conversations
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[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(2 y-3)^{2}\n\\) \\( 4 y^{2}-9 \\)"
},
{
"from": "gpt",
"value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(2 y-3)^{2}\n\\) \\( 4 y^{2}+9 \\)"
},
{
"from": "gpt",
"value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets"
}
] |
[
{
"from": "human",
"value": "Convert integer percentages with 2 digits to decimals How do you write \\( 23 \\% \\) as a decimal? \\( 2.3 \\)"
},
{
"from": "gpt",
"value": "Divided by 10 rather than 100"
}
] |
[
{
"from": "human",
"value": "Convert integer percentages with 2 digits to decimals How do you write \\( 23 \\% \\) as a decimal? \\( 23 \\)"
},
{
"from": "gpt",
"value": "Thinks you need to just remove the percentage sign to convert from a percentage to a decimal"
}
] |
[
{
"from": "human",
"value": "Convert integer percentages with 2 digits to decimals How do you write \\( 23 \\% \\) as a decimal? \\( 23.00 \\)"
},
{
"from": "gpt",
"value": "Does not understand a percentage is out of 100"
}
] |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence ![Square then subtract \\( 2 \\)]() The first three terms of which sequence below is produced by this term-to-term rule? \\( -1,2,7 \\)"
},
{
"from": "gpt",
"value": "Believes term to term rule is applied to position number, not previous term"
}
] |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence ![Square then subtract \\( 2 \\)]() The first three terms of which sequence below is produced by this term-to-term rule? \\( -1,-3,-11 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence ![Square then subtract \\( 2 \\)]() The first three terms of which sequence below is produced by this term-to-term rule? \\( -1,-4,-10 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Express a non-linear equation as a function machine Which function machine matches the equation \\( y=x^{2}+4 ? \\) ![A function machine which has 4 parts joined by arrows pointing from left to right. \"𝑥\" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has \"+ 4\" written inside it, followed by a horizontal arrow pointing to a rectangle that has \"square\" written inside it, followed by a horizontal arrow pointing to \"y\".]()"
},
{
"from": "gpt",
"value": "Does not follow the arrows through a function machine, changes the order of the operations asked."
}
] |
[
{
"from": "human",
"value": "Express a non-linear equation as a function machine Which function machine matches the equation \\( y=x^{2}+4 ? \\) ![A function machine which has 4 parts joined by arrows pointing from left to right. \"𝑥\" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has \"✕ 2\" written inside it, followed by a horizontal arrow pointing to a rectangle that has \"+ 4\" written inside it, followed by a horizontal arrow pointing to \"y\".]()"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Express a non-linear equation as a function machine Which function machine matches the equation \\( y=x^{2}+4 ? \\) ![A function machine which has 4 parts joined by arrows pointing from left to right. \"y\" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has \"+ 4\" written inside it, followed by a horizontal arrow pointing to a rectangle that has \"square\" written inside it, followed by a horizontal arrow pointing to \"𝑥\"]()"
},
{
"from": "gpt",
"value": "When using a function machine, confuses the input and the output."
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart This pie chart shows how an average American household uses water.\n\nWhich of the following can not be found from this pie chart? ![A pie chart showing multiple sections: Toilet 26.7%, Leaks 13.7%, Other 5.3%, Clothes Washer 21.7%, Faucet 15.7%, Shower 16.8% ]() The fraction of the different uses of water"
},
{
"from": "gpt",
"value": "Believes percentages cannot be converted into fractions"
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart This pie chart shows how an average American household uses water.\n\nWhich of the following can not be found from this pie chart? ![A pie chart showing multiple sections: Toilet 26.7%, Leaks 13.7%, Other 5.3%, Clothes Washer 21.7%, Faucet 15.7%, Shower 16.8% ]() The angle of each of the sectors"
},
{
"from": "gpt",
"value": "Believes you cannot find the angle size in a pie chart when given its percentage value"
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart This pie chart shows how an average American household uses water.\n\nWhich of the following can not be found from this pie chart? ![A pie chart showing multiple sections: Toilet 26.7%, Leaks 13.7%, Other 5.3%, Clothes Washer 21.7%, Faucet 15.7%, Shower 16.8% ]() The modal use of water"
},
{
"from": "gpt",
"value": "Does not know how to read information off a pie chart"
}
] |
[
{
"from": "human",
"value": "Add surds in the form va + vb \\( \\sqrt{12}+\\sqrt{27} \\) Simplify, if possible. \\( 3 \\sqrt{5} \\)"
},
{
"from": "gpt",
"value": "When simplifying surds, leaves the square root of the biggest square number under the root and puts the other number on the outside"
}
] |
[
{
"from": "human",
"value": "Add surds in the form va + vb \\( \\sqrt{12}+\\sqrt{27} \\) Simplify, if possible. \\( \\sqrt{39} \\)"
},
{
"from": "gpt",
"value": "When adding or subtracting surds, just adds or subtracts the numbers under the surd rather than first trying to simplifying to find like surds"
}
] |
[
{
"from": "human",
"value": "Add surds in the form va + vb \\( \\sqrt{12}+\\sqrt{27} \\) Simplify, if possible. Cannot be simplified"
},
{
"from": "gpt",
"value": "Does not recognise when a surd can be simplified"
}
] |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 180° and 270° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The outer scale goes from 0 to 360 clockwise. The angle is between one red line that is at 0 (outer scale) and 180 (inner scale), clockwise to the other red line that is half way between 210 and 220 (outer scale) and halfway between 330 and 320 (inner scale).\n]() \\( 335^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Reads the wrong scale on the protractor when measuring reflex angles"
}
] |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 180° and 270° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The outer scale goes from 0 to 360 clockwise. The angle is between one red line that is at 0 (outer scale) and 180 (inner scale), clockwise to the other red line that is half way between 210 and 220 (outer scale) and halfway between 330 and 320 (inner scale).\n]() \\( 345^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Reads the wrong scale on the protractor when measuring reflex angles"
}
] |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 180° and 270° What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The outer scale goes from 0 to 360 clockwise. The angle is between one red line that is at 0 (outer scale) and 180 (inner scale), clockwise to the other red line that is half way between 210 and 220 (outer scale) and halfway between 330 and 320 (inner scale).\n]() \\( 210^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Correct scale but wrong value on protractor reading."
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![A set of axes: x-axis from 0 to 5, y-axis from 0 to 5. A purple triangle symbol is at point (2,1) and a yellow star symbol is at point (1, 4).]() \\( 1 \\) square left, \\( 3 \\) squares up"
},
{
"from": "gpt",
"value": "When describing a translation, goes from the image to the original"
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![A set of axes: x-axis from 0 to 5, y-axis from 0 to 5. A purple triangle symbol is at point (2,1) and a yellow star symbol is at point (1, 4).]() \\( 1 \\) square down, \\( 3 \\) squares right"
},
{
"from": "gpt",
"value": "Confuses left and right"
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors How would you describe the movement to get from the star to the triangle? ![A set of axes: x-axis from 0 to 5, y-axis from 0 to 5. A purple triangle symbol is at point (2,1) and a yellow star symbol is at point (1, 4).]() \\( 1 \\) squares right,\\( 4 \\) squares down"
},
{
"from": "gpt",
"value": "When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares."
}
] |
[
{
"from": "human",
"value": "Interpret discrete data using a line graph ![A line graph with title \"Goals scored in the UK\". \nThe x-axis scale is labelled: Aug, Sept, Oct, Nov, Dec, Jan, Feb, Mar, Apr, May. \nThe y-axis is titled \"Number of goals\" and the scale is labelled from 0 to 3000 in steps of 500. The following points are plotted and joined together: (Aug, 500), (Sept, 850 approx.), (Oct, 950 approx.),(Nov, 1000), (Dec, 1175 approx.), (Jan, 1200 approx.), (Feb, 500), (Mar, 1000), (Apr, 1500), (May, 2000).\n]() What was the total number of goals scored in the winter season (Dec, Jan, Feb)? \\( 3375 \\)"
},
{
"from": "gpt",
"value": "Has used the wrong data point on the graph"
}
] |
[
{
"from": "human",
"value": "Determine the function of a single function machine used to create an algebraic expression Tom and Katie are discussing this function machine ![A function machine with an input of a+4, the function is not labelled and then an output of 4a+4]() Tom says the function could be \\( +3 a \\)\nKatie says the function could be \\( \\times 4 \\)\nWho do you agree with? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Only multiplies the first term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "Translate a shape given vector notation where all values are positive Sam has translated the red flag \\( \\left(\\begin{array}{l}2 \\\\ 3\\end{array}\\right) \\) ![Image showing two identical shapes on a coordinate grid. The red shape has the point (2,1) and the corresponding point on the blue shape is (4,3).]() What error has Sam made? Sam has gone left when he should have gone right"
},
{
"from": "gpt",
"value": "Thinks a positive x value in a column vector means to move left rather than right"
}
] |
[
{
"from": "human",
"value": "Translate a shape given vector notation where all values are positive Sam has translated the red flag \\( \\left(\\begin{array}{l}2 \\\\ 3\\end{array}\\right) \\) ![Image showing two identical shapes on a coordinate grid. The red shape has the point (2,1) and the corresponding point on the blue shape is (4,3).]() What error has Sam made? Sam has not moved right the correct number of places"
},
{
"from": "gpt",
"value": "When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares."
}
] |
[
{
"from": "human",
"value": "Translate a shape given vector notation where all values are positive Sam has translated the red flag \\( \\left(\\begin{array}{l}2 \\\\ 3\\end{array}\\right) \\) ![Image showing two identical shapes on a coordinate grid. The red shape has the point (2,1) and the corresponding point on the blue shape is (4,3).]() What error has Sam made? Sam has started counting from his initial position when counting right"
},
{
"from": "gpt",
"value": "When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares."
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable that require three or more steps where the variable appears on one side of the equation Solve\n\\[\n36 \\leq 4(5 n-1)\n\\] \\( n \\leq 2 \\)"
},
{
"from": "gpt",
"value": "Believes the sides of an inequality can be switched without changing the direction of the sign"
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable that require three or more steps where the variable appears on one side of the equation Solve\n\\[\n36 \\leq 4(5 n-1)\n\\] \\( \\frac{37}{20} \\leq n \\)"
},
{
"from": "gpt",
"value": "Only multiplies the first term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring addition or subtraction, with all positive integers Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.\nWhat operation should replace the star? ![The image shows two lines of working and an arrow from the top line to the bottom line with a star next to it where the operation would be labelled. The top line of working is x - 7 = ..., and the bottom line is x = ...]() \\( \\times 7 \\)"
},
{
"from": "gpt",
"value": "Thinks the inverse of subtraction is multiplication"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring addition or subtraction, with all positive integers Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.\nWhat operation should replace the star? ![The image shows two lines of working and an arrow from the top line to the bottom line with a star next to it where the operation would be labelled. The top line of working is x - 7 = ..., and the bottom line is x = ...]() \\( \\div 7 \\)"
},
{
"from": "gpt",
"value": "Thinks the inverse of subtraction is division"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring addition or subtraction, with all positive integers Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.\nWhat operation should replace the star? ![The image shows two lines of working and an arrow from the top line to the bottom line with a star next to it where the operation would be labelled. The top line of working is x - 7 = ..., and the bottom line is x = ...]() \\( -7 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Mental multiplication and the laws of arithmetic \\[\n15 \\times 12=15 \\times(4 \\times \\text { 年 })\n\\]\nWhat should replace the star to make this calculation correct? \\( 8 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of divides"
}
] |
[
{
"from": "human",
"value": "Find missing angles in an isosceles triangle What is the size of angle \\( w \\) ? ![An isosceles triangle with a base angle labelled with w and the angle vertically opposite the vertex angle labelled with 33 degrees]() \\( 49^{\\degree} \\)"
},
{
"from": "gpt",
"value": "Confuses isosceles and equilateral triangles"
}
] |
[
{
"from": "human",
"value": "Find missing angles in an isosceles triangle What is the size of angle \\( w \\) ? ![An isosceles triangle with a base angle labelled with w and the angle vertically opposite the vertex angle labelled with 33 degrees]() \\( 34^{\\degree} \\)"
},
{
"from": "gpt",
"value": "Does not know that vertically opposite angles are equal"
}
] |
[
{
"from": "human",
"value": "Find missing angles in an isosceles triangle What is the size of angle \\( w \\) ? ![An isosceles triangle with a base angle labelled with w and the angle vertically opposite the vertex angle labelled with 33 degrees]() \\( 54^{\\degree} \\)"
},
{
"from": "gpt",
"value": "Does not know that vertically opposite angles are equal"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition or subtraction with multiplication There are \\( 7 \\) shelves of plates. Three of the shelves hold \\( 17 \\) plates each. Two of the shelves hold \\( 21 \\) plates each. The other shelves hold \\( 19 \\) plates each.\nHow many plates are there in total? \\( 57 \\)"
},
{
"from": "gpt",
"value": "Does not recognise when to find a multiple from a worded question"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order fractions whose denominators are multiples of the same number Which symbol makes the following statement correct?\n\\(\n\\frac{3}{4}\\space \\square\\space \\frac{5}{8}\n\\) \\( = \\)"
},
{
"from": "gpt",
"value": "Believes that fractions with larger denominators are greater in size"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order fractions whose denominators are multiples of the same number Which symbol makes the following statement correct?\n\\(\n\\frac{3}{4}\\space \\square\\space \\frac{5}{8}\n\\) \\( < \\)"
},
{
"from": "gpt",
"value": "Believes that fractions with larger denominators are greater in size"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order fractions whose denominators are multiples of the same number Which symbol makes the following statement correct?\n\\(\n\\frac{3}{4}\\space \\square\\space \\frac{5}{8}\n\\) None of these"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Work out the size of each interior angle in a regular polygon What is the size of each interior angle in a regular octagon? \\( 80^{\\degree} \\)"
},
{
"from": "gpt",
"value": "Does not know how to calculate the sum of interior angles"
}
] |
[
{
"from": "human",
"value": "Work out the size of each interior angle in a regular polygon What is the size of each interior angle in a regular octagon? \\( 120^{\\degree} \\)"
},
{
"from": "gpt",
"value": "Does not know how to calculate the sum of interior angles"
}
] |
[
{
"from": "human",
"value": "Work out the size of each interior angle in a regular polygon What is the size of each interior angle in a regular octagon? \\( 180^{\\degree} \\)"
},
{
"from": "gpt",
"value": "Does not understand to find each interior angle of a regular polygon you divide the sum by the number of sides"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with the same number of decimal places \\( 0.3 \\times 0.9= \\) \\( 2.7 \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with the same number of decimal places \\( 0.3 \\times 0.9= \\) \\( 1.2 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with the same number of decimal places \\( 0.3 \\times 0.9= \\) \\( 0.027 \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal"
}
] |
[
{
"from": "human",
"value": "Convert from kilometers to miles \\( 3 \\) miles \\( \\approx 5 \\mathrm{~km} \\) \\( 300 \\mathrm{~km} \\approx \\square \\) miles \\( 298 \\)"
},
{
"from": "gpt",
"value": "Added rather than multiplied by a scale factor"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving negative integers Jo and Paul are arguing about a first step to solve this equation:\n\\(5-2 v=3-6 v\\)\n\nJo says you can write: \\( 2 v=8-6 v \\)\n\nPaul says you can write: \\( 5+8 v=3 \\)\n\nWho is correct? Only Paul"
},
{
"from": "gpt",
"value": "Ignores the negative signs when adding positive and negative numbers"
}
] |
[
{
"from": "human",
"value": "Interpret what the numbers in each region of a double Venn diagram mean All the students in a class were asked if they have a brother, sister, both or none.\n\nThe Venn Diagram shows the results. ![A Venn diagram with two sets, one labelled Brother and one labelled Sister. The number 10 is written in Brother without the intersection , number 5 is in Sister without the intersection, the number 7 is in the intersection of Brother and Sister. The number 9 is outside the circles.]() How many students are in the class? \\( 4 \\)"
},
{
"from": "gpt",
"value": "Confuses the number of regions in a Venn diagram as the total number of entries in the diagram"
}
] |
[
{
"from": "human",
"value": "Interpret what the numbers in each region of a double Venn diagram mean All the students in a class were asked if they have a brother, sister, both or none.\n\nThe Venn Diagram shows the results. ![A Venn diagram with two sets, one labelled Brother and one labelled Sister. The number 10 is written in Brother without the intersection , number 5 is in Sister without the intersection, the number 7 is in the intersection of Brother and Sister. The number 9 is outside the circles.]() How many students are in the class? \\( 21 \\)"
},
{
"from": "gpt",
"value": "Forgets to include values outside of the Venn diagram when finding the total"
}
] |
[
{
"from": "human",
"value": "Solve missing number mental multiplication questions What number belongs in the box to make the calculation correct?\n\n\n\\[\n6 \\times \\square=108\n\\] \\( 648 \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation"
}
] |
[
{
"from": "human",
"value": "Solve missing number mental multiplication questions What number belongs in the box to make the calculation correct?\n\n\n\\[\n6 \\times \\square=108\n\\] \\( 102 \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does subtraction when division is required"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a trapezium where the dimensions are given in the same units Sally wants to calculate the area of this trapezium using the formula: Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) ![A trapezium with the parallel sides labelled 5cm and 1cm, the slant height labelled 6cm and the perpendicular height labelled 4cm.]() What is the values of \\( h \\) ? \\( 5 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Does not recognise the height of a trapezium as the perpendicular length between the parallel sides"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a trapezium where the dimensions are given in the same units Sally wants to calculate the area of this trapezium using the formula: Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) ![A trapezium with the parallel sides labelled 5cm and 1cm, the slant height labelled 6cm and the perpendicular height labelled 4cm.]() What is the values of \\( h \\) ? \\( 6 \\mathrm{~cm} \\)"
},
{
"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 the same units Sally wants to calculate the area of this trapezium using the formula: Area \\( =\\left(\\frac{a+b}{2}\\right) h \\) ![A trapezium with the parallel sides labelled 5cm and 1cm, the slant height labelled 6cm and the perpendicular height labelled 4cm.]() What is the values of \\( h \\) ? \\( 1 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Does not recognise the height of a trapezium as the perpendicular length between the parallel sides"
}
] |
[
{
"from": "human",
"value": "Identify and count the faces, vertices and edges of a 3D shape How many vertices does this shape have? ![cuboid]() \\( 6 \\)"
},
{
"from": "gpt",
"value": "Confuses the terms faces and vertices"
}
] |
[
{
"from": "human",
"value": "Identify and count the faces, vertices and edges of a 3D shape How many vertices does this shape have? ![cuboid]() \\( 4 \\)"
},
{
"from": "gpt",
"value": "Believes the number of vertices on a 3D shape match those of the 2D cross section"
}
] |
[
{
"from": "human",
"value": "Identify and count the faces, vertices and edges of a 3D shape How many vertices does this shape have? ![cuboid]() \\( 7 \\)"
},
{
"from": "gpt",
"value": "Only counts visible vertices"
}
] |
[
{
"from": "human",
"value": "Calculate the midpoint between two coordinates in 2D, where all the values are positive integers Millie is working out the midpoint of these two points. What should replace the triangle? ![An x and y axis showing 3 points. (1,8) (star, triangle) and (7,3)]() ![\\( \\triangle=5 \\)]()"
},
{
"from": "gpt",
"value": "Finds the difference in a coordinate pair rather than the midpoint"
}
] |
[
{
"from": "human",
"value": "Calculate the midpoint between two coordinates in 2D, where all the values are positive integers Millie is working out the midpoint of these two points. What should replace the triangle? ![An x and y axis showing 3 points. (1,8) (star, triangle) and (7,3)]() ![\\( \\triangle=11 \\)]()"
},
{
"from": "gpt",
"value": "Does not divide by 2 when finding midpoint"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable What could go in the missing gaps? \\begin{tabular}{|l|l|l|l|}\n\\hline \\multicolumn{4}{|c|}{\\( 8 a+7 \\)} \\\\\n\\hline \\( 3 a \\) & \\( -3 \\) & \\( ? \\) & \\( ? \\) \\\\\n\\hline\n\\end{tabular} \\( 5 a \\) and \\( 4 \\)"
},
{
"from": "gpt",
"value": "When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored "
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line Which calculation is a correct procedure to find the angle marked [?]\nA\n\\( 360-(54 \\times 2) \\)\nB\n\\( 180-54 \\) ![Two intersecting lines and one adjacent line. One line is marked with the angle 54 degrees. Between the two adjacent lines there is a box with a question mark in it [?]]() Neither A nor B"
},
{
"from": "gpt",
"value": "Does not know that angles on a straight line sum to 180 degrees"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number \\( 0.8^{2}= \\) \\( 6.4 \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number \\( 0.8^{2}= \\) \\( 1.6 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number \\( 0.8^{2}= \\) \\( 0.16 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 40 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![Trapezium with parallel sides of lengths 6cm and 10cm]() \\( h=8 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Believes h in the formula for area of a trapezium stands for half the sum of the parallel sides"
}
] |
[
{
"from": "human",
"value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 40 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![Trapezium with parallel sides of lengths 6cm and 10cm]() \\( h=2.5 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Does not divide by 2 when calculating the area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Given the area of a trapezium, calculate a missing dimension The area of this trapezium is \\( 40 \\mathrm{~cm}^{2} \\). What would the perpendicular height, \\( h \\), of the trapezium be? ![Trapezium with parallel sides of lengths 6cm and 10cm]() \\( h=13.3 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Uses only the base and perpendicular height when calculating the area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest other power of 10 What is \\( 875,599 \\) rounded to the nearest \\( 10,000 \\) ? \\( 870,000 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest other power of 10 What is \\( 875,599 \\) rounded to the nearest \\( 10,000 \\) ? \\( 900,000 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest other power of 10 What is \\( 875,599 \\) rounded to the nearest \\( 10,000 \\) ? \\( 876,000 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too little)"
}
] |
[
{
"from": "human",
"value": "Interpret a bar chart The bar chart shows the drinks sold in Caroline's Café on Monday and Tuesday last week.\n\nApproximately how many Hot Chocs were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.\nThe Hot Chocs bar's lower section is 5 ticks high, and the whole bar is 2 ticks above 100 on the vertical scale.]() \\( 110 \\)"
},
{
"from": "gpt",
"value": "When reading a composite bar chart, just reads total height of bar"
}
] |
[
{
"from": "human",
"value": "Interpret a bar chart The bar chart shows the drinks sold in Caroline's Café on Monday and Tuesday last week.\n\nApproximately how many Hot Chocs were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.\nThe Hot Chocs bar's lower section is 5 ticks high, and the whole bar is 2 ticks above 100 on the vertical scale.]() \\( 51 \\)"
},
{
"from": "gpt",
"value": "Misreads scale"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate real life graph Imran slept really well until a car alarm woke him up and he couldn't get back to sleep.\n\nWhich of the following sketches best shows Imran's sleep? ![This graph shows depth of sleep increasing quickly and then maintaining a consistent level until it starts to gradually decrease until the end of the night when it reaches 0.]()"
},
{
"from": "gpt",
"value": "Believes infinite gradient is not possible in real life. "
}
] |
[
{
"from": "human",
"value": "Recognise the place value of each digit in integers What is the value of the \\( 3 \\) in the number\n\\[\n7,359,250 \\text { ? }\n\\] \\( 3 \\)"
},
{
"from": "gpt",
"value": "Does not understand the meaning of \"value\""
}
] |
[
{
"from": "human",
"value": "Recognise the place value of each digit in integers What is the value of the \\( 3 \\) in the number\n\\[\n7,359,250 \\text { ? }\n\\] \\( 30,000 \\)"
},
{
"from": "gpt",
"value": "Thinks the hundred thousands column is the ten thousands column"
}
] |
[
{
"from": "human",
"value": "Recognise the place value of each digit in integers What is the value of the \\( 3 \\) in the number\n\\[\n7,359,250 \\text { ? }\n\\] \\( 300 \\)"
},
{
"from": "gpt",
"value": "Confuses the hundreds and hundred thousands place value columns"
}
] |
[
{
"from": "human",
"value": "Recognise and use associativity of multiplication \\(\n(-20) \\times(-5)=2 \\times(-10) \\times(-5)\n\\)\nIs this... true because of distributivity"
},
{
"from": "gpt",
"value": "Does not correctly apply the distributive property of multiplication"
}
] |
[
{
"from": "human",
"value": "Recognise and use associativity of multiplication \\(\n(-20) \\times(-5)=2 \\times(-10) \\times(-5)\n\\)\nIs this... true because of commutativity"
},
{
"from": "gpt",
"value": "Does not understand the meaning of the word commutative "
}
] |
[
{
"from": "human",
"value": "Find the area of rectilinear shapes by counting squares What is the area of this shape? ![A square cm grid showing a shape made up of 3 small squares.]() \\( 8 \\)"
},
{
"from": "gpt",
"value": "Calculates perimeter when asked for area"
}
] |
[
{
"from": "human",
"value": "Find the area of rectilinear shapes by counting squares What is the area of this shape? ![A square cm grid showing a shape made up of 3 small squares.]() \\( 20 \\)"
},
{
"from": "gpt",
"value": "Finds the area of the whole grid instead of the shaded shape"
}
] |
[
{
"from": "human",
"value": "Find the area of rectilinear shapes by counting squares What is the area of this shape? ![A square cm grid showing a shape made up of 3 small squares.]() \\( 4 \\)"
},
{
"from": "gpt",
"value": "When calculating the area of a rectilinear compound shape, calculates the are of the surrounding rectangle"
}
] |
[
{
"from": "human",
"value": "Given an equation, form or identify related equations \\(k<\\frac{m}{3} +1\\)\nUsing the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']() sometimes true"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Given an equation, form or identify related equations \\(k<\\frac{m}{3} +1\\)\nUsing the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']() never true"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Given an equation, form or identify related equations \\(k<\\frac{m}{3} +1\\)\nUsing the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']() Need more information"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Calculate the perimeter of a rectilinear shape by adding lengths expressed in the same units What is the perimeter of this rectangle? ![A rectangle with a base length of 8 cm and a perpendicular height of 5 cm.]() \\( 13 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "When calculating perimeter, only adds the marked lengths"
}
] |
[
{
"from": "human",
"value": "Calculate the perimeter of a rectilinear shape by adding lengths expressed in the same units What is the perimeter of this rectangle? ![A rectangle with a base length of 8 cm and a perpendicular height of 5 cm.]() \\( 40 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Calculates area when asked for perimeter"
}
] |
[
{
"from": "human",
"value": "Calculate the perimeter of a rectilinear shape by adding lengths expressed in the same units What is the perimeter of this rectangle? ![A rectangle with a base length of 8 cm and a perpendicular height of 5 cm.]() Not enough information in the diagram"
},
{
"from": "gpt",
"value": "Does not recall rectangle side length property"
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for a descending integer linear sequence \\[\n20,14,8,2,-4, \\ldots\n\\]\n\nWhen calculating the nth-term rule of this sequence, what should replace the star? nth-term rule: \\(\\color{gold}\\bigstar\\)n \\(\\square\\) \\( 6 \\)"
},
{
"from": "gpt",
"value": "Goes the wrong direction in the sequence when identifying term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for a descending integer linear sequence \\[\n20,14,8,2,-4, \\ldots\n\\]\n\nWhen calculating the nth-term rule of this sequence, what should replace the star? nth-term rule: \\(\\color{gold}\\bigstar\\)n \\(\\square\\) \\( 20 \\)"
},
{
"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": "Convert fractions less than 1 to terminating decimals of 3 or more decimal places Convert \\( \\frac{7}{40} \\) into a decimal \\( 0.7 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by using only the numerator after the decimal point"
}
] |
[
{
"from": "human",
"value": "Convert fractions less than 1 to terminating decimals of 3 or more decimal places Convert \\( \\frac{7}{40} \\) into a decimal \\( 7.40 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by placing a decimal point between the numerator and denominator"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators where one is a multiple of the other \\( \\frac{7}{8}-\\frac{1}{4}= \\) \\( \\frac{6}{4} \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators where one is a multiple of the other \\( \\frac{7}{8}-\\frac{1}{4}= \\) \\( \\frac{9}{8} \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators where one is a multiple of the other \\( \\frac{7}{8}-\\frac{1}{4}= \\) \\( \\frac{6}{8} \\)"
},
{
"from": "gpt",
"value": "Does not understand how to maintain equivalence in fractions"
}
] |
[
{
"from": "human",
"value": "Find missing angles in a scalene triangle What is the size of angle \\( k \\) ? ![A triangle with two labelled interior angles. One angle is 65 degrees. One angle is k degrees. The third angle has no label.]() \\( 50\\degree\\)"
},
{
"from": "gpt",
"value": "Assumes an angle is the size that it looks in the (not to scale) diagram"
}
] |
[
{
"from": "human",
"value": "Find missing angles in a scalene triangle What is the size of angle \\( k \\) ? ![A triangle with two labelled interior angles. One angle is 65 degrees. One angle is k degrees. The third angle has no label.]() \\( 65\\degree\\)"
},
{
"from": "gpt",
"value": "Thinks angles which look the same on diagram will be equal"
}
] |
[
{
"from": "human",
"value": "Find missing angles in a scalene triangle What is the size of angle \\( k \\) ? ![A triangle with two labelled interior angles. One angle is 65 degrees. One angle is k degrees. The third angle has no label.]() \\( 90\\degree\\)"
},
{
"from": "gpt",
"value": "Believes all triangles have a right angle"
}
] |
[
{
"from": "human",
"value": "Identify a unit of volume or capacity Sally has answered a question on volume. Her answer is \\( 500 \\).\nBehind the star she has written the units that she used.\nWhich of the following units is definitely wrong?\n\n\\( 500 \\,\\bigstar \\)\n\n \\( \\mathrm{mm}^{3} \\)"
},
{
"from": "gpt",
"value": "Does not know that units of volume are usually cubed"
}
] |
Subsets and Splits