bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number \\( \\begin{array}{llllll}\\frac{8}{10} & \\frac{41}{50} & \\frac{7}{20} & 0.77 & \\frac{4}{5} & \\frac{79}{100}\\end{array} \\) Which value is the outlier in this set of data? \\( \\frac{79}{100} \\)" }, { "from": "gpt", "value": "Believes an outlier is the value in a data set with the biggest denominator, even if this value is close to the mean" } ]
[ { "from": "human", "value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 2 \\) days? \\( 2 \\times 12 \\times 60 \\times 60 \\)" }, { "from": "gpt", "value": "Thinks there are 12 hours in 1 day" } ]
[ { "from": "human", "value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 2 \\) days? \\( 2 \\times 24 \\times 60 \\)" }, { "from": "gpt", "value": "Converted hours to minutes instead of hours to seconds" } ]
[ { "from": "human", "value": "Describe a translation using vector notation where at least one value is negative Which of the following vectors describes how to get from point \\( P \\) to point \\( Q \\)? ![The image shows a square grid and 2 points, P and Q. Point P is 4 squares left and 2 squares up from point Q. ]() \\( \\left(\\begin{array}{l}4 \\\\ 2\\end{array}\\right) \\)" }, { "from": "gpt", "value": "Thinks a positive y value in a column vector means to move down rather than up " } ]
[ { "from": "human", "value": "Describe a translation using vector notation where at least one value is negative Which of the following vectors describes how to get from point \\( P \\) to point \\( Q \\)? ![The image shows a square grid and 2 points, P and Q. Point P is 4 squares left and 2 squares up from point Q. ]() \\( \\left(\\begin{array}{c}-2 \\\\ 4\\end{array}\\right) \\)" }, { "from": "gpt", "value": "Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round" } ]
[ { "from": "human", "value": "Solve one-step linear equations requiring addition or subtraction, involving positive fractions Solve the equation:\n\\(\np-3=\\frac{1}{12}\n\\) \\( p=\\frac{4}{12} \\)" }, { "from": "gpt", "value": "When adding an integer to a fraction, thinks you add the integer to the numerator" } ]
[ { "from": "human", "value": "Solve one-step linear equations requiring addition or subtraction, involving positive fractions Solve the equation:\n\\(\np-3=\\frac{1}{12}\n\\) \\( p=\\frac{3}{36} \\)" }, { "from": "gpt", "value": "When solving an equation, multiplies instead of adding" } ]
[ { "from": "human", "value": "Substitute into simple formulae given in words To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.\nWhat is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]() \\( 15 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Does not divide by 2 when calculating the area of a triangle" } ]
[ { "from": "human", "value": "Substitute into simple formulae given in words To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.\nWhat is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]() \\( 4 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Adds instead of multiples" } ]
[ { "from": "human", "value": "Substitute into simple formulae given in words To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.\nWhat is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]() \\( 30 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Thinks halving is the same as multiplying by 2" } ]
[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\n\\( \\frac{18}{30} \\) \\( \\frac{4.5}{7.5} \\)" }, { "from": "gpt", "value": "Believes you can have decimals in a simplified fraction" } ]
[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\n\\( \\frac{18}{30} \\) \\( \\frac{9}{15} \\)" }, { "from": "gpt", "value": "Does not fully simplify fraction" } ]
[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\n\\( \\frac{18}{30} \\) Cannot be simplified" }, { "from": "gpt", "value": "Does not understand how to simplify fractions" } ]
[ { "from": "human", "value": "Calculate the square of a number What is the value of \\( 4^{2} \\) ? \\( 8 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]
[ { "from": "human", "value": "Calculate the square of a number What is the value of \\( 4^{2} \\) ? \\( 6 \\)" }, { "from": "gpt", "value": "Adds the index to the number" } ]
[ { "from": "human", "value": "Calculate the square of a number What is the value of \\( 4^{2} \\) ? \\( 4 \\)" }, { "from": "gpt", "value": "Believes a power of 2 has no impact on its value" } ]
[ { "from": "human", "value": "Estimate the gradient at a point on a non-linear section of a real life graph The graph shows information about the velocity, \\( v \\mathrm{~m} / \\mathrm{s} \\), of a parachutist \\( t \\) seconds after leaving a plane.\n\nWhich of the following is the best estimate for the gradient of the curve when \\( t=6 \\) ![The image is of a velocity-time graph. There is a straight line, a tangent, drawn so that it is touching the curve at t=6. The tangent goes through (2, 31), (6, 47) and (8,55). ]() \\( 46 \\)" }, { "from": "gpt", "value": "Does not understand the difference between a value on a graph and the gradient of a graph" } ]
[ { "from": "human", "value": "Estimate the gradient at a point on a non-linear section of a real life graph The graph shows information about the velocity, \\( v \\mathrm{~m} / \\mathrm{s} \\), of a parachutist \\( t \\) seconds after leaving a plane.\n\nWhich of the following is the best estimate for the gradient of the curve when \\( t=6 \\) ![The image is of a velocity-time graph. There is a straight line, a tangent, drawn so that it is touching the curve at t=6. The tangent goes through (2, 31), (6, 47) and (8,55). ]() \\( 7.66 \\ldots \\)" }, { "from": "gpt", "value": "Believes gradient at a point = y coordinate/x coordinate" } ]
[ { "from": "human", "value": "Recognise other roots of numbers \\( \\sqrt[4]{16}=? \\) \\( 64 \\)" }, { "from": "gpt", "value": "Has multiplied by the root power" } ]
[ { "from": "human", "value": "Recognise other roots of numbers \\( \\sqrt[4]{16}=? \\) \\( 16 \\)" }, { "from": "gpt", "value": "Does not understand the root power of 4" } ]
[ { "from": "human", "value": "Recognise other roots of numbers \\( \\sqrt[4]{16}=? \\) \\( 4 \\)" }, { "from": "gpt", "value": "Divides by the order of the root" } ]
[ { "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 \\) & & \\( -1 \\) & \n\\end{tabular} This is a table of values for \\( y=x^{2}-x+1 \\) What should replace the star? \\( 1 \\)" }, { "from": "gpt", "value": "Does not realise that subtracting a negative is the same as adding it's additive inverse" } ]
[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c What is the gradient of this line?\n\\(4 x-5 y=20\\) \\( 4 \\)" }, { "from": "gpt", "value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c" } ]
[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c What is the gradient of this line?\n\\(4 x-5 y=20\\) \\( -\\frac{4}{5} \\)" }, { "from": "gpt", "value": "When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value" } ]
[ { "from": "human", "value": "Read values off a real life graph This is a conversion graph between pints and litres.\nWhich of the following is the best estimate for the number of pints equivalent to \\( 50 \\) litres? ![A graph on gridded paper showing litres on the y axis from 0 to 50 and pints on the x axis from 0 to 90. A straight line goes from the origin and passes through (35,20) (not marked - just a point it goes through) but extends the whole way up the graph.]() \\( 28 \\) pints" }, { "from": "gpt", "value": "When reading value from graph, reads from the wrong axes." } ]
[ { "from": "human", "value": "Read values off a real life graph This is a conversion graph between pints and litres.\nWhich of the following is the best estimate for the number of pints equivalent to \\( 50 \\) litres? ![A graph on gridded paper showing litres on the y axis from 0 to 50 and pints on the x axis from 0 to 90. A straight line goes from the origin and passes through (35,20) (not marked - just a point it goes through) but extends the whole way up the graph.]() \\( 85 \\) pints" }, { "from": "gpt", "value": "When reading graph, chooses nearest marked value on axis instead of reading accurately" } ]
[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation \\( y=3 x \\) ![A table with two rows and two columns. The top left box has 'x', with a star in the top right box. The bottom left box has 'y' with a 9 in the bottom right box. ]() What should replace the star? \\( 6 \\)" }, { "from": "gpt", "value": "Thinks the inverse of subtraction is multiplication" } ]
[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation \\( y=3 x \\) ![A table with two rows and two columns. The top left box has 'x', with a star in the top right box. The bottom left box has 'y' with a 9 in the bottom right box. ]() What should replace the star? \\( 27 \\)" }, { "from": "gpt", "value": "Mixes up the value of two terms when substituting" } ]
[ { "from": "human", "value": "Identify data which is qualitative or quantitative Leanne has written a questionnaire on the topic of holidays. One of her questions is,\n\n\"Describe how you feel when you are about to go on holiday.\"\n\nWhat type of data is she collecting by asking this question? Primary\nQuantitative\ndata" }, { "from": "gpt", "value": "Mixes up quantitative and qualitative data types" } ]
[ { "from": "human", "value": "Identify data which is qualitative or quantitative Leanne has written a questionnaire on the topic of holidays. One of her questions is,\n\n\"Describe how you feel when you are about to go on holiday.\"\n\nWhat type of data is she collecting by asking this question? Attribute data" }, { "from": "gpt", "value": "Does not know the meaning of attribute data" } ]
[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b \\( m^{2}+6 m+1 \\equiv(m \\bigstar )^{2} \\triangle \\) \\(\\bigstar =+6 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is the coefficient of x" } ]
[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b \\( m^{2}+6 m+1 \\equiv(m \\bigstar )^{2} \\triangle \\) \\(\\bigstar =+12 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is double the coefficient of x" } ]
[ { "from": "human", "value": "Answer negative number problems that require the use of BIDMAS Which calculation is equal to \\( -20 \\) ? \\( 2 \\times(-2)-(-4) \\times 4 \\)" }, { "from": "gpt", "value": "Does not realise that subtracting a negative is the same as adding it's additive inverse" } ]
[ { "from": "human", "value": "Answer negative number problems that require the use of BIDMAS Which calculation is equal to \\( -20 \\) ? \\( (-5)^{2}+5 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]
[ { "from": "human", "value": "Answer negative number problems that require the use of BIDMAS Which calculation is equal to \\( -20 \\) ? \\( (-42) \\div(-2)+1 \\)" }, { "from": "gpt", "value": "Believes dividing a negative by a negative gives a negative answer" } ]
[ { "from": "human", "value": "Carry out addition problems involving two negative integers \\( (-5)+(-2)= \\) \\( 7 \\)" }, { "from": "gpt", "value": "Believes adding two negatives gives a positive answer" } ]
[ { "from": "human", "value": "Carry out addition problems involving two negative integers \\( (-5)+(-2)= \\) \\( -3 \\)" }, { "from": "gpt", "value": "Believes that adding a negative will increase the value of the original number" } ]
[ { "from": "human", "value": "Write the next term of an ascending integer linear sequence \\[\n5,12,19,26, \\ldots ?\n\\]\n\nWhat number comes next in this sequence? \\( 40 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the term after" } ]
[ { "from": "human", "value": "Read values off a speed-time graph This velocity-time graph shows the first \\( 5 \\) seconds of Mo's journey which starts at home.\n\nAt what time did he first start travelling at \\( 4 \\mathrm{~m} / \\mathrm{s} \\) ? ![The image is of a graph. Its vertical axis labelled Velocity (m/s) and has the scale 0, 2, 4, 6 marked in even steps. Its horizontal axis is labelled Time (secs) and has the scale 0, 1, 2, 3, 4, 5 marked in even steps. \nThe graph is in three sections. The first section is a straight slanted line from (0,0) to (1, 4). The second section is a horizontal line from (1, 4) to (3, 4). The third section is a slanted line from (3, 4) to (5, 0).]() \\( 4 \\) secs" }, { "from": "gpt", "value": "When reading value from graph, reads from the wrong axes." } ]
[ { "from": "human", "value": "Identify the order of rotational symmetry of a shape Tom and Katie are arguing about the order of rotational symmetry of quadrilaterals.\n\nTom says some quadrilaterals have an order of rotational symmetry of \\( 1 \\).\nKatie says some quadrilaterals have an order of rotational symmetry of \\( 3 \\).\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Does not connect rotational symmetry to number of sides/vertices" } ]
[ { "from": "human", "value": "Identify the order of rotational symmetry of a shape Tom and Katie are arguing about the order of rotational symmetry of quadrilaterals.\n\nTom says some quadrilaterals have an order of rotational symmetry of \\( 1 \\).\nKatie says some quadrilaterals have an order of rotational symmetry of \\( 3 \\).\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not connect rotational symmetry to number of sides/vertices" } ]
[ { "from": "human", "value": "Read a negative integer temperature from a thermometer What temperature does the thermometer show? ![A thermometer showing the temperature in degrees Celsius. There are five steps on the scale between 10 and 0, and five steps between 0 and -10. The temperature is shown at 4 steps below 0.]() \\( -9^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "When reading integers on a number line, assumes each dash is 1" } ]
[ { "from": "human", "value": "Read a negative integer temperature from a thermometer What temperature does the thermometer show? ![A thermometer showing the temperature in degrees Celsius. There are five steps on the scale between 10 and 0, and five steps between 0 and -10. The temperature is shown at 4 steps below 0.]() \\( -4^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "When reading integers on a number line, assumes each dash is 1" } ]
[ { "from": "human", "value": "Calculate the surface area of a cuboid where the dimensions are given in the same units Which of the following calculations would give you the total surface area of this cuboid in \\( \\mathrm{cm}^{2} \\) ? ![A cuboid. The top measures 4cm by 2cm, and the height is 7cm.]() \\( (2 \\times 7)+(4 \\times 2)+(4 \\times 7) \\)" }, { "from": "gpt", "value": "When calculating surface area, only includes visible faces" } ]
[ { "from": "human", "value": "Calculate the surface area of a cuboid where the dimensions are given in the same units Which of the following calculations would give you the total surface area of this cuboid in \\( \\mathrm{cm}^{2} \\) ? ![A cuboid. The top measures 4cm by 2cm, and the height is 7cm.]() \\( 2 \\times 4 \\times 7 \\)" }, { "from": "gpt", "value": "Finds volume when asked for surface area" } ]
[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using the grid method What should replace the star when solving the following problem using the grid method?\n\\(52 \\times 326\\) \\begin{tabular}{\|c\|c\|c\|c\|}\n\\hline\\( \\times \\) & \\( 300 \\) & \\( 20 \\) & \\( 6 \\) \\\\\n\\hline \\( 50 \\) & & \\( \\bigstar \\) & \\\\\n\\hline \\( 2 \\) & & \\\\\n\\hline\n\\end{tabular} \\( 10 \\)" }, { "from": "gpt", "value": "When multiplying involving a multiple of 10, just multiplies the digits and ignores the zeros " } ]
[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using the grid method What should replace the star when solving the following problem using the grid method?\n\\(52 \\times 326\\) \\begin{tabular}{\|c\|c\|c\|c\|}\n\\hline\\( \\times \\) & \\( 300 \\) & \\( 20 \\) & \\( 6 \\) \\\\\n\\hline \\( 50 \\) & & \\( \\bigstar \\) & \\\\\n\\hline \\( 2 \\) & & \\\\\n\\hline\n\\end{tabular} \\( 70 \\)" }, { "from": "gpt", "value": "Adds instead of multiples" } ]
[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using the grid method What should replace the star when solving the following problem using the grid method?\n\\(52 \\times 326\\) \\begin{tabular}{\|c\|c\|c\|c\|}\n\\hline\\( \\times \\) & \\( 300 \\) & \\( 20 \\) & \\( 6 \\) \\\\\n\\hline \\( 50 \\) & & \\( \\bigstar \\) & \\\\\n\\hline \\( 2 \\) & & \\\\\n\\hline\n\\end{tabular} \\( 100 \\)" }, { "from": "gpt", "value": "When multiplying involving a multiple of 10, gives an answer 10 times smaller than it should be" } ]
[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{3 6} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() B" }, { "from": "gpt", "value": "Mixes up odd and even numbers" } ]
[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{3 6} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() C" }, { "from": "gpt", "value": "Mixes up odd and even numbers" } ]
[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{3 6} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() D" }, { "from": "gpt", "value": "Mixes up odd and even numbers" } ]
[ { "from": "human", "value": "Complete missing number mental addition problems with numbers over 1000 A \\( 3 \\) digit number belongs in this box to make the calculation true\n\\(\n258+\\square=1162\n\\)\nWhat is the \\( 3^{\\text {rd }} \\) digit of the number that belongs in the box? \\( 0 \\)" }, { "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 with numbers over 1000 A \\( 3 \\) digit number belongs in this box to make the calculation true\n\\(\n258+\\square=1162\n\\)\nWhat is the \\( 3^{\\text {rd }} \\) digit of the number that belongs in the box? \\( 6 \\)" }, { "from": "gpt", "value": "Subtracts the smallest digit from the largest digit" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p-5)(p+2) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=-3 \\)" }, { "from": "gpt", "value": "Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets" } ]
[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p-5)(p+2) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=+10 \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]
[ { "from": "human", "value": "Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (2,5) \\)\nThe point is reflected in the line \\( x=2 \\)\nWhat are the new coordinates of point \\( Q \\) ? \\( (-2,5) \\)" }, { "from": "gpt", "value": "Thinks x = ? is the y axis" } ]
[ { "from": "human", "value": "Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (2,5) \\)\nThe point is reflected in the line \\( x=2 \\)\nWhat are the new coordinates of point \\( Q \\) ? \\( (5,2) \\)" }, { "from": "gpt", "value": "Thinks x = ? or y = ? is y = x" } ]
[ { "from": "human", "value": "Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (2,5) \\)\nThe point is reflected in the line \\( x=2 \\)\nWhat are the new coordinates of point \\( Q \\) ? \\( (2,-5) \\)" }, { "from": "gpt", "value": "Thinks y = ? is the x axis" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}3 h^{2}=75 \\\\ (3 h)^{2}=75\\end{array} \\)" }, { "from": "gpt", "value": "Answers order of operations questions with brackets as if the brackets are not there" } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}3 h^{2}=225 \\\\ (3 h)^{2}=225\\end{array} \\)" }, { "from": "gpt", "value": "Multiplies before applying a power " } ]
[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}3 h^{2}=225 \\\\ (3 h)^{2}=75\\end{array} \\)" }, { "from": "gpt", "value": "Multiplies before applying a power " } ]
[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for reciprocal graphs This is a part of the table of values for the equation \\( y=\\frac{3}{x} \\) \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\( 0.1 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 2.9 \\)" }, { "from": "gpt", "value": "Thinks the fraction bar means subtract rather than divide" } ]
[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for reciprocal graphs This is a part of the table of values for the equation \\( y=\\frac{3}{x} \\) \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\( 0.1 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 0.3 \\)" }, { "from": "gpt", "value": "Multiplies instead of divides when division is written as a fraction" } ]
[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for reciprocal graphs This is a part of the table of values for the equation \\( y=\\frac{3}{x} \\) \\begin{tabular}{\|l\|l\|}\n\\hline\\( x \\) & \\( 0.1 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 3.1 \\)" }, { "from": "gpt", "value": "Believes the fraction line represents addition" } ]
[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 4 \\mathrm{~km} \\approx \\square \\) miles \\( 4.6 \\)" }, { "from": "gpt", "value": "Added rather than multiplied by a scale factor" } ]
[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 4 \\mathrm{~km} \\approx \\square \\) miles \\( 0.24 \\)" }, { "from": "gpt", "value": "When multiplying decimals, ignores place value and just multiplies the digits" } ]
[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 4 \\mathrm{~km} \\approx \\square \\) miles \\( 3.6 \\)" }, { "from": "gpt", "value": "Subtracted rather than divided by a scale factor" } ]
[ { "from": "human", "value": "Add fractions involving mixed number fractions with the same denominator \\(\n1 \\frac{2}{3}+\\frac{1}{3}\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( \\frac{4}{3} \\)" }, { "from": "gpt", "value": "Thinks you add the number of wholes to the numerator when converting a mixed number to an improper fraction." } ]
[ { "from": "human", "value": "Add fractions involving mixed number fractions with the same denominator \\(\n1 \\frac{2}{3}+\\frac{1}{3}\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 4 \\)" }, { "from": "gpt", "value": "Believes you add the whole to the numerators, ignoring denominators, when adding a mixed number to a proper fraction with the same denominator." } ]
[ { "from": "human", "value": "Given the description of an algebraic term with powers, write the term using algebra Write the following using correct algebraic notation \\( m \\) multiplied by the cube of \\( n \\) \\( (m n)^{3} \\)" }, { "from": "gpt", "value": "Has not realised that the answer may be changed by the insertion of brackets" } ]
[ { "from": "human", "value": "Given the description of an algebraic term with powers, write the term using algebra Write the following using correct algebraic notation \\( m \\) multiplied by the cube of \\( n \\) \\( m n+3 \\)" }, { "from": "gpt", "value": "Thinks cubing a number means adding 3 to that number" } ]
[ { "from": "human", "value": "Given the description of an algebraic term with powers, write the term using algebra Write the following using correct algebraic notation \\( m \\) multiplied by the cube of \\( n \\) \\( 3 m n \\)" }, { "from": "gpt", "value": "Believes cubing a number means you multiply it by 3" } ]
[ { "from": "human", "value": "Solve quadratic equations using factorisation in the form (x + a)(x + b) In which region would \\( x^{2}-10 x-25=0 \\) belong? ![A Venn diagram made up of two overlapping circles. One is labelled 'Factorises' and the other is labelled 'Has one solution equal to 0'.\nA is in the 'Factorises' circle only, B is in the overlap of the two circles, C is in the 'Has one solution equal to 0' circle only, and D is outside the circles.]() C" }, { "from": "gpt", "value": "Believes all quadratic equations have a solution of 0" } ]
[ { "from": "human", "value": "Continue linear sequences expressed as patterns by drawing the next pattern What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]() ![This pattern is the same as Pattern 4: it is made up of 9 squares as a 4 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]
[ { "from": "human", "value": "Continue linear sequences expressed as patterns by drawing the next pattern What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]() ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then 2 extra squares on top of the top left square of the rectangle.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]
[ { "from": "human", "value": "Continue linear sequences expressed as patterns by drawing the next pattern What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]() ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle, and one more square to the right of that one.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 4 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 next rectangle has \"− 1\" written inside it, the next rectangle has \"✕ 2\" written inside it and the final rectangle on the right has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 15 \\)" }, { "from": "gpt", "value": "Reverses the order of operations but does not apply the inverse operations when finding the input of a function machine" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 4 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 next rectangle has \"− 1\" written inside it, the next rectangle has \"✕ 2\" written inside it and the final rectangle on the right has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 14 \\)" }, { "from": "gpt", "value": "Does not reverse the order of operations when finding the input of a function machine" } ]
[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 4 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 next rectangle has \"− 1\" written inside it, the next rectangle has \"✕ 2\" written inside it and the final rectangle on the right has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 4.5 \\)" }, { "from": "gpt", "value": "Does not reverse the order of operations when finding the input of a function machine" } ]
[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}-5 p\n\\) \\( (p+5)(p-5) \\)" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]
[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}-5 p\n\\) \\( (p+\\sqrt{5})(p-\\sqrt{5}) \\)" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]
[ { "from": "human", "value": "Recognise an arithmetic sequence Tom and Katie are discussing arithmetic sequences.\n\nTom says this is an arithmetic sequence: \\( 5,8,11,14,17, \\ldots \\)\n\nKatie says this is an arithmetic sequence: \\( 5,15,45,135,405, \\ldots \\)\n\nWho is correct?\n Only Katie" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]
[ { "from": "human", "value": "Recognise an arithmetic sequence Tom and Katie are discussing arithmetic sequences.\n\nTom says this is an arithmetic sequence: \\( 5,8,11,14,17, \\ldots \\)\n\nKatie says this is an arithmetic sequence: \\( 5,15,45,135,405, \\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 an arithmetic sequence Tom and Katie are discussing arithmetic sequences.\n\nTom says this is an arithmetic sequence: \\( 5,8,11,14,17, \\ldots \\)\n\nKatie says this is an arithmetic sequence: \\( 5,15,45,135,405, \\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": "Read a fraction on a scale where the required number is marked by a dash between two numbers What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]() \\( \\frac{3}{4} \\)" }, { "from": "gpt", "value": "When reading a dash on a number line does not take into account the number at the start or the width of each division" } ]
[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]() \\( \\frac{2}{6} \\)" }, { "from": "gpt", "value": "Believes the arrow on a number line points to the middle value" } ]
[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]() There is no such fraction" }, { "from": "gpt", "value": "Does not realise you can use equivalent fractions to break fractions up into smaller divisions" } ]
[ { "from": "human", "value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio \\( 3: 1 \\). What fraction of the drink is water? \\( \\frac{3}{4} \\)" }, { "from": "gpt", "value": "Gets order of ratio wrong" } ]
[ { "from": "human", "value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio \\( 3: 1 \\). What fraction of the drink is water? \\( \\frac{1}{3} \\)" }, { "from": "gpt", "value": "When converting ratio to fractions, puts the other side of the ratio as the denominator rather than the total" } ]
[ { "from": "human", "value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio \\( 3: 1 \\). What fraction of the drink is water? Not enough information" }, { "from": "gpt", "value": "Does not understand the relationship between a ratio and fraction" } ]
[ { "from": "human", "value": "Read values off a displacement-time graph How far away from home was Rachel at 12:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). \n]() \\( 0 \\mathrm{~km} \\)" }, { "from": "gpt", "value": "Thinks a horizontal line on a distance time graph means a distance of 0" } ]
[ { "from": "human", "value": "Read values off a displacement-time graph How far away from home was Rachel at 12:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). \n]() \\( 7.5 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "When reading values from graphs, writes down the wrong units" } ]
[ { "from": "human", "value": "Read values off a displacement-time graph How far away from home was Rachel at 12:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). \n]() \\( 750 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Thinks there are 100m and a km" } ]
[ { "from": "human", "value": "Solve quadratic equations using balancing One of these equations has no real solutions.\nWhich is it? \\( t^{3}=-27 \\)" }, { "from": "gpt", "value": "Believes a number raised to a power will always give a positive answer" } ]
[ { "from": "human", "value": "Solve quadratic equations using balancing One of these equations has no real solutions.\nWhich is it? \\( t-27=-27 \\)" }, { "from": "gpt", "value": "Believes 0 is not a real solution to an equation" } ]
[ { "from": "human", "value": "Calculate the probability of two dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() Kate picks a yellow ball out and does not replace it.\n\nShe then has a second pick.\nWhat is the probability the second pick is a red ball? \\( \\frac{4}{7} \\)" }, { "from": "gpt", "value": "Does not reduce the denominator when an item is not replaced in a probability question" } ]
[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, with all positive integers What is the solution for this equation? \\( 4(3 x-2)=2(6 x-8) \\) \\( x=0 \\)" }, { "from": "gpt", "value": "Believes the solution to an equation with matching coefficients of variables on both sides will always be 0" } ]
[ { "from": "human", "value": "Identify parallel lines written in the form y = mx + c Tom and Katie are discussing parallel lines\nTom says \\( y=2 x+5 \\) and \\( y=2 x-7 \\) are parallel \nKatie says \\( y=2 x+5 \\) and \\( y=3 x+5 \\) are parallel\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes lines can be parallel by having the same y intercept OR gradient" } ]
[ { "from": "human", "value": "Identify equivalent fractions when presented as shapes or objects By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out? ![A rectangle with 1/3 shaded in red]()" }, { "from": "gpt", "value": "Does not understand equivalent fractions" } ]
[ { "from": "human", "value": "Identify equivalent fractions when presented as shapes or objects By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out? ![A rectangle with 2/6 shaded in blue]()" }, { "from": "gpt", "value": "Does not understand equivalent fractions" } ]

[ { "from": "human", "value": "Order fractions whose denominators are multiples of the same number \\( \\begin{array}{llllll}\\frac{8}{10} & \\frac{41}{50} & \\frac{7}{20} & 0.77 & \\frac{4}{5} & \\frac{79}{100}\\end{array} \\) Which value is the outlier in this set of data? \\( \\frac{79}{100} \\)" }, { "from": "gpt", "value": "Believes an outlier is the value in a data set with the biggest denominator, even if this value is close to the mean" } ]

[ { "from": "human", "value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 2 \\) days? \\( 2 \\times 12 \\times 60 \\times 60 \\)" }, { "from": "gpt", "value": "Thinks there are 12 hours in 1 day" } ]

[ { "from": "human", "value": "Convert from days to seconds Which of the following would correctly calculate the number of seconds in \\( 2 \\) days? \\( 2 \\times 24 \\times 60 \\)" }, { "from": "gpt", "value": "Converted hours to minutes instead of hours to seconds" } ]

[ { "from": "human", "value": "Describe a translation using vector notation where at least one value is negative Which of the following vectors describes how to get from point \\( P \\) to point \\( Q \\)? ![The image shows a square grid and 2 points, P and Q. Point P is 4 squares left and 2 squares up from point Q. ]() \\( \\left(\\begin{array}{l}4 \\\\ 2\\end{array}\\right) \\)" }, { "from": "gpt", "value": "Thinks a positive y value in a column vector means to move down rather than up " } ]

[ { "from": "human", "value": "Describe a translation using vector notation where at least one value is negative Which of the following vectors describes how to get from point \\( P \\) to point \\( Q \\)? ![The image shows a square grid and 2 points, P and Q. Point P is 4 squares left and 2 squares up from point Q. ]() \\( \\left(\\begin{array}{c}-2 \\\\ 4\\end{array}\\right) \\)" }, { "from": "gpt", "value": "Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round" } ]

[ { "from": "human", "value": "Solve one-step linear equations requiring addition or subtraction, involving positive fractions Solve the equation:\n\\(\np-3=\\frac{1}{12}\n\\) \\( p=\\frac{4}{12} \\)" }, { "from": "gpt", "value": "When adding an integer to a fraction, thinks you add the integer to the numerator" } ]

[ { "from": "human", "value": "Solve one-step linear equations requiring addition or subtraction, involving positive fractions Solve the equation:\n\\(\np-3=\\frac{1}{12}\n\\) \\( p=\\frac{3}{36} \\)" }, { "from": "gpt", "value": "When solving an equation, multiplies instead of adding" } ]

[ { "from": "human", "value": "Substitute into simple formulae given in words To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.\nWhat is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]() \\( 15 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Does not divide by 2 when calculating the area of a triangle" } ]

[ { "from": "human", "value": "Substitute into simple formulae given in words To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.\nWhat is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]() \\( 4 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Adds instead of multiples" } ]

[ { "from": "human", "value": "Substitute into simple formulae given in words To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.\nWhat is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]() \\( 30 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Thinks halving is the same as multiplying by 2" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\n\\( \\frac{18}{30} \\) \\( \\frac{4.5}{7.5} \\)" }, { "from": "gpt", "value": "Believes you can have decimals in a simplified fraction" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\n\\( \\frac{18}{30} \\) \\( \\frac{9}{15} \\)" }, { "from": "gpt", "value": "Does not fully simplify fraction" } ]

[ { "from": "human", "value": "Simplify fractions that simplify to a non-unit fraction Simplify fully (if possible):\n\n\\( \\frac{18}{30} \\) Cannot be simplified" }, { "from": "gpt", "value": "Does not understand how to simplify fractions" } ]

[ { "from": "human", "value": "Calculate the square of a number What is the value of \\( 4^{2} \\) ? \\( 8 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]

[ { "from": "human", "value": "Calculate the square of a number What is the value of \\( 4^{2} \\) ? \\( 6 \\)" }, { "from": "gpt", "value": "Adds the index to the number" } ]

[ { "from": "human", "value": "Calculate the square of a number What is the value of \\( 4^{2} \\) ? \\( 4 \\)" }, { "from": "gpt", "value": "Believes a power of 2 has no impact on its value" } ]

[ { "from": "human", "value": "Estimate the gradient at a point on a non-linear section of a real life graph The graph shows information about the velocity, \\( v \\mathrm{~m} / \\mathrm{s} \\), of a parachutist \\( t \\) seconds after leaving a plane.\n\nWhich of the following is the best estimate for the gradient of the curve when \\( t=6 \\) ![The image is of a velocity-time graph. There is a straight line, a tangent, drawn so that it is touching the curve at t=6. The tangent goes through (2, 31), (6, 47) and (8,55). ]() \\( 46 \\)" }, { "from": "gpt", "value": "Does not understand the difference between a value on a graph and the gradient of a graph" } ]

[ { "from": "human", "value": "Estimate the gradient at a point on a non-linear section of a real life graph The graph shows information about the velocity, \\( v \\mathrm{~m} / \\mathrm{s} \\), of a parachutist \\( t \\) seconds after leaving a plane.\n\nWhich of the following is the best estimate for the gradient of the curve when \\( t=6 \\) ![The image is of a velocity-time graph. There is a straight line, a tangent, drawn so that it is touching the curve at t=6. The tangent goes through (2, 31), (6, 47) and (8,55). ]() \\( 7.66 \\ldots \\)" }, { "from": "gpt", "value": "Believes gradient at a point = y coordinate/x coordinate" } ]

[ { "from": "human", "value": "Recognise other roots of numbers \\( \\sqrt[4]{16}=? \\) \\( 64 \\)" }, { "from": "gpt", "value": "Has multiplied by the root power" } ]

[ { "from": "human", "value": "Recognise other roots of numbers \\( \\sqrt[4]{16}=? \\) \\( 16 \\)" }, { "from": "gpt", "value": "Does not understand the root power of 4" } ]

[ { "from": "human", "value": "Recognise other roots of numbers \\( \\sqrt[4]{16}=? \\) \\( 4 \\)" }, { "from": "gpt", "value": "Divides by the order of the root" } ]

[ { "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 \\) & & \\( -1 \\) & \n\\end{tabular} This is a table of values for \\( y=x^{2}-x+1 \\) What should replace the star? \\( 1 \\)" }, { "from": "gpt", "value": "Does not realise that subtracting a negative is the same as adding it's additive inverse" } ]

[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c What is the gradient of this line?\n\\(4 x-5 y=20\\) \\( 4 \\)" }, { "from": "gpt", "value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c" } ]

[ { "from": "human", "value": "Find the gradient of a line written in the form ax + by = c What is the gradient of this line?\n\\(4 x-5 y=20\\) \\( -\\frac{4}{5} \\)" }, { "from": "gpt", "value": "When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value" } ]

[ { "from": "human", "value": "Read values off a real life graph This is a conversion graph between pints and litres.\nWhich of the following is the best estimate for the number of pints equivalent to \\( 50 \\) litres? ![A graph on gridded paper showing litres on the y axis from 0 to 50 and pints on the x axis from 0 to 90. A straight line goes from the origin and passes through (35,20) (not marked - just a point it goes through) but extends the whole way up the graph.]() \\( 28 \\) pints" }, { "from": "gpt", "value": "When reading value from graph, reads from the wrong axes." } ]

[ { "from": "human", "value": "Read values off a real life graph This is a conversion graph between pints and litres.\nWhich of the following is the best estimate for the number of pints equivalent to \\( 50 \\) litres? ![A graph on gridded paper showing litres on the y axis from 0 to 50 and pints on the x axis from 0 to 90. A straight line goes from the origin and passes through (35,20) (not marked - just a point it goes through) but extends the whole way up the graph.]() \\( 85 \\) pints" }, { "from": "gpt", "value": "When reading graph, chooses nearest marked value on axis instead of reading accurately" } ]

[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation \\( y=3 x \\) ![A table with two rows and two columns. The top left box has 'x', with a star in the top right box. The bottom left box has 'y' with a 9 in the bottom right box. ]() What should replace the star? \\( 6 \\)" }, { "from": "gpt", "value": "Thinks the inverse of subtraction is multiplication" } ]

[ { "from": "human", "value": "Given a positive y value, find an x value in a table of values for lines in the form y = mx + c This is a part of the table of values for the equation \\( y=3 x \\) ![A table with two rows and two columns. The top left box has 'x', with a star in the top right box. The bottom left box has 'y' with a 9 in the bottom right box. ]() What should replace the star? \\( 27 \\)" }, { "from": "gpt", "value": "Mixes up the value of two terms when substituting" } ]

[ { "from": "human", "value": "Identify data which is qualitative or quantitative Leanne has written a questionnaire on the topic of holidays. One of her questions is,\n\n\"Describe how you feel when you are about to go on holiday.\"\n\nWhat type of data is she collecting by asking this question? Primary\nQuantitative\ndata" }, { "from": "gpt", "value": "Mixes up quantitative and qualitative data types" } ]

[ { "from": "human", "value": "Identify data which is qualitative or quantitative Leanne has written a questionnaire on the topic of holidays. One of her questions is,\n\n\"Describe how you feel when you are about to go on holiday.\"\n\nWhat type of data is she collecting by asking this question? Attribute data" }, { "from": "gpt", "value": "Does not know the meaning of attribute data" } ]

[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b \\( m^{2}+6 m+1 \\equiv(m \\bigstar )^{2} \\triangle \\) \\(\\bigstar =+6 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is the coefficient of x" } ]

[ { "from": "human", "value": "Complete the square for expressions that end up in the form (x + a)² + b \\( m^{2}+6 m+1 \\equiv(m \\bigstar )^{2} \\triangle \\) \\(\\bigstar =+12 \\)" }, { "from": "gpt", "value": "When completing the square, believes the constant in the bracket is double the coefficient of x" } ]

[ { "from": "human", "value": "Answer negative number problems that require the use of BIDMAS Which calculation is equal to \\( -20 \\) ? \\( 2 \\times(-2)-(-4) \\times 4 \\)" }, { "from": "gpt", "value": "Does not realise that subtracting a negative is the same as adding it's additive inverse" } ]

[ { "from": "human", "value": "Answer negative number problems that require the use of BIDMAS Which calculation is equal to \\( -20 \\) ? \\( (-5)^{2}+5 \\)" }, { "from": "gpt", "value": "Believes multiplying two negatives gives a negative answer" } ]

[ { "from": "human", "value": "Answer negative number problems that require the use of BIDMAS Which calculation is equal to \\( -20 \\) ? \\( (-42) \\div(-2)+1 \\)" }, { "from": "gpt", "value": "Believes dividing a negative by a negative gives a negative answer" } ]

[ { "from": "human", "value": "Carry out addition problems involving two negative integers \\( (-5)+(-2)= \\) \\( 7 \\)" }, { "from": "gpt", "value": "Believes adding two negatives gives a positive answer" } ]

[ { "from": "human", "value": "Carry out addition problems involving two negative integers \\( (-5)+(-2)= \\) \\( -3 \\)" }, { "from": "gpt", "value": "Believes that adding a negative will increase the value of the original number" } ]

[ { "from": "human", "value": "Write the next term of an ascending integer linear sequence \\[\n5,12,19,26, \\ldots ?\n\\]\n\nWhat number comes next in this sequence? \\( 40 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the term after" } ]

[ { "from": "human", "value": "Read values off a speed-time graph This velocity-time graph shows the first \\( 5 \\) seconds of Mo's journey which starts at home.\n\nAt what time did he first start travelling at \\( 4 \\mathrm{~m} / \\mathrm{s} \\) ? ![The image is of a graph. Its vertical axis labelled Velocity (m/s) and has the scale 0, 2, 4, 6 marked in even steps. Its horizontal axis is labelled Time (secs) and has the scale 0, 1, 2, 3, 4, 5 marked in even steps. \nThe graph is in three sections. The first section is a straight slanted line from (0,0) to (1, 4). The second section is a horizontal line from (1, 4) to (3, 4). The third section is a slanted line from (3, 4) to (5, 0).]() \\( 4 \\) secs" }, { "from": "gpt", "value": "When reading value from graph, reads from the wrong axes." } ]

[ { "from": "human", "value": "Identify the order of rotational symmetry of a shape Tom and Katie are arguing about the order of rotational symmetry of quadrilaterals.\n\nTom says some quadrilaterals have an order of rotational symmetry of \\( 1 \\).\nKatie says some quadrilaterals have an order of rotational symmetry of \\( 3 \\).\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Does not connect rotational symmetry to number of sides/vertices" } ]

[ { "from": "human", "value": "Identify the order of rotational symmetry of a shape Tom and Katie are arguing about the order of rotational symmetry of quadrilaterals.\n\nTom says some quadrilaterals have an order of rotational symmetry of \\( 1 \\).\nKatie says some quadrilaterals have an order of rotational symmetry of \\( 3 \\).\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Does not connect rotational symmetry to number of sides/vertices" } ]

[ { "from": "human", "value": "Read a negative integer temperature from a thermometer What temperature does the thermometer show? ![A thermometer showing the temperature in degrees Celsius. There are five steps on the scale between 10 and 0, and five steps between 0 and -10. The temperature is shown at 4 steps below 0.]() \\( -9^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "When reading integers on a number line, assumes each dash is 1" } ]

[ { "from": "human", "value": "Read a negative integer temperature from a thermometer What temperature does the thermometer show? ![A thermometer showing the temperature in degrees Celsius. There are five steps on the scale between 10 and 0, and five steps between 0 and -10. The temperature is shown at 4 steps below 0.]() \\( -4^{\\circ} \\mathrm{C} \\)" }, { "from": "gpt", "value": "When reading integers on a number line, assumes each dash is 1" } ]

[ { "from": "human", "value": "Calculate the surface area of a cuboid where the dimensions are given in the same units Which of the following calculations would give you the total surface area of this cuboid in \\( \\mathrm{cm}^{2} \\) ? ![A cuboid. The top measures 4cm by 2cm, and the height is 7cm.]() \\( (2 \\times 7)+(4 \\times 2)+(4 \\times 7) \\)" }, { "from": "gpt", "value": "When calculating surface area, only includes visible faces" } ]

[ { "from": "human", "value": "Calculate the surface area of a cuboid where the dimensions are given in the same units Which of the following calculations would give you the total surface area of this cuboid in \\( \\mathrm{cm}^{2} \\) ? ![A cuboid. The top measures 4cm by 2cm, and the height is 7cm.]() \\( 2 \\times 4 \\times 7 \\)" }, { "from": "gpt", "value": "Finds volume when asked for surface area" } ]

[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using the grid method What should replace the star when solving the following problem using the grid method?\n\\(52 \\times 326\\) \\begin{tabular}{|c|c|c|c|}\n\\hline\\( \\times \\) & \\( 300 \\) & \\( 20 \\) & \\( 6 \\) \\\\\n\\hline \\( 50 \\) & & \\( \\bigstar \\) & \\\\\n\\hline \\( 2 \\) & & \\\\\n\\hline\n\\end{tabular} \\( 10 \\)" }, { "from": "gpt", "value": "When multiplying involving a multiple of 10, just multiplies the digits and ignores the zeros " } ]

[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using the grid method What should replace the star when solving the following problem using the grid method?\n\\(52 \\times 326\\) \\begin{tabular}{|c|c|c|c|}\n\\hline\\( \\times \\) & \\( 300 \\) & \\( 20 \\) & \\( 6 \\) \\\\\n\\hline \\( 50 \\) & & \\( \\bigstar \\) & \\\\\n\\hline \\( 2 \\) & & \\\\\n\\hline\n\\end{tabular} \\( 70 \\)" }, { "from": "gpt", "value": "Adds instead of multiples" } ]

[ { "from": "human", "value": "Multiply 3 digit integers by 2 digit integers using the grid method What should replace the star when solving the following problem using the grid method?\n\\(52 \\times 326\\) \\begin{tabular}{|c|c|c|c|}\n\\hline\\( \\times \\) & \\( 300 \\) & \\( 20 \\) & \\( 6 \\) \\\\\n\\hline \\( 50 \\) & & \\( \\bigstar \\) & \\\\\n\\hline \\( 2 \\) & & \\\\\n\\hline\n\\end{tabular} \\( 100 \\)" }, { "from": "gpt", "value": "When multiplying involving a multiple of 10, gives an answer 10 times smaller than it should be" } ]

[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{3 6} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() B" }, { "from": "gpt", "value": "Mixes up odd and even numbers" } ]

[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{3 6} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() C" }, { "from": "gpt", "value": "Mixes up odd and even numbers" } ]

[ { "from": "human", "value": "Fill in regions of a double Venn diagram with numbers from given information In which region would \\( \\mathbf{3 6} \\) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() D" }, { "from": "gpt", "value": "Mixes up odd and even numbers" } ]

[ { "from": "human", "value": "Complete missing number mental addition problems with numbers over 1000 A \\( 3 \\) digit number belongs in this box to make the calculation true\n\\(\n258+\\square=1162\n\\)\nWhat is the \\( 3^{\\text {rd }} \\) digit of the number that belongs in the box? \\( 0 \\)" }, { "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 with numbers over 1000 A \\( 3 \\) digit number belongs in this box to make the calculation true\n\\(\n258+\\square=1162\n\\)\nWhat is the \\( 3^{\\text {rd }} \\) digit of the number that belongs in the box? \\( 6 \\)" }, { "from": "gpt", "value": "Subtracts the smallest digit from the largest digit" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p-5)(p+2) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=-3 \\)" }, { "from": "gpt", "value": "Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets" } ]

[ { "from": "human", "value": "Expand two brackets with linear terms in the form (x + a)(x + b) What should replace the circle when these two brackets are expanded and simplified?\n\\(\n(p-5)(p+2) \\equiv p^{2} \\triangle p \\bigcirc\n\\) \\( \\bigcirc=+10 \\)" }, { "from": "gpt", "value": "Believes multiplying a positive by a negative gives a positive answer" } ]

[ { "from": "human", "value": "Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (2,5) \\)\nThe point is reflected in the line \\( x=2 \\)\nWhat are the new coordinates of point \\( Q \\) ? \\( (-2,5) \\)" }, { "from": "gpt", "value": "Thinks x = ? is the y axis" } ]

[ { "from": "human", "value": "Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (2,5) \\)\nThe point is reflected in the line \\( x=2 \\)\nWhat are the new coordinates of point \\( Q \\) ? \\( (5,2) \\)" }, { "from": "gpt", "value": "Thinks x = ? or y = ? is y = x" } ]

[ { "from": "human", "value": "Reflect an object or a point in a vertical line with the line of reflection given as an equation, where the line of reflection lies on the edge or outside the object A point, \\( Q \\), has coordinates \\( (2,5) \\)\nThe point is reflected in the line \\( x=2 \\)\nWhat are the new coordinates of point \\( Q \\) ? \\( (2,-5) \\)" }, { "from": "gpt", "value": "Thinks y = ? is the x axis" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}3 h^{2}=75 \\\\ (3 h)^{2}=75\\end{array} \\)" }, { "from": "gpt", "value": "Answers order of operations questions with brackets as if the brackets are not there" } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}3 h^{2}=225 \\\\ (3 h)^{2}=225\\end{array} \\)" }, { "from": "gpt", "value": "Multiplies before applying a power " } ]

[ { "from": "human", "value": "Substitute positive integer values into expressions involving powers or roots When \\( h=5 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}3 h^{2}=225 \\\\ (3 h)^{2}=75\\end{array} \\)" }, { "from": "gpt", "value": "Multiplies before applying a power " } ]

[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for reciprocal graphs This is a part of the table of values for the equation \\( y=\\frac{3}{x} \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.1 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 2.9 \\)" }, { "from": "gpt", "value": "Thinks the fraction bar means subtract rather than divide" } ]

[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for reciprocal graphs This is a part of the table of values for the equation \\( y=\\frac{3}{x} \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.1 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 0.3 \\)" }, { "from": "gpt", "value": "Multiplies instead of divides when division is written as a fraction" } ]

[ { "from": "human", "value": "Given a positive x value, find the corresponding y value for reciprocal graphs This is a part of the table of values for the equation \\( y=\\frac{3}{x} \\) \\begin{tabular}{|l|l|}\n\\hline\\( x \\) & \\( 0.1 \\) \\\\\n\\hline\\( y \\) & \\(\\color{gold}\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 3.1 \\)" }, { "from": "gpt", "value": "Believes the fraction line represents addition" } ]

[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 4 \\mathrm{~km} \\approx \\square \\) miles \\( 4.6 \\)" }, { "from": "gpt", "value": "Added rather than multiplied by a scale factor" } ]

[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 4 \\mathrm{~km} \\approx \\square \\) miles \\( 0.24 \\)" }, { "from": "gpt", "value": "When multiplying decimals, ignores place value and just multiplies the digits" } ]

[ { "from": "human", "value": "Convert from kilometers to miles \\( 1 \\mathrm{~km} \\approx 0.6 \\) miles \\( 4 \\mathrm{~km} \\approx \\square \\) miles \\( 3.6 \\)" }, { "from": "gpt", "value": "Subtracted rather than divided by a scale factor" } ]

[ { "from": "human", "value": "Add fractions involving mixed number fractions with the same denominator \\(\n1 \\frac{2}{3}+\\frac{1}{3}\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( \\frac{4}{3} \\)" }, { "from": "gpt", "value": "Thinks you add the number of wholes to the numerator when converting a mixed number to an improper fraction." } ]

[ { "from": "human", "value": "Add fractions involving mixed number fractions with the same denominator \\(\n1 \\frac{2}{3}+\\frac{1}{3}\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 4 \\)" }, { "from": "gpt", "value": "Believes you add the whole to the numerators, ignoring denominators, when adding a mixed number to a proper fraction with the same denominator." } ]

[ { "from": "human", "value": "Given the description of an algebraic term with powers, write the term using algebra Write the following using correct algebraic notation \\( m \\) multiplied by the cube of \\( n \\) \\( (m n)^{3} \\)" }, { "from": "gpt", "value": "Has not realised that the answer may be changed by the insertion of brackets" } ]

[ { "from": "human", "value": "Given the description of an algebraic term with powers, write the term using algebra Write the following using correct algebraic notation \\( m \\) multiplied by the cube of \\( n \\) \\( m n+3 \\)" }, { "from": "gpt", "value": "Thinks cubing a number means adding 3 to that number" } ]

[ { "from": "human", "value": "Given the description of an algebraic term with powers, write the term using algebra Write the following using correct algebraic notation \\( m \\) multiplied by the cube of \\( n \\) \\( 3 m n \\)" }, { "from": "gpt", "value": "Believes cubing a number means you multiply it by 3" } ]

[ { "from": "human", "value": "Solve quadratic equations using factorisation in the form (x + a)(x + b) In which region would \\( x^{2}-10 x-25=0 \\) belong? ![A Venn diagram made up of two overlapping circles. One is labelled 'Factorises' and the other is labelled 'Has one solution equal to 0'.\nA is in the 'Factorises' circle only, B is in the overlap of the two circles, C is in the 'Has one solution equal to 0' circle only, and D is outside the circles.]() C" }, { "from": "gpt", "value": "Believes all quadratic equations have a solution of 0" } ]

[ { "from": "human", "value": "Continue linear sequences expressed as patterns by drawing the next pattern What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]() ![This pattern is the same as Pattern 4: it is made up of 9 squares as a 4 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]

[ { "from": "human", "value": "Continue linear sequences expressed as patterns by drawing the next pattern What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]() ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then 2 extra squares on top of the top left square of the rectangle.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]

[ { "from": "human", "value": "Continue linear sequences expressed as patterns by drawing the next pattern What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]() ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle, and one more square to the right of that one.]()" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 4 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 next rectangle has \"− 1\" written inside it, the next rectangle has \"✕ 2\" written inside it and the final rectangle on the right has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 15 \\)" }, { "from": "gpt", "value": "Reverses the order of operations but does not apply the inverse operations when finding the input of a function machine" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 4 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 next rectangle has \"− 1\" written inside it, the next rectangle has \"✕ 2\" written inside it and the final rectangle on the right has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 14 \\)" }, { "from": "gpt", "value": "Does not reverse the order of operations when finding the input of a function machine" } ]

[ { "from": "human", "value": "For a given output find the input of a function machine ![A function machine with 4 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 next rectangle has \"− 1\" written inside it, the next rectangle has \"✕ 2\" written inside it and the final rectangle on the right has \"output\" written above it and \"8\" written inside it.]() What is the input of this function machine? \\( 4.5 \\)" }, { "from": "gpt", "value": "Does not reverse the order of operations when finding the input of a function machine" } ]

[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}-5 p\n\\) \\( (p+5)(p-5) \\)" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]

[ { "from": "human", "value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Factorise this expression, if possible:\n\\(\np^{2}-5 p\n\\) \\( (p+\\sqrt{5})(p-\\sqrt{5}) \\)" }, { "from": "gpt", "value": "When factorising a quadratic without a non variable term, tries to double bracket factorise" } ]

[ { "from": "human", "value": "Recognise an arithmetic sequence Tom and Katie are discussing arithmetic sequences.\n\nTom says this is an arithmetic sequence: \\( 5,8,11,14,17, \\ldots \\)\n\nKatie says this is an arithmetic sequence: \\( 5,15,45,135,405, \\ldots \\)\n\nWho is correct?\n Only Katie" }, { "from": "gpt", "value": "Does not recognise that a linear sequence must increase or decrease by same amount" } ]

[ { "from": "human", "value": "Recognise an arithmetic sequence Tom and Katie are discussing arithmetic sequences.\n\nTom says this is an arithmetic sequence: \\( 5,8,11,14,17, \\ldots \\)\n\nKatie says this is an arithmetic sequence: \\( 5,15,45,135,405, \\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 an arithmetic sequence Tom and Katie are discussing arithmetic sequences.\n\nTom says this is an arithmetic sequence: \\( 5,8,11,14,17, \\ldots \\)\n\nKatie says this is an arithmetic sequence: \\( 5,15,45,135,405, \\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": "Read a fraction on a scale where the required number is marked by a dash between two numbers What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]() \\( \\frac{3}{4} \\)" }, { "from": "gpt", "value": "When reading a dash on a number line does not take into account the number at the start or the width of each division" } ]

[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]() \\( \\frac{2}{6} \\)" }, { "from": "gpt", "value": "Believes the arrow on a number line points to the middle value" } ]

[ { "from": "human", "value": "Read a fraction on a scale where the required number is marked by a dash between two numbers What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]() There is no such fraction" }, { "from": "gpt", "value": "Does not realise you can use equivalent fractions to break fractions up into smaller divisions" } ]

[ { "from": "human", "value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio \\( 3: 1 \\). What fraction of the drink is water? \\( \\frac{3}{4} \\)" }, { "from": "gpt", "value": "Gets order of ratio wrong" } ]

[ { "from": "human", "value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio \\( 3: 1 \\). What fraction of the drink is water? \\( \\frac{1}{3} \\)" }, { "from": "gpt", "value": "When converting ratio to fractions, puts the other side of the ratio as the denominator rather than the total" } ]

[ { "from": "human", "value": "Convert ratios to fractions A lassi drink is made of yoghurt and water in the ratio \\( 3: 1 \\). What fraction of the drink is water? Not enough information" }, { "from": "gpt", "value": "Does not understand the relationship between a ratio and fraction" } ]

[ { "from": "human", "value": "Read values off a displacement-time graph How far away from home was Rachel at 12:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). \n]() \\( 0 \\mathrm{~km} \\)" }, { "from": "gpt", "value": "Thinks a horizontal line on a distance time graph means a distance of 0" } ]

[ { "from": "human", "value": "Read values off a displacement-time graph How far away from home was Rachel at 12:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). \n]() \\( 7.5 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "When reading values from graphs, writes down the wrong units" } ]

[ { "from": "human", "value": "Read values off a displacement-time graph How far away from home was Rachel at 12:15? ![A line graph with title \"A graph to show the distance Rachel travels from her home on her daily run.\" \nThe x-axis is titled \"Time\" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.\nThe y-axis is titled \"Distance from home (Km)\" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0). \n]() \\( 750 \\mathrm{~m} \\)" }, { "from": "gpt", "value": "Thinks there are 100m and a km" } ]

[ { "from": "human", "value": "Solve quadratic equations using balancing One of these equations has no real solutions.\nWhich is it? \\( t^{3}=-27 \\)" }, { "from": "gpt", "value": "Believes a number raised to a power will always give a positive answer" } ]

[ { "from": "human", "value": "Solve quadratic equations using balancing One of these equations has no real solutions.\nWhich is it? \\( t-27=-27 \\)" }, { "from": "gpt", "value": "Believes 0 is not a real solution to an equation" } ]

[ { "from": "human", "value": "Calculate the probability of two dependent events occurring without drawing a tree diagram There are \\( 4 \\) red balls and \\( 3 \\) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() Kate picks a yellow ball out and does not replace it.\n\nShe then has a second pick.\nWhat is the probability the second pick is a red ball? \\( \\frac{4}{7} \\)" }, { "from": "gpt", "value": "Does not reduce the denominator when an item is not replaced in a probability question" } ]

[ { "from": "human", "value": "Solve linear equations with the variable appearing on both sides, with all positive integers What is the solution for this equation? \\( 4(3 x-2)=2(6 x-8) \\) \\( x=0 \\)" }, { "from": "gpt", "value": "Believes the solution to an equation with matching coefficients of variables on both sides will always be 0" } ]

[ { "from": "human", "value": "Identify parallel lines written in the form y = mx + c Tom and Katie are discussing parallel lines\nTom says \\( y=2 x+5 \\) and \\( y=2 x-7 \\) are parallel \nKatie says \\( y=2 x+5 \\) and \\( y=3 x+5 \\) are parallel\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes lines can be parallel by having the same y intercept OR gradient" } ]

[ { "from": "human", "value": "Identify equivalent fractions when presented as shapes or objects By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out? ![A rectangle with 1/3 shaded in red]()" }, { "from": "gpt", "value": "Does not understand equivalent fractions" } ]

[ { "from": "human", "value": "Identify equivalent fractions when presented as shapes or objects By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out? ![A rectangle with 2/6 shaded in blue]()" }, { "from": "gpt", "value": "Does not understand equivalent fractions" } ]