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[
{
"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} \\( 25 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies when using grid method"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{6}{9} \\div 3\n\\) \\( \\frac{6}{3} \\)"
},
{
"from": "gpt",
"value": "When dividing a fraction by an integer, divides the denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{6}{9} \\div 3\n\\) \\( \\frac{2}{18} \\)"
},
{
"from": "gpt",
"value": "when dividing a fraction by an integer, both multiplies the denominator and divides the denominator"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{6}{9} \\div 3\n\\) \\( \\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "When dividing a fraction by an integer, divides both the numerator and denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Know the functionality of other non-numeric buttons on a calculator Which of the following would allow you to type \\( \\frac{3}{7} \\) on your calculator? ![A scientific calculator]() ![The number 3, then a calculator button labelled \\( x^{-1} \\), then the number 7]()"
},
{
"from": "gpt",
"value": "Believes the reciprocal button writes a fraction"
}
] |
[
{
"from": "human",
"value": "Know the functionality of other non-numeric buttons on a calculator Which of the following would allow you to type \\( \\frac{3}{7} \\) on your calculator? ![A scientific calculator]() ![The number 3, then a calculator button labelled \\(\\cdot\\), then the number 7]()"
},
{
"from": "gpt",
"value": "Believes the decimal point button writes a fraction"
}
] |
[
{
"from": "human",
"value": "Know the functionality of other non-numeric buttons on a calculator Which of the following would allow you to type \\( \\frac{3}{7} \\) on your calculator? ![A scientific calculator]() ![The number 3, then a calculator button labelled \\(-\\), then the number 7]()"
},
{
"from": "gpt",
"value": "Believes the subtraction button writes a fraction"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)(x + c) When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\n(3 m+2)(m-2) \\equiv \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\) \\(\n\\triangle=+0\n\\)\n(no \\( \\mathrm{m} \\) term)"
},
{
"from": "gpt",
"value": "Believes they can ignore the coefficient when expanding double brackets "
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)(x + c) When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\n(3 m+2)(m-2) \\equiv \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\) \\( \\triangle=+8 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying a positive by a negative gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)(x + c) When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\n(3 m+2)(m-2) \\equiv \\bigstar \\ m^{2} \\triangle \\ m \\bigcirc\n\\) \\( \\triangle=+4 \\)"
},
{
"from": "gpt",
"value": "Thinks signs are interchangeable when adding or subtracting positive and negative numbers"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{5 r+6}{6 r}=7\\) \\( \\frac{5 r}{6 r}=1 \\)"
},
{
"from": "gpt",
"value": "Adds or subtracts from numerator first when solving an equation with a fraction"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{5 r+6}{6 r}=7\\) \\( 5 r+1=7 r \\)"
},
{
"from": "gpt",
"value": "Does not understand how to maintain equivalence in fractions"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{5 r+6}{6 r}=7\\) \\( \\frac{5}{6}+r=7 \\)"
},
{
"from": "gpt",
"value": "Does not understand equivalent fractions"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (x + a)² Which of the following answers shows a correct expansion and simplification of the expression below?\n\n\\(\n(x-3)^{2}\n\\) \\( x^{2}-6 x-9 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (x + a)² Which of the following answers shows a correct expansion and simplification of the expression below?\n\n\\(\n(x-3)^{2}\n\\) \\( x^{2}+9 \\)"
},
{
"from": "gpt",
"value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets"
}
] |
[
{
"from": "human",
"value": "Identify factors of a number Which of these is not a factor of \\( 12 \\) ? Twelve"
},
{
"from": "gpt",
"value": "Does not think a number can be a factor of itself"
}
] |
[
{
"from": "human",
"value": "Identify the Lowest Common Multiple of two numbers What is the lowest common multiple of \\( 6 \\) and \\( 7 \\) ? \\( 1 \\)"
},
{
"from": "gpt",
"value": "Confuses factors and multiples"
}
] |
[
{
"from": "human",
"value": "Identify the Lowest Common Multiple of two numbers What is the lowest common multiple of \\( 6 \\) and \\( 7 \\) ? \\( 13 \\)"
},
{
"from": "gpt",
"value": "Believes adding two numbers finds their lowest common multiple"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n2,2,4,17,-10\n\\] \\( 15 \\)"
},
{
"from": "gpt",
"value": "Ignores the negative sign"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n2,2,4,17,-10\n\\] \\( 12 \\)"
},
{
"from": "gpt",
"value": "When calculating the range does not reorder the data to find the largest number minus the smallest number"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n2,2,4,17,-10\n\\] \\( 7 \\)"
},
{
"from": "gpt",
"value": "To find the range adds the biggest and smallest number rather than subtract"
}
] |
[
{
"from": "human",
"value": "Convert between m and mm A \\( 2 \\) metre long rope has \\( 0.5 \\) centimetres chopped off the end.\nWhat is the length of the rope that remains?\nGive your answer in millimetres \\( 1950 \\mathrm{~mm} \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100mm in a centimetre"
}
] |
[
{
"from": "human",
"value": "Expand double brackets with an extra variable outside When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+2)(m-2) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m\n\\) \\(\n\\triangle=+0\n\\)\n(no \\( m \\) term)"
},
{
"from": "gpt",
"value": "Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets"
}
] |
[
{
"from": "human",
"value": "Expand double brackets with an extra variable outside When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+2)(m-2) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m\n\\) \\( \\triangle=+4 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying a positive by a negative gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Expand double brackets with an extra variable outside When you multiply out the brackets and simplify, what replaces the triangle?\n\\(\nm(m+2)(m-2) \\equiv m^{3} \\bigstar \\ m^{2} \\triangle \\ m\n\\) \\( \\triangle=+2 \\)"
},
{
"from": "gpt",
"value": "When multiplying out 2 or more brackets, does not multiply all the combinations of terms"
}
] |
[
{
"from": "human",
"value": "Recognise the place value of each digit in integers What is the value of the \\( 4 \\) in this number?\n\\( 31405 \\) \\( 4 \\)"
},
{
"from": "gpt",
"value": "Does not equate the value of a number with the place value column it is in"
}
] |
[
{
"from": "human",
"value": "Recognise the place value of each digit in integers What is the value of the \\( 4 \\) in this number?\n\\( 31405 \\) \\( 40 \\)"
},
{
"from": "gpt",
"value": "Confuses the hundreds and tens place value columns"
}
] |
[
{
"from": "human",
"value": "Recognise the place value of each digit in integers What is the value of the \\( 4 \\) in this number?\n\\( 31405 \\) \\( 4000 \\)"
},
{
"from": "gpt",
"value": "Confuses the hundreds and thousands place value columns"
}
] |
[
{
"from": "human",
"value": "Solve linear simultaneous equations requiring a scaling of both expressions If five cups of tea and two cups of coffee cost \\( £ 3.70 \\), and two cups of tea and five cups of coffee cost \\( £ 4.00 \\), what is the cost of a cup of tea and a cup of coffee? \\( \\begin{array}{l}\\text { Tea }=0.5 \\\\ \\text { coffee }=0.6\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not include units in answer."
}
] |
[
{
"from": "human",
"value": "Solve linear simultaneous equations requiring a scaling of both expressions If five cups of tea and two cups of coffee cost \\( £ 3.70 \\), and two cups of tea and five cups of coffee cost \\( £ 4.00 \\), what is the cost of a cup of tea and a cup of coffee? \\( \\begin{array}{l}\\text { Tea }=30 p, \\\\ \\text { coffee }=£ 1.10\\end{array} \\)"
},
{
"from": "gpt",
"value": "When asked to solve simultaneous equations, believes they can just find values that work in one equation"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths involve algebraic expressions What length replaces the \\( \\color{green}\\bigstar \\)? ![A diagram showing a compound shape. It is an L shape rotated 90 degrees clockwise. The top full width is 3x+4, the partial width to the right is 2x. The left full height is 5, the partial height on the right is 2. There is a green star on the left partial width at the bottom of the diagram.]() \\( x-3 \\)"
},
{
"from": "gpt",
"value": "Does not know how to find missing lengths in a composite shape"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths involve algebraic expressions What length replaces the \\( \\color{green}\\bigstar \\)? ![A diagram showing a compound shape. It is an L shape rotated 90 degrees clockwise. The top full width is 3x+4, the partial width to the right is 2x. The left full height is 5, the partial height on the right is 2. There is a green star on the left partial width at the bottom of the diagram.]() Not enough information"
},
{
"from": "gpt",
"value": "Does not know how to find missing lengths in a composite shape"
}
] |
[
{
"from": "human",
"value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Expand:\n\\[\n3(1-2 p)\n\\] \\( 4-6 p \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplying when expanding bracket"
}
] |
[
{
"from": "human",
"value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Expand:\n\\[\n3(1-2 p)\n\\] \\( 1-6 p \\)"
},
{
"from": "gpt",
"value": "Only multiplies second term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "Multiply a single term over a bracket where the term on the outside is a number and the inside contains a linear expression Expand:\n\\[\n3(1-2 p)\n\\] \\( 6 p-3 \\)"
},
{
"from": "gpt",
"value": "Believes subtraction is commutative "
}
] |
[
{
"from": "human",
"value": "Answer fraction problems that require the use of BIDMAS \\( \\frac{3}{4}-\\frac{1}{4} \\times \\frac{1}{5}= \\) \\( \\frac{2}{16} \\)"
},
{
"from": "gpt",
"value": "Does not find a common denominator when adding/subtracting fractions"
}
] |
[
{
"from": "human",
"value": "Answer fraction problems that require the use of BIDMAS \\( \\frac{3}{4}-\\frac{1}{4} \\times \\frac{1}{5}= \\) \\( \\frac{1}{10} \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Identify that a problem needs to be solved using addition Which of the following calculations would solve this problem?\nHarvey is monitoring the growth of his plant. The plant was \\( 35 \\mathrm{~cm} \\) tall. It grew \\( 7 \\mathrm{~cm} \\) more.\nHow tall is the plant now? \\( 35 \\div 7 \\)"
},
{
"from": "gpt",
"value": "Divides rather than adds when answering worded problems"
}
] |
[
{
"from": "human",
"value": "Identify that a problem needs to be solved using addition Which of the following calculations would solve this problem?\nHarvey is monitoring the growth of his plant. The plant was \\( 35 \\mathrm{~cm} \\) tall. It grew \\( 7 \\mathrm{~cm} \\) more.\nHow tall is the plant now? \\( 35-7 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of adds when answering worded problems "
}
] |
[
{
"from": "human",
"value": "Identify that a problem needs to be solved using addition Which of the following calculations would solve this problem?\nHarvey is monitoring the growth of his plant. The plant was \\( 35 \\mathrm{~cm} \\) tall. It grew \\( 7 \\mathrm{~cm} \\) more.\nHow tall is the plant now? \\( 35 \\times 7 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than adds when given the command word 'more'"
}
] |
[
{
"from": "human",
"value": "Identify the net of a prism This is the net of a.. ![An image of a square with shapes attached to each of its sides. To the left hand side are three identical squares all connected, in a row. On the top side is a hexagon. On the right hand side are two squares identical to the central square and the squares on the left. So there is a row of 5 squares along the middle of the image. On the bottom side is an identical hexagon to the top.]() Hexagonalbased pyramid"
},
{
"from": "gpt",
"value": "Confuses pyramid with prism"
}
] |
[
{
"from": "human",
"value": "Identify the net of a prism This is the net of a.. ![An image of a square with shapes attached to each of its sides. To the left hand side are three identical squares all connected, in a row. On the top side is a hexagon. On the right hand side are two squares identical to the central square and the squares on the left. So there is a row of 5 squares along the middle of the image. On the bottom side is an identical hexagon to the top.]() Hexagon"
},
{
"from": "gpt",
"value": "Names one of the faces of a 3D shape rather than the 3D shape name"
}
] |
[
{
"from": "human",
"value": "Solve three or more step linear equations, with the variable on one side, with all positive integers Tom and Katie are discussing how to solve:\n\\(\n \\frac{3 x}{2} + 1 =5 \n\\)\n\nTom says a correct next line of working could be: \\( \\frac{3 x}{2}=4 \\)\n\nKatie says a correct next line of working could be: \\( 3 x+1=10 \\)\n\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount"
}
] |
[
{
"from": "human",
"value": "Solve three or more step linear equations, with the variable on one side, with all positive integers Tom and Katie are discussing how to solve:\n\\(\n \\frac{3 x}{2} + 1 =5 \n\\)\n\nTom says a correct next line of working could be: \\( \\frac{3 x}{2}=4 \\)\n\nKatie says a correct next line of working could be: \\( 3 x+1=10 \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount"
}
] |
[
{
"from": "human",
"value": "Interpret remainders from written division problems \\( 321 \\) children are going on a school trip. One adult is needed for every seven children.\n\nHow many adults are needed? \\( 45 \\) r6"
},
{
"from": "gpt",
"value": "Difficulty with translating a mathematical answer into a real world context"
}
] |
[
{
"from": "human",
"value": "Interpret remainders from written division problems \\( 321 \\) children are going on a school trip. One adult is needed for every seven children.\n\nHow many adults are needed? \\( 45 \\frac{6}{7} \\)"
},
{
"from": "gpt",
"value": "Difficulty with translating a mathematical answer into a real world context"
}
] |
[
{
"from": "human",
"value": "Interpret remainders from written division problems \\( 321 \\) children are going on a school trip. One adult is needed for every seven children.\n\nHow many adults are needed? \\( 45 \\)"
},
{
"from": "gpt",
"value": "Difficulty with translating a mathematical answer into a real world context"
}
] |
[
{
"from": "human",
"value": "Interpret what the numbers in each region of a double Venn diagram mean All the students in a class were asked if they have a brother, sister, both or none.\n\nThe Venn Diagram shows the results. ![A Venn diagram with two sets, one labelled Brother and one labelled Sister. The number 11 is written in Brother without the intersection , number 7 is in Sister without the intersection, the number 4 is in the intersection of Brother and Sister. The number 6 is outside the circles.]() How many students are in the class? \\( 4 \\)"
},
{
"from": "gpt",
"value": "Confuses the number of regions in a Venn diagram as the total number of entries in the diagram"
}
] |
[
{
"from": "human",
"value": "Interpret what the numbers in each region of a double Venn diagram mean All the students in a class were asked if they have a brother, sister, both or none.\n\nThe Venn Diagram shows the results. ![A Venn diagram with two sets, one labelled Brother and one labelled Sister. The number 11 is written in Brother without the intersection , number 7 is in Sister without the intersection, the number 4 is in the intersection of Brother and Sister. The number 6 is outside the circles.]() How many students are in the class? \\( 22 \\)"
},
{
"from": "gpt",
"value": "Forgets to include values outside of the Venn diagram when finding the total"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient strategies for mental addition This is how Dora calculates the answer to \\( 12.3+4.5 \\) mentally Dora uses the same method to calculate \\( 2.7+35.9 \\). Which of the following shows how she would do this? ![A diagram showing 3 thought bubbles from Dora's head. The first bubble says \"I added the whole part first 12 + 4 = 16\". The second bubble says \"I then added the decimal part 0.3 + 0.5 = 0.8\". The third bubble says \"I then added 16 and 0.8 to get 16.8. So 12.3 + 4.5 = 16.8\".]() \\( \\begin{array}{c}2.7+35=37.7 \\\\ 37.7+0.9=38.6\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not interpret the correct order of operations from a worded problem"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient strategies for mental addition This is how Dora calculates the answer to \\( 12.3+4.5 \\) mentally Dora uses the same method to calculate \\( 2.7+35.9 \\). Which of the following shows how she would do this? ![A diagram showing 3 thought bubbles from Dora's head. The first bubble says \"I added the whole part first 12 + 4 = 16\". The second bubble says \"I then added the decimal part 0.3 + 0.5 = 0.8\". The third bubble says \"I then added 16 and 0.8 to get 16.8. So 12.3 + 4.5 = 16.8\".]() \\( \\begin{array}{c}2+35=37 \\\\ 0.7+0.9=1.6 \\\\ 37+1.6=37.16\\end{array} \\)"
},
{
"from": "gpt",
"value": "Ignores place value when adding a whole number and a decimal"
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable that require three or more steps where the variable appears on one side of the equation Solve\n\\[\n42 \\geq 6(2 n+1)\n\\] \\( n \\geq 3 \\)"
},
{
"from": "gpt",
"value": "Believes the sides of an inequality can be switched without changing the direction of the sign"
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable that require three or more steps where the variable appears on one side of the equation Solve\n\\[\n42 \\geq 6(2 n+1)\n\\] \\( \\frac{35}{12} \\geq n \\)"
},
{
"from": "gpt",
"value": "When expanding brackets, multiplies out the first term correctly but adds together the number outside the bracket with the second term inside the bracket."
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for ascending quadratic sequences in the form x² + bx + c \\[\n-1,4,11,20,31, \\ldots\n\\]\n\nWhen calculating the nth-term rule of this sequence, what should replace the square? nth-term rule:\n\\(\nn^{2}+2 n \\) \\(\\square\\)\n \\[\n+0\n\\]\n(no number term)"
},
{
"from": "gpt",
"value": "Mixes up term in a sequence and position of a term"
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for ascending quadratic sequences in the form x² + bx + c \\[\n-1,4,11,20,31, \\ldots\n\\]\n\nWhen calculating the nth-term rule of this sequence, what should replace the square? nth-term rule:\n\\(\nn^{2}+2 n \\) \\(\\square\\)\n \\( -6 \\)"
},
{
"from": "gpt",
"value": "Uses only the first two terms of a sequence to work out a term-to-term rule"
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for ascending quadratic sequences in the form x² + bx + c \\[\n-1,4,11,20,31, \\ldots\n\\]\n\nWhen calculating the nth-term rule of this sequence, what should replace the square? nth-term rule:\n\\(\nn^{2}+2 n \\) \\(\\square\\)\n \\( +4 \\)"
},
{
"from": "gpt",
"value": "Believes subtraction is commutative "
}
] |
[
{
"from": "human",
"value": "Use perimeter to write algebraic expressions What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length a and side length b]() \\( a b \\)"
},
{
"from": "gpt",
"value": "When calculating perimeter, multiplies instead of adds"
}
] |
[
{
"from": "human",
"value": "Use perimeter to write algebraic expressions What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length a and side length b]() \\( a+b \\)"
},
{
"from": "gpt",
"value": "When calculating perimeter, only adds the marked lengths"
}
] |
[
{
"from": "human",
"value": "Use perimeter to write algebraic expressions What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length a and side length b]() Not enough information"
},
{
"from": "gpt",
"value": "Fails to use the properties of simple shapes to work out missing lengths"
}
] |
[
{
"from": "human",
"value": "Identify reflex angles An angle measures \\( 212^{\\degree} \\). This means it is... Obtuse"
},
{
"from": "gpt",
"value": "Does not understand that an obtuse angle is between 90 and 180 degrees"
}
] |
[
{
"from": "human",
"value": "Identify reflex angles An angle measures \\( 212^{\\degree} \\). This means it is... Acute"
},
{
"from": "gpt",
"value": "Does not understand that an acute angle is between 0 and 90 degrees"
}
] |
[
{
"from": "human",
"value": "Identify reflex angles An angle measures \\( 212^{\\degree} \\). This means it is... A right angle"
},
{
"from": "gpt",
"value": "Does not know that a right angle is 90 degrees"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles What type of angles are highlighted in this diagram? ![The diagram is of a pair of parallel lines with a line crossing them. The two highlighted angles each have a parallel line above it and the transverse line to the left of it.]() alternate angles"
},
{
"from": "gpt",
"value": "Confuses corresponding and alternate angles"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles What type of angles are highlighted in this diagram? ![The diagram is of a pair of parallel lines with a line crossing them. The two highlighted angles each have a parallel line above it and the transverse line to the left of it.]() co-interior angles"
},
{
"from": "gpt",
"value": "Confuses co-interior and corresponding angles"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles What type of angles are highlighted in this diagram? ![The diagram is of a pair of parallel lines with a line crossing them. The two highlighted angles each have a parallel line above it and the transverse line to the left of it.]() opposite angles"
},
{
"from": "gpt",
"value": "Confuses corresponding and vertically opposite angles"
}
] |
[
{
"from": "human",
"value": "Identify the line of symmetry of curves in the form (x + a)(x + b) This is the graph of\n\\(y=(x+1)(x-3)\\) ![A set of axes with the graph y=(x+1)(x-3) drawn on.]() What is the equation of the line of symmetry? \\( y=-3 \\)"
},
{
"from": "gpt",
"value": "Confuses the y-intercept with the turning point of a curve"
}
] |
[
{
"from": "human",
"value": "Identify the line of symmetry of curves in the form (x + a)(x + b) This is the graph of\n\\(y=(x+1)(x-3)\\) ![A set of axes with the graph y=(x+1)(x-3) drawn on.]() What is the equation of the line of symmetry? \\( x=-3 \\)"
},
{
"from": "gpt",
"value": "Confuses the y-intercept with the turning point of a curve"
}
] |
[
{
"from": "human",
"value": "Identify the line of symmetry of curves in the form (x + a)(x + b) This is the graph of\n\\(y=(x+1)(x-3)\\) ![A set of axes with the graph y=(x+1)(x-3) drawn on.]() What is the equation of the line of symmetry? \\( y=1 \\)"
},
{
"from": "gpt",
"value": "Confuses the equations of vertical and horizontal lines"
}
] |
[
{
"from": "human",
"value": "Recognise that a sequence is quadratic when expressed as a pattern Which of the following is the best way to describe this sequence: ![First three patterns in a sequence. They are all rectangles made up of small squares. Pattern 1 is three small squares on top of one another, so the dimensions of the rectangle are 1 across and 3 up. Pattern 2 is a rectangle of dimensions 2 squares across and 6 up. Pattern 3 is a rectangle of dimensions 3 squares across and 9 squares up.]() Linear"
},
{
"from": "gpt",
"value": "Does not recognise that a linear sequence must increase or decrease by same amount"
}
] |
[
{
"from": "human",
"value": "Recognise that a sequence is quadratic when expressed as a pattern Which of the following is the best way to describe this sequence: ![First three patterns in a sequence. They are all rectangles made up of small squares. Pattern 1 is three small squares on top of one another, so the dimensions of the rectangle are 1 across and 3 up. Pattern 2 is a rectangle of dimensions 2 squares across and 6 up. Pattern 3 is a rectangle of dimensions 3 squares across and 9 squares up.]() Geometric"
},
{
"from": "gpt",
"value": "Does not understand the term quadratic"
}
] |
[
{
"from": "human",
"value": "Recognise that a sequence is quadratic when expressed as a pattern Which of the following is the best way to describe this sequence: ![First three patterns in a sequence. They are all rectangles made up of small squares. Pattern 1 is three small squares on top of one another, so the dimensions of the rectangle are 1 across and 3 up. Pattern 2 is a rectangle of dimensions 2 squares across and 6 up. Pattern 3 is a rectangle of dimensions 3 squares across and 9 squares up.]() Fibonacci"
},
{
"from": "gpt",
"value": "Does not know what a Fibonacci sequence is"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving three or more linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-z+3 y\\) \\( 6 x-y-z \\)"
},
{
"from": "gpt",
"value": "When collecting like terms, assigns positivity or negativity incorrectly."
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving three or more linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-z+3 y\\) \\( 6 x-5 y-z \\)"
},
{
"from": "gpt",
"value": "When collecting like terms, assigns positivity or negativity incorrectly."
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving three or more linear variables Simplify the following expression by collecting\nlike terms\n\\(6 x-2 y-z+3 y\\) Does not simplify"
},
{
"from": "gpt",
"value": "Does not understand when like terms can be collected"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally I increase \\( £ 150 \\) by \\( 60 \\% \\).\nThen, I increase the new amount by \\( 10 \\% \\).\nWhat percentage of the original amount do I have now? \\( 170 \\% \\)"
},
{
"from": "gpt",
"value": "Has taken the percentage from the original "
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally I increase \\( £ 150 \\) by \\( 60 \\% \\).\nThen, I increase the new amount by \\( 10 \\% \\).\nWhat percentage of the original amount do I have now? \\( 166 \\% \\)"
},
{
"from": "gpt",
"value": "Has taken the percentage from the original "
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally I increase \\( £ 150 \\) by \\( 60 \\% \\).\nThen, I increase the new amount by \\( 10 \\% \\).\nWhat percentage of the original amount do I have now? \\( 264 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks they had to give the new amount rather than the total percentage that the original has been increased by."
}
] |
[
{
"from": "human",
"value": "Generate an ascending quadratic sequence from the nth term rule in the form ax² + bx + c Find the first \\( 2 \\) numbers in the sequence using the \\( n \\)th term \\( 4 n^{2}+2 n-5 \\) \\( 13,63 \\)"
},
{
"from": "gpt",
"value": "When squaring a variable, believes they also need to square the coefficient"
}
] |
[
{
"from": "human",
"value": "Use the properties of an equilateral triangle to find missing lengths Triangle \\( A B C \\) is an equilateral triangle. Find length \\(AC\\). ![A triangle with vertices labelled A, B, C. Side BC is 8cm, side AC is labelled with a question mark.]() \\( 7 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of equilateral"
}
] |
[
{
"from": "human",
"value": "Use the properties of an equilateral triangle to find missing lengths Triangle \\( A B C \\) is an equilateral triangle. Find length \\(AC\\). ![A triangle with vertices labelled A, B, C. Side BC is 8cm, side AC is labelled with a question mark.]() \\( 90 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of equilateral"
}
] |
[
{
"from": "human",
"value": "Use the properties of an equilateral triangle to find missing lengths Triangle \\( A B C \\) is an equilateral triangle. Find length \\(AC\\). ![A triangle with vertices labelled A, B, C. Side BC is 8cm, side AC is labelled with a question mark.]() \\( 60 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of equilateral"
}
] |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis \\(\ny=x^{2}-10 x+25\n\\)\n\nWhere does this curve intercept the \\( x \\) axis? \\( (-5,0) \\)"
},
{
"from": "gpt",
"value": "Believes the solutions of a quadratic equation are the constants in the factorised form"
}
] |
[
{
"from": "human",
"value": "Describe how many degrees you would turn, and in what direction, to move between North-West, North-East, South-West and South-East Ada turns clockwise from facing \\( \\mathrm{NW} \\) to facing \\( \\mathrm{S} \\)\n\nHow many degrees has Ada turned? ![A image of a compass.]() \\( 135^{\\degree} \\)"
},
{
"from": "gpt",
"value": "Mixes up clockwise and anticlockwise"
}
] |
[
{
"from": "human",
"value": "Describe a reflection in a diagonal line by giving the line of reflection as an equation, where the line of reflection lies on the edge or outside the object Which line gives the reflection of shape \\( P \\) onto shape Q? ![A coordinate grid with two right angled triangles drawn, labelled P and Q. P has the coordinates: (2,5) (2,8) and (4,5). Q has the coordinates: (5,2) (8,2) and (5,4).]() \\( y=4.5 \\)"
},
{
"from": "gpt",
"value": "Believes lines of reflection must be vertical or horizontal"
}
] |
[
{
"from": "human",
"value": "Describe a reflection in a diagonal line by giving the line of reflection as an equation, where the line of reflection lies on the edge or outside the object Which line gives the reflection of shape \\( P \\) onto shape Q? ![A coordinate grid with two right angled triangles drawn, labelled P and Q. P has the coordinates: (2,5) (2,8) and (4,5). Q has the coordinates: (5,2) (8,2) and (5,4).]() \\( y=-x \\)"
},
{
"from": "gpt",
"value": "Confuses the lines y=x and y=-x"
}
] |
[
{
"from": "human",
"value": "Describe a reflection in a diagonal line by giving the line of reflection as an equation, where the line of reflection lies on the edge or outside the object Which line gives the reflection of shape \\( P \\) onto shape Q? ![A coordinate grid with two right angled triangles drawn, labelled P and Q. P has the coordinates: (2,5) (2,8) and (4,5). Q has the coordinates: (5,2) (8,2) and (5,4).]() This is not a reflection"
},
{
"from": "gpt",
"value": "Believes lines of reflection must be vertical or horizontal"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 2 decimal place to percentages What is \\( 0.07 \\) written as a percentage? \\( 0.07 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks you need to just add a % sign to a decimal to convert to a percentage"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 2 decimal place to percentages What is \\( 0.07 \\) written as a percentage? \\( 70 \\% \\)"
},
{
"from": "gpt",
"value": "Believes a decimal with one significant figure is a multiple of 10 when converted to a percentage, regardless of place value"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 2 decimal place to percentages What is \\( 0.07 \\) written as a percentage? \\( 0.7 \\% \\)"
},
{
"from": "gpt",
"value": "Multiplies by 10 instead of 100 when converting decimal to percentage"
}
] |
[
{
"from": "human",
"value": "Answer fraction problems that require the use of BIDMAS \\( \\frac{1}{4} \\times\\left(\\frac{2}{3}\\right)^{2}= \\) \\( \\frac{1}{6} \\)"
},
{
"from": "gpt",
"value": "Believes squaring a fraction requires you to double both parts"
}
] |
[
{
"from": "human",
"value": "Round numbers to an appropriate degree to estimate the answer to a calculation Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct\n\\[\n397 \\div 209\n\\] \\( 1.332 \\ldots \\)"
},
{
"from": "gpt",
"value": "Rounds every number up when estimating"
}
] |
[
{
"from": "human",
"value": "Round numbers to an appropriate degree to estimate the answer to a calculation Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct\n\\[\n397 \\div 209\n\\] \\( 1.533 \\ldots \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Identify perpendicular lines written in any other form Which of the following lines is perpendicular to x = -10 ? \\(x=-10\\)"
},
{
"from": "gpt",
"value": "Does not know the meaning of perpendicular"
}
] |
[
{
"from": "human",
"value": "Identify perpendicular lines written in any other form Which of the following lines is perpendicular to x = -10 ? \\( x=-\\frac{1}{10} \\)"
},
{
"from": "gpt",
"value": "Thinks that in the equation x=a, a is the gradient"
}
] |
[
{
"from": "human",
"value": "Divide two decimals with the same number of decimal places \\( 0.4 \\div 0.8= \\) \\( 0.4 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of divides"
}
] |
[
{
"from": "human",
"value": "Divide two decimals with the same number of decimal places \\( 0.4 \\div 0.8= \\) \\( 2 \\)"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Divide two decimals with the same number of decimal places \\( 0.4 \\div 0.8= \\) \\( 0.32 \\)"
},
{
"from": "gpt",
"value": "Multiplies rather than divides"
}
] |
[
{
"from": "human",
"value": "Calculate the distance travelled using a speed-time graph Here is a speed-time graph for a car.\n\nWhich of the following gives the best estimate for the distance travelled between \\( 8 \\) and \\( 10 \\) seconds? ![A graph showing time in seconds on the x axis and speed in metres per second on the y axis. The curve passes through the points (8,15) and (10,24)]() \\( 48 m \\)"
},
{
"from": "gpt",
"value": "Believes that when finding area under graph you can use the upper y value rather than average of upper and lower"
}
] |
[
{
"from": "human",
"value": "Calculate the distance travelled using a speed-time graph Here is a speed-time graph for a car.\n\nWhich of the following gives the best estimate for the distance travelled between \\( 8 \\) and \\( 10 \\) seconds? ![A graph showing time in seconds on the x axis and speed in metres per second on the y axis. The curve passes through the points (8,15) and (10,24)]() \\( 120 m \\)"
},
{
"from": "gpt",
"value": "Does not understand that area under a speed time graph gives distance because distance = speed x time"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(2 y-3)^{2}\n\\) \\( (2 y-3)(2 y-3) \\)"
},
{
"from": "gpt",
"value": "Believes expanding a squared expression means writing it as a set of double brackets"
}
] |
Subsets and Splits