conversations
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[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence?\n\\[\n2, \\quad 5, \\quad 14, \\quad 41 \\ldots\n\\] To get the next term you add \\( 3 \\) to the previous term"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence?\n\\[\n2, \\quad 5, \\quad 14, \\quad 41 \\ldots\n\\] To get the next term you double the previous term and add \\( 1 \\)"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence?\n\\[\n2, \\quad 5, \\quad 14, \\quad 41 \\ldots\n\\] To get the next term you square the previous term and add \\( 1 \\)"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out other parts Tom shares some money with his brother in the ratio \\( 5: 4 \\) If Tom gets \\( £180 \\), how much does his brother get? \\( £ 100 \\)"
},
{
"from": "gpt",
"value": "In ratio question where one side of ratio is given, treats that as the total"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out other parts Tom shares some money with his brother in the ratio \\( 5: 4 \\) If Tom gets \\( £180 \\), how much does his brother get? \\( £ 80 \\)"
},
{
"from": "gpt",
"value": "In ratio question where one side of ratio is given, treats that as the total"
}
] |
[
{
"from": "human",
"value": "Given information about one part, work out other parts Tom shares some money with his brother in the ratio \\( 5: 4 \\) If Tom gets \\( £180 \\), how much does his brother get? \\( £ 720 \\)"
},
{
"from": "gpt",
"value": "In ratio question where one side of ratio is given, uses that as one part in ratio without dividing"
}
] |
[
{
"from": "human",
"value": "Write 3 digit numbers as words How do you write this number in words?\n\\( 107 \\) Ten seven"
},
{
"from": "gpt",
"value": "The student does not understand the place value of 3-digit numbers"
}
] |
[
{
"from": "human",
"value": "Write 3 digit numbers as words How do you write this number in words?\n\\( 107 \\) One hundred and seventy"
},
{
"from": "gpt",
"value": "The student does not understand the place value of 3-digit numbers"
}
] |
[
{
"from": "human",
"value": "Write 3 digit numbers as words How do you write this number in words?\n\\( 107 \\) Seventeen"
},
{
"from": "gpt",
"value": "The student does not understand the place value of 3-digit numbers"
}
] |
[
{
"from": "human",
"value": "Calculate the probability of two dependent events occurring without drawing a tree diagram There are \\( 5 \\) red balls and \\( 4 \\) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks a yellow ball out and does not replace it.\n\nShe then has a second pick.\n\nWhat is the probability the second pick is a red ball? \\( \\frac{5}{9} \\)"
},
{
"from": "gpt",
"value": "Does not reduce the denominator when an item is not replaced in a probability question"
}
] |
[
{
"from": "human",
"value": "Expand products of three binomials in the form (x + a)(x + b)(x + c) When Nadia expands these brackets, how many terms should she get after she simplifies?\n\\(\n(p+8)(p+2)(p+1)\n\\) \\( 3 \\)"
},
{
"from": "gpt",
"value": "Believes a cubic expression should have three terms"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data Without using a calculator, what is the mean of the following numbers?\n\n\\[\n3,4,3,4,4\n\\] \\( 3 \\)"
},
{
"from": "gpt",
"value": "Believes the mean is the middle number"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data Without using a calculator, what is the mean of the following numbers?\n\n\\[\n3,4,3,4,4\n\\] \\( 4 \\)"
},
{
"from": "gpt",
"value": "When asked for the mean of a list of data, gives the mode"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators which do not share a common factor \\(\n\\frac{1}{3}+\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Does not find a common denominator when adding/subtracting fractions"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators which do not share a common factor \\(\n\\frac{1}{3}+\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star? \\( 4 \\)"
},
{
"from": "gpt",
"value": "Does not find a common denominator when adding/subtracting fractions"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators which do not share a common factor \\(\n\\frac{1}{3}+\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star? \\( 11 \\)"
},
{
"from": "gpt",
"value": "Does not find a common denominator when adding/subtracting fractions"
}
] |
[
{
"from": "human",
"value": "Calculate the mode as an average from a list of data when there are two or more modes What is the mode of the following numbers?\n\\[\n1,1,4,6,7,7\n\\] \\( 7 \\)"
},
{
"from": "gpt",
"value": "Believes you can only have one mode"
}
] |
[
{
"from": "human",
"value": "Calculate the mode as an average from a list of data when there are two or more modes What is the mode of the following numbers?\n\\[\n1,1,4,6,7,7\n\\] \\( 4 \\)"
},
{
"from": "gpt",
"value": "When there are two modes, finds the mean of these values and gives that as the mode"
}
] |
[
{
"from": "human",
"value": "Calculate the mode as an average from a list of data when there are two or more modes What is the mode of the following numbers?\n\\[\n1,1,4,6,7,7\n\\] There is no mode"
},
{
"from": "gpt",
"value": "Believes if there are two numbers with the same frequency, there isn't a mode"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number Which is the best estimate for \\( (4.2)^{2} \\) ? \\( 25 \\)"
},
{
"from": "gpt",
"value": "Rounds up instead of down"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number Which is the best estimate for \\( (4.2)^{2} \\) ? \\( 8 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line ![Two angles meeting on a straight line labelled n and 48 degrees, one angle further down the straight line labelled 30 degrees]() What is the size of angle \\( n \\) ? \\( 142^{\\circ} \\)"
},
{
"from": "gpt",
"value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line ![Two angles meeting on a straight line labelled n and 48 degrees, one angle further down the straight line labelled 30 degrees]() What is the size of angle \\( n \\) ? \\( 102^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Thinks that all angles anywhere along a straight line add to 180"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line ![Two angles meeting on a straight line labelled n and 48 degrees, one angle further down the straight line labelled 30 degrees]() What is the size of angle \\( n \\) ? \\( 312^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 360 degrees"
}
] |
[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence? \\( 2, \\quad 9, \\quad 11, \\quad 20, \\quad \\ldots \\) To get the next term you add \\( 7 \\) to the previous term"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence? \\( 2, \\quad 9, \\quad 11, \\quad 20, \\quad \\ldots \\) To get the next term you square the previous term and add \\( 5 \\)"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence? \\( 2, \\quad 9, \\quad 11, \\quad 20, \\quad \\ldots \\) To get the next term you multiply the previous term by \\( 5 \\) and subtract \\( 1 \\)"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Given the name of a polygon, draw or identify a corresponding diagram Which of the following shapes is a hexagon? ![An irregular, five sided shape]()"
},
{
"from": "gpt",
"value": "Confuses pentagon and hexagon"
}
] |
[
{
"from": "human",
"value": "Given the name of a polygon, draw or identify a corresponding diagram Which of the following shapes is a hexagon? ![A regular, five sided shape]()"
},
{
"from": "gpt",
"value": "Confuses pentagon and hexagon"
}
] |
[
{
"from": "human",
"value": "Given the name of a polygon, draw or identify a corresponding diagram Which of the following shapes is a hexagon? ![A regular, eight sided shape]()"
},
{
"from": "gpt",
"value": "Confuses octagon and hexagon"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a fraction of another Write \\( 16 \\) over \\( 28 \\) as a fraction in its simplest terms. \\( \\frac{16}{28} \\)"
},
{
"from": "gpt",
"value": "Forgot to simplify the fraction"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a fraction of another Write \\( 16 \\) over \\( 28 \\) as a fraction in its simplest terms. \\( \\frac{1}{13} \\)"
},
{
"from": "gpt",
"value": "Simplifies a fraction by adding or subtracting the same amount from the numerator and denominator"
}
] |
[
{
"from": "human",
"value": "Manipulate both equations so that they are in a form to be added or subtracted Tom and Katie are discussing how to get this pair of simultaneous equations in a form where they can eliminate \\( y \\) \\(( 1)\\) \\(-2 x+6 y=4 \\)\n\\( (2)\\) \\( x+2 y=8 \\) Tom says you need to multiply equation \\( (2) \\) by \\( 3 \\).\n\nKatie says you need to multiply equation \\( (1) \\) by \\( 2 \\) and multiply equation \\( (2) \\) by \\( 6 \\).\n\nWho is correct? Only Tom"
},
{
"from": "gpt",
"value": "When solving simultaneous equations, thinks they can't multiply each equation by a different number"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing ways to calculate \\( 28 \\times 15 \\) mentally Tom does \\( 28 \\times 5 \\) and then multiplies his answer by \\( 3 \\) Katie does \\( 14 \\times 15 \\) and then doubles her answer Who would get the correct answer? Neither is correct"
},
{
"from": "gpt",
"value": "Does not realise that multiplication can be broken down into factors"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are not multiples of the same number Which fraction is closest to \\( 1 \\) ? \\( 1 \\frac{1}{3} \\)"
},
{
"from": "gpt",
"value": "Believes that fractions with larger denominators are greater in size"
}
] |
[
{
"from": "human",
"value": "Use angles around a point to form and solve algebraic equations Which of the following equations is true based on the diagram? ![Angles around a point made up of two angles labelled: f and f-20]() \\( 2 f-20=180 \\)"
},
{
"from": "gpt",
"value": "Believes angles around a point sum to 180"
}
] |
[
{
"from": "human",
"value": "Use angles around a point to form and solve algebraic equations Which of the following equations is true based on the diagram? ![Angles around a point made up of two angles labelled: f and f-20]() \\( f^{2}-20=360 \\)"
},
{
"from": "gpt",
"value": "Thinks index notation represents repeated addition rather than repeated multiplication"
}
] |
[
{
"from": "human",
"value": "Use angles around a point to form and solve algebraic equations Which of the following equations is true based on the diagram? ![Angles around a point made up of two angles labelled: f and f-20]() \\( f-20=f \\)"
},
{
"from": "gpt",
"value": "Confuses vertically opposite angles and angles around a point"
}
] |
[
{
"from": "human",
"value": "Given the area of a square, calculate a missing dimension A square has an area of \\( 100 \\mathrm{~cm}^{2} \\)\nWhat is the length of each side of the square? \\( 25 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Confuses perimeter and area"
}
] |
[
{
"from": "human",
"value": "Given the area of a square, calculate a missing dimension A square has an area of \\( 100 \\mathrm{~cm}^{2} \\)\nWhat is the length of each side of the square? \\( 50 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Confuses square rooting and halving the number"
}
] |
[
{
"from": "human",
"value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE. D lies 1/3 from C on the line CE and is connected to A by a line. Attached to the square at line CE is a pentagon CEFGH. G is connected to C and E by lines. The angle highlighted is the interior angle at G.]() \\( \\mathrm{GFH} \\)"
},
{
"from": "gpt",
"value": "Gives 3-letter angle notation in the wrong order"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (4,-4) \\)\n\nThe point is reflected in the line \\( y=-x \\)\n\nWhat are the new coordinates of point Q? \\( (4.4) \\)"
},
{
"from": "gpt",
"value": "Does not understand that a point on the line of reflection will stay the same when reflected "
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (4,-4) \\)\n\nThe point is reflected in the line \\( y=-x \\)\n\nWhat are the new coordinates of point Q? \\( (-4,-4) \\)"
},
{
"from": "gpt",
"value": "Does not understand that a point on the line of reflection will stay the same when reflected "
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (4,-4) \\)\n\nThe point is reflected in the line \\( y=-x \\)\n\nWhat are the new coordinates of point Q? \\( (-4,4) \\)"
},
{
"from": "gpt",
"value": "Believes reflection in y = -x switches x and y coordinates"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\( 12 \\div 2+1 \\times 2= \\) \\( 3 \\)"
},
{
"from": "gpt",
"value": "Confuses the order of operations, believes addition comes before division"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\( 12 \\div 2+1 \\times 2= \\) \\( 14 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Represent positive unit fractions on a number line The probability of picking a green ball is \\( \\frac{1}{5} \\)\nWhere is this value on the probability scale? ![A diagram showing a probability scale with 10 segments. The scale starts at 0.0, has 0.5 marked after 5 segments, and 1.0 marked at the end, after 10 segments. A is marked after 2 segments, B after 4, C after 5 and D after 7.]() C"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by using the denominator after the decimal point"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{3}{4}-\\frac{1}{3}=\\frac{\\bigstar}{12}\n\\)\nWhat should replace the star? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Does not find a common denominator when adding/subtracting fractions"
}
] |
[
{
"from": "human",
"value": "Identify when rounding a calculation will give an over or under approximation Tom and Katie are discussing how to estimate the answer to\n\\[\n38.8745 \\div 7.9302\n\\]\n\nTom says \\( 40 \\div 7.9302 \\) would give an overestimate.\n\nKatie says \\( 38.8745 \\div 8 \\) would give an overestimate.\n\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Believes that the larger the divisor, the larger the answer."
}
] |
[
{
"from": "human",
"value": "Identify when rounding a calculation will give an over or under approximation Tom and Katie are discussing how to estimate the answer to\n\\[\n38.8745 \\div 7.9302\n\\]\n\nTom says \\( 40 \\div 7.9302 \\) would give an overestimate.\n\nKatie says \\( 38.8745 \\div 8 \\) would give an overestimate.\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes that the larger the divisor, the larger the answer."
}
] |
[
{
"from": "human",
"value": "Identify when rounding a calculation will give an over or under approximation Tom and Katie are discussing how to estimate the answer to\n\\[\n38.8745 \\div 7.9302\n\\]\n\nTom says \\( 40 \\div 7.9302 \\) would give an overestimate.\n\nKatie says \\( 38.8745 \\div 8 \\) would give an overestimate.\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Believes that the larger the dividend, the smaller the answer."
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table This table shows the ages of people on a university running team.\nTo calculate the mean age, what is the most sensible heading for the third column? \\begin{tabular}{|c|c|l|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} Age + Frequency"
},
{
"from": "gpt",
"value": "Adds instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table This table shows the ages of people on a university running team.\nTo calculate the mean age, what is the most sensible heading for the third column? \\begin{tabular}{|c|c|l|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} Age - Frequency"
},
{
"from": "gpt",
"value": "Subtracts instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table This table shows the ages of people on a university running team.\nTo calculate the mean age, what is the most sensible heading for the third column? \\begin{tabular}{|c|c|l|}\n\\hline Age & Frequency & \\\\\n\\hline \\( 18 \\) & \\( 7 \\) & \\\\\n\\hline \\( 19 \\) & \\( 3 \\) & \\\\\n\\hline \\( 20 \\) & \\( 1 \\) & \\\\\n\\hline \\( 21 \\) & \\( 2 \\) & \\\\\n\\hline\n\\end{tabular} Age \\( \\div \\)\nFrequency"
},
{
"from": "gpt",
"value": "Divides rather than multiplies "
}
] |
[
{
"from": "human",
"value": "Identify triangular numbers \\( 1,3,6,10,15,21,28 \\ldots \\) What is the name commonly given to this sequence of numbers? The cube numbers"
},
{
"from": "gpt",
"value": "Thinks cube numbers are triangular numbers"
}
] |
[
{
"from": "human",
"value": "Identify triangular numbers \\( 1,3,6,10,15,21,28 \\ldots \\) What is the name commonly given to this sequence of numbers? The Fibonacci numbers"
},
{
"from": "gpt",
"value": "Believes Fibonacci numbers are triangle numbers"
}
] |
[
{
"from": "human",
"value": "Identify triangular numbers \\( 1,3,6,10,15,21,28 \\ldots \\) What is the name commonly given to this sequence of numbers? The square numbers"
},
{
"from": "gpt",
"value": "Believes square numbers are triangle numbers"
}
] |
[
{
"from": "human",
"value": "Manipulate both equations so that they are in a form to be added or subtracted Sandeep wants to eliminate \\( l \\) from these simultaneous equations.\n\\(\\begin{array}{l}\n2 l+3 m=13 \\\\\n3 l+4 m=17\n\\end{array}\\)\n\nFirst he will transform both of them to get them in an appropriate form.\nWhich of the following is a correct transformation? \\( \\begin{array}{l}6 l+9 m=13 \\\\ 6 l+8 m=17\\end{array} \\)"
},
{
"from": "gpt",
"value": "When solving simultaneous equations, thinks you only transform the algebraic terms, rather than the whole equation."
}
] |
[
{
"from": "human",
"value": "Manipulate both equations so that they are in a form to be added or subtracted Sandeep wants to eliminate \\( l \\) from these simultaneous equations.\n\\(\\begin{array}{l}\n2 l+3 m=13 \\\\\n3 l+4 m=17\n\\end{array}\\)\n\nFirst he will transform both of them to get them in an appropriate form.\nWhich of the following is a correct transformation? \\( \\begin{array}{l}6 l+3 m=13 \\\\ 6 l+4 m=17\\end{array} \\)"
},
{
"from": "gpt",
"value": "When solving simultaneous equations, thinks you only transform the term that is being eliminated, rather than the whole equation."
}
] |
[
{
"from": "human",
"value": "Multiply 2 digit integers by 2 digit integers using the grid method If you use the grid method to calculate \\( 27 \\times 42 \\) what should replace the star? \\begin{tabular}{|c|c|c|}\n\\hline\\( \\times \\) & \\( 20 \\) & \\( 7 \\) \\\\\n\\hline \\( 40 \\) & \\(\\space\\) & \\(\\color{gold}\\bigstar\\)\\\\\n\\hline \\( 2 \\) & \\(\\space\\) & \\\\\n\\hline\n\\end{tabular} \\( 47 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Multiply 2 digit integers by 2 digit integers using the grid method If you use the grid method to calculate \\( 27 \\times 42 \\) what should replace the star? \\begin{tabular}{|c|c|c|}\n\\hline\\( \\times \\) & \\( 20 \\) & \\( 7 \\) \\\\\n\\hline \\( 40 \\) & \\(\\space\\) & \\(\\color{gold}\\bigstar\\)\\\\\n\\hline \\( 2 \\) & \\(\\space\\) & \\\\\n\\hline\n\\end{tabular} \\( 28 \\)"
},
{
"from": "gpt",
"value": "When multiplying involving a multiple of 10, gives an answer 10 times smaller than it should be"
}
] |
[
{
"from": "human",
"value": "Multiply 2 digit integers by 2 digit integers using the grid method If you use the grid method to calculate \\( 27 \\times 42 \\) what should replace the star? \\begin{tabular}{|c|c|c|}\n\\hline\\( \\times \\) & \\( 20 \\) & \\( 7 \\) \\\\\n\\hline \\( 40 \\) & \\(\\space\\) & \\(\\color{gold}\\bigstar\\)\\\\\n\\hline \\( 2 \\) & \\(\\space\\) & \\\\\n\\hline\n\\end{tabular} \\( 2800 \\)"
},
{
"from": "gpt",
"value": "When multiplying by a multiple of 10, gives an answer 10 times bigger than it should be"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring addition or subtraction, involving negative integers Solve the equation:\n\\[\n-3=p+12\n\\] \\( p=9 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Multiply 2 digit integers by 2 digit integers using long multiplication \\( \\begin{array}{r}\\quad35 \\\\ \\times 46 \\\\ \\hline\\end{array} \\) What number will be in the ones/units column of the final answer? \\( 30 \\)"
},
{
"from": "gpt",
"value": "Believes you write the carried value in the number rather than adding it to the next place value column"
}
] |
[
{
"from": "human",
"value": "Division law of indices with positive integer powers and the same base number Simplify (if possible):\n\\(\n6^{9} \\div 6^{3}\n\\) \\( 6^{3} \\)"
},
{
"from": "gpt",
"value": "Believes when dividing numbers with the same base you divide the powers, rather than subtracting"
}
] |
[
{
"from": "human",
"value": "Division law of indices with positive integer powers and the same base number Simplify (if possible):\n\\(\n6^{9} \\div 6^{3}\n\\) \\( 1^{3} \\)"
},
{
"from": "gpt",
"value": "When dividing numbers with the same base divides the base numbers and the powers"
}
] |
[
{
"from": "human",
"value": "Division law of indices with positive integer powers and the same base number Simplify (if possible):\n\\(\n6^{9} \\div 6^{3}\n\\) \\( 1^{6} \\)"
},
{
"from": "gpt",
"value": "When dividing numbers with the same base correctly subtracts the powers but divides the base numbers."
}
] |
[
{
"from": "human",
"value": "Solve a non-linear equation using a function machine Which function machine will solve the equation \\( x^{2}+5=14 ? \\) ![A function machine showing x as the input then +5 then squaring to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input square root and then -5]()"
},
{
"from": "gpt",
"value": "Does not follow the arrows through a function machine, changes the order of the operations asked."
}
] |
[
{
"from": "human",
"value": "Solve a non-linear equation using a function machine Which function machine will solve the equation \\( x^{2}+5=14 ? \\) ![A function machine showing 14 as the input then squaring and +5 to give the output]()"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Solve a non-linear equation using a function machine Which function machine will solve the equation \\( x^{2}+5=14 ? \\) ![A function machine showing x as the input then x2 then +5 to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input -5 and then divide by 2]()"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to two significant figures Tom and Katie are arguing about rounding.\n\nTom says \\( \\mathbf{0 . 0 3 4 5 6} \\) rounded to \\( 2 \\) significant figures is \\( \\mathbf{0 . 0 3} \\)\n\nKatie says \\( 0.03456 \\) rounded to \\( 2 \\) decimal places is \\( \\mathbf{0 . 0 3} \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Rounds to wrong degree of accuracy (decimal places rather than significant figures)"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to two significant figures Tom and Katie are arguing about rounding.\n\nTom says \\( \\mathbf{0 . 0 3 4 5 6} \\) rounded to \\( 2 \\) significant figures is \\( \\mathbf{0 . 0 3} \\)\n\nKatie says \\( 0.03456 \\) rounded to \\( 2 \\) decimal places is \\( \\mathbf{0 . 0 3} \\)\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (significant figures rather than decimal places)"
}
] |
[
{
"from": "human",
"value": "Round non-integers to other non-integer values (e.g. 0.02) What is \\( \\mathbf{1 . 5 1 6} \\) rounded to the nearest \\( \\mathbf{0 . 0 5} \\) ? \\( 1.55 \\)"
},
{
"from": "gpt",
"value": "Rounds up instead of down"
}
] |
[
{
"from": "human",
"value": "Round non-integers to other non-integer values (e.g. 0.02) What is \\( \\mathbf{1 . 5 1 6} \\) rounded to the nearest \\( \\mathbf{0 . 0 5} \\) ? \\( 1.52 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too little)"
}
] |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms STEP \\( 2 \\)\n\nWhich of the options is a correct second step to express the following as a single fraction?\n\\(\n\\begin{array}{c}\n\\frac{9}{x+3}-\\frac{2}{x} \\\\\n=\\frac{9 x}{x(x+3)}-\\frac{2(x+3)}{x(x+3)}\n\\end{array}\n\\) \\( \\frac{9}{3}-\\frac{2(3)}{3} \\)"
},
{
"from": "gpt",
"value": "Incorrectly cancels what they believe is a factor in algebraic fractions"
}
] |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms STEP \\( 2 \\)\n\nWhich of the options is a correct second step to express the following as a single fraction?\n\\(\n\\begin{array}{c}\n\\frac{9}{x+3}-\\frac{2}{x} \\\\\n=\\frac{9 x}{x(x+3)}-\\frac{2(x+3)}{x(x+3)}\n\\end{array}\n\\) \\( \\frac{9}{x+3}-\\frac{2}{x} \\)"
},
{
"from": "gpt",
"value": "Does not understand how to subtract algebraic fractions"
}
] |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms STEP \\( 2 \\)\n\nWhich of the options is a correct second step to express the following as a single fraction?\n\\(\n\\begin{array}{c}\n\\frac{9}{x+3}-\\frac{2}{x} \\\\\n=\\frac{9 x}{x(x+3)}-\\frac{2(x+3)}{x(x+3)}\n\\end{array}\n\\) \\( \\frac{9 x-2(x+3)}{x(x+3)-x(x+3)} \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio 5:1. What fraction of the drink is water? \\( \\frac{1}{5} \\)"
},
{
"from": "gpt",
"value": "When converting ratio to fractions, puts the other side of the ratio as the denominator rather than the total"
}
] |
[
{
"from": "human",
"value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio 5:1. What fraction of the drink is water? \\( \\frac{5}{6} \\)"
},
{
"from": "gpt",
"value": "Gets order of ratio wrong"
}
] |
[
{
"from": "human",
"value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio 5:1. What fraction of the drink is water? Not enough information"
},
{
"from": "gpt",
"value": "Does not understand the relationship between a ratio and fraction"
}
] |
[
{
"from": "human",
"value": "Identify the circumference Which of the following diagrams shows the circumference of a circle? ![Circle with a line from the centre to the edge]()"
},
{
"from": "gpt",
"value": "Confuses circumference and radius"
}
] |
[
{
"from": "human",
"value": "Identify the circumference Which of the following diagrams shows the circumference of a circle? ![Circle with a line below it, touching the circle in one place]()"
},
{
"from": "gpt",
"value": "Confuses tangent and circumference"
}
] |
[
{
"from": "human",
"value": "Identify the circumference Which of the following diagrams shows the circumference of a circle? ![Circle with a line across from edge to edge, not passing through the centre]()"
},
{
"from": "gpt",
"value": "Confuses chord and circumference"
}
] |
[
{
"from": "human",
"value": "Identify equivalent fractions when presented as numbers Which of the following fractions is equivalent to \\( \\frac{9}{12} \\) ? \\( \\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "Believes when simplifying a fraction you can divide the numerator and denominator by different values"
}
] |
[
{
"from": "human",
"value": "Identify equivalent fractions when presented as numbers Which of the following fractions is equivalent to \\( \\frac{9}{12} \\) ? \\( \\frac{12}{15} \\)"
},
{
"from": "gpt",
"value": "Believes equivalent fractions are formed with addition not multiplication"
}
] |
[
{
"from": "human",
"value": "Understand the non-commutativity of subtraction Miran says the following:\n\n“It doesn't matter if you do \\( 81-53 \\) or \\( 53-81 \\), you get the same answer.\"\n\nWhat do you think? Miran is correct because subtraction is commutative"
},
{
"from": "gpt",
"value": "Believes subtraction is commutative "
}
] |
[
{
"from": "human",
"value": "Understand the non-commutativity of subtraction Miran says the following:\n\n“It doesn't matter if you do \\( 81-53 \\) or \\( 53-81 \\), you get the same answer.\"\n\nWhat do you think? Miran is incorrect because subtraction is commutative"
},
{
"from": "gpt",
"value": "Does not understand the meaning of the word commutative "
}
] |
[
{
"from": "human",
"value": "Understand the non-commutativity of subtraction Miran says the following:\n\n“It doesn't matter if you do \\( 81-53 \\) or \\( 53-81 \\), you get the same answer.\"\n\nWhat do you think? Miran is correct because subtraction is not commutative"
},
{
"from": "gpt",
"value": "Does not understand the meaning of the word commutative "
}
] |
[
{
"from": "human",
"value": "Represent a linear inequality with a single tail on a numberline Which inequality is represented by the diagram? ![A number line with a hollow circle above -1with an arrow coming out of it over the numbers -2, -3, -4, -5 etc]() \\( x \\leq-1 \\)"
},
{
"from": "gpt",
"value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning."
}
] |
[
{
"from": "human",
"value": "Represent a linear inequality with a single tail on a numberline Which inequality is represented by the diagram? ![A number line with a hollow circle above -1with an arrow coming out of it over the numbers -2, -3, -4, -5 etc]() \\( x>-1 \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Find the volume scale factor of similar shapes given the length scale factor ![Two cuboids. Cuboid P has width 5cm, and cuboid Q has width 15cm.]() Shape P and Shape Q are similar.\n\nWhat is the volume scale factor to get from Shape \\( P \\) to Shape \\( Q \\) ? \\( \\times 3 \\)"
},
{
"from": "gpt",
"value": "Does not understand that the volume of an enlarged shape is the volume of the original multiplied by the cube of the scale factor of the lengths."
}
] |
[
{
"from": "human",
"value": "Find the volume scale factor of similar shapes given the length scale factor ![Two cuboids. Cuboid P has width 5cm, and cuboid Q has width 15cm.]() Shape P and Shape Q are similar.\n\nWhat is the volume scale factor to get from Shape \\( P \\) to Shape \\( Q \\) ? \\( \\times 6 \\)"
},
{
"from": "gpt",
"value": "Does not understand that the volume of an enlarged shape is the volume of the original multiplied by the cube of the scale factor of the lengths."
}
] |
[
{
"from": "human",
"value": "Find the volume scale factor of similar shapes given the length scale factor ![Two cuboids. Cuboid P has width 5cm, and cuboid Q has width 15cm.]() Shape P and Shape Q are similar.\n\nWhat is the volume scale factor to get from Shape \\( P \\) to Shape \\( Q \\) ? \\( \\times 9 \\)"
},
{
"from": "gpt",
"value": "Does not understand that the volume of an enlarged shape is the volume of the original multiplied by the cube of the scale factor of the lengths."
}
] |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Parallelogram with the vertices labelled A, B, C and D]() \\( A B \\) and \\( B C \\)"
},
{
"from": "gpt",
"value": "Believes adjacent sides of a rhombus are always perpendicular"
}
] |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Parallelogram with the vertices labelled A, B, C and D]() \\( A B \\) and \\( D C \\)"
},
{
"from": "gpt",
"value": "Confuses the meaning of parallel and perpendicular"
}
] |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Parallelogram with the vertices labelled A, B, C and D]() None of them"
},
{
"from": "gpt",
"value": "Does not know the properties of a rhombus"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is greater than 100 \\( 300 \\% \\) of \\( 25= \\) You cannot have\na percentage\ngreater than \\( 100 \\)"
},
{
"from": "gpt",
"value": "Does not understand that you can have percentages greater than 100%"
}
] |
[
{
"from": "human",
"value": "Continue linear sequences expressed as patterns by drawing the next pattern How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequences. Pattern 1 contains 7 squares, pattern 2 contains 5 squares and pattern 3 contains 3 squares.]() \\( 2 \\)"
},
{
"from": "gpt",
"value": "Identifies the term-to-term rule rather than the next term"
}
] |
[
{
"from": "human",
"value": "Continue linear sequences expressed as patterns by drawing the next pattern How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequences. Pattern 1 contains 7 squares, pattern 2 contains 5 squares and pattern 3 contains 3 squares.]() \\( 0 \\)"
},
{
"from": "gpt",
"value": "Does not notice all changes in a sequence of visual patterns"
}
] |
[
{
"from": "human",
"value": "Continue linear sequences expressed as patterns by drawing the next pattern How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequences. Pattern 1 contains 7 squares, pattern 2 contains 5 squares and pattern 3 contains 3 squares.]() \\( 1.5 \\)"
},
{
"from": "gpt",
"value": "Does not notice all changes in a sequence of visual patterns"
}
] |
Subsets and Splits