conversations
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[
{
"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 \\( m^{3} \\)"
},
{
"from": "gpt",
"value": "Does not know that units of volume are usually cubed"
}
] |
[
{
"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 \\( l \\)"
},
{
"from": "gpt",
"value": "Does not recognise litres as a unit of volume"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with a reflection line drawn and a triangle. The reflection line passes through the coordinates: (-1,-1) (0,0) (1,1) (2,2) etc. The triangle has coordinates: (2,2) (3,3) and (4,2). P is the coordinate (4,2).]() \\( (2,2) \\)"
},
{
"from": "gpt",
"value": "Fails to reflect across mirror line"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with a reflection line drawn and a triangle. The reflection line passes through the coordinates: (-1,-1) (0,0) (1,1) (2,2) etc. The triangle has coordinates: (2,2) (3,3) and (4,2). P is the coordinate (4,2).]() \\( (2,0) \\)"
},
{
"from": "gpt",
"value": "Fails to reflect across mirror line"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with a reflection line drawn and a triangle. The reflection line passes through the coordinates: (-1,-1) (0,0) (1,1) (2,2) etc. The triangle has coordinates: (2,2) (3,3) and (4,2). P is the coordinate (4,2).]() \\( (0,2) \\)"
},
{
"from": "gpt",
"value": "Counts the squares rather than the diagonals when reflecting in y=x or y=-x "
}
] |
[
{
"from": "human",
"value": "Round numbers to two decimal places \\( 0.009753 \\)\nWhat is this number rounded to \\( 2 \\) decimal places? \\( 0.0098 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (significant figures rather than decimal places)"
}
] |
[
{
"from": "human",
"value": "Round numbers to two decimal places \\( 0.009753 \\)\nWhat is this number rounded to \\( 2 \\) decimal places? \\( 0.0097 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (significant figures rather than decimal places)"
}
] |
[
{
"from": "human",
"value": "Round numbers to two decimal places \\( 0.009753 \\)\nWhat is this number rounded to \\( 2 \\) decimal places? \\( 0.00 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 0.55-0.2= \\) \\( 0.33 \\)"
},
{
"from": "gpt",
"value": "When subtracting decimals with a different number of decimals, subtracts one digit from more than one column"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 0.55-0.2= \\) \\( 0.53 \\)"
},
{
"from": "gpt",
"value": "When subtracting decimals with a different number of decimal places, lines up the digits incorrectly"
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities involving two inequality signs What is the solution to the following inequality?\n\\(\n-5<2 x+1<5\n\\) \\( -9<x<11 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities involving two inequality signs What is the solution to the following inequality?\n\\(\n-5<2 x+1<5\n\\) \\( -2<x<2 \\)"
},
{
"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\\(\n-5<2 x+1<5\n\\) \\( -3.5<x<1.5 \\)"
},
{
"from": "gpt",
"value": "Does not reverse the order of operations when solving an equation"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are multiples of the same number In a bakery \\( \\frac{3}{7} \\) of the cakes are chocolate, \\( \\frac{5}{14} \\) of the cakes are vanilla and \\( \\frac{6}{28} \\) are lemon.\nWhich flavour cake is there more of? Vanilla"
},
{
"from": "gpt",
"value": "Does not find a common denominator when comparing fractions"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are multiples of the same number In a bakery \\( \\frac{3}{7} \\) of the cakes are chocolate, \\( \\frac{5}{14} \\) of the cakes are vanilla and \\( \\frac{6}{28} \\) are lemon.\nWhich flavour cake is there more of? There is the same amount of each."
},
{
"from": "gpt",
"value": "Does not find a common denominator when comparing fractions"
}
] |
[
{
"from": "human",
"value": "Estimate the size of obtuse angles Which of the following is the best estimate of the size of this angle? ![An obtuse angle]() \\( 60^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Estimates angle without using knowledge of degrees in quarter turns"
}
] |
[
{
"from": "human",
"value": "Estimate the size of obtuse angles Which of the following is the best estimate of the size of this angle? ![An obtuse angle]() \\( 90^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Estimates angle without using knowledge of degrees in quarter turns"
}
] |
[
{
"from": "human",
"value": "Estimate the size of obtuse angles Which of the following is the best estimate of the size of this angle? ![An obtuse angle]() \\( 160^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Estimates angle without using knowledge of degrees in quarter turns"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\(y=\\frac{1}{2} x^{2}\\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( \\frac{2}{3} \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( \\frac{1}{9} \\)"
},
{
"from": "gpt",
"value": "When substituting a value into a non-linear term with a coefficient, multiplies by the coefficient then calculates the power."
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for curves in the form y = ax² + bx + c This is a part of the table of values for the equation\n\\(y=\\frac{1}{2} x^{2}\\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( \\frac{2}{3} \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( \\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Recognise cube numbers What is the smallest odd cube number? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Thinks numbers are a multiple of their index"
}
] |
[
{
"from": "human",
"value": "Recognise cube numbers What is the smallest odd cube number? \\( 8 \\)"
},
{
"from": "gpt",
"value": "Mixes up odd and even numbers"
}
] |
[
{
"from": "human",
"value": "Given the description of an algebraic term with no powers, write the term using algebra Write the following using correct algebraic notation \\( p \\) multiplied by three lots of \\( q \\) \\( p q^{3} \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number What is the value of \\( 3^{2} \\) ? \\( 12 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 4"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number What is the value of \\( 3^{2} \\) ? \\( 6 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number What is the value of \\( 3^{2} \\) ? \\( 5 \\)"
},
{
"from": "gpt",
"value": "Adds the index to the number"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention involving powers Simplify, if possible:\n\\(\nm^{2} \\times m^{2}\n\\) \\( 4 m \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention involving powers Simplify, if possible:\n\\(\nm^{2} \\times m^{2}\n\\) \\( 2 m^{2} \\)"
},
{
"from": "gpt",
"value": "Confuses collecting like terms with multiplication"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p-3)(p+1) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=+3 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying a positive by a negative gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p-3)(p+1) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=-2 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplying when expanding bracket"
}
] |
[
{
"from": "human",
"value": "Interpret a bar chart The bar chart shows the number of students in each year group who study French, Spanish and Chinese.\n\nHow many more Year 8s than Year 7s study French? ![An image of a vertical bar chart with bars striped red and white for French, solid blue for Spanish and solid white for Chinese (a key shows this). The x-axis is titled 'year group' with labels for Years 7 to 11. The y-axis is titled 'number of children' and its scale is from 0 to 80 in steps of 10. The following data is shown on the bar chart.\nYear 7: French 42, Spanish 35, Chinese 60; Year 8: French 80, Spanish 27, Chinese 25; Year 9: French 35, Spanish 70, Chinese 12; Year 10: French 12, Spanish 35, Chinese 0; Year 11: French 33, Spanish 26, Chinese 0.]() \\( 122 \\)"
},
{
"from": "gpt",
"value": "Finds total instead of difference when asked 'How many more'"
}
] |
[
{
"from": "human",
"value": "Construct a triangle using Side-Side-Side What is the length of the side marked \\( q \\) ? ![Two, intersecting circles drawn with a compass and used to construct a triangle with one side labelled with q]() \\( 2.5 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Estimates a measurement on a diagram rather than working it out"
}
] |
[
{
"from": "human",
"value": "Given a midpoint and a coordinate work out the position of the other coordinate, where all the values are integers but at least one is negative Here are two points and their midpoint. What should replace the star? ![A set of axis showing all four quadrants. Three points are marked in a straight line with a negative gradient. One lilac circle marks a point in the 1st quadrant and is labelled (-5, 5). One red circle marks a point in the 1st quadrant and is labelled (-2,1). Another lilac circle marks a point in the 4th quadrant and is labelled (gold star icon, green triangle icon) as the coordinates are unknown. ]() \\(\\color{gold}\\bigstar\\) = 5"
},
{
"from": "gpt",
"value": "Given a line segment with a midpoint that is not the origin, assumes that the two end points will still have the same absolute value"
}
] |
[
{
"from": "human",
"value": "Given a midpoint and a coordinate work out the position of the other coordinate, where all the values are integers but at least one is negative Here are two points and their midpoint. What should replace the star? ![A set of axis showing all four quadrants. Three points are marked in a straight line with a negative gradient. One lilac circle marks a point in the 1st quadrant and is labelled (-5, 5). One red circle marks a point in the 1st quadrant and is labelled (-2,1). Another lilac circle marks a point in the 4th quadrant and is labelled (gold star icon, green triangle icon) as the coordinates are unknown. ]() \\(\\color{gold}\\bigstar\\) = -7"
},
{
"from": "gpt",
"value": "Believes adding coordinates of endpoint and midpoint of a line will give the other endpoint"
}
] |
[
{
"from": "human",
"value": "Find the area of non-rectilinear shapes by counting squares, where all squares are either whole or exactly half-squares Each square is \\( 1 \\mathrm{~cm} \\) by \\( 1 \\mathrm{~cm} \\)\n\nWhat is the area of this shape? ![A 6 by 5 centimetre squared grid. A purple right angled triangle is drawn on the grid with a base of 3cm and a perpendicular height of 3cm.]() \\( 5 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Underestimates the area of shapes when counting squares when some squares are neither wholes nor halves"
}
] |
[
{
"from": "human",
"value": "Find the area of non-rectilinear shapes by counting squares, where all squares are either whole or exactly half-squares Each square is \\( 1 \\mathrm{~cm} \\) by \\( 1 \\mathrm{~cm} \\)\n\nWhat is the area of this shape? ![A 6 by 5 centimetre squared grid. A purple right angled triangle is drawn on the grid with a base of 3cm and a perpendicular height of 3cm.]() \\( 3 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Adds when calculating area instead of multiplying"
}
] |
[
{
"from": "human",
"value": "Find the area of non-rectilinear shapes by counting squares, where all squares are either whole or exactly half-squares Each square is \\( 1 \\mathrm{~cm} \\) by \\( 1 \\mathrm{~cm} \\)\n\nWhat is the area of this shape? ![A 6 by 5 centimetre squared grid. A purple right angled triangle is drawn on the grid with a base of 3cm and a perpendicular height of 3cm.]() \\( 9 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Does not divide by 2 when calculating the area of a triangle"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing ways to calculate \\( 49 \\times 9 \\) mentally\nTom multiplies \\( 49 \\) by \\( 10 \\) and then subtracts \\( 49 \\) from the answer.\nKatie does \\( 50 \\times 9 \\) and then subtracts \\( 9 \\) from the answer\nWho would get the correct answer? Only Tom"
},
{
"from": "gpt",
"value": "Believes that the compensation strategy for the multiplication of 2 numbers can only be used one way round."
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing ways to calculate \\( 49 \\times 9 \\) mentally\nTom multiplies \\( 49 \\) by \\( 10 \\) and then subtracts \\( 49 \\) from the answer.\nKatie does \\( 50 \\times 9 \\) and then subtracts \\( 9 \\) from the answer\nWho would get the correct answer? Only\nKatie"
},
{
"from": "gpt",
"value": "Believes that the compensation strategy for the multiplication of 2 numbers can only be used one way round."
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing ways to calculate \\( 49 \\times 9 \\) mentally\nTom multiplies \\( 49 \\) by \\( 10 \\) and then subtracts \\( 49 \\) from the answer.\nKatie does \\( 50 \\times 9 \\) and then subtracts \\( 9 \\) from the answer\nWho would get the correct answer? Neither is correct"
},
{
"from": "gpt",
"value": "Does not think that the compensation strategy for the multiplication of 2 numbers is valid."
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to the power of 0 \\( (16)^{0}=? \\) \\( 16 \\)"
},
{
"from": "gpt",
"value": "Forgotten that anything to the power of 0 equals 1"
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to the power of 0 \\( (16)^{0}=? \\) \\( 0 \\)"
},
{
"from": "gpt",
"value": "Forgotten that anything to the power of 0 equals 1"
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to the power of 0 \\( (16)^{0}=? \\) You cannot have a power of \\( 0 \\)"
},
{
"from": "gpt",
"value": "Forgotten that anything to the power of 0 equals 1"
}
] |
[
{
"from": "human",
"value": "Read an integer on a scale where the required measurement is marked by a dash between two numbers What number is the arrow pointing to? ![Number line from 100 to 200 with an arrow pointing to the value 145]() \\( 140 \\)"
},
{
"from": "gpt",
"value": "When reading integers on a number line, assumes each dash is 10"
}
] |
[
{
"from": "human",
"value": "Read an integer on a scale where the required measurement is marked by a dash between two numbers What number is the arrow pointing to? ![Number line from 100 to 200 with an arrow pointing to the value 145]() \\( 149 \\)"
},
{
"from": "gpt",
"value": "When reading integers on a number line, assumes each dash is 1"
}
] |
[
{
"from": "human",
"value": "Read an integer on a scale where the required measurement is marked by a dash between two numbers What number is the arrow pointing to? ![Number line from 100 to 200 with an arrow pointing to the value 145]() \\( 148 \\)"
},
{
"from": "gpt",
"value": "When reading integers on a number line, assumes each dash is 2"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with the same number of decimal places \\( 0.01^{3}= \\) \\( 0.0001 \\)"
},
{
"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 \\( 0.01^{3}= \\) \\( 0.03 \\)"
},
{
"from": "gpt",
"value": "Believes cubing a number means you multiply it by 3"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with the same number of decimal places \\( 0.01^{3}= \\) \\( 0.00001 \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal"
}
] |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a non-unit fraction Tom and Katie are arguing about how to leave answers to some fractions questions they are working on.\n\nTom says he is going to leave one of his answers as \\( \\frac{143}{2} \\)\n\nKatie says she is going to leave one of her answers as \\( \\frac{4.2}{9} \\)\n\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Believes you can have decimals in a simplified fraction"
}
] |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a non-unit fraction Tom and Katie are arguing about how to leave answers to some fractions questions they are working on.\n\nTom says he is going to leave one of his answers as \\( \\frac{143}{2} \\)\n\nKatie says she is going to leave one of her answers as \\( \\frac{4.2}{9} \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes you can have decimals in a simplified fraction"
}
] |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a non-unit fraction Tom and Katie are arguing about how to leave answers to some fractions questions they are working on.\n\nTom says he is going to leave one of his answers as \\( \\frac{143}{2} \\)\n\nKatie says she is going to leave one of her answers as \\( \\frac{4.2}{9} \\)\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not know that you can leave a fraction in improper form"
}
] |
[
{
"from": "human",
"value": "Recognise other roots of numbers \\( \\sqrt[3]{27}=? \\) \\( 9 \\)"
},
{
"from": "gpt",
"value": "Divides by the order of the root"
}
] |
[
{
"from": "human",
"value": "Recognise other roots of numbers \\( \\sqrt[3]{27}=? \\) \\( 81 \\)"
},
{
"from": "gpt",
"value": "Has multiplied by the root power"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles \\( \\mathrm{M} \\) and \\( \\mathrm{N} \\) are the intersections of the line \\( X Y \\) with the lines \\( P Q \\) and \\( R S \\).\nWhich angle is corresponding to angle QMY? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.\nA red straight line, XY, crosses the parallel lines. X is on the left of the diagram.\nLine XY crosses line PQ at a point marked M.\nLine XY crosses line RS at a point marked N.\nThe angle QMY is marked in red.]() XMP"
},
{
"from": "gpt",
"value": "Confuses corresponding and vertically opposite angles"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles \\( \\mathrm{M} \\) and \\( \\mathrm{N} \\) are the intersections of the line \\( X Y \\) with the lines \\( P Q \\) and \\( R S \\).\nWhich angle is corresponding to angle QMY? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.\nA red straight line, XY, crosses the parallel lines. X is on the left of the diagram.\nLine XY crosses line PQ at a point marked M.\nLine XY crosses line RS at a point marked N.\nThe angle QMY is marked in red.]() SNX"
},
{
"from": "gpt",
"value": "Confuses co-interior and corresponding angles"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles \\( \\mathrm{M} \\) and \\( \\mathrm{N} \\) are the intersections of the line \\( X Y \\) with the lines \\( P Q \\) and \\( R S \\).\nWhich angle is corresponding to angle QMY? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.\nA red straight line, XY, crosses the parallel lines. X is on the left of the diagram.\nLine XY crosses line PQ at a point marked M.\nLine XY crosses line RS at a point marked N.\nThe angle QMY is marked in red.]() XNR"
},
{
"from": "gpt",
"value": "Confuses corresponding and alternate angles"
}
] |
[
{
"from": "human",
"value": "Identify common factors of two numbers A common factor of \\( 8 \\) and \\( 20 \\) is... \\( 40 \\)"
},
{
"from": "gpt",
"value": "Confuses factors and multiples"
}
] |
[
{
"from": "human",
"value": "Identify common factors of two numbers A common factor of \\( 8 \\) and \\( 20 \\) is... \\( 20 \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of common, eg. common factor"
}
] |
[
{
"from": "human",
"value": "Identify common factors of two numbers A common factor of \\( 8 \\) and \\( 20 \\) is... \\( 8 \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of common, eg. common factor"
}
] |
[
{
"from": "human",
"value": "Describe a translation using vector notation where at least one value is negative Which vector correctly describes the translation that maps object \\( P \\) onto object \\( Q \\)? ![The image shows a pair of axes and two congruent trapezia labelled P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (3, 3), (4, 5), (6, 5), (7, 3).]() \\( \\left(\\begin{array}{c}-4 \\\\ 2\\end{array}\\right) \\)"
},
{
"from": "gpt",
"value": "Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round"
}
] |
[
{
"from": "human",
"value": "Describe a translation using vector notation where at least one value is negative Which vector correctly describes the translation that maps object \\( P \\) onto object \\( Q \\)? ![The image shows a pair of axes and two congruent trapezia labelled P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (3, 3), (4, 5), (6, 5), (7, 3).]() \\( \\left(\\begin{array}{c}-2 \\\\ 4\\end{array}\\right) \\)"
},
{
"from": "gpt",
"value": "When describing a translation, goes from the image to the original"
}
] |
[
{
"from": "human",
"value": "Recognise perpendicular lines ![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a vertical line measuring 2 units. EF is a diagonal line with a positive gradient of 4. GH is a diagonal line with a negative gradient of -4. IJ is a horizontal line measuring 3 units. KL is a diagonal line with a negative gradient of -1. MN is a diagonal line with a positive gradient of 1. OP is a diagonal line with a positive gradient of 4.]() Which line segment is perpendicular to \\( \\mathrm{MN} \\) ? \\( \\mathrm{GH} \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of perpendicular"
}
] |
[
{
"from": "human",
"value": "Recognise perpendicular lines ![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a vertical line measuring 2 units. EF is a diagonal line with a positive gradient of 4. GH is a diagonal line with a negative gradient of -4. IJ is a horizontal line measuring 3 units. KL is a diagonal line with a negative gradient of -1. MN is a diagonal line with a positive gradient of 1. OP is a diagonal line with a positive gradient of 4.]() Which line segment is perpendicular to \\( \\mathrm{MN} \\) ? \\( C D \\)"
},
{
"from": "gpt",
"value": "Confuses the meaning of perpendicular and vertical "
}
] |
[
{
"from": "human",
"value": "Recognise perpendicular lines ![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a vertical line measuring 2 units. EF is a diagonal line with a positive gradient of 4. GH is a diagonal line with a negative gradient of -4. IJ is a horizontal line measuring 3 units. KL is a diagonal line with a negative gradient of -1. MN is a diagonal line with a positive gradient of 1. OP is a diagonal line with a positive gradient of 4.]() Which line segment is perpendicular to \\( \\mathrm{MN} \\) ? OP"
},
{
"from": "gpt",
"value": "Does not know the meaning of perpendicular"
}
] |
[
{
"from": "human",
"value": "Interpret a bar chart The bar chart shows the number of students in each year group who study French, Spanish and Chinese.\n\nHow many more Year \\( 7 s \\) than Year 8s study Chinese? ![An image of a bar chart with bars striped red and white for French, blue for Spanish and white for Chinese. The x-axis is marked 'year group' with options 7-11, and the y-axis is marked 'number of children'. ]() \\( 85 \\)"
},
{
"from": "gpt",
"value": "Finds total instead of difference when asked 'How many more'"
}
] |
[
{
"from": "human",
"value": "Recognise perpendicular lines Tom and Katie are discussing this pair of lines\nTom says they are parallel\nKatie says they are perpendicular\nWho do you agree with? ![Two blue lines, each with a small red line marked across them about halfway up. The two blue lines do not touch, but they are closer together at one end.]() Only\nTom"
},
{
"from": "gpt",
"value": "Thinks that if two lines do not intersect on a diagram then they will never intersect and are therefore parallel"
}
] |
[
{
"from": "human",
"value": "Recognise perpendicular lines Tom and Katie are discussing this pair of lines\nTom says they are parallel\nKatie says they are perpendicular\nWho do you agree with? ![Two blue lines, each with a small red line marked across them about halfway up. The two blue lines do not touch, but they are closer together at one end.]() Only Katie"
},
{
"from": "gpt",
"value": "Believes any lines that cross are perpendicular"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a negative integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{2}^{\\boldsymbol{x}} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( -5 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( -32 \\)"
},
{
"from": "gpt",
"value": "Believes a negative power results in a negative answer"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a negative integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{2}^{\\boldsymbol{x}} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( -5 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( -\\frac{1}{32} \\)"
},
{
"from": "gpt",
"value": "Believes a negative power results in a negative answer"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a negative integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{2}^{\\boldsymbol{x}} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( -5 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( -10 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending decimal linear sequence \\( \\begin{array}{llll}7.5, & 6.6, & 5.7, & ?\\end{array} \\)\n\nWhat is the next term in this linear sequence? \\( 4.7 \\)"
},
{
"from": "gpt",
"value": "When asked for the next term in the sequence subtracts one from the last term given, despite the sequence not going down in ones."
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending decimal linear sequence \\( \\begin{array}{llll}7.5, & 6.6, & 5.7, & ?\\end{array} \\)\n\nWhat is the next term in this linear sequence? \\( 4.9 \\)"
},
{
"from": "gpt",
"value": "Does not recognise that a linear sequence must increase or decrease by same amount"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the value of the angle marked \\( \\mathbf{\\square} \\) ? ![Image showing three vertices of a polygon. We do not see how many sides the polygon has. The angles shown are marked 20 degrees, 120 degrees and the third is marked with a square.]() \\( 60^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Misinterprets the meaning of angles on a straight line angle fact"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the value of the angle marked \\( \\mathbf{\\square} \\) ? ![Image showing three vertices of a polygon. We do not see how many sides the polygon has. The angles shown are marked 20 degrees, 120 degrees and the third is marked with a square.]() \\( 120^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Thinks angles which look the same on diagram will be equal"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the value of the angle marked \\( \\mathbf{\\square} \\) ? ![Image showing three vertices of a polygon. We do not see how many sides the polygon has. The angles shown are marked 20 degrees, 120 degrees and the third is marked with a square.]() \\( 40^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Misinterprets the meaning of angles on a straight line angle fact"
}
] |
[
{
"from": "human",
"value": "Round the elements of a calculation to one significant figure to perform an estimation Estimate the value of\n\\(\n\\frac{4.12 \\times 18.3}{0.226}\n\\) \\( 16 \\)"
},
{
"from": "gpt",
"value": "Believes that dividing by a decimal is the same as dividing by its reciprocal"
}
] |
[
{
"from": "human",
"value": "Round the elements of a calculation to one significant figure to perform an estimation Estimate the value of\n\\(\n\\frac{4.12 \\times 18.3}{0.226}\n\\) \\( 360 \\)"
},
{
"from": "gpt",
"value": "Rounds to the nearest integer when estimating"
}
] |
[
{
"from": "human",
"value": "Identify a transversal What is the name given to the red line that intersects the two dashed lines? ![Shows two straight horizontal dashed lines that are converging and are both intersected by a solid red line]() Parallel"
},
{
"from": "gpt",
"value": "Does not know the meaning of the word parallel"
}
] |
[
{
"from": "human",
"value": "Identify a transversal What is the name given to the red line that intersects the two dashed lines? ![Shows two straight horizontal dashed lines that are converging and are both intersected by a solid red line]() Corresponding"
},
{
"from": "gpt",
"value": "Does not know the meaning of corresponding"
}
] |
[
{
"from": "human",
"value": "Identify a transversal What is the name given to the red line that intersects the two dashed lines? ![Shows two straight horizontal dashed lines that are converging and are both intersected by a solid red line]() Alternate"
},
{
"from": "gpt",
"value": "Does not know the meaning of alternate"
}
] |
[
{
"from": "human",
"value": "Convert between m³ and cm³ \\(\n1 m^3 =\\bigstar cm^3\n\\)\n\nWhat should replace the star? \\( 1000 \\)"
},
{
"from": "gpt",
"value": "Thinks 1 cubic metre = 1000 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Convert between m³ and cm³ \\(\n1 m^3 =\\bigstar cm^3\n\\)\n\nWhat should replace the star? \\( 100 \\)"
},
{
"from": "gpt",
"value": "Does not cube the conversion factor when converting cubed units"
}
] |
[
{
"from": "human",
"value": "Convert between m³ and cm³ \\(\n1 m^3 =\\bigstar cm^3\n\\)\n\nWhat should replace the star? \\( 10000 \\)"
},
{
"from": "gpt",
"value": "Does not cube the conversion factor when converting cubed units"
}
] |
[
{
"from": "human",
"value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... three \\( 60^{\\circ} \\) angles."
},
{
"from": "gpt",
"value": "Confuses isosceles and equilateral triangles"
}
] |
[
{
"from": "human",
"value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... a right angle."
},
{
"from": "gpt",
"value": "Confuses isosceles and right angle triangles"
}
] |
[
{
"from": "human",
"value": "Describe the properties of an isosceles triangle An isosceles triangle must have ... three equal side lengths."
},
{
"from": "gpt",
"value": "Confuses isosceles and equilateral triangles"
}
] |
[
{
"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 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"m\" written inside it. The middle rectangle is empty and the final rectangle has \"output\" written above it and \"4m\" written inside it.]() Tom says the function could be \\( +3 m \\)\n\nKatie says the function could be \\( \\times 4 \\)\n\nWho do you agree with? Only Tom"
},
{
"from": "gpt",
"value": "Does not realise that two letters together, or a number and letter together, are multiplying"
}
] |
[
{
"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 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"m\" written inside it. The middle rectangle is empty and the final rectangle has \"output\" written above it and \"4m\" written inside it.]() Tom says the function could be \\( +3 m \\)\n\nKatie says the function could be \\( \\times 4 \\)\n\nWho do you agree with? Only Katie"
},
{
"from": "gpt",
"value": "Does not understand when like terms can be collected"
}
] |
[
{
"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 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"m\" written inside it. The middle rectangle is empty and the final rectangle has \"output\" written above it and \"4m\" written inside it.]() Tom says the function could be \\( +3 m \\)\n\nKatie says the function could be \\( \\times 4 \\)\n\nWho do you agree with? Neither is correct"
},
{
"from": "gpt",
"value": "Does not realise that two letters together, or a number and letter together, are multiplying"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order integers with the same number of digits Which symbol makes the following statement correct?\n\\[\n1,959,909 \\quad\n \\square \\quad\n1,995,902\n\\] \\( > \\)"
},
{
"from": "gpt",
"value": "When ordering integers, orders from the digits at the end of the number instead of the digits at the start"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order integers with the same number of digits Which symbol makes the following statement correct?\n\\[\n1,959,909 \\quad\n \\square \\quad\n1,995,902\n\\] \\( = \\)"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order integers with the same number of digits Which symbol makes the following statement correct?\n\\[\n1,959,909 \\quad\n \\square \\quad\n1,995,902\n\\] None of these"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate real life graph \\( £ 1 \\) is \\( 1.5 \\) US dollars.\nWhich of these graphs shows the value of up to \\( £ 10 \\) in US dollars? ![A straight horizontal line graph from 15 on the y axis. Y axis labelled US dollars extending to 15, x axis labelled pounds extending to 10]()"
},
{
"from": "gpt",
"value": "Believes a direct proportion graph is a horizontal line"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate real life graph \\( £ 1 \\) is \\( 1.5 \\) US dollars.\nWhich of these graphs shows the value of up to \\( £ 10 \\) in US dollars? ![A straight line graph from approx 5 on the y axis. Y axis labelled US dollars extending to 15, x axis labelled pounds extending to 10]()"
},
{
"from": "gpt",
"value": "Believes a direct proportion graph does not have to start at the origin"
}
] |
[
{
"from": "human",
"value": "Calculate the probability of two dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. The balls are all the same size.]() Kate picks out two balls at the same time.\n\nWhat is the probability at least one ball is red? \\( \\frac{12}{42} \\)"
},
{
"from": "gpt",
"value": "Does not work out all possibilites when given an 'at least' question in probability"
}
] |
[
{
"from": "human",
"value": "Calculate the probability of two dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. The balls are all the same size.]() Kate picks out two balls at the same time.\n\nWhat is the probability at least one ball is red? \\( \\frac{24}{42} \\)"
},
{
"from": "gpt",
"value": "Does not work out all possibilites when given an 'at least' question in probability"
}
] |
[
{
"from": "human",
"value": "Calculate the probability of two dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. The balls are all the same size.]() Kate picks out two balls at the same time.\n\nWhat is the probability at least one ball is red? \\( \\frac{37}{42} \\)"
},
{
"from": "gpt",
"value": "Adds the numerators when working out a combined probability"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers What answer would your calculator give if you typed in \\(-5^{2}\\) ![A scientific calculator]() \\( 25 \\)"
},
{
"from": "gpt",
"value": "Believes the negative of a positive squared (where there are no brackets) gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers What answer would your calculator give if you typed in \\(-5^{2}\\) ![A scientific calculator]() \\( -10 \\)"
},
{
"from": "gpt",
"value": "Has multiplied the base number and the power"
}
] |
Subsets and Splits