conversations
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[
{
"from": "human",
"value": "Calculate the volume of a cylinder when the dimensions are given in the same units What is the area of the face marked \\( F \\) ![A cylinder with height 9cm and radius 5cm. An arrow points to the circular face at the bottom of the cylinder.]() \\( 100 \\pi\\ \\mathrm{cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Confuses diameter and radius"
}
] |
[
{
"from": "human",
"value": "Calculate the distance travelled using a speed-time graph The velocity-time graph shows the velocity of a car during a journey ![A velocity-time graph. Section A goes from (0,0) to (10,20). With the 10 being 10 seconds and the 20 being 20 m/s.]() What was the distance travelled during section\nA? \\( 200 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Thinks the shape of the graph does not affect the area calculation"
}
] |
[
{
"from": "human",
"value": "Calculate the distance travelled using a speed-time graph The velocity-time graph shows the velocity of a car during a journey ![A velocity-time graph. Section A goes from (0,0) to (10,20). With the 10 being 10 seconds and the 20 being 20 m/s.]() What was the distance travelled during section\nA? \\( 2 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Believes distance = speed/time"
}
] |
[
{
"from": "human",
"value": "Calculate the distance travelled using a speed-time graph The velocity-time graph shows the velocity of a car during a journey ![A velocity-time graph. Section A goes from (0,0) to (10,20). With the 10 being 10 seconds and the 20 being 20 m/s.]() What was the distance travelled during section\nA? \\( 22.36 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Believes the length of the line in a velocity time graph gives the distance (rather than the area underneath that line)."
}
] |
[
{
"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}-3 x-6=2\\) ![A set of axes with the quadratic graph y=x^2-3x-6 drawn on.]() \\( x=-1.4, \\quad x=4.3 \\)"
},
{
"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}-3 x-6=2\\) ![A set of axes with the quadratic graph y=x^2-3x-6 drawn on.]() \\( y=-6 \\)"
},
{
"from": "gpt",
"value": "Finds the y intercept when asked to read the solution to a quadratic equation from a graph"
}
] |
[
{
"from": "human",
"value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\nTom says \\( 3 \\) is a common factor of \\( 12 x \\) and \\( 15 y^{2} \\)\nKatie says \\( x \\) is a common factor of \\( 12 x \\) and \\( 15 y^{2} \\)\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not know how to identify common factors from algebraic terms"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 100 What is \\( 356,958 \\) rounded to the nearest \\( 100 \\) ? \\( 356,900 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 100 What is \\( 356,958 \\) rounded to the nearest \\( 100 \\) ? \\( 356,960 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too little)"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 100 What is \\( 356,958 \\) rounded to the nearest \\( 100 \\) ? \\( 400,000 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Compare real life graphs Tom and Katie are discussing graphs that show the volume of water\n(V) flowing from a kitchen tap over time (t). Tom says this graph shows water flowing at a constant rate ![A sketch of a graph showing V on the y axis and t on the x axis. A line starts at the origin and slopes upwards getting gradually steeper. ]() Katie says this graph shows water flowing at a constant rate ![A sketch of a graph showing V on the y axis and t on the x axis. A horizontal straight line goes from halfway up the y axis straight across the graph. ]() Who is correct? Only Tom"
},
{
"from": "gpt",
"value": "Believes a curve can show a constant rate"
}
] |
[
{
"from": "human",
"value": "Compare real life graphs Tom and Katie are discussing graphs that show the volume of water\n(V) flowing from a kitchen tap over time (t). Tom says this graph shows water flowing at a constant rate ![A sketch of a graph showing V on the y axis and t on the x axis. A line starts at the origin and slopes upwards getting gradually steeper. ]() Katie says this graph shows water flowing at a constant rate ![A sketch of a graph showing V on the y axis and t on the x axis. A horizontal straight line goes from halfway up the y axis straight across the graph. ]() Who is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes a curve can show a constant rate"
}
] |
[
{
"from": "human",
"value": "Multiply algebraic terms, where both are linear versions of different letters (e.g. 4a x 2b) Simplify, if possible:\n\\[\n6 a \\times 4 b\n\\] \\( 10 a b \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Multiply algebraic terms, where both are linear versions of different letters (e.g. 4a x 2b) Simplify, if possible:\n\\[\n6 a \\times 4 b\n\\] \\( 24+a b \\)"
},
{
"from": "gpt",
"value": "Multiplies coefficients and letters separately and writes as an addition"
}
] |
[
{
"from": "human",
"value": "Multiply algebraic terms, where both are linear versions of different letters (e.g. 4a x 2b) Simplify, if possible:\n\\[\n6 a \\times 4 b\n\\] Does not simplify"
},
{
"from": "gpt",
"value": "Does not understand how to multiply algebraic terms"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, with all positive integers Jo and Paul are arguing about a first step to solve this equation:\n\\(\n6(m+4)=24\n\\)\nJo says you can write: \\( m+4=4 \\)\nPaul says you can write: \\( 6 m=20 \\)\nWho is correct? Both Jo and Paul"
},
{
"from": "gpt",
"value": "Believes you can subtract from inside brackets without expanding when solving an equation"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, with all positive integers Jo and Paul are arguing about a first step to solve this equation:\n\\(\n6(m+4)=24\n\\)\nJo says you can write: \\( m+4=4 \\)\nPaul says you can write: \\( 6 m=20 \\)\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Believes they must expand brackets before solving an equation"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to one significant figure Round \\( 0.0735 \\) to \\( 1 \\) significant figure \\( 0.1 \\)"
},
{
"from": "gpt",
"value": "Rounds to wrong degree of accuracy (decimal places rather than significant figures)"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to one significant figure Round \\( 0.0735 \\) to \\( 1 \\) significant figure \\( 0.7 \\)"
},
{
"from": "gpt",
"value": "Changes wrong place value column when rounding"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to one significant figure Round \\( 0.0735 \\) to \\( 1 \\) significant figure \\( 1.0 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Recognise and name an identity Tom and Katie are discussing identities\nTom says an identity sign should replace the star here: \\( 5 y+7 \\underset{\\star}{2} 7+5 y \\) Katie says an identity sign should replace the star here: \\( 5 y-7 \\underset{\\star} 7-5 y \\) Who is correct? Only Katie"
},
{
"from": "gpt",
"value": "Does not know the meaning of the word identity "
}
] |
[
{
"from": "human",
"value": "Recognise and name an identity Tom and Katie are discussing identities\nTom says an identity sign should replace the star here: \\( 5 y+7 \\underset{\\star}{2} 7+5 y \\) Katie says an identity sign should replace the star here: \\( 5 y-7 \\underset{\\star} 7-5 y \\) Who is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Ignores the negative sign when thinking about the value of a term"
}
] |
[
{
"from": "human",
"value": "Recognise and name an identity Tom and Katie are discussing identities\nTom says an identity sign should replace the star here: \\( 5 y+7 \\underset{\\star}{2} 7+5 y \\) Katie says an identity sign should replace the star here: \\( 5 y-7 \\underset{\\star} 7-5 y \\) Who is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not realise addition is commutative"
}
] |
[
{
"from": "human",
"value": "Solve coordinate geometry questions involving quadrilaterals Tom and Katie are discussing what coordinates would complete a square.\nTom says \\( (1,8) \\) and \\( (5,8) \\)\nKatie says \\( (3,6) \\) and \\( (3,2) \\)\nWho is correct? ![A pair of axes with no labels, 1st quadrant only. 2 points are marked with red dots and are labelled with co-ordinates: (1, 4) and (5, 4).]() Only Tom"
},
{
"from": "gpt",
"value": "Believes the sides of a square must be horizontal and vertical, not diagonal"
}
] |
[
{
"from": "human",
"value": "Solve coordinate geometry questions involving quadrilaterals Tom and Katie are discussing what coordinates would complete a square.\nTom says \\( (1,8) \\) and \\( (5,8) \\)\nKatie says \\( (3,6) \\) and \\( (3,2) \\)\nWho is correct? ![A pair of axes with no labels, 1st quadrant only. 2 points are marked with red dots and are labelled with co-ordinates: (1, 4) and (5, 4).]() Neither is correct"
},
{
"from": "gpt",
"value": "Does not know how to find the length of a line segment from coordinates"
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities involving two inequality signs What is the solution to the following inequality?\n\\(-3<2 x+1<7\\) \\( -1<x<3 \\)"
},
{
"from": "gpt",
"value": "Believes subtracting a positive number from a negative number makes the answer less negative"
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities involving two inequality signs What is the solution to the following inequality?\n\\(-3<2 x+1<7\\) \\( -0.5<x<2.5 \\)"
},
{
"from": "gpt",
"value": "Does not reverse the order of operations when solving an equation"
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities involving two inequality signs What is the solution to the following inequality?\n\\(-3<2 x+1<7\\) \\( -5<x<15 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable \\(\n3(4 x+6)-2(x-9) \\equiv A x+B\n\\)\n\nWhat is the value of \\( A \\) ? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Only multiplies the numerical terms when expanding a bracket"
}
] |
[
{
"from": "human",
"value": "Subtract integers with more than 4 digits using a written method where carrying is not needed Colm wins \\( £ 55750 \\) on the lottery and gives \\( £ 25250 \\) to charity.\nHow much money does Colm keep? \\( £ 81000 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of adds when answering worded problems "
}
] |
[
{
"from": "human",
"value": "Subtract integers with more than 4 digits using a written method where carrying is not needed Colm wins \\( £ 55750 \\) on the lottery and gives \\( £ 25250 \\) to charity.\nHow much money does Colm keep? \\( £ 80000 \\)"
},
{
"from": "gpt",
"value": "Adds rather than subtracts when answering worded problems"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{1}{6} \\times 6=? \\) \\( \\frac{6}{36} \\)"
},
{
"from": "gpt",
"value": "When multiplying a fraction by an integer, multiplies both numerator and denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{1}{6} \\times 6=? \\) \\( \\frac{1}{36} \\)"
},
{
"from": "gpt",
"value": "When multiplying a fraction by an integer, multiplies the denominator instead of the numerator"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{1}{6} \\times 6=? \\) \\( 6 \\)"
},
{
"from": "gpt",
"value": "Thinks converting an integer to a fraction means both the numerator and denominator are equal"
}
] |
[
{
"from": "human",
"value": "Understand the limitations of the mean Which of the following would not be representative of this data?\n\\[\n5,6,7,8,8,9,11,12,320\n\\] Median"
},
{
"from": "gpt",
"value": "Believes extreme values can affect the median"
}
] |
[
{
"from": "human",
"value": "Understand the limitations of the mean Which of the following would not be representative of this data?\n\\[\n5,6,7,8,8,9,11,12,320\n\\] Mode"
},
{
"from": "gpt",
"value": "Believes extreme values can affect the mode"
}
] |
[
{
"from": "human",
"value": "Understand the limitations of the mean Which of the following would not be representative of this data?\n\\[\n5,6,7,8,8,9,11,12,320\n\\] All are representative"
},
{
"from": "gpt",
"value": "Believes the mean is always representative"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order integers with a different number of digits Which symbol makes the following statement correct?\n\\(\n725,912 \\quad \\square \\quad 2,705,291\n\\) \\( > \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order integers with a different number of digits Which symbol makes the following statement correct?\n\\(\n725,912 \\quad \\square \\quad 2,705,291\n\\) None of these"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order integers with a different number of digits Which symbol makes the following statement correct?\n\\(\n725,912 \\quad \\square \\quad 2,705,291\n\\) \\( = \\)"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Understand key loci terms like equidistant and perpendicular ![A set of axes: x-axis from -4 to 4, y-axis from -4 to 4. A red line is drawn from (-2,2) to (2,2).]() The red line is _________ to the y axis. Opposite"
},
{
"from": "gpt",
"value": "Believes a line segment can be opposite an axis"
}
] |
[
{
"from": "human",
"value": "Understand key loci terms like equidistant and perpendicular ![A set of axes: x-axis from -4 to 4, y-axis from -4 to 4. A red line is drawn from (-2,2) to (2,2).]() The red line is _________ to the y axis. Equidistant"
},
{
"from": "gpt",
"value": "Does not know the meaning of perpendicular"
}
] |
[
{
"from": "human",
"value": "Solve length problems involving similar shapes where the missing length is the longer one What is the ratio of \\( x \\) to \\( y \\) ? ![A triangle. The bottom width is marked '15cm'. One side is split into two parts, one part is called 'x', the other is marked 'y'. A second line goes across the triangle from where the side is split into two parts. It is marked '5cm'. ]() \\( 1: 3 \\)"
},
{
"from": "gpt",
"value": "Does not understand that in the ratio 1:n the total number of parts would be 1+n "
}
] |
[
{
"from": "human",
"value": "Solve length problems involving similar shapes where the missing length is the longer one What is the ratio of \\( x \\) to \\( y \\) ? ![A triangle. The bottom width is marked '15cm'. One side is split into two parts, one part is called 'x', the other is marked 'y'. A second line goes across the triangle from where the side is split into two parts. It is marked '5cm'. ]() \\( 1: 4 \\)"
},
{
"from": "gpt",
"value": "Does not understand that in the ratio 1:n the total number of parts would be 1+n "
}
] |
[
{
"from": "human",
"value": "Solve length problems involving similar shapes where the missing length is the longer one What is the ratio of \\( x \\) to \\( y \\) ? ![A triangle. The bottom width is marked '15cm'. One side is split into two parts, one part is called 'x', the other is marked 'y'. A second line goes across the triangle from where the side is split into two parts. It is marked '5cm'. ]() \\( 1: 5 \\)"
},
{
"from": "gpt",
"value": "Does not understand that in the ratio 1:n the total number of parts would be 1+n "
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using balancing Solve this equation, giving all solutions:\n\\(\n3 p^{2}+9=39\n\\) \\[\nn=5\n\\]\nor\n\\[\nn=-5\n\\]"
},
{
"from": "gpt",
"value": "Believes the inverse of square rooting is halving"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using balancing Solve this equation, giving all solutions:\n\\(\n3 p^{2}+9=39\n\\) \\[\np=2\n\\]\nor\n\\[\np=-2\n\\]"
},
{
"from": "gpt",
"value": "Does not reverse the order of operations when solving an equation"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using balancing Solve this equation, giving all solutions:\n\\(\n3 p^{2}+9=39\n\\) \\[\np=4\n\\]\nor\n\\[\np=-4\n\\]"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Use angles around a point with algebra to prove results Which of the following statements can you prove from this diagram? ![Angles around a point split into three parts with the parts labelled: m+50, 2m+n and 220-2m]() \\( m=n \\)"
},
{
"from": "gpt",
"value": "Ignores numerical terms when setting up an equation from a question"
}
] |
[
{
"from": "human",
"value": "Use angles around a point with algebra to prove results Which of the following statements can you prove from this diagram? ![Angles around a point split into three parts with the parts labelled: m+50, 2m+n and 220-2m]() \\( m+n=270 \\)"
},
{
"from": "gpt",
"value": "Does not use angle facts when setting up an equation from an angle diagram"
}
] |
[
{
"from": "human",
"value": "Use angles around a point with algebra to prove results Which of the following statements can you prove from this diagram? ![Angles around a point split into three parts with the parts labelled: m+50, 2m+n and 220-2m]() \\( m+n=360 \\)"
},
{
"from": "gpt",
"value": "Ignores numerical terms when setting up an equation from a question"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which of the following is the correct way of writing: \\( p \\) divided by \\( q \\), then add \\( 3 \\) using algebraic convention? \\( p q+3 \\)"
},
{
"from": "gpt",
"value": "Thinks two letters next to each other is a division"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which of the following is the correct way of writing: \\( p \\) divided by \\( q \\), then add \\( 3 \\) using algebraic convention? \\( \\frac{p}{q+3} \\)"
},
{
"from": "gpt",
"value": "Does not account for grammar when writing algebra e.g. ,then making a group"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which of the following is the correct way of writing: \\( p \\) divided by \\( q \\), then add \\( 3 \\) using algebraic convention? \\( p-q+3 \\)"
},
{
"from": "gpt",
"value": "Has used a subtraction sign to represent division"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n0.2, \\quad 0.22, \\quad 0.212\n\\] \\( 0.012 \\)"
},
{
"from": "gpt",
"value": "When calculating the range does not reorder the data to find the largest number minus the smallest number"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n0.2, \\quad 0.22, \\quad 0.212\n\\] \\( 0.21 \\)"
},
{
"from": "gpt",
"value": "When calculating the range does not reorder the data to find the largest number minus the smallest number"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n0.2, \\quad 0.22, \\quad 0.212\n\\] \\( 0.2 \\)"
},
{
"from": "gpt",
"value": "When subtracting decimals with a different number of decimal places, lines up the digits incorrectly"
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to a positive integer power Which of the following is a power of \\( 5 \\) ? \\( 55 \\)"
},
{
"from": "gpt",
"value": "Confuses powers and multiples"
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to a positive integer power Which of the following is a power of \\( 5 \\) ? \\( 100 \\)"
},
{
"from": "gpt",
"value": "Confuses powers and multiples"
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to a positive integer power Which of the following is a power of \\( 5 \\) ? \\( 500 \\)"
},
{
"from": "gpt",
"value": "Confuses powers and multiples"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 \\( 20 \\% \\) of \\( 35= \\) \\( 3.5 \\)"
},
{
"from": "gpt",
"value": "Finds 10% of an amount rather than the percentage being asked"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 \\( 20 \\% \\) of \\( 35= \\) \\( 70 \\)"
},
{
"from": "gpt",
"value": "When finding a percentage of an amount, assumes they divide the percentage by 10, but not the amount, before multiplying"
}
] |
[
{
"from": "human",
"value": "Sort and class quadrilaterals into hierarchical families Tom and Katie are arguing about parallelograms. Tom says this shape is a parallelogram ![A four sided shape. All sides are equal, opposite angles are equal. There are no right angles.]() Katie says this shape is a parallelogram ![A four sided shape. Opposite sides are equal, all angles are right angles.]() Who is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Does not know a rectangle is a type of parallelogram "
}
] |
[
{
"from": "human",
"value": "Sort and class quadrilaterals into hierarchical families Tom and Katie are arguing about parallelograms. Tom says this shape is a parallelogram ![A four sided shape. All sides are equal, opposite angles are equal. There are no right angles.]() Katie says this shape is a parallelogram ![A four sided shape. Opposite sides are equal, all angles are right angles.]() Who is correct? Only\nKatie"
},
{
"from": "gpt",
"value": "Does not know a rhombus is a type of parallelogram "
}
] |
[
{
"from": "human",
"value": "Sort and class quadrilaterals into hierarchical families Tom and Katie are arguing about parallelograms. Tom says this shape is a parallelogram ![A four sided shape. All sides are equal, opposite angles are equal. There are no right angles.]() Katie says this shape is a parallelogram ![A four sided shape. Opposite sides are equal, all angles are right angles.]() Who is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not believe a shape can have two correct names e.g. rectangle and parallelogram"
}
] |
[
{
"from": "human",
"value": "Complete the square for expressions that end up in the form (x + a)² + b When Sarah completes the square, what should replace the triangle?\n\\[\np^{2}-10 p-1 \\equiv(p-5)^{2} \\Delta\n\\] \\( \\Delta=+24 \\)"
},
{
"from": "gpt",
"value": "When completing the square in the form (x - a)^2 + b, believes b = a^2 + the original constant"
}
] |
[
{
"from": "human",
"value": "Complete the square for expressions that end up in the form (x + a)² + b When Sarah completes the square, what should replace the triangle?\n\\[\np^{2}-10 p-1 \\equiv(p-5)^{2} \\Delta\n\\] \\( \\Delta =-11 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Rotate an object or point 180° about a point, where the point lies on the edge or outside of the object ![A pair of axes: x-axis is from -2 to 4; y-axis is from -2 to 4. A 6-sided polygon, labelled \"P\", is made by joining the following points, in order, with straight lines: (1, 2), (2, 2), (2, 3), (4, 3), (4, 4), (1, 4) and back to (1, 2).\nThe point (2, 2) is marked with a red dot.\nAlso, the following points are plotted and labelled with the following letters: A (-2, -2); B (2, -2); C (-1, -2); D (-2, -1).]() Shape \\( \\mathrm{P} \\) is rotated \\( 180^{\\circ} \\) through the origin.\n\nWhere will the red point be on the rotated shape? B"
},
{
"from": "gpt",
"value": "Reflects instead of rotates"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for reciprocal graphs This is a part of the table of values for the equation \\( y=\\frac{3}{x} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Forgets that a number divided by itself is 1"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for reciprocal graphs This is a part of the table of values for the equation \\( y=\\frac{3}{x} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 0 \\)"
},
{
"from": "gpt",
"value": "Believes that a fraction with equal numerator and denominator cancels to 0"
}
] |
[
{
"from": "human",
"value": "Calculate the cube root of a number \\( \\sqrt[3]{216}= \\) \\( 72 \\)"
},
{
"from": "gpt",
"value": "Divides by the order of the root"
}
] |
[
{
"from": "human",
"value": "Calculate the cube root of a number \\( \\sqrt[3]{216}= \\) \\( 108 \\)"
},
{
"from": "gpt",
"value": "Halves when asked to find the cube root"
}
] |
[
{
"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 \\) & \\( \\bigstar \\) \\\\\n\\hline 1 & \\( \\) & \\( 144 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 4 \\) & \\( \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 30 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\n\nWhich of the following calculations would work out what replaces the star? \\( \\frac{30}{360} \\times 7 \\)"
},
{
"from": "gpt",
"value": "Believes that to find an angle for a pie chart sector you divide the total frequency by 360 and multiply by its frequency"
}
] |
[
{
"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 \\) & \\( \\bigstar \\) \\\\\n\\hline 1 & \\( \\) & \\( 144 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 4 \\) & \\( \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 30 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\n\nWhich of the following calculations would work out what replaces the star? \\( \\frac{30}{7} \\times 360 \\)"
},
{
"from": "gpt",
"value": "Believes that a fraction means dividing the denominator by the numerator"
}
] |
[
{
"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 \\) & \\( \\bigstar \\) \\\\\n\\hline 1 & \\( \\) & \\( 144 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 4 \\) & \\( \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 30 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\n\nWhich of the following calculations would work out what replaces the star? \\( 7 \\times 30 \\)"
},
{
"from": "gpt",
"value": "Believes you find the angle for a pie chart sector by doing its frequency multiplied by total frequency"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 2 decimal place to percentages What is \\( 0.03 \\) written as a percentage? \\( 30 \\% \\)"
},
{
"from": "gpt",
"value": "Multiplied by 1000 instead of 100"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 2 decimal place to percentages What is \\( 0.03 \\) written as a percentage? \\( 0.03 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks you need to just add a % sign to a decimal to convert to a percentage"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 2 decimal place to percentages What is \\( 0.03 \\) written as a percentage? \\( 0.3 \\% \\)"
},
{
"from": "gpt",
"value": "Multiplied by 10 rather than 100"
}
] |
[
{
"from": "human",
"value": "Recognise graphical representations of inverse proportion in the form y = k/x Which of the following graphs show that \\( \\mathrm{x} \\) is inversely proportional to \\( y \\) ? ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape]()"
},
{
"from": "gpt",
"value": "Confuses reciprocal and quadratic graphs"
}
] |
[
{
"from": "human",
"value": "Recognise graphical representations of inverse proportion in the form y = k/x Which of the following graphs show that \\( \\mathrm{x} \\) is inversely proportional to \\( y \\) ? ![A graph with a straight line going from bottom left to top right. The graph starts from 0 on the y axis. ]()"
},
{
"from": "gpt",
"value": "Confuses the graphs of direct and inverse proportion"
}
] |
[
{
"from": "human",
"value": "Divide mixed number fraction in the form: Integer ÷ Fraction \\( 4 \\div 2 \\frac{4}{5} \\) Which of the following is a correct way to write the answer to this calculation? \\( \\frac{7}{10} \\)"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Which expression should replace the star in the addition pyramid? ![A pyramid showing the expressions 2a, -b and 2a-2b across the base from left to right. Above the 2a and -b is a star. Above the -b and the 2a-2b is written 2a-3b]() \\( 4 a-3 b \\)"
},
{
"from": "gpt",
"value": "Thinks you add all the bricks in a row in an addition pyramid."
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Which expression should replace the star in the addition pyramid? ![A pyramid showing the expressions 2a, -b and 2a-2b across the base from left to right. Above the 2a and -b is a star. Above the -b and the 2a-2b is written 2a-3b]() \\( -2 a b \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than adds "
}
] |
[
{
"from": "human",
"value": "Calculate questions involving the power law of indices with positive integer powers \\( \\left(4^{6}\\right)^{2}= \\) \\( 4^{8} \\)"
},
{
"from": "gpt",
"value": "Has added the powers rather than multiplying them"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Use the graph to approximate the solution to \\( x^{2}-x-6<-4 \\) ![A set of axes with the quadratic graph y=x^2-x-6 drawn on.]() \\( x<-1, x>2 \\)"
},
{
"from": "gpt",
"value": "Selects y>a solutions instead of y<a solutions for a quadratic inequality"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Use the graph to approximate the solution to \\( x^{2}-x-6<-4 \\) ![A set of axes with the quadratic graph y=x^2-x-6 drawn on.]() \\( -2<x<3 \\)"
},
{
"from": "gpt",
"value": "Solves for y=0 instead of given y-value when reading from a quadratic graph"
}
] |
[
{
"from": "human",
"value": "Read values off a real life graph This graph shows the relationship between journey time and the speed of a car.\nHow long will the journey take if the car travels at \\( 30 \\mathrm{mph} \\) ? ![A graph showing speed in miles per hour on the x axis and journey time in hours on the y axis. A curve is shown that has a steep negative gradient to start with, that gradually becomes less steep until it is nearly horizontal. The curve passes through the points (8,30) and (30,7)]() \\( 8 \\) hours"
},
{
"from": "gpt",
"value": "When reading value from graph, reads from the wrong axes."
}
] |
[
{
"from": "human",
"value": "Read values off a real life graph This graph shows the relationship between journey time and the speed of a car.\nHow long will the journey take if the car travels at \\( 30 \\mathrm{mph} \\) ? ![A graph showing speed in miles per hour on the x axis and journey time in hours on the y axis. A curve is shown that has a steep negative gradient to start with, that gradually becomes less steep until it is nearly horizontal. The curve passes through the points (8,30) and (30,7)]() \\( 30 \\) hours"
},
{
"from": "gpt",
"value": "When asked to read a value from a graph, thinks they give the corresponding value on the other axis, rather than reading from the graph"
}
] |
[
{
"from": "human",
"value": "Read values off a real life graph This graph shows the relationship between journey time and the speed of a car.\nHow long will the journey take if the car travels at \\( 30 \\mathrm{mph} \\) ? ![A graph showing speed in miles per hour on the x axis and journey time in hours on the y axis. A curve is shown that has a steep negative gradient to start with, that gradually becomes less steep until it is nearly horizontal. The curve passes through the points (8,30) and (30,7)]() \\( 15 \\) hours"
},
{
"from": "gpt",
"value": "Makes an assumption about the squares on a scale representing either 1 or 10"
}
] |
[
{
"from": "human",
"value": "Add surds in the form mva + nvb \\(\n2 \\sqrt{5}+2 \\sqrt{45} \\equiv d \\sqrt{5}\n\\)\n\nWhat is the value of \\( d \\) ? \\( 7 \\)"
},
{
"from": "gpt",
"value": "When simplifying surds, does not multiply the number in front of the surd with the square root of the largest square number that has been removed from the surd"
}
] |
[
{
"from": "human",
"value": "Add surds in the form mva + nvb \\(\n2 \\sqrt{5}+2 \\sqrt{45} \\equiv d \\sqrt{5}\n\\)\n\nWhat is the value of \\( d \\) ? \\( 20 \\)"
},
{
"from": "gpt",
"value": "When simplifying surds, does not square root the largest square number that goes into the number under the surd before putting it in front of the surd"
}
] |
[
{
"from": "human",
"value": "Add surds in the form mva + nvb \\(\n2 \\sqrt{5}+2 \\sqrt{45} \\equiv d \\sqrt{5}\n\\)\n\nWhat is the value of \\( d \\) ? \\( 4 \\)"
},
{
"from": "gpt",
"value": "When adding or subtracting surds, does not simplify the surd before adding the numbers in front of the surd"
}
] |
[
{
"from": "human",
"value": "Solve three or more step linear equations, with the variable on one side, with all positive integers Tom and Katie are discussing how to solve:\n\\(\\frac{5 x-1}{3}=2\\)\n\nTom says a correct next line of working could be: \\( 5 x-1=6 \\)\n\nKatie says a correct next line of working could be: \\( \\frac{5 x}{3}=3 \\)\n\nWho is correct? Only\nKatie"
},
{
"from": "gpt",
"value": "Adds or subtracts from numerator first when solving an equation with a fraction"
}
] |
[
{
"from": "human",
"value": "Solve three or more step linear equations, with the variable on one side, with all positive integers Tom and Katie are discussing how to solve:\n\\(\\frac{5 x-1}{3}=2\\)\n\nTom says a correct next line of working could be: \\( 5 x-1=6 \\)\n\nKatie says a correct next line of working could be: \\( \\frac{5 x}{3}=3 \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Adds or subtracts from numerator first when solving an equation with a fraction"
}
] |
[
{
"from": "human",
"value": "Solve three or more step linear equations, with the variable on one side, with all positive integers Tom and Katie are discussing how to solve:\n\\(\\frac{5 x-1}{3}=2\\)\n\nTom says a correct next line of working could be: \\( 5 x-1=6 \\)\n\nKatie says a correct next line of working could be: \\( \\frac{5 x}{3}=3 \\)\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not understand the concept of inverse operations in algebra"
}
] |
[
{
"from": "human",
"value": "Identify triangular numbers ![The triangle numbers represented using purple circles with the first term having 3 purple circles. The second and third terms are also shown.]() How many circles will the next term in this sequence have? \\( 20 \\)"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Identify triangular numbers ![The triangle numbers represented using purple circles with the first term having 3 purple circles. The second and third terms are also shown.]() How many circles will the next term in this sequence have? \\( 14 \\)"
},
{
"from": "gpt",
"value": "Only looks at the difference between one pair of terms when discerning the pattern"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles around a point What is the size of angle \\( z \\) ? ![Angles around a point made up of two angles labelled 162 degrees and z]() \\( 18^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles around a point sum to 180"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles around a point What is the size of angle \\( z \\) ? ![Angles around a point made up of two angles labelled 162 degrees and z]() \\( 162^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Confuses vertically opposite angles and angles around a point"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles around a point What is the size of angle \\( z \\) ? ![Angles around a point made up of two angles labelled 162 degrees and z]() \\( 208^{\\circ} \\)"
},
{
"from": "gpt",
"value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit"
}
] |
Subsets and Splits