conversations
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[
{
"from": "human",
"value": "Calculate the square of a number ![An image of a function machine. The input is 20 and the function is squared.]() What is the output of this function machine? \\( 40 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number ![An image of a function machine. The input is 20 and the function is squared.]() What is the output of this function machine? \\( 22 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and addition"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number ![An image of a function machine. The input is 20 and the function is squared.]() What is the output of this function machine? \\( 10 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and halving"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing ways to calculate \\( 21 \\times 12 \\) mentally Tom does \\( 12 \\times 7 \\) and then multiplies his answer by \\( 3 \\) Katie does \\( 21 \\times 6 \\) and then doubles her answer Who would get the correct answer? Only Tom"
},
{
"from": "gpt",
"value": "Does not correctly apply the distributive property of multiplication"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing ways to calculate \\( 21 \\times 12 \\) mentally Tom does \\( 12 \\times 7 \\) and then multiplies his answer by \\( 3 \\) Katie does \\( 21 \\times 6 \\) and then doubles her answer Who would get the correct answer? Only Katie"
},
{
"from": "gpt",
"value": "Does not correctly apply the distributive property of multiplication"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing ways to calculate \\( 21 \\times 12 \\) mentally Tom does \\( 12 \\times 7 \\) and then multiplies his answer by \\( 3 \\) Katie does \\( 21 \\times 6 \\) and then doubles her answer Who would get the correct answer? Neither is correct"
},
{
"from": "gpt",
"value": "Does not correctly apply the distributive property of multiplication"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by dividing by a single letter Tom and Katie are arguing about simplifying fractions. Tom says \\( \\frac{3 p-1}{p} \\equiv 2 \\) Katie says \\( \\frac{3 p-1}{p} \\equiv 3-\\frac{1}{p} \\) Who is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Only applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction"
}
] |
[
{
"from": "human",
"value": "Multiply a decimal by an integer Work out:\n\\[\n0.6 \\times 11\n\\] \\( 7 \\)"
},
{
"from": "gpt",
"value": "Gives a rounded whole number instead of a decimal"
}
] |
[
{
"from": "human",
"value": "Multiply a decimal by an integer Work out:\n\\[\n0.6 \\times 11\n\\] \\( 66 \\)"
},
{
"from": "gpt",
"value": "When multiplying a decimal by an integer, ignores decimal point and just multiplies the digits"
}
] |
[
{
"from": "human",
"value": "Convert between cl and l \\[\n650 \\text { centilitres }=\\bigstar \\text { litres }\n\\]\nWhat should replace the star? \\( 0.65 \\)"
},
{
"from": "gpt",
"value": "Confuses cl and ml"
}
] |
[
{
"from": "human",
"value": "Convert between cl and l \\[\n650 \\text { centilitres }=\\bigstar \\text { litres }\n\\]\nWhat should replace the star? \\( 65000 \\)"
},
{
"from": "gpt",
"value": "Multiplies when converting to a larger unit"
}
] |
[
{
"from": "human",
"value": "Convert between cl and l \\[\n650 \\text { centilitres }=\\bigstar \\text { litres }\n\\]\nWhat should replace the star? \\( 65 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10cl in a litre"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order a negative and a positive integer One of these pairs of numbers does not fit \nthe inequality \\( d \\geq h \\)\n\nCan you find which pair? \\( \\begin{array}{c}d=1 \\\\ h=-4\\end{array} \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order a negative and a positive integer One of these pairs of numbers does not fit \nthe inequality \\( d \\geq h \\)\n\nCan you find which pair? \\( \\begin{array}{l}d=2 \\\\ h=2\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order a negative and a positive integer One of these pairs of numbers does not fit \nthe inequality \\( d \\geq h \\)\n\nCan you find which pair? \\( \\begin{array}{l}d=5 \\\\ h=4\\end{array} \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Calculate the cube root of a number \\( \\sqrt[3]{8}= \\) \\( 2 . \\dot{6} \\)"
},
{
"from": "gpt",
"value": "Divides by the order of the root"
}
] |
[
{
"from": "human",
"value": "Calculate the cube root of a number \\( \\sqrt[3]{8}= \\) \\( 4 \\)"
},
{
"from": "gpt",
"value": "Halves when asked to find the cube root"
}
] |
[
{
"from": "human",
"value": "Calculate the cube root of a number \\( \\sqrt[3]{8}= \\) \\( 64 \\)"
},
{
"from": "gpt",
"value": "Confuses cube rooting with squaring a number"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Mo wants to solve this equation using the quadratic formula.\n\\(\n5 h^{2}-3 h-2=0\n\\)\n\nWhat should replace the triangle? \\( ?\\pm \\sqrt{\\triangle-?} \\) \\( -6 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Mo wants to solve this equation using the quadratic formula.\n\\(\n5 h^{2}-3 h-2=0\n\\)\n\nWhat should replace the triangle? \\( ?\\pm \\sqrt{\\triangle-?} \\) \\( -9 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Interpret the gradient on a linear section on a real life graph Jadon decides to go for a run starting from home.\nThe graph on the right shows Jadon's distance in metres \\( (d) \\) over time in seconds\n\\( (t) \\).\n\nThe gradient of the negative sloping section of the graph is \\( 0.5 \\).\n\nWhich of the following does that \\( 0.5 \\) best represent? ![A sketch of a graph with d on the y axis and t on the x axis. A straight line slopes upwards from the origin 2/3 of the way up the graph, 1/5 across the graph. It then becomes horizontal for the next 1/5 of the graph, before sloping downwards in a straight line for the remainder of the graph. ]() Jadon is travelling away from home at a speed of \\( 0.5 \\mathrm{~m} / \\mathrm{s} \\)"
},
{
"from": "gpt",
"value": "Believes a downward slope on a distance-time graph means travelling away"
}
] |
[
{
"from": "human",
"value": "Interpret the gradient on a linear section on a real life graph Jadon decides to go for a run starting from home.\nThe graph on the right shows Jadon's distance in metres \\( (d) \\) over time in seconds\n\\( (t) \\).\n\nThe gradient of the negative sloping section of the graph is \\( 0.5 \\).\n\nWhich of the following does that \\( 0.5 \\) best represent? ![A sketch of a graph with d on the y axis and t on the x axis. A straight line slopes upwards from the origin 2/3 of the way up the graph, 1/5 across the graph. It then becomes horizontal for the next 1/5 of the graph, before sloping downwards in a straight line for the remainder of the graph. ]() Jadon is decelerating at a rate of \\( 0.5 \\mathrm{~m} / \\mathrm{s}^{2} \\)"
},
{
"from": "gpt",
"value": "Believes the gradient of a distance-time graph is the acceleration"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division What does the following equal?\n\\[\n3-5+4 \\times 2\n\\] \\( 4 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division What does the following equal?\n\\[\n3-5+4 \\times 2\n\\] \\( -12 \\)"
},
{
"from": "gpt",
"value": "Performs addition ahead of subtraction"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division What does the following equal?\n\\[\n3-5+4 \\times 2\n\\] \\( -10 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of adds"
}
] |
[
{
"from": "human",
"value": "Use a protractor to draw angles between 0° and 90° When drawing an angle, which step will you complete last? Make sure the centre of the protractor is at the end of the line segment."
},
{
"from": "gpt",
"value": "Does not recall the steps required to draw an angle"
}
] |
[
{
"from": "human",
"value": "Use a protractor to draw angles between 0° and 90° When drawing an angle, which step will you complete last? Draw a marker to show where the angle needs to be drawn."
},
{
"from": "gpt",
"value": "Does not recall the steps required to draw an angle"
}
] |
[
{
"from": "human",
"value": "Use a protractor to draw angles between 0° and 90° When drawing an angle, which step will you complete last? Draw a line segment"
},
{
"from": "gpt",
"value": "Does not recall the steps required to draw an angle"
}
] |
[
{
"from": "human",
"value": "Use a protractor to draw angles between 0° and 90° Which diagram shows an angle of \\( 55^{\\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 130 and 140 (inner scale) and halfway between 50 and 40 (outer scale).]()"
},
{
"from": "gpt",
"value": "Reads the wrong scale on the protractor when measuring obtuse angles"
}
] |
[
{
"from": "human",
"value": "Use a protractor to draw angles between 0° and 90° Which diagram shows an angle of \\( 55^{\\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": "Reads the wrong scale on the protractor when measuring obtuse angles"
}
] |
[
{
"from": "human",
"value": "Use a protractor to draw angles between 0° and 90° Which diagram shows an angle of \\( 55^{\\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": "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": "Expand two brackets with linear terms in the form (x + a)(x + b) Which of the following answers shows a correct expansion of the expression below? \\( (x+5)(x-2) \\) \\( x^{2}-2 x+5 x+3 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplying when expanding bracket"
}
] |
[
{
"from": "human",
"value": "Calculate the midpoint between two coordinates in 2D, where all the values are integers but at least one is negative Points \\( P, Q \\) and \\( R \\) are equally spaced along the line segment, as shown in the sketch.\n\nThe coordinates of \\( \\mathrm{P} \\) and \\( \\mathrm{R} \\) are marked on the diagram.\n\nWhat are the coordinates of \\( Q \\) ? ![A graph with 4 quadrants showing a line joining points R(2, 7), Q (unknown coordinate in 3rd quadrant) and P (-4, -10)]() \\( (-2,-3) \\)"
},
{
"from": "gpt",
"value": "Does not divide by 2 when finding midpoint"
}
] |
[
{
"from": "human",
"value": "Identify the mode from a frequency table The frequency table shows the grade achieved by some students in a maths exam.\nWhat was the modal grade? ![\\begin{tabular}{|c|c|}\n\\hline Grade & Frequency \\\\\n\\hline \\( 1 \\) & \\( 3 \\) \\\\\n\\hline \\( 2 \\) & \\( 7 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 9 \\) \\\\\n\\hline \\( 5 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 3 \\)"
},
{
"from": "gpt",
"value": "Believes the mode is the most common frequency rather than the highest frequency"
}
] |
[
{
"from": "human",
"value": "Identify the mode from a frequency table The frequency table shows the grade achieved by some students in a maths exam.\nWhat was the modal grade? ![\\begin{tabular}{|c|c|}\n\\hline Grade & Frequency \\\\\n\\hline \\( 1 \\) & \\( 3 \\) \\\\\n\\hline \\( 2 \\) & \\( 7 \\) \\\\\n\\hline \\( 3 \\) & \\( 3 \\) \\\\\n\\hline \\( 4 \\) & \\( 9 \\) \\\\\n\\hline \\( 5 \\) & \\( 1 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 9 \\)"
},
{
"from": "gpt",
"value": "Believes the mode is the frequency rather than the value/group"
}
] |
[
{
"from": "human",
"value": "Express pictorial representations of objects as a ratio \\( \\square \\square \\square \\triangle \\square \\square \\square \\triangle \\square \\square \\square \\triangle \\) For every \\( 3 \\) triangles there are \\(___\\) squares \\( 3 \\)"
},
{
"from": "gpt",
"value": "Finds one part of a ratio but doesn't multiply that by the number of parts needed"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition or subtraction with multiplication There are \\( 8 \\) shelves of plates. Four of the shelves hold \\( 15 \\) plates each. Two of the shelves hold \\( 23 \\) plates each. The other shelves hold \\( 17 \\) plates each.\nHow many plates are there in total? \\( 55 \\)"
},
{
"from": "gpt",
"value": "Ignores numbers written as words in worded questions, and just calculates using those written in digits"
}
] |
[
{
"from": "human",
"value": "Solve problems that combine addition or subtraction with multiplication There are \\( 8 \\) shelves of plates. Four of the shelves hold \\( 15 \\) plates each. Two of the shelves hold \\( 23 \\) plates each. The other shelves hold \\( 17 \\) plates each.\nHow many plates are there in total? \\( 63 \\)"
},
{
"from": "gpt",
"value": "Ignores numbers written as words in worded questions, and just calculates using those written in digits"
}
] |
[
{
"from": "human",
"value": "Divide a quantity into two parts for a given a ratio, where each part is an integer For every \\( 3 \\) green squares there are \\( 1 \\) red squares.\n\nHow many squares should be coloured green in the grid on the right? \\begin{tabular}{|l|l|l|l|}\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline\n\\end{tabular} \\( 3 \\)"
},
{
"from": "gpt",
"value": "Does not believe you can scale up a proportional statement"
}
] |
[
{
"from": "human",
"value": "Divide a quantity into two parts for a given a ratio, where each part is an integer For every \\( 3 \\) green squares there are \\( 1 \\) red squares.\n\nHow many squares should be coloured green in the grid on the right? \\begin{tabular}{|l|l|l|l|}\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline\n\\end{tabular} \\( 8 \\)"
},
{
"from": "gpt",
"value": "Shares equally instead of in given ratio"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving brackets \\[\n6-3+2\n\\]\nTom and Katie are trying to make the calculation above equal to \\( 5 \\).\nTom says you can write it like this: \\( (6-3)+2 \\)\nKatie says you can leave it like this: \\( 6-3+2 \\)\nWho is correct? Only Tom"
},
{
"from": "gpt",
"value": "Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\( 1, \\quad 0.1, \\quad 0.01,\\quad 0.001 \\) \\( 0.22 \\)"
},
{
"from": "gpt",
"value": "Does not divide by 2 when finding midpoint"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an even numbered list of data What is the median of the following numbers?\n\\( 1, \\quad 0.1, \\quad 0.01,\\quad 0.001 \\) \\( 0.11 \\)"
},
{
"from": "gpt",
"value": "When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle"
}
] |
[
{
"from": "human",
"value": "Recognise a Fibonacci sequence expressed as a pattern Which of the following is the best way to describe this sequence: ![A pattern with 6 terms made of green and red dots. The first term is a green dot, the second a red dot, the third is one red and one green dot. The fourth term is made of one green and two red dots. The fifth term is made from two green dots and three red dots. The sixth term is made of five red dots and three green dots. ]() Linear"
},
{
"from": "gpt",
"value": "Does not recognise that a linear sequence must increase or decrease by same amount"
}
] |
[
{
"from": "human",
"value": "Recognise a Fibonacci sequence expressed as a pattern Which of the following is the best way to describe this sequence: ![A pattern with 6 terms made of green and red dots. The first term is a green dot, the second a red dot, the third is one red and one green dot. The fourth term is made of one green and two red dots. The fifth term is made from two green dots and three red dots. The sixth term is made of five red dots and three green dots. ]() Quadratic"
},
{
"from": "gpt",
"value": "Does not understand the term quadratic"
}
] |
[
{
"from": "human",
"value": "Recognise a Fibonacci sequence expressed as a pattern Which of the following is the best way to describe this sequence: ![A pattern with 6 terms made of green and red dots. The first term is a green dot, the second a red dot, the third is one red and one green dot. The fourth term is made of one green and two red dots. The fifth term is made from two green dots and three red dots. The sixth term is made of five red dots and three green dots. ]() Geometric"
},
{
"from": "gpt",
"value": "Does not know what a Fibonacci sequence is"
}
] |
[
{
"from": "human",
"value": "Represent the solution to a graphical inequality involving a combination of vertical, horizontal and diagonal lines Which letter describes the region where \\( \\boldsymbol{x}+\\boldsymbol{y} \\leq \\mathbf{3} \\) and \\( \\boldsymbol{y} \\leq \\mathbf{1} \\) ? ![A set of axes with two straight lines drawn on. The line x+y=3 goes through points (3,0) and (0,3). The line y=1 is a horizontal line going through (0,1). The lines intersect one another at (2,1).\nA is the region below x+y=3 and above y=1.\nB is the region above both lines.\nC is the region below y=1 but above x+y=3.\nD is the region below both lines. ]() B"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors Describe the movements to get from\n\n\\[\n(5,-2) \\text { to }(0,1)\n\\] Left \\( 5 \\) squares, down \\( 1 \\) square"
},
{
"from": "gpt",
"value": "Confuses negative and positive coordinates when working with graphs in four quadrants"
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors Describe the movements to get from\n\n\\[\n(5,-2) \\text { to }(0,1)\n\\] Left \\( 5 \\) squares, up \\( 4 \\) squares"
},
{
"from": "gpt",
"value": "When finding the distance between coordinates, includes the starting number"
}
] |
[
{
"from": "human",
"value": "Convert between g and kg \\( 4000 \\mathrm{~g} \\) is the same as \\( k g \\) \\( 400 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10g in a kilogram"
}
] |
[
{
"from": "human",
"value": "Convert between g and kg \\( 4000 \\mathrm{~g} \\) is the same as \\( k g \\) \\( 4000000 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than divides"
}
] |
[
{
"from": "human",
"value": "Convert between g and kg \\( 4000 \\mathrm{~g} \\) is the same as \\( k g \\) \\( 40 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100g in a kilogram"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 100 \\( 3.06 \\div 100= \\) \\( 0.36 \\)"
},
{
"from": "gpt",
"value": "Does not understand the value of zeros as placeholders"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 100 \\( 3.06 \\div 100= \\) \\( 0.036 \\)"
},
{
"from": "gpt",
"value": "Does not understand the value of zeros as placeholders"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 100 \\( 3.06 \\div 100= \\) \\( 0.00306 \\)"
},
{
"from": "gpt",
"value": "Divided by 100 rather than 10"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number \\( 0.7^{2}= \\) \\( 1.4 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number \\( 0.7^{2}= \\) \\( 0.14 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number \\( 0.7^{2}= \\) \\( 4.9 \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal"
}
] |
[
{
"from": "human",
"value": "Find missing angles using vertically opposite angles What is the size of angle \\( y \\) ? ![A diagram showing 3 lines crossing at a point to form 6 angles. One angle is marked as 43 degrees. Another angle is marked as y. There are two blank angles between each marked angle.]() \\( 137^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes vertically opposite angles sum to 180 degrees"
}
] |
[
{
"from": "human",
"value": "Find missing angles using vertically opposite angles What is the size of angle \\( y \\) ? ![A diagram showing 3 lines crossing at a point to form 6 angles. One angle is marked as 43 degrees. Another angle is marked as y. There are two blank angles between each marked angle.]() \\( 47^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes vertically opposite angles sum to 90 degrees"
}
] |
[
{
"from": "human",
"value": "Find missing angles using vertically opposite angles What is the size of angle \\( y \\) ? ![A diagram showing 3 lines crossing at a point to form 6 angles. One angle is marked as 43 degrees. Another angle is marked as y. There are two blank angles between each marked angle.]() Not enough information"
},
{
"from": "gpt",
"value": "Does not know that vertically opposite angles are equal"
}
] |
[
{
"from": "human",
"value": "Identify unit fractions when part of a shape What fraction of the shape is shaded? ![A rectangle split in half. One half is split in half again, and one half of that is split in half again, with one of those parts shaded.]() \\( \\frac{1}{3} \\)"
},
{
"from": "gpt",
"value": "Does not understand a denominator represents equal parts"
}
] |
[
{
"from": "human",
"value": "Identify unit fractions when part of a shape What fraction of the shape is shaded? ![A rectangle split in half. One half is split in half again, and one half of that is split in half again, with one of those parts shaded.]() \\( 1 \\)"
},
{
"from": "gpt",
"value": "Does not know how to write a fraction - just given an integer answer"
}
] |
[
{
"from": "human",
"value": "Identify unit fractions when part of a shape What fraction of the shape is shaded? ![A rectangle split in half. One half is split in half again, and one half of that is split in half again, with one of those parts shaded.]() \\( \\frac{1}{4} \\)"
},
{
"from": "gpt",
"value": "Does not understand a denominator represents equal parts"
}
] |
[
{
"from": "human",
"value": "Calculate the cube of a number What is the value of \"\\( 3 \\) cubed\"? \\( 9 \\)"
},
{
"from": "gpt",
"value": "Mixes up square numbers and cube numbers"
}
] |
[
{
"from": "human",
"value": "Calculate the cube of a number What is the value of \"\\( 3 \\) cubed\"? \\( 33 \\)"
},
{
"from": "gpt",
"value": "Adds the index to the number"
}
] |
[
{
"from": "human",
"value": "Calculate the cube of a number What is the value of \"\\( 3 \\) cubed\"? \\( 333 \\)"
},
{
"from": "gpt",
"value": "Repeats the digits three times when cubing a number"
}
] |
[
{
"from": "human",
"value": "Substitute negative integer values into expressions involving no powers or roots Amy is trying to work out the distance between these two points: \\( (1,-6) \\) and \\( (-5,2) \\) She labels them like this: \\( \\begin{array}{rrrr}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (1, & -6) & (-5, & 2)\\end{array} \\) And then decides to use this formula: \\( \\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}} \\) What does the second bracket equal? \\( (-8)^{2} \\)"
},
{
"from": "gpt",
"value": "Believes subtraction is commutative "
}
] |
[
{
"from": "human",
"value": "Substitute negative integer values into expressions involving no powers or roots Amy is trying to work out the distance between these two points: \\( (1,-6) \\) and \\( (-5,2) \\) She labels them like this: \\( \\begin{array}{rrrr}x_{1} & y_{1} & x_{2} & y_{2} \\\\ (1, & -6) & (-5, & 2)\\end{array} \\) And then decides to use this formula: \\( \\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}} \\) What does the second bracket equal? \\( (-4)^{2} \\)"
},
{
"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": "Add decimals where the numbers involved have a different number of decimal places How should you line up the digits to calculate \\( 0.7+0.54 \\) ? ![A column addition of 0.7 + 0.54. The 0 of 0.7 is directly above the decimal point of 0.54, the decimal point of 0.7 is directly above the 5 of 0.54 and the 7 of 0.7 is directly above the 4 of 0.54.]()"
},
{
"from": "gpt",
"value": "Thinks that when adding decimals with a different number of decimal places, you should line up the digits to the right "
}
] |
[
{
"from": "human",
"value": "Add decimals where the numbers involved have a different number of decimal places How should you line up the digits to calculate \\( 0.7+0.54 \\) ? ![A column addition of 0.07 + 0.54 with the decimal points lined up.]()"
},
{
"from": "gpt",
"value": "Does not understand the value of zeros as placeholders"
}
] |
[
{
"from": "human",
"value": "Identify a unit of volume or capacity Tom and Katie are discussing units of volume\nTom says litres is a unit of volume\nKatie says \\( m^{3} \\) is a unit of volume\nWho is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Does not know that units of volume are usually cubed"
}
] |
[
{
"from": "human",
"value": "Identify a unit of volume or capacity Tom and Katie are discussing units of volume\nTom says litres is a unit of volume\nKatie says \\( m^{3} \\) is a unit of volume\nWho is correct? Only\nKatie"
},
{
"from": "gpt",
"value": "Does not recognise litres as a unit of volume"
}
] |
[
{
"from": "human",
"value": "Identify a unit of volume or capacity Tom and Katie are discussing units of volume\nTom says litres is a unit of volume\nKatie says \\( m^{3} \\) is a unit of volume\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not recognise a unit of volume"
}
] |
[
{
"from": "human",
"value": "Understand the notation for powers To calculate \\( 53^{2} \\) you need to do... \\( 53+2 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and addition"
}
] |
[
{
"from": "human",
"value": "Understand the notation for powers To calculate \\( 53^{2} \\) you need to do... \\( 53 \\times 2 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Identify a unit of length Sally has answered a question on perimeter and got an answer of \\( 500 \\).\n\nBehind the star she has written the units that she used.\nWhich of the following units is definitely wrong? \\( 500 \\bigstar \\) \\( \\mathrm{cm} \\)"
},
{
"from": "gpt",
"value": "Does not recognise a unit of length"
}
] |
[
{
"from": "human",
"value": "Identify a unit of length Sally has answered a question on perimeter and got an answer of \\( 500 \\).\n\nBehind the star she has written the units that she used.\nWhich of the following units is definitely wrong? \\( 500 \\bigstar \\) \\( \\mathrm{mm} \\)"
},
{
"from": "gpt",
"value": "Does not recognise a unit of length"
}
] |
[
{
"from": "human",
"value": "Identify a unit of length Sally has answered a question on perimeter and got an answer of \\( 500 \\).\n\nBehind the star she has written the units that she used.\nWhich of the following units is definitely wrong? \\( 500 \\bigstar \\) \\( \\mathrm{km} \\)"
},
{
"from": "gpt",
"value": "Does not recognise a unit of length"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\n\nIn which \\( 4 \\) hour period did the temperature fall the most? ![A graph showing the temperature in Dan's house over a 24 hours period. At 00:00 the temperature is -2 degrees, at 04:00 it is -4 degrees, at 08:00 it is 0 degrees, at 12:00 it is 5 degrees, at 16:00 it is 8 degrees, at 20:00 it is 3 degrees and at 00:00 it is 0 degrees.]() \\( \\begin{array}{c}00: 00 \\text { to } \\\\ 04: 00\\end{array} \\)"
},
{
"from": "gpt",
"value": "Believes a steeper downwards line on a graph means a slower decrease"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\n\nIn which \\( 4 \\) hour period did the temperature fall the most? ![A graph showing the temperature in Dan's house over a 24 hours period. At 00:00 the temperature is -2 degrees, at 04:00 it is -4 degrees, at 08:00 it is 0 degrees, at 12:00 it is 5 degrees, at 16:00 it is 8 degrees, at 20:00 it is 3 degrees and at 00:00 it is 0 degrees.]() \\( \\begin{array}{c}08: 00 \\text { to } \\\\ 12: 00\\end{array} \\)"
},
{
"from": "gpt",
"value": "Mixes up colder and hotter when comparing temperatures"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph This graph shows the temperature in Dan's garden in a \\( 24 \\) hour period.\n\nIn which \\( 4 \\) hour period did the temperature fall the most? ![A graph showing the temperature in Dan's house over a 24 hours period. At 00:00 the temperature is -2 degrees, at 04:00 it is -4 degrees, at 08:00 it is 0 degrees, at 12:00 it is 5 degrees, at 16:00 it is 8 degrees, at 20:00 it is 3 degrees and at 00:00 it is 0 degrees.]() \\( \\begin{aligned} 20 & : 00 \\text { to } \\\\ 00 & : 00\\end{aligned} \\)"
},
{
"from": "gpt",
"value": "Believes a steeper downwards line on a graph means a slower decrease"
}
] |
[
{
"from": "human",
"value": "Raise negative numbers to powers \\( (-2)^{4}= \\) \\( -16 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Raise negative numbers to powers \\( (-2)^{4}= \\) \\( -8 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Certain"
},
{
"from": "gpt",
"value": "Does not understand that a probability of 0 represents something that is impossible"
}
] |
[
{
"from": "human",
"value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Unlikely"
},
{
"from": "gpt",
"value": "Does not understand that a probability of 0 represents something that is impossible"
}
] |
[
{
"from": "human",
"value": "Know that probabilities must lie between 0, impossible, and 1, certain The probability of an event occurring is \\( 0 \\).\n\nWhich of the following most accurately describes the likelihood of the event occurring? Even chance"
},
{
"from": "gpt",
"value": "Does not understand that a probability of 0 represents something that is impossible"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers \\( 8-7 \\div 6^{3}= \\) Which calculation should you do first? \\( 7 \\div 6 \\)"
},
{
"from": "gpt",
"value": "Believes division is carried out before a power"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers \\( 8-7 \\div 6^{3}= \\) Which calculation should you do first? \\( 8-7 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers \\( 8-7 \\div 6^{3}= \\) Which calculation should you do first? It doesn't matter: you get the same answer"
},
{
"from": "gpt",
"value": "Believes order of operations does not affect the answer to a calculation"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words Which expression correctly represents the following description?\n\"Subtract five from \\( \\mathrm{h} \\) and then multiply by six.\" \\( 6(5-h) \\)"
},
{
"from": "gpt",
"value": "Subtracts from left to right, ignoring the word ‘from’"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words Which expression correctly represents the following description?\n\"Subtract five from \\( \\mathrm{h} \\) and then multiply by six.\" \\( (5-h) \\times 6 \\)"
},
{
"from": "gpt",
"value": "Subtracts from left to right, ignoring the word ‘from’"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words Which expression correctly represents the following description?\n\"Subtract five from \\( \\mathrm{h} \\) and then multiply by six.\" \\( (h-5) \\times 6 \\)"
},
{
"from": "gpt",
"value": "Does not realize we can omit the multiplication symbol in algebraic expressions"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Tom and Katie are arguing about what term could replace the star in this addition pyramid.\nTom says it could be: \\( f \\)\nKatie says it could be: \\( 2 f \\)\nWho is correct? ![A diagram showing 3 rows of boxes. the bottom row has 3 boxes, containing a star, 3g and 2g from left to right. The next row up contains two boxes, overlapping the joins of the boxes below. Both are empty. The top row is one box, centered over the join of the two below, containing 2f + 8g.]() Only Tom"
},
{
"from": "gpt",
"value": "Assumes an addition pyramid works in a different way to how it actually does"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Tom and Katie are arguing about what term could replace the star in this addition pyramid.\nTom says it could be: \\( f \\)\nKatie says it could be: \\( 2 f \\)\nWho is correct? ![A diagram showing 3 rows of boxes. the bottom row has 3 boxes, containing a star, 3g and 2g from left to right. The next row up contains two boxes, overlapping the joins of the boxes below. Both are empty. The top row is one box, centered over the join of the two below, containing 2f + 8g.]() Both Tom and Katie"
},
{
"from": "gpt",
"value": "Assumes an addition pyramid works in a different way to how it actually does"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for curves in the form y = x² + c This is a part of the table of values for the equation\n\\(\ny=x^{2}\n\\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 8 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Using the graph of\n\\(\ny=x^{2}-3 x-10\n\\)\n\nWhat is the correct way to write the solution to\n\\(\nx^{2}-3 x-10 \\leq 0 ?\n\\) ![A quadratic parabola which crosses the x axis at (-2,0) and (5,0) and crosses the y axis at (0, -10)]() \\( \\{x \\leq-2\\} \\cup\\{x \\geq 5\\} \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Using the graph of\n\\(\ny=x^{2}-3 x-10\n\\)\n\nWhat is the correct way to write the solution to\n\\(\nx^{2}-3 x-10 \\leq 0 ?\n\\) ![A quadratic parabola which crosses the x axis at (-2,0) and (5,0) and crosses the y axis at (0, -10)]() \\( \\{-2 \\geq x \\geq 5\\} \\)"
},
{
"from": "gpt",
"value": "Does not understand inequality notation"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Using the graph of\n\\(\ny=x^{2}-3 x-10\n\\)\n\nWhat is the correct way to write the solution to\n\\(\nx^{2}-3 x-10 \\leq 0 ?\n\\) ![A quadratic parabola which crosses the x axis at (-2,0) and (5,0) and crosses the y axis at (0, -10)]() \\( \\{x \\geq-2\\} \\cup\\{x \\leq 5\\} \\)"
},
{
"from": "gpt",
"value": "Believes inequalities cannot be combined"
}
] |
[
{
"from": "human",
"value": "Describe how many degrees you would turn, and in what direction, to move between North, South, East and West on a compass I am facing East. \\( \\mathrm{E} \\longrightarrow \\) How many degrees anti-clockwise will I need to turn so I am facing South? \\( 90^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Mixes up clockwise and anticlockwise"
}
] |
Subsets and Splits