conversations
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[
{
"from": "human",
"value": "Understand the notation for powers To calculate \\( 47^{2} \\) you need to do... \\( 47 \\times 2 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Calculate the perimeter of a rectilinear shape by adding lengths expressed in the same units What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form upside down step structure. The base of the shape is horizontal and is 12m long. The vertical height of the whole shape is 27m. The horizontal width of the top part of the shape is 32m. The horizontal width of the top step is 15m. The vertical height of the top rectangle is 9m. The vertical height of the bottom rectangle is 10m. ]() \\( 121 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Does not know how to find missing lengths in a composite shape"
}
] |
[
{
"from": "human",
"value": "Calculate the perimeter of a rectilinear shape by adding lengths expressed in the same units What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form upside down step structure. The base of the shape is horizontal and is 12m long. The vertical height of the whole shape is 27m. The horizontal width of the top part of the shape is 32m. The horizontal width of the top step is 15m. The vertical height of the top rectangle is 9m. The vertical height of the bottom rectangle is 10m. ]() \\( 130 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Does not know how to find missing lengths in a composite shape"
}
] |
[
{
"from": "human",
"value": "Calculate the perimeter of a rectilinear shape by adding lengths expressed in the same units What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form upside down step structure. The base of the shape is horizontal and is 12m long. The vertical height of the whole shape is 27m. The horizontal width of the top part of the shape is 32m. The horizontal width of the top step is 15m. The vertical height of the top rectangle is 9m. The vertical height of the bottom rectangle is 10m. ]() \\( 105 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "When calculating perimeter, only adds the marked lengths"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out other parts Kate and Isaac share some sweets in the ratio \\( 3: 2 \\)\n\nKate receives \\( 60 \\) sweets.\n\nHow many sweets does Isaac receive? \\( 20 \\)"
},
{
"from": "gpt",
"value": "Finds one part of a ratio but doesn't multiply that by the number of parts needed"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out other parts Kate and Isaac share some sweets in the ratio \\( 3: 2 \\)\n\nKate receives \\( 60 \\) sweets.\n\nHow many sweets does Isaac receive? \\( 24 \\)"
},
{
"from": "gpt",
"value": "In ratio question where one side of ratio is given, treats that as the total"
}
] |
[
{
"from": "human",
"value": "Carry out, interpret and represent subtraction using the part-whole model \\[\n8+12 \\div 4 \\square(8+12) \\div 4\n\\]\nWhich symbol belongs in the box? \\( < \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Carry out, interpret and represent subtraction using the part-whole model \\[\n8+12 \\div 4 \\square(8+12) \\div 4\n\\]\nWhich symbol belongs in the box? \\( = \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Carry out, interpret and represent subtraction using the part-whole model \\[\n8+12 \\div 4 \\square(8+12) \\div 4\n\\]\nWhich symbol belongs in the box? \\( \\geq \\)"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Find missing angles in an isosceles triangle What is value of the shaded angle in this diagram? ![[not to scale]]() \\( 80^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Assumes an angle has been split into equal parts"
}
] |
[
{
"from": "human",
"value": "Find missing angles in an isosceles triangle What is value of the shaded angle in this diagram? ![[not to scale]]() \\( 140^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Assumes an angle has been split into equal parts"
}
] |
[
{
"from": "human",
"value": "Describe the meaning algebraic terms with powers Which of the following means the same as\n\\(a^{2} b\\) \\( 2 \\times a \\times b \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Describe the meaning algebraic terms with powers Which of the following means the same as\n\\(a^{2} b\\) \\( a \\times b \\times a \\times b \\)"
},
{
"from": "gpt",
"value": "When a variable in an expression has a power, thinks the power applies to the whole expression"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are not multiples of the same number Which diagram represents the largest fraction? ![A rectangle divided horizontally into 3 smaller rectangles that are identical to each other in size and shape. The top rectangle, of the 3, is shaded orange, the rest are white.]()"
},
{
"from": "gpt",
"value": "Thinks that a larger shaded area represents a larger fraction"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are not multiples of the same number Which diagram represents the largest fraction? ![A rectangle divided into a grid of 30 smaller rectangles (5 high by 6 wide) that are identical to each other in size and shape. 8 of these smaller rectangles are shaded orange, the rest are white.]()"
},
{
"from": "gpt",
"value": "Thinks a greater number of shaded parts represents a greater fraction"
}
] |
[
{
"from": "human",
"value": "Identify when rounding a calculation will give an over or under approximation Jo and Paul are discussing how to estimate the answer to\n\\[\n188.945 \\div 15.3382\n\\]\n\nJo says \\( 200 \\div 15.3382 \\) would give an overestimate.\n\nPaul says \\( 188.945 \\div 15 \\) would give an overestimate.\n\nWho is correct? Only Jo"
},
{
"from": "gpt",
"value": "Believes that the smaller a divisor is, the smaller the answer will be"
}
] |
[
{
"from": "human",
"value": "Identify when rounding a calculation will give an over or under approximation Jo and Paul are discussing how to estimate the answer to\n\\[\n188.945 \\div 15.3382\n\\]\n\nJo says \\( 200 \\div 15.3382 \\) would give an overestimate.\n\nPaul says \\( 188.945 \\div 15 \\) would give an overestimate.\n\nWho is correct? Only Paul"
},
{
"from": "gpt",
"value": "Believes that the larger the dividend, the smaller the answer."
}
] |
[
{
"from": "human",
"value": "Multiplication law of indices with positive integer powers and a different base number Tom and Katie are arguing about \\( 4^{2} \\times 2^{2} \\)\nTom says \\( 4^{2} \\times 2^{2}=64 \\)\nKatie says \\( 4^{2} \\times 2^{2}=8^{4} \\)\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "When multiplying numbers with different bases, multiplies the powers and multiplies the base numbers."
}
] |
[
{
"from": "human",
"value": "Substitute into simple formulae given in words A quick way to change approximately from miles to kilometers is to divide the number of miles by \\( 3 \\) and then multiply by \\( 5 \\).\nUsing this method, how many kilometres are equal to \\( 15 \\) miles? \\( 17 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of divides"
}
] |
[
{
"from": "human",
"value": "Substitute into simple formulae given in words A quick way to change approximately from miles to kilometers is to divide the number of miles by \\( 3 \\) and then multiply by \\( 5 \\).\nUsing this method, how many kilometres are equal to \\( 15 \\) miles? \\( 15 \\)"
},
{
"from": "gpt",
"value": "Think 1km = 1 mile"
}
] |
[
{
"from": "human",
"value": "Order numbers in standard form that are between 0 and 1 Tom and Katie are discussing standard form.\n\nTom says \\( 9.3 \\times 10^{5}>2.3 \\times 10^{6} \\)\n\nKatie says \\( 9.3 \\times 10^{-5}>2.3 \\times 10^{-6} \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "When ordering numbers in standard form just looks at the decimal without multiplying by a power of 10"
}
] |
[
{
"from": "human",
"value": "Find missing angles in an isosceles triangle This is an isosceles triangle.\nCalculate the size of angle \\( p \\). ![An isosceles triangle with one angle labelled 56 degrees and one angle labelled p [not to scale]]() \\( 56^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes there is only one orientation for the isosceles triangle base angles"
}
] |
[
{
"from": "human",
"value": "Find missing angles in an isosceles triangle This is an isosceles triangle.\nCalculate the size of angle \\( p \\). ![An isosceles triangle with one angle labelled 56 degrees and one angle labelled p [not to scale]]() \\( 68^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes there is only one orientation for the isosceles triangle base angles"
}
] |
[
{
"from": "human",
"value": "Find missing angles in an isosceles triangle This is an isosceles triangle.\nCalculate the size of angle \\( p \\). ![An isosceles triangle with one angle labelled 56 degrees and one angle labelled p [not to scale]]() \\( 124^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Forgets to subtract sum of angles we know from 180 to find missing angle in a triangle"
}
] |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 5 \\) litres \\( = \\) ________\\( \\mathrm{cm}^{3} \\) \\( 5 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 1 cubic centimetre"
}
] |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 5 \\) litres \\( = \\) ________\\( \\mathrm{cm}^{3} \\) \\( 500 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 100 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 5 \\) litres \\( = \\) ________\\( \\mathrm{cm}^{3} \\) \\( 50 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 10 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Understand the non-commutativity of division Tom and Katie want to share £2 between \\( 4 \\) people.\nTom says you would calculate the amount each person gets by doing \\( 4 \\div 2 \\)\nKatie says you would calculate the amount each person gets by doing \\( 2 \\div 4 \\)\nWho do you agree with? Only Tom"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Understand the non-commutativity of division Tom and Katie want to share £2 between \\( 4 \\) people.\nTom says you would calculate the amount each person gets by doing \\( 4 \\div 2 \\)\nKatie says you would calculate the amount each person gets by doing \\( 2 \\div 4 \\)\nWho do you agree with? Both of them"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that makes a backwards \"L\" shape from 2 rectangles. The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The left handed rectangle is shaded blue.]() \\( 44 \\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 that makes a backwards \"L\" shape from 2 rectangles. The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The left handed rectangle is shaded blue.]() \\( 22 \\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 that makes a backwards \"L\" shape from 2 rectangles. The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The left handed rectangle is shaded blue.]() \\( 28 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Uses an incorrect side length when splitting a composite shape into parts"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object Which is the correct point for \\( \\mathrm{E} \\) when reflected in the line \\( x=0 \\) ? ![A 4 quadrant, coordinate grid with a triangle drawn on it with the coordinates (-4,1) (-1,1) and (-2,3). E is the point (-2,3)]() B is the coordinate (-2,-3)"
},
{
"from": "gpt",
"value": "Thinks x = 0 is the x axis"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object Which is the correct point for \\( \\mathrm{E} \\) when reflected in the line \\( x=0 \\) ? ![A 4 quadrant, coordinate grid with a triangle drawn on it with the coordinates (-4,1) (-1,1) and (-2,3). E is the point (-2,3)]() C is the coordinate (2,-3)"
},
{
"from": "gpt",
"value": "Rotates instead of reflects"
}
] |
[
{
"from": "human",
"value": "Identify a rhombus from a description of the properties Tom and Katie have been asked to give the name of a quadrilateral with four equal sides\nTom says rectangle\nKatie says rhombus\nWho do you agree with? Only\nTom"
},
{
"from": "gpt",
"value": "Believes a rectangle has four equal sides"
}
] |
[
{
"from": "human",
"value": "Identify a rhombus from a description of the properties Tom and Katie have been asked to give the name of a quadrilateral with four equal sides\nTom says rectangle\nKatie says rhombus\nWho do you agree with? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes a rectangle has four equal sides"
}
] |
[
{
"from": "human",
"value": "Identify a rhombus from a description of the properties Tom and Katie have been asked to give the name of a quadrilateral with four equal sides\nTom says rectangle\nKatie says rhombus\nWho do you agree with? Neither is correct"
},
{
"from": "gpt",
"value": "Believes a rectangle has four equal sides"
}
] |
[
{
"from": "human",
"value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes Tom says these two shapes are congruent ![Two identical 6-sided \"L shape\" polygons. One of the polygons has been rotated through 90 degrees.]() Katie says these two shapes are congruent ![Two 6-sided \"L shape\" polygons. One of the polygons has a wider upright section than the other.]() Who is correct? Only Katie"
},
{
"from": "gpt",
"value": "Thinks congruent shapes are the same shape but can be different sizes"
}
] |
[
{
"from": "human",
"value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes Tom says these two shapes are congruent ![Two identical 6-sided \"L shape\" polygons. One of the polygons has been rotated through 90 degrees.]() Katie says these two shapes are congruent ![Two 6-sided \"L shape\" polygons. One of the polygons has a wider upright section than the other.]() Who is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Thinks congruent shapes are the same shape but can be different sizes"
}
] |
[
{
"from": "human",
"value": "Identify congruence in shapes other than triangles Tom and Katie are discussing congruent shapes Tom says these two shapes are congruent ![Two identical 6-sided \"L shape\" polygons. One of the polygons has been rotated through 90 degrees.]() Katie says these two shapes are congruent ![Two 6-sided \"L shape\" polygons. One of the polygons has a wider upright section than the other.]() Who is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not understand that shapes are congruent if they have the same size and shape"
}
] |
[
{
"from": "human",
"value": "Identify a unit of length Sally has answered a question on perimeter and worked out an answer of \\( 120 \\).\n\nBehind the star she has written the units that she used.\n\nWhich of the following units is definitely wrong? \\( 120 \\color{yellow}\\bigstar \\) \\( m \\)"
},
{
"from": "gpt",
"value": "Does not recognise metres as a unit of length"
}
] |
[
{
"from": "human",
"value": "Identify a unit of length Sally has answered a question on perimeter and worked out an answer of \\( 120 \\).\n\nBehind the star she has written the units that she used.\n\nWhich of the following units is definitely wrong? \\( 120 \\color{yellow}\\bigstar \\) \\( \\mathrm{km} \\)"
},
{
"from": "gpt",
"value": "Does not recognise km as a unit of length "
}
] |
[
{
"from": "human",
"value": "Identify a unit of length Sally has answered a question on perimeter and worked out an answer of \\( 120 \\).\n\nBehind the star she has written the units that she used.\n\nWhich of the following units is definitely wrong? \\( 120 \\color{yellow}\\bigstar \\) \\( 11 \\)"
},
{
"from": "gpt",
"value": "Does not recognise inches (\") as a unit of length"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(20 t-5=0\\) \\( t=4 \\)"
},
{
"from": "gpt",
"value": "Swaps the dividend and divisor in order to get an integer answer"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(20 t-5=0\\) \\( t=-\\frac{1}{4} \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Complete multi-step mental calculations What is the value of:\n\\(\n\\frac{54+58}{2}\n\\) \\( 224 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than divides"
}
] |
[
{
"from": "human",
"value": "Complete multi-step mental calculations What is the value of:\n\\(\n\\frac{54+58}{2}\n\\) \\( 85 \\)"
},
{
"from": "gpt",
"value": "Does not interpret the correct order of operations in a fraction when there is an addition on the numerator"
}
] |
[
{
"from": "human",
"value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative Cara is trying to work out the midpoint of these two points: \\( (-5,7) \\) and \\( (-2,-1) \\) She labels them like this: \\( \\left.\\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (-5, & 7) & (-2, & -1) \\end{array}\\right.\\) And then decides to use this formula: \\( \\left(\\frac{x_{1}+x_{2}}{2}, \\frac{y_{1}+y_{2}}{2}\\right) \\) What is the \\( \\boldsymbol{y} \\) value of the midpoint? \\( 6 \\)"
},
{
"from": "gpt",
"value": "Does not divide by 2 when finding midpoint"
}
] |
[
{
"from": "human",
"value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative Cara is trying to work out the midpoint of these two points: \\( (-5,7) \\) and \\( (-2,-1) \\) She labels them like this: \\( \\left.\\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (-5, & 7) & (-2, & -1) \\end{array}\\right.\\) And then decides to use this formula: \\( \\left(\\frac{x_{1}+x_{2}}{2}, \\frac{y_{1}+y_{2}}{2}\\right) \\) What is the \\( \\boldsymbol{y} \\) value of the midpoint? \\( 4 \\)"
},
{
"from": "gpt",
"value": "Believes that adding a negative will increase the value of the original number"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![Two angles on a straight line, one is labelled 62 degrees and the other is q]() \\( 62^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Student thinks that any two angles along a straight line are equal"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![Two angles on a straight line, one is labelled 62 degrees and the other is q]() \\( 128^{\\circ} \\)"
},
{
"from": "gpt",
"value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( q \\) ? ![Two angles on a straight line, one is labelled 62 degrees and the other is q]() \\( 298^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 360 degrees"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line Adjacent angles on a straight line sum to... \\( 90^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 90 degrees"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line Adjacent angles on a straight line sum to... \\( 100^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 100 degrees"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line Adjacent angles on a straight line sum to... \\( 360^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 360 degrees"
}
] |
[
{
"from": "human",
"value": "Solve length problems involving similar shapes where the missing length is the longer one The shape below has a perimeter of \\( p \\). If the length of all the sides are doubled, what is the perimeter of the enlarged shape? ![A trapezium]() \\( p+2 \\)"
},
{
"from": "gpt",
"value": "Confuses additive and multiplicative relationships"
}
] |
[
{
"from": "human",
"value": "Solve length problems involving similar shapes where the missing length is the longer one The shape below has a perimeter of \\( p \\). If the length of all the sides are doubled, what is the perimeter of the enlarged shape? ![A trapezium]() Not enough information"
},
{
"from": "gpt",
"value": "Does not realise we can scale the perimeter as a whole, rather than finding individual side lengths"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible:\n\\(\np^{2}-9\n\\) \\( (p-3)(p-3) \\)"
},
{
"from": "gpt",
"value": "Factorises difference of two squares with the same sign in both brackets"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible:\n\\(\np^{2}-9\n\\) \\( p(p-9) \\)"
},
{
"from": "gpt",
"value": "Believes only the first term needs to be divided when factorising an expression"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible:\n\\(\np^{2}-9\n\\) Does not factorise"
},
{
"from": "gpt",
"value": "Does not recognise difference of two squares"
}
] |
[
{
"from": "human",
"value": "Divide a decimal by an integer What is the mean of the following numbers?\n\\[\n2, \\quad 0.2, \\quad 0.02\n\\] \\( 0.2 \\)"
},
{
"from": "gpt",
"value": "Finds the median instead of the mean"
}
] |
[
{
"from": "human",
"value": "Substitute numbers into a SUVAT equation to work out distance \\( s=u t+\\frac{1}{2} a t^{2} \\) What is the value of \\( s \\) when\na=6 \nu=3 \nt=4\n \\( 156 \\)"
},
{
"from": "gpt",
"value": "When a variable in an expression has a power, thinks the power applies to the whole expression"
}
] |
[
{
"from": "human",
"value": "Substitute numbers into a SUVAT equation to work out distance \\( s=u t+\\frac{1}{2} a t^{2} \\) What is the value of \\( s \\) when\na=6 \nu=3 \nt=4\n \\( 576 \\)"
},
{
"from": "gpt",
"value": "When a variable in an expression has a power, thinks the power applies to the whole expression"
}
] |
[
{
"from": "human",
"value": "Determine the input of a double function machine used to create an algebraic expression ![A function machine with 4 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 next rectangle has \"− 4\" written inside it, the next rectangle has \"✕ 4\" written inside it and the final rectangle on the right has \"output\" written above it and \"8m − 20\" written inside it.]() What is the input of this function machine? \\( 2 m-16 \\)"
},
{
"from": "gpt",
"value": "Thinks you apply one inverse operation to one term and the other inverse operation to the other term"
}
] |
[
{
"from": "human",
"value": "Determine the input of a double function machine used to create an algebraic expression ![A function machine with 4 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 next rectangle has \"− 4\" written inside it, the next rectangle has \"✕ 4\" written inside it and the final rectangle on the right has \"output\" written above it and \"8m − 20\" written inside it.]() What is the input of this function machine? \\( 2 m-20 \\)"
},
{
"from": "gpt",
"value": "Does not apply the inverse function to every term in an expression"
}
] |
[
{
"from": "human",
"value": "Determine the input of a double function machine used to create an algebraic expression ![A function machine with 4 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 next rectangle has \"− 4\" written inside it, the next rectangle has \"✕ 4\" written inside it and the final rectangle on the right has \"output\" written above it and \"8m − 20\" written inside it.]() What is the input of this function machine? \\( 2 m-5 \\)"
},
{
"from": "gpt",
"value": "Has completed only one of the two operations."
}
] |
[
{
"from": "human",
"value": "Determine if a given point lies on a line Jo and Paul are arguing about points on the line\n\\(4 x-5 y=20\\)\n\nJo says \\( (10,-4) \\) lies on the line \\( \\mathbf{4 x}-\\mathbf{5 y}=\\mathbf{2 0} \\)\n\nPaul says \\( (-4,10) \\) lies on the line \\( \\mathbf{4} \\boldsymbol{x}-\\mathbf{5 y}=\\mathbf{2 0} \\)\n\nWho is correct? Only\nJo"
},
{
"from": "gpt",
"value": "When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored "
}
] |
[
{
"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} \\) ? ![A coordinate grid with the reflection line y=-x drawn and a triangle with the coordinates (-2,3) (-1,4) and (0,3). P is the point (0,3)]() \\( (-6,3) \\)"
},
{
"from": "gpt",
"value": "Counts the squares rather than the diagonals when reflecting in y=x or y=-x "
}
] |
[
{
"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} \\) ? ![A coordinate grid with the reflection line y=-x drawn and a triangle with the coordinates (-2,3) (-1,4) and (0,3). P is the point (0,3)]() \\( (-3,6) \\)"
},
{
"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} \\) ? ![A coordinate grid with the reflection line y=-x drawn and a triangle with the coordinates (-2,3) (-1,4) and (0,3). P is the point (0,3)]() \\( (-3,3) \\)"
},
{
"from": "gpt",
"value": "Fails to reflect across mirror line"
}
] |
[
{
"from": "human",
"value": "Construct a triangle using Side-Angle-Side Which combination of mathematical instruments has been used to construct this triangle? ![A triangle construction with one angle and two sides labelled ]() Protractor \nCompass"
},
{
"from": "gpt",
"value": "Forgets you need a ruler to measure lengths"
}
] |
[
{
"from": "human",
"value": "Construct a triangle using Side-Angle-Side Which combination of mathematical instruments has been used to construct this triangle? ![A triangle construction with one angle and two sides labelled ]() Ruler \nCompass"
},
{
"from": "gpt",
"value": "Forgets you need a protractor to measure angles"
}
] |
[
{
"from": "human",
"value": "Construct a triangle using Side-Angle-Side Which combination of mathematical instruments has been used to construct this triangle? ![A triangle construction with one angle and two sides labelled ]() Ruler \nProtractor"
},
{
"from": "gpt",
"value": "Forgets you need a compass to draw arcs"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition or subtraction with multiplication Every week for \\( 4 \\) weeks, Cara buys a magazine for \\( £ 6 \\) and gets her nails painted for \\( £ 28 \\).\n\nHow much money does Cara spend altogether? \\( £ 34 \\)"
},
{
"from": "gpt",
"value": "Forgets to multiply up for the correct time frame in a worded question"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition or subtraction with multiplication Every week for \\( 4 \\) weeks, Cara buys a magazine for \\( £ 6 \\) and gets her nails painted for \\( £ 28 \\).\n\nHow much money does Cara spend altogether? \\( £ 52 \\)"
},
{
"from": "gpt",
"value": "Does not interpret the correct order of operations from a worded problem"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition or subtraction with multiplication Every week for \\( 4 \\) weeks, Cara buys a magazine for \\( £ 6 \\) and gets her nails painted for \\( £ 28 \\).\n\nHow much money does Cara spend altogether? \\( £ 118 \\)"
},
{
"from": "gpt",
"value": "Does not interpret the correct order of operations from a worded problem"
}
] |
[
{
"from": "human",
"value": "Calculate the cube root of a number \\( \\sqrt[3]{125}= \\) \\( \\frac{125}{3} \\)"
},
{
"from": "gpt",
"value": "Divides by the order of the root"
}
] |
[
{
"from": "human",
"value": "Calculate the cube root of a number \\( \\sqrt[3]{125}= \\) \\( 375 \\)"
},
{
"from": "gpt",
"value": "Has multiplied by the root power"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles \\( \\mathrm{M} \\) and \\( \\mathrm{N} \\) are the intersections of the line \\( X Y \\) with the lines \\( P Q \\) and RS.\nWhich angle is corresponding to angle MNS? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.\nA red straight line, XY, crosses the parallel lines. X is on the left of the diagram.\nLine XY crosses line PQ at a point marked M.\nLine XY crosses line RS at a point marked N.\nThe angle MNS is marked in red.]() YNR"
},
{
"from": "gpt",
"value": "Confuses corresponding and vertically opposite angles"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles \\( \\mathrm{M} \\) and \\( \\mathrm{N} \\) are the intersections of the line \\( X Y \\) with the lines \\( P Q \\) and RS.\nWhich angle is corresponding to angle MNS? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.\nA red straight line, XY, crosses the parallel lines. X is on the left of the diagram.\nLine XY crosses line PQ at a point marked M.\nLine XY crosses line RS at a point marked N.\nThe angle MNS is marked in red.]() QMN"
},
{
"from": "gpt",
"value": "Confuses co-interior and corresponding angles"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles \\( \\mathrm{M} \\) and \\( \\mathrm{N} \\) are the intersections of the line \\( X Y \\) with the lines \\( P Q \\) and RS.\nWhich angle is corresponding to angle MNS? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.\nA red straight line, XY, crosses the parallel lines. X is on the left of the diagram.\nLine XY crosses line PQ at a point marked M.\nLine XY crosses line RS at a point marked N.\nThe angle MNS is marked in red.]() NMP"
},
{
"from": "gpt",
"value": "Confuses corresponding and alternate angles"
}
] |
[
{
"from": "human",
"value": "Convert between cl and l \\[\n30 \\text { centilitres }=\\bigstar \\text { litres }\n\\]\nWhat should replace the star? \\( 3000 \\)"
},
{
"from": "gpt",
"value": "Multiplies when converting to a larger unit"
}
] |
[
{
"from": "human",
"value": "Convert between cl and l \\[\n30 \\text { centilitres }=\\bigstar \\text { litres }\n\\]\nWhat should replace the star? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10cl in a litre"
}
] |
[
{
"from": "human",
"value": "Convert between cl and l \\[\n30 \\text { centilitres }=\\bigstar \\text { litres }\n\\]\nWhat should replace the star? \\( 0.03 \\)"
},
{
"from": "gpt",
"value": "Confuses cl and ml"
}
] |
[
{
"from": "human",
"value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable What do you need to do to eliminate the \\( q s \\) in each of these pairs of simultaneous equations?\n Pair \\( 1 \\)\n\\(\n\\begin{array}{l}\n5 p+2 q=12 \\\\\n3 p+2 q=8\n\\end{array}\n\\) Pair \\( 2 \\)\n\\(\n\\begin{array}{l}\n5 p-2 q=12 \\\\\n3 p-2 q=8\n\\end{array}\n\\) Add Pair \\( 1 \\)\nSubtract Pair \\( 2 \\)"
},
{
"from": "gpt",
"value": "Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we do the operation matching the sign (+ if positive, - if negative)"
}
] |
[
{
"from": "human",
"value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable What do you need to do to eliminate the \\( q s \\) in each of these pairs of simultaneous equations?\n Pair \\( 1 \\)\n\\(\n\\begin{array}{l}\n5 p+2 q=12 \\\\\n3 p+2 q=8\n\\end{array}\n\\) Pair \\( 2 \\)\n\\(\n\\begin{array}{l}\n5 p-2 q=12 \\\\\n3 p-2 q=8\n\\end{array}\n\\) Add Pair \\( 1 \\)\nAdd Pair \\( 2 \\)"
},
{
"from": "gpt",
"value": "Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations."
}
] |
[
{
"from": "human",
"value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable What do you need to do to eliminate the \\( q s \\) in each of these pairs of simultaneous equations?\n Pair \\( 1 \\)\n\\(\n\\begin{array}{l}\n5 p+2 q=12 \\\\\n3 p+2 q=8\n\\end{array}\n\\) Pair \\( 2 \\)\n\\(\n\\begin{array}{l}\n5 p-2 q=12 \\\\\n3 p-2 q=8\n\\end{array}\n\\) Subtract Pair \\( 1 \\)\nAdd Pair \\( 2 \\)"
},
{
"from": "gpt",
"value": "Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we do the operation inverse to the sign (- if positive, + if negative)"
}
] |
[
{
"from": "human",
"value": "Read values off a displacement-time graph How far away from home was Rachel at 10:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). ]() \\( 6.5 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "When reading values from graphs, writes down the wrong units"
}
] |
[
{
"from": "human",
"value": "Read values off a displacement-time graph How far away from home was Rachel at 10:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). ]() \\( 650 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100m and a km"
}
] |
[
{
"from": "human",
"value": "Read values off a displacement-time graph How far away from home was Rachel at 10:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). ]() \\( 7 \\mathrm{~km} \\)"
},
{
"from": "gpt",
"value": "Misreads scale"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate real life graph Johan wants to plot a graph to show the distance a ball travels over time.\n\nAfter \\( 2 \\) seconds the ball has travelled \\( 3 \\) metres.\n\nWhere on the graph should Johan plot this? ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. B is plotted above 3 on the horizontal axis and right of 2 on the vertical axis.]()"
},
{
"from": "gpt",
"value": "When reading value from graph, reads from the wrong axes."
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate real life graph Johan wants to plot a graph to show the distance a ball travels over time.\n\nAfter \\( 2 \\) seconds the ball has travelled \\( 3 \\) metres.\n\nWhere on the graph should Johan plot this? ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. C is plotted below 3 on the horizontal axis and right of -2 on the vertical axis.]()"
},
{
"from": "gpt",
"value": "When reading value from graph, reads from the wrong axes."
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate real life graph Johan wants to plot a graph to show the distance a ball travels over time.\n\nAfter \\( 2 \\) seconds the ball has travelled \\( 3 \\) metres.\n\nWhere on the graph should Johan plot this? ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. D is plotted below 2 on the horizontal axis and right of -3 on the vertical axis.]()"
},
{
"from": "gpt",
"value": "Confuses negative and positive coordinates when working with graphs in four quadrants"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one side labelled 5 cm.]() \\( 120 \\mathrm{~cm}^{3} \\)"
},
{
"from": "gpt",
"value": "Calculates perimeter when asked for area"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one side labelled 5 cm.]() \\( 100 \\mathrm{~cm}^{3} \\)"
},
{
"from": "gpt",
"value": "Does not recognise that all lengths on a cube are equal"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cube What is the volume of this cube? ![A cube with one side labelled 5 cm.]() \\( 150 \\mathrm{~cm}^{3} \\)"
},
{
"from": "gpt",
"value": "Finds surface area when asked for volume"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Fraction Calculate:\n\\(\n\\frac{1}{9} \\times \\frac{1}{5}\n\\) \\( \\frac{2}{14} \\)"
},
{
"from": "gpt",
"value": "When multiplying fractions, adds the numerators and the denominators"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Fraction Calculate:\n\\(\n\\frac{1}{9} \\times \\frac{1}{5}\n\\) \\( \\frac{5}{9} \\)"
},
{
"from": "gpt",
"value": "when multiplying fractions multiplies by the reciprocal of the 2nd fraction instead"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Fraction Calculate:\n\\(\n\\frac{1}{9} \\times \\frac{1}{5}\n\\) \\( \\frac{1}{14} \\)"
},
{
"from": "gpt",
"value": "When multiplying fractions, multiplies the numerator and adds the denominator"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number ![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 \"30\" written inside it. The middle rectangle has \"squared\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 60 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
Subsets and Splits