conversations
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[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The top rectangle is shaded red.]() \\( 78 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "When calculating the area of a rectilinear compound shape, calculates the are of the surrounding rectangle"
}
] |
[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an \"L\" shape. The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The top rectangle is shaded red.]() \\( 28 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Calculates perimeter when asked for area"
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Tom and Katie are discussing regular polygons.\nTom says if all the angles are Katie says if all the sides are equal equal then the polygon must be length then the polygon must be regular regular\nWho is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Thinks that only the angles need to be the same for a polygon to be regular"
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Tom and Katie are discussing regular polygons.\nTom says if all the angles are Katie says if all the sides are equal equal then the polygon must be length then the polygon must be regular regular\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Thinks that only the sides need to be equal for a polygon to be regular"
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Tom and Katie are discussing regular polygons.\nTom says if all the angles are Katie says if all the sides are equal equal then the polygon must be length then the polygon must be regular regular\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not understand that all angles and sides must be equal for regular shapes"
}
] |
[
{
"from": "human",
"value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{17}{40} \\) written as a percentage? \\( 34 \\% \\)"
},
{
"from": "gpt",
"value": "Believes a fraction out of a number other than 100 represents a percentage"
}
] |
[
{
"from": "human",
"value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{17}{40} \\) written as a percentage? \\( 68 \\% \\)"
},
{
"from": "gpt",
"value": "Believes a fraction out of a number other than 100 represents a percentage"
}
] |
[
{
"from": "human",
"value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{17}{40} \\) written as a percentage? 17%"
},
{
"from": "gpt",
"value": "Believes a fraction out of a number other than 100 represents a percentage"
}
] |
[
{
"from": "human",
"value": "Construct a pictogram involving fractions of symbols This pictogram shows the different types of music Bob has in his music collection.\nBob has \\( 2 \\) rave CDs.\n\nHow would he display this on the pictogram? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]() ![\\( 00 \\)]()"
},
{
"from": "gpt",
"value": "When interpreting a pictogram, thinks each symbol stands for 1"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate speed-time graph Sunita accelerates quickly, then travels at a constant speed, then slowly comes to rest. Which of the following velocity \\( (v) \\) time \\( (t) \\) graphs is most likely to illustrate Sunita's journey? ![A graph with time on the horizontal axis and distance on the vertical axis. The graph starts at the origin, travels right and up in a straight line, travels horizontally right, then travels right and down in a more steep straight line than the start, until it reaches the horizontal axis.]()"
},
{
"from": "gpt",
"value": "Believes a steeper downwards line on a graph means a slower decrease"
}
] |
[
{
"from": "human",
"value": "Identify non-unit fractions when part of a shape What mixed number fraction is represented below? ![Four bars, each split into six equal parts. In three of the shapes, all six parts are shaded. In the fourth shape, five out of six parts are shaded.]() \\( 2 \\frac{3}{6} \\)"
},
{
"from": "gpt",
"value": "When converting from an improper fraction to a mixed number, just writes the tens digit as the number of wholes"
}
] |
[
{
"from": "human",
"value": "Identify non-unit fractions when part of a shape What mixed number fraction is represented below? ![Four bars, each split into six equal parts. In three of the shapes, all six parts are shaded. In the fourth shape, five out of six parts are shaded.]() \\( \\frac{23}{6} \\)"
},
{
"from": "gpt",
"value": "Confused mixed numbers with improper fractions"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one What is the 7th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is 1 orange square. The second pattern is 3 orange squares arranged as an incomplete rectangle of base 2 and height 2, with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle of base 3 and height 2, with the top left orange square missing.]() ![7 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left orange square missing.]()"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence just gives the next term"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one What is the 7th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is 1 orange square. The second pattern is 3 orange squares arranged as an incomplete rectangle of base 2 and height 2, with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle of base 3 and height 2, with the top left orange square missing.]() ![9 orange squares arranged as an incomplete rectangle of base 5 and height 2, with the top left orange square missing.]()"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence gives a different term, which is not the next"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one What is the 7th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is 1 orange square. The second pattern is 3 orange squares arranged as an incomplete rectangle of base 2 and height 2, with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle of base 3 and height 2, with the top left orange square missing.]() ![11 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left orange square missing.]()"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence gives a different term, which is not the next"
}
] |
[
{
"from": "human",
"value": "Find another power of 10 more than a given number What number is \\( 10,000 \\) more than \\( 298,603 \\) ? \\( 398,603 \\)"
},
{
"from": "gpt",
"value": "When adding powers of 10 adds onto the wrong column"
}
] |
[
{
"from": "human",
"value": "Find another power of 10 more than a given number What number is \\( 10,000 \\) more than \\( 298,603 \\) ? \\( 2,986,030,000 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than adds when given the command word 'more'"
}
] |
[
{
"from": "human",
"value": "Find another power of 10 more than a given number What number is \\( 10,000 \\) more than \\( 298,603 \\) ? \\( 208,603 \\)"
},
{
"from": "gpt",
"value": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit"
}
] |
[
{
"from": "human",
"value": "Find missing angles in a scalene triangle What is the size of angle \\( p \\) ? ![A triangle with angles labelled 49 degrees, 51 degrees and p [not to scale]]() \\( 51^{\\circ} \\)"
},
{
"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 \\( p \\) ? ![A triangle with angles labelled 49 degrees, 51 degrees and p [not to scale]]() Not enough information"
},
{
"from": "gpt",
"value": "Does not know that angles in a triangle sum to 180 degrees"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a positive non-integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{8}^{\\boldsymbol{x}} \\) \\begin{tabular}{|l|c|}\n\\hline\\( x \\) & \\( \\frac{1}{3} \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( \\frac{8}{3} \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a positive non-integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{8}^{\\boldsymbol{x}} \\) \\begin{tabular}{|l|c|}\n\\hline\\( x \\) & \\( \\frac{1}{3} \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( \\sqrt{8} \\)"
},
{
"from": "gpt",
"value": "Mixes up square rooting and cube rooting"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a positive non-integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{8}^{\\boldsymbol{x}} \\) \\begin{tabular}{|l|c|}\n\\hline\\( x \\) & \\( \\frac{1}{3} \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 24 \\)"
},
{
"from": "gpt",
"value": "Divides by the index"
}
] |
[
{
"from": "human",
"value": "Write numbers between 0 and 1 in standard form Write the following number in standard form:\n\\[\n0.0003001\n\\] \\( 3.001 \\times 10^{4} \\)"
},
{
"from": "gpt",
"value": "Does not think we can have negative powers in standard form"
}
] |
[
{
"from": "human",
"value": "Write numbers between 0 and 1 in standard form Write the following number in standard form:\n\\[\n0.0003001\n\\] \\( 3.1 \\times 10^{-4} \\)"
},
{
"from": "gpt",
"value": "When changing a number to standard form omits zero's of significance "
}
] |
[
{
"from": "human",
"value": "Write numbers between 0 and 1 in standard form Write the following number in standard form:\n\\[\n0.0003001\n\\] \\( 3.1 \\times 10^{-7} \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of adds when answering worded problems "
}
] |
[
{
"from": "human",
"value": "Convert from mixed number fractions to improper fractions Convert this into an improper fraction:\n\\(\n4 \\frac{2}{3}\n\\) \\( \\frac{42}{3} \\)"
},
{
"from": "gpt",
"value": "Thinks the number of wholes in a mixed number represents the tens from the numerator of an improper fraction"
}
] |
[
{
"from": "human",
"value": "Convert from mixed number fractions to improper fractions Convert this into an improper fraction:\n\\(\n4 \\frac{2}{3}\n\\) \\( \\frac{11}{3} \\)"
},
{
"from": "gpt",
"value": "Thinks you multiply by the numerator and add the denominator when converting a mixed number to an improper fraction"
}
] |
[
{
"from": "human",
"value": "Convert from mixed number fractions to improper fractions Convert this into an improper fraction:\n\\(\n4 \\frac{2}{3}\n\\) \\( \\frac{12}{3} \\)"
},
{
"from": "gpt",
"value": "Forgets to add the numerator when converting from a mixed number to an improper fraction "
}
] |
[
{
"from": "human",
"value": "Recognise the equations of vertical lines from a diagram ![A set of axes with a vertical line going through 3 on the x axis]() What is the equation of this line? \\( y=3 \\)"
},
{
"from": "gpt",
"value": "Confuses the equations of vertical and horizontal lines"
}
] |
[
{
"from": "human",
"value": "Recognise the equations of vertical lines from a diagram ![A set of axes with a vertical line going through 3 on the x axis]() What is the equation of this line? \\( y=3 x \\)"
},
{
"from": "gpt",
"value": "Confuses lines of the form y = a and y= ax"
}
] |
[
{
"from": "human",
"value": "Identify a unit of length George has answered a question on perimeter and worked out an answer of \\( 310 \\).\n\nBehind the star he has written the units that he used.\n\nWhich of the following units is definitely wrong? \\( 310 \\color{yellow} \\bigstar\\) \\( m \\)"
},
{
"from": "gpt",
"value": "Does not recognise metres as a unit of length"
}
] |
[
{
"from": "human",
"value": "Identify a unit of length George has answered a question on perimeter and worked out an answer of \\( 310 \\).\n\nBehind the star he has written the units that he used.\n\nWhich of the following units is definitely wrong? \\( 310 \\color{yellow} \\bigstar\\) \\(mm \\)"
},
{
"from": "gpt",
"value": "Does not recognise millimetres as a unit of length"
}
] |
[
{
"from": "human",
"value": "Identify a unit of length George has answered a question on perimeter and worked out an answer of \\( 310 \\).\n\nBehind the star he has written the units that he used.\n\nWhich of the following units is definitely wrong? \\( 310 \\color{yellow} \\bigstar\\) \\( f t \\)"
},
{
"from": "gpt",
"value": "Does not recognise feet (ft) as a unit of length"
}
] |
[
{
"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": "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 addition 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 addition is division"
}
] |
[
{
"from": "human",
"value": "Given the sketch of a curve in the form (x + a)(x + b), work out its factorised form Which of the following could be the equation of this curve? ![A graph of a quadratic curve that crosses the x axis at (1,0) and (3,0) and crosses the y axis at (0,3).]() \\( y=(x+1)(x+3) \\)"
},
{
"from": "gpt",
"value": "Forgets to swap the sign of roots when placing into brackets"
}
] |
[
{
"from": "human",
"value": "Given the sketch of a curve in the form (x + a)(x + b), work out its factorised form Which of the following could be the equation of this curve? ![A graph of a quadratic curve that crosses the x axis at (1,0) and (3,0) and crosses the y axis at (0,3).]() \\( y=(x+1)(x-3) \\)"
},
{
"from": "gpt",
"value": "Does not understand the link between the sign of the root and the sign in the bracket"
}
] |
[
{
"from": "human",
"value": "Given the sketch of a curve in the form (x + a)(x + b), work out its factorised form Which of the following could be the equation of this curve? ![A graph of a quadratic curve that crosses the x axis at (1,0) and (3,0) and crosses the y axis at (0,3).]() \\( y=(x-1)(x+3) \\)"
},
{
"from": "gpt",
"value": "Does not understand the link between the sign of the root and the sign in the bracket"
}
] |
[
{
"from": "human",
"value": "Use a bar model to express a ratio problem Tom and Katie share \\( £ 30 \\) in the ratio \\( 3\\;: 2 \\).\nWhich of the following diagrams best represents this situation? ![A bar split into 3 pink blocks and 2 blue blocks. All the blocks are the same size and each block is labelled £30.]()"
},
{
"from": "gpt",
"value": "In ratio where total is given, treats that as one part without dividing"
}
] |
[
{
"from": "human",
"value": "Use a bar model to express a ratio problem Tom and Katie share \\( £ 30 \\) in the ratio \\( 3\\;: 2 \\).\nWhich of the following diagrams best represents this situation? ![A pink bar split into 3 blocks, and below it a shorter blue bar split into 2 blocks. All the blocks are the same size. The difference in length between the pink bar and the blue bar is labelled £30.]()"
},
{
"from": "gpt",
"value": "When drawing bar diagram for ratio, shows the total as the difference between parts"
}
] |
[
{
"from": "human",
"value": "Use a bar model to express a ratio problem Tom and Katie share \\( £ 30 \\) in the ratio \\( 3\\;: 2 \\).\nWhich of the following diagrams best represents this situation? ![A pink bar split into 3 blocks, and below it a shorter blue bar split into 2 blocks. All the blocks are the same size. The length of the pink bar is labelled £30.]()"
},
{
"from": "gpt",
"value": "When drawing bar diagram for ratio, shows the total amount as the total of one side"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with the same denominator Calculate:\n\\(\n\\frac{2}{7}+\\frac{1}{7}\n\\) \\( \\frac{2}{7} \\)"
},
{
"from": "gpt",
"value": "Multiplies the numerators when adding fractions with a common denominator"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with the same denominator Calculate:\n\\(\n\\frac{2}{7}+\\frac{1}{7}\n\\) \\( \\frac{2}{49} \\)"
},
{
"from": "gpt",
"value": "When asked to add fractions, multiplies instead"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with the same denominator Calculate:\n\\(\n\\frac{2}{7}+\\frac{1}{7}\n\\) \\( \\frac{3}{14} \\)"
},
{
"from": "gpt",
"value": "When adding fractions, adds the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Calculate the square root of a number What is the value of the missing number? ![\\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{\\( 15^{2} \\)} \\\\\n\\hline\\( \\square^{2} \\) & \\( 2 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 3 \\)"
},
{
"from": "gpt",
"value": "Thinks the sum of 2 numbers, each squared first, is the same as adding the two numbers and then squaring the total"
}
] |
[
{
"from": "human",
"value": "Calculate the square root of a number What is the value of the missing number? ![\\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{\\( 15^{2} \\)} \\\\\n\\hline\\( \\square^{2} \\) & \\( 2 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 40.5 \\)"
},
{
"from": "gpt",
"value": "Halves when asked to find the square root"
}
] |
[
{
"from": "human",
"value": "Complete missing number mental subtraction problems with numbers over 1000 A \\( 4 \\) digit number belongs in this box to make the calculation true\n\\(\n\\square -7806=1253\n\\)\nWhat is the \\( 4^{\\text {th }} \\) digit of the number that belongs in the box? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of adds"
}
] |
[
{
"from": "human",
"value": "Complete missing number mental subtraction problems with numbers over 1000 A \\( 4 \\) digit number belongs in this box to make the calculation true\n\\(\n\\square -7806=1253\n\\)\nWhat is the \\( 4^{\\text {th }} \\) digit of the number that belongs in the box? \\( 8 \\)"
},
{
"from": "gpt",
"value": "does not know the meaning of the word digit"
}
] |
[
{
"from": "human",
"value": "Complete missing number mental subtraction problems with numbers over 1000 A \\( 4 \\) digit number belongs in this box to make the calculation true\n\\(\n\\square -7806=1253\n\\)\nWhat is the \\( 4^{\\text {th }} \\) digit of the number that belongs in the box? Not possible"
},
{
"from": "gpt",
"value": "Does not recognise that addition is the inverse operation of subtraction"
}
] |
[
{
"from": "human",
"value": "Carry out addition problems involving two negative integers \\( (-9)+(-4)= \\) \\( -5 \\)"
},
{
"from": "gpt",
"value": "Believes that adding a negative will increase the value of the original number"
}
] |
[
{
"from": "human",
"value": "Carry out addition problems involving two negative integers \\( (-9)+(-4)= \\) \\( 13 \\)"
},
{
"from": "gpt",
"value": "Believes adding two negatives gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences Tom says \\( (2 n+1)^{2} \\) would produce a linear sequence Katie says \\( 1-\\frac{n}{2} \\) would produce a linear sequence Who is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Does not recognise that a linear sequence must increase or decrease by same amount"
}
] |
[
{
"from": "human",
"value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences Tom says \\( (2 n+1)^{2} \\) would produce a linear sequence Katie says \\( 1-\\frac{n}{2} \\) would produce a linear sequence Who is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not recognise that a linear sequence must increase or decrease by same amount"
}
] |
[
{
"from": "human",
"value": "Generate a descending integer linear sequence from the nth term rule Tom and Katie are discussing sequences Tom says \\( (2 n+1)^{2} \\) would produce a linear sequence Katie says \\( 1-\\frac{n}{2} \\) would produce a linear sequence Who is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Believes linear sequences cannot include fractions"
}
] |
[
{
"from": "human",
"value": "Add decimals with the same number of decimals places \\( 3.52+2.75= \\) \\( 5.27 \\)"
},
{
"from": "gpt",
"value": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit"
}
] |
[
{
"from": "human",
"value": "Add decimals with the same number of decimals places \\( 3.52+2.75= \\) \\( 7.17 \\)"
},
{
"from": "gpt",
"value": "When adding decimals, just adds the digits and ignores place value"
}
] |
[
{
"from": "human",
"value": "Add decimals with the same number of decimals places \\( 3.52+2.75= \\) \\( 5.127 \\)"
},
{
"from": "gpt",
"value": "When adding decimals, just adds the digits and ignores place value"
}
] |
[
{
"from": "human",
"value": "Know the equation of the axes What is the equation of the \\( x \\) axis? \\( x=1 \\)"
},
{
"from": "gpt",
"value": "Thinks x = 1 at the x axis"
}
] |
[
{
"from": "human",
"value": "Know the equation of the axes What is the equation of the \\( x \\) axis? \\( x=0 \\)"
},
{
"from": "gpt",
"value": "Confuses the equations of vertical and horizontal lines"
}
] |
[
{
"from": "human",
"value": "Know the equation of the axes What is the equation of the \\( x \\) axis? \\( x=y \\)"
},
{
"from": "gpt",
"value": "Thinks x = y is an axis"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of this set of data?\n\\[\n4 \\mathrm{~cm}, \\quad 22 \\mathrm{~cm}, \\quad 5 \\mathrm{~cm}, \\quad 7 \\mathrm{~cm}\n\\] \\( 22 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Identifies the biggest value for the range"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of this set of data?\n\\[\n4 \\mathrm{~cm}, \\quad 22 \\mathrm{~cm}, \\quad 5 \\mathrm{~cm}, \\quad 7 \\mathrm{~cm}\n\\] \\( 3 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Thinks the range is just the first value subtracted from the last value, without ordering"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of this set of data?\n\\[\n4 \\mathrm{~cm}, \\quad 22 \\mathrm{~cm}, \\quad 5 \\mathrm{~cm}, \\quad 7 \\mathrm{~cm}\n\\] \\( 26 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "To find the range adds the biggest and smallest number rather than subtract"
}
] |
[
{
"from": "human",
"value": "Describe an ascending linear sequence in words Which of the following is the most accurate way to describe this sequence?\n\n\\[\n4,10,16,22,28, \\ldots\n\\] The first term is \\( 6 \\) and the common difference is positive \\( 4 \\)"
},
{
"from": "gpt",
"value": "Does not know the definition of term or term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Describe an ascending linear sequence in words Which of the following is the most accurate way to describe this sequence?\n\n\\[\n4,10,16,22,28, \\ldots\n\\] The first term is \\( 6 \\) and the common difference is negative \\( 4 \\)"
},
{
"from": "gpt",
"value": "Does not know the definition of term or term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Complete mental addition problems up to 1000 \\( 23+108= \\) \\( 338 \\)"
},
{
"from": "gpt",
"value": "Lines up the digits incorrectly when doing an addition involving two numbers with a different amount of digits"
}
] |
[
{
"from": "human",
"value": "Complete mental addition problems up to 1000 \\( 23+108= \\) \\( 121 \\)"
},
{
"from": "gpt",
"value": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.2=\\frac{1}{5}=? \\% \\) \\( 15 \\% \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a percentage by writing the numerator followed by the denominator"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.2=\\frac{1}{5}=? \\% \\) \\( 2 \\% \\)"
},
{
"from": "gpt",
"value": "Multiplies by 10 instead of 100 when converting decimal to percentage"
}
] |
[
{
"from": "human",
"value": "Factorise a single bracket containing a linear expression by taking out a single numeric common factor (e.g. 6) What should replace the star and triangle when this expression is fully factorised? \\( 8 m - 10 \\equiv {\\bigstar}(\\triangle m-\\bigcirc) \\) \\( \\begin{array}{l}{\\bigstar}=8 \\\\ \\Delta=1\\end{array} \\)"
},
{
"from": "gpt",
"value": "When factorising, finds a factor that goes into only the first term of the expression"
}
] |
[
{
"from": "human",
"value": "Factorise a single bracket containing a linear expression by taking out a single numeric common factor (e.g. 6) What should replace the star and triangle when this expression is fully factorised? \\( 8 m - 10 \\equiv {\\bigstar}(\\triangle m-\\bigcirc) \\) \\( \\begin{array}{l}{\\bigstar}=5 \\\\ \\Delta=3\\end{array} \\)"
},
{
"from": "gpt",
"value": "Believes factors add to give a number"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a horizontal line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object The triangle is reflected in the \\( x \\)-axis\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -1 to 8, y-axis from -5 to 6. Three points are plotted and joined to make a triangle: (2, 0), (4, 0), (2, 3). Point (2, 3) is labelled with the letter \"P\". ]() \\( (2,3) \\)"
},
{
"from": "gpt",
"value": "Believes that when a shape touches the mirror line, all of its vertices will stay the same when reflected"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a horizontal line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object The triangle is reflected in the \\( x \\)-axis\nWhat are the new coordinates of point \\( P \\) ? ![A set of axes: x-axis from -1 to 8, y-axis from -5 to 6. Three points are plotted and joined to make a triangle: (2, 0), (4, 0), (2, 3). Point (2, 3) is labelled with the letter \"P\". ]() \\( (3,2) \\)"
},
{
"from": "gpt",
"value": "Believes that reflection always switches the x and y coordinates"
}
] |
[
{
"from": "human",
"value": "Recognise the equations of horizontal lines from a diagram What is the equation of this line? ![A graph showing a horizontal line going through 4 on the y axis.]() \\( x=4 y \\)"
},
{
"from": "gpt",
"value": "Believes the equation of a horizontal line is in the form x = ay, where a is the y intercept"
}
] |
[
{
"from": "human",
"value": "Recognise the equations of horizontal lines from a diagram What is the equation of this line? ![A graph showing a horizontal line going through 4 on the y axis.]() \\( y=4 x \\)"
},
{
"from": "gpt",
"value": "Includes the x variable when giving the equation of a horizontal line"
}
] |
[
{
"from": "human",
"value": "Recognise the equations of horizontal lines from a diagram What is the equation of this line? ![A graph showing a horizontal line going through 4 on the y axis.]() \\( x=4 \\)"
},
{
"from": "gpt",
"value": "Confuses the equations of vertical and horizontal lines"
}
] |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 90° and 180° Which diagram shows an angle of \\( 135^{\\circ} \\) ? ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise, to the red line that is half way between 120 and 130 (inner scale) and halfway between 60 and 50 (outer scale).]()"
},
{
"from": "gpt",
"value": "Chooses the correct scale when measuring angles on a protractor but starts from the wrong number when the angle is in between two labelled dashes"
}
] |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 90° and 180° Which diagram shows an angle of \\( 135^{\\circ} \\) ? ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise , to the red line that is half way between 40 and 50 (inner scale) and halfway between 140 and 130 (outer scale).]()"
},
{
"from": "gpt",
"value": "Reads the wrong scale on the protractor when measuring obtuse angles"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data The data is in ascending order.\n\\(\n\\begin{array}{llllll}\nx & 5 & 8 & y & 19 & 25\n\\end{array}\n\\)\nWrite an expression for the range. \\( x-25 \\)"
},
{
"from": "gpt",
"value": "subtracts the highest from the lowest when calculating the range"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data The data is in ascending order.\n\\(\n\\begin{array}{llllll}\nx & 5 & 8 & y & 19 & 25\n\\end{array}\n\\)\nWrite an expression for the range. \\( \\frac{57+y+x}{6} \\)"
},
{
"from": "gpt",
"value": "Finds the mean instead of the range"
}
] |
[
{
"from": "human",
"value": "Match linear sequences to other representations, such as tables and graphs Which sequence matches this graph? ![Position]() ![The sequence 5, 7, 9 represented pictorially using black line segments shaped into triangles which share a side.]()"
},
{
"from": "gpt",
"value": "When given a linear sequence, cannot match it to a visual pattern"
}
] |
[
{
"from": "human",
"value": "Match linear sequences to other representations, such as tables and graphs Which sequence matches this graph? ![Position]() ![The sequence 3, 5, 7 represented pictorially using squares. For the first term 3 squares are placed with two squares as the base and one square stacked on top of the square on the left hand side. For each additional term, 2 squares, stacked on top of each other are added to the left hand side of the previous term's image.]()"
},
{
"from": "gpt",
"value": "When given a linear sequence, cannot match it to a visual pattern"
}
] |
[
{
"from": "human",
"value": "Match linear sequences to other representations, such as tables and graphs Which sequence matches this graph? ![Position]() ![The first three triangular numbers represented using purple dots.]()"
},
{
"from": "gpt",
"value": "When given a linear sequence, cannot match it to a visual pattern"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, with all positive integers Solve the following equation for \\( a \\) :\n\\[\n2=3 a-4\n\\] \\( a=-\\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of adds when using inverse operations to solve an equation"
}
] |
[
{
"from": "human",
"value": "Interpret linear sections of real life graphs The graph on the right shows the mass of sand in a bucket over time\n\nThe gradient of the positive sloping section would tell us... ![A graph with time (secs) on the horizontal axis and mass (g) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis, more steeply than the start. ]() The mass of sand in the bucket"
},
{
"from": "gpt",
"value": "Does not realise that gradient represents rate of change"
}
] |
[
{
"from": "human",
"value": "Answer negative number problems that require the use of BIDMAS \\( -4+(-5) \\times 3= \\) \\( -27 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape ![A solid yellow equilateral triangle (3 sided polygon with all 3 sides of equal length).]() What is the order of rotational symmetry of this equilateral triangle? \\( 1 \\)"
},
{
"from": "gpt",
"value": "Does not know how to find order of rotational symmetry"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape ![A solid yellow equilateral triangle (3 sided polygon with all 3 sides of equal length).]() What is the order of rotational symmetry of this equilateral triangle? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Gives one fewer order of rotational symmetry than there is"
}
] |
[
{
"from": "human",
"value": "Recognise that a sequence is linear sequences when expressed as a pattern Tom and Katie are discussing linear sequences Tom says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares so the bottom line is two squares long. The second shape is also an L but with a bottom line of three squares. The fourth shape is the same but the bottom line is four squares long. ]() Katie says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares. The second shape is an L made of 5 squares, two on the top row and three on the bottom row. The third shape is an L made of 7 squares, 3 on the top row and four on the bottom. ]() Who is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Does not recognise that a linear sequence must increase or decrease by same amount"
}
] |
[
{
"from": "human",
"value": "Recognise that a sequence is linear sequences when expressed as a pattern Tom and Katie are discussing linear sequences Tom says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares so the bottom line is two squares long. The second shape is also an L but with a bottom line of three squares. The fourth shape is the same but the bottom line is four squares long. ]() Katie says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares. The second shape is an L made of 5 squares, two on the top row and three on the bottom row. The third shape is an L made of 7 squares, 3 on the top row and four on the bottom. ]() Who is correct? Only\nKatie"
},
{
"from": "gpt",
"value": "Does not recognise that a linear sequence must increase or decrease by same amount"
}
] |
[
{
"from": "human",
"value": "Recognise that a sequence is linear sequences when expressed as a pattern Tom and Katie are discussing linear sequences Tom says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares so the bottom line is two squares long. The second shape is also an L but with a bottom line of three squares. The fourth shape is the same but the bottom line is four squares long. ]() Katie says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares. The second shape is an L made of 5 squares, two on the top row and three on the bottom row. The third shape is an L made of 7 squares, 3 on the top row and four on the bottom. ]() Who is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not recognise that a linear sequence must increase or decrease by same amount"
}
] |
[
{
"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 \\( \\boldsymbol{y}=\\frac{\\mathbf{1}}{\\boldsymbol{x}} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 0 \\) \\\\\n\\hline\\( y \\) & \\(\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 1 \\)"
},
{
"from": "gpt",
"value": "Believes that a number divided by itself equals 0"
}
] |
[
{
"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 \\( \\boldsymbol{y}=\\frac{\\mathbf{1}}{\\boldsymbol{x}} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 0 \\) \\\\\n\\hline\\( y \\) & \\(\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 0 \\)"
},
{
"from": "gpt",
"value": "Believes that a reciprocal equation is defined when the denominator is 0"
}
] |
[
{
"from": "human",
"value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative What is the midpoint of these two coordinates? ![A set of axes with two points (-4,5) and (6,2) plotted.]() \\( (5,3.5) \\)"
},
{
"from": "gpt",
"value": "Believes midpoint calculation is just half of the difference"
}
] |
[
{
"from": "human",
"value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative What is the midpoint of these two coordinates? ![A set of axes with two points (-4,5) and (6,2) plotted.]() \\( (2,7) \\)"
},
{
"from": "gpt",
"value": "Does not divide by 2 when finding midpoint"
}
] |
[
{
"from": "human",
"value": "Solve linear simultaneous equations requiring a scaling of both expressions If three cups of tea and two cups of coffee cost \\( £ 2.40 \\), and two cups of tea and five cups of coffee cost £3.80, what is the cost of a cup of tea and a cup of coffee? \\( \\begin{array}{l}\\text { Tea }=80 p, \\\\ \\text { coffee }=44 p\\end{array} \\)"
},
{
"from": "gpt",
"value": "When asked to solve simultaneous equations, believes they can just find values that work in one equation"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words I think of a number. I add on five and then multiply the result by four. The answer I get is \\( 17 \\).\nWhich of the following equations represents this? \\( n+5 \\times 4=17 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words I think of a number. I add on five and then multiply the result by four. The answer I get is \\( 17 \\).\nWhich of the following equations represents this? \\( 4 n+5=17 \\)"
},
{
"from": "gpt",
"value": "Does not include brackets when attempting to multiply an expression"
}
] |
Subsets and Splits