, writes total as denominator" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Jo and Paul are arguing about rounding.\n\nJo says \\( \\mathbf{9 9 . 9 6} \\) rounded to \\( 1 \\) significant figure is \\( \\mathbf{1 0 0} \\)\n\nPaul says \\( \\mathbf{9 9 . 9 6} \\) rounded to \\( 1 \\) decimal place is \\( \\mathbf{1 0 0} \\)\nWho is correct? Both Jo and Paul" }, { "from": "gpt", "value": "When rounding to decimal places and the only digits after the decimal point will be zeros, just gives the integer as the answer." } ]

[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and three or more steps are needed Tom and Katie are discussing rearranging \\( t=\\sqrt{u+9} \\) to make \\( u \\) the subject\nTom says a correct first line of working could be: \\( t=\\sqrt{u}+3 \\)\nKatie says a correct first line of working could be: \\( t^{2}=u+9 \\)\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Thinks that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression" } ]

[ { "from": "human", "value": "Rearrange formulae to change the subject where the subject appears once and three or more steps are needed Tom and Katie are discussing rearranging \\( t=\\sqrt{u+9} \\) to make \\( u \\) the subject\nTom says a correct first line of working could be: \\( t=\\sqrt{u}+3 \\)\nKatie says a correct first line of working could be: \\( t^{2}=u+9 \\)\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Thinks that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression" } ]

[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 0.3 \\)" }, { "from": "gpt", "value": "Subtracts instead of divides" } ]

[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 0.025 \\)" }, { "from": "gpt", "value": "When dividing a decimal by an integer, divides by the wrong power of 10 when reinserting the decimal." } ]

[ { "from": "human", "value": "Divide a decimal by an integer \\( 0.5 \\div 2= \\) \\( 1 \\)" }, { "from": "gpt", "value": "Multiplies rather than divides" } ]

[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 0.81 \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]

[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 1.8 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]

[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\[y=3 x^{2}\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 2.7 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 95365 \\) \\( 10000 \\)" }, { "from": "gpt", "value": "When rounding up from a 9, does not add one on to the digit to the left" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 95365 \\) \\( 90000 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.15 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.154 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]

[ { "from": "human", "value": "Round numbers to three or more decimal places What is \\( 20.15349 \\) rounded to \\( 3 \\) decimal places? \\( 20.253 \\)" }, { "from": "gpt", "value": "Rounds incorrectly by changing multiple place values" } ]

[ { "from": "human", "value": "Convert between cm³ and mm³ \\( 1 \\mathrm{~cm}^{3} \\) is the same as _______ \\( \\mathrm{mm}^{3} \\) \\( 10 \\)" }, { "from": "gpt", "value": "Does not cube the conversion factor when converting cubed units" } ]

[ { "from": "human", "value": "Convert between cm³ and mm³ \\( 1 \\mathrm{~cm}^{3} \\) is the same as _______ \\( \\mathrm{mm}^{3} \\) \\( 100 \\)" }, { "from": "gpt", "value": "Does not cube the conversion factor when converting cubed units" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 0.64 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 1.12 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Calculates perimeter when asked for area" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]() \\( 0.56 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]

[ { "from": "human", "value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 1 \\) hexagon\n\\( 6 \\) triangles" }, { "from": "gpt", "value": "Confuses pyramid with prism" } ]

[ { "from": "human", "value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 1 \\) hexagon\n\\( 6 \\) rectangles" }, { "from": "gpt", "value": "Confuses pyramid with prism" } ]

[ { "from": "human", "value": "Draw the net of a prism Which of the following collections of shapes would allow you to draw the net of a hexagonal prism? \\( 2 \\) hexagons\n\\( 6 \\) triangles" }, { "from": "gpt", "value": "Struggles to visualise nets of 3D shapes" } ]

[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 3 \\)" }, { "from": "gpt", "value": "Misremembers the quadratic formula" } ]

[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 5 \\)" }, { "from": "gpt", "value": "Thinks a variable next to a number means addition rather than multiplication" } ]

[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Vera wants to solve this equation using the quadratic formula.\n\\(\n3 h^{2}-10 h+4=0\n\\)\n\nWhat should replace the circle? \\( \\frac{? \\pm \\sqrt{?-?}}{\\bigcirc} \\) \\( 9 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]

[ { "from": "human", "value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) digits" }, { "from": "gpt", "value": "Does not recognise when to find a factor from a worded question" } ]

[ { "from": "human", "value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) multiples" }, { "from": "gpt", "value": "Confuses factors and multiples" } ]

[ { "from": "human", "value": "Recognise when to find a factor to solve a problem Emma has \\( 24 \\) cakes to give away to her friends.\nTo work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \\( 24 \\) reciprocal" }, { "from": "gpt", "value": "Does not recognise when to find a factor from a worded question" } ]

[ { "from": "human", "value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hline \\( 6 \\) & \\( 4 \\) \\\\\n\\hline \\( 7 \\) & \\( 12 \\) \\\\\n\\hline \\( 8 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 0.2(1 \\mathrm{dp}) \\)" }, { "from": "gpt", "value": "Believes the mean is total frequency divided by sum of categories given" } ]

[ { "from": "human", "value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hline \\( 6 \\) & \\( 4 \\) \\\\\n\\hline \\( 7 \\) & \\( 12 \\) \\\\\n\\hline \\( 8 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 32.75 \\)" }, { "from": "gpt", "value": "Believes mean is total divided by number of groups" } ]

[ { "from": "human", "value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 20 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\n\nNumber of Spots & Frequency \\\\\n\\hline \\( 5 \\) & \\( 3 \\) \\\\\n\\hline \\( 6 \\) & \\( 4 \\) \\\\\n\\hline \\( 7 \\) & \\( 12 \\) \\\\\n\\hline \\( 8 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 6.5(1 \\mathrm{dp}) \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![Positive coordinate grid from 0 to 5 in the x and y directions with a gold star at (1,4) and a purple triangle at (4,3)]() \\( 4 \\) squares right,\n\\( 1 \\) square down" }, { "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": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![Positive coordinate grid from 0 to 5 in the x and y directions with a gold star at (1,4) and a purple triangle at (4,3)]() \\( 3 \\) squares down,\n\\( 1 \\) square right" }, { "from": "gpt", "value": "When describing a translation, identifies the correct number of jumps but mixes up the directions ." } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+6 x+8 \\) we need two numbers that: Add to give \\( 6 x \\) and multiply to give \\( 8 \\)" }, { "from": "gpt", "value": "When factorising into double brackets, believes the sum of the two values in the brackets equals bx rather than b" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+6 x+8 \\) we need two numbers that: Add to give \\( 8 \\) and multiply to give \\( 6 \\)" }, { "from": "gpt", "value": "Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term\n" } ]

[ { "from": "human", "value": "Identify and represent sets using set notation Tom and Katie are discussing the probability spinner\n\nTom says the sample space can be written as: \\( S=\\{1,2\\} \\)\n\nKatie says the sample space can be written as: \\( S=\\{1,1,2,2,2\\} \\)\nWho do you agree with? ![Circle divided into 5 equal sections. 2 sections labelled with a blue number 1. 3 sections labelled with a red number 2.]() Only\nKatie" }, { "from": "gpt", "value": "Believes a sample space should show repeated outcomes, not just unique possible outcomes." } ]

[ { "from": "human", "value": "Recognise and name a formula Which of the following is the most appropriate word to describe: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() 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: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() 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: \\( A=\\frac{b h}{2} \\) ![A triangle with base labelled b and height labelled h.]() Expression" }, { "from": "gpt", "value": "Confuses a formula with an expression" } ]

[ { "from": "human", "value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 650 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 600 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Round integers to the nearest 10 What is \\( 637 \\) rounded to the nearest \\( 10 \\) ? \\( 630 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Determine if a given point lies on a line Tom and Katie are arguing about points on the line\n\\[\ny=2 x-3\n\\]\n\nTom says \\( (5,7) \\) lies on the line \\( \\boldsymbol{y}=\\mathbf{2} \\boldsymbol{x}-\\mathbf{3} \\)\n\nKatie says \\( (-5,-7) \\) lies on the line \\( \\boldsymbol{y}=\\mathbf{2 x}-\\mathbf{3} \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes subtracting a positive number from a negative number makes the answer less negative" } ]

[ { "from": "human", "value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{|l|l|l|l|l|l|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabular} This is a table of values for \\( 4 x+2 y=10 \\) \nWhat should replace the star? \\( 20 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{|l|l|l|l|l|l|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabular} This is a table of values for \\( 4 x+2 y=10 \\) \nWhat should replace the star? \\( 3 \\)" }, { "from": "gpt", "value": "Believes 0 multiplied by a number gives the number" } ]

[ { "from": "human", "value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c \\begin{tabular}{|l|l|l|l|l|l|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \n\\end{tabular} This is a table of values for \\( 4 x+2 y=10 \\) \nWhat should replace the star? \\( 2.5 \\)" }, { "from": "gpt", "value": "Mixes up the value of two terms when substituting" } ]

[ { "from": "human", "value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=1 \\)" }, { "from": "gpt", "value": "Believes dividing a negative by a positive gives a positive answer" } ]

[ { "from": "human", "value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=9 \\)" }, { "from": "gpt", "value": "Ignores the negative signs when adding positive and negative numbers" } ]

[ { "from": "human", "value": "Substitute a solution back into the remaining equation and find the second solution Isaac is halfway through solving a pair of simultaneous equations, one of which is below.\n\n\\(\n2 j-k=-10\n\\)\n\nIsaac found that \\( k=8 \\)\nWhat does \\( j \\) equal? \\( j=-9 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - bx - c Tom and Katie are arguing about factorising. Tom says \\( x^{2}+5 x+6 \\equiv(x+3)(x+2) \\) \nKatie says \\( x^{2}-5 x-6 \\equiv(x-3)(x-2) \\) \nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]

[ { "from": "human", "value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 90 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 90.7 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Round decimals to the nearest whole number What is \\( \\mathbf{9 0 . 6 8 2} \\) rounded to the nearest integer? \\( 92 \\)" }, { "from": "gpt", "value": "Rounds incorrectly by changing multiple place values" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer Peter is counting up in threes. He starts at \\( -16 \\)\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -28 \\)" }, { "from": "gpt", "value": "Counts on in the wrong direction on a number line" } ]

[ { "from": "human", "value": "Carry out addition problems involving one negative integer Peter is counting up in threes. He starts at \\( -16 \\)\nWhat is the \\( 5^{\\text {th }} \\) number he says? \\( -31 \\)" }, { "from": "gpt", "value": "Counts on in the wrong direction on a number line" } ]