conversations
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[
{
"from": "human",
"value": "Identify the regions on a double Venn diagram given in set notation Which element(s) is/are in \\( P^{\\prime} \\) ? ![A diagram showing a Venn diagram of 2 circles. The left cicle is for Set P and contains cat in its left part, horse in the intersection. The right circle is for set Q and contains goat in its right part, horse in the intersection. Outside of the circles it says toad.]() cat"
},
{
"from": "gpt",
"value": "Does not understand set notation for complement (eg. A')"
}
] |
[
{
"from": "human",
"value": "Identify the regions on a double Venn diagram given in set notation Which element(s) is/are in \\( P^{\\prime} \\) ? ![A diagram showing a Venn diagram of 2 circles. The left cicle is for Set P and contains cat in its left part, horse in the intersection. The right circle is for set Q and contains goat in its right part, horse in the intersection. Outside of the circles it says toad.]() horse, goat\n& toad"
},
{
"from": "gpt",
"value": "Believes that the complement of a set includes any elements which are also in another set."
}
] |
[
{
"from": "human",
"value": "Order integers with the same number of digits Which of these options show the numbers\n\\[\n8,605,527 \\quad 8,605,572 \\quad 8,650,527 \\quad 8,605,752\n\\]\nin order from smallest to largest? \\( \\begin{array}{l}8,605,752 \\\\ 8,605,572 \\\\ 8,650,527 \\\\ 8,605,527\\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": "Calculate the volume of a triangular-based prism when the dimensions are given in the same units Amy wants to calculate the volume of this shape.\n\nWhich face should she work out the area of to help her? ![The diagram shows a right angled triangular prism with arrows pointing to one of the right angled triangle faces and the three rectangular faces.]() ![A points to 'the slope' which is the rectangular face coming off the hypotenuse of the right angled triangle]()"
},
{
"from": "gpt",
"value": "Think cross section of a prism is the biggest face"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a triangular-based prism when the dimensions are given in the same units Amy wants to calculate the volume of this shape.\n\nWhich face should she work out the area of to help her? ![The diagram shows a right angled triangular prism with arrows pointing to one of the right angled triangle faces and the three rectangular faces.]() ![C points to 'the back' which is the rectangular face coming off the short vertical side of the right angled triangle]()"
},
{
"from": "gpt",
"value": "Thinks cross section of a prism can be any face"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a triangular-based prism when the dimensions are given in the same units Amy wants to calculate the volume of this shape.\n\nWhich face should she work out the area of to help her? ![The diagram shows a right angled triangular prism with arrows pointing to one of the right angled triangle faces and the three rectangular faces.]() ![D points to 'the base' which is the rectangular face coming off the long horizontal side of the right angled triangle]()"
},
{
"from": "gpt",
"value": "Thinks cross section of a prism can be any face"
}
] |
[
{
"from": "human",
"value": "Recognise when to find the Lowest Common Multiple to solve a problem A hot tap drips every \\( 12 \\) seconds\nA cold tap drips every \\( 8 \\) seconds\nThey both drip at exactly the same time\nAfter how many seconds will they next drip at the same time?\nTo solve this problem you need to work out the \\( _____ \\) of \\( 12 \\) and \\( 8 \\) Highest Common Factor"
},
{
"from": "gpt",
"value": "Confuses factors and multiples"
}
] |
[
{
"from": "human",
"value": "Recognise when to find the Lowest Common Multiple to solve a problem A hot tap drips every \\( 12 \\) seconds\nA cold tap drips every \\( 8 \\) seconds\nThey both drip at exactly the same time\nAfter how many seconds will they next drip at the same time?\nTo solve this problem you need to work out the \\( _____ \\) of \\( 12 \\) and \\( 8 \\) Product"
},
{
"from": "gpt",
"value": "Finds a common multiple but not the lowest common multiple"
}
] |
[
{
"from": "human",
"value": "Recognise when to find the Lowest Common Multiple to solve a problem A hot tap drips every \\( 12 \\) seconds\nA cold tap drips every \\( 8 \\) seconds\nThey both drip at exactly the same time\nAfter how many seconds will they next drip at the same time?\nTo solve this problem you need to work out the \\( _____ \\) of \\( 12 \\) and \\( 8 \\) Sum"
},
{
"from": "gpt",
"value": "Believes adding two numbers finds their lowest common multiple"
}
] |
[
{
"from": "human",
"value": "Round numbers to two decimal places What is \\( \\mathbf{1 1 . 4 7 8 1} \\) rounded to \\( 2 \\) decimal places? \\( 11.47 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round numbers to two decimal places What is \\( \\mathbf{1 1 . 4 7 8 1} \\) rounded to \\( 2 \\) decimal places? \\( 11.58 \\)"
},
{
"from": "gpt",
"value": "Rounds incorrectly by changing multiple place values"
}
] |
[
{
"from": "human",
"value": "Round numbers to two decimal places What is \\( \\mathbf{1 1 . 4 7 8 1} \\) rounded to \\( 2 \\) decimal places? \\( 11.59 \\)"
},
{
"from": "gpt",
"value": "Rounds incorrectly by changing multiple place values"
}
] |
[
{
"from": "human",
"value": "Assign probabilities to single events using percentages This five-sided spinner is fair.\nWhat is the probability of spinning a \\( \\mathbf{3} \\) ?\nGive your answer as a percentage ![A five sided spinner labelled with 1, 1, 2, 3 and 4]() \\( 25 \\% \\)"
},
{
"from": "gpt",
"value": "Believes all possible outcomes must have equal probability"
}
] |
[
{
"from": "human",
"value": "Add fractions involving mixed number fractions with different denominators \\(\n2 \\frac{1}{3}+\\frac{3}{4}=3 \\frac{\\bigstar}{12}\n\\)\nWhat should replace the star? \\( 13 \\)"
},
{
"from": "gpt",
"value": "Believes a mixed number can contain an improper fraction"
}
] |
[
{
"from": "human",
"value": "Add fractions involving mixed number fractions with different denominators \\(\n2 \\frac{1}{3}+\\frac{3}{4}=3 \\frac{\\bigstar}{12}\n\\)\nWhat should replace the star? \\( 37 \\)"
},
{
"from": "gpt",
"value": "Finds an equivalent improper fraction when asked for a mixed number"
}
] |
[
{
"from": "human",
"value": "Construct a triangle using Side-Angle-Side Which combination of mathematical instruments has been used to construct this triangle? ![Constructed triangle with two sides and an angle labelled]() Protractor \nCompass"
},
{
"from": "gpt",
"value": "Forgets you need a ruler to measure lengths"
}
] |
[
{
"from": "human",
"value": "Construct a triangle using Side-Angle-Side Which combination of mathematical instruments has been used to construct this triangle? ![Constructed triangle with two sides and an angle labelled]() Ruler \nCompass"
},
{
"from": "gpt",
"value": "Forgets you need a protractor to measure angles"
}
] |
[
{
"from": "human",
"value": "Construct a triangle using Side-Angle-Side Which combination of mathematical instruments has been used to construct this triangle? ![Constructed triangle with two sides and an angle labelled]() Ruler\nProtractor\nCompass"
},
{
"from": "gpt",
"value": "Believes constructing a triangle with given SAS requires a compass"
}
] |
[
{
"from": "human",
"value": "Convert between l and ml 3 litres = \\( \\color{gold}\\bigstar \\) millilitres What should replace the star? \\( 0.3 \\)"
},
{
"from": "gpt",
"value": "Divides when converting to a smaller unit"
}
] |
[
{
"from": "human",
"value": "Convert between l and ml 3 litres = \\( \\color{gold}\\bigstar \\) millilitres What should replace the star? \\( 30 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10ml in a litre"
}
] |
[
{
"from": "human",
"value": "Convert between l and ml 3 litres = \\( \\color{gold}\\bigstar \\) millilitres What should replace the star? \\( 300 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100 ml in a litre"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c Factorise \\( x^{2}+20 x+64 \\) \\( (x+8)(x+8) \\)"
},
{
"from": "gpt",
"value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c Factorise \\( x^{2}+20 x+64 \\) \\( (x+12)(x+8) \\)"
},
{
"from": "gpt",
"value": "Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c Factorise \\( x^{2}+20 x+64 \\) \\( (x+14)(x+6) \\)"
},
{
"from": "gpt",
"value": "Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x"
}
] |
[
{
"from": "human",
"value": "Given the distance travelled, complete missing values on a speed-time graph Work out the speed \\( v \\) if the distance travelled is \\( 50 \\) miles. ![A speed-time graph. The vertical axis is labelled Speed (mph) and has no scale marked except for the letter v four squares up.\nThe horizontal axis is labelled Time (seconds) and the scale is 0, 1, 2, 3, 4 in even steps.\nThe graph consists of two sloped lines. The first is from (0,0) to (2, v) and the second is from (2, v) to (4, 0).]() \\( 100 \\mathrm{mph} \\)"
},
{
"from": "gpt",
"value": "Believes speed is distance multiplied by time"
}
] |
[
{
"from": "human",
"value": "Given the distance travelled, complete missing values on a speed-time graph Work out the speed \\( v \\) if the distance travelled is \\( 50 \\) miles. ![A speed-time graph. The vertical axis is labelled Speed (mph) and has no scale marked except for the letter v four squares up.\nThe horizontal axis is labelled Time (seconds) and the scale is 0, 1, 2, 3, 4 in even steps.\nThe graph consists of two sloped lines. The first is from (0,0) to (2, v) and the second is from (2, v) to (4, 0).]() \\( 12.5 \\mathrm{mph} \\)"
},
{
"from": "gpt",
"value": "Thinks the shape of the graph does not affect the area calculation"
}
] |
[
{
"from": "human",
"value": "Write a formula to describe a situation Jodie was \\( y \\) years old on her birthday \\( 3 \\) years ago.\nHer father was \\( 43 \\) years old. This year Jodie is half her father's age.\nWhich answer does not correctly represent this scenario? ![A bar model showing a bar for Jodie's age as y + 3 which is half the width of her father's bar. Her father's bar is shown as 2 lots of y + 3, where the first y + 3 + y total to 43.]()"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Write a formula to describe a situation Jodie was \\( y \\) years old on her birthday \\( 3 \\) years ago.\nHer father was \\( 43 \\) years old. This year Jodie is half her father's age.\nWhich answer does not correctly represent this scenario? ![A bar model showing a bar for Jodie's age as y + 3 which is half the width of her father's bar. Her father's bar is shown as 46 in total, split into 2 lots of 23.]()"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear inequalities in one variable where the variable appears on one side of the equation In which of the following inequalities could \\( \\boldsymbol{d}=\\mathbf{5} \\) ? \\begin{tabular}{ll}\nInequality \\( 1 \\) & Inequality 2 \\\\\n\\( 2 d>11 \\) & \\( 11>d+2 \\)\n\\end{tabular} Only Inequality \\( 1 \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Round decimals to the nearest whole number Jane measures the length and width of her rectangular classroom as \\( 8.3 \\mathrm{~m} \\) and \\( 12.9 \\mathrm{~m} \\).\nWhich calculation will give the best estimate of the area? \\( 9 \\times 13 \\)"
},
{
"from": "gpt",
"value": "Rounds up instead of down"
}
] |
[
{
"from": "human",
"value": "Round decimals to the nearest whole number Jane measures the length and width of her rectangular classroom as \\( 8.3 \\mathrm{~m} \\) and \\( 12.9 \\mathrm{~m} \\).\nWhich calculation will give the best estimate of the area? \\( 8 \\times 12 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round decimals to the nearest whole number Jane measures the length and width of her rectangular classroom as \\( 8.3 \\mathrm{~m} \\) and \\( 12.9 \\mathrm{~m} \\).\nWhich calculation will give the best estimate of the area? \\( 9 \\times 12 \\)"
},
{
"from": "gpt",
"value": "Rounds up rather than to one significant figure"
}
] |
[
{
"from": "human",
"value": "Solve problems involving adding a period of time on to a given start time A coach takes \\( 2 \\) hours \\( 40 \\) minutes to complete a journey from Manchester to Milton Keynes.\n\nIf the coach leaves Manchester at 10:45, what time does it arrive in Milton Keynes? 01:25"
},
{
"from": "gpt",
"value": "Writes times in the afternoon as if they are morning on a 24 hour clock"
}
] |
[
{
"from": "human",
"value": "Solve problems involving adding a period of time on to a given start time A coach takes \\( 2 \\) hours \\( 40 \\) minutes to complete a journey from Manchester to Milton Keynes.\n\nIf the coach leaves Manchester at 10:45, what time does it arrive in Milton Keynes? \\( 12: 85 \\)"
},
{
"from": "gpt",
"value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes"
}
] |
[
{
"from": "human",
"value": "Given a negative y value, find an x value in a table of values for lines in the form y = c - x This is a part of the table of values for the equation\n\\[\ny=3-x\n\\] ![\\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\(\\bigstar\\) \\\\\n\\hline\\( y \\) & \\( -9 \\) \\\\\n\\hline\n\\end{tabular}\n\n]() What should replace the star? \\( -12 \\)"
},
{
"from": "gpt",
"value": "When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 5.39-2.1= \\) \\( 3.38 \\)"
},
{
"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 \\( 5.39-2.1= \\) \\( 7.49 \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 5.39-2.1= \\) \\( 5.18 \\)"
},
{
"from": "gpt",
"value": "Hasn't lined up the place value columns when writing out the calculation"
}
] |
[
{
"from": "human",
"value": "Express a division as a fraction Samia has \\( 12 \\) cakes to share between \\( 5 \\) people.\nWhat fraction of a cake does each person get? \\( \\frac{5}{12} \\)"
},
{
"from": "gpt",
"value": "Mixes up the numerator and denominator when writing a division as a fraction"
}
] |
[
{
"from": "human",
"value": "Express a division as a fraction Samia has \\( 12 \\) cakes to share between \\( 5 \\) people.\nWhat fraction of a cake does each person get? \\( \\frac{1}{5} \\)"
},
{
"from": "gpt",
"value": "Thinks the fraction 1/n can express sharing any number of items between n people"
}
] |
[
{
"from": "human",
"value": "Express a division as a fraction Samia has \\( 12 \\) cakes to share between \\( 5 \\) people.\nWhat fraction of a cake does each person get? \\( \\frac{1}{12} \\)"
},
{
"from": "gpt",
"value": "Does not know how to interpret a fraction worded problem "
}
] |
[
{
"from": "human",
"value": "Subtract decimals from integers How should you line up the digits to calculate \\( 7-0.612 \\) ? ![A column subtraction written as 0.007 - 0.612 with the decimal points lined up.]()"
},
{
"from": "gpt",
"value": "Does not know the units column is before the decimal point"
}
] |
[
{
"from": "human",
"value": "Subtract decimals from integers How should you line up the digits to calculate \\( 7-0.612 \\) ? ![A column subtraction written as 0.700 - 0.612 with the decimal points lined up.]()"
},
{
"from": "gpt",
"value": "Does not know the units column is before the decimal point"
}
] |
[
{
"from": "human",
"value": "Subtract decimals from integers How should you line up the digits to calculate \\( 7-0.612 \\) ? ![A column subtraction written as 7.0 - 0.612 The 7 is above the 6, the decimal point in 7.0 is above the 1 and the 0 of 7.0 is above the 2.]()"
},
{
"from": "gpt",
"value": "Lines up the digits incorrectly when doing a subtraction involving two numbers with a different amount of digits"
}
] |
[
{
"from": "human",
"value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. \"-6\" below the 2nd dash and \"3\" below the last dash are the only numbers marked on the line. An arrow, labelled \"A\" is pointing halfway between the 4th and 5th dashes. ]() \\( -4.5 \\)"
},
{
"from": "gpt",
"value": "Student thinks that negative decimals behave the same as positive decimals when positioning a decimal between two consecutive negative integers, placing the decimal with a greater absolute value to the right. "
}
] |
[
{
"from": "human",
"value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. \"-6\" below the 2nd dash and \"3\" below the last dash are the only numbers marked on the line. An arrow, labelled \"A\" is pointing halfway between the 4th and 5th dashes. ]() \\( -8.5 \\)"
},
{
"from": "gpt",
"value": "When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right."
}
] |
[
{
"from": "human",
"value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. \"-6\" below the 2nd dash and \"3\" below the last dash are the only numbers marked on the line. An arrow, labelled \"A\" is pointing halfway between the 4th and 5th dashes. ]() \\( -1 \\)"
},
{
"from": "gpt",
"value": "When reading integers on a number line, assumes each dash is 2"
}
] |
[
{
"from": "human",
"value": "Write a missing term of an ascending integer linear sequence The \\( 1^{\\text {st }} \\) term in a linear sequence is \\( 8 \\). The \\( 4^{\\text {th }} \\) term of the sequence is \\( 41 \\). What is the \\( 8^{\\text {th }} \\) term of the sequence? \\( 82 \\)"
},
{
"from": "gpt",
"value": "Believes there is a multiplicative relationship between values of terms in a linear sequence e.g. 10th term is double 5th term"
}
] |
[
{
"from": "human",
"value": "Write a missing term of an ascending integer linear sequence The \\( 1^{\\text {st }} \\) term in a linear sequence is \\( 8 \\). The \\( 4^{\\text {th }} \\) term of the sequence is \\( 41 \\). What is the \\( 8^{\\text {th }} \\) term of the sequence? \\( 88 \\)"
},
{
"from": "gpt",
"value": "Believes you multiply the constant difference by the term number to get the term value"
}
] |
[
{
"from": "human",
"value": "Subtract fractions involving mixed number fractions with the same denominator \\( 2 \\frac{4}{5}-1 \\frac{2}{5}= \\) Leave your answer as a mixed number \\( \\frac{7}{5} \\)"
},
{
"from": "gpt",
"value": "Confused mixed numbers with improper fractions"
}
] |
[
{
"from": "human",
"value": "Subtract fractions involving mixed number fractions with the same denominator \\( 2 \\frac{4}{5}-1 \\frac{2}{5}= \\) Leave your answer as a mixed number \\( 1 \\frac{2}{0} \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a fraction of another A group of \\( 8 \\) friends share \\( £6 \\) equally.\nWhat fraction of the money do they each get? \\( \\frac{1}{8} \\)"
},
{
"from": "gpt",
"value": "Thinks the fraction 1/n can express sharing any number of items between n people"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a fraction of another A group of \\( 8 \\) friends share \\( £6 \\) equally.\nWhat fraction of the money do they each get? \\( \\frac{1}{6} \\)"
},
{
"from": "gpt",
"value": "Thinks the fraction 1/n can express sharing n items between any number of people"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a fraction of another A group of \\( 8 \\) friends share \\( £6 \\) equally.\nWhat fraction of the money do they each get? \\( \\frac{8}{6} \\)"
},
{
"from": "gpt",
"value": "Believes that a fraction means dividing the denominator by the numerator"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{8}-\\frac{1}{5} \\) Give your answer in the simplest form. \\( \\frac{33}{40} \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{8}-\\frac{1}{5} \\) Give your answer in the simplest form. \\( \\frac{4}{3} \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor Work out: \\( \\frac{5}{8}-\\frac{1}{5} \\) Give your answer in the simplest form. \\( \\frac{1}{10} \\)"
},
{
"from": "gpt",
"value": "When adding fractions, changes to common denominator but leaves numerators the same"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c Factorise this expression, if possible:\n\\(\np^{2}+25 p+100\n\\) \\( (p+25)(p+4) \\)"
},
{
"from": "gpt",
"value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c Factorise this expression, if possible:\n\\(\np^{2}+25 p+100\n\\) \\( (p+5)(p+5) \\)"
},
{
"from": "gpt",
"value": "Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets"
}
] |
[
{
"from": "human",
"value": "Convert fractions to percentages containing 2 or more decimal places \\( \\frac{5}{15}= \\) \\( 0.5 \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a decimal by using only the numerator after the decimal point"
}
] |
[
{
"from": "human",
"value": "Convert between l and ml A can of pop is \\( 330 \\mathrm{ml} \\).\n\nWhat is this in litres? \\( 3.3 \\) litres"
},
{
"from": "gpt",
"value": "Thinks there are 100 ml in a litre"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object Tom and Katie are discussing reflections ![Tom says this reflection will create a rectangle. There is a diagonal dashed line with a square sitting on the line.]() ![Katie says this reflection will create a square. There is a diagonal dashed line with a rectangle sitting on the line.]() Who do you agree with? Neither is correct"
},
{
"from": "gpt",
"value": "Cannot reflect shape when line of symmetry is diagonal "
}
] |
[
{
"from": "human",
"value": "Convert from years to days \\( 1 \\) leap year \\( =\\square \\) days \\( 364 \\)"
},
{
"from": "gpt",
"value": "Does not know how many days are in a leap year"
}
] |
[
{
"from": "human",
"value": "Convert from years to days \\( 1 \\) leap year \\( =\\square \\) days \\( 365 \\)"
},
{
"from": "gpt",
"value": "Does not know how many days are in a leap year"
}
] |
[
{
"from": "human",
"value": "Write a missing term of a descending integer linear sequence ![An image of 5 boxes, each box representing a number in a sequence. The first box contains a star, the second is empty, the third contains the number 488 and the fourth and fifth boxes are also empty.]() A descending linear sequence has a constant difference of \\( 17 \\) and the \\( 3^{\\text {rd }} \\) term is \\( 488 \\).\nWhat should replace the star? \\( 471 \\)"
},
{
"from": "gpt",
"value": "Thinks you subtract rather than add when finding the previous term in a descending linear sequence"
}
] |
[
{
"from": "human",
"value": "Write a missing term of a descending integer linear sequence ![An image of 5 boxes, each box representing a number in a sequence. The first box contains a star, the second is empty, the third contains the number 488 and the fourth and fifth boxes are also empty.]() A descending linear sequence has a constant difference of \\( 17 \\) and the \\( 3^{\\text {rd }} \\) term is \\( 488 \\).\nWhat should replace the star? \\( 454 \\)"
},
{
"from": "gpt",
"value": "Thinks you subtract rather than add when finding the previous term in a descending linear sequence"
}
] |
[
{
"from": "human",
"value": "Given a description of a descending linear sequence in words, write some terms of that sequence If the first term of a sequence is \\( 100 \\) and the term-to-term rule is \\( -5 \\), what is the \\( 10^{\\text {th }} \\) term in this sequence? \\( 95 \\)"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence just gives the next term"
}
] |
[
{
"from": "human",
"value": "Given a description of a descending linear sequence in words, write some terms of that sequence If the first term of a sequence is \\( 100 \\) and the term-to-term rule is \\( -5 \\), what is the \\( 10^{\\text {th }} \\) term in this sequence? \\( 50 \\)"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence gives the term after"
}
] |
[
{
"from": "human",
"value": "Given a description of a descending linear sequence in words, write some terms of that sequence If the first term of a sequence is \\( 100 \\) and the term-to-term rule is \\( -5 \\), what is the \\( 10^{\\text {th }} \\) term in this sequence? \\( 45 \\)"
},
{
"from": "gpt",
"value": "Identifies how much repeated use of the term-to-term rule changes a number but does not apply to the sequence"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\\(\nx^{2}<64\n\\) \\( \\{-32<x<32\\} \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\\(\nx^{2}<64\n\\) \\( \\{x<8\\} \\)"
},
{
"from": "gpt",
"value": "Does not think a square root can be negative"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\\(\nx^{2}<64\n\\) \\( \\{x<-8\\} \\cup\\{x>8\\} \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Divide two decimals with the same number of decimal places \\( 0.9 \\div 0.3= \\) \\( 0.3 \\)"
},
{
"from": "gpt",
"value": "When dividing decimals with the same number of decimal places as each other, assumes the answer also has the same number of decimal places"
}
] |
[
{
"from": "human",
"value": "Divide two decimals with the same number of decimal places \\( 0.9 \\div 0.3= \\) \\( 0.333 \\ldots \\)"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Identify a chord What is the correct name for the line marked on the circle? ![\\( \\theta \\)]() Radius"
},
{
"from": "gpt",
"value": "Confuses chord and radius"
}
] |
[
{
"from": "human",
"value": "Identify a chord What is the correct name for the line marked on the circle? ![\\( \\theta \\)]() Tangent"
},
{
"from": "gpt",
"value": "Confuses tangent and chord"
}
] |
[
{
"from": "human",
"value": "Identify a chord What is the correct name for the line marked on the circle? ![\\( \\theta \\)]() Diameter"
},
{
"from": "gpt",
"value": "Confuses diameter and chord"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c This is a part of the table of values for the equation\n\\[\n10 x-6 y=30\n\\] \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( \\bigstar \\) \\\\\n\\hline\\( y \\) & \\( 0.5 \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 2.7 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Carry out division problems involving one negative integer \\(\nn-2 \\geq \\frac{n}{2}\n\\)\n\nIf \\( n \\) can represent any number, is the statement above... always true"
},
{
"from": "gpt",
"value": "Assumes a fact without considering enough examples"
}
] |
[
{
"from": "human",
"value": "Carry out division problems involving one negative integer \\(\nn-2 \\geq \\frac{n}{2}\n\\)\n\nIf \\( n \\) can represent any number, is the statement above... never true"
},
{
"from": "gpt",
"value": "Assumes a fact without considering enough examples"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Which inequality is represented by the shaded region? ![A graph of a quadratic equation. There are dashed vertical lines through the roots of the quadratic. The shaded region is between these vertical lines. ]() \\( x^{2}+x-5 \\leq 0 \\)"
},
{
"from": "gpt",
"value": "Thinks a dashed line marking a region means the line is included"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Which inequality is represented by the shaded region? ![A graph of a quadratic equation. There are dashed vertical lines through the roots of the quadratic. The shaded region is between these vertical lines. ]() \\( x^{2}+x-5>0 \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Describe an enlargement, with no centre of enlargement given, by a positive scale factor bigger than 1 Shape A has been enlarged to get shape B. What is the scale factor of the enlargement? ![Triangle A is two squares across one square up. Triangle B is six squares across and three squares up.]() \\( \\frac{1}{3} \\)"
},
{
"from": "gpt",
"value": "Divides length of original by length of image rather finding length of image divided by length of original to find an enlargement scale factor."
}
] |
[
{
"from": "human",
"value": "Describe an enlargement, with no centre of enlargement given, by a positive scale factor bigger than 1 Shape A has been enlarged to get shape B. What is the scale factor of the enlargement? ![Triangle A is two squares across one square up. Triangle B is six squares across and three squares up.]() \\( -3 \\)"
},
{
"from": "gpt",
"value": "Divides length of original by length of image rather finding length of image divided by length of original to find an enlargement scale factor."
}
] |
[
{
"from": "human",
"value": "Calculate points that lie on the equation of a circle in the form x² + y² = r² Which of the following points lies on the circle with equation:\n\\(\nx^{2}+y^{2}=10\n\\) \\( (-9,1) \\)"
},
{
"from": "gpt",
"value": "Believes squaring a negative number just changes the sign"
}
] |
[
{
"from": "human",
"value": "Calculate points that lie on the equation of a circle in the form x² + y² = r² Which of the following points lies on the circle with equation:\n\\(\nx^{2}+y^{2}=10\n\\) \\( (0,5) \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Use area to write algebraic expressions Which of the following formulae gives the area of this rectangle? ![Rectangle with base 3 and height 2x.]() \\( A=36 x^{2} \\)"
},
{
"from": "gpt",
"value": "Thinks measures of area must end in squared"
}
] |
[
{
"from": "human",
"value": "Use area to write algebraic expressions Which of the following formulae gives the area of this rectangle? ![Rectangle with base 3 and height 2x.]() \\( A=3+2 x \\)"
},
{
"from": "gpt",
"value": "Adds when calculating area instead of multiplying"
}
] |
[
{
"from": "human",
"value": "Use area to write algebraic expressions Which of the following formulae gives the area of this rectangle? ![Rectangle with base 3 and height 2x.]() \\( A=6+4 x \\)"
},
{
"from": "gpt",
"value": "Calculates perimeter when asked for area"
}
] |
[
{
"from": "human",
"value": "Round numbers to an appropriate degree to estimate the answer to a calculation Which option is the best estimate for\n\\[\n17,984-2,407 ?\n\\] \\( 17,000-2,000 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round numbers to an appropriate degree to estimate the answer to a calculation Which option is the best estimate for\n\\[\n17,984-2,407 ?\n\\] \\( 18,000-3,000 \\)"
},
{
"from": "gpt",
"value": "Rounds up instead of down"
}
] |
[
{
"from": "human",
"value": "Interpret a pictogram involving fractions of symbols This pictogram shows the different types of music Bob has in his music collection.\n\nWhich of the following numbers of CDs could Bob represent with whole symbols? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]() \\( 2 \\)"
},
{
"from": "gpt",
"value": "When interpreting a pictogram, thinks each symbol stands for 1"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n105, \\quad 97, \\quad 89, \\quad \\ldots\n\\] \\( 8 \\)"
},
{
"from": "gpt",
"value": "Identifies the term-to-term rule rather than the next term in a sequence"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n105, \\quad 97, \\quad 89, \\quad \\ldots\n\\] Not enough information"
},
{
"from": "gpt",
"value": "Does not know how to find the next term in a sequence"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using factorisation in the form x(x + b) Solve this equation, giving all solutions:\n\\[\nk^{2}=4 k\n\\] \\( k=4 \\)"
},
{
"from": "gpt",
"value": "Believes they can divide by a variable without checking whether it could equal zero"
}
] |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Tom and Katie are arguing about how to fully describe the rotation from shape \\( P \\) to shape \\( Q \\)\n\nTom says: \"a rotation of \\( 90^{\\degree} \\) about point \\( (1,1) \\) \"\n\nKatie says: \"a rotation of \\( 90^{\\degree} \\) clockwise\"\n\nWho is correct? ![A coordinate grid with two pentagons drawn on it labelled P and Q. Pentagon P has the coordinates: (-3,-1) (-3,0) (-2,3) (-1,0) and (-1,-1). Pentagon A has the coordinates: (-1,5) (0,5) (3,4) (0,3) and -1,3).]() Only\nTom"
},
{
"from": "gpt",
"value": "Believes you do not need to give the direction when describing a rotation"
}
] |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Tom and Katie are arguing about how to fully describe the rotation from shape \\( P \\) to shape \\( Q \\)\n\nTom says: \"a rotation of \\( 90^{\\degree} \\) about point \\( (1,1) \\) \"\n\nKatie says: \"a rotation of \\( 90^{\\degree} \\) clockwise\"\n\nWho is correct? ![A coordinate grid with two pentagons drawn on it labelled P and Q. Pentagon P has the coordinates: (-3,-1) (-3,0) (-2,3) (-1,0) and (-1,-1). Pentagon A has the coordinates: (-1,5) (0,5) (3,4) (0,3) and -1,3).]() Only Katie"
},
{
"from": "gpt",
"value": "Forgets to give the centre of rotation"
}
] |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Tom and Katie are arguing about how to fully describe the rotation from shape \\( P \\) to shape \\( Q \\)\n\nTom says: \"a rotation of \\( 90^{\\degree} \\) about point \\( (1,1) \\) \"\n\nKatie says: \"a rotation of \\( 90^{\\degree} \\) clockwise\"\n\nWho is correct? ![A coordinate grid with two pentagons drawn on it labelled P and Q. Pentagon P has the coordinates: (-3,-1) (-3,0) (-2,3) (-1,0) and (-1,-1). Pentagon A has the coordinates: (-1,5) (0,5) (3,4) (0,3) and -1,3).]() Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes you do not need to give the direction when describing a rotation"
}
] |
[
{
"from": "human",
"value": "Multiply 2 digit integers by 2 digit integers using the grid method If you use the grid method to calculate \\( 35 \\times 26 \\) what should replace the star? \\begin{tabular}{|c|c|c|}\n\\hline\\( \\times \\) & \\( 30 \\) & \\( 5 \\) \\\\\n\\hline \\( 20 \\) & & \\(\\bigstar\\) \\\\\n\\hline \\( 6 \\) & \\\\\n\\hline\n\\end{tabular} \\( 10 \\)"
},
{
"from": "gpt",
"value": "When multiplying a multiple of 10, just multiplies the non-zero digits"
}
] |
[
{
"from": "human",
"value": "Multiply 2 digit integers by 2 digit integers using the grid method If you use the grid method to calculate \\( 35 \\times 26 \\) what should replace the star? \\begin{tabular}{|c|c|c|}\n\\hline\\( \\times \\) & \\( 30 \\) & \\( 5 \\) \\\\\n\\hline \\( 20 \\) & & \\(\\bigstar\\) \\\\\n\\hline \\( 6 \\) & \\\\\n\\hline\n\\end{tabular} \\( 1000 \\)"
},
{
"from": "gpt",
"value": "When multiplying by a multiple of 10, gives an answer 10 times bigger than it should be"
}
] |
Subsets and Splits