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 = ... |
[
{
"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... |
[
{
"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":... |
[
{
"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... |
[
{
"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": "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... |
[
{
"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 ... |
[
{
"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":... |
[
{
"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"... |
[
{
"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 ... |
[
{
"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 po... |
[
{
"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 po... |
[
{
"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": "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 ... |
[
{
"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 co... |
[
{
"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 R... |
[
{
"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 R... |
[
{
"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 R... |
[
{
"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 ... |
[
{
"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 ... |
[
{
"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 betwe... |
[
{
"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 betwe... |
[
{
"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 betwe... |
[
{
"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 substi... |
[
{
"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... |
[
{
"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",
... |
[
{
"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",
... |
[
{
"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",
"... |
[
{
"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 ... |
[
{
"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 ... |
[
{
"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 ... |
[
{
"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 a... |
[
{
"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 a... |
[
{
"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 a... |
[
{
"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](... |
[
{
"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](... |
[
{
"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](... |
[
{
"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 ... |
[
{
"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 t... |
[
{
"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 ... |
[
{
"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 ... |
[
{
"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 ... |
[
{
"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\\hli... |
[
{
"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\\hli... |
[
{
"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 i... |
[
{
"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 fract... |
[
{
"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 th... |
[
{
"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 th... |
[
{
"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 qua... |
[
{
"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 qua... |
[
{
"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 kilog... |
[
{
"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 t... |
[
{
"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": "... |
[
{
"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": "W... |
[
{
"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":... |
[
{
"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... |
[
{
"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 ... |
[
{
"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 p... |
[
{
"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",
"va... |
[
{
"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",
"val... |
[
{
"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",
"va... |
[
{
"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 4... |
[
{
"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 4... |
[
{
"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 4... |
[
{
"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 ... |
[
{
"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 ... |
[
{
"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} \\)... |
[
{
"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} \\)... |
[
{
"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} \\)... |
[
{
"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... |
[
{
"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... |
[
{
"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... |
[
{
"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 ... |
[
{
"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"
}
] |
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