conversations
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[
{
"from": "human",
"value": "Carry out subtraction problems involving two negative integers What number belongs in the box?\n\\(\n(-8)-(-5)=\n\\square\\) \\( 3 \\)"
},
{
"from": "gpt",
"value": "When subtracting from a negative thinks the answer must be positive"
}
] |
[
{
"from": "human",
"value": "Prove statements involving multiples On what line is the first mistake when proving \\( (n+1)^{2}-(n-1)^{2} \\) is divisible by \\( 4 \\) ? \\( n^{2}+2 n+1-\\left(n^{2}-2 n+1\\right) \\quad \\) Line \\( 1 \\) \\( n^{2}+2 n+1-n^{2}-2 n+1 \\quad \\) Line \\( 2 \\) \\[\n2\n\\]\n\nLine \\( 3 \\) Line \\( 1 \\)"
},
{
"from": "gpt",
"value": "Ignores negative sign when expanding bracket"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]() \\( 48 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Uses an incorrect side length when splitting a composite shape into parts"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]() \\( 104 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Uses an incorrect side length when splitting a composite shape into parts"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]() \\( 56 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Uses an incorrect side length when splitting a composite shape into parts"
}
] |
[
{
"from": "human",
"value": "Find the gradient of a line written in the form ax + by = c In which region would \\( x+y=1 \\) belong? ![A Venn diagram with two intersecting sets. The set on the right is 'Crosses the y-axis at (0,1)' and the set of the right is 'Has a positive gradient'. A is in the 'Crosses the y-axis at (0,1)' set only, B is in the intersection, C is in the 'Has a positive gradient' only and D is outside both sets.]() B"
},
{
"from": "gpt",
"value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c"
}
] |
[
{
"from": "human",
"value": "Use brackets to write function machines as calculations Jo and Paul are arguing about the result of this Function Machine:\nJo says the output is: \\( \\frac{n}{5}+3 \\)\nPaul says the output is: \\( \\frac{n+3}{5} \\)\nWho is correct? ![A function machine showing an input of n and operations divide by 5 and add 3]() Only\nPaul"
},
{
"from": "gpt",
"value": "Does not follow the arrows through a function machine, changes the order of the operations asked."
}
] |
[
{
"from": "human",
"value": "Use brackets to write function machines as calculations Jo and Paul are arguing about the result of this Function Machine:\nJo says the output is: \\( \\frac{n}{5}+3 \\)\nPaul says the output is: \\( \\frac{n+3}{5} \\)\nWho is correct? ![A function machine showing an input of n and operations divide by 5 and add 3]() Both Jo and Paul"
},
{
"from": "gpt",
"value": "Does not follow the arrows through a function machine, changes the order of the operations asked."
}
] |
[
{
"from": "human",
"value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=10 \\)\n\\(\n\\frac{h}{2}=\n\\) \\( 8 \\)"
},
{
"from": "gpt",
"value": "Thinks the fraction bar means subtract rather than divide"
}
] |
[
{
"from": "human",
"value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=10 \\)\n\\(\n\\frac{h}{2}=\n\\) \\( -5 \\)"
},
{
"from": "gpt",
"value": "Believes dividing two positives will give a negative answer"
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for ascending quadratic sequences in the form ax² + bx + c \\(\n6,14,28,48,74, \\ldots\n\\)\n\nWhen calculating the nth-term rule of this sequence, what should replace the triangle?\n\nnth-term rule: \\( 3 n^{2} \\)\\( \\color{red}\\triangle \\) \\(n\\) \\( \\color{purple}\\square \\)\n \\[\n+1\n\\]\n(or just a + sign)"
},
{
"from": "gpt",
"value": "When finding the differences between terms in a sequence, believes they can do so from right to left "
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for ascending quadratic sequences in the form ax² + bx + c \\(\n6,14,28,48,74, \\ldots\n\\)\n\nWhen calculating the nth-term rule of this sequence, what should replace the triangle?\n\nnth-term rule: \\( 3 n^{2} \\)\\( \\color{red}\\triangle \\) \\(n\\) \\( \\color{purple}\\square \\)\n \\( +3 \\)"
},
{
"from": "gpt",
"value": "When finding the nth term rule for a quadratic sequence, believes they only need to use the first term to calculate the coefficient of n "
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring addition or subtraction, involving positive fractions Solve the equation:\n\\(\np-5=\\frac{1}{10}\n\\) \\( p=\\frac{6}{10} \\)"
},
{
"from": "gpt",
"value": "When adding an integer to a fraction, thinks you add the integer to the numerator"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring addition or subtraction, involving positive fractions Solve the equation:\n\\(\np-5=\\frac{1}{10}\n\\) \\( p=\\frac{5}{50} \\)"
},
{
"from": "gpt",
"value": "When solving an equation, multiplies instead of adding"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear inequalities in one variable where the variable appears on one side of the equation Tom and Katie are arguing about solving inequalities.\nTom says \\( -2 m>12 \\) gives \\( m>-6 \\)\nKatie says \\( -2+m>12 \\) gives \\( m>14 \\)\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes they can multiply/divide through by a negative number without changing the direction of the inequality"
}
] |
[
{
"from": "human",
"value": "Work out the size of each interior angle in a regular polygon Tom and Katie are discussing how to calculate the size of each interior angle in a regular \\( 20 \\) sided shape\n\nTom says you can do \\( \\frac{18 \\times 180}{20} \\)\n\nKatie says you can do \\( 180-\\frac{360}{20} \\)\n\nWho is correct? Only Tom"
},
{
"from": "gpt",
"value": "Does not recognise that interior and exterior angles are supplementary"
}
] |
[
{
"from": "human",
"value": "Work out the size of each interior angle in a regular polygon Tom and Katie are discussing how to calculate the size of each interior angle in a regular \\( 20 \\) sided shape\n\nTom says you can do \\( \\frac{18 \\times 180}{20} \\)\n\nKatie says you can do \\( 180-\\frac{360}{20} \\)\n\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Believes the only way to find the interior angle of a regular polygon is to subtract the exterior angle from 180."
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to one significant figure \\(\n0.095643\n\\)\n\nWhat is this number rounded to \\( 1 \\) significant figure? \\( 0 \\)"
},
{
"from": "gpt",
"value": "Counts leading zero as a significant figure"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to one significant figure \\(\n0.095643\n\\)\n\nWhat is this number rounded to \\( 1 \\) significant figure? \\( 0.09 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up when next digit is 5"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to one significant figure \\(\n0.095643\n\\)\n\nWhat is this number rounded to \\( 1 \\) significant figure? \\( 0.01 \\)"
},
{
"from": "gpt",
"value": "When rounding up from a 9, does not add one on to the digit to the left"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]() \\( 100 \\% \\)"
},
{
"from": "gpt",
"value": "Identifies the wrong part of a fraction model as the whole"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]() \\( 60 \\% \\)"
},
{
"from": "gpt",
"value": "Believes to complete a part whole model you select a value already given in the model"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]() \\( 0.4 \\)"
},
{
"from": "gpt",
"value": "Believes to complete a part whole model you select a value already given in the model"
}
] |
[
{
"from": "human",
"value": "Carry out multiplication problems involving one negative integer The product of two numbers is \\( -24 \\).\nWhat could the two numbers be? \\( -3 \\) and \\( -8 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Carry out multiplication problems involving one negative integer The product of two numbers is \\( -24 \\).\nWhat could the two numbers be? \\( -10 \\) and \\( -14 \\)"
},
{
"from": "gpt",
"value": "Believes that product means add rather than multiply"
}
] |
[
{
"from": "human",
"value": "Read values from piecewise functions Tom is has correctly drawn the graph of the following function:\n\\(\ny=\\left\\{\\begin{array}{c}\n3 \\text { for } 0 \\leq x<Q \\\\\nP \\text { for } 1.5 \\leq x<4 \\\\\n2.5 \\text { for } 4 \\leq x<7\n\\end{array}\\right.\n\\)\n\nWhat are the values of \\( P \\) and \\( Q \\) ? ![The graph is three separate horizontal lines. It goes from (0,3) to (1.5, 3), then (1.5, 2) to (4, 2) and the last section is from (4, 2.5) to (7, 2.5)]() \\( \\begin{array}{c}P=1.5 \\\\ Q=2\\end{array} \\)"
},
{
"from": "gpt",
"value": "When reading value from graph, reads from the wrong axes."
}
] |
[
{
"from": "human",
"value": "Read values from piecewise functions Tom is has correctly drawn the graph of the following function:\n\\(\ny=\\left\\{\\begin{array}{c}\n3 \\text { for } 0 \\leq x<Q \\\\\nP \\text { for } 1.5 \\leq x<4 \\\\\n2.5 \\text { for } 4 \\leq x<7\n\\end{array}\\right.\n\\)\n\nWhat are the values of \\( P \\) and \\( Q \\) ? ![The graph is three separate horizontal lines. It goes from (0,3) to (1.5, 3), then (1.5, 2) to (4, 2) and the last section is from (4, 2.5) to (7, 2.5)]() \\( \\begin{array}{l}P=2 \\\\ Q=1\\end{array} \\)"
},
{
"from": "gpt",
"value": "When reading graph, chooses nearest marked value on axis instead of reading accurately"
}
] |
[
{
"from": "human",
"value": "Identify the net of a non-prism This is the net of a... ![An image with an equilateral triangle in the centre. Connected to each of the three sides of the equilateral triangle are 3 more identical, equilateral triangles forming a larger triangle shape.]() Triangle"
},
{
"from": "gpt",
"value": "Names one of the faces of a 3D shape rather than the 3D shape name"
}
] |
[
{
"from": "human",
"value": "Identify the net of a non-prism This is the net of a... ![An image with an equilateral triangle in the centre. Connected to each of the three sides of the equilateral triangle are 3 more identical, equilateral triangles forming a larger triangle shape.]() Triangular prism"
},
{
"from": "gpt",
"value": "Confuses pyramid with prism"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)(cx + d) Alison is expanding these two brackets.\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the -4 in the first bracket and the -3 in the second bracket.]() \\( -12 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)(cx + d) Alison is expanding these two brackets.\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the -4 in the first bracket and the -3 in the second bracket.]() \\( -7 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}-99p\n\\) \\( (p+9)(p-9) \\)"
},
{
"from": "gpt",
"value": "When factorising a quadratic without a non variable term, tries to double bracket factorise"
}
] |
[
{
"from": "human",
"value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}-99p\n\\) \\( (p+3 \\sqrt{11})(p-3 \\sqrt{11}) \\)"
},
{
"from": "gpt",
"value": "When factorising a quadratic without a non variable term, tries to double bracket factorise"
}
] |
[
{
"from": "human",
"value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + c Tom and Katie are discussing the table of values for \\( y=x^{2}-1 \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( \\bigstar \\) \\\\\n\\hline\\( y \\) & \\( 15 \\) \\\\\n\\hline\n\\end{tabular} Tom says the star could be \\( 4 \\)\n\nKatie says the star could be \\( -4 \\)\n\nWho is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Believes the square of a negative will also be negative"
}
] |
[
{
"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 a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).\n]() \\( 345^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Correct scale but wrong value on protractor reading."
}
] |
[
{
"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 a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).\n]() \\( 215^{\\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 a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).\n]() \\( 205^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Reads the wrong scale on the protractor when measuring reflex angles"
}
] |
[
{
"from": "human",
"value": "Complete the square for expressions that end up in the form a(x + b)² + c When Sarah completes the square, what should replace the star? \\( 2 g^{2}-6 g-5 \\equiv 2(g \\bigstar)^{2} \\triangle \\) \\( \\bigstar=-6 \\)"
},
{
"from": "gpt",
"value": "When completing the square, believes the constant in the bracket is the coefficient of x"
}
] |
[
{
"from": "human",
"value": "Complete the square for expressions that end up in the form a(x + b)² + c When Sarah completes the square, what should replace the star? \\( 2 g^{2}-6 g-5 \\equiv 2(g \\bigstar)^{2} \\triangle \\) \\( \\bigstar=-3 \\)"
},
{
"from": "gpt",
"value": "When completing the square, believes that a is always half the x-coefficient. "
}
] |
[
{
"from": "human",
"value": "Complete the square for expressions that end up in the form a(x + b)² + c When Sarah completes the square, what should replace the star? \\( 2 g^{2}-6 g-5 \\equiv 2(g \\bigstar)^{2} \\triangle \\) \\( \\bigstar=-\\sqrt{6} \\)"
},
{
"from": "gpt",
"value": "When completing the square, believes the constant in the bracket is the square root of the coefficient of x"
}
] |
[
{
"from": "human",
"value": "Continue a sequence involving triangle numbers If you add together consecutive triangle numbers you get... another triangle number"
},
{
"from": "gpt",
"value": "Believes triangle numbers are formed differently to the correct way"
}
] |
[
{
"from": "human",
"value": "Multiply mixed number fraction in the form: Fraction × Fraction \\( 1 \\frac{1}{2} \\times 3 \\frac{2}{3}=\\bigstar\\frac{3}{6} \\) What should replace the star? \\( 3 \\)"
},
{
"from": "gpt",
"value": "When multiplying mixed numbers, forgets to multiply the fraction"
}
] |
[
{
"from": "human",
"value": "Multiply mixed number fraction in the form: Fraction × Fraction \\( 1 \\frac{1}{2} \\times 3 \\frac{2}{3}=\\bigstar\\frac{3}{6} \\) What should replace the star? \\( 4 \\)"
},
{
"from": "gpt",
"value": "When multiplying mixed numbers thinks they add the integers"
}
] |
[
{
"from": "human",
"value": "Read fractions How do you say this fraction?\n\\(\n\\frac{3}{5}\n\\) Three point five"
},
{
"from": "gpt",
"value": "Has used the decimal point to separate numerator and denominator"
}
] |
[
{
"from": "human",
"value": "Read fractions How do you say this fraction?\n\\(\n\\frac{3}{5}\n\\) Three fives"
},
{
"from": "gpt",
"value": "Does not know how to say a fraction"
}
] |
[
{
"from": "human",
"value": "Read fractions How do you say this fraction?\n\\(\n\\frac{3}{5}\n\\) Third fifths"
},
{
"from": "gpt",
"value": "Does not know how to say a fraction"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order decimals with the same number of digits Which signs belong in the boxes to make the statement correct?\n\n\\( 0.705 \\)\\[ {\\color{blue}\\square} \\]\\( 0.750 \\)\\[ {\\color{orange}\\square} \\]\\( 0.570 \\) ![A blue box containing a \"greater than\" symbol and an orange box containing a \"less than\" symbol]()"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Convert terminating decimals greater than 1 to fractions Convert this to a fraction:\n\\( 1.4 \\) \\( \\frac{1}{4} \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by using the denominator after the decimal point"
}
] |
[
{
"from": "human",
"value": "Convert terminating decimals greater than 1 to fractions Convert this to a fraction:\n\\( 1.4 \\) Not possible as it is greater than \\( 1 \\)"
},
{
"from": "gpt",
"value": "Thinks numbers greater than 1 cannot be converted into fractions"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n0.31,0.30,0.331\n\\] \\( 0.021 \\)"
},
{
"from": "gpt",
"value": "When calculating the range does not reorder the data to find the largest number minus the smallest number"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n0.31,0.30,0.331\n\\] \\( 0.301 \\)"
},
{
"from": "gpt",
"value": "When subtracting decimals with a different number of decimal places, lines up the digits incorrectly"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n0.31,0.30,0.331\n\\] \\( 0.21 \\)"
},
{
"from": "gpt",
"value": "When calculating the range does not reorder the data to find the largest number minus the smallest number"
}
] |
[
{
"from": "human",
"value": "Identify a unit of volume or capacity Which of the following is not a measure of volume? Cubic metres"
},
{
"from": "gpt",
"value": "Does not know that cubic means the same as cubed in units"
}
] |
[
{
"from": "human",
"value": "Identify a unit of volume or capacity Which of the following is not a measure of volume? Centimetres cubed"
},
{
"from": "gpt",
"value": "Does not know that units of volume are usually cubed"
}
] |
[
{
"from": "human",
"value": "Identify a unit of volume or capacity Which of the following is not a measure of volume? Litres"
},
{
"from": "gpt",
"value": "Does not recognise litres as a unit of volume"
}
] |
[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence? \\( 4, \\quad 10, \\quad 14, \\quad 24, \\quad \\ldots \\) To get the next term you add \\( 6 \\) to the previous term"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence? \\( 4, \\quad 10, \\quad 14, \\quad 24, \\quad \\ldots \\) To get the next term you double the previous term and add \\( 2 \\)"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence? \\( 4, \\quad 10, \\quad 14, \\quad 24, \\quad \\ldots \\) To get the next term you multiply the previous term by \\( 3 \\) and subtract \\( 2 \\)"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 5050 \\) rounded to the nearest \\( 10 \\) ? \\( 5100 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 5050 \\) rounded to the nearest \\( 10 \\) ? \\( 5000 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 5050 \\) rounded to the nearest \\( 10 \\) ? \\( 5010 \\)"
},
{
"from": "gpt",
"value": "Believes that rounding must change the number"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(12 d-3=0\\) \\( d=-\\frac{1}{4} \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(12 d-3=0\\) \\( d=4 \\)"
},
{
"from": "gpt",
"value": "Swaps the dividend and divisor in order to get an integer answer"
}
] |
[
{
"from": "human",
"value": "Calculate time where speed and distance are in the appropriate units This displacement-time graph shows the start of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 4 \\mathrm{~m} / \\mathrm{s} \\).\nWhat are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).\nThe marked point is one square in on the Time axis and at 40 on the Distance axis.]() \\( (1,40) \\)"
},
{
"from": "gpt",
"value": "Makes an assumption about the squares on a scale representing either 1 or 10"
}
] |
[
{
"from": "human",
"value": "Calculate time where speed and distance are in the appropriate units This displacement-time graph shows the start of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 4 \\mathrm{~m} / \\mathrm{s} \\).\nWhat are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).\nThe marked point is one square in on the Time axis and at 40 on the Distance axis.]() \\( (10,40) \\)"
},
{
"from": "gpt",
"value": "Makes an assumption about the squares on a scale representing either 1 or 10"
}
] |
[
{
"from": "human",
"value": "Calculate time where speed and distance are in the appropriate units This displacement-time graph shows the start of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 4 \\mathrm{~m} / \\mathrm{s} \\).\nWhat are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).\nThe marked point is one square in on the Time axis and at 40 on the Distance axis.]() \\( (20,40) \\)"
},
{
"from": "gpt",
"value": "Believes scales on graphs must match on both axes"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a trapezium where the dimensions are given in the same units When calculating the area of this trapezium, what are the values of \\( a \\) and \\( b \\) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) \\( 7+7.5 \\)"
},
{
"from": "gpt",
"value": "Uses slant heights instead of parallel sides to find area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a trapezium where the dimensions are given in the same units When calculating the area of this trapezium, what are the values of \\( a \\) and \\( b \\) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) \\( 7+6 \\)"
},
{
"from": "gpt",
"value": "Uses slant heights instead of parallel sides to find area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a trapezium where the dimensions are given in the same units When calculating the area of this trapezium, what are the values of \\( a \\) and \\( b \\) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) \\( 6+7.5 \\)"
},
{
"from": "gpt",
"value": "Uses slant heights instead of parallel sides to find area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a unit fraction Write the following fraction in its simplest form: \\( 6 \\frac{3}{18} \\) \\( 3 \\frac{1}{2} \\)"
},
{
"from": "gpt",
"value": "Simplifies integers when simplifying a mixed number"
}
] |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a unit fraction Write the following fraction in its simplest form: \\( 6 \\frac{3}{18} \\) Cannot be simplified"
},
{
"from": "gpt",
"value": "Does not understand how to simplify fractions"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify the following by collecting like terms.\n\\[\n5 s-6 s+12 s-11 s\n\\] \\( 0 s \\)"
},
{
"from": "gpt",
"value": "In algebra, thinks it's ok to write (for example) 0x rather than just 0"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data When finding the range of a data set, what is the first step? Write the numbers in ascending order."
},
{
"from": "gpt",
"value": "Finds the median instead of the range"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data When finding the range of a data set, what is the first step? Add all the numbers together."
},
{
"from": "gpt",
"value": "Finds the mean instead of the range"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data When finding the range of a data set, what is the first step? Write the numbers in ascending or descending order."
},
{
"from": "gpt",
"value": "Finds the median instead of the range"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using factorisation in the form (x + a)(x + b) This is the final stage of Lucy's solution to a quadratic equation.\nWhat should replace the star?\n\\[\n(h+4)(h-3)=0\n\\] \\( h=\\bigstar \\) or \\( h=3 \\) \\( 4 \\)"
},
{
"from": "gpt",
"value": "Believes the solutions of a quadratic equation are the absolute values of the constants in the factorised form"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using factorisation in the form (x + a)(x + b) This is the final stage of Lucy's solution to a quadratic equation.\nWhat should replace the star?\n\\[\n(h+4)(h-3)=0\n\\] \\( h=\\bigstar \\) or \\( h=3 \\) \\( 0 \\)"
},
{
"from": "gpt",
"value": "Believes all quadratic equations have a solution of 0"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using factorisation in the form (x + a)(x + b) The area of the trapezium on the right is \\( 40 \\mathrm{~cm}^{2} \\). ![A trapezium with the parallel sides a and b labelled with x+2 and x+4 and the perpendicular height x.]() Based on the information given, Adam writes this formula:\n\\(x^{2}+3 x=40\\)\n\nWhat are the two solutions to this equation? \\( \\begin{array}{c}x=8 \\\\ \\text { and } \\\\ x=-5\\end{array} \\)"
},
{
"from": "gpt",
"value": "Believes the solutions of a quadratic equation are the constants in the factorised form"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Without drawing any more terms, how many circles do you predict will be in the \\( 7 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 42 \\)"
},
{
"from": "gpt",
"value": "Has multiplied the value of the first term by the the term being asked"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Without drawing any more terms, how many circles do you predict will be in the \\( 7 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 26 \\)"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence gives the term before"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Without drawing any more terms, how many circles do you predict will be in the \\( 7 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 34 \\)"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence gives the term after"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18,-4\n\\] \\( 12 \\)"
},
{
"from": "gpt",
"value": "Believes you don't need to numerically order the data before calculating the median"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18,-4\n\\] \\( 6 \\)"
},
{
"from": "gpt",
"value": "When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\[\n3,5,6,18,18,-4\n\\] \\( 18 \\)"
},
{
"from": "gpt",
"value": "Finds the mode instead of the median"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+5 x+6 \\) we need two numbers that: Add to give \\( 6 \\) and multiply to give \\( 5 \\)"
},
{
"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": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+5 x+6 \\) we need two numbers that: Add to give \\( 6 x \\) and multiply to give \\( 5 \\)"
},
{
"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": "Factorise a quadratic expression in the form x² + bx + c When factorising \\( x^{2}+5 x+6 \\) we need two numbers that: Add to give \\( 5 x \\) 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\n"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]() \\( 88 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Does not divide by 2 when calculating the area of a triangle"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]() \\( 71.5 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Has used slant height and base to find area of a triangle rather than perpendicular height and base"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]() \\( 1144 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Multiplies all given dimensions when calculating an area"
}
] |
[
{
"from": "human",
"value": "Triple numbers If you triple \\( 8 \\) you get... \\( 38 \\)"
},
{
"from": "gpt",
"value": "When multiplying just writes the numbers next to each other"
}
] |
[
{
"from": "human",
"value": "Triple numbers If you triple \\( 8 \\) you get... \\( 11 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiples"
}
] |
[
{
"from": "human",
"value": "Triple numbers If you triple \\( 8 \\) you get... \\( 888 \\)"
},
{
"from": "gpt",
"value": "When asked to triple, writes the digit out three times"
}
] |
[
{
"from": "human",
"value": "Divide algebraic fractions involving non-linear expressions STEP \\( 2 \\)\nWhich of the options is a correct second step to express the following as a single fraction?\n\n\\(\n\\begin{aligned}\n& \\frac{x-1}{6} \\div \\frac{x^{2}-1}{9} \\\\\n= & \\frac{x-1}{6} \\times \\frac{9}{x^{2}-1}\n\\end{aligned}\n\\) \\( \\frac{9 x-1}{6 x^{2}-1} \\)"
},
{
"from": "gpt",
"value": "Answers order of operations questions with brackets as if the brackets are not there"
}
] |
[
{
"from": "human",
"value": "Divide algebraic fractions involving non-linear expressions STEP \\( 2 \\)\nWhich of the options is a correct second step to express the following as a single fraction?\n\n\\(\n\\begin{aligned}\n& \\frac{x-1}{6} \\div \\frac{x^{2}-1}{9} \\\\\n= & \\frac{x-1}{6} \\times \\frac{9}{x^{2}-1}\n\\end{aligned}\n\\) \\( \\frac{-1}{6} \\times \\frac{9}{x-1} \\)"
},
{
"from": "gpt",
"value": "Incorrectly cancels what they believe is a factor in algebraic fractions"
}
] |
[
{
"from": "human",
"value": "Divide algebraic fractions involving non-linear expressions STEP \\( 2 \\)\nWhich of the options is a correct second step to express the following as a single fraction?\n\n\\(\n\\begin{aligned}\n& \\frac{x-1}{6} \\div \\frac{x^{2}-1}{9} \\\\\n= & \\frac{x-1}{6} \\times \\frac{9}{x^{2}-1}\n\\end{aligned}\n\\) \\( \\frac{x-1}{6} \\times \\frac{9}{(x-1)(x-1)} \\)"
},
{
"from": "gpt",
"value": "Factorises difference of two squares with the same sign in both brackets"
}
] |
[
{
"from": "human",
"value": "Read an integer on a scale where the required measurement is marked by a dash between two numbers What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-10\" next to the bottom dash and \"2\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the middle dash. ]() \\( -7 \\)"
},
{
"from": "gpt",
"value": "When reading integers on a number line, assumes each dash is 1"
}
] |
[
{
"from": "human",
"value": "Read an integer on a scale where the required measurement is marked by a dash between two numbers What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-10\" next to the bottom dash and \"2\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the middle dash. ]() \\( -1 \\)"
},
{
"from": "gpt",
"value": "When reading integers on a number line, assumes each dash is 1"
}
] |
[
{
"from": "human",
"value": "Read an integer on a scale where the required measurement is marked by a dash between two numbers What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. \"-10\" next to the bottom dash and \"2\" next to the top dash are the only numbers marked on the line. An arrow, labelled \"B\" is pointing at the middle dash. ]() \\( 8 \\)"
},
{
"from": "gpt",
"value": "Counts on in the wrong direction on a number line"
}
] |
[
{
"from": "human",
"value": "Interpret a pictogram involving full symbols The pictogram shows how many people came to watch a netball match.\nWhat is the mean number of people at each game? ![A pictogram with a key showing a smiley face represents 12 people. Game 1 has 4 smiley faces, Game 2 has 2 smiley faces, Game 3 has 3 smiley faces and Game 4 has 1 smiley face.]() \\( 12 \\)"
},
{
"from": "gpt",
"value": "Does not know you can find the mean from a pictogram"
}
] |