bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.15 \\times 0.2= \\) \\( 0.003 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]
[ { "from": "human", "value": "Represent a linear inequality with a single tail on a numberline Which of the following diagrams represents \\( x \\leq 1 \\) ? ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is a filled in circle above 1, with an arrow pointing to the right coming off it.]()" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]
[ { "from": "human", "value": "Represent a linear inequality with a single tail on a numberline Which of the following diagrams represents \\( x \\leq 1 \\) ? ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is an empty circle above 1, with an arrow pointing to the left coming off it.]()" }, { "from": "gpt", "value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning." } ]
[ { "from": "human", "value": "Complete missing number mental addition problems up to 1000 What number belongs in the box to make the calculation correct? \\( 263+\\square=900 \\) \\( 1163 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]
[ { "from": "human", "value": "Complete missing number mental addition problems up to 1000 What number belongs in the box to make the calculation correct? \\( 263+\\square=900 \\) \\( 747 \\)" }, { "from": "gpt", "value": "Treats zero as a ten when subtracting" } ]
[ { "from": "human", "value": "Find missing angles in a scalene triangle What is the size of angle \\( k \\) ? ![A triangle with one angle of 40 degrees. One angle of 32 degrees and the third angle is labelled k. ]() \\( 90\\degree\\)" }, { "from": "gpt", "value": "Believes all triangles have a right angle" } ]
[ { "from": "human", "value": "Find missing angles in a scalene triangle What is the size of angle \\( k \\) ? ![A triangle with one angle of 40 degrees. One angle of 32 degrees and the third angle is labelled k. ]() \\( 118\\degree\\)" }, { "from": "gpt", "value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 4 \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nKatie says \\( y \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Does not know how to identify common factors from algebraic terms" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 4 \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nKatie says \\( y \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nWho is correct? Only\nKatie" }, { "from": "gpt", "value": "Does not know how to identify common factors from algebraic terms" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 4 \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nKatie says \\( y \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not know how to identify common factors from algebraic terms" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c When factorised, \\( 9 x^{2}-16 \\) will become... \\( 9 x(x-16) \\)" }, { "from": "gpt", "value": "Believes only the first term needs to be divided when factorising an expression" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c When factorised, \\( 9 x^{2}-16 \\) will become... \\( 3 x(3 x-16-) \\)" }, { "from": "gpt", "value": "Believes only the first term needs to be divided when factorising an expression" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c When factorised, \\( 9 x^{2}-16 \\) will become... \\( (3 x+4)(3 x+4) \\)" }, { "from": "gpt", "value": "Factorises difference of two squares with the same sign in both brackets" } ]
[ { "from": "human", "value": "Carry out division problems involving negative non-integers \\( \\frac{(-3) \\times(-2)}{(-0.2)}= \\) \\( -3 \\)" }, { "from": "gpt", "value": "When dividing a decimal by a whole number, ignores decimal point and just divides the digits" } ]
[ { "from": "human", "value": "Carry out division problems involving negative non-integers \\( \\frac{(-3) \\times(-2)}{(-0.2)}= \\) \\( 30 \\)" }, { "from": "gpt", "value": "Believes dividing 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) Molly is expanding these two brackets.\n\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The brackets shown are (2p-1)(3p-4). The arrows are pointing at the -1 in the first bracket and the -4 in the second bracket.]() \\( -4 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)(cx + d) Molly is expanding these two brackets.\n\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The brackets shown are (2p-1)(3p-4). The arrows are pointing at the -1 in the first bracket and the -4 in the second bracket.]() \\( -5 \\)" }, { "from": "gpt", "value": "Adds instead of multiplying when expanding bracket" } ]
[ { "from": "human", "value": "Find missing angles in an isosceles triangle What is the size of angle \\( w \\) ? ![An isosceles triangle with one of the base angles labelled with a w and the angle vertically opposite the vertex angle labelled with 27 degrees]() \\( 27^{\\degree} \\)" }, { "from": "gpt", "value": "Incorrectly identifies angles as vertically opposite" } ]
[ { "from": "human", "value": "Find missing angles in an isosceles triangle What is the size of angle \\( w \\) ? ![An isosceles triangle with one of the base angles labelled with a w and the angle vertically opposite the vertex angle labelled with 27 degrees]() \\( 54^{\\degree} \\)" }, { "from": "gpt", "value": "Does not know that vertically opposite angles are equal" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to two significant figures What is \\( \\mathbf{1 8 7 . 2 5 9} \\) rounded to two significant figures? \\( 180 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to two significant figures What is \\( \\mathbf{1 8 7 . 2 5 9} \\) rounded to two significant figures? \\( 187.26 \\)" }, { "from": "gpt", "value": "Rounds to wrong degree of accuracy (decimal places rather than significant figures)" } ]
[ { "from": "human", "value": "Multiply surds by an integer \\(9 \\times \\sqrt{3}\\)\n\nSimplify, if possible. \\( \\sqrt{12} \\)" }, { "from": "gpt", "value": "When multiplying a surd by an integer, adds the integer to the number under the surd" } ]
[ { "from": "human", "value": "Multiply surds by an integer \\(9 \\times \\sqrt{3}\\)\n\nSimplify, if possible. \\( \\sqrt{27} \\)" }, { "from": "gpt", "value": "When multiplying a surd by an integer, multiplies the integer with the number under the surd" } ]
[ { "from": "human", "value": "Multiply surds by an integer \\(9 \\times \\sqrt{3}\\)\n\nSimplify, if possible. Cannot be simplified" }, { "from": "gpt", "value": "Does not recognise that an integer multiplied by a surd can be simplified" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(3 y-4)^{2}\n\\) \\( 9 y^{2}-16 \\)" }, { "from": "gpt", "value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(3 y-4)^{2}\n\\) \\( 9 y^{2}+16 \\)" }, { "from": "gpt", "value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(3 y-4)^{2}\n\\) \\( (3 y-4)(3 y-4) \\)" }, { "from": "gpt", "value": "Believes expanding a squared expression means writing it as a set of double brackets" } ]
[ { "from": "human", "value": "Multiply a decimal by an integer Tom and Katie are discussing multiplying decimals.\n\nTom says \\( 5 \\times 3.9=3 \\times 5.9 \\)\n\nKatie says \\( 5 \\times 3.9=3.9 \\times 5 \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Does not correctly apply the commutative property of multiplication" } ]
[ { "from": "human", "value": "Multiply a decimal by an integer Tom and Katie are discussing multiplying decimals.\n\nTom says \\( 5 \\times 3.9=3 \\times 5.9 \\)\n\nKatie says \\( 5 \\times 3.9=3.9 \\times 5 \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not correctly apply the commutative property of multiplication" } ]
[ { "from": "human", "value": "Multiply a decimal by an integer Tom and Katie are discussing multiplying decimals.\n\nTom says \\( 5 \\times 3.9=3 \\times 5.9 \\)\n\nKatie says \\( 5 \\times 3.9=3.9 \\times 5 \\)\n\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Believes multiplication is not commutative" } ]
[ { "from": "human", "value": "Describe the properties of an isosceles triangle Which description describes an isosceles triangle? A triangle with one right angle." }, { "from": "gpt", "value": "Confuses isosceles and right angle triangles" } ]
[ { "from": "human", "value": "Describe the properties of an isosceles triangle Which description describes an isosceles triangle? A triangle with three sides of equal length and three equal angles." }, { "from": "gpt", "value": "Confuses isosceles and equilateral triangles" } ]
[ { "from": "human", "value": "Describe the properties of an isosceles triangle Which description describes an isosceles triangle? A triangle with no sides of equal length and no equal angles." }, { "from": "gpt", "value": "Confuses isosceles and scalene triangles" } ]
[ { "from": "human", "value": "Use brackets to write function machines as calculations Tom and Katie are arguing about the result of this Function Machine:\nTom says the output is: \\( 3 n-12 \\)\nKatie says the output is: \\( 3(n-4) \\)\nWho is correct? ![A function machine with input n and operations subtract 4, multiply by 3]() Only Tom" }, { "from": "gpt", "value": "Does not think a factorised expression is equivalent to its multiplied out form" } ]
[ { "from": "human", "value": "Use brackets to write function machines as calculations Tom and Katie are arguing about the result of this Function Machine:\nTom says the output is: \\( 3 n-12 \\)\nKatie says the output is: \\( 3(n-4) \\)\nWho is correct? ![A function machine with input n and operations subtract 4, multiply by 3]() Only\nKatie" }, { "from": "gpt", "value": "Does not think a factorised expression is equivalent to its multiplied out form" } ]
[ { "from": "human", "value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence?\n\\[\n4, \\quad 10, \\quad 28, \\quad 82, \\quad \\ldots\n\\] To get the next term you add \\( 6 \\) to the previous term" }, { "from": "gpt", "value": "Uses only the first two terms of a sequence to work out a term-to-term rule" } ]
[ { "from": "human", "value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence?\n\\[\n4, \\quad 10, \\quad 28, \\quad 82, \\quad \\ldots\n\\] To get the next term you double the previous term and add \\( 2 \\)" }, { "from": "gpt", "value": "Uses only the first two terms of a sequence to work out a term-to-term rule" } ]
[ { "from": "human", "value": "Round numbers between 0 and 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 0.00809 \\) \\( 0.01 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Round numbers between 0 and 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 0.00809 \\) \\( 0 \\)" }, { "from": "gpt", "value": "Counts leading zero as a significant figure" } ]
[ { "from": "human", "value": "Round numbers between 0 and 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 0.00809 \\) \\( 0.009 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{m^{2}-2 m-3}{m-3} \\) Does not simplify" }, { "from": "gpt", "value": "Does not recognise factorising a quadratic" } ]
[ { "from": "human", "value": "Carry out missing number multiplication problems involving negative integers What should replace the star?\n\n\\(\n(-6) \\times \\color{gold}\\bigstar \\color{black} =-8\n\\) \\( \\frac{6}{8} \\)" }, { "from": "gpt", "value": "Uses dividing fractions method for multiplying fractions" } ]
[ { "from": "human", "value": "Carry out missing number multiplication problems involving negative integers What should replace the star?\n\n\\(\n(-6) \\times \\color{gold}\\bigstar \\color{black} =-8\n\\) \\( -\\frac{8}{6} \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]
[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 40 \\) ? \\( 43 \\)" }, { "from": "gpt", "value": "Has confused cube numbers with prime numbers" } ]
[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 40 \\) ? \\( 49 \\)" }, { "from": "gpt", "value": "Mixes up square numbers and cube numbers" } ]
[ { "from": "human", "value": "Order integers with the same number of digits Tom and Katie are discussing how to order integers\n\nTom says \\( 5000 \\) is greater than \\( 4987 \\)\n\nKatie says \\( 3050 \\) is greater than \\( 3500 \\)\n\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Does not equate the value of a number with the place value column it is in" } ]
[ { "from": "human", "value": "Order integers with the same number of digits Tom and Katie are discussing how to order integers\n\nTom says \\( 5000 \\) is greater than \\( 4987 \\)\n\nKatie says \\( 3050 \\) is greater than \\( 3500 \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not equate the value of a number with the place value column it is in" } ]
[ { "from": "human", "value": "Order integers with the same number of digits Tom and Katie are discussing how to order integers\n\nTom says \\( 5000 \\) is greater than \\( 4987 \\)\n\nKatie says \\( 3050 \\) is greater than \\( 3500 \\)\n\nWho is correct? Neither is correct" }, { "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": "Work out the y-intercept of a line from an accurate drawing Use a graphing program (e.g. Desmos) to plot the following pairs of functions.\n\\[\ny=x^{2} - 4 \\quad \\text { and } \\quad y=x-4\n\\]\n\nTom says both functions are linear\n\nKatie says both functions cross the \\( y \\)-axis at the same point\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not know the properties of a linear graph" } ]
[ { "from": "human", "value": "Work out the y-intercept of a line from an accurate drawing Use a graphing program (e.g. Desmos) to plot the following pairs of functions.\n\\[\ny=x^{2} - 4 \\quad \\text { and } \\quad y=x-4\n\\]\n\nTom says both functions are linear\n\nKatie says both functions cross the \\( y \\)-axis at the same point\n\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Believes the constant only gives the y-intercept for linear graphs" } ]
[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon Tom and Katie are discussing how to calculate the size of each interior angle in a regular \\( 18 \\) sided shape Tom says you can do \\( \\frac{20 \\times 180}{18} \\) Katie says you can do \\( 360-\\frac{180}{18} \\) Who is correct? Only\nTom" }, { "from": "gpt", "value": "Believes an interior angle in a regular polygon can be found using 180(n+2)/n" } ]
[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon Tom and Katie are discussing how to calculate the size of each interior angle in a regular \\( 18 \\) sided shape Tom says you can do \\( \\frac{20 \\times 180}{18} \\) Katie says you can do \\( 360-\\frac{180}{18} \\) Who is correct? Only Katie" }, { "from": "gpt", "value": "Believes an interior angle in a regular polygon can be found using 360 subtract (180 over number of sides)" } ]
[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c A line has equation \\( 5 x+3 y=7 \\)\nWhat is its gradient? \\( \\frac{3}{5} \\)" }, { "from": "gpt", "value": "When finding the gradient from the equation of a line in the form ax + by = c, believes b/a is the gradient" } ]
[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c A line has equation \\( 5 x+3 y=7 \\)\nWhat is its gradient? \\( -5 \\)" }, { "from": "gpt", "value": "When solving an equation forgets to eliminate the coefficient in front of the variable in the last step" } ]
[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c A line has equation \\( 5 x+3 y=7 \\)\nWhat is its gradient? \\( 5 \\)" }, { "from": "gpt", "value": "Believes that for a line written in the form ax + by = c, a is the gradient" } ]
[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this shape? ![Purple, right angled triangle on square grid with area of 5 square units. Base length 5 and perpendicular height 2]() \\( 6 \\)" }, { "from": "gpt", "value": "Does not realise that the area of a triangle is half the area of the contatining rectangle" } ]
[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this shape? ![Purple, right angled triangle on square grid with area of 5 square units. Base length 5 and perpendicular height 2]() Not enough information" }, { "from": "gpt", "value": "Does not realise that the area of a triangle is half the area of the contatining rectangle" } ]
[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape The perimeter of this rectangle is \\( 5.6 \\mathrm{~cm} \\).\n\nWhat is the length of the side marked with a star? ![Rectangle with base length labelled 1.02 cm and side length labelled with a gold star]() \\( 4.58 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When calculating perimeter, only adds the marked lengths" } ]
[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape The perimeter of this rectangle is \\( 5.6 \\mathrm{~cm} \\).\n\nWhat is the length of the side marked with a star? ![Rectangle with base length labelled 1.02 cm and side length labelled with a gold star]() \\( 1.6 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When doing operations with decimals, ignores significant zeros after the decimal point" } ]
[ { "from": "human", "value": "Recognise and use efficient methods for mental division This is how Teddy calculates the answer to \\( 600 \\div 25 \\) mentally \"There are \\( 4 \\) lots of \\( 25 \\) in 100. I then multiplied \\( 4 \\) by \\( 6 \\) to get \\( 24 \\). So \\( 600 \\) divided by \\( 25 \\) is \\( 24 \\)\" Teddy uses the same method to calculate \\( 800 \\div 25 \\). Which of the following shows how he would do this? There are \\( 4 \\) lots of \\( 25 \\) in \\( 100 \\) \nThen I multiplied \\( 8 \\) by \\( 6 \\) \nSo the answer is \\( 48 \\)" }, { "from": "gpt", "value": "Does not copy a given method accurately" } ]
[ { "from": "human", "value": "Round numbers to two decimal places Two different numbers are equal to \\( 4.37 \\) to two decimal places.\nThe numbers could be.... \\[\n4.3728\n\\]\nand\n\\[\n4.3628\n\\]" }, { "from": "gpt", "value": "Rounds up instead of down" } ]
[ { "from": "human", "value": "Round numbers to two decimal places Two different numbers are equal to \\( 4.37 \\) to two decimal places.\nThe numbers could be.... \\[\n4.3751\n\\]\nand\n\\[\n4.3659\n\\]" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Understand the meaning of congruency Tom and Katie are discussing congruent shapes.\nTom says you can reflect a shape and it will still be congruent to the original.\n\nKatie says you can rotate a shape and it will still be congruent to the original.\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Does not understand that shapes are congruent if they have the same size and shape" } ]
[ { "from": "human", "value": "Understand the meaning of congruency Tom and Katie are discussing congruent shapes.\nTom says you can reflect a shape and it will still be congruent to the original.\n\nKatie says you can rotate a shape and it will still be congruent to the original.\nWho is correct? Only\nKatie" }, { "from": "gpt", "value": "Does not understand that shapes are congruent if they have the same size and shape" } ]
[ { "from": "human", "value": "Understand the meaning of congruency Tom and Katie are discussing congruent shapes.\nTom says you can reflect a shape and it will still be congruent to the original.\n\nKatie says you can rotate a shape and it will still be congruent to the original.\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not understand that shapes are congruent if they have the same size and shape" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 100 \\[\n34590.8549\n\\]\nWhat is this number rounded to the nearest \\( 100 \\) ? \\( 34590 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 100 \\[\n34590.8549\n\\]\nWhat is this number rounded to the nearest \\( 100 \\) ? \\( 34500 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 100 \\[\n34590.8549\n\\]\nWhat is this number rounded to the nearest \\( 100 \\) ? \\( 35000 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Convert decimals greater than 1 to percentages How do you write \\( 4.6 \\) as a percentage? \\( 46 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]
[ { "from": "human", "value": "Convert decimals greater than 1 to percentages How do you write \\( 4.6 \\) as a percentage? \\( 0.046 \\% \\)" }, { "from": "gpt", "value": "Divides instead of multiplies when converting a decimal to a percentage" } ]
[ { "from": "human", "value": "Convert decimals greater than 1 to percentages How do you write \\( 4.6 \\) as a percentage? \\( 4.6 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a decimal to convert to a percentage" } ]
[ { "from": "human", "value": "Calculate the mode as an average from a list of data when there is a single mode What is the mode of the following numbers?\n\\[\n0,0,2,2\n\\] \\( 0 \\) and \\( 2 \\)" }, { "from": "gpt", "value": "Believes every number is the mode when you have data with no mode" } ]
[ { "from": "human", "value": "Calculate the mode as an average from a list of data when there is a single mode What is the mode of the following numbers?\n\\[\n0,0,2,2\n\\] \\( 2 \\)" }, { "from": "gpt", "value": "Believes you can only have one mode" } ]
[ { "from": "human", "value": "Calculate the mode as an average from a list of data when there is a single mode What is the mode of the following numbers?\n\\[\n0,0,2,2\n\\] \\( 1 \\)" }, { "from": "gpt", "value": "Finds the median instead of the mode" } ]
[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon The diagram shows a regular hexagon and a square.\nWhat is the size of angle \\( a \\) ? ![A regular hexagon and square, joined on one side, with the angle between them labelled a. Not to scale]() \\( 210^{\\circ} \\)" }, { "from": "gpt", "value": "Believes interior angles are outside a shape" } ]
[ { "from": "human", "value": "Calculate the change from purchases between £1 and £5 A magazine costs \\( £ 2.70 \\).\n\nIsaac pays for it with a \\( £ 5 \\) note.\n\nHow much change should he receive? \\( £ 2.70 \\)" }, { "from": "gpt", "value": "In a worded problem, does not complete all calculations" } ]
[ { "from": "human", "value": "Calculate the change from purchases between £1 and £5 A magazine costs \\( £ 2.70 \\).\n\nIsaac pays for it with a \\( £ 5 \\) note.\n\nHow much change should he receive? \\( £ 3.30 \\)" }, { "from": "gpt", "value": "Ends up £1 out when dealing with change in money" } ]
[ { "from": "human", "value": "Calculate the change from purchases between £1 and £5 A magazine costs \\( £ 2.70 \\).\n\nIsaac pays for it with a \\( £ 5 \\) note.\n\nHow much change should he receive? \\( £ 7.70 \\)" }, { "from": "gpt", "value": "Adds rather than subtracts when answering worded problems" } ]
[ { "from": "human", "value": "Identify a right-angled triangle from a description of the properties A triangle has the following angles: \\( 90^{\\degree}, 45^{\\degree}, 45^{\\degree} \\) Statement 1. It must be a right angled triangle \nStatement 2. It must be an isosceles triangle\nWhich is true? Statement \\( 1 \\)" }, { "from": "gpt", "value": "Believes isosceles triangles cannot have right angles" } ]
[ { "from": "human", "value": "Identify a right-angled triangle from a description of the properties A triangle has the following angles: \\( 90^{\\degree}, 45^{\\degree}, 45^{\\degree} \\) Statement 1. It must be a right angled triangle \nStatement 2. It must be an isosceles triangle\nWhich is true? Statement \\( 2 \\)" }, { "from": "gpt", "value": "Does not know that a right angle is 90 degrees" } ]
[ { "from": "human", "value": "Identify the number of degrees in fractions of a turn How many degrees are there in three-quarters of a turn? \\( 75\\degree \\)" }, { "from": "gpt", "value": "Believes there are 100 degrees in a full turn" } ]
[ { "from": "human", "value": "Identify the number of degrees in fractions of a turn How many degrees are there in three-quarters of a turn? \\( 90\\degree \\)" }, { "from": "gpt", "value": "Finds the unit fraction when asked to find a non-unit fraction of an amount" } ]
[ { "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 The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]() \\( (2,2) \\)" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]
[ { "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 The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]() \\( (1,2) \\)" }, { "from": "gpt", "value": "Counts the squares rather than the diagonals when reflecting in y=x or y=-x " } ]
[ { "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 The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]() \\( (3,4) \\)" }, { "from": "gpt", "value": "Counts the squares rather than the diagonals when reflecting in y=x or y=-x " } ]
[ { "from": "human", "value": "Divide a quantity into two parts for a given a ratio, where each part is an integer For every \\( 3 \\) green squares there is \\( 1 \\) red square.\nHow many squares should be coloured green in the grid on the right? \\begin{tabular}{\|c\|c\|c\|}\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline\n\\end{tabular} \\( 3 \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]
[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A number line from 0 to 1 split into 5 parts with a red arrow pointing to the marker for the value 0.4]() What number is the arrow pointing to? \\( 0.2 \\)" }, { "from": "gpt", "value": "When reading decimals on a number line, assumes each dash is 0.1" } ]
[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A number line from 0 to 1 split into 5 parts with a red arrow pointing to the marker for the value 0.4]() What number is the arrow pointing to? \\( 2 \\)" }, { "from": "gpt", "value": "When reading integers on a number line, assumes each dash is 1" } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\ne+e+e\n\\] \\( e^{3} \\)" }, { "from": "gpt", "value": "Confuses adding 3 with cubing, in algebra" } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\ne+e+e\n\\] e3" }, { "from": "gpt", "value": "Writes the variable before the coefficient in an algebraic term" } ]
[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\ne+e+e\n\\] Does not simplify" }, { "from": "gpt", "value": "Does not understand when like terms can be collected" } ]
[ { "from": "human", "value": "Use perimeter to write algebraic expressions What is the perimeter of this rectangle? ![A rectangle. The length of a short side is labelled x, and the length of a long side is labelled y.]() \\( x+y \\)" }, { "from": "gpt", "value": "Thinks only labelled dimensions need to be included when calculating the perimeter" } ]
[ { "from": "human", "value": "Use perimeter to write algebraic expressions What is the perimeter of this rectangle? ![A rectangle. The length of a short side is labelled x, and the length of a long side is labelled y.]() \\( x y \\)" }, { "from": "gpt", "value": "Calculates area when asked for perimeter" } ]
[ { "from": "human", "value": "Complete multi-step mental calculations What is the value of:\n\n\\[\n485+78-9\n\\] \\( 398 \\)" }, { "from": "gpt", "value": "Thinks positive or negative sign affects the term before it" } ]
[ { "from": "human", "value": "Complete multi-step mental calculations What is the value of:\n\n\\[\n485+78-9\n\\] \\( 444 \\)" }, { "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": "Convert the reminders from written division problems into decimals John has been asked to work out the answer to:\n\\[\n231 \\div 4\n\\]\nHe gets the answer \\( 57 \\) remainder \\( 3 \\)\nWhat is the exact value of that remainder? \\( 3 \\)" }, { "from": "gpt", "value": "Does not understand that a remainder can be written as a fraction" } ]
[ { "from": "human", "value": "Convert the reminders from written division problems into decimals John has been asked to work out the answer to:\n\\[\n231 \\div 4\n\\]\nHe gets the answer \\( 57 \\) remainder \\( 3 \\)\nWhat is the exact value of that remainder? \\( 0.34 \\)" }, { "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\\[\n231 \\div 4\n\\]\nHe gets the answer \\( 57 \\) remainder \\( 3 \\)\nWhat is the exact value of that remainder? \\( 0.3 \\)" }, { "from": "gpt", "value": "Writes the remainder as the digit after the decimal point" } ]
[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Jo and Paul are arguing about factorising.\n\nJo says \\( p^{2}+16 p \\equiv(p+4)(p+4) \\)\n\nPaul says \\( p^{2}+16 p \\equiv p(p+4) \\)\n\nWho is correct? Only Jo" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]
[ { "from": "human", "value": "Solve one-step linear inequalities in one variable where the variable appears on one side of the equation Tom and Katie are arguing about the solution to this inequality:\n\\[\n15 \\geq 4 m\n\\]\n\nTom says \\( m \\) could be \\( 4 \\)\n\nKatie says \\( m \\) could be \\( 3.75 \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.15 \\times 0.2= \\) \\( 0.003 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]

[ { "from": "human", "value": "Represent a linear inequality with a single tail on a numberline Which of the following diagrams represents \\( x \\leq 1 \\) ? ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is a filled in circle above 1, with an arrow pointing to the right coming off it.]()" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Represent a linear inequality with a single tail on a numberline Which of the following diagrams represents \\( x \\leq 1 \\) ? ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is an empty circle above 1, with an arrow pointing to the left coming off it.]()" }, { "from": "gpt", "value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning." } ]

[ { "from": "human", "value": "Complete missing number mental addition problems up to 1000 What number belongs in the box to make the calculation correct? \\( 263+\\square=900 \\) \\( 1163 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]

[ { "from": "human", "value": "Complete missing number mental addition problems up to 1000 What number belongs in the box to make the calculation correct? \\( 263+\\square=900 \\) \\( 747 \\)" }, { "from": "gpt", "value": "Treats zero as a ten when subtracting" } ]

[ { "from": "human", "value": "Find missing angles in a scalene triangle What is the size of angle \\( k \\) ? ![A triangle with one angle of 40 degrees. One angle of 32 degrees and the third angle is labelled k. ]() \\( 90\\degree\\)" }, { "from": "gpt", "value": "Believes all triangles have a right angle" } ]

[ { "from": "human", "value": "Find missing angles in a scalene triangle What is the size of angle \\( k \\) ? ![A triangle with one angle of 40 degrees. One angle of 32 degrees and the third angle is labelled k. ]() \\( 118\\degree\\)" }, { "from": "gpt", "value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 4 \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nKatie says \\( y \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Does not know how to identify common factors from algebraic terms" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 4 \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nKatie says \\( y \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nWho is correct? Only\nKatie" }, { "from": "gpt", "value": "Does not know how to identify common factors from algebraic terms" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors\n\nTom says \\( 4 \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nKatie says \\( y \\) is a common factor of \\( 6 x \\) and \\( 9 y^{2} \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not know how to identify common factors from algebraic terms" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c When factorised, \\( 9 x^{2}-16 \\) will become... \\( 9 x(x-16) \\)" }, { "from": "gpt", "value": "Believes only the first term needs to be divided when factorising an expression" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c When factorised, \\( 9 x^{2}-16 \\) will become... \\( 3 x(3 x-16-) \\)" }, { "from": "gpt", "value": "Believes only the first term needs to be divided when factorising an expression" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form ax² - c When factorised, \\( 9 x^{2}-16 \\) will become... \\( (3 x+4)(3 x+4) \\)" }, { "from": "gpt", "value": "Factorises difference of two squares with the same sign in both brackets" } ]

[ { "from": "human", "value": "Carry out division problems involving negative non-integers \\( \\frac{(-3) \\times(-2)}{(-0.2)}= \\) \\( -3 \\)" }, { "from": "gpt", "value": "When dividing a decimal by a whole number, ignores decimal point and just divides the digits" } ]

[ { "from": "human", "value": "Carry out division problems involving negative non-integers \\( \\frac{(-3) \\times(-2)}{(-0.2)}= \\) \\( 30 \\)" }, { "from": "gpt", "value": "Believes dividing 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) Molly is expanding these two brackets.\n\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The brackets shown are (2p-1)(3p-4). The arrows are pointing at the -1 in the first bracket and the -4 in the second bracket.]() \\( -4 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)(cx + d) Molly is expanding these two brackets.\n\nWhat should she get when she multiplies the two terms indicated by the arrows? ![The brackets shown are (2p-1)(3p-4). The arrows are pointing at the -1 in the first bracket and the -4 in the second bracket.]() \\( -5 \\)" }, { "from": "gpt", "value": "Adds instead of multiplying when expanding bracket" } ]

[ { "from": "human", "value": "Find missing angles in an isosceles triangle What is the size of angle \\( w \\) ? ![An isosceles triangle with one of the base angles labelled with a w and the angle vertically opposite the vertex angle labelled with 27 degrees]() \\( 27^{\\degree} \\)" }, { "from": "gpt", "value": "Incorrectly identifies angles as vertically opposite" } ]

[ { "from": "human", "value": "Find missing angles in an isosceles triangle What is the size of angle \\( w \\) ? ![An isosceles triangle with one of the base angles labelled with a w and the angle vertically opposite the vertex angle labelled with 27 degrees]() \\( 54^{\\degree} \\)" }, { "from": "gpt", "value": "Does not know that vertically opposite angles are equal" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to two significant figures What is \\( \\mathbf{1 8 7 . 2 5 9} \\) rounded to two significant figures? \\( 180 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to two significant figures What is \\( \\mathbf{1 8 7 . 2 5 9} \\) rounded to two significant figures? \\( 187.26 \\)" }, { "from": "gpt", "value": "Rounds to wrong degree of accuracy (decimal places rather than significant figures)" } ]

[ { "from": "human", "value": "Multiply surds by an integer \\(9 \\times \\sqrt{3}\\)\n\nSimplify, if possible. \\( \\sqrt{12} \\)" }, { "from": "gpt", "value": "When multiplying a surd by an integer, adds the integer to the number under the surd" } ]

[ { "from": "human", "value": "Multiply surds by an integer \\(9 \\times \\sqrt{3}\\)\n\nSimplify, if possible. \\( \\sqrt{27} \\)" }, { "from": "gpt", "value": "When multiplying a surd by an integer, multiplies the integer with the number under the surd" } ]

[ { "from": "human", "value": "Multiply surds by an integer \\(9 \\times \\sqrt{3}\\)\n\nSimplify, if possible. Cannot be simplified" }, { "from": "gpt", "value": "Does not recognise that an integer multiplied by a surd can be simplified" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(3 y-4)^{2}\n\\) \\( 9 y^{2}-16 \\)" }, { "from": "gpt", "value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(3 y-4)^{2}\n\\) \\( 9 y^{2}+16 \\)" }, { "from": "gpt", "value": "Believes they only need to multiply the first and last pairs of terms when expanding double brackets" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (ax + b)² Expand and simplify:\n\\(\n(3 y-4)^{2}\n\\) \\( (3 y-4)(3 y-4) \\)" }, { "from": "gpt", "value": "Believes expanding a squared expression means writing it as a set of double brackets" } ]

[ { "from": "human", "value": "Multiply a decimal by an integer Tom and Katie are discussing multiplying decimals.\n\nTom says \\( 5 \\times 3.9=3 \\times 5.9 \\)\n\nKatie says \\( 5 \\times 3.9=3.9 \\times 5 \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Does not correctly apply the commutative property of multiplication" } ]

[ { "from": "human", "value": "Multiply a decimal by an integer Tom and Katie are discussing multiplying decimals.\n\nTom says \\( 5 \\times 3.9=3 \\times 5.9 \\)\n\nKatie says \\( 5 \\times 3.9=3.9 \\times 5 \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not correctly apply the commutative property of multiplication" } ]

[ { "from": "human", "value": "Multiply a decimal by an integer Tom and Katie are discussing multiplying decimals.\n\nTom says \\( 5 \\times 3.9=3 \\times 5.9 \\)\n\nKatie says \\( 5 \\times 3.9=3.9 \\times 5 \\)\n\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Believes multiplication is not commutative" } ]

[ { "from": "human", "value": "Describe the properties of an isosceles triangle Which description describes an isosceles triangle? A triangle with one right angle." }, { "from": "gpt", "value": "Confuses isosceles and right angle triangles" } ]

[ { "from": "human", "value": "Describe the properties of an isosceles triangle Which description describes an isosceles triangle? A triangle with three sides of equal length and three equal angles." }, { "from": "gpt", "value": "Confuses isosceles and equilateral triangles" } ]

[ { "from": "human", "value": "Describe the properties of an isosceles triangle Which description describes an isosceles triangle? A triangle with no sides of equal length and no equal angles." }, { "from": "gpt", "value": "Confuses isosceles and scalene triangles" } ]

[ { "from": "human", "value": "Use brackets to write function machines as calculations Tom and Katie are arguing about the result of this Function Machine:\nTom says the output is: \\( 3 n-12 \\)\nKatie says the output is: \\( 3(n-4) \\)\nWho is correct? ![A function machine with input n and operations subtract 4, multiply by 3]() Only Tom" }, { "from": "gpt", "value": "Does not think a factorised expression is equivalent to its multiplied out form" } ]

[ { "from": "human", "value": "Use brackets to write function machines as calculations Tom and Katie are arguing about the result of this Function Machine:\nTom says the output is: \\( 3 n-12 \\)\nKatie says the output is: \\( 3(n-4) \\)\nWho is correct? ![A function machine with input n and operations subtract 4, multiply by 3]() Only\nKatie" }, { "from": "gpt", "value": "Does not think a factorised expression is equivalent to its multiplied out form" } ]

[ { "from": "human", "value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence?\n\\[\n4, \\quad 10, \\quad 28, \\quad 82, \\quad \\ldots\n\\] To get the next term you add \\( 6 \\) to the previous term" }, { "from": "gpt", "value": "Uses only the first two terms of a sequence to work out a term-to-term rule" } ]

[ { "from": "human", "value": "Describe a term-to-term sequence Which of the following term-to-term rule describes this sequence?\n\\[\n4, \\quad 10, \\quad 28, \\quad 82, \\quad \\ldots\n\\] To get the next term you double the previous term and add \\( 2 \\)" }, { "from": "gpt", "value": "Uses only the first two terms of a sequence to work out a term-to-term rule" } ]

[ { "from": "human", "value": "Round numbers between 0 and 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 0.00809 \\) \\( 0.01 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Round numbers between 0 and 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 0.00809 \\) \\( 0 \\)" }, { "from": "gpt", "value": "Counts leading zero as a significant figure" } ]

[ { "from": "human", "value": "Round numbers between 0 and 1 to one significant figure Round this number to \\( 1 \\) significant figure:\n\\( 0.00809 \\) \\( 0.009 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{m^{2}-2 m-3}{m-3} \\) Does not simplify" }, { "from": "gpt", "value": "Does not recognise factorising a quadratic" } ]

[ { "from": "human", "value": "Carry out missing number multiplication problems involving negative integers What should replace the star?\n\n\\(\n(-6) \\times \\color{gold}\\bigstar \\color{black} =-8\n\\) \\( \\frac{6}{8} \\)" }, { "from": "gpt", "value": "Uses dividing fractions method for multiplying fractions" } ]

[ { "from": "human", "value": "Carry out missing number multiplication problems involving negative integers What should replace the star?\n\n\\(\n(-6) \\times \\color{gold}\\bigstar \\color{black} =-8\n\\) \\( -\\frac{8}{6} \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]

[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 40 \\) ? \\( 43 \\)" }, { "from": "gpt", "value": "Has confused cube numbers with prime numbers" } ]

[ { "from": "human", "value": "Recognise cube numbers What is the first cube number greater than \\( 40 \\) ? \\( 49 \\)" }, { "from": "gpt", "value": "Mixes up square numbers and cube numbers" } ]

[ { "from": "human", "value": "Order integers with the same number of digits Tom and Katie are discussing how to order integers\n\nTom says \\( 5000 \\) is greater than \\( 4987 \\)\n\nKatie says \\( 3050 \\) is greater than \\( 3500 \\)\n\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Does not equate the value of a number with the place value column it is in" } ]

[ { "from": "human", "value": "Order integers with the same number of digits Tom and Katie are discussing how to order integers\n\nTom says \\( 5000 \\) is greater than \\( 4987 \\)\n\nKatie says \\( 3050 \\) is greater than \\( 3500 \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not equate the value of a number with the place value column it is in" } ]

[ { "from": "human", "value": "Order integers with the same number of digits Tom and Katie are discussing how to order integers\n\nTom says \\( 5000 \\) is greater than \\( 4987 \\)\n\nKatie says \\( 3050 \\) is greater than \\( 3500 \\)\n\nWho is correct? Neither is correct" }, { "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": "Work out the y-intercept of a line from an accurate drawing Use a graphing program (e.g. Desmos) to plot the following pairs of functions.\n\\[\ny=x^{2} - 4 \\quad \\text { and } \\quad y=x-4\n\\]\n\nTom says both functions are linear\n\nKatie says both functions cross the \\( y \\)-axis at the same point\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not know the properties of a linear graph" } ]

[ { "from": "human", "value": "Work out the y-intercept of a line from an accurate drawing Use a graphing program (e.g. Desmos) to plot the following pairs of functions.\n\\[\ny=x^{2} - 4 \\quad \\text { and } \\quad y=x-4\n\\]\n\nTom says both functions are linear\n\nKatie says both functions cross the \\( y \\)-axis at the same point\n\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Believes the constant only gives the y-intercept for linear graphs" } ]

[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon Tom and Katie are discussing how to calculate the size of each interior angle in a regular \\( 18 \\) sided shape Tom says you can do \\( \\frac{20 \\times 180}{18} \\) Katie says you can do \\( 360-\\frac{180}{18} \\) Who is correct? Only\nTom" }, { "from": "gpt", "value": "Believes an interior angle in a regular polygon can be found using 180(n+2)/n" } ]

[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon Tom and Katie are discussing how to calculate the size of each interior angle in a regular \\( 18 \\) sided shape Tom says you can do \\( \\frac{20 \\times 180}{18} \\) Katie says you can do \\( 360-\\frac{180}{18} \\) Who is correct? Only Katie" }, { "from": "gpt", "value": "Believes an interior angle in a regular polygon can be found using 360 subtract (180 over number of sides)" } ]

[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c A line has equation \\( 5 x+3 y=7 \\)\nWhat is its gradient? \\( \\frac{3}{5} \\)" }, { "from": "gpt", "value": "When finding the gradient from the equation of a line in the form ax + by = c, believes b/a is the gradient" } ]

[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c A line has equation \\( 5 x+3 y=7 \\)\nWhat is its gradient? \\( -5 \\)" }, { "from": "gpt", "value": "When solving an equation forgets to eliminate the coefficient in front of the variable in the last step" } ]

[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c A line has equation \\( 5 x+3 y=7 \\)\nWhat is its gradient? \\( 5 \\)" }, { "from": "gpt", "value": "Believes that for a line written in the form ax + by = c, a is the gradient" } ]

[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this shape? ![Purple, right angled triangle on square grid with area of 5 square units. Base length 5 and perpendicular height 2]() \\( 6 \\)" }, { "from": "gpt", "value": "Does not realise that the area of a triangle is half the area of the contatining rectangle" } ]

[ { "from": "human", "value": "Calculate the area of a right-angled triangle where the dimensions are given in the same units What is the area of this shape? ![Purple, right angled triangle on square grid with area of 5 square units. Base length 5 and perpendicular height 2]() Not enough information" }, { "from": "gpt", "value": "Does not realise that the area of a triangle is half the area of the contatining rectangle" } ]

[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape The perimeter of this rectangle is \\( 5.6 \\mathrm{~cm} \\).\n\nWhat is the length of the side marked with a star? ![Rectangle with base length labelled 1.02 cm and side length labelled with a gold star]() \\( 4.58 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When calculating perimeter, only adds the marked lengths" } ]

[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape The perimeter of this rectangle is \\( 5.6 \\mathrm{~cm} \\).\n\nWhat is the length of the side marked with a star? ![Rectangle with base length labelled 1.02 cm and side length labelled with a gold star]() \\( 1.6 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "When doing operations with decimals, ignores significant zeros after the decimal point" } ]

[ { "from": "human", "value": "Recognise and use efficient methods for mental division This is how Teddy calculates the answer to \\( 600 \\div 25 \\) mentally \"There are \\( 4 \\) lots of \\( 25 \\) in 100. I then multiplied \\( 4 \\) by \\( 6 \\) to get \\( 24 \\). So \\( 600 \\) divided by \\( 25 \\) is \\( 24 \\)\" Teddy uses the same method to calculate \\( 800 \\div 25 \\). Which of the following shows how he would do this? There are \\( 4 \\) lots of \\( 25 \\) in \\( 100 \\) \nThen I multiplied \\( 8 \\) by \\( 6 \\) \nSo the answer is \\( 48 \\)" }, { "from": "gpt", "value": "Does not copy a given method accurately" } ]

[ { "from": "human", "value": "Round numbers to two decimal places Two different numbers are equal to \\( 4.37 \\) to two decimal places.\nThe numbers could be.... \\[\n4.3728\n\\]\nand\n\\[\n4.3628\n\\]" }, { "from": "gpt", "value": "Rounds up instead of down" } ]

[ { "from": "human", "value": "Round numbers to two decimal places Two different numbers are equal to \\( 4.37 \\) to two decimal places.\nThe numbers could be.... \\[\n4.3751\n\\]\nand\n\\[\n4.3659\n\\]" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Understand the meaning of congruency Tom and Katie are discussing congruent shapes.\nTom says you can reflect a shape and it will still be congruent to the original.\n\nKatie says you can rotate a shape and it will still be congruent to the original.\nWho is correct? Only\nTom" }, { "from": "gpt", "value": "Does not understand that shapes are congruent if they have the same size and shape" } ]

[ { "from": "human", "value": "Understand the meaning of congruency Tom and Katie are discussing congruent shapes.\nTom says you can reflect a shape and it will still be congruent to the original.\n\nKatie says you can rotate a shape and it will still be congruent to the original.\nWho is correct? Only\nKatie" }, { "from": "gpt", "value": "Does not understand that shapes are congruent if they have the same size and shape" } ]

[ { "from": "human", "value": "Understand the meaning of congruency Tom and Katie are discussing congruent shapes.\nTom says you can reflect a shape and it will still be congruent to the original.\n\nKatie says you can rotate a shape and it will still be congruent to the original.\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not understand that shapes are congruent if they have the same size and shape" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 100 \\[\n34590.8549\n\\]\nWhat is this number rounded to the nearest \\( 100 \\) ? \\( 34590 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 100 \\[\n34590.8549\n\\]\nWhat is this number rounded to the nearest \\( 100 \\) ? \\( 34500 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 100 \\[\n34590.8549\n\\]\nWhat is this number rounded to the nearest \\( 100 \\) ? \\( 35000 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Convert decimals greater than 1 to percentages How do you write \\( 4.6 \\) as a percentage? \\( 46 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]

[ { "from": "human", "value": "Convert decimals greater than 1 to percentages How do you write \\( 4.6 \\) as a percentage? \\( 0.046 \\% \\)" }, { "from": "gpt", "value": "Divides instead of multiplies when converting a decimal to a percentage" } ]

[ { "from": "human", "value": "Convert decimals greater than 1 to percentages How do you write \\( 4.6 \\) as a percentage? \\( 4.6 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a decimal to convert to a percentage" } ]

[ { "from": "human", "value": "Calculate the mode as an average from a list of data when there is a single mode What is the mode of the following numbers?\n\\[\n0,0,2,2\n\\] \\( 0 \\) and \\( 2 \\)" }, { "from": "gpt", "value": "Believes every number is the mode when you have data with no mode" } ]

[ { "from": "human", "value": "Calculate the mode as an average from a list of data when there is a single mode What is the mode of the following numbers?\n\\[\n0,0,2,2\n\\] \\( 2 \\)" }, { "from": "gpt", "value": "Believes you can only have one mode" } ]

[ { "from": "human", "value": "Calculate the mode as an average from a list of data when there is a single mode What is the mode of the following numbers?\n\\[\n0,0,2,2\n\\] \\( 1 \\)" }, { "from": "gpt", "value": "Finds the median instead of the mode" } ]

[ { "from": "human", "value": "Work out the size of each interior angle in a regular polygon The diagram shows a regular hexagon and a square.\nWhat is the size of angle \\( a \\) ? ![A regular hexagon and square, joined on one side, with the angle between them labelled a. Not to scale]() \\( 210^{\\circ} \\)" }, { "from": "gpt", "value": "Believes interior angles are outside a shape" } ]

[ { "from": "human", "value": "Calculate the change from purchases between £1 and £5 A magazine costs \\( £ 2.70 \\).\n\nIsaac pays for it with a \\( £ 5 \\) note.\n\nHow much change should he receive? \\( £ 2.70 \\)" }, { "from": "gpt", "value": "In a worded problem, does not complete all calculations" } ]

[ { "from": "human", "value": "Calculate the change from purchases between £1 and £5 A magazine costs \\( £ 2.70 \\).\n\nIsaac pays for it with a \\( £ 5 \\) note.\n\nHow much change should he receive? \\( £ 3.30 \\)" }, { "from": "gpt", "value": "Ends up £1 out when dealing with change in money" } ]

[ { "from": "human", "value": "Calculate the change from purchases between £1 and £5 A magazine costs \\( £ 2.70 \\).\n\nIsaac pays for it with a \\( £ 5 \\) note.\n\nHow much change should he receive? \\( £ 7.70 \\)" }, { "from": "gpt", "value": "Adds rather than subtracts when answering worded problems" } ]

[ { "from": "human", "value": "Identify a right-angled triangle from a description of the properties A triangle has the following angles: \\( 90^{\\degree}, 45^{\\degree}, 45^{\\degree} \\) Statement 1. It must be a right angled triangle \nStatement 2. It must be an isosceles triangle\nWhich is true? Statement \\( 1 \\)" }, { "from": "gpt", "value": "Believes isosceles triangles cannot have right angles" } ]

[ { "from": "human", "value": "Identify a right-angled triangle from a description of the properties A triangle has the following angles: \\( 90^{\\degree}, 45^{\\degree}, 45^{\\degree} \\) Statement 1. It must be a right angled triangle \nStatement 2. It must be an isosceles triangle\nWhich is true? Statement \\( 2 \\)" }, { "from": "gpt", "value": "Does not know that a right angle is 90 degrees" } ]

[ { "from": "human", "value": "Identify the number of degrees in fractions of a turn How many degrees are there in three-quarters of a turn? \\( 75\\degree \\)" }, { "from": "gpt", "value": "Believes there are 100 degrees in a full turn" } ]

[ { "from": "human", "value": "Identify the number of degrees in fractions of a turn How many degrees are there in three-quarters of a turn? \\( 90\\degree \\)" }, { "from": "gpt", "value": "Finds the unit fraction when asked to find a non-unit fraction of an amount" } ]

[ { "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 The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]() \\( (2,2) \\)" }, { "from": "gpt", "value": "Fails to reflect across mirror line" } ]

[ { "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 The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]() \\( (1,2) \\)" }, { "from": "gpt", "value": "Counts the squares rather than the diagonals when reflecting in y=x or y=-x " } ]

[ { "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 The triangle is reflected in the dashed line.\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]() \\( (3,4) \\)" }, { "from": "gpt", "value": "Counts the squares rather than the diagonals when reflecting in y=x or y=-x " } ]

[ { "from": "human", "value": "Divide a quantity into two parts for a given a ratio, where each part is an integer For every \\( 3 \\) green squares there is \\( 1 \\) red square.\nHow many squares should be coloured green in the grid on the right? \\begin{tabular}{|c|c|c|}\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline \\(\\;\\) & \\(\\;\\) & \\(\\;\\) \\\\\n\\hline\n\\end{tabular} \\( 3 \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]

[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A number line from 0 to 1 split into 5 parts with a red arrow pointing to the marker for the value 0.4]() What number is the arrow pointing to? \\( 0.2 \\)" }, { "from": "gpt", "value": "When reading decimals on a number line, assumes each dash is 0.1" } ]

[ { "from": "human", "value": "Read a decimal on a scale where the required measurement is marked by a dash between two numbers ![A number line from 0 to 1 split into 5 parts with a red arrow pointing to the marker for the value 0.4]() What number is the arrow pointing to? \\( 2 \\)" }, { "from": "gpt", "value": "When reading integers on a number line, assumes each dash is 1" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\ne+e+e\n\\] \\( e^{3} \\)" }, { "from": "gpt", "value": "Confuses adding 3 with cubing, in algebra" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\ne+e+e\n\\] e3" }, { "from": "gpt", "value": "Writes the variable before the coefficient in an algebraic term" } ]

[ { "from": "human", "value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify, if possible:\n\\[\ne+e+e\n\\] Does not simplify" }, { "from": "gpt", "value": "Does not understand when like terms can be collected" } ]

[ { "from": "human", "value": "Use perimeter to write algebraic expressions What is the perimeter of this rectangle? ![A rectangle. The length of a short side is labelled x, and the length of a long side is labelled y.]() \\( x+y \\)" }, { "from": "gpt", "value": "Thinks only labelled dimensions need to be included when calculating the perimeter" } ]

[ { "from": "human", "value": "Use perimeter to write algebraic expressions What is the perimeter of this rectangle? ![A rectangle. The length of a short side is labelled x, and the length of a long side is labelled y.]() \\( x y \\)" }, { "from": "gpt", "value": "Calculates area when asked for perimeter" } ]

[ { "from": "human", "value": "Complete multi-step mental calculations What is the value of:\n\n\\[\n485+78-9\n\\] \\( 398 \\)" }, { "from": "gpt", "value": "Thinks positive or negative sign affects the term before it" } ]

[ { "from": "human", "value": "Complete multi-step mental calculations What is the value of:\n\n\\[\n485+78-9\n\\] \\( 444 \\)" }, { "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": "Convert the reminders from written division problems into decimals John has been asked to work out the answer to:\n\\[\n231 \\div 4\n\\]\nHe gets the answer \\( 57 \\) remainder \\( 3 \\)\nWhat is the exact value of that remainder? \\( 3 \\)" }, { "from": "gpt", "value": "Does not understand that a remainder can be written as a fraction" } ]

[ { "from": "human", "value": "Convert the reminders from written division problems into decimals John has been asked to work out the answer to:\n\\[\n231 \\div 4\n\\]\nHe gets the answer \\( 57 \\) remainder \\( 3 \\)\nWhat is the exact value of that remainder? \\( 0.34 \\)" }, { "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\\[\n231 \\div 4\n\\]\nHe gets the answer \\( 57 \\) remainder \\( 3 \\)\nWhat is the exact value of that remainder? \\( 0.3 \\)" }, { "from": "gpt", "value": "Writes the remainder as the digit after the decimal point" } ]

[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Jo and Paul are arguing about factorising.\n\nJo says \\( p^{2}+16 p \\equiv(p+4)(p+4) \\)\n\nPaul says \\( p^{2}+16 p \\equiv p(p+4) \\)\n\nWho is correct? Only Jo" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]

[ { "from": "human", "value": "Solve one-step linear inequalities in one variable where the variable appears on one side of the equation Tom and Katie are arguing about the solution to this inequality:\n\\[\n15 \\geq 4 m\n\\]\n\nTom says \\( m \\) could be \\( 4 \\)\n\nKatie says \\( m \\) could be \\( 3.75 \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]