conversations
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[
{
"from": "human",
"value": "Subtract proper fractions with different denominators where one is a multiple of the other Calculate:\n\\( \\frac{5}{9}-\\frac{1}{3} \\) \\( \\frac{4}{6} \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators where one is a multiple of the other Calculate:\n\\( \\frac{5}{9}-\\frac{1}{3} \\) \\( \\frac{4}{9} \\)"
},
{
"from": "gpt",
"value": "Does not consider the denominator when adding/ subtracting fractions. Adds/subtracts the numerator and makes the denominator the one with the highest value."
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators where one is a multiple of the other Calculate:\n\\( \\frac{5}{9}-\\frac{1}{3} \\) \\( \\frac{8}{9} \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts"
}
] |
[
{
"from": "human",
"value": "Round numbers to three or more decimal places What is \\( 29.156828 \\) rounded to \\( 3 \\) decimal places? \\( 29.267 \\)"
},
{
"from": "gpt",
"value": "Rounds incorrectly by changing multiple place values"
}
] |
[
{
"from": "human",
"value": "Round numbers to three or more decimal places What is \\( 29.156828 \\) rounded to \\( 3 \\) decimal places? \\( 29.16 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too little)"
}
] |
[
{
"from": "human",
"value": "Round numbers to three or more decimal places What is \\( 29.156828 \\) rounded to \\( 3 \\) decimal places? \\( 29.156 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible: \\( \\frac{4 t^{2}+1}{4 t-2} \\) \\( t+\\frac{1}{2} \\)"
},
{
"from": "gpt",
"value": "Believes the difference of 2 squares method of factorising also works for the addition of 2 squares"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible: \\( \\frac{4 t^{2}+1}{4 t-2} \\) \\( t-\\frac{1}{2} \\)"
},
{
"from": "gpt",
"value": "Thinks you can divide terms by different factors when simplifying an algebraic fraction"
}
] |
[
{
"from": "human",
"value": "Interpret discrete data using a line graph This graph shows the amount of potatoes consumed by a restaurant in a week.\n\nHow many potatoes were consumed on Friday? ![Graph of potatoes consumed with kilos against day of week]() \\( 3 \\mathrm{~kg} \\)"
},
{
"from": "gpt",
"value": "Counts squares instead of the correct scale when plotting coordinates"
}
] |
[
{
"from": "human",
"value": "Round numbers to two decimal places Two different numbers are equal to \\( 7.46 \\) to two decimal places.\nThe numbers could be.... \\( 7.4651 \\)\nand\n\\( 7.4559 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up when next digit is 5"
}
] |
[
{
"from": "human",
"value": "Round numbers to two decimal places Two different numbers are equal to \\( 7.46 \\) to two decimal places.\nThe numbers could be.... \\( 7.4628 \\)\nand\n\\( 7.4528 \\)"
},
{
"from": "gpt",
"value": "Rounds up instead of down"
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to a positive integer power Which of the following is a power of \\( 4 \\) ? \\( 44 \\)"
},
{
"from": "gpt",
"value": "Confuses powers and multiples"
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to a positive integer power Which of the following is a power of \\( 4 \\) ? \\( 400 \\)"
},
{
"from": "gpt",
"value": "Confuses powers and multiples"
}
] |
[
{
"from": "human",
"value": "Raise a positive integer to a positive integer power Which of the following is a power of \\( 4 \\) ? \\( 8 \\)"
},
{
"from": "gpt",
"value": "Confuses powers and multiples"
}
] |
[
{
"from": "human",
"value": "Construct a triangle using Angle-Side-Angle Which of the following best describes how to construct a triangle with side length \\( 7 \\mathrm{~cm} \\) with angles of \\( 40^{\\degree} \\) and \\( 50^{\\degree} \\) either side? - Draw a line \\( 7 \\mathrm{~cm} \\) long\n- Place a protractor at one end of the line, measure \\( 40^{\\degree} \\) and place a dot\n- Place a protractor at the same end of the line, measure \\( 50^{\\degree} \\) and place a dot\n- Draw straight lines through the end of the lines through the dots\n- Where these lines cross completes the triangle"
},
{
"from": "gpt",
"value": "Draws both angles at the same end of the line when constructing a triangle"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Which option gives a correct substitution into the quadratic formula to solve the quadratic equation? \\( 2 x^{2}-8 x+7=0 \\) \\( -8 \\pm \\frac{\\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \\)"
},
{
"from": "gpt",
"value": "Misremembers the quadratic formula"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Which option gives a correct substitution into the quadratic formula to solve the quadratic equation? \\( 2 x^{2}-8 x+7=0 \\) \\( 8 \\pm \\frac{\\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \\)"
},
{
"from": "gpt",
"value": "Misremembers the quadratic formula"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Which option gives a correct substitution into the quadratic formula to solve the quadratic equation? \\( 2 x^{2}-8 x+7=0 \\) \\( \\frac{-8 \\pm \\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \\)"
},
{
"from": "gpt",
"value": "Misremembers the quadratic formula"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 6 \\) out of \\( 25 \\) as a percentage? \\( 12 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks they double the numerator to turn a fraction into a percentage"
}
] |
[
{
"from": "human",
"value": "Express one quantity as a percentage of another mentally What is \\( 6 \\) out of \\( 25 \\) as a percentage? \\( 62.5 \\% \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a percentage by writing the numerator followed by the denominator"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\( 3+6 \\div 2+1= \\) \\( 3 \\)"
},
{
"from": "gpt",
"value": "Confuses the order of operations, believes addition comes before division"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division \\( 3+6 \\div 2+1= \\) \\( 5.5 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Find \\( d \\) in the following equation \\( \\frac{5 d-2}{3}=2 d-1 \\) \\( d=-1 \\)"
},
{
"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": "Multiply a decimal by an integer Work out:\n\\[\n0.04 \\times 21\n\\] \\( 8.4 \\)"
},
{
"from": "gpt",
"value": "When multiplying a decimal less than 1 by an integer, gives an answer 10 times bigger than it should be"
}
] |
[
{
"from": "human",
"value": "Multiply a decimal by an integer Work out:\n\\[\n0.04 \\times 21\n\\] \\( 8.04 \\)"
},
{
"from": "gpt",
"value": "When multiplying decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant."
}
] |
[
{
"from": "human",
"value": "Multiply a decimal by an integer Work out:\n\\[\n0.04 \\times 21\n\\] \\( 0.084 \\)"
},
{
"from": "gpt",
"value": "When multiplying a decimal less than 1 by an integer, gives an answer 10 times smaller than it should be"
}
] |
[
{
"from": "human",
"value": "Read values from piecewise functions Tom has correctly drawn the graph of the following function:\n\\(\ny=\\left\\{\\begin{array}{c}\nP \\text { for } 0 \\leq x<Q \\\\\n2.5 \\text { for } 2 \\leq x<4 \\\\\n1 \\text { for } 4 \\leq x \\leq 6\n\\end{array}\\right.\n\\)\n\nWhat are the values of \\( P \\) and Q? ![The graph is three separate horizontal lines. It goes from (0,3.5) to (2, 3.5), then (2, 2.5) to (4, 2.5) and the last section is from (4, 1) to (6, 1)]() \\( \\begin{array}{c}P=2 \\\\ Q=3.5\\end{array} \\)"
},
{
"from": "gpt",
"value": "When reading value from graph, reads from the wrong axes."
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving roots \\( \\sqrt{8^{2}}= \\) \\( 64 \\)"
},
{
"from": "gpt",
"value": "Has completed only one of the two operations."
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving roots \\( \\sqrt{8^{2}}= \\) \\( 4 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving roots \\( \\sqrt{8^{2}}= \\) \\( 16 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling, and not square rooted"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are multiples of the same number In a bakery \\( \\frac{2}{5} \\) of the cakes are chocolate, \\( \\frac{3}{8} \\) of the cakes are vanilla and \\( \\frac{13}{40} \\) are lemon.\nWhich flavour cake is there more of? Vanilla"
},
{
"from": "gpt",
"value": "Does not find a common denominator when comparing fractions"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are multiples of the same number In a bakery \\( \\frac{2}{5} \\) of the cakes are chocolate, \\( \\frac{3}{8} \\) of the cakes are vanilla and \\( \\frac{13}{40} \\) are lemon.\nWhich flavour cake is there more of? Lemon"
},
{
"from": "gpt",
"value": "Does not find a common denominator when comparing fractions"
}
] |
[
{
"from": "human",
"value": "Order fractions whose denominators are multiples of the same number In a bakery \\( \\frac{2}{5} \\) of the cakes are chocolate, \\( \\frac{3}{8} \\) of the cakes are vanilla and \\( \\frac{13}{40} \\) are lemon.\nWhich flavour cake is there more of? There is the same amount of each."
},
{
"from": "gpt",
"value": "Does not find a common denominator when comparing fractions"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Tom and Katie are arguing about working out percentages of amounts.\n\nTom says to find \\( 30 \\% \\) you divide by \\( 3 \\).\n\nKatie says to find \\( 30 \\% \\) you divide by \\( 100 \\) and multiply by \\( 3 \\).\n\nWho is correct? Only Tom"
},
{
"from": "gpt",
"value": "Does not understand a percentage is out of 100"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Tom and Katie are arguing about working out percentages of amounts.\n\nTom says to find \\( 30 \\% \\) you divide by \\( 3 \\).\n\nKatie says to find \\( 30 \\% \\) you divide by \\( 100 \\) and multiply by \\( 3 \\).\n\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Error finding percentage value after finding 1%"
}
] |
[
{
"from": "human",
"value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Tom and Katie are arguing about working out percentages of amounts.\n\nTom says to find \\( 30 \\% \\) you divide by \\( 3 \\).\n\nKatie says to find \\( 30 \\% \\) you divide by \\( 100 \\) and multiply by \\( 3 \\).\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not understand a percentage is out of 100"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate displacement-time graph John walks from home at a constant speed to a bench, stops for a rest, and then runs home at a constant speed. Which of the following displacement \\( (d) \\) time \\( (t) \\) graphs is most likely to illustrate John's journey? ![The graph has three sections.\nThe first section starts at (0, 0) and is a sloped line with steep, positive, uphill gradient, then a horizontal line. The third section is a sloped line with gentle, negative gradient that ends when it touches the horizontal axis.]()"
},
{
"from": "gpt",
"value": "Believes a less steep gradient corresponds to a faster speed"
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate displacement-time graph John walks from home at a constant speed to a bench, stops for a rest, and then runs home at a constant speed. Which of the following displacement \\( (d) \\) time \\( (t) \\) graphs is most likely to illustrate John's journey? ![The graph has three sections.\nThe first section starts at (0, 0) and is a sloped line with positive, uphill gradient, then a horizontal line. The third section is another sloped line with a steeper positive gradient.]()"
},
{
"from": "gpt",
"value": "Believes displacement continues to increase even when returning to starting point"
}
] |
[
{
"from": "human",
"value": "Complete multi-step conversions of length that use multiplication How many millimetres in \\( 100 \\) kilometres? One hundred thousand"
},
{
"from": "gpt",
"value": "Thinks there are 1000mm in a km"
}
] |
[
{
"from": "human",
"value": "Complete multi-step conversions of length that use multiplication How many millimetres in \\( 100 \\) kilometres? One million"
},
{
"from": "gpt",
"value": "Thinks there are 10000mm in a km"
}
] |
[
{
"from": "human",
"value": "Complete multi-step conversions of length that use multiplication How many millimetres in \\( 100 \\) kilometres? One billion"
},
{
"from": "gpt",
"value": "Thinks there are 10 million mm in 1 km"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables Which of the following is a correct simplification of: \\( 4 x^{2}+2 x-x \\) \\( 4 x^{2}+3 x \\)"
},
{
"from": "gpt",
"value": "When collecting like terms, treats subtractions as if they are additions"
}
] |
[
{
"from": "human",
"value": "Identify the net of a non-prism Which is the correct net for this shape? ![A 3D image of a triangular prism]() ![Net showing 3 rectangles and two triangles]()"
},
{
"from": "gpt",
"value": "Confuses pyramid with prism"
}
] |
[
{
"from": "human",
"value": "Identify the net of a non-prism Which is the correct net for this shape? ![A 3D image of a triangular prism]() ![\\( \\theta \\)]()"
},
{
"from": "gpt",
"value": "Struggles to visualise nets of 3D shapes"
}
] |
[
{
"from": "human",
"value": "Identify the net of a non-prism Which is the correct net for this shape? ![A 3D image of a triangular prism]() ![None of the above]()"
},
{
"from": "gpt",
"value": "Struggles to visualise nets of 3D shapes"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Tom and Katie are discussing this sequence. ![3 consecutive patterns of a sequence are shown. The first pattern is a green triangle inside a square shape that is made from 4 separate red sticks. The second term is Pattern 1 but with 1 more green triangle and 3 more red sticks so that the 2 triangles are enclosed by squares made from red sticks. The third term is Pattern 2 but with 1 more green triangle and 3 more red sticks so that the 3 triangles are enclosed by squares made from red sticks.]() Tom says the number of triangles in the \\( 6^{\\text {th }} \\) term will be \ndouble the number of triangles in the \\( 3^{\\text {rd }} \\) term.\n\nKatie says the number of sticks in the \\( 6^{\\text {th }} \\) term will be \ndouble the number of sticks in the \\( 3^{\\text {rd }} \\) term.\n\nWho do you agree with? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes there is a multiplicative relationship between values of terms in a linear sequence e.g. 10th term is double 5th term"
}
] |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=3 x-7\\)\nto the graph of\n\\(y=7-3 x\\) Reflection in the line\n\\[\ny=x\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a reflection in y=x"
}
] |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=3 x-7\\)\nto the graph of\n\\(y=7-3 x\\) Reflection in the line\n\\[\ny=-x\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a reflection in y=-x"
}
] |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=3 x-7\\)\nto the graph of\n\\(y=7-3 x\\) Reflection in the\n\\[\ny \\text {-axis }\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a reflection in the y-axis"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths involve algebraic expressions What length replaces the \\( \\color{green}\\bigstar \\) ? ![A diagram showing a compound shape. It is an L shape rotated 90 degrees clockwise. The top full width is 3x+4, the partial width to the right is x+4. The left full height is 5, the partial height on the right is 3. There is a green star on the left partial width at the bottom of the diagram.]() \\( 3 \\)"
},
{
"from": "gpt",
"value": "Does not realise that two letters together, or a number and letter together, are multiplying"
}
] |
[
{
"from": "human",
"value": "Calculate missing lengths of shapes by geometrical inference, where the lengths involve algebraic expressions What length replaces the \\( \\color{green}\\bigstar \\) ? ![A diagram showing a compound shape. It is an L shape rotated 90 degrees clockwise. The top full width is 3x+4, the partial width to the right is x+4. The left full height is 5, the partial height on the right is 3. There is a green star on the left partial width at the bottom of the diagram.]() Not enough information"
},
{
"from": "gpt",
"value": "Does not know how to find missing lengths in a composite shape"
}
] |
[
{
"from": "human",
"value": "Interpret a bar chart ![A bar chart with blue bars. The x-axis is labelled with fruits and the y-axis is titled \"Number of Children\" and its scale is from 0 to 60 in steps of 10. The bars represent the following numbers of children: Banana, 20; Apple, 40; Kiwi Fruits, 50; Orange, 30; Pineapple, 25.]() Which of the following statements is true? Banana is the most popular fruit"
},
{
"from": "gpt",
"value": "Thinks the smallest bar in a bar chart is the mode"
}
] |
[
{
"from": "human",
"value": "Recognise if two linear expressions are in an appropriate form to be added or subtracted Tom and Katie are discussing whether simultaneous equations are in an appropriate form to be added or subtracted, or whether they need transforming first. Tom says these equations are in an appropriate form\n\\(\n\\begin{array}{l}\n2 x-3 y=10 \\\\\n5 x+3 y=18\n\\end{array}\n\\) Katie says these equations are in an appropriate form\n\\(\n\\begin{array}{l}\n2 x-3 y=10 \\\\\n2 x+y=4\n\\end{array}\n\\) Who is correct? Only Tom"
},
{
"from": "gpt",
"value": "When solving simultaneous equations, believes the terms must be of opposite signs in order to be eliminated."
}
] |
[
{
"from": "human",
"value": "Recognise if two linear expressions are in an appropriate form to be added or subtracted Tom and Katie are discussing whether simultaneous equations are in an appropriate form to be added or subtracted, or whether they need transforming first. Tom says these equations are in an appropriate form\n\\(\n\\begin{array}{l}\n2 x-3 y=10 \\\\\n5 x+3 y=18\n\\end{array}\n\\) Katie says these equations are in an appropriate form\n\\(\n\\begin{array}{l}\n2 x-3 y=10 \\\\\n2 x+y=4\n\\end{array}\n\\) Who is correct? Only Katie"
},
{
"from": "gpt",
"value": "When solving simultaneous equations, believes the terms must have the same sign in order to be eliminated."
}
] |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate non linear real life graph \\( p \\) increases slowly at first, then quickly, then slowly again\nWhich of the following sketches best shows this? ![A graph with time on the horizontal axis and p on the vertical axis. The graph starts at the origin and curves right and upwards very steeply, then begins to level off slightly, then travels more steeply again.]()"
},
{
"from": "gpt",
"value": "Believes a less steep gradient corresponds to a faster speed"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² - bx - c When \\( x^{2}-x-12 \\) is factorised, what will appear in the box below ![\\( (x+3) \\)]() \\( (x-15) \\)"
},
{
"from": "gpt",
"value": "Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators which do not share a common factor The fractions in the two circles below add to give the fraction in the circle above.\n\nWhat should replace the question mark? ![Two circles containing the fractions 3/5 and 2/7, both linked to a third circle above]() \\( \\frac{11}{35} \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of adds"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators which do not share a common factor The fractions in the two circles below add to give the fraction in the circle above.\n\nWhat should replace the question mark? ![Two circles containing the fractions 3/5 and 2/7, both linked to a third circle above]() \\( \\frac{5}{12} \\)"
},
{
"from": "gpt",
"value": "When adding fractions, adds the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Add proper fractions with different denominators which do not share a common factor The fractions in the two circles below add to give the fraction in the circle above.\n\nWhat should replace the question mark? ![Two circles containing the fractions 3/5 and 2/7, both linked to a third circle above]() \\( \\frac{5}{35} \\)"
},
{
"from": "gpt",
"value": "Forgets to change the numerators when finding equivalent fractions"
}
] |
[
{
"from": "human",
"value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE and three triangles attached to it. The marked angle is between the lines EG and GH.]() EGCE"
},
{
"from": "gpt",
"value": "Uses more than 3 letters to describe an angle"
}
] |
[
{
"from": "human",
"value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE and three triangles attached to it. The marked angle is between the lines EG and GH.]() HCE"
},
{
"from": "gpt",
"value": "Chooses the wrong 3 letters to describe an angle"
}
] |
[
{
"from": "human",
"value": "Label angles using correct 3-letter notation (e.g. angle ADB) Which of the following correctly describes the marked angle? ![An image of square ABCE and three triangles attached to it. The marked angle is between the lines EG and GH.]() CGE"
},
{
"from": "gpt",
"value": "Chooses the wrong 3 letters to describe an angle"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplify the following by collecting like terms.\n\\[\n10 t-4 h-15 t+4 h\n\\] \\( 0-5 t \\)"
},
{
"from": "gpt",
"value": "When simplifying, thinks they write 0 in front of a negative number in the final answer, instead of just writing the negative number"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just two linear variables Simplify the following by collecting like terms.\n\\[\n10 t-4 h-15 t+4 h\n\\] \\( h-5 t \\)"
},
{
"from": "gpt",
"value": "Does not think that a variable with no coefficient has a coefficient of 1."
}
] |
[
{
"from": "human",
"value": "Answer decimal problems that require the use of BIDMAS \\( 0.4-\\frac{1}{5} \\times 3= \\) \\( 0.2 \\)"
},
{
"from": "gpt",
"value": "Believes subtraction is commutative "
}
] |
[
{
"from": "human",
"value": "Answer decimal problems that require the use of BIDMAS \\( 0.4-\\frac{1}{5} \\times 3= \\) \\( 0.6 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Multiply algebraic terms, where both are linear versions of different letters (e.g. 4a x 2b) What is the answer to \\( 4 c \\times 5 d \\) ? \\( 45 c d \\)"
},
{
"from": "gpt",
"value": "When multiplying just writes the numbers next to each other"
}
] |
[
{
"from": "human",
"value": "Multiply algebraic terms, where both are linear versions of different letters (e.g. 4a x 2b) What is the answer to \\( 4 c \\times 5 d \\) ? \\( 20 c d^{2} \\)"
},
{
"from": "gpt",
"value": "Thinks any 2 values multiplied together can be denoted with a squared symbol"
}
] |
[
{
"from": "human",
"value": "Multiply algebraic terms, where both are linear versions of different letters (e.g. 4a x 2b) What is the answer to \\( 4 c \\times 5 d \\) ? \\( 9 c d \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplies when multiplying algebraic terms"
}
] |
[
{
"from": "human",
"value": "Solve length problems involving similar shapes where the missing length is the shorter one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The bigger one has sides 9 cm and 7.5 cm. On the smaller triangle, the side corresponding to the 9 cm is 6 cm, and the side corresponding to the 7.5 cm is marked with a star.]() \\( 3.75 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Doubles side length for similar shape instead of using correct scale factor"
}
] |
[
{
"from": "human",
"value": "Solve length problems involving similar shapes where the missing length is the shorter one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The bigger one has sides 9 cm and 7.5 cm. On the smaller triangle, the side corresponding to the 9 cm is 6 cm, and the side corresponding to the 7.5 cm is marked with a star.]() \\( 4.5 \\mathrm{~cm} \\)"
},
{
"from": "gpt",
"value": "Thinks adding the same value to each side makes shapes similar"
}
] |
[
{
"from": "human",
"value": "Solve length problems involving similar shapes where the missing length is the shorter one These two shapes are similar (not drawn to scale).\nWhat should replace the star? ![Two scalene triangles. The bigger one has sides 9 cm and 7.5 cm. On the smaller triangle, the side corresponding to the 9 cm is 6 cm, and the side corresponding to the 7.5 cm is marked with a star.]() Not enough information"
},
{
"from": "gpt",
"value": "Does not understand how to find a scale factor"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient strategies for mental addition This is how Ron calculates the answer to \\( 46+28 \\) mentally ![Cartoon picture of a boy's head with 2 thought bubbles:\nFirst thought bubble says: \"46+20 is equal to 66\"\nSecond thought bubble says: \"Then I am going to add on the 8. 66+8=74\"]() Ron uses the same method to calculate \\( 38+45 \\). \nWhich of the following shows how he would do this? \\( \\begin{array}{c}38+5=43 \\\\ 43+40=83\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not copy a given method accurately"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient strategies for mental addition This is how Ron calculates the answer to \\( 46+28 \\) mentally ![Cartoon picture of a boy's head with 2 thought bubbles:\nFirst thought bubble says: \"46+20 is equal to 66\"\nSecond thought bubble says: \"Then I am going to add on the 8. 66+8=74\"]() Ron uses the same method to calculate \\( 38+45 \\). \nWhich of the following shows how he would do this? \\( \\begin{array}{c}38+40=78 \\\\ 78+5=83\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not copy a given method accurately"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient strategies for mental addition This is how Ron calculates the answer to \\( 46+28 \\) mentally ![Cartoon picture of a boy's head with 2 thought bubbles:\nFirst thought bubble says: \"46+20 is equal to 66\"\nSecond thought bubble says: \"Then I am going to add on the 8. 66+8=74\"]() Ron uses the same method to calculate \\( 38+45 \\). \nWhich of the following shows how he would do this? \\( \\begin{array}{c}8+5=13 \\\\ 30+13=43 \\\\ 43+40=83\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not copy a given method accurately"
}
] |
[
{
"from": "human",
"value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Natalie is working out the distance between these two points. She has worked out the lengths of the triangle.\nWhat is the distance? ![The image is of two points (-7, -3) and (4,2) joined by a sloped straight line, and then a horizontal and vertical line to create a right-angled triangle. The horizontal line is marked 11 and the vertical line is marked 5.]() \\( 55 \\)"
},
{
"from": "gpt",
"value": "Does not link Pythagoras Theorem to finding distance between two points"
}
] |
[
{
"from": "human",
"value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Natalie is working out the distance between these two points. She has worked out the lengths of the triangle.\nWhat is the distance? ![The image is of two points (-7, -3) and (4,2) joined by a sloped straight line, and then a horizontal and vertical line to create a right-angled triangle. The horizontal line is marked 11 and the vertical line is marked 5.]() \\( \\sqrt{32} \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Calculate the distance between two coordinates in 2D, where all the values are integers but at least one is negative Natalie is working out the distance between these two points. She has worked out the lengths of the triangle.\nWhat is the distance? ![The image is of two points (-7, -3) and (4,2) joined by a sloped straight line, and then a horizontal and vertical line to create a right-angled triangle. The horizontal line is marked 11 and the vertical line is marked 5.]() \\( \\sqrt{96} \\)"
},
{
"from": "gpt",
"value": "Does not rearrange the Pythagoras' Theorem formula accurately"
}
] |
[
{
"from": "human",
"value": "Divide integers of 3 or more digits using long division When using long-division to solve this problem, what digit should replace the rectangle to give the correct answer (quotient)? ![Division sum written out in Bus Stop format with dividend = 771, divisor = 3, the digits of the quotient are represented by a yellow star, a purple triangle and a blue rectangle.]() \\( 0 \\)"
},
{
"from": "gpt",
"value": "When dividing, ignores any remainders"
}
] |
[
{
"from": "human",
"value": "Identify reflex angles An angle measures \\( 192^{\\degree} \\).\nThis means it is... Acute"
},
{
"from": "gpt",
"value": "Does not understand that an acute angle is between 0 and 90 degrees"
}
] |
[
{
"from": "human",
"value": "Identify reflex angles An angle measures \\( 192^{\\degree} \\).\nThis means it is... Obtuse"
},
{
"from": "gpt",
"value": "Does not understand that an obtuse angle is between 90 and 180 degrees"
}
] |
[
{
"from": "human",
"value": "Identify reflex angles An angle measures \\( 192^{\\degree} \\).\nThis means it is... A right angle"
},
{
"from": "gpt",
"value": "Does not know that a right angle is 90 degrees"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data What is the mean of the following numbers?\n\n\\[\n2,2,3,5,8\n\\] \\( 20 \\)"
},
{
"from": "gpt",
"value": "When calculating the mean from a list of data, adds up the numbers but does not divide"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data What is the mean of the following numbers?\n\n\\[\n2,2,3,5,8\n\\] \\( 3 \\)"
},
{
"from": "gpt",
"value": "When asked for the mean of a list of data, gives the median"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data What is the mean of the following numbers?\n\n\\[\n2,2,3,5,8\n\\] \\( 2 \\)"
},
{
"from": "gpt",
"value": "When asked for the mean of a list of data, gives the mode"
}
] |
[
{
"from": "human",
"value": "Order decimals with a different number of digits Tom and Katie are discussing how to order decimals\nTom says \\( 0.06 \\) is greater than \\( 0.006 \\)\nKatie says \\( 0.5 \\) is greater than \\( 0.6087 \\)\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Thinks the more digits a number has the greater it is, regardless of place value"
}
] |
[
{
"from": "human",
"value": "Order decimals with a different number of digits Tom and Katie are discussing how to order decimals\nTom says \\( 0.06 \\) is greater than \\( 0.006 \\)\nKatie says \\( 0.5 \\) is greater than \\( 0.6087 \\)\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "When ordering integers, orders from the digits at the end of the number instead of the digits at the start"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of this shape? ![A parallelogram drawn on a square grid in purple with an area of 9 square units. The base is length 3 squares and the perpendicular height is also length 3 squares.]() \\( 12 \\)"
},
{
"from": "gpt",
"value": "Counts half-squares as full squares when calculating area on a square grid"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of this shape? ![A parallelogram drawn on a square grid in purple with an area of 9 square units. The base is length 3 squares and the perpendicular height is also length 3 squares.]() \\( 8 \\)"
},
{
"from": "gpt",
"value": "Underestimates the area of shapes when counting squares when some squares are neither wholes nor halves"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a parallelogram where the dimensions are given in the same units What is the area of this shape? ![A parallelogram drawn on a square grid in purple with an area of 9 square units. The base is length 3 squares and the perpendicular height is also length 3 squares.]() \\( 6 \\)"
},
{
"from": "gpt",
"value": "Only includes fully shaded squares when counting area"
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart People from Iceland were asked to pick their favourite from: lamb, fish and hotdog. A pie chart was made and \\( 90 \\) degrees represented fish.\nWhat does this mean? Fish are the least preferred food from the list"
},
{
"from": "gpt",
"value": "Believes you can make assumptions about size of pie chart sectors without enough information"
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart People from Iceland were asked to pick their favourite from: lamb, fish and hotdog. A pie chart was made and \\( 90 \\) degrees represented fish.\nWhat does this mean? Lamb is the most preferred food from the list"
},
{
"from": "gpt",
"value": "Believes you can make assumptions about size of pie chart sectors without enough information"
}
] |
[
{
"from": "human",
"value": "Interpret a pie chart People from Iceland were asked to pick their favourite from: lamb, fish and hotdog. A pie chart was made and \\( 90 \\) degrees represented fish.\nWhat does this mean? \\( 90 \\% \\) of the people prefer fish"
},
{
"from": "gpt",
"value": "Believes a pie chart makes 360% not 360 degrees"
}
] |
[
{
"from": "human",
"value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c This is part of a table of values for\n\\[y=x^{2} -2 x+1\\] \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( -1 \\) \\\\\n\\hline\\( y \\) & \\(\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( -2 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c This is part of a table of values for\n\\[y=x^{2} -2 x+1\\] \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( -1 \\) \\\\\n\\hline\\( y \\) & \\(\\bigstar\\) \\\\\n\\hline\n\\end{tabular} What should replace the star? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Believes the square of a negative will also be negative"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give exactly one solution.\nWhich one? \\( \\frac{-3 \\pm \\sqrt{11}}{5} \\)"
},
{
"from": "gpt",
"value": "Does not think a square root can be negative"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give exactly one solution.\nWhich one? \\( \\frac{-3 \\pm \\sqrt{-16}}{5} \\)"
},
{
"from": "gpt",
"value": "Believes you can square root a negative number"
}
] |
[
{
"from": "human",
"value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 One of these quadratic equations will give exactly one solution.\nWhich one? \\( \\frac{-3 \\pm \\sqrt{16}}{-5} \\)"
},
{
"from": "gpt",
"value": "Does not think a square root can be negative"
}
] |
[
{
"from": "human",
"value": "Understand the notation for powers To calculate \\( 47^{2} \\) you need to do... \\( 47 \\div 2 \\)"
},
{
"from": "gpt",
"value": "Divides by the index"
}
] |
[
{
"from": "human",
"value": "Understand the notation for powers To calculate \\( 47^{2} \\) you need to do... \\( 47+2 \\)"
},
{
"from": "gpt",
"value": "Adds the index to the number"
}
] |
Subsets and Splits