conversations
listlengths 2
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|
|---|
[
{
"from": "human",
"value": "Represent an equation using a bar model Tom and Katie are discussing bar models. Tom says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l}\n\\hline \\( 5 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l|l|l|l|}\n\\( x \\) & \\( x \\) & \\( x \\) & \\( 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": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Tom and Katie are discussing regular polygons Tom says this is a regular polygon: ![A rhombus]() Katie says this is a regular polygon: ![A rectangle]() Who is correct? Only\nTom"
},
{
"from": "gpt",
"value": "Thinks that only the sides need to be equal for a polygon to be regular"
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Tom and Katie are discussing regular polygons Tom says this is a regular polygon: ![A rhombus]() Katie says this is a regular polygon: ![A rectangle]() Who is correct? Only Katie"
},
{
"from": "gpt",
"value": "Thinks that only the angles need to be the same for a polygon to be regular"
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons Tom and Katie are discussing regular polygons Tom says this is a regular polygon: ![A rhombus]() Katie says this is a regular polygon: ![A rectangle]() Who is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not understand that all angles and sides must be equal for regular shapes"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for curves in the form y = x² + c This is a part of the table of values for the equation\n\\(\ny=x^{2}-1\n\\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 5 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 9 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for curves in the form y = x² + c This is a part of the table of values for the equation\n\\(\ny=x^{2}-1\n\\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 5 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 16 \\)"
},
{
"from": "gpt",
"value": "Believes order of operations does not affect the answer to a calculation"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Mo wants to solve this equation using the quadratic formula.\n\\(\n5 h^{2}-3 h-2=0\n\\)\n\nWhat total should replace the square? \\( \\begin{array}{l} \\frac{ ?\\pm \\sqrt{9-(-40)}}{?} \\\\ = \\frac{ ?\\pm \\sqrt{\\square}}{?} \\end{array} \\) \\( -49 \\)"
},
{
"from": "gpt",
"value": "When subtracting a negative number, adds the absolute values and then writes the answer with a negative sign"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Mo wants to solve this equation using the quadratic formula.\n\\(\n5 h^{2}-3 h-2=0\n\\)\n\nWhat total should replace the square? \\( \\begin{array}{l} \\frac{ ?\\pm \\sqrt{9-(-40)}}{?} \\\\ = \\frac{ ?\\pm \\sqrt{\\square}}{?} \\end{array} \\) \\( -31 \\)"
},
{
"from": "gpt",
"value": "When subtracting a negative number, subtracts the absolute value rather than adding it"
}
] |
[
{
"from": "human",
"value": "Use common conventions for labelling the sides of shapes Which of the following is a correct way to describe the highlighted side of this shape? ![A 4 sided shape with two pairs of parallel sides. Each vertex (corner) is labelled with a letter. The bottom right is S, the bottom left is P, the top left is Q and the top right is R. The side joining P and Q is highlighted in red.]() \\( Q \\)"
},
{
"from": "gpt",
"value": "Does not know that a single letter labels a vertex"
}
] |
[
{
"from": "human",
"value": "Use common conventions for labelling the sides of shapes Which of the following is a correct way to describe the highlighted side of this shape? ![A 4 sided shape with two pairs of parallel sides. Each vertex (corner) is labelled with a letter. The bottom right is S, the bottom left is P, the top left is Q and the top right is R. The side joining P and Q is highlighted in red.]() P"
},
{
"from": "gpt",
"value": "Does not know that a single letter labels a vertex"
}
] |
[
{
"from": "human",
"value": "Use common conventions for labelling the sides of shapes Which of the following is a correct way to describe the highlighted side of this shape? ![A 4 sided shape with two pairs of parallel sides. Each vertex (corner) is labelled with a letter. The bottom right is S, the bottom left is P, the top left is Q and the top right is R. The side joining P and Q is highlighted in red.]() QPRS"
},
{
"from": "gpt",
"value": "Does not know the correct notation for labelling a side length"
}
] |
[
{
"from": "human",
"value": "Multiply algebraic terms, involving non-linear versions of different letters (e.g. 4a2 x 5ab) \\( 5 p^{2} \\times 2 p q \\equiv \\) \\( 7 p^{3} q \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies when multiplying algebraic terms"
}
] |
[
{
"from": "human",
"value": "Multiply algebraic terms, involving non-linear versions of different letters (e.g. 4a2 x 5ab) \\( 5 p^{2} \\times 2 p q \\equiv \\) Does not simplify"
},
{
"from": "gpt",
"value": "Does not understand how to multiply algebraic terms"
}
] |
[
{
"from": "human",
"value": "Interpret and carry out mental division using a bar model Tom and Katie are discussing this bar model ![A comparison bar model showing 188 is the same as four lots of 47]() Tom uses the bar model to write:\n\\[\n188 \\div 4=47\n\\] Katie uses the bar model to write:\n\\[\n188 \\div 47=4\n\\] Who do you agree with? Only Tom"
},
{
"from": "gpt",
"value": "Does not know how to use a bar model to write division facts"
}
] |
[
{
"from": "human",
"value": "Interpret and carry out mental division using a bar model Tom and Katie are discussing this bar model ![A comparison bar model showing 188 is the same as four lots of 47]() Tom uses the bar model to write:\n\\[\n188 \\div 4=47\n\\] Katie uses the bar model to write:\n\\[\n188 \\div 47=4\n\\] Who do you agree with? Only Katie"
},
{
"from": "gpt",
"value": "Does not know how to use a bar model to write division facts"
}
] |
[
{
"from": "human",
"value": "Interpret and carry out mental division using a bar model Tom and Katie are discussing this bar model ![A comparison bar model showing 188 is the same as four lots of 47]() Tom uses the bar model to write:\n\\[\n188 \\div 4=47\n\\] Katie uses the bar model to write:\n\\[\n188 \\div 47=4\n\\] Who do you agree with? Neither is correct"
},
{
"from": "gpt",
"value": "Does not know how to use a bar model to write division facts"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are multiples of the same number \\begin{tabular}{llllll}\n\\( \\frac{2}{10} \\) & \\( \\frac{9}{50} \\) & \\( \\frac{9}{20} \\) & \\( 0.21 \\) & \\( \\frac{1}{5} \\) & \\( \\frac{19}{100} \\) \\\\\n\\hline\n\\end{tabular} Which value is the outlier in this set of data? \\( \\frac{2}{10} \\)"
},
{
"from": "gpt",
"value": "Believes an outlier is a value that does not fit the same characteristics as the other values"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are multiples of the same number \\begin{tabular}{llllll}\n\\( \\frac{2}{10} \\) & \\( \\frac{9}{50} \\) & \\( \\frac{9}{20} \\) & \\( 0.21 \\) & \\( \\frac{1}{5} \\) & \\( \\frac{19}{100} \\) \\\\\n\\hline\n\\end{tabular} Which value is the outlier in this set of data? \\( \\frac{19}{100} \\)"
},
{
"from": "gpt",
"value": "Believes an outlier is the value in a data set with the biggest denominator, even if this value is close to the mean"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are multiples of the same number \\begin{tabular}{llllll}\n\\( \\frac{2}{10} \\) & \\( \\frac{9}{50} \\) & \\( \\frac{9}{20} \\) & \\( 0.21 \\) & \\( \\frac{1}{5} \\) & \\( \\frac{19}{100} \\) \\\\\n\\hline\n\\end{tabular} Which value is the outlier in this set of data? \\( 0.21 \\)"
},
{
"from": "gpt",
"value": "Believes an outlier is a value that does not fit the same characteristics as the other values"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point, split into 2 parts. One is labelled 310 degrees and the other x.]() \\( 310^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Incorrectly identifies angles as vertically opposite"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point, split into 2 parts. One is labelled 310 degrees and the other x.]() \\( 90^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Does not know that angles around a point sum to 360"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles around a point What is the size of angle \\( x \\) ? ![Angles around a point, split into 2 parts. One is labelled 310 degrees and the other x.]() \\( 45^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Estimates angle rather than calculating"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as simply as possible:\n\\(\n\\frac{(x+3)(x+5)}{(x+3)(x+10)}\n\\) \\( \\frac{x+1}{x+2} \\)"
},
{
"from": "gpt",
"value": "Misunderstands the concept of common factors in algebra"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as simply as possible:\n\\(\n\\frac{(x+3)(x+5)}{(x+3)(x+10)}\n\\) \\( \\frac{x^{2}+8 x+15}{x^{2}+13 x+30} \\)"
},
{
"from": "gpt",
"value": "Expands when asked to simplify"
}
] |
[
{
"from": "human",
"value": "Calculate the surface area of a cuboid where the dimensions are given in the same units Which of the following calculations would give you the total surface area of this cuboid in \\( \\mathrm{cm}^{2} \\) ? ![A cuboid. The height is 4cm, the depth is 3cm and the width is 6cm.]() \\( (6 \\times 4)+(6 \\times 3)+(4 \\times 3) \\)"
},
{
"from": "gpt",
"value": "When calculating surface area, only includes visible faces"
}
] |
[
{
"from": "human",
"value": "Calculate the surface area of a cuboid where the dimensions are given in the same units Which of the following calculations would give you the total surface area of this cuboid in \\( \\mathrm{cm}^{2} \\) ? ![A cuboid. The height is 4cm, the depth is 3cm and the width is 6cm.]() \\( 6 \\times 4 \\times 3 \\)"
},
{
"from": "gpt",
"value": "Finds volume when asked for surface area"
}
] |
[
{
"from": "human",
"value": "Calculate the surface area of a cuboid where the dimensions are given in the same units Which of the following calculations would give you the total surface area of this cuboid in \\( \\mathrm{cm}^{2} \\) ? ![A cuboid. The height is 4cm, the depth is 3cm and the width is 6cm.]() \\( (6 \\times 4) \\times(6 \\times 3) \\times(4 \\times 3) \\)"
},
{
"from": "gpt",
"value": "When calculating surface area, only includes visible faces"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving brackets \\[\n1+2 \\times(3-4)=\n\\]\n\nWhich calculation should you do first? \\( 1+2 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving brackets \\[\n1+2 \\times(3-4)=\n\\]\n\nWhich calculation should you do first? \\( 2 \\times 3 \\)"
},
{
"from": "gpt",
"value": "Answers order of operations questions with brackets as if the brackets are not there"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving brackets \\[\n1+2 \\times(3-4)=\n\\]\n\nWhich calculation should you do first? It doesn't matter: you get the same answer"
},
{
"from": "gpt",
"value": "Believes order of operations does not affect the answer to a calculation"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear equations requiring multiplication or division, involving positive fractions Solve the equation:\n\\(\n5 p=\\frac{1}{10}\n\\) \\( p=\\frac{1}{2} \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division Problem P: \\( 4-5+6= \\)\nProblem Q: \\( 4+5 \\times 6= \\)\n\nWhich calculation should you do first in each problem? Problem P: \\( 4-5 \\)\nProblem Q: \\( 4+5 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division Problem P: \\( 4-5+6= \\)\nProblem Q: \\( 4+5 \\times 6= \\)\n\nWhich calculation should you do first in each problem? Problem P: \\( 5+6 \\)\nProblem Q: \\( 4+5 \\)"
},
{
"from": "gpt",
"value": "Performs addition ahead of any other operation"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division Problem P: \\( 4-5+6= \\)\nProblem Q: \\( 4+5 \\times 6= \\)\n\nWhich calculation should you do first in each problem? Problem P: \\( 5+6 \\)\nProblem Q: \\( 5 \\times 6 \\)"
},
{
"from": "gpt",
"value": "Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)"
}
] |
[
{
"from": "human",
"value": "Use the nth term rule of an ascending integer linear sequence to test whether a term belongs in the sequence or not Eliza is trying to work out if \\( 82 \\) is a term in the sequence \\( 3 n+1 \\)\n\nBelow is her working out. What conclusion should Eliza draw?\n\n \\( \\begin{aligned} 3 n+1 & =82 \\\\ 3 n & =81 \\\\ n & =27\\end{aligned} \\) \\( 27 \\) is in the sequence and is the \\( 82^{\\text {nd }} \\) term"
},
{
"from": "gpt",
"value": "Mixes up term in a sequence and position of a term"
}
] |
[
{
"from": "human",
"value": "Use the nth term rule of an ascending integer linear sequence to test whether a term belongs in the sequence or not Eliza is trying to work out if \\( 82 \\) is a term in the sequence \\( 3 n+1 \\)\n\nBelow is her working out. What conclusion should Eliza draw?\n\n \\( \\begin{aligned} 3 n+1 & =82 \\\\ 3 n & =81 \\\\ n & =27\\end{aligned} \\) \\( 82 \\) is not in the sequence because \\( 27 \\) is an integer"
},
{
"from": "gpt",
"value": "Believes the position of a sequence cannot be an integer"
}
] |
[
{
"from": "human",
"value": "Use the nth term rule of an ascending integer linear sequence to test whether a term belongs in the sequence or not Eliza is trying to work out if \\( 82 \\) is a term in the sequence \\( 3 n+1 \\)\n\nBelow is her working out. What conclusion should Eliza draw?\n\n \\( \\begin{aligned} 3 n+1 & =82 \\\\ 3 n & =81 \\\\ n & =27\\end{aligned} \\) Eliza's method does not answer this question"
},
{
"from": "gpt",
"value": "Does not know how to calculate the position of a term in a sequence"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{t^{2}+2 t+1}{t+1} \\) \\( t+2 \\)"
},
{
"from": "gpt",
"value": "Incorrectly cancels what they believe is a factor in algebraic fractions"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{t^{2}+2 t+1}{t+1} \\) \\( t^{2}+t \\)"
},
{
"from": "gpt",
"value": "Simplifies a fraction by adding or subtracting the same amount from the numerator and denominator"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{t^{2}+2 t+1}{t+1} \\) Does not simplify"
},
{
"from": "gpt",
"value": "Does not recognise factorising a quadratic"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Fraction Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 2 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]() \\( \\frac{2}{5} \\times \\frac{1}{2} \\)"
},
{
"from": "gpt",
"value": "Does not understand parts must be equal in a fraction diagram"
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Fraction Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 2 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]() \\( \\frac{1}{4} \\div \\frac{1}{2} \\)"
},
{
"from": "gpt",
"value": "Divides rather than multiplies "
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Fraction Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 2 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]() \\( \\frac{2}{5} \\div 2 \\)"
},
{
"from": "gpt",
"value": "Does not understand parts must be equal in a fraction diagram"
}
] |
[
{
"from": "human",
"value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE. D lies 1/3 from C on the line CE and is connected to A by a line. Attached to the square at line CE is a pentagon CEFGH. G is connected to C and E by lines. The angle highlighted is the entire, interior angle at E.]() EFA"
},
{
"from": "gpt",
"value": "Gives 3-letter angle notation in the wrong order"
}
] |
[
{
"from": "human",
"value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE. D lies 1/3 from C on the line CE and is connected to A by a line. Attached to the square at line CE is a pentagon CEFGH. G is connected to C and E by lines. The angle highlighted is the entire, interior angle at E.]() E"
},
{
"from": "gpt",
"value": "Gives the vertex instead of the 3-letter angle notation"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Jo and Paul are arguing about the best way to count the number of squares in Pattern \\( 15 \\).\nJo does: \\( 15 \\times 3+4 \\)\nPaul does: \\( (15+2) \\times 3-4 \\)\nWho is correct? ![The 3rd and 4th terms in a sequence of patterns. Each pattern is made from red squares. Pattern 3 is 11 squares: they are arranged as a rectangle, 3 squares high and 3 squares wide and then 2 more squares, 1 each side of the middle squares (vertically). Pattern 4 is 14 squares arranged as a rectangle, 3 squares high and 4 squares wide and then 2 more squares, 1 each side of the middle squares.]() Only Jo"
},
{
"from": "gpt",
"value": "Believes nth term rules for patterns must be given in standard an + b form"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Jo and Paul are arguing about the best way to count the number of squares in Pattern \\( 15 \\).\nJo does: \\( 15 \\times 3+4 \\)\nPaul does: \\( (15+2) \\times 3-4 \\)\nWho is correct? ![The 3rd and 4th terms in a sequence of patterns. Each pattern is made from red squares. Pattern 3 is 11 squares: they are arranged as a rectangle, 3 squares high and 3 squares wide and then 2 more squares, 1 each side of the middle squares (vertically). Pattern 4 is 14 squares arranged as a rectangle, 3 squares high and 4 squares wide and then 2 more squares, 1 each side of the middle squares.]() Neither is correct"
},
{
"from": "gpt",
"value": "Believes nth term rules for patterns must be given in standard an + b form"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention involving powers Simplify, if possible:\n\\(\na^{2} \\times a\n\\) \\( 2 a^{2} \\)"
},
{
"from": "gpt",
"value": "Does not understand how to multiply algebraic terms"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention involving powers Simplify, if possible:\n\\(\na^{2} \\times a\n\\) \\( 3 a \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention involving powers Simplify, if possible:\n\\(\na^{2} \\times a\n\\) Does not simplify"
},
{
"from": "gpt",
"value": "Does not understand how to multiply algebraic terms"
}
] |
[
{
"from": "human",
"value": "Carry out multiplication problems involving one negative integer \\( 3 \\times(-5)= \\) \\( 15 \\)"
},
{
"from": "gpt",
"value": "When multiplying with negative numbers, assumes any negative sign can be ignored"
}
] |
[
{
"from": "human",
"value": "Convert the reminders from written division problems into decimals John has been asked to work out the answer to:\n\\[\n232 \\div 5\n\\]\nHe gets the answer \\( 46 \\) remainder \\( 2 \\)\nWhat is the exact value of that remainder? \\( 0.2 \\)"
},
{
"from": "gpt",
"value": "Writes the remainder as the digit after the decimal point"
}
] |
[
{
"from": "human",
"value": "Convert the reminders from written division problems into decimals John has been asked to work out the answer to:\n\\[\n232 \\div 5\n\\]\nHe gets the answer \\( 46 \\) remainder \\( 2 \\)\nWhat is the exact value of that remainder? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Does not understand remainders in division"
}
] |
[
{
"from": "human",
"value": "Convert the reminders from written division problems into decimals John has been asked to work out the answer to:\n\\[\n232 \\div 5\n\\]\nHe gets the answer \\( 46 \\) remainder \\( 2 \\)\nWhat is the exact value of that remainder? \\( 0.25 \\)"
},
{
"from": "gpt",
"value": "Does not understand remainders in division"
}
] |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms STEP \\( 1 \\)\nWhich of the options is a correct first step to express the following as a single fraction?\n\\(\n\\frac{3}{x-2}-\\frac{5}{x}\n\\) \\( \\frac{3-5}{x-2-x} \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms STEP \\( 1 \\)\nWhich of the options is a correct first step to express the following as a single fraction?\n\\(\n\\frac{3}{x-2}-\\frac{5}{x}\n\\) \\( \\frac{3(x-2)}{x(x-2)}-\\frac{5 x}{x(x-2)} \\)"
},
{
"from": "gpt",
"value": "Does not understand how to maintain equivalence in fractions"
}
] |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are linear expressions, eg (x + 5) and (x - 3), and the numerators are single terms STEP \\( 1 \\)\nWhich of the options is a correct first step to express the following as a single fraction?\n\\(\n\\frac{3}{x-2}-\\frac{5}{x}\n\\) \\( 9 x-5(x-2) \\)"
},
{
"from": "gpt",
"value": "Removes the common denominator when making equivalent algebraic fractions"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to two significant figures Which of the numbers is the same when rounded to \\( 2 \\) decimal places or to \\( 2 \\) significant figures? \\( 23.725 \\)"
},
{
"from": "gpt",
"value": "Rounds to wrong degree of accuracy (decimal places rather than significant figures)"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to two significant figures Which of the numbers is the same when rounded to \\( 2 \\) decimal places or to \\( 2 \\) significant figures? \\( 0.038 \\)"
},
{
"from": "gpt",
"value": "Does not understand the first significant value is the first non-zero digit number"
}
] |
[
{
"from": "human",
"value": "Round numbers between 0 and 1 to two significant figures Which of the numbers is the same when rounded to \\( 2 \\) decimal places or to \\( 2 \\) significant figures? \\( 0.0599 \\)"
},
{
"from": "gpt",
"value": "Does not understand the first significant value is the first non-zero digit number"
}
] |
[
{
"from": "human",
"value": "Add decimals with the same number of decimals places \\( 1.39+2.53= \\) \\( 4.01 \\)"
},
{
"from": "gpt",
"value": "When adding decimals, just adds the digits and ignores place value"
}
] |
[
{
"from": "human",
"value": "Add decimals with the same number of decimals places \\( 1.39+2.53= \\) \\( 3.812 \\)"
},
{
"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": "Add decimals with the same number of decimals places \\( 1.39+2.53= \\) \\( 3.82 \\)"
},
{
"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": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Which option gives a correct substitution into the quadratic formula to solve the quadratic equation?\n\n\\(\n3 x^{2}+2 x-5=0\n\\) \\( -2 \\pm \\frac{\\sqrt{2^{2}-4(3)(-5)}}{2(3)} \\)"
},
{
"from": "gpt",
"value": "Misremembers the quadratic formula"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Which option gives a correct substitution into the quadratic formula to solve the quadratic equation?\n\n\\(\n3 x^{2}+2 x-5=0\n\\) \\( 2 \\pm \\frac{\\sqrt{2^{2}-4(3)(-5)}}{2(3)} \\)"
},
{
"from": "gpt",
"value": "Misremembers the quadratic formula"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Which option gives a correct substitution into the quadratic formula to solve the quadratic equation?\n\n\\(\n3 x^{2}+2 x-5=0\n\\) \\( \\frac{2 \\pm \\sqrt{2^{2}-4(3)(-5)}}{2(3)} \\)"
},
{
"from": "gpt",
"value": "Misremembers the quadratic formula"
}
] |
[
{
"from": "human",
"value": "Divide two decimals with the same number of decimal places What should replace the star?\n\\(\n0.3 \\div \\bigstar=1.2\n\\) \\( 4 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, multiplies instead of dividing "
}
] |
[
{
"from": "human",
"value": "Divide two decimals with the same number of decimal places What should replace the star?\n\\(\n0.3 \\div \\bigstar=1.2\n\\) \\( 0.9 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, adds instead of dividing"
}
] |
[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units What is the area of this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled 10 cm, 7 cm, 3 cm and 4 cm. Two sides are unlabelled]() \\( 840 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Multiplies all given dimensions when calculating an area"
}
] |
[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units What is the area of this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled 10 cm, 7 cm, 3 cm and 4 cm. Two sides are unlabelled]() \\( 52 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Makes an assumption about line segments being equal within a shape"
}
] |
[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units What is the area of this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled 10 cm, 7 cm, 3 cm and 4 cm. Two sides are unlabelled]() \\( 51 \\mathrm{~cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Uses an incorrect side length when splitting a composite shape into parts"
}
] |
[
{
"from": "human",
"value": "Expand two brackets with linear terms in the form (ax + b)(cx + d) Alison is expanding these two brackets.\n\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the 5p in the first bracket and the -3 in the second bracket.]() \\( +15 p \\)"
},
{
"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)(cx + d) Alison is expanding these two brackets.\n\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the 5p in the first bracket and the -3 in the second bracket.]() \\( +2 p \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplying when expanding bracket"
}
] |
[
{
"from": "human",
"value": "Multiply a decimal by an integer Work out:\n\\[\n0.3 \\times 12\n\\] \\( 36 \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, ignores place value and just multiplies the digits"
}
] |
[
{
"from": "human",
"value": "Multiply a decimal by an integer Work out:\n\\[\n0.3 \\times 12\n\\] \\( 0.36 \\)"
},
{
"from": "gpt",
"value": "When multiplying a decimal less than 1 by an integer, gives an answer 10 times smaller than it should be"
}
] |
[
{
"from": "human",
"value": "Multiply a decimal by an integer Work out:\n\\[\n0.3 \\times 12\n\\] \\( 0.036 \\)"
},
{
"from": "gpt",
"value": "When multiplying a decimal less than 1 by an integer, gives an answer 100 times smaller than it should be"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² + bx + c Factorise \\( x^{2}+15 x+36 \\) Factorise \\( x^{2}+15 x+36 \\) \\( (x+4)(x+9) \\) \\( (x+4)(x+9) \\)"
},
{
"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}+15 x+36 \\) Factorise \\( x^{2}+15 x+36 \\) \\( (x+1)(x+36) \\) \\( (x+1)(x+36) \\)"
},
{
"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}+15 x+36 \\) Factorise \\( x^{2}+15 x+36 \\) \\( (x+7)(x+18) \\) \\( (x+7)(x+18) \\)"
},
{
"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": "Identify a kite from a description of the properties Which of the following quadrilaterals could not be classified as a kite? Square"
},
{
"from": "gpt",
"value": "Does not recognise the properties of a kite"
}
] |
[
{
"from": "human",
"value": "Identify a kite from a description of the properties Which of the following quadrilaterals could not be classified as a kite? Rhombus"
},
{
"from": "gpt",
"value": "Does not recognise the properties of a kite"
}
] |
[
{
"from": "human",
"value": "Identify a kite from a description of the properties Which of the following quadrilaterals could not be classified as a kite? None of them are kites"
},
{
"from": "gpt",
"value": "Does not believe a shape can have two correct names e.g. rectangle and parallelogram"
}
] |
[
{
"from": "human",
"value": "Identify the number of degrees in fractions of a turn How many degrees are there in \\( 1 \\frac{1}{4} \\) full turns? \\( 385^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Assumes a 1/4 of a whole is 25"
}
] |
[
{
"from": "human",
"value": "Identify the number of degrees in fractions of a turn How many degrees are there in \\( 1 \\frac{1}{4} \\) full turns? \\( 125^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes there are 100 degrees in a full turn"
}
] |
[
{
"from": "human",
"value": "Find a negative reciprocal \\( \\frac{2}{5} \\times \\star=-1 \\) What should replace the star? \\( -\\frac{2}{5} \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation"
}
] |
[
{
"from": "human",
"value": "Round non-integers to the nearest 10 What is \\( \\mathbf{9 9 9 . 9 9 9} \\) rounded to the nearest ten? \\( 990 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round non-integers to the nearest 10 What is \\( \\mathbf{9 9 9 . 9 9 9} \\) rounded to the nearest ten? \\( 100 \\)"
},
{
"from": "gpt",
"value": "When rounding up from a 9, does not add one on to the digit to the left"
}
] |
[
{
"from": "human",
"value": "Round non-integers to the nearest 10 What is \\( \\mathbf{9 9 9 . 9 9 9} \\) rounded to the nearest ten? \\( 900 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators where one is a multiple of the other Calculate:\n\\(\n\\frac{2}{9}+\\frac{1}{3}\n\\) \\( \\frac{3}{12} \\)"
},
{
"from": "gpt",
"value": "When adding fractions, adds the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators where one is a multiple of the other Calculate:\n\\(\n\\frac{2}{9}+\\frac{1}{3}\n\\) \\( \\frac{3}{9} \\)"
},
{
"from": "gpt",
"value": "Does not consider the denominator when adding/ subtracting fractions. Adds/subtracts the numerator and makes the denominator the one with the highest value."
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators where one is a multiple of the other Calculate:\n\\(\n\\frac{2}{9}+\\frac{1}{3}\n\\) \\( \\frac{1}{6} \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of adds"
}
] |
[
{
"from": "human",
"value": "Answer decimal problems that require the use of BIDMAS Tom and Katie are discussing the order of operations\nTom says: \\( 0.1-0.2 \\div 0.3 \\equiv 0.1-(0.2 \\div 0.3) \\)\nKatie says: \\( 0.1-0.2 \\div 0.3 \\equiv 0.2 \\div 0.3-0.1 \\)\nWho is correct? Only\nKatie"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Answer decimal problems that require the use of BIDMAS Tom and Katie are discussing the order of operations\nTom says: \\( 0.1-0.2 \\div 0.3 \\equiv 0.1-(0.2 \\div 0.3) \\)\nKatie says: \\( 0.1-0.2 \\div 0.3 \\equiv 0.2 \\div 0.3-0.1 \\)\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Performs subtraction right to left if priority order means doing a calculation to the right first"
}
] |
[
{
"from": "human",
"value": "Answer decimal problems that require the use of BIDMAS Tom and Katie are discussing the order of operations\nTom says: \\( 0.1-0.2 \\div 0.3 \\equiv 0.1-(0.2 \\div 0.3) \\)\nKatie says: \\( 0.1-0.2 \\div 0.3 \\equiv 0.2 \\div 0.3-0.1 \\)\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Subtract fractions involving mixed number fractions with different denominators \\(\n2 \\frac{2}{5}-\\frac{1}{15}=2 \\frac{1}{\\bigstar}\n\\)\nWhat should replace the star? \\( 10 \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Subtract fractions involving mixed number fractions with different denominators \\(\n2 \\frac{2}{5}-\\frac{1}{15}=2 \\frac{1}{\\bigstar}\n\\)\nWhat should replace the star? \\( 15 \\)"
},
{
"from": "gpt",
"value": "Forgot to simplify the fraction"
}
] |
[
{
"from": "human",
"value": "Subtract fractions involving mixed number fractions with different denominators \\(\n2 \\frac{2}{5}-\\frac{1}{15}=2 \\frac{1}{\\bigstar}\n\\)\nWhat should replace the star? \\( 5 \\)"
},
{
"from": "gpt",
"value": "Believes when simplifying a fraction you can divide the numerator and denominator by different values"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a positive integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{9}^{x} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 0 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 9 \\)"
},
{
"from": "gpt",
"value": "Forgotten that anything to the power of 0 equals 1"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a positive integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{9}^{x} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 0 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 0 \\)"
},
{
"from": "gpt",
"value": "Forgotten that anything to the power of 0 equals 1"
}
] |
[
{
"from": "human",
"value": "Calculate coordinates of points on the graph of y = ax, where x is a positive integer This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\mathbf{9}^{x} \\) \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 0 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? The equation is undefined at this value"
},
{
"from": "gpt",
"value": "Forgotten that anything to the power of 0 equals 1"
}
] |