conversations
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[
{
"from": "human",
"value": "Given a gradient, state the gradient of a line parallel to it A line has a gradient of \\( 5 \\)\n\nA line parallel to this line would have a gradient of... Not enough information"
},
{
"from": "gpt",
"value": "Does not know parallel lines have equal gradients "
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate: \\( \\frac{4}{8} \\div 2 \\) \\( \\frac{2}{4} \\)"
},
{
"from": "gpt",
"value": "When dividing a fraction by an integer, divides both the numerator and denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate: \\( \\frac{4}{8} \\div 2 \\) \\( \\frac{4}{4} \\)"
},
{
"from": "gpt",
"value": "When dividing a fraction by an integer, divides the denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Identify a right-angled triangle when presented non-conventionally \\( A B C D \\) is a rectangle.\nWhat type of triangle is triangle \\( \\mathrm{BCD} \\) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]() Scalene"
},
{
"from": "gpt",
"value": "Confuses scalene and right angle triangles"
}
] |
[
{
"from": "human",
"value": "Identify a right-angled triangle when presented non-conventionally \\( A B C D \\) is a rectangle.\nWhat type of triangle is triangle \\( \\mathrm{BCD} \\) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]() Isosceles"
},
{
"from": "gpt",
"value": "Confuses isosceles and right angle triangles"
}
] |
[
{
"from": "human",
"value": "Identify a right-angled triangle when presented non-conventionally \\( A B C D \\) is a rectangle.\nWhat type of triangle is triangle \\( \\mathrm{BCD} \\) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]() Equilateral"
},
{
"from": "gpt",
"value": "Confuses isosceles and right angle triangles"
}
] |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"5a + 2\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 10 a+2 \\)"
},
{
"from": "gpt",
"value": "Only multiplies the first term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"5a + 2\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 5 a+4 \\)"
},
{
"from": "gpt",
"value": "Only multiplies second term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "For a given algebraic input, find the output of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"5a + 2\" written inside it. The middle rectangle has \"✕ 2\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 7 a+4 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies when multiplying algebraic terms"
}
] |
[
{
"from": "human",
"value": "Represent an equation using a bar model ![Tom and Katie are discussing bar models.]() Tom says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline \\( 2 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Who do you agree with? Only Tom"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Represent an equation using a bar model ![Tom and Katie are discussing bar models.]() Tom says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline \\( 2 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Who do you agree with? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Represent an equation using a bar model ![Tom and Katie are discussing bar models.]() Tom says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline \\( 2 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 2 x \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Who do you agree with? Neither is correct"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Calculate the whole amount, given a fraction of the amount What should replace the star?\n\\(\n\\frac{1}{3} \\text { of } \\color{yellow}\\bigstar\\)\\(=27\n\\) \\( 61 \\)"
},
{
"from": "gpt",
"value": "When two digits multiply to 10 or more during a multiplication problem, does not add carried value to the preceding digit"
}
] |
[
{
"from": "human",
"value": "Calculate the whole amount, given a fraction of the amount What should replace the star?\n\\(\n\\frac{1}{3} \\text { of } \\color{yellow}\\bigstar\\)\\(=27\n\\) \\( 9 \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation"
}
] |
[
{
"from": "human",
"value": "Determine the input of a double function machine used to create an algebraic expression input \\(\\Rightarrow-3 \\Rightarrow \\times 3 \\Rightarrow 9a-21 \\) What is the input of this function machine? \\( 3 a-18 \\)"
},
{
"from": "gpt",
"value": "Does not apply the inverse function to every term in an expression"
}
] |
[
{
"from": "human",
"value": "Determine the input of a double function machine used to create an algebraic expression input \\(\\Rightarrow-3 \\Rightarrow \\times 3 \\Rightarrow 9a-21 \\) What is the input of this function machine? \\( 3 a-21 \\)"
},
{
"from": "gpt",
"value": "Has completed only one of the two operations."
}
] |
[
{
"from": "human",
"value": "Determine the input of a double function machine used to create an algebraic expression input \\(\\Rightarrow-3 \\Rightarrow \\times 3 \\Rightarrow 9a-21 \\) What is the input of this function machine? \\( 3 a-7 \\)"
},
{
"from": "gpt",
"value": "Has completed only one of the two operations."
}
] |
[
{
"from": "human",
"value": "Convert from years to days \\( 2 \\) leap years \\( =\\square \\) days \\( 728 \\)"
},
{
"from": "gpt",
"value": "Does not know how many days are in a leap year"
}
] |
[
{
"from": "human",
"value": "Convert from years to days \\( 2 \\) leap years \\( =\\square \\) days \\( 730 \\)"
},
{
"from": "gpt",
"value": "Does not know how many days are in a leap year"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 1000 What is the value of:\n\\[\n23.04 \\div 1000\n\\] \\( 0.2304 \\)"
},
{
"from": "gpt",
"value": "When dividing involving a power of 10, gives an answer 10 times bigger than it should be"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 1000 What is the value of:\n\\[\n23.04 \\div 1000\n\\] \\( 0.0002304 \\)"
},
{
"from": "gpt",
"value": "When dividing a decimal by a power of 10 adds zeroes to start of the number ignoring the placement of the initial decimal point"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 1000 What is the value of:\n\\[\n23.04 \\div 1000\n\\] \\( 0.002304 \\)"
},
{
"from": "gpt",
"value": "When dividing involving a power of 10, gives an answer 10 times smaller than it should be"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 1 digit integers using the grid method \\( 427 \\times 6= \\) \\( 240+120+42 \\)"
},
{
"from": "gpt",
"value": "When multiplying multiples of ten and the answer requires an extra digit, leaves off that extra digit"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention?\n\\(\nb \\div a\n\\) \\( a \\div b \\)"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention?\n\\(\nb \\div a\n\\) \\( \\frac{a}{b} \\)"
},
{
"from": "gpt",
"value": "Believes that a fraction means dividing the denominator by the numerator"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention?\n\\(\nb \\div a\n\\) \\( a b \\)"
},
{
"from": "gpt",
"value": "Thinks that we can remove a division symbol and just write the variables next to each other"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape In which region would a rectangle belong? ![Venn diagram with two circles labelled with 'exactly two lines of symmetry' and 'rotational symmetry of order 2'. A is in the only exactly two lines of symmetry region, B is in the intersection, C is in the only rotational symmetry of order 2 region and D is outside the two circles.]() A"
},
{
"from": "gpt",
"value": "Thinks rectangles have rotational symmetry or order 4"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape In which region would a rectangle belong? ![Venn diagram with two circles labelled with 'exactly two lines of symmetry' and 'rotational symmetry of order 2'. A is in the only exactly two lines of symmetry region, B is in the intersection, C is in the only rotational symmetry of order 2 region and D is outside the two circles.]() C"
},
{
"from": "gpt",
"value": "Thinks rectangles have line symmetry in the diagonals "
}
] |
[
{
"from": "human",
"value": "Identify non-unit fractions when part of a shape What fraction of the rectangle is shaded? ![A rectangle split into 10 equal parts with 3 parts shaded in yellow]() \\( 3 \\)"
},
{
"from": "gpt",
"value": "Does not know how to write a fraction - just given an integer answer"
}
] |
[
{
"from": "human",
"value": "Identify non-unit fractions when part of a shape What fraction of the rectangle is shaded? ![A rectangle split into 10 equal parts with 3 parts shaded in yellow]() \\( \\frac{3}{7} \\)"
},
{
"from": "gpt",
"value": "Denominator used for other parts rather than total parts"
}
] |
[
{
"from": "human",
"value": "Complete missing number mental subtraction problems up to 100 What should replace the star? \\( \\bigstar-37=38 \\) \\( 1 \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation"
}
] |
[
{
"from": "human",
"value": "Complete missing number mental subtraction problems up to 100 What should replace the star? \\( \\bigstar-37=38 \\) \\( -1 \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation"
}
] |
[
{
"from": "human",
"value": "Complete missing number mental subtraction problems up to 100 What should replace the star? \\( \\bigstar-37=38 \\) \\( 65 \\)"
},
{
"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": "Represent written scenarios as ratios For every \\( 5 \\) marbles Karen has, Marty has three times as many.\n\nWrite the number of marbles Karen and Marty have as a ratio, with Karen's part first. None of these"
},
{
"from": "gpt",
"value": "Does not realise ratio in worded problem can be simplified"
}
] |
[
{
"from": "human",
"value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]() \\( \\operatorname{Sin} \\)"
},
{
"from": "gpt",
"value": "Uses sin when tan is required"
}
] |
[
{
"from": "human",
"value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]() Cos"
},
{
"from": "gpt",
"value": "Uses cos when tan is required"
}
] |
[
{
"from": "human",
"value": "Identify questions involving a 2D right-angled triangle that require the use of the Tangent (tan) ratio Which ratio would you use to find the value of \\( p \\) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]() None of these"
},
{
"from": "gpt",
"value": "Does not understand how to apply sohcahtoa"
}
] |
[
{
"from": "human",
"value": "Represent a linear inequality with a single tail on a numberline Which of the following diagrams represents \\( x>-1 \\) ? ![Image of a number line. At -1 there is an open, unfilled circle drawn, with a arrow pointing to the left, towards the negative numbers in the number line.]()"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Represent a linear inequality with a single tail on a numberline Which of the following diagrams represents \\( x>-1 \\) ? ![Image of a number line. At -1 there is a red, filled circle drawn, with a arrow pointing to the right, towards the higher positive numbers in the number line.]()"
},
{
"from": "gpt",
"value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning."
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is greater than 100 \\( 130 \\% \\) of \\( 40= \\) \\( 12 \\)"
},
{
"from": "gpt",
"value": "Found the percentage but forgot to add to 100%"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is greater than 100 \\( 130 \\% \\) of \\( 40= \\) \\( 170 \\)"
},
{
"from": "gpt",
"value": "Added the values together instead of finding the percentage"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is greater than 100 \\( 130 \\% \\) of \\( 40= \\) Impossible as you cannot have a percentage greater than \\( 100 \\)"
},
{
"from": "gpt",
"value": "Does not understand that you can have percentages greater than 100%"
}
] |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a unit fraction Write the following fraction in its simplest form: \\( 3 \\frac{7}{21} \\) \\( 1 \\frac{1}{3} \\)"
},
{
"from": "gpt",
"value": "Simplifies integers when simplifying a mixed number"
}
] |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a unit fraction Write the following fraction in its simplest form: \\( 3 \\frac{7}{21} \\) Cannot be simplified"
},
{
"from": "gpt",
"value": "Believes mixed numbers cannot be simplified"
}
] |
[
{
"from": "human",
"value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What fraction should replace the star? ![A number line marked with 1/4, 2/4, 3/4, 4/4, 5/4. The star is halfway between 2/4 and 3/4.]() None of these"
},
{
"from": "gpt",
"value": "Does not realise you can use equivalent fractions to break fractions up into smaller divisions"
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table This table shows the number of pets a group of students owns.\nIf calculating the mean number of pets owned, what would replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Number of pets & Frequency & \\\\\n\\hline \\( 0 \\) & \\( 9 \\) & \\\\\n\\hline \\( 1 \\) & \\( 5 \\) & \\\\\n\\hline \\( 2 \\) & \\( 4 \\) & \\( \\color{gold}\\bigstar \\)\n\\hline \\( 3 \\) & \\( 2 \\) & \\\\\n\\hline \\( 4 \\) & \\( 3 \\) & \\\\\n\\hline\n\\end{tabular} \\( 2+4=6 \\)"
},
{
"from": "gpt",
"value": "Believes the fx column for calculating mean is value + frequency"
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table This table shows the number of pets a group of students owns.\nIf calculating the mean number of pets owned, what would replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Number of pets & Frequency & \\\\\n\\hline \\( 0 \\) & \\( 9 \\) & \\\\\n\\hline \\( 1 \\) & \\( 5 \\) & \\\\\n\\hline \\( 2 \\) & \\( 4 \\) & \\( \\color{gold}\\bigstar \\)\n\\hline \\( 3 \\) & \\( 2 \\) & \\\\\n\\hline \\( 4 \\) & \\( 3 \\) & \\\\\n\\hline\n\\end{tabular} \\( 2-4=(-2) \\)"
},
{
"from": "gpt",
"value": "Believes the fx column for calculating mean is value - frequency"
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table This table shows the number of pets a group of students owns.\nIf calculating the mean number of pets owned, what would replace the star? \\begin{tabular}{|c|c|c|}\n\\hline Number of pets & Frequency & \\\\\n\\hline \\( 0 \\) & \\( 9 \\) & \\\\\n\\hline \\( 1 \\) & \\( 5 \\) & \\\\\n\\hline \\( 2 \\) & \\( 4 \\) & \\( \\color{gold}\\bigstar \\)\n\\hline \\( 3 \\) & \\( 2 \\) & \\\\\n\\hline \\( 4 \\) & \\( 3 \\) & \\\\\n\\hline\n\\end{tabular} \\( 2 \\div 4=0.5 \\)"
},
{
"from": "gpt",
"value": "Believes the fx column for calculating mean is value/frequency"
}
] |
[
{
"from": "human",
"value": "Subtract integers up to 4 digits using a written method where carrying is needed What number should replace the star? \\begin{tabular}{cccc}\n\\(\\space\\) & \\( 9 \\) & \\( 3 \\) & \\( 5 \\) & \\( 2 \\) \\\\\n\\(-\\) & \\(4\\) & \\(5\\) & \\(7\\) & \\(\\bigstar\\)\\\\\n\\(\\space\\) & \\(4\\) & \\(7\\) & \\(7\\) & \\(3\\)\\\\\n\\end{tabular} \\( 1 \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation"
}
] |
[
{
"from": "human",
"value": "Subtract integers up to 4 digits using a written method where carrying is needed What number should replace the star? \\begin{tabular}{cccc}\n\\(\\space\\) & \\( 9 \\) & \\( 3 \\) & \\( 5 \\) & \\( 2 \\) \\\\\n\\(-\\) & \\(4\\) & \\(5\\) & \\(7\\) & \\(\\bigstar\\)\\\\\n\\(\\space\\) & \\(4\\) & \\(7\\) & \\(7\\) & \\(3\\)\\\\\n\\end{tabular} \\( 5 \\)"
},
{
"from": "gpt",
"value": "Confuses the part and the whole in missing number subtraction problems"
}
] |
[
{
"from": "human",
"value": "Subtract integers up to 4 digits using a written method where carrying is needed What number should replace the star? \\begin{tabular}{cccc}\n\\(\\space\\) & \\( 9 \\) & \\( 3 \\) & \\( 5 \\) & \\( 2 \\) \\\\\n\\(-\\) & \\(4\\) & \\(5\\) & \\(7\\) & \\(\\bigstar\\)\\\\\n\\(\\space\\) & \\(4\\) & \\(7\\) & \\(7\\) & \\(3\\)\\\\\n\\end{tabular} It is not possible"
},
{
"from": "gpt",
"value": "Does not realise we can borrow from the preceding digit in a subtraction problem"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring multiplication or division, involving positive decimals Solve the equation:\n\\[\n0.45=0.3 p\n\\] \\( p=\\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring multiplication or division, involving positive decimals Solve the equation:\n\\[\n0.45=0.3 p\n\\] \\( p=0.135 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, multiplies instead of dividing "
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is 1 Vera wants to solve this equation using the quadratic formula.\n\\(\nh^{2}+4=5 h\n\\)\n\nWhat should replace the triangle? ![The image shows the structure of the quadratic formula. It says plus or minus the square root, and the triangle is the first thing after the square root sign, with a minus sign after it.]() \\( -10 \\)"
},
{
"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 1 Vera wants to solve this equation using the quadratic formula.\n\\(\nh^{2}+4=5 h\n\\)\n\nWhat should replace the triangle? ![The image shows the structure of the quadratic formula. It says plus or minus the square root, and the triangle is the first thing after the square root sign, with a minus sign after it.]() \\( 16 \\)"
},
{
"from": "gpt",
"value": "When using the formula to solve a quadratic equation, believes that a, b and c are always taken from the 1st, 2nd and 3rd terms, respectively, of the quadratic. "
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 4.72-3.1 \\) What should replace the star? \\( 4.41 \\)"
},
{
"from": "gpt",
"value": "Hasn't lined up the place value columns when writing out the calculation"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 4.72-3.1 \\) What should replace the star? \\( 1.71 \\)"
},
{
"from": "gpt",
"value": "Hasn't lined up the place value columns when writing out the calculation"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 4.72-3.1 \\) What should replace the star? \\( 7.82 \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts"
}
] |
[
{
"from": "human",
"value": "Calculate the square root of a number What is the square root of nine? \\( 4.5 \\)"
},
{
"from": "gpt",
"value": "Halves when asked to find the square root"
}
] |
[
{
"from": "human",
"value": "Calculate the square root of a number What is the square root of nine? \\( 81 \\)"
},
{
"from": "gpt",
"value": "Squares when asked to find the square root"
}
] |
[
{
"from": "human",
"value": "Calculate the square root of a number What is the square root of nine? \\( 18 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using completing the square in the form (x + q)² + r One of these equations has no real solutions\nWhich is it? \\( (w-4)^{2}=0 \\)"
},
{
"from": "gpt",
"value": "Believes 0 has no square root"
}
] |
[
{
"from": "human",
"value": "Compare relative frequencies in order to determine which prediction is likely to be more reliable A vegetarian restaurant wants to know people's eating habits\n\\( 50 \\) people in Town \\( A \\) are asked if they eat meat. \\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{ Town A } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 39 \\) \\\\\n\\hline No & \\( 11 \\) \\\\\n\\hline\n\\end{tabular} \\( 200 \\) people in Town B are asked if they eat meat. \\begin{tabular}{|cc|}\n\\hline \\multicolumn{2}{|c|}{ Town B } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 143 \\) \\\\\n\\hline No & \\( 57 \\) \\\\\n\\hline\n\\end{tabular} Which results are more reliable? Town A"
},
{
"from": "gpt",
"value": "Does not know that sample size affects reliability"
}
] |
[
{
"from": "human",
"value": "Compare relative frequencies in order to determine which prediction is likely to be more reliable A vegetarian restaurant wants to know people's eating habits\n\\( 50 \\) people in Town \\( A \\) are asked if they eat meat. \\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{ Town A } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 39 \\) \\\\\n\\hline No & \\( 11 \\) \\\\\n\\hline\n\\end{tabular} \\( 200 \\) people in Town B are asked if they eat meat. \\begin{tabular}{|cc|}\n\\hline \\multicolumn{2}{|c|}{ Town B } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 143 \\) \\\\\n\\hline No & \\( 57 \\) \\\\\n\\hline\n\\end{tabular} Which results are more reliable? They are the same"
},
{
"from": "gpt",
"value": "Does not know that sample size affects reliability"
}
] |
[
{
"from": "human",
"value": "Compare relative frequencies in order to determine which prediction is likely to be more reliable A vegetarian restaurant wants to know people's eating habits\n\\( 50 \\) people in Town \\( A \\) are asked if they eat meat. \\begin{tabular}{|c|c|}\n\\hline \\multicolumn{2}{|c|}{ Town A } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 39 \\) \\\\\n\\hline No & \\( 11 \\) \\\\\n\\hline\n\\end{tabular} \\( 200 \\) people in Town B are asked if they eat meat. \\begin{tabular}{|cc|}\n\\hline \\multicolumn{2}{|c|}{ Town B } \\\\\n\\hline Do you eat meat? & Frequency \\\\\n\\hline Yes & \\( 143 \\) \\\\\n\\hline No & \\( 57 \\) \\\\\n\\hline\n\\end{tabular} Which results are more reliable? Impossible to say"
},
{
"from": "gpt",
"value": "Does not know that sample size affects reliability"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount using a calculator where the percent is an integer What should replace the star? ![A percentage number line representing the value 630 with a star above the 84% mark]() Use your calculator, if needed, and give your answer to \\( 1 \\) decimal place. \\( 750 \\)"
},
{
"from": "gpt",
"value": "Thinks when finding a percentage you divide by the percentage being asked"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph ![A line graph with title \"Height of rocket\". \nThe x-axis is titled \"Time in seconds\" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.\nThe y-axis is titled \"Height in metres\" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).\n]() How many metres did the rocket travel between \\( 20 \\) and \\( 50 \\) seconds? \\( 85 \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts when asked to find the difference"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph ![A line graph with title \"Height of rocket\". \nThe x-axis is titled \"Time in seconds\" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.\nThe y-axis is titled \"Height in metres\" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).\n]() How many metres did the rocket travel between \\( 20 \\) and \\( 50 \\) seconds? \\( 30 \\)"
},
{
"from": "gpt",
"value": "When finding the difference between two points on a time series graph, only uses one of the points. "
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph ![A line graph with title \"Height of rocket\". \nThe x-axis is titled \"Time in seconds\" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.\nThe y-axis is titled \"Height in metres\" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).\n]() How many metres did the rocket travel between \\( 20 \\) and \\( 50 \\) seconds? \\( 55 \\)"
},
{
"from": "gpt",
"value": "When finding the difference between two points on a time series graph, only uses one of the points. "
}
] |
[
{
"from": "human",
"value": "Know the equation of the axes What is the equation of the \\( y \\) axis? \\( y=1 \\)"
},
{
"from": "gpt",
"value": "Thinks y =1 is the y axis"
}
] |
[
{
"from": "human",
"value": "Know the equation of the axes What is the equation of the \\( y \\) axis? \\( y=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 \\( y \\) axis? \\( y=x \\)"
},
{
"from": "gpt",
"value": "Thinks x = y is an axis"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 1000 What is \\( 326 \\) rounded to the nearest \\( 1000 \\) ? \\( 1000 \\)"
},
{
"from": "gpt",
"value": "Rounds up instead of down"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 1000 What is \\( 326 \\) rounded to the nearest \\( 1000 \\) ? \\( 500 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too little)"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using balancing One of these equations has no real solutions.\nWhich is it? \\( t^{2}-45=-45 \\)"
},
{
"from": "gpt",
"value": "Believes 0 is not a real solution to an equation"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using balancing One of these equations has no real solutions.\nWhich is it? \\( t^{3}=-45 \\)"
},
{
"from": "gpt",
"value": "Believes a number raised to a power will always give a positive answer"
}
] |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nTo find the value of \\( x \\), Sally uses:\n\\(x_{n+1}=\\frac{8}{9}-\\frac{x^{3}{ }_{n}}{9}\\)\n\nIf \\( x_{0}=0 \\), what is the value of \\( x \\) to \\( 3 \\) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]() \\( 0.830 \\)"
},
{
"from": "gpt",
"value": "Stops iteration too early when solving equations"
}
] |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nTo find the value of \\( x \\), Sally uses:\n\\(x_{n+1}=\\frac{8}{9}-\\frac{x^{3}{ }_{n}}{9}\\)\n\nIf \\( x_{0}=0 \\), what is the value of \\( x \\) to \\( 3 \\) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]() \\( 0.825 \\)"
},
{
"from": "gpt",
"value": "Stops iteration too early when solving equations"
}
] |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nTo find the value of \\( x \\), Sally uses:\n\\(x_{n+1}=\\frac{8}{9}-\\frac{x^{3}{ }_{n}}{9}\\)\n\nIf \\( x_{0}=0 \\), what is the value of \\( x \\) to \\( 3 \\) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]() \\( 0.8101 \\)"
},
{
"from": "gpt",
"value": "Stops iteration too early when solving equations"
}
] |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rectangle The diagonals of a rectangle with different length sides \\(_____________\\) intersect at right-angles ![A rectangle]() always"
},
{
"from": "gpt",
"value": "Does not know the properties of a rectangle"
}
] |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rectangle The diagonals of a rectangle with different length sides \\(_____________\\) intersect at right-angles ![A rectangle]() sometimes"
},
{
"from": "gpt",
"value": "Does not know the properties of a rectangle"
}
] |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rectangle The diagonals of a rectangle with different length sides \\(_____________\\) intersect at right-angles ![A rectangle]() I don't know"
},
{
"from": "gpt",
"value": "Does not know the properties of a rectangle"
}
] |
[
{
"from": "human",
"value": "Identify perpendicular lines written in the form y = mx + c Which of the following lines is perpendicular to\n\\[\ny=3 x-2 ?\n\\] \\( y=\\frac{1}{3} x+1 \\)"
},
{
"from": "gpt",
"value": "Believes the gradients of perpendicular lines are reciprocals of the same sign"
}
] |
[
{
"from": "human",
"value": "Identify perpendicular lines written in the form y = mx + c Which of the following lines is perpendicular to\n\\[\ny=3 x-2 ?\n\\] \\( y=3 x+7 \\)"
},
{
"from": "gpt",
"value": "Confuses the meaning of parallel and perpendicular"
}
] |
[
{
"from": "human",
"value": "Given the area of a parallelogram, calculate a missing dimension The area of this parallelogram is \\( 24 \\mathrm{~cm}^{2} \\)\n\nWhat measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]() \\( 2 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "When finding a missing side of a parallelogram given the area completes an extra step of dividing by 2"
}
] |
[
{
"from": "human",
"value": "Given the area of a parallelogram, calculate a missing dimension The area of this parallelogram is \\( 24 \\mathrm{~cm}^{2} \\)\n\nWhat measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]() \\( 8 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "When finding the area of a parallelogram finds base x perpendicular height but divides the answer by 2 "
}
] |
[
{
"from": "human",
"value": "Given the area of a parallelogram, calculate a missing dimension The area of this parallelogram is \\( 24 \\mathrm{~cm}^{2} \\)\n\nWhat measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]() Not enough information"
},
{
"from": "gpt",
"value": "Does not realise we can find a missing length if we know the base of a parallelogram and its area. "
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Using the graph of\n\\(\ny=x^{2}-x-6\n\\)\n\nWhat is the correct way to write the solution to\n\\(\ny=x^{2}-x-6 \\geq 0 ?\n\\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]() \\( \\{-2 \\leq x \\leq 3\\} \\)"
},
{
"from": "gpt",
"value": "Believes the solution of a quadratic inequality is always the interval between the roots"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Using the graph of\n\\(\ny=x^{2}-x-6\n\\)\n\nWhat is the correct way to write the solution to\n\\(\ny=x^{2}-x-6 \\geq 0 ?\n\\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]() \\( \\{-2 \\geq x \\geq 3\\} \\)"
},
{
"from": "gpt",
"value": "Believes any two inequalities can be combined into a double inequality"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Using the graph of\n\\(\ny=x^{2}-x-6\n\\)\n\nWhat is the correct way to write the solution to\n\\(\ny=x^{2}-x-6 \\geq 0 ?\n\\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]() \\( \\{x \\geq-2\\} \\cup\\{x \\leq 3\\} \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{1 5} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() A"
},
{
"from": "gpt",
"value": "Does not know what a square number is"
}
] |
[
{
"from": "human",
"value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{1 5} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() B"
},
{
"from": "gpt",
"value": "Does not know what a square number is"
}
] |
[
{
"from": "human",
"value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{1 5} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() D"
},
{
"from": "gpt",
"value": "Mixes up odd and even numbers"
}
] |
[
{
"from": "human",
"value": "Order integers with a different number of digits Which of these options show the numbers\n650,312 \n3,506,212\n3,652\n605,321\nin order from smallest to largest? \\( \\begin{array}{l}3,506,212 \\\\ 3,652 \\\\ 605,321 \\\\ 650,312\\end{array} \\)"
},
{
"from": "gpt",
"value": "Orders integers based on first digits without taking into account place value"
}
] |
[
{
"from": "human",
"value": "Order integers with a different number of digits Which of these options show the numbers\n650,312 \n3,506,212\n3,652\n605,321\nin order from smallest to largest? \\( \\begin{array}{l}605,321 \\\\ 3,506,212 \\\\ 650,312 \\\\ 3,652\\end{array} \\)"
},
{
"from": "gpt",
"value": "When ordering integers, orders from the digits at the end of the number instead of the digits at the start"
}
] |
[
{
"from": "human",
"value": "Understand inequality notation Which of the following shows \" \\( x \\) is greater than \\( 9 \\) \"? \\( x<9 \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Understand inequality notation Which of the following shows \" \\( x \\) is greater than \\( 9 \\) \"? \\( x \\geq 9 \\)"
},
{
"from": "gpt",
"value": "When using inequality notation, thinks \"greater than/less than or equal to\" symbols are instead the \"greater than/less than\" symbols and vice versa"
}
] |
[
{
"from": "human",
"value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 400099 \\) \\( 500000 \\)"
},
{
"from": "gpt",
"value": "Rounds up instead of down"
}
] |
[
{
"from": "human",
"value": "Round numbers greater than 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 400099 \\) \\( 400100 \\)"
},
{
"from": "gpt",
"value": "Rounded to nearest 100 instead of 1sf"
}
] |
[
{
"from": "human",
"value": "Recognise the equations of horizontal lines from a diagram What is the equation of this line? ![A graph of a horizontal line going through 3 on the y axis. ]() \\( y=3 x \\)"
},
{
"from": "gpt",
"value": "Includes the x variable when giving the equation of a horizontal line"
}
] |