conversations
listlengths 2
2
|
|---|
[
{
"from": "human",
"value": "Recognise the equations of horizontal lines from a diagram What is the equation of this line? ![A graph of a horizontal line going through 3 on the y axis. ]() \\( x=3 \\)"
},
{
"from": "gpt",
"value": "Thinks x = ? is a horizontal line through ? "
}
] |
[
{
"from": "human",
"value": "Recognise the equations of horizontal lines from a diagram What is the equation of this line? ![A graph of a horizontal line going through 3 on the y axis. ]() \\( x=3 y \\)"
},
{
"from": "gpt",
"value": "Believes the equation of a horizontal line is in the form x = ay, where a is the y intercept"
}
] |
[
{
"from": "human",
"value": "Generate a descending integer linear sequence from the nth term rule What is the first term of the sequence given by this rule:\n\\[\n2-7 n\n\\] \\( 1 \\)"
},
{
"from": "gpt",
"value": "Thinks the first term of a sequence must be 1"
}
] |
[
{
"from": "human",
"value": "Generate a descending integer linear sequence from the nth term rule What is the first term of the sequence given by this rule:\n\\[\n2-7 n\n\\] \\( -7 \\)"
},
{
"from": "gpt",
"value": "When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n."
}
] |
[
{
"from": "human",
"value": "Add proper fractions with the same denominator Work out:\n\\(\n\\frac{4}{11}+\\frac{7}{11}\n\\)\nWrite your answer in its simplest form. \\( \\frac{11}{22} \\)"
},
{
"from": "gpt",
"value": "When adding fractions, adds the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with the same denominator Work out:\n\\(\n\\frac{4}{11}+\\frac{7}{11}\n\\)\nWrite your answer in its simplest form. \\( \\frac{1}{2} \\)"
},
{
"from": "gpt",
"value": "When adding fractions, adds the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with the same denominator Work out:\n\\(\n\\frac{4}{11}+\\frac{7}{11}\n\\)\nWrite your answer in its simplest form. \\( \\frac{11}{11} \\)"
},
{
"from": "gpt",
"value": "Forgot to simplify the fraction"
}
] |
[
{
"from": "human",
"value": "Given a sketch of a quadratic graph, f(x), write down the solutions to f(x) = a According to the graph, what is the approximate solution to\n\\(x^{2}+4 x-1=-6\\) ![A set of axes with the quadratic graph y=x^2+4x-1 drawn on.]() \\( x=-4.25, \\quad x=0.25 \\)"
},
{
"from": "gpt",
"value": "Solves for y=0 instead of given y-value when reading from a quadratic graph"
}
] |
[
{
"from": "human",
"value": "Given a sketch of a quadratic graph, f(x), write down the solutions to f(x) = a According to the graph, what is the approximate solution to\n\\(x^{2}+4 x-1=-6\\) ![A set of axes with the quadratic graph y=x^2+4x-1 drawn on.]() \\( x=-1 \\)"
},
{
"from": "gpt",
"value": "Finds the y intercept when asked to read the solution to a quadratic equation from a graph"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of other prisms when the dimensions are given in the same units ![A triangular based prism]() Tom likes to remember:\n\nVolume of a prism = Area of cross section \\( X \\) depth\n\nIn this shape, what length is the \"depth\"? \\( 5 \\mathrm{~mm} \\)"
},
{
"from": "gpt",
"value": "Thinks depth always goes front to back in a diagram of a 3D shape"
}
] |
[
{
"from": "human",
"value": "Generate a descending integer linear sequence from the nth term rule What is the first term of the sequence given by this rule:\n\\[\n1-5 n\n\\] \\( 1 \\)"
},
{
"from": "gpt",
"value": "Thinks the first term of a sequence must be 1"
}
] |
[
{
"from": "human",
"value": "Generate a descending integer linear sequence from the nth term rule What is the first term of the sequence given by this rule:\n\\[\n1-5 n\n\\] \\( -5 \\)"
},
{
"from": "gpt",
"value": "When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n."
}
] |
[
{
"from": "human",
"value": "Find missing angles in a non-special quadrilateral What is the size of angle \\( p \\) in this quadrilateral? ![Not drawn to scale]() \\( 120^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Assumes that opposite angles are equal in a quadrilateral"
}
] |
[
{
"from": "human",
"value": "Find missing angles in a non-special quadrilateral What is the size of angle \\( p \\) in this quadrilateral? ![Not drawn to scale]() \\( 50^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Does not know what dashes on the sides of shapes mean"
}
] |
[
{
"from": "human",
"value": "Find missing angles in a non-special quadrilateral What is the size of angle \\( p \\) in this quadrilateral? ![Not drawn to scale]() \\( 70^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Does not know what dashes on the sides of shapes mean"
}
] |
[
{
"from": "human",
"value": "Rearrange a quadratic equation so that it is in the correct form to be factorised What would be the most useful first step if we wanted to solve the following quadratic equation? \\( x^{2}+7 x=8 \\) Divide by \\( x \\)"
},
{
"from": "gpt",
"value": "Does not realise a quadratic must be in the form ax^2+bx+c=0 to be factorised"
}
] |
[
{
"from": "human",
"value": "Rearrange a quadratic equation so that it is in the correct form to be factorised What would be the most useful first step if we wanted to solve the following quadratic equation? \\( x^{2}+7 x=8 \\) Square root both sides of the equation"
},
{
"from": "gpt",
"value": "Does not realise a quadratic must be in the form ax^2+bx+c=0 to be factorised"
}
] |
[
{
"from": "human",
"value": "Rearrange a quadratic equation so that it is in the correct form to be factorised What would be the most useful first step if we wanted to solve the following quadratic equation? \\( x^{2}+7 x=8 \\) Subtract \\( 7 x \\) from both sides of the equation"
},
{
"from": "gpt",
"value": "Does not realise a quadratic must be in the form ax^2+bx+c=0 to be factorised"
}
] |
[
{
"from": "human",
"value": "Reduce a ratio involving two numbers to its simplest form Write the following ratio in its simplest form so both sides of the ratio are integers:\n\\(\n\\frac{1}{4}: \\frac{1}{2}\n\\) \\( 2: 4 \\)"
},
{
"from": "gpt",
"value": "Does not fully simplify ratio"
}
] |
[
{
"from": "human",
"value": "Given the sketch of a curve in the form (x + a)², work out its factorised form What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]() \\( y=(x+1)^{2} \\)"
},
{
"from": "gpt",
"value": "Forgets to swap the sign of roots when placing into brackets"
}
] |
[
{
"from": "human",
"value": "Given the sketch of a curve in the form (x + a)², work out its factorised form What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]() \\( y=x^{2}-1 \\)"
},
{
"from": "gpt",
"value": "Believes the graph of x squared + c has the turning point of (-c, 0)"
}
] |
[
{
"from": "human",
"value": "Given the sketch of a curve in the form (x + a)², work out its factorised form What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]() \\( y=x^{2}+1 \\)"
},
{
"from": "gpt",
"value": "Believes the graph of x squared + c has the turning point of (c, 0)"
}
] |
[
{
"from": "human",
"value": "Recognise when a descending sequence is quadratic Tom and Katie are discussing quadratic sequences.\n\nTom says this is a quadratic sequence: \\( 24,15,8,3,0 \\ldots \\)\n\nKatie says this is a quadratic sequence: \\( 124,63,26,7,3,0, \\ldots \\)\n\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Does not understand the term quadratic"
}
] |
[
{
"from": "human",
"value": "Recognise when a descending sequence is quadratic Tom and Katie are discussing quadratic sequences.\n\nTom says this is a quadratic sequence: \\( 24,15,8,3,0 \\ldots \\)\n\nKatie says this is a quadratic sequence: \\( 124,63,26,7,3,0, \\ldots \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not understand the term quadratic"
}
] |
[
{
"from": "human",
"value": "Recognise when a descending sequence is quadratic Tom and Katie are discussing quadratic sequences.\n\nTom says this is a quadratic sequence: \\( 24,15,8,3,0 \\ldots \\)\n\nKatie says this is a quadratic sequence: \\( 124,63,26,7,3,0, \\ldots \\)\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Thinks a decreasing sequence cannot be quadratic"
}
] |
[
{
"from": "human",
"value": "Given information about the relationship between two parts (e.g. one part is worth 5 more than another), work out other parts Percy, Quentin and Robbie share gold coins in the ratio of\n\\[\n3: 7: 8\n\\]\nPercy gets \\( 36 \\) fewer coins than Quentin.\nHow many gold coins did Robbie get? \\( 96 \\)"
},
{
"from": "gpt",
"value": "In ratio question where the difference between the sides is given, uses that as the total for one side instead"
}
] |
[
{
"from": "human",
"value": "Given information about the relationship between two parts (e.g. one part is worth 5 more than another), work out other parts Percy, Quentin and Robbie share gold coins in the ratio of\n\\[\n3: 7: 8\n\\]\nPercy gets \\( 36 \\) fewer coins than Quentin.\nHow many gold coins did Robbie get? \\( 12 \\)"
},
{
"from": "gpt",
"value": "In ratio question where the difference between the sides is given, uses that as the total"
}
] |
[
{
"from": "human",
"value": "Given information about the relationship between two parts (e.g. one part is worth 5 more than another), work out other parts Percy, Quentin and Robbie share gold coins in the ratio of\n\\[\n3: 7: 8\n\\]\nPercy gets \\( 36 \\) fewer coins than Quentin.\nHow many gold coins did Robbie get? \\( 63 \\)"
},
{
"from": "gpt",
"value": "Mixes up sides of a ratio"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, with all positive integers Tom and Katie are arguing about a first step to solve this equation:\n\\(4 v+1=9 v-3\\)\n\nTom says you can write: \\( 5 v+1=-3 \\)\n\nKatie says you can write: \\( 4 v+4=9 v \\)\n\nWho is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Subtracts the smallest digit from the largest digit"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, with all positive integers Tom and Katie are arguing about a first step to solve this equation:\n\\(4 v+1=9 v-3\\)\n\nTom says you can write: \\( 5 v+1=-3 \\)\n\nKatie says you can write: \\( 4 v+4=9 v \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Subtracts the smallest digit from the largest digit"
}
] |
[
{
"from": "human",
"value": "Recognise the vertically opposite angles relationship Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]() Alternate angles"
},
{
"from": "gpt",
"value": "Confuses alternate and opposite angles"
}
] |
[
{
"from": "human",
"value": "Recognise the vertically opposite angles relationship Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]() Corresponding angles"
},
{
"from": "gpt",
"value": "Confuses corresponding and vertically opposite angles"
}
] |
[
{
"from": "human",
"value": "Recognise the vertically opposite angles relationship Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]() Angles on a straight line"
},
{
"from": "gpt",
"value": "Confuses vertically opposite angles with angles on a straight line"
}
] |
[
{
"from": "human",
"value": "Given a sketch of a linear graph solve f(x) = n This is a graph of\n\\(y=0.4 x-3\\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve\n\\(0.4 x-3=-1\\) \\( x=-3.3 \\)"
},
{
"from": "gpt",
"value": "Mixes up the value of two terms when substituting"
}
] |
[
{
"from": "human",
"value": "Given a sketch of a linear graph solve f(x) = n This is a graph of\n\\(y=0.4 x-3\\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve\n\\(0.4 x-3=-1\\) \\( x=7.5 \\)"
},
{
"from": "gpt",
"value": "Believes the solution to mx + c = a is the x intercept of y = mx +c"
}
] |
[
{
"from": "human",
"value": "Given a sketch of a linear graph solve f(x) = n This is a graph of\n\\(y=0.4 x-3\\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve\n\\(0.4 x-3=-1\\) \\( x=-1 \\)"
},
{
"from": "gpt",
"value": "Believes the solution of mx + c = a is x =a"
}
] |
[
{
"from": "human",
"value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular pentagon has a total perimeter of \\( 17 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? \\( 85 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "When given the perimeter of a regular polygon, multiplies instead of divides to find each side length"
}
] |
[
{
"from": "human",
"value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular pentagon has a total perimeter of \\( 17 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? \\( 12 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "When given the perimeter of a regular polygon, subtracts instead of divides to find each side length"
}
] |
[
{
"from": "human",
"value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A regular pentagon has a total perimeter of \\( 17 \\mathrm{~cm} \\).\nWhat is the length of each of its sides? Not enough information"
},
{
"from": "gpt",
"value": "Does not know the meaning of the word regular "
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue? \\( \\frac{1}{4} \\)"
},
{
"from": "gpt",
"value": "Reads the complement of what is required from a pie chart"
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue? \\( 75 \\)"
},
{
"from": "gpt",
"value": "Finds a percentage when asked for a fraction"
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue? Impossible to say"
},
{
"from": "gpt",
"value": "Does not know the meaning of square sign for right angle"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 8 \\) out of \\( 40 \\) as a percentage? \\( 8.4 \\% \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a percentage by writing the numerator followed by the denominator"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 8 \\) out of \\( 40 \\) as a percentage? \\( 16 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks they double the numerator to turn a fraction into a percentage"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is value of \\( p \\) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]() \\( 6 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Makes an assumption about line segments being equal within a shape"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is value of \\( p \\) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]() \\( 7 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Makes an assumption about line segments being equal within a shape"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is value of \\( p \\) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]() Not enough information"
},
{
"from": "gpt",
"value": "Does not know that we can use the conservation of perimeter to find missing lengths"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]() \\( 120 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "When finding the area of a parallelogram does not understand which lengths to use"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]() \\( 40 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Has used slant height and base to find area of a parallelogram rather than perpendicular height and base"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]() \\( 15 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Has found the area of a triangle rather than an area of a parallelogram"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using balancing A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d-6)^{2}-16=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d-6)^{2}=16\n\\) \\( d^{2}=22 \\)"
},
{
"from": "gpt",
"value": "Believes you can subtract from inside brackets without expanding when solving an equation"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using balancing A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d-6)^{2}-16=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d-6)^{2}=16\n\\) \\( d-6=4 \\)"
},
{
"from": "gpt",
"value": "Only considers the positive solution when calculating a square root"
}
] |
[
{
"from": "human",
"value": "Find missing angles using vertically opposite angles What is the size of angle \\( p \\) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]() \\( 53^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Mistakes lines as parallel"
}
] |
[
{
"from": "human",
"value": "Find missing angles using vertically opposite angles What is the size of angle \\( p \\) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]() \\( 138^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Student thinks that any two angles along a straight line are equal"
}
] |
[
{
"from": "human",
"value": "Find missing angles using vertically opposite angles What is the size of angle \\( p \\) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]() Not enough information"
},
{
"from": "gpt",
"value": "Does not know that vertically opposite angles are equal"
}
] |
[
{
"from": "human",
"value": "Calculate the sector angle on a pie chart for a given group A class of students were surveyed about how many siblings they have.\n\nA selection of results are shown in the table. \\begin{tabular}{|c|c|c|}\n\\hline Number of siblings & Frequency & Angle on a pie chart \\\\\n\\hline 0 & \\( 7 \\) & \\( \\) \\\\\n\\hline 1 & \\( \\) & \\( 144 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 4 \\) & \\( \\bigstar \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 30 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\nWhat should replace the star? \\( 40^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes that the angle on a pie chart is the frequency multiplied by 10"
}
] |
[
{
"from": "human",
"value": "Calculate the sector angle on a pie chart for a given group A class of students were surveyed about how many siblings they have.\n\nA selection of results are shown in the table. \\begin{tabular}{|c|c|c|}\n\\hline Number of siblings & Frequency & Angle on a pie chart \\\\\n\\hline 0 & \\( 7 \\) & \\( \\) \\\\\n\\hline 1 & \\( \\) & \\( 144 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 4 \\) & \\( \\bigstar \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 30 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\nWhat should replace the star? \\( 120^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes you find the angle for a pie chart sector by doing its frequency multiplied by total frequency"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Integer ÷ Fraction How many times does \\( \\frac{3}{5} \\) go into \\( 15 \\) ? \\( \\frac{45}{75} \\)"
},
{
"from": "gpt",
"value": "When dividing an integer by a fraction, thinks they multiply numerator and denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Integer ÷ Fraction How many times does \\( \\frac{3}{5} \\) go into \\( 15 \\) ? \\( 75 \\)"
},
{
"from": "gpt",
"value": "When dividing by a non unit fraction, thinks you multiply by the reciprocal of the corresponding unit fraction rather than the fraction given. "
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Integer ÷ Fraction How many times does \\( \\frac{3}{5} \\) go into \\( 15 \\) ? \\( 9 \\)"
},
{
"from": "gpt",
"value": "when dividing a fraction by an integer, multiplies the numerator by the integer"
}
] |
[
{
"from": "human",
"value": "Carry out multiplication problems involving one negative integer John is expanding these two brackets.\n\nWhat should he get when he multiplies the two terms indicated by the arrows? ![The two brackets are (x+5)(x-3). The arrows are pointing at the +5 in the first bracket and the -3 in the second bracket.]() \\( +2 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplying when expanding bracket"
}
] |
[
{
"from": "human",
"value": "Carry out multiplication problems involving one negative integer John is expanding these two brackets.\n\nWhat should he get when he multiplies the two terms indicated by the arrows? ![The two brackets are (x+5)(x-3). The arrows are pointing at the +5 in the first bracket and the -3 in the second bracket.]() \\( +15 \\)"
},
{
"from": "gpt",
"value": "Ignores negative sign when expanding bracket"
}
] |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis Tom and Katie are discussing quadratic graphs.\n\nTom says a quadratic expression that cannot be factorised will not intercept the \\( x \\) axis.\n\nKatie says a graph of a quadratic that does not intercept the \\( x \\) axis cannot be factorised.\nWho is correct? Only Tom"
},
{
"from": "gpt",
"value": "When solving simultaneous equations graphically, they think the solutions are the x-intercepts"
}
] |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis Tom and Katie are discussing quadratic graphs.\n\nTom says a quadratic expression that cannot be factorised will not intercept the \\( x \\) axis.\n\nKatie says a graph of a quadratic that does not intercept the \\( x \\) axis cannot be factorised.\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "When solving simultaneous equations graphically, they think the solutions are the x-intercepts"
}
] |
[
{
"from": "human",
"value": "Read values off a real life graph This is a conversion graph between kilograms and pounds.\n\nWhich of the following is the best estimate for the number of kilograms equivalent to \\( 20 \\) pounds? ![A graph on gridded paper with pounds (lb) on the y axis from 0 to 80 and kilograms (kg) on the x axis from 0 to 80. Both axis are labelled in increments of 20, with each increment split by gridlines into another 4 squares. A straight line goes from the origin and sloped upwards going through (25, 55) (not labelled - just a coordinate that it goes through) ]() \\( 44 \\) kilograms"
},
{
"from": "gpt",
"value": "When reading value from graph, reads from the wrong axes."
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Which quadrilateral below is a regular polygon? ![Trapezium]()"
},
{
"from": "gpt",
"value": "Does not know the meaning of the word regular "
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Which quadrilateral below is a regular polygon? ![Rhombus]()"
},
{
"from": "gpt",
"value": "Does not know the meaning of the word regular "
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Which quadrilateral below is a regular polygon? ![Rectangle]()"
},
{
"from": "gpt",
"value": "Does not know the meaning of the word regular "
}
] |
[
{
"from": "human",
"value": "Express a division as a fraction Which calculation is equivalent to the fraction \\( \\frac{3}{4} \\) ? \\( 3-4 \\)"
},
{
"from": "gpt",
"value": "Thinks the fraction bar means subtract rather than divide"
}
] |
[
{
"from": "human",
"value": "Express a division as a fraction Which calculation is equivalent to the fraction \\( \\frac{3}{4} \\) ? \\( 4-3 \\)"
},
{
"from": "gpt",
"value": "Thinks the fraction bar means subtract rather than divide"
}
] |
[
{
"from": "human",
"value": "Express a division as a fraction Which calculation is equivalent to the fraction \\( \\frac{3}{4} \\) ? \\( 4 \\div 3 \\)"
},
{
"from": "gpt",
"value": "Believes that a fraction means dividing the denominator by the numerator"
}
] |
[
{
"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 and simplify:\n\\[\n4(2 x+1)-(5 x-9)\n\\] \\( 3 x-5 \\)"
},
{
"from": "gpt",
"value": "Does not realise that subtracting a negative is the same as adding it's additive inverse"
}
] |
[
{
"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 and simplify:\n\\[\n4(2 x+1)-(5 x-9)\n\\] \\( 13 x-5 \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts"
}
] |
[
{
"from": "human",
"value": "Expand double brackets with an extra variable outside When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+5)(m-5) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\) \\( \\triangle=+25 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying a positive by a negative gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Expand double brackets with an extra variable outside When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+5)(m-5) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\) \\( \\triangle=+5 \\)"
},
{
"from": "gpt",
"value": "When multiplying out 2 or more brackets, does not multiply all the combinations of terms"
}
] |
[
{
"from": "human",
"value": "Expand double brackets with an extra variable outside When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+5)(m-5) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\) \\(\n\\triangle=+0\n\\)\n(no \\( m \\) term)"
},
{
"from": "gpt",
"value": "Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets"
}
] |
[
{
"from": "human",
"value": "Write a given translation in vector notation Three left and five down in vector notation is... \\( \\left(\\begin{array}{c}\\triangle \\\\ \\bigcirc\\end{array}\\right) \\) What should replace the \\( \\triangle \\) ? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Thinks a negative x value in a column vector means to move right rather than left "
}
] |
[
{
"from": "human",
"value": "Write a given translation in vector notation Three left and five down in vector notation is... \\( \\left(\\begin{array}{c}\\triangle \\\\ \\bigcirc\\end{array}\\right) \\) What should replace the \\( \\triangle \\) ? \\( -5 \\)"
},
{
"from": "gpt",
"value": "Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round"
}
] |
[
{
"from": "human",
"value": "Find missing numbers in a fraction multiplication \\( \\frac{3}{5} \\times ?=\\frac{1}{2} \\) \\( \\frac{3}{10} \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation"
}
] |
[
{
"from": "human",
"value": "Find missing numbers in a fraction multiplication \\( \\frac{3}{5} \\times ?=\\frac{1}{2} \\) There are no values that make this calculation work"
},
{
"from": "gpt",
"value": "Does not realise that division can be used to find the missing value in a multiplication problem"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out other parts To make pink paint, you mix red paint with white paint in the ratio \\( 3: 4 \\).\nWhat should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]() \\( 1201 \\ \\mathrm{ml} \\)"
},
{
"from": "gpt",
"value": "Thinks a difference of one part in a ratio means the quantities will differ by one unit"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out other parts To make pink paint, you mix red paint with white paint in the ratio \\( 3: 4 \\).\nWhat should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]() \\( 900 \\ \\mathrm{ml} \\)"
},
{
"from": "gpt",
"value": "Mixes up sides of a ratio"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out other parts To make pink paint, you mix red paint with white paint in the ratio \\( 3: 4 \\).\nWhat should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]() \\( 4800 \\ \\mathrm{ml} \\)"
},
{
"from": "gpt",
"value": "In ratio question where one side of ratio is given, uses that as one part in ratio without dividing"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a trapezium where the dimensions are given in different units What should replace the star to calculate the area of this trapezium?\n Area \\( =\\frac{90+40}{2} \\times \\) \\(\\color{gold}\\bigstar\\)\n ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]() \\( 5 \\)"
},
{
"from": "gpt",
"value": "Does not convert measurements to have the same units before calculating area or volume"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a trapezium where the dimensions are given in different units What should replace the star to calculate the area of this trapezium?\n Area \\( =\\frac{90+40}{2} \\times \\) \\(\\color{gold}\\bigstar\\)\n ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]() \\( 6 \\)"
},
{
"from": "gpt",
"value": "Uses slant height instead of perpendicular height to find area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a trapezium where the dimensions are given in different units What should replace the star to calculate the area of this trapezium?\n Area \\( =\\frac{90+40}{2} \\times \\) \\(\\color{gold}\\bigstar\\)\n ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]() \\( 60 \\)"
},
{
"from": "gpt",
"value": "Uses slant height instead of perpendicular height to find area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Carry out division problems involving one negative integer Tom and Katie are trying to write different calculations for the diagram on the left.\nTom writes: \\( -3 \\times(-8)=-24 \\)\nKatie writes: \\( \\frac{(-24)}{-3}=-8 \\)\nWho is correct? ![A diagram showing an arrow to the left, marked with a value of -24. Underneath this arrow there is a smaller arrow, still pointing to the left, that is a third of the length of the larger arrow]() Only\nTom"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Carry out division problems involving one negative integer Tom and Katie are trying to write different calculations for the diagram on the left.\nTom writes: \\( -3 \\times(-8)=-24 \\)\nKatie writes: \\( \\frac{(-24)}{-3}=-8 \\)\nWho is correct? ![A diagram showing an arrow to the left, marked with a value of -24. Underneath this arrow there is a smaller arrow, still pointing to the left, that is a third of the length of the larger arrow]() Only\nKatie"
},
{
"from": "gpt",
"value": "Believes dividing a negative by a negative gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Perform calculations with areas when given in different units Square \\( \\mathrm{P} \\) has an area of \\( 4 \\mathrm{~cm}^{2} \\)\nSquare \\( Q \\) has an area of \\( 4 \\mathrm{~mm}^{2} \\)\nWhat is the total area of squares \\( P \\) and \\( Q \\) in \\( \\mathrm{mm}^{2} \\) ? \\( 8 \\mathrm{~mm}^{2} \\)"
},
{
"from": "gpt",
"value": "Does not convert measurements to have the same units before calculating area or volume"
}
] |
[
{
"from": "human",
"value": "Perform calculations with areas when given in different units Square \\( \\mathrm{P} \\) has an area of \\( 4 \\mathrm{~cm}^{2} \\)\nSquare \\( Q \\) has an area of \\( 4 \\mathrm{~mm}^{2} \\)\nWhat is the total area of squares \\( P \\) and \\( Q \\) in \\( \\mathrm{mm}^{2} \\) ? \\( 44 \\mathrm{~mm}^{2} \\)"
},
{
"from": "gpt",
"value": "Does not square the conversion factor when converting squared units"
}
] |
[
{
"from": "human",
"value": "Perform calculations with areas when given in different units Square \\( \\mathrm{P} \\) has an area of \\( 4 \\mathrm{~cm}^{2} \\)\nSquare \\( Q \\) has an area of \\( 4 \\mathrm{~mm}^{2} \\)\nWhat is the total area of squares \\( P \\) and \\( Q \\) in \\( \\mathrm{mm}^{2} \\) ? \\( 40004 \\mathrm{~mm}^{2} \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100mm in a centimetre"
}
] |
[
{
"from": "human",
"value": "Find the gradient of a line written in the form ax + by = c What is the gradient of this line?\n\\(5 x+3 y=15\\) \\( 5 \\)"
},
{
"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": "Find the gradient of a line written in the form ax + by = c What is the gradient of this line?\n\\(5 x+3 y=15\\) \\( -5 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, believes that when they get to ax = b, b is the solution"
}
] |
[
{
"from": "human",
"value": "Find the gradient of a line written in the form ax + by = c What is the gradient of this line?\n\\(5 x+3 y=15\\) \\( \\frac{5}{3} \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Compare sets of data using the range The table shows the summary statistics from some girls and boys who took a test.\nWho performed the most consistently? ![\\begin{tabular}{|c|c|c|}\n\\hline Gender & Mean & Range \\\\\n\\hline Girls & \\( 75 \\) & \\( 20 \\) \\\\\n\\hline Boys & \\( 60 \\) & \\( 40 \\) \\\\\n\\hline\n\\end{tabular}]() The boys because their mean is lower"
},
{
"from": "gpt",
"value": "Thinks a lower average means the data is more consistent"
}
] |
[
{
"from": "human",
"value": "Compare sets of data using the range The table shows the summary statistics from some girls and boys who took a test.\nWho performed the most consistently? ![\\begin{tabular}{|c|c|c|}\n\\hline Gender & Mean & Range \\\\\n\\hline Girls & \\( 75 \\) & \\( 20 \\) \\\\\n\\hline Boys & \\( 60 \\) & \\( 40 \\) \\\\\n\\hline\n\\end{tabular}]() The boys because their range is higher"
},
{
"from": "gpt",
"value": "Thinks a greater range means more consistent data"
}
] |
[
{
"from": "human",
"value": "Compare sets of data using the range The table shows the summary statistics from some girls and boys who took a test.\nWho performed the most consistently? ![\\begin{tabular}{|c|c|c|}\n\\hline Gender & Mean & Range \\\\\n\\hline Girls & \\( 75 \\) & \\( 20 \\) \\\\\n\\hline Boys & \\( 60 \\) & \\( 40 \\) \\\\\n\\hline\n\\end{tabular}]() The girls because their mean is higher"
},
{
"from": "gpt",
"value": "Thinks a higher average means more consistent data"
}
] |
[
{
"from": "human",
"value": "Recognise the notation for parallel lines Tom and Katie are discussing parallel lines. Tom says these two lines are parallel ![Image of a grid of squares with 2 lines on it. One line goes two squares to the right and one square up. The second line goes four squares to the right and two squares up.]() Katie says these two lines are parallel ![Image of a grid of squares with 2 lines on it. One line goes two squares to the right and one square up. The second line goes two squares to the right and one square down.]() Who is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes two lines of the same length are parallel"
}
] |
[
{
"from": "human",
"value": "Carry out subtraction problems involving two negative integers What number belongs in the box?\n\\(\n(-8)-(-5)=\n\\square\\) \\( -13 \\)"
},
{
"from": "gpt",
"value": "When subtracting a negative thinks the answer must be negative "
}
] |
[
{
"from": "human",
"value": "Carry out subtraction problems involving two negative integers What number belongs in the box?\n\\(\n(-8)-(-5)=\n\\square\\) \\( 13 \\)"
},
{
"from": "gpt",
"value": "When subtracting from a negative thinks the answer must be positive"
}
] |