conversations
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[
{
"from": "human",
"value": "Calculate the square of a number ![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has \"input\" written above it and \"30\" written inside it. The middle rectangle has \"squared\" written inside it and the final rectangle is empty and has \"output\" written above it.]() What is the output of this function machine? \\( 15 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and halving"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Integer ÷ Fraction Calculate\n\\(\n2 \\div \\frac{1}{5}\n\\) \\( \\frac{2}{5} \\)"
},
{
"from": "gpt",
"value": "When dividing an integer by a fraction, thinks they can just multiply instead."
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Integer ÷ Fraction Calculate\n\\(\n2 \\div \\frac{1}{5}\n\\) \\( \\frac{1}{10} \\)"
},
{
"from": "gpt",
"value": "When dividing fractions, does the reciprocal of the first fraction instead of the second"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Integer ÷ Fraction Calculate\n\\(\n2 \\div \\frac{1}{5}\n\\) \\( \\frac{5}{2} \\)"
},
{
"from": "gpt",
"value": "When dividing fractions, does the reciprocal of both fractions"
}
] |
[
{
"from": "human",
"value": "Write numbers between 0 and 1 in standard form Write the following number in standard form:\n\\[\n0.00506\n\\] \\( 5.06 \\times 10^{3} \\)"
},
{
"from": "gpt",
"value": "Does not think we can have negative powers in standard form"
}
] |
[
{
"from": "human",
"value": "Write numbers between 0 and 1 in standard form Write the following number in standard form:\n\\[\n0.00506\n\\] \\( 5.6 \\times 10^{-3} \\)"
},
{
"from": "gpt",
"value": "When changing a number to standard form omits zero's of significance "
}
] |
[
{
"from": "human",
"value": "Write numbers between 0 and 1 in standard form Write the following number in standard form:\n\\[\n0.00506\n\\] \\( 5.06 \\times 10^{-5} \\)"
},
{
"from": "gpt",
"value": "When changing a number to standard form omits zero's of significance "
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form ax² + bx + c Factorise \\( 9 x^{2}-24 x+16 \\) \\( (3 x+4)^{2} \\)"
},
{
"from": "gpt",
"value": "When factorising a quadratic with a coefficient of x squared, believes the signs and/or positions of the constants are interchangeable"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form ax² + bx + c Factorise \\( 9 x^{2}-24 x+16 \\) \\( (9 x-4)^{2} \\)"
},
{
"from": "gpt",
"value": "When factorising a quadratic with a non-unit coefficient of x squared, believes that coefficient will be in front of both x terms in the factorised form"
}
] |
[
{
"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 1/5. On the rightmost dash is the number 3/5. An arrow points to the 4th dash from the left]() \\( \\frac{2}{5} \\)"
},
{
"from": "gpt",
"value": "Does not realise you can use equivalent fractions to break fractions up into smaller divisions"
}
] |
[
{
"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 1/5. On the rightmost dash is the number 3/5. 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 1/5. On the rightmost dash is the number 3/5. 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": "Identify the order of rotational symmetry of a shape Which shape has the lowest order of rotational symmetry? ![Equilateral triangle]()"
},
{
"from": "gpt",
"value": "Does not know how to find order of rotational symmetry"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape Which shape has the lowest order of rotational symmetry? ![Circle]()"
},
{
"from": "gpt",
"value": "Does not know how to find order of rotational symmetry"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape Which shape has the lowest order of rotational symmetry? ![Square]()"
},
{
"from": "gpt",
"value": "Does not know how to find order of rotational symmetry"
}
] |
[
{
"from": "human",
"value": "Round numbers to an appropriate degree to estimate the answer to a calculation When estimating the answer to a complicated problem involving \\( 0.482 \\), you should instead use... \\( 0 \\)"
},
{
"from": "gpt",
"value": "Rounds to the nearest integer rather than one significant figure"
}
] |
[
{
"from": "human",
"value": "Round numbers to an appropriate degree to estimate the answer to a calculation When estimating the answer to a complicated problem involving \\( 0.482 \\), you should instead use... \\( 0.4 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round numbers to an appropriate degree to estimate the answer to a calculation When estimating the answer to a complicated problem involving \\( 0.482 \\), you should instead use... \\( 0.48 \\)"
},
{
"from": "gpt",
"value": "Rounds to the nearest hundredth, rather than one significant figure"
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors Which of the following describes how to get from point \\( P \\) to point \\( Q \\) ? ![Point P and Point Q are marked on a grid. Q is 4 squares to the right and 2 squares above P]() \\( 5 \\) squares right \\( 3 \\) squares up"
},
{
"from": "gpt",
"value": "When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares."
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors Which of the following describes how to get from point \\( P \\) to point \\( Q \\) ? ![Point P and Point Q are marked on a grid. Q is 4 squares to the right and 2 squares above P]() \\( 4 \\) squares left \\( 2 \\) squares down"
},
{
"from": "gpt",
"value": "When describing a translation, goes from the image to the original"
}
] |
[
{
"from": "human",
"value": "Describe simple directions to translate a shape or object using words not vectors Which of the following describes how to get from point \\( P \\) to point \\( Q \\) ? ![Point P and Point Q are marked on a grid. Q is 4 squares to the right and 2 squares above P]() \\( 5 \\) squares right \\( 2 \\) squares up"
},
{
"from": "gpt",
"value": "When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares."
}
] |
[
{
"from": "human",
"value": "Calculate the volume of other prisms when the dimensions are given in the same units What is the area of the shaded face? ![A prism of length 11mm. The cross-section, which is shaded, is a trapezium. The perpendicular height of the trapezium is 6mm. The two parallel sides of the trapezium are 6mm and 10mm.]() \\( 80 \\mathrm{~mm}^{2} \\)"
},
{
"from": "gpt",
"value": "Does not half sum of parallel sides when finding area of a trapezium"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of other prisms when the dimensions are given in the same units What is the area of the shaded face? ![A prism of length 11mm. The cross-section, which is shaded, is a trapezium. The perpendicular height of the trapezium is 6mm. The two parallel sides of the trapezium are 6mm and 10mm.]() \\( 300 \\mathrm{~mm}^{2} \\)"
},
{
"from": "gpt",
"value": "Multiplies all given dimensions when calculating an area"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of other prisms when the dimensions are given in the same units What is the area of the shaded face? ![A prism of length 11mm. The cross-section, which is shaded, is a trapezium. The perpendicular height of the trapezium is 6mm. The two parallel sides of the trapezium are 6mm and 10mm.]() \\( 150 \\mathrm{~mm}^{2} \\)"
},
{
"from": "gpt",
"value": "Multiplies all given dimensions when calculating an area"
}
] |
[
{
"from": "human",
"value": "Identify non-unit fractions when part of a shape What fraction of the rectangle is shaded? ![Rectangle split into 100 equal parts with 27 parts shaded in yellow]() \\( \\frac{27}{73} \\)"
},
{
"from": "gpt",
"value": "Denominator used for other parts rather than total parts"
}
] |
[
{
"from": "human",
"value": "Identify non-unit fractions when part of a shape What fraction of the rectangle is shaded? ![Rectangle split into 100 equal parts with 27 parts shaded in yellow]() \\( 27 \\)"
},
{
"from": "gpt",
"value": "Does not know how to write a fraction - just given an integer answer"
}
] |
[
{
"from": "human",
"value": "Identify a transversal Line JK is.. ![A pair of parallel lines are drawn with the arrow on each pointing to the right.\nA straight red line, KJ, is drawn so that diagonally crosses both parallel lines.]() Skew"
},
{
"from": "gpt",
"value": "Does not know the term transversal"
}
] |
[
{
"from": "human",
"value": "Identify a transversal Line JK is.. ![A pair of parallel lines are drawn with the arrow on each pointing to the right.\nA straight red line, KJ, is drawn so that diagonally crosses both parallel lines.]() Perpendicular"
},
{
"from": "gpt",
"value": "Believes any lines that cross are perpendicular"
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons What do the dashes tell you about the sides of this polygon? ![A hexagon with a dash on each side.]() They are parallel"
},
{
"from": "gpt",
"value": "Confuses the sign for parallel lines as being dashes"
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons What do the dashes tell you about the sides of this polygon? ![A hexagon with a dash on each side.]() They are straight"
},
{
"from": "gpt",
"value": "Confuses the signs for straight lines as being dashes"
}
] |
[
{
"from": "human",
"value": "Understand the terms equilateral and regular, and recognise the notation for regular polygons What do the dashes tell you about the sides of this polygon? ![A hexagon with a dash on each side.]() They are the midpoints"
},
{
"from": "gpt",
"value": "Misunderstands dashed lines as being the midpoint"
}
] |
[
{
"from": "human",
"value": "Read values off a displacement-time graph This graph shows the position of a ball, relative to a fixed point, over time.\n\nApproximately how far away from its starting point is the ball after \\( 8 \\) seconds? ![A graph showing time (secs) on the horizontal axis and position (m) on the vertical axis. The graph starts at (0,6) travels in a straight line to (8,15), then a straight line to (16,-15) then a straight line to (24,0). ]() \\( 14.5 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Assumes that a graph always starts at the origin"
}
] |
[
{
"from": "human",
"value": "Calculate unit fractions of an amount \\( \\frac{1}{12} \\) of an hour \\( = ____\\) minutes \\( 8.3 \\)"
},
{
"from": "gpt",
"value": "Answers as if there are 100 minutes in an hour"
}
] |
[
{
"from": "human",
"value": "Perform calculator calculations with powers Which button would you press to raise a number to a power? Which button would you press to raise a number to a power? ![A scientific calculator]() ![A scientific calculator]() ![Image of a calculator button. The symbol on the button is \\(\\frac{\\square}{\\square}\\)]() ![Image of a calculator button. The symbol on the button is \\(\\frac{\\square}{\\square}\\)]()"
},
{
"from": "gpt",
"value": "Thinks the fraction button on a calculator converts fractions to decimals"
}
] |
[
{
"from": "human",
"value": "Perform calculator calculations with powers Which button would you press to raise a number to a power? Which button would you press to raise a number to a power? ![A scientific calculator]() ![A scientific calculator]() ![Image of a calculator button. The symbol on the button is \\( x^{-1} \\)]() ![Image of a calculator button. The symbol on the button is \\( x^{-1} \\)]()"
},
{
"from": "gpt",
"value": "Does not recognise a reciprocal equation"
}
] |
[
{
"from": "human",
"value": "Perform calculator calculations with powers Which button would you press to raise a number to a power? Which button would you press to raise a number to a power? ![A scientific calculator]() ![A scientific calculator]() ![Image of a calculator button. The symbol on the button is \\( S \\Leftrightarrow D \\)]() ![Image of a calculator button. The symbol on the button is \\( S \\Leftrightarrow D \\)]()"
},
{
"from": "gpt",
"value": "Thinks the fraction to decimal conversion button on a calculator can be used to raise to a power"
}
] |
[
{
"from": "human",
"value": "Identify where negative non-integers lie on a number line Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with \"-6\", the 3rd dash is labelled \"-4\", the 5th dash is labelled \"-2\", the 7th dash is labelled \"0\", the 9th dash is labelled \"2\", the 11th dash is labelled \"4\" and the 13th dash is labelled \"6\" A red arrow, labelled with a question mark is pointing halfway between the 3rd and 4th dashes. ]() Which of the following numbers could be indicated by the arrow? \\( -3 \\)"
},
{
"from": "gpt",
"value": "Reads the position of a number from the space between the line marked, rather than the line marked"
}
] |
[
{
"from": "human",
"value": "Identify where negative non-integers lie on a number line Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with \"-6\", the 3rd dash is labelled \"-4\", the 5th dash is labelled \"-2\", the 7th dash is labelled \"0\", the 9th dash is labelled \"2\", the 11th dash is labelled \"4\" and the 13th dash is labelled \"6\" A red arrow, labelled with a question mark is pointing halfway between the 3rd and 4th dashes. ]() Which of the following numbers could be indicated by the arrow? \\( -2.75 \\)"
},
{
"from": "gpt",
"value": "Believes a gap of 2 is a gap of 1 on a numberline"
}
] |
[
{
"from": "human",
"value": "Identify where negative non-integers lie on a number line Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with \"-6\", the 3rd dash is labelled \"-4\", the 5th dash is labelled \"-2\", the 7th dash is labelled \"0\", the 9th dash is labelled \"2\", the 11th dash is labelled \"4\" and the 13th dash is labelled \"6\" A red arrow, labelled with a question mark is pointing halfway between the 3rd and 4th dashes. ]() Which of the following numbers could be indicated by the arrow? \\( -4.5 \\)"
},
{
"from": "gpt",
"value": "Counts on in the wrong direction on a number line"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention? \\( c \\div(h+4) \\) \\( \\frac{c+4}{h+4} \\)"
},
{
"from": "gpt",
"value": "Does not correctly apply the distributive property of multiplication"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention? \\( c \\div(h+4) \\) \\( \\frac{c}{h}+4 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Which answer shows the following calculation using the correct algebraic convention? \\( c \\div(h+4) \\) \\( \\frac{h+4}{c} \\)"
},
{
"from": "gpt",
"value": "Believes that a fraction means dividing the denominator by the numerator"
}
] |
[
{
"from": "human",
"value": "Solve quadratic inequalities from the graph of the quadratic Use the graph to approximate the solution to \\( x^{2}<2 \\) ![A set of axes with the quadratic graph y=x^2 drawn on.]() \\( x<-1.4, x>1.4 \\)"
},
{
"from": "gpt",
"value": "Selects y>a solutions instead of y<a solutions for a quadratic inequality"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable \\(\n2(5 x+4)-4(x-7) \\equiv A x+B\n\\)\n\nWhat is the value of \\( A \\) ? \\( 4 \\)"
},
{
"from": "gpt",
"value": "Only multiplies the numerical terms when expanding a bracket"
}
] |
[
{
"from": "human",
"value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) Tom and Katie are arguing about factorising \n\nTom says \\( p^{2}+9 p \\equiv(p+3)(p+3) \\) \n\nKatie says \\( p^{2}+9 p \\equiv p(p+9) \\) \n\nWho is correct? Only Tom"
},
{
"from": "gpt",
"value": "When factorising a quadratic without a non variable term, tries to double bracket factorise"
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for an ascending integer linear sequence \\[\n7,10,13,16,19, \\ldots\n\\]\n\nWhen calculating the nth-term rule of this sequence, what should replace the star? nth-term rule: ![\\( \\hat{\\omega}^{n} \\)]() \\( 7 \\)"
},
{
"from": "gpt",
"value": "When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n."
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number What is the value of \\( 1^{2} \\) ? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number What is the value of \\( 1^{2} \\) ? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Adds the index to the number"
}
] |
[
{
"from": "human",
"value": "Calculate the square of a number What is the value of \\( 1^{2} \\) ? \\( 12 \\)"
},
{
"from": "gpt",
"value": "Writes the index as a digit on the end of a number"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with the same number of decimal places \\( 0.2 \\times 0.8= \\) \\( 0.28 \\)"
},
{
"from": "gpt",
"value": "When multiplying just writes the numbers next to each other"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with the same number of decimal places \\( 0.2 \\times 0.8= \\) \\( 1.6 \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal"
}
] |
[
{
"from": "human",
"value": "Multiply two decimals together with the same number of decimal places \\( 0.2 \\times 0.8= \\) \\( 1 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies"
}
] |
[
{
"from": "human",
"value": "Prove statements involving positive and negative numbers \"If \\( n \\) is a positive integer, then \\( (2 n-13)^{3} \\) is negative\"\n\nIs the above statement always true, sometimes true, or never true? Never true"
},
{
"from": "gpt",
"value": "Believes raising a negative number to an odd power will give a positive answer"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, with all positive integers Isaac is trying to solve the equation on the right. \\( 15=\\frac{1+k}{4} \\) Here are his steps. Step \\( 1: \\) \\(\n60=1+k\n\\)\n\nStep \\( 2: \\) \\(\n61=k\n\\) Which steps, if any, are correct? Only ste.p \\( 2 \\)"
},
{
"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, with all positive integers Isaac is trying to solve the equation on the right. \\( 15=\\frac{1+k}{4} \\) Here are his steps. Step \\( 1: \\) \\(\n60=1+k\n\\)\n\nStep \\( 2: \\) \\(\n61=k\n\\) Which steps, if any, are correct? Both steps are correct"
},
{
"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, with all positive integers Isaac is trying to solve the equation on the right. \\( 15=\\frac{1+k}{4} \\) Here are his steps. Step \\( 1: \\) \\(\n60=1+k\n\\)\n\nStep \\( 2: \\) \\(\n61=k\n\\) Which steps, if any, are correct? Both step.s are incorrect"
},
{
"from": "gpt",
"value": "Does not know how to solve linear equations involving fractions"
}
] |
[
{
"from": "human",
"value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +5 going from -1 up to 4]() Which of the following calculations is represented on the thermometer? \\( 4+5=-1 \\)"
},
{
"from": "gpt",
"value": "Believes we move down a number line when we add"
}
] |
[
{
"from": "human",
"value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +5 going from -1 up to 4]() Which of the following calculations is represented on the thermometer? \\( -1+4=5 \\)"
},
{
"from": "gpt",
"value": "Believes the number of jumps between two numbers on a numberline represents the sum of those 2 numbers "
}
] |
[
{
"from": "human",
"value": "Carry out addition problems involving one negative integer ![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +5 going from -1 up to 4]() Which of the following calculations is represented on the thermometer? \\( 1+4=5 \\)"
},
{
"from": "gpt",
"value": "Believes a negative number can be replaced with its positive equivalent when answering an addition problem from a numberline"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape ![\\( \\nabla \\)]() What is the order of rotational symmetry of this shape? \\( 0 \\)"
},
{
"from": "gpt",
"value": "Does not know how to find order of rotational symmetry"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape ![\\( \\nabla \\)]() What is the order of rotational symmetry of this shape? \\( 1 \\)"
},
{
"from": "gpt",
"value": "Does not know how to find order of rotational symmetry"
}
] |
[
{
"from": "human",
"value": "Identify the order of rotational symmetry of a shape ![\\( \\nabla \\)]() What is the order of rotational symmetry of this shape? \\( 9 \\)"
},
{
"from": "gpt",
"value": "Does not know how to find order of rotational symmetry"
}
] |
[
{
"from": "human",
"value": "Can write Roman numerals between 100 and 1000 Which of the following is the correct way to write \\( 900 \\) using Roman numerals? DCCCC"
},
{
"from": "gpt",
"value": "Writes four symbols after rather than one before in Roman numerals"
}
] |
[
{
"from": "human",
"value": "Can write Roman numerals between 100 and 1000 Which of the following is the correct way to write \\( 900 \\) using Roman numerals? IXOO"
},
{
"from": "gpt",
"value": "Thinks that we can use O as zero for place value in Roman numerals"
}
] |
[
{
"from": "human",
"value": "Can write Roman numerals between 100 and 1000 Which of the following is the correct way to write \\( 900 \\) using Roman numerals? ССССССССС"
},
{
"from": "gpt",
"value": "Does not know how to combine different symbols in Roman numerals"
}
] |
[
{
"from": "human",
"value": "Round non-integers to the nearest 10 Jo and Paul are arguing about rounding.\nJo says \\( \\mathbf{1 2 0 6 . 9 7 8} \\) rounded to the nearest hundred is \\( \\mathbf{1 2 0 0} \\)\nPaul says \\( \\mathbf{1 2 0 6 . 9 7 8} \\) rounded to the nearest ten is \\( \\mathbf{1 2 0 0} \\)\nWho is correct? Both Jo and Paul"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 0.51-0.202= \\) \\( 0.151 \\)"
},
{
"from": "gpt",
"value": "Believes subtraction is commutative "
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 0.51-0.202= \\) \\( 0.312 \\)"
},
{
"from": "gpt",
"value": "Believes you subtract the smaller digit from the larger digit in column subtraction, regardless of position"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 0.51-0.202= \\) \\( 0.318 \\)"
},
{
"from": "gpt",
"value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit"
}
] |
[
{
"from": "human",
"value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable Tom and Katie are discussing simultaneous equations Tom says you need to add these equations to eliminate \\( y \\)\n\\(\\begin{array}{r}\n4 x-3 y=12 \\\\\nx+3 y=15\n\\end{array}\\) Katie says you need to add these equations to eliminate \\( y \\)\n\\(\\begin{array}{r}\n4 x+3 y=12 \\\\\nx-3 y=15\n\\end{array}\\) Who is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not think that -n + n = 0"
}
] |
[
{
"from": "human",
"value": "Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative Which of the following sketches could represent \\( y=1-4 x ? \\) ![2 axes showing a positive gradient, crossing the y axis at a positive number]()"
},
{
"from": "gpt",
"value": "When given the equation of a straight line, believes the first term always gives the gradient, even when the first term is actually c"
}
] |
[
{
"from": "human",
"value": "Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative Which of the following sketches could represent \\( y=1-4 x ? \\) ![2 axes showing a positive gradient with a negative y intercept ]()"
},
{
"from": "gpt",
"value": "When given the equation of a straight line, believes the first term always gives the gradient, even when the first term is actually c"
}
] |
[
{
"from": "human",
"value": "Sketch, or identify a sketch, of a line given in the form y = mx + c, where m is negative Which of the following sketches could represent \\( y=1-4 x ? \\) ![2 axes with a negative gradient and a negative y intercept]()"
},
{
"from": "gpt",
"value": "Believes that in y=mx+c, m is the y-intercept"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words I think of a number. I take away six and then divide the result by three. The answer I get is \\( 21 \\).\nWhich of the following equations represents this? \\( n-6 \\div 3=21 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words I think of a number. I take away six and then divide the result by three. The answer I get is \\( 21 \\).\nWhich of the following equations represents this? \\( 3(n-6)=21 \\)"
},
{
"from": "gpt",
"value": "Thinks that a number in front of a bracket means divide"
}
] |
[
{
"from": "human",
"value": "Form expressions from situations described in words I think of a number. I take away six and then divide the result by three. The answer I get is \\( 21 \\).\nWhich of the following equations represents this? \\( \\frac{n}{3}-6=21 \\)"
},
{
"from": "gpt",
"value": "Believes that the order of a worded calculation should be changed to follow BIDMAS "
}
] |
[
{
"from": "human",
"value": "Given the sector angle on a pie chart, calculate the frequency of a group A class of students were surveyed about how many siblings they have.\n\nA selection of results are shown in the table. \\begin{tabular}{|c|c|c|}\n\\hline Number of siblings & Frequency & Angle on a pie chart \\\\\n\\hline 0 & \\( 5 \\) & \\( \\) \\\\\n\\hline 1 & \\( \\bigstar \\) & \\( 165 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 2 \\) & \\( \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 24 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\n\nWhich of the following calculations would work out what replaces the star? \\( 165 \\div 24 \\)"
},
{
"from": "gpt",
"value": "Believes you find the frequency for a pie chart sector by calculating its angle divided by the total frequency"
}
] |
[
{
"from": "human",
"value": "Given the sector angle on a pie chart, calculate the frequency of a group A class of students were surveyed about how many siblings they have.\n\nA selection of results are shown in the table. \\begin{tabular}{|c|c|c|}\n\\hline Number of siblings & Frequency & Angle on a pie chart \\\\\n\\hline 0 & \\( 5 \\) & \\( \\) \\\\\n\\hline 1 & \\( \\bigstar \\) & \\( 165 \\degree \\) \\\\\n\\hline 2 & \\( \\) & \\( \\) \\\\\n\\hline 3 & \\( 2 \\) & \\( \\) \\\\\n\\hline 4 or more & \\( \\) & \\( \\) \\\\\n\\hline TOTAL & 24 & \\( \\) \\\\\n\\end{tabular} Jenny wants to draw a pie chart of the information.\n\nWhich of the following calculations would work out what replaces the star? \\( \\frac{165}{360} \\div 24 \\)"
},
{
"from": "gpt",
"value": "Divides rather than multiplies "
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{3}{11} \\div 3\n\\) \\( \\frac{9}{11} \\)"
},
{
"from": "gpt",
"value": "when dividing a fraction by an integer, multiplies the numerator by the integer"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{3}{11} \\div 3\n\\) \\( \\frac{9}{33} \\)"
},
{
"from": "gpt",
"value": "When dividing a fraction by an integer, multiplies both the numerator and denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Identify non-prisms from a diagram Which of the following is a correct name of this shape? ![A 3D shape with 1 square face and 4 triangular faces. 1 triangular face is attached to each side of the square face.]() Triangular prism"
},
{
"from": "gpt",
"value": "Does not know the definition of a prism"
}
] |
[
{
"from": "human",
"value": "Identify non-prisms from a diagram Which of the following is a correct name of this shape? ![A 3D shape with 1 square face and 4 triangular faces. 1 triangular face is attached to each side of the square face.]() Cone"
},
{
"from": "gpt",
"value": "Does not know the definition of a cone"
}
] |
[
{
"from": "human",
"value": "Identify non-prisms from a diagram Which of the following is a correct name of this shape? ![A 3D shape with 1 square face and 4 triangular faces. 1 triangular face is attached to each side of the square face.]() Triangular-based pyramid"
},
{
"from": "gpt",
"value": "Only counts visible faces"
}
] |
[
{
"from": "human",
"value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=15 \\) and \\( j=3 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=75 \\\\ h(2+j)=-75\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not realise addition is commutative"
}
] |
[
{
"from": "human",
"value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=15 \\) and \\( j=3 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=23 \\\\ h(2+j)=32\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not realise addition is commutative"
}
] |
[
{
"from": "human",
"value": "Substitute positive integer values into expressions involving no powers or roots When \\( h=15 \\) and \\( j=3 \\)\nWhich of the following pairs of statements is true? \\( \\begin{array}{l}h(j+2)=32 \\\\ h(2+j)=23\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not realise addition is commutative"
}
] |
[
{
"from": "human",
"value": "Use the nth term rule for descending integer linear sequences to find another term in a the sequence What is the 11th term of this sequence? \\( u_{n}=2-5 n \\) \\( -57 \\)"
},
{
"from": "gpt",
"value": "When subtracting past zero, adds the absolute values and then writes the answer with a negative sign"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles Which of the following are corresponding angles on this diagram? ![Three almost horizontal lines, two marked with arrows. One almost vertical line crossing them. The twelve angles created are marked a-l. ]() \\( c \\) and \\( g \\)"
},
{
"from": "gpt",
"value": "Mistakes lines as parallel"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles Which of the following are corresponding angles on this diagram? ![Three almost horizontal lines, two marked with arrows. One almost vertical line crossing them. The twelve angles created are marked a-l. ]() \\( d \\) and \\( j \\)"
},
{
"from": "gpt",
"value": "Confuses co-interior and corresponding angles"
}
] |
[
{
"from": "human",
"value": "Identify corresponding angles Which of the following are corresponding angles on this diagram? ![Three almost horizontal lines, two marked with arrows. One almost vertical line crossing them. The twelve angles created are marked a-l. ]() \\( b \\) and \\( f \\)"
},
{
"from": "gpt",
"value": "Mistakes lines as parallel"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c This is a table of values for \\( 3 x+2 y=6 \\) \nWhat should replace the star? \\begin{tabular}{|l|c|c|c|c|c|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \\\\\n\\hline\n\\end{tabular} \\( 2 \\)"
},
{
"from": "gpt",
"value": "Mixes up the value of two terms when substituting"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c This is a table of values for \\( 3 x+2 y=6 \\) \nWhat should replace the star? \\begin{tabular}{|l|c|c|c|c|c|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \\\\\n\\hline\n\\end{tabular} \\( 1.5 \\)"
},
{
"from": "gpt",
"value": "Believes 0 multiplied by a number gives the number"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find a y value in a table of values for lines in the form ax + by = c This is a table of values for \\( 3 x+2 y=6 \\) \nWhat should replace the star? \\begin{tabular}{|l|c|c|c|c|c|}\n\\hline\\( x \\) & \\( 0 \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\( 4 \\) \\\\\n\\hline\\( y \\) & \\( \\color{gold}\\bigstar \\) & \\\\\n\\hline\n\\end{tabular} \\( 12 \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph How many months have an average temperature above 23⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"Months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 7 \\)"
},
{
"from": "gpt",
"value": "When asked to find data points above a certain value, gives the number of data points below this value"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph How many months have an average temperature above 23⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"Months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 5 \\)"
},
{
"from": "gpt",
"value": "Includes a data point with the value, when asked to find the number of data points above a value"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph How many months have an average temperature above 23⁰C ? ![A line graph with title \"Monthly Average temperatures for Zakynthos, Greece. (⁰C)\". \nThe x-axis is labelled with the first letter of every month of the year and is titled \"Months\". \nThe y-axis is titled \"Average temperature (⁰C)\" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]() \\( 8 \\)"
},
{
"from": "gpt",
"value": "When asked to find data points above a certain value, gives the number of data points below this value"
}
] |
[
{
"from": "human",
"value": "Identify factors of a number Which of these is not a factor of \\( 18 \\) ? Eighteen"
},
{
"from": "gpt",
"value": "Does not think a number can be a factor of itself"
}
] |
[
{
"from": "human",
"value": "Round non-integers to other non-integer values (e.g. 0.02) What is \\( \\mathbf{3 . 1 5 3} \\) rounded to the nearest \\( \\mathbf{0 . 0 2} \\) ? \\( 3.2 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round non-integers to other non-integer values (e.g. 0.02) What is \\( \\mathbf{3 . 1 5 3} \\) rounded to the nearest \\( \\mathbf{0 . 0 2} \\) ? \\( 3.15 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too little)"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cylinder when the dimensions are given in the same units What is the area of the face marked \\( F \\) ![A cylinder with height 9cm and radius 5cm. An arrow points to the circular face at the bottom of the cylinder.]() \\( 10 \\pi\\ \\mathrm{cm}^{2} \\)"
},
{
"from": "gpt",
"value": "Calculates circumference when asked for area"
}
] |
Subsets and Splits