bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "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? Neither is correct" }, { "from": "gpt", "value": "When using inequality notation, thinks \"greater than/less than or equal to\" symbols are instead the \"greater than/less than\" symbols and vice versa" } ]
[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making a T shape where there is a rectangle across the top and a rectangle attached below this, slightly to the left of the centre. The full width across the top is 32m, the partial width on the left is 10m, the partial width on the right is 11m. The full height on the right is 25m, the partial height on the lower block is 14m. The shaded section is the top rectangle across the full width.]() \\( 320 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Uses an incorrect side length when splitting a composite shape into parts" } ]
[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making a T shape where there is a rectangle across the top and a rectangle attached below this, slightly to the left of the centre. The full width across the top is 32m, the partial width on the left is 10m, the partial width on the right is 11m. The full height on the right is 25m, the partial height on the lower block is 14m. The shaded section is the top rectangle across the full width.]() \\( 288 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Uses an incorrect side length when splitting a composite shape into parts" } ]
[ { "from": "human", "value": "Recognise cube numbers Which of the following numbers is a cube number? \\( 3 \\)" }, { "from": "gpt", "value": "Does not know what a cube number is" } ]
[ { "from": "human", "value": "Recognise cube numbers Which of the following numbers is a cube number? \\( 6 \\)" }, { "from": "gpt", "value": "Does not know what a cube number is" } ]
[ { "from": "human", "value": "Recognise cube numbers Which of the following numbers is a cube number? \\( 9 \\)" }, { "from": "gpt", "value": "Mixes up square numbers and cube numbers" } ]
[ { "from": "human", "value": "Subtract integers up to 4 digits using a written method where carrying is not needed How should you line up the digits to calculate \\( 3152-809 \\) ? \\( \\begin{array}{r}\\quad\\space3152 \\\\ -809\\end{array} \\)" }, { "from": "gpt", "value": "Lines up the digits incorrectly when doing a subtraction involving two numbers with a different amount of digits" } ]
[ { "from": "human", "value": "Subtract integers up to 4 digits using a written method where carrying is not needed How should you line up the digits to calculate \\( 3152-809 \\) ? \\( \\begin{array}{r}\\quad\\quad3152 \\\\ -89\\end{array} \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]
[ { "from": "human", "value": "Subtract integers up to 4 digits using a written method where carrying is not needed How should you line up the digits to calculate \\( 3152-809 \\) ? \\( \\begin{array}{r}3152 \\\\ -\\space 89\\end{array} \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]
[ { "from": "human", "value": "Identify common factors of two numbers A common factor of \\( 6 \\) and \\( 9 \\) is... \\( 6 \\)" }, { "from": "gpt", "value": "Does not know the 9 timestable" } ]
[ { "from": "human", "value": "Identify common factors of two numbers A common factor of \\( 6 \\) and \\( 9 \\) is... \\( 9 \\)" }, { "from": "gpt", "value": "Does not know the 6 timestable" } ]
[ { "from": "human", "value": "Identify common factors of two numbers A common factor of \\( 6 \\) and \\( 9 \\) is... \\( 18 \\)" }, { "from": "gpt", "value": "Confuses factors and multiples" } ]
[ { "from": "human", "value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c \\begin{tabular}{llll\|l\|l}\n\\( x \\) & \\( -1 \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) & & \\( 3 \\) \n\\end{tabular} This is a table of values for \\( y=x^{2}-x+3 \\) What should replace the star? \\( -3 \\)" }, { "from": "gpt", "value": "Thinks tables of values are symmetrical about (0,0)" } ]
[ { "from": "human", "value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c \\begin{tabular}{llll\|l\|l}\n\\( x \\) & \\( -1 \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) & & \\( 3 \\) \n\\end{tabular} This is a table of values for \\( y=x^{2}-x+3 \\) What should replace the star? \\( 3 \\)" }, { "from": "gpt", "value": "Does not realise that subtracting a negative is the same as adding it's additive inverse" } ]
[ { "from": "human", "value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c \\begin{tabular}{llll\|l\|l}\n\\( x \\) & \\( -1 \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) & & \\( 3 \\) \n\\end{tabular} This is a table of values for \\( y=x^{2}-x+3 \\) What should replace the star? \\( 6 \\)" }, { "from": "gpt", "value": "Thinks 1 squared is 2" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 10 What is \\( \\mathbf{8 6 9 8 . 9} \\) rounded to the nearest ten? \\( 8699 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 10 What is \\( \\mathbf{8 6 9 8 . 9} \\) rounded to the nearest ten? \\( 8690 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round non-integers to the nearest 10 What is \\( \\mathbf{8 6 9 8 . 9} \\) rounded to the nearest ten? \\( 9000 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]
[ { "from": "human", "value": "Recognise the angles on a straight line relationship What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]() They are equal" }, { "from": "gpt", "value": "Student thinks that any two angles along a straight line are equal" } ]
[ { "from": "human", "value": "Recognise the angles on a straight line relationship What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]() They are parallel" }, { "from": "gpt", "value": "Does not know the meaning of the word parallel" } ]
[ { "from": "human", "value": "Recognise the angles on a straight line relationship What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]() They add together to make\n\\[\n360^{\\circ}\n\\]" }, { "from": "gpt", "value": "Believes angles on a straight line add to 360 degrees" } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n10=\\frac{5}{p}\n\\) \\( p=50 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n10=\\frac{5}{p}\n\\) \\( p=2 \\)" }, { "from": "gpt", "value": "Assumes the denominator is divided by the numerator" } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n10=\\frac{5}{p}\n\\) There are no solutions" }, { "from": "gpt", "value": "Does not know how to solve linear equations involving fractions" } ]
[ { "from": "human", "value": "Recognise when an ascending sequence is linear Tom and Katie are discussing linear sequences.\n\nTom says this is a linear sequence: \\( 1,2,4,7,11, \\ldots \\) \n\nKatie says this is a linear sequence: \\( 1.2,1.4,1.6,1.8,2, \\ldots \\) \n\nWho is correct?\n Only Tom" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]
[ { "from": "human", "value": "Recognise when an ascending sequence is linear Tom and Katie are discussing linear sequences.\n\nTom says this is a linear sequence: \\( 1,2,4,7,11, \\ldots \\) \n\nKatie says this is a linear sequence: \\( 1.2,1.4,1.6,1.8,2, \\ldots \\) \n\nWho is correct?\n Both Tom and Katie" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]
[ { "from": "human", "value": "Recognise when an ascending sequence is linear Tom and Katie are discussing linear sequences.\n\nTom says this is a linear sequence: \\( 1,2,4,7,11, \\ldots \\) \n\nKatie says this is a linear sequence: \\( 1.2,1.4,1.6,1.8,2, \\ldots \\) \n\nWho is correct?\n Neither is correct" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]
[ { "from": "human", "value": "Convert between cm and m \\( 27 \\mathrm{~cm}=\\square \\mathrm{m} \\) \\( 0.3 \\)" }, { "from": "gpt", "value": "Believes they can round when converting units" } ]
[ { "from": "human", "value": "Convert between cm and m \\( 27 \\mathrm{~cm}=\\square \\mathrm{m} \\) \\( 2700 \\)" }, { "from": "gpt", "value": "Multiplies when converting to a larger unit" } ]
[ { "from": "human", "value": "Convert between cm and m \\( 27 \\mathrm{~cm}=\\square \\mathrm{m} \\) \\( 2.7 \\)" }, { "from": "gpt", "value": "Thinks there are 10cm in a metre" } ]
[ { "from": "human", "value": "Solve missing number mental multiplication problems with decimals What should replace the star? \\( 0.03 \\times \\bigstar=0.00009 \\) \\( 0.03 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]
[ { "from": "human", "value": "Solve missing number mental multiplication problems with decimals What should replace the star? \\( 0.03 \\times \\bigstar=0.00009 \\) \\( 0.3 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]
[ { "from": "human", "value": "Solve missing number mental multiplication problems with decimals What should replace the star? \\( 0.03 \\times \\bigstar=0.00009 \\) \\( 0.0003 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]
[ { "from": "human", "value": "Complete missing number mental subtraction problems up to 100 What should replace the star?\n\\[\n\\bigstar-26=28\n\\] \\( 2 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]
[ { "from": "human", "value": "Complete missing number mental subtraction problems up to 100 What should replace the star?\n\\[\n\\bigstar-26=28\n\\] \\( -2 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]
[ { "from": "human", "value": "Complete missing number mental subtraction problems up to 100 What should replace the star?\n\\[\n\\bigstar-26=28\n\\] \\( 44 \\)" }, { "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": "Multiply algebraic fractions where the numerators and denominators are all single terms Express the following as a single fraction, writing your answer as simply as possible:\n\n\\(\n\\frac{1}{s} \\times \\frac{2}{t}\n\\) \\( \\frac{t+2 s}{s t} \\)" }, { "from": "gpt", "value": "When asked to multiply fractions, uses the method for adding instead" } ]
[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators are all single terms Express the following as a single fraction, writing your answer as simply as possible:\n\n\\(\n\\frac{1}{s} \\times \\frac{2}{t}\n\\) \\( \\frac{3}{s+t} \\)" }, { "from": "gpt", "value": "When multiplying fractions, adds the numerators and the denominators" } ]
[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators are all single terms Express the following as a single fraction, writing your answer as simply as possible:\n\n\\(\n\\frac{1}{s} \\times \\frac{2}{t}\n\\) \\( \\frac{3}{s t} \\)" }, { "from": "gpt", "value": "When multiplying fractions, adds the numerators and multiplies the denominators" } ]
[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\( 18 \\div 2+2 \\times 2= \\) \\( 3 \\)" }, { "from": "gpt", "value": "Confuses the order of operations, believes addition comes before division" } ]
[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\( 18 \\div 2+2 \\times 2= \\) \\( 22 \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]
[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]() \\( \\frac{2}{3} \\)" }, { "from": "gpt", "value": "Cannot identify a fraction on a number line" } ]
[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]() \\( 1 \\frac{2}{3} \\)" }, { "from": "gpt", "value": "Confused mixed numbers with improper fractions" } ]
[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]() \\( \\frac{4}{2} \\)" }, { "from": "gpt", "value": "Cannot identify a fraction on a number line" } ]
[ { "from": "human", "value": "Calculate the mean as an average from a list of data Without using a calculator, what is the mean of the following numbers?\n\n\\[\n2,2,3,3,2\n\\] \\( 2 \\)" }, { "from": "gpt", "value": "When asked for the mean of a list of data, gives the mode" } ]
[ { "from": "human", "value": "Calculate the mean as an average from a list of data Without using a calculator, what is the mean of the following numbers?\n\n\\[\n2,2,3,3,2\n\\] \\( 3 \\)" }, { "from": "gpt", "value": "Believes the mean is the middle number" } ]
[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram ![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners\nWhat is the probability of getting a \\( 1 \\) on both spinners? \\( \\frac{1}{9} \\)" }, { "from": "gpt", "value": "When multiplying fractions, multiplies the numerator and adds the denominator" } ]
[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram ![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners\nWhat is the probability of getting a \\( 1 \\) on both spinners? \\( \\frac{2}{9} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]
[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram ![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners\nWhat is the probability of getting a \\( 1 \\) on both spinners? \\( \\frac{2}{20} \\)" }, { "from": "gpt", "value": "When multiplying fractions, adds the numerators and multiplies the denominators" } ]
[ { "from": "human", "value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\[\n23 \\mathrm{~cm}, \\quad 17 \\mathrm{~cm}, \\quad 40 \\mathrm{~cm}, \\quad 25 \\mathrm{~cm}, \\quad 31 \\mathrm{~cm}\n\\]\n\nTom says if all the plants doubled in height, the range wouldn't change.\n\nKatie says if all the plants grew by \\( 12 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with? Only Tom" }, { "from": "gpt", "value": "Believes if you changed all values by the same proportion the range would not change" } ]
[ { "from": "human", "value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\[\n23 \\mathrm{~cm}, \\quad 17 \\mathrm{~cm}, \\quad 40 \\mathrm{~cm}, \\quad 25 \\mathrm{~cm}, \\quad 31 \\mathrm{~cm}\n\\]\n\nTom says if all the plants doubled in height, the range wouldn't change.\n\nKatie says if all the plants grew by \\( 12 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with? Both Tom and Katie" }, { "from": "gpt", "value": "Believes if you changed all values by the same proportion the range would not change" } ]
[ { "from": "human", "value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\[\n23 \\mathrm{~cm}, \\quad 17 \\mathrm{~cm}, \\quad 40 \\mathrm{~cm}, \\quad 25 \\mathrm{~cm}, \\quad 31 \\mathrm{~cm}\n\\]\n\nTom says if all the plants doubled in height, the range wouldn't change.\n\nKatie says if all the plants grew by \\( 12 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with? Neither is correct" }, { "from": "gpt", "value": "Believes if you add the same value to all numbers in the dataset the range will change" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible: \\( \\frac{t^{2}-1}{t+1} \\) \\( t \\)" }, { "from": "gpt", "value": "Thinks you can divide terms by different factors when simplifying an algebraic fraction" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible: \\( \\frac{t^{2}-1}{t+1} \\) Does not simplify" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]
[ { "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 If the original sequence looks like this: ![Two patterns made of squares. Pattern 1 consists of a central column of three squares, with an extra square either side, making a cross. Pattern two consists of two central columns of three squares with one extra square either side. ]() There are \\( 302 \\) squares in Pattern \\( 100 \\). But if the shape changes to this: ![These patterns are the same as those in the first picture except that in each, the second block from each column of three has been removed. ]() How many squares would there be in Pattern \\( 100 \\) now? \\( 301 \\)" }, { "from": "gpt", "value": "Only looks at the difference between one pair of terms when discerning the pattern" } ]
[ { "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 If the original sequence looks like this: ![Two patterns made of squares. Pattern 1 consists of a central column of three squares, with an extra square either side, making a cross. Pattern two consists of two central columns of three squares with one extra square either side. ]() There are \\( 302 \\) squares in Pattern \\( 100 \\). But if the shape changes to this: ![These patterns are the same as those in the first picture except that in each, the second block from each column of three has been removed. ]() How many squares would there be in Pattern \\( 100 \\) now? \\( 300 \\)" }, { "from": "gpt", "value": "Only looks at the difference between one pair of terms when discerning the pattern" } ]
[ { "from": "human", "value": "Round decimals to the nearest whole number \\[\n0.059623\n\\]\nWhat is this number rounded to the nearest integer? \\( 0.06 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]
[ { "from": "human", "value": "Round decimals to the nearest whole number \\[\n0.059623\n\\]\nWhat is this number rounded to the nearest integer? \\( 0.05 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]
[ { "from": "human", "value": "Round decimals to the nearest whole number \\[\n0.059623\n\\]\nWhat is this number rounded to the nearest integer? \\( 1 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]
[ { "from": "human", "value": "Find missing angles in a parallelogram What is the size of angle \\( p \\) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]() \\( 65^{\\circ} \\)" }, { "from": "gpt", "value": "Thinks co-interior angles are equal" } ]
[ { "from": "human", "value": "Find missing angles in a parallelogram What is the size of angle \\( p \\) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]() \\( 125^{\\circ} \\)" }, { "from": "gpt", "value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit" } ]
[ { "from": "human", "value": "Find missing angles in a parallelogram What is the size of angle \\( p \\) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]() Not enough information to work it out" }, { "from": "gpt", "value": "Does not recognise parallel lines angle rules applied inside a shape" } ]
[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A shape is made up of a square and a rectangle. ![\\begin{tabular}{\|l\|l\|}\n\\hline & \\\\\n\\hline & \\\\\n\\hline\n\\end{tabular}]() The perimeter of the shape is \\( 30 \\mathrm{~cm} \\). The area of the square is \\( 16 \\mathrm{~cm}^{2} \\).\nWhat is the area of the shape? \\( 4 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Does not know how to find missing lengths in a composite shape" } ]
[ { "from": "human", "value": "Round integers to the nearest 100 A number rounds to \\( 20,000 \\) when rounded to the nearest ten thousand, thousand and hundred.\nWhich number could this be? \\( 19199 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]
[ { "from": "human", "value": "Round integers to the nearest 100 A number rounds to \\( 20,000 \\) when rounded to the nearest ten thousand, thousand and hundred.\nWhich number could this be? \\( 20074 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]
[ { "from": "human", "value": "Round integers to the nearest 100 A number rounds to \\( 20,000 \\) when rounded to the nearest ten thousand, thousand and hundred.\nWhich number could this be? \\( 19949 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]
[ { "from": "human", "value": "Identify corresponding angles These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]() Alternate" }, { "from": "gpt", "value": "Confuses corresponding and alternate angles" } ]
[ { "from": "human", "value": "Identify corresponding angles These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]() Co-Interior" }, { "from": "gpt", "value": "Confuses co-interior and alternate angles" } ]
[ { "from": "human", "value": "Identify corresponding angles These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]() Parallel" }, { "from": "gpt", "value": "Describes lines when asked to describe angles" } ]
[ { "from": "human", "value": "Read values off a real life graph ![A linear graph showing that 10 miles = £8. ]() The graph can be used to work out how much Kay's company pays her for travel.\n\nKay's company paid her \\( £ 80 \\)\n\nHow many miles did she travel? \\( 64 \\)" }, { "from": "gpt", "value": "When reading value from graph, reads from the wrong axes." } ]
[ { "from": "human", "value": "Read values off a real life graph ![A linear graph showing that 10 miles = £8. ]() The graph can be used to work out how much Kay's company pays her for travel.\n\nKay's company paid her \\( £ 80 \\)\n\nHow many miles did she travel? \\( 80 \\)" }, { "from": "gpt", "value": "Believes direct proportion means a 1:1 ratio" } ]
[ { "from": "human", "value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.4=\\frac{2}{5}=? \\% \\) \\( 25 \\% \\)" }, { "from": "gpt", "value": "Converts a fraction to a percentage by writing the numerator followed by the denominator" } ]
[ { "from": "human", "value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.4=\\frac{2}{5}=? \\% \\) \\( 4 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]
[ { "from": "human", "value": "Recognise the equations of vertical lines from a diagram What is the equation of this line? ![A coordinate grid with a red line drawn on passing through the points: (-2,-10) (-2,-2) (-2, 0) (-2,4) (-2,10)]() \\( x=-1 \\)" }, { "from": "gpt", "value": "Counts squares instead of the correct scale when plotting coordinates" } ]
[ { "from": "human", "value": "Recognise the equations of vertical lines from a diagram What is the equation of this line? ![A coordinate grid with a red line drawn on passing through the points: (-2,-10) (-2,-2) (-2, 0) (-2,4) (-2,10)]() \\( y=-2 \\)" }, { "from": "gpt", "value": "Confuses the equations of vertical and horizontal lines" } ]
[ { "from": "human", "value": "Identify a rectangle when presented non-conventionally ![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape? Square" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]
[ { "from": "human", "value": "Identify a rectangle when presented non-conventionally ![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape? Rhombus" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]
[ { "from": "human", "value": "Identify a rectangle when presented non-conventionally ![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape? Kite" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]
[ { "from": "human", "value": "Write a missing term of a descending integer linear sequence \\( 53, \\quad 46, \\quad 39, \\quad \\ldots \\) What is the \\( 8^{\\text {th }} \\) term in this linear sequence? \\( 32 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the next term" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"+¼\" written inside it and the final rectangle has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 8 \\frac{1}{4} \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"+¼\" written inside it and the final rectangle has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 2 \\)" }, { "from": "gpt", "value": "Thinks the inverse of addition is multiplication" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"+¼\" written inside it and the final rectangle has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 32 \\)" }, { "from": "gpt", "value": "Thinks the inverse of addition is division" } ]
[ { "from": "human", "value": "Given the sector angle on a pie chart, calculate the frequency of a group The pie chart shows the meal choices of guests at a wedding.\n\nIf there were \\( 540 \\) people at the wedding, which of the following would calculate how many people chose pork? ![A pie chart split into four parts, labelled with meal choices. The part for Beef is 150 degrees, Pork is 40 degrees and Other is 80 degrees. The angle for Vegetarian is labelled with a square right angle symbol.]() \\( \\frac{360}{40} \\times 540 \\)" }, { "from": "gpt", "value": "Believes a proportion of a whole is whole/part not part/whole" } ]
[ { "from": "human", "value": "Given the sector angle on a pie chart, calculate the frequency of a group The pie chart shows the meal choices of guests at a wedding.\n\nIf there were \\( 540 \\) people at the wedding, which of the following would calculate how many people chose pork? ![A pie chart split into four parts, labelled with meal choices. The part for Beef is 150 degrees, Pork is 40 degrees and Other is 80 degrees. The angle for Vegetarian is labelled with a square right angle symbol.]() You need more information" }, { "from": "gpt", "value": "Believes it is not possible to calculate the frequency for a pie chart sector despite being given enough information to do so" } ]
[ { "from": "human", "value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 609-1000= \\) \\( 391 \\)" }, { "from": "gpt", "value": "Performs subtraction in wrong order" } ]
[ { "from": "human", "value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 609-1000= \\) This problem cannot be solved" }, { "from": "gpt", "value": "Believes you can not take away a larger number from a smaller one" } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Tom and Katie are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{4}-1=20\n\\)\nTom says you can write: \\( \\frac{m}{4}=21 \\)\nKatie says you can write: \\( m-1=80 \\)\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount" } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Tom and Katie are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{4}-1=20\n\\)\nTom says you can write: \\( \\frac{m}{4}=21 \\)\nKatie says you can write: \\( m-1=80 \\)\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount" } ]
[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Tom and Katie are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{4}-1=20\n\\)\nTom says you can write: \\( \\frac{m}{4}=21 \\)\nKatie says you can write: \\( m-1=80 \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not know how to solve linear equations involving fractions" } ]
[ { "from": "human", "value": "Know the bearings of North-West, North-East, South-West and South-East On what bearing is North-West? ![Shows a compass.]() \\( 270^{\\circ} \\)" }, { "from": "gpt", "value": "Does not understand direction of North East, North West, South East and South West cardinal points" } ]
[ { "from": "human", "value": "Know the bearings of North-West, North-East, South-West and South-East On what bearing is North-West? ![Shows a compass.]() \\( 045^{\\circ} \\)" }, { "from": "gpt", "value": "Does not measure bearing clockwise from the north line" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible: \\( p^{2}-100 \\) \\( p(p-10) \\)" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible: \\( p^{2}-100 \\) \\( (p-10)(p-10) \\)" }, { "from": "gpt", "value": "Factorises difference of two squares with the same sign in both brackets" } ]
[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible: \\( p^{2}-100 \\) Does not factorise" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors of \\( \\mathbf{1 2 y} \\)\nTom says \\( y \\) is a factor of \\( 12 y \\)\nKatie says \\( 3 \\) is a factor of \\( 12 y \\)\nWho do you agree with? Only\nTom" }, { "from": "gpt", "value": "Does not understand the term factor" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors of \\( \\mathbf{1 2 y} \\)\nTom says \\( y \\) is a factor of \\( 12 y \\)\nKatie says \\( 3 \\) is a factor of \\( 12 y \\)\nWho do you agree with? Only\nKatie" }, { "from": "gpt", "value": "Believes factors of algebraic terms/expressions will only be numbers" } ]
[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors of \\( \\mathbf{1 2 y} \\)\nTom says \\( y \\) is a factor of \\( 12 y \\)\nKatie says \\( 3 \\) is a factor of \\( 12 y \\)\nWho do you agree with? Neither is correct" }, { "from": "gpt", "value": "Does not understand the term factor" } ]
[ { "from": "human", "value": "Round integers to the nearest 100 What is \\( \\mathbf{3 2 0} 050 \\) rounded to the nearest hundred? \\( 320050 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]
[ { "from": "human", "value": "Prove statements involving multiples Which of the following expressions is always a multiple of \\( 5 \\) if \\( n \\) is a positive integer. \\( n+5 \\)" }, { "from": "gpt", "value": "Believes adding b to any integer gives a multiple of b" } ]
[ { "from": "human", "value": "Prove statements involving multiples Which of the following expressions is always a multiple of \\( 5 \\) if \\( n \\) is a positive integer. \\( 2 n+3 \\)" }, { "from": "gpt", "value": "Believes they can find the nth term based on the first term only" } ]

[ { "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? Neither is correct" }, { "from": "gpt", "value": "When using inequality notation, thinks \"greater than/less than or equal to\" symbols are instead the \"greater than/less than\" symbols and vice versa" } ]

[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making a T shape where there is a rectangle across the top and a rectangle attached below this, slightly to the left of the centre. The full width across the top is 32m, the partial width on the left is 10m, the partial width on the right is 11m. The full height on the right is 25m, the partial height on the lower block is 14m. The shaded section is the top rectangle across the full width.]() \\( 320 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Uses an incorrect side length when splitting a composite shape into parts" } ]

[ { "from": "human", "value": "Calculate missing lengths of shapes by geometrical inference, where the lengths given are in the same units What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making a T shape where there is a rectangle across the top and a rectangle attached below this, slightly to the left of the centre. The full width across the top is 32m, the partial width on the left is 10m, the partial width on the right is 11m. The full height on the right is 25m, the partial height on the lower block is 14m. The shaded section is the top rectangle across the full width.]() \\( 288 \\mathrm{~m}^{2} \\)" }, { "from": "gpt", "value": "Uses an incorrect side length when splitting a composite shape into parts" } ]

[ { "from": "human", "value": "Recognise cube numbers Which of the following numbers is a cube number? \\( 3 \\)" }, { "from": "gpt", "value": "Does not know what a cube number is" } ]

[ { "from": "human", "value": "Recognise cube numbers Which of the following numbers is a cube number? \\( 6 \\)" }, { "from": "gpt", "value": "Does not know what a cube number is" } ]

[ { "from": "human", "value": "Recognise cube numbers Which of the following numbers is a cube number? \\( 9 \\)" }, { "from": "gpt", "value": "Mixes up square numbers and cube numbers" } ]

[ { "from": "human", "value": "Subtract integers up to 4 digits using a written method where carrying is not needed How should you line up the digits to calculate \\( 3152-809 \\) ? \\( \\begin{array}{r}\\quad\\space3152 \\\\ -809\\end{array} \\)" }, { "from": "gpt", "value": "Lines up the digits incorrectly when doing a subtraction involving two numbers with a different amount of digits" } ]

[ { "from": "human", "value": "Subtract integers up to 4 digits using a written method where carrying is not needed How should you line up the digits to calculate \\( 3152-809 \\) ? \\( \\begin{array}{r}\\quad\\quad3152 \\\\ -89\\end{array} \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]

[ { "from": "human", "value": "Subtract integers up to 4 digits using a written method where carrying is not needed How should you line up the digits to calculate \\( 3152-809 \\) ? \\( \\begin{array}{r}3152 \\\\ -\\space 89\\end{array} \\)" }, { "from": "gpt", "value": "Does not understand the value of zeros as placeholders" } ]

[ { "from": "human", "value": "Identify common factors of two numbers A common factor of \\( 6 \\) and \\( 9 \\) is... \\( 6 \\)" }, { "from": "gpt", "value": "Does not know the 9 timestable" } ]

[ { "from": "human", "value": "Identify common factors of two numbers A common factor of \\( 6 \\) and \\( 9 \\) is... \\( 9 \\)" }, { "from": "gpt", "value": "Does not know the 6 timestable" } ]

[ { "from": "human", "value": "Identify common factors of two numbers A common factor of \\( 6 \\) and \\( 9 \\) is... \\( 18 \\)" }, { "from": "gpt", "value": "Confuses factors and multiples" } ]

[ { "from": "human", "value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c \\begin{tabular}{llll|l|l}\n\\( x \\) & \\( -1 \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) & & \\( 3 \\) \n\\end{tabular} This is a table of values for \\( y=x^{2}-x+3 \\) What should replace the star? \\( -3 \\)" }, { "from": "gpt", "value": "Thinks tables of values are symmetrical about (0,0)" } ]

[ { "from": "human", "value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c \\begin{tabular}{llll|l|l}\n\\( x \\) & \\( -1 \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) & & \\( 3 \\) \n\\end{tabular} This is a table of values for \\( y=x^{2}-x+3 \\) What should replace the star? \\( 3 \\)" }, { "from": "gpt", "value": "Does not realise that subtracting a negative is the same as adding it's additive inverse" } ]

[ { "from": "human", "value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c \\begin{tabular}{llll|l|l}\n\\( x \\) & \\( -1 \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) \\\\\n\\hline\\( y \\) & \\( \\bigstar \\) & & \\( 3 \\) \n\\end{tabular} This is a table of values for \\( y=x^{2}-x+3 \\) What should replace the star? \\( 6 \\)" }, { "from": "gpt", "value": "Thinks 1 squared is 2" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 10 What is \\( \\mathbf{8 6 9 8 . 9} \\) rounded to the nearest ten? \\( 8699 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too much)" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 10 What is \\( \\mathbf{8 6 9 8 . 9} \\) rounded to the nearest ten? \\( 8690 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round non-integers to the nearest 10 What is \\( \\mathbf{8 6 9 8 . 9} \\) rounded to the nearest ten? \\( 9000 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Recognise the angles on a straight line relationship What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]() They are equal" }, { "from": "gpt", "value": "Student thinks that any two angles along a straight line are equal" } ]

[ { "from": "human", "value": "Recognise the angles on a straight line relationship What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]() They are parallel" }, { "from": "gpt", "value": "Does not know the meaning of the word parallel" } ]

[ { "from": "human", "value": "Recognise the angles on a straight line relationship What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]() They add together to make\n\\[\n360^{\\circ}\n\\]" }, { "from": "gpt", "value": "Believes angles on a straight line add to 360 degrees" } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n10=\\frac{5}{p}\n\\) \\( p=50 \\)" }, { "from": "gpt", "value": "When solving an equation, uses the same operation rather than the inverse." } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n10=\\frac{5}{p}\n\\) \\( p=2 \\)" }, { "from": "gpt", "value": "Assumes the denominator is divided by the numerator" } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n10=\\frac{5}{p}\n\\) There are no solutions" }, { "from": "gpt", "value": "Does not know how to solve linear equations involving fractions" } ]

[ { "from": "human", "value": "Recognise when an ascending sequence is linear Tom and Katie are discussing linear sequences.\n\nTom says this is a linear sequence: \\( 1,2,4,7,11, \\ldots \\) \n\nKatie says this is a linear sequence: \\( 1.2,1.4,1.6,1.8,2, \\ldots \\) \n\nWho is correct?\n Only Tom" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]

[ { "from": "human", "value": "Recognise when an ascending sequence is linear Tom and Katie are discussing linear sequences.\n\nTom says this is a linear sequence: \\( 1,2,4,7,11, \\ldots \\) \n\nKatie says this is a linear sequence: \\( 1.2,1.4,1.6,1.8,2, \\ldots \\) \n\nWho is correct?\n Both Tom and Katie" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]

[ { "from": "human", "value": "Recognise when an ascending sequence is linear Tom and Katie are discussing linear sequences.\n\nTom says this is a linear sequence: \\( 1,2,4,7,11, \\ldots \\) \n\nKatie says this is a linear sequence: \\( 1.2,1.4,1.6,1.8,2, \\ldots \\) \n\nWho is correct?\n Neither is correct" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]

[ { "from": "human", "value": "Convert between cm and m \\( 27 \\mathrm{~cm}=\\square \\mathrm{m} \\) \\( 0.3 \\)" }, { "from": "gpt", "value": "Believes they can round when converting units" } ]

[ { "from": "human", "value": "Convert between cm and m \\( 27 \\mathrm{~cm}=\\square \\mathrm{m} \\) \\( 2700 \\)" }, { "from": "gpt", "value": "Multiplies when converting to a larger unit" } ]

[ { "from": "human", "value": "Convert between cm and m \\( 27 \\mathrm{~cm}=\\square \\mathrm{m} \\) \\( 2.7 \\)" }, { "from": "gpt", "value": "Thinks there are 10cm in a metre" } ]

[ { "from": "human", "value": "Solve missing number mental multiplication problems with decimals What should replace the star? \\( 0.03 \\times \\bigstar=0.00009 \\) \\( 0.03 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]

[ { "from": "human", "value": "Solve missing number mental multiplication problems with decimals What should replace the star? \\( 0.03 \\times \\bigstar=0.00009 \\) \\( 0.3 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]

[ { "from": "human", "value": "Solve missing number mental multiplication problems with decimals What should replace the star? \\( 0.03 \\times \\bigstar=0.00009 \\) \\( 0.0003 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]

[ { "from": "human", "value": "Complete missing number mental subtraction problems up to 100 What should replace the star?\n\\[\n\\bigstar-26=28\n\\] \\( 2 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]

[ { "from": "human", "value": "Complete missing number mental subtraction problems up to 100 What should replace the star?\n\\[\n\\bigstar-26=28\n\\] \\( -2 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]

[ { "from": "human", "value": "Complete missing number mental subtraction problems up to 100 What should replace the star?\n\\[\n\\bigstar-26=28\n\\] \\( 44 \\)" }, { "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": "Multiply algebraic fractions where the numerators and denominators are all single terms Express the following as a single fraction, writing your answer as simply as possible:\n\n\\(\n\\frac{1}{s} \\times \\frac{2}{t}\n\\) \\( \\frac{t+2 s}{s t} \\)" }, { "from": "gpt", "value": "When asked to multiply fractions, uses the method for adding instead" } ]

[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators are all single terms Express the following as a single fraction, writing your answer as simply as possible:\n\n\\(\n\\frac{1}{s} \\times \\frac{2}{t}\n\\) \\( \\frac{3}{s+t} \\)" }, { "from": "gpt", "value": "When multiplying fractions, adds the numerators and the denominators" } ]

[ { "from": "human", "value": "Multiply algebraic fractions where the numerators and denominators are all single terms Express the following as a single fraction, writing your answer as simply as possible:\n\n\\(\n\\frac{1}{s} \\times \\frac{2}{t}\n\\) \\( \\frac{3}{s t} \\)" }, { "from": "gpt", "value": "When multiplying fractions, adds the numerators and multiplies the denominators" } ]

[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\( 18 \\div 2+2 \\times 2= \\) \\( 3 \\)" }, { "from": "gpt", "value": "Confuses the order of operations, believes addition comes before division" } ]

[ { "from": "human", "value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\( 18 \\div 2+2 \\times 2= \\) \\( 22 \\)" }, { "from": "gpt", "value": "Carries out operations from left to right regardless of priority order" } ]

[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]() \\( \\frac{2}{3} \\)" }, { "from": "gpt", "value": "Cannot identify a fraction on a number line" } ]

[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]() \\( 1 \\frac{2}{3} \\)" }, { "from": "gpt", "value": "Confused mixed numbers with improper fractions" } ]

[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]() \\( \\frac{4}{2} \\)" }, { "from": "gpt", "value": "Cannot identify a fraction on a number line" } ]

[ { "from": "human", "value": "Calculate the mean as an average from a list of data Without using a calculator, what is the mean of the following numbers?\n\n\\[\n2,2,3,3,2\n\\] \\( 2 \\)" }, { "from": "gpt", "value": "When asked for the mean of a list of data, gives the mode" } ]

[ { "from": "human", "value": "Calculate the mean as an average from a list of data Without using a calculator, what is the mean of the following numbers?\n\n\\[\n2,2,3,3,2\n\\] \\( 3 \\)" }, { "from": "gpt", "value": "Believes the mean is the middle number" } ]

[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram ![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners\nWhat is the probability of getting a \\( 1 \\) on both spinners? \\( \\frac{1}{9} \\)" }, { "from": "gpt", "value": "When multiplying fractions, multiplies the numerator and adds the denominator" } ]

[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram ![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners\nWhat is the probability of getting a \\( 1 \\) on both spinners? \\( \\frac{2}{9} \\)" }, { "from": "gpt", "value": "When adding fractions, adds the numerators and denominators" } ]

[ { "from": "human", "value": "Calculate the probability of two independent events occurring without drawing a tree diagram ![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners\nWhat is the probability of getting a \\( 1 \\) on both spinners? \\( \\frac{2}{20} \\)" }, { "from": "gpt", "value": "When multiplying fractions, adds the numerators and multiplies the denominators" } ]

[ { "from": "human", "value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\[\n23 \\mathrm{~cm}, \\quad 17 \\mathrm{~cm}, \\quad 40 \\mathrm{~cm}, \\quad 25 \\mathrm{~cm}, \\quad 31 \\mathrm{~cm}\n\\]\n\nTom says if all the plants doubled in height, the range wouldn't change.\n\nKatie says if all the plants grew by \\( 12 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with? Only Tom" }, { "from": "gpt", "value": "Believes if you changed all values by the same proportion the range would not change" } ]

[ { "from": "human", "value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\[\n23 \\mathrm{~cm}, \\quad 17 \\mathrm{~cm}, \\quad 40 \\mathrm{~cm}, \\quad 25 \\mathrm{~cm}, \\quad 31 \\mathrm{~cm}\n\\]\n\nTom says if all the plants doubled in height, the range wouldn't change.\n\nKatie says if all the plants grew by \\( 12 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with? Both Tom and Katie" }, { "from": "gpt", "value": "Believes if you changed all values by the same proportion the range would not change" } ]

[ { "from": "human", "value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\[\n23 \\mathrm{~cm}, \\quad 17 \\mathrm{~cm}, \\quad 40 \\mathrm{~cm}, \\quad 25 \\mathrm{~cm}, \\quad 31 \\mathrm{~cm}\n\\]\n\nTom says if all the plants doubled in height, the range wouldn't change.\n\nKatie says if all the plants grew by \\( 12 \\mathrm{~cm} \\) each, the range wouldn't change.\nWho do you agree with? Neither is correct" }, { "from": "gpt", "value": "Believes if you add the same value to all numbers in the dataset the range will change" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible: \\( \\frac{t^{2}-1}{t+1} \\) \\( t \\)" }, { "from": "gpt", "value": "Thinks you can divide terms by different factors when simplifying an algebraic fraction" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible: \\( \\frac{t^{2}-1}{t+1} \\) Does not simplify" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]

[ { "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 If the original sequence looks like this: ![Two patterns made of squares. Pattern 1 consists of a central column of three squares, with an extra square either side, making a cross. Pattern two consists of two central columns of three squares with one extra square either side. ]() There are \\( 302 \\) squares in Pattern \\( 100 \\). But if the shape changes to this: ![These patterns are the same as those in the first picture except that in each, the second block from each column of three has been removed. ]() How many squares would there be in Pattern \\( 100 \\) now? \\( 301 \\)" }, { "from": "gpt", "value": "Only looks at the difference between one pair of terms when discerning the pattern" } ]

[ { "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 If the original sequence looks like this: ![Two patterns made of squares. Pattern 1 consists of a central column of three squares, with an extra square either side, making a cross. Pattern two consists of two central columns of three squares with one extra square either side. ]() There are \\( 302 \\) squares in Pattern \\( 100 \\). But if the shape changes to this: ![These patterns are the same as those in the first picture except that in each, the second block from each column of three has been removed. ]() How many squares would there be in Pattern \\( 100 \\) now? \\( 300 \\)" }, { "from": "gpt", "value": "Only looks at the difference between one pair of terms when discerning the pattern" } ]

[ { "from": "human", "value": "Round decimals to the nearest whole number \\[\n0.059623\n\\]\nWhat is this number rounded to the nearest integer? \\( 0.06 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Round decimals to the nearest whole number \\[\n0.059623\n\\]\nWhat is this number rounded to the nearest integer? \\( 0.05 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Round decimals to the nearest whole number \\[\n0.059623\n\\]\nWhat is this number rounded to the nearest integer? \\( 1 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]

[ { "from": "human", "value": "Find missing angles in a parallelogram What is the size of angle \\( p \\) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]() \\( 65^{\\circ} \\)" }, { "from": "gpt", "value": "Thinks co-interior angles are equal" } ]

[ { "from": "human", "value": "Find missing angles in a parallelogram What is the size of angle \\( p \\) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]() \\( 125^{\\circ} \\)" }, { "from": "gpt", "value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit" } ]

[ { "from": "human", "value": "Find missing angles in a parallelogram What is the size of angle \\( p \\) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]() Not enough information to work it out" }, { "from": "gpt", "value": "Does not recognise parallel lines angle rules applied inside a shape" } ]

[ { "from": "human", "value": "Given the perimeter, work out a missing length requiring knowledge of the geometrical properties of the shape A shape is made up of a square and a rectangle. ![\\begin{tabular}{|l|l|}\n\\hline & \\\\\n\\hline & \\\\\n\\hline\n\\end{tabular}]() The perimeter of the shape is \\( 30 \\mathrm{~cm} \\). The area of the square is \\( 16 \\mathrm{~cm}^{2} \\).\nWhat is the area of the shape? \\( 4 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Does not know how to find missing lengths in a composite shape" } ]

[ { "from": "human", "value": "Round integers to the nearest 100 A number rounds to \\( 20,000 \\) when rounded to the nearest ten thousand, thousand and hundred.\nWhich number could this be? \\( 19199 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]

[ { "from": "human", "value": "Round integers to the nearest 100 A number rounds to \\( 20,000 \\) when rounded to the nearest ten thousand, thousand and hundred.\nWhich number could this be? \\( 20074 \\)" }, { "from": "gpt", "value": "Rounds down instead of up" } ]

[ { "from": "human", "value": "Round integers to the nearest 100 A number rounds to \\( 20,000 \\) when rounded to the nearest ten thousand, thousand and hundred.\nWhich number could this be? \\( 19949 \\)" }, { "from": "gpt", "value": "Rounds up instead of down" } ]

[ { "from": "human", "value": "Identify corresponding angles These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]() Alternate" }, { "from": "gpt", "value": "Confuses corresponding and alternate angles" } ]

[ { "from": "human", "value": "Identify corresponding angles These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]() Co-Interior" }, { "from": "gpt", "value": "Confuses co-interior and alternate angles" } ]

[ { "from": "human", "value": "Identify corresponding angles These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]() Parallel" }, { "from": "gpt", "value": "Describes lines when asked to describe angles" } ]

[ { "from": "human", "value": "Read values off a real life graph ![A linear graph showing that 10 miles = £8. ]() The graph can be used to work out how much Kay's company pays her for travel.\n\nKay's company paid her \\( £ 80 \\)\n\nHow many miles did she travel? \\( 64 \\)" }, { "from": "gpt", "value": "When reading value from graph, reads from the wrong axes." } ]

[ { "from": "human", "value": "Read values off a real life graph ![A linear graph showing that 10 miles = £8. ]() The graph can be used to work out how much Kay's company pays her for travel.\n\nKay's company paid her \\( £ 80 \\)\n\nHow many miles did she travel? \\( 80 \\)" }, { "from": "gpt", "value": "Believes direct proportion means a 1:1 ratio" } ]

[ { "from": "human", "value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.4=\\frac{2}{5}=? \\% \\) \\( 25 \\% \\)" }, { "from": "gpt", "value": "Converts a fraction to a percentage by writing the numerator followed by the denominator" } ]

[ { "from": "human", "value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.4=\\frac{2}{5}=? \\% \\) \\( 4 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]

[ { "from": "human", "value": "Recognise the equations of vertical lines from a diagram What is the equation of this line? ![A coordinate grid with a red line drawn on passing through the points: (-2,-10) (-2,-2) (-2, 0) (-2,4) (-2,10)]() \\( x=-1 \\)" }, { "from": "gpt", "value": "Counts squares instead of the correct scale when plotting coordinates" } ]

[ { "from": "human", "value": "Recognise the equations of vertical lines from a diagram What is the equation of this line? ![A coordinate grid with a red line drawn on passing through the points: (-2,-10) (-2,-2) (-2, 0) (-2,4) (-2,10)]() \\( y=-2 \\)" }, { "from": "gpt", "value": "Confuses the equations of vertical and horizontal lines" } ]

[ { "from": "human", "value": "Identify a rectangle when presented non-conventionally ![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape? Square" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]

[ { "from": "human", "value": "Identify a rectangle when presented non-conventionally ![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape? Rhombus" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]

[ { "from": "human", "value": "Identify a rectangle when presented non-conventionally ![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape? Kite" }, { "from": "gpt", "value": "Does not know the properties of a rectangle" } ]

[ { "from": "human", "value": "Write a missing term of a descending integer linear sequence \\( 53, \\quad 46, \\quad 39, \\quad \\ldots \\) What is the \\( 8^{\\text {th }} \\) term in this linear sequence? \\( 32 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the next term" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"+¼\" written inside it and the final rectangle has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 8 \\frac{1}{4} \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"+¼\" written inside it and the final rectangle has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 2 \\)" }, { "from": "gpt", "value": "Thinks the inverse of addition is multiplication" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says \"input\" above it. The middle rectangle has \"+¼\" written inside it and the final rectangle has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 32 \\)" }, { "from": "gpt", "value": "Thinks the inverse of addition is division" } ]

[ { "from": "human", "value": "Given the sector angle on a pie chart, calculate the frequency of a group The pie chart shows the meal choices of guests at a wedding.\n\nIf there were \\( 540 \\) people at the wedding, which of the following would calculate how many people chose pork? ![A pie chart split into four parts, labelled with meal choices. The part for Beef is 150 degrees, Pork is 40 degrees and Other is 80 degrees. The angle for Vegetarian is labelled with a square right angle symbol.]() \\( \\frac{360}{40} \\times 540 \\)" }, { "from": "gpt", "value": "Believes a proportion of a whole is whole/part not part/whole" } ]

[ { "from": "human", "value": "Given the sector angle on a pie chart, calculate the frequency of a group The pie chart shows the meal choices of guests at a wedding.\n\nIf there were \\( 540 \\) people at the wedding, which of the following would calculate how many people chose pork? ![A pie chart split into four parts, labelled with meal choices. The part for Beef is 150 degrees, Pork is 40 degrees and Other is 80 degrees. The angle for Vegetarian is labelled with a square right angle symbol.]() You need more information" }, { "from": "gpt", "value": "Believes it is not possible to calculate the frequency for a pie chart sector despite being given enough information to do so" } ]

[ { "from": "human", "value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 609-1000= \\) \\( 391 \\)" }, { "from": "gpt", "value": "Performs subtraction in wrong order" } ]

[ { "from": "human", "value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 609-1000= \\) This problem cannot be solved" }, { "from": "gpt", "value": "Believes you can not take away a larger number from a smaller one" } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Tom and Katie are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{4}-1=20\n\\)\nTom says you can write: \\( \\frac{m}{4}=21 \\)\nKatie says you can write: \\( m-1=80 \\)\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount" } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Tom and Katie are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{4}-1=20\n\\)\nTom says you can write: \\( \\frac{m}{4}=21 \\)\nKatie says you can write: \\( m-1=80 \\)\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount" } ]

[ { "from": "human", "value": "Solve two-step linear equations, with the variable on one side, with all positive integers Tom and Katie are arguing about a first step to solve this equation:\n\\(\n\\frac{m}{4}-1=20\n\\)\nTom says you can write: \\( \\frac{m}{4}=21 \\)\nKatie says you can write: \\( m-1=80 \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not know how to solve linear equations involving fractions" } ]

[ { "from": "human", "value": "Know the bearings of North-West, North-East, South-West and South-East On what bearing is North-West? ![Shows a compass.]() \\( 270^{\\circ} \\)" }, { "from": "gpt", "value": "Does not understand direction of North East, North West, South East and South West cardinal points" } ]

[ { "from": "human", "value": "Know the bearings of North-West, North-East, South-West and South-East On what bearing is North-West? ![Shows a compass.]() \\( 045^{\\circ} \\)" }, { "from": "gpt", "value": "Does not measure bearing clockwise from the north line" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible: \\( p^{2}-100 \\) \\( p(p-10) \\)" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible: \\( p^{2}-100 \\) \\( (p-10)(p-10) \\)" }, { "from": "gpt", "value": "Factorises difference of two squares with the same sign in both brackets" } ]

[ { "from": "human", "value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible: \\( p^{2}-100 \\) Does not factorise" }, { "from": "gpt", "value": "Does not recognise difference of two squares" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors of \\( \\mathbf{1 2 y} \\)\nTom says \\( y \\) is a factor of \\( 12 y \\)\nKatie says \\( 3 \\) is a factor of \\( 12 y \\)\nWho do you agree with? Only\nTom" }, { "from": "gpt", "value": "Does not understand the term factor" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors of \\( \\mathbf{1 2 y} \\)\nTom says \\( y \\) is a factor of \\( 12 y \\)\nKatie says \\( 3 \\) is a factor of \\( 12 y \\)\nWho do you agree with? Only\nKatie" }, { "from": "gpt", "value": "Believes factors of algebraic terms/expressions will only be numbers" } ]

[ { "from": "human", "value": "Identify factors of algebraic expressions Tom and Katie are discussing factors of \\( \\mathbf{1 2 y} \\)\nTom says \\( y \\) is a factor of \\( 12 y \\)\nKatie says \\( 3 \\) is a factor of \\( 12 y \\)\nWho do you agree with? Neither is correct" }, { "from": "gpt", "value": "Does not understand the term factor" } ]

[ { "from": "human", "value": "Round integers to the nearest 100 What is \\( \\mathbf{3 2 0} 050 \\) rounded to the nearest hundred? \\( 320050 \\)" }, { "from": "gpt", "value": "Rounds to the wrong degree of accuracy (rounds too little)" } ]

[ { "from": "human", "value": "Prove statements involving multiples Which of the following expressions is always a multiple of \\( 5 \\) if \\( n \\) is a positive integer. \\( n+5 \\)" }, { "from": "gpt", "value": "Believes adding b to any integer gives a multiple of b" } ]

[ { "from": "human", "value": "Prove statements involving multiples Which of the following expressions is always a multiple of \\( 5 \\) if \\( n \\) is a positive integer. \\( 2 n+3 \\)" }, { "from": "gpt", "value": "Believes they can find the nth term based on the first term only" } ]