bwowe/mis_conv · Datasets at Hugging Face

conversations listlengths 2 2
[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![Four quadrant, coordinate grid with the reflection line y=-x drawn and a triangle. The triangle has coordinates: (-2,3) (-2,6) and (0,5). The point P is the coordinate (0,5)]() \\( (-4,5) \\)" }, { "from": "gpt", "value": "Reflects horizontally or vertically instead of across a diagonal line of symmetry" } ]
[ { "from": "human", "value": "Add integers up to 4 digits using a written method where carrying is needed What number should replace the star? \\begin{tabular}{\|c\|c\|c\|c\|c\|}\n\\hline & \\( 4 \\) & \\( 2 \\) & \\(5\\) & \\(4\\)\\\\\n\\hline+ & \\( 2 \\) & \\(\\bigstar\\) & \\(7\\) & \\(1\\) \\\\\n\\hline \\(\\space\\) & \\(6\\) & \\(3\\) & \\(2\\) & \\(5\\)\n\\end{tabular} \\( 6 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]
[ { "from": "human", "value": "Add integers up to 4 digits using a written method where carrying is needed What number should replace the star? \\begin{tabular}{\|c\|c\|c\|c\|c\|}\n\\hline & \\( 4 \\) & \\( 2 \\) & \\(5\\) & \\(4\\)\\\\\n\\hline+ & \\( 2 \\) & \\(\\bigstar\\) & \\(7\\) & \\(1\\) \\\\\n\\hline \\(\\space\\) & \\(6\\) & \\(3\\) & \\(2\\) & \\(5\\)\n\\end{tabular} \\( 1 \\)" }, { "from": "gpt", "value": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Find \\( 20 \\% \\) of \\( 80 \\) \\( 8 \\)" }, { "from": "gpt", "value": "Does not understand how to find percentages of an amount" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Find \\( 20 \\% \\) of \\( 80 \\) \\( 20 \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a number to make it a percentage" } ]
[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Find \\( 20 \\% \\) of \\( 80 \\) \\( 96 \\)" }, { "from": "gpt", "value": "Found the percentage but added it to 100%" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as simply as possible: \\( \\frac{q^{2}+q-12}{q^{2}-2 q-3} \\) \\( \\frac{q-4}{q-1} \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]
[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as simply as possible: \\( \\frac{q^{2}+q-12}{q^{2}-2 q-3} \\) \\( \\frac{q-4}{-2 q-1} \\)" }, { "from": "gpt", "value": "Thinks that when you cancel identical terms from the numerator and denominator, they just disappear" } ]
[ { "from": "human", "value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate\n\\(\n\\frac{1}{6} \\div 3\n\\) \\( 2 \\)" }, { "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: Fraction ÷ Integer Calculate\n\\(\n\\frac{1}{6} \\div 3\n\\) \\( 18 \\)" }, { "from": "gpt", "value": "Believes division is commutative " } ]
[ { "from": "human", "value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate\n\\(\n\\frac{1}{6} \\div 3\n\\) \\( \\frac{1}{2} \\)" }, { "from": "gpt", "value": "When dividing a fraction by an integer, divides the denominator by the integer" } ]
[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages Write \\( 0.15 \\) as a percentage. \\( 0.15 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a decimal to convert to a percentage" } ]
[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages Write \\( 0.15 \\) as a percentage. \\( 1.5 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]
[ { "from": "human", "value": "Represent a linear inequality with a single tail on a numberline Which inequality is represented by the diagram? ![A number line with a filled in circle above 1with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]() \\( x>1 \\)" }, { "from": "gpt", "value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning." } ]
[ { "from": "human", "value": "Represent a linear inequality with a single tail on a numberline Which inequality is represented by the diagram? ![A number line with a filled in circle above 1with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]() \\( x \\leq 1 \\)" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]
[ { "from": "human", "value": "Solve basic introduction simultaneous equation problems, often involving shapes and symbols Chris orders \\( 2 \\) cups of tea and a cake, and his bill comes to £1.40\n\nAmy orders \\( 4 \\) cups of tea and a cake, and her bill comes to £2.20.\n\nHow much does one cup of tea cost? \\( 80 p \\)" }, { "from": "gpt", "value": "When solving an equation forgets to eliminate the coefficient in front of the variable in the last step" } ]
[ { "from": "human", "value": "Solve basic introduction simultaneous equation problems, often involving shapes and symbols Chris orders \\( 2 \\) cups of tea and a cake, and his bill comes to £1.40\n\nAmy orders \\( 4 \\) cups of tea and a cake, and her bill comes to £2.20.\n\nHow much does one cup of tea cost? \\( 55 p \\)" }, { "from": "gpt", "value": "When asked to solve simultaneous equations, believes they can just find values that work in one equation" } ]
[ { "from": "human", "value": "Identify a diameter The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]() Diagram" }, { "from": "gpt", "value": "Does not know the term 'diameter'" } ]
[ { "from": "human", "value": "Identify a diameter The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]() Diagonal" }, { "from": "gpt", "value": "Does not know the term 'diameter'" } ]
[ { "from": "human", "value": "Identify a diameter The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]() Diamond" }, { "from": "gpt", "value": "Does not know the term 'diameter'" } ]
[ { "from": "human", "value": "Calculate non-unit fractions of an amount \\( \\frac{3}{5} \\) of \\( 30= \\) \\( 6 \\)" }, { "from": "gpt", "value": "Finds the unit fraction when asked to find a non-unit fraction of an amount" } ]
[ { "from": "human", "value": "Calculate non-unit fractions of an amount \\( \\frac{3}{5} \\) of \\( 30= \\) \\( 50 \\)" }, { "from": "gpt", "value": "Divides by the numerator and multiplies by the denominator when finding a fraction of an amount" } ]
[ { "from": "human", "value": "Interpret numbers in a frequency table Bob recorded the number of cars he sold in one week.\nHow many cars did he sell altogether? \\begin{tabular}{\|c\|c\|}\n\\hline Colour & Frequency \\\\\n\\hline Blue & \\( 3 \\) \\\\\n\\hline Black & \\( 2 \\) \\\\\n\\hline Silver & \\( 4 \\) \\\\\n\\hline Red & \\( 1 \\) \\\\\n\\hline Other & \\( 3 \\) \\\\\n\\hline\n\\end{tabular} \\( 5 \\)" }, { "from": "gpt", "value": "Believes total in a grouped table is found by counting rows" } ]
[ { "from": "human", "value": "Interpret numbers in a frequency table Bob recorded the number of cars he sold in one week.\nHow many cars did he sell altogether? \\begin{tabular}{\|c\|c\|}\n\\hline Colour & Frequency \\\\\n\\hline Blue & \\( 3 \\) \\\\\n\\hline Black & \\( 2 \\) \\\\\n\\hline Silver & \\( 4 \\) \\\\\n\\hline Red & \\( 1 \\) \\\\\n\\hline Other & \\( 3 \\) \\\\\n\\hline\n\\end{tabular} \\( 10 \\)" }, { "from": "gpt", "value": "Believes you do not include an \"other\" category when finding a total frequency" } ]
[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places \\( 0.4^{2}= \\) \\( 0.8 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]
[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places \\( 0.4^{2}= \\) \\( 1.6 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]
[ { "from": "human", "value": "Interpret a bar chart The bar chart shows the drinks sold in Caroline's Café on Monday and Tuesday last week.\n\nApproximately how many Teas were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.\nThe Teas bar lower section is 1 tick below 50 on the vertical scale, and the whole bar's height is 2 ticks above 100 on the vertical scale.\n]() \\( 62 \\)" }, { "from": "gpt", "value": "Misreads scale" } ]
[ { "from": "human", "value": "Interpret a bar chart The bar chart shows the drinks sold in Caroline's Café on Monday and Tuesday last week.\n\nApproximately how many Teas were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.\nThe Teas bar lower section is 1 tick below 50 on the vertical scale, and the whole bar's height is 2 ticks above 100 on the vertical scale.\n]() \\( 120 \\)" }, { "from": "gpt", "value": "When reading a composite bar chart, just reads total height of bar" } ]
[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 81 \\) ? \\( 3 \\)" }, { "from": "gpt", "value": "Mixes up square rooting and fourth rooting" } ]
[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 81 \\) ? \\( 162 \\)" }, { "from": "gpt", "value": "Mixes up square rooting and multiplying by 2 or doubling" } ]
[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 81 \\) ? \\( 6561 \\)" }, { "from": "gpt", "value": "Squares when asked to find the square root" } ]
[ { "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 \\( 40 \\% \\) you divide by \\( 100 \\) and multiply by \\( 4 \\). \nKatie says to find \\( 40 \\% \\) you divide by \\( 5 \\) and multiply by \\( 2 \\).\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Believes that dividing by 100 gives 10%" } ]
[ { "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 \\( 40 \\% \\) you divide by \\( 100 \\) and multiply by \\( 4 \\). \nKatie says to find \\( 40 \\% \\) you divide by \\( 5 \\) and multiply by \\( 2 \\).\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes that dividing by 100 gives 10%" } ]
[ { "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 \\( 40 \\% \\) you divide by \\( 100 \\) and multiply by \\( 4 \\). \nKatie says to find \\( 40 \\% \\) you divide by \\( 5 \\) and multiply by \\( 2 \\).\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Unable to equate a division and multiplication to a single division" } ]
[ { "from": "human", "value": "Recognise a Fibonacci sequence Tom and Katie are discussing Fibonacci sequences.\n\nTom says this is a Fibonacci sequence: \\( 1,1,2,3,5,8, \\ldots \\)\n\nKatie says this is a Fibonacci sequence: \\( 1,2,3,5,8,13, \\ldots \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Thinks a Fibonacci sequence must start with 1, 1" } ]
[ { "from": "human", "value": "Recognise a Fibonacci sequence Tom and Katie are discussing Fibonacci sequences.\n\nTom says this is a Fibonacci sequence: \\( 1,1,2,3,5,8, \\ldots \\)\n\nKatie says this is a Fibonacci sequence: \\( 1,2,3,5,8,13, \\ldots \\)\n\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Thinks it can't be called a sequence with a repeated number at the start" } ]
[ { "from": "human", "value": "Recognise a Fibonacci sequence Tom and Katie are discussing Fibonacci sequences.\n\nTom says this is a Fibonacci sequence: \\( 1,1,2,3,5,8, \\ldots \\)\n\nKatie says this is a Fibonacci sequence: \\( 1,2,3,5,8,13, \\ldots \\)\n\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not know what a Fibonacci sequence is" } ]
[ { "from": "human", "value": "Convert between any other time periods To work out how many hours in a year you could do... \\( 365 \\times 7 \\)" }, { "from": "gpt", "value": "Thinks there are 7 hours in 1 day" } ]
[ { "from": "human", "value": "Convert between any other time periods To work out how many hours in a year you could do... \\( 365 \\times 60 \\)" }, { "from": "gpt", "value": "Answers as if there are 60 hours in a day" } ]
[ { "from": "human", "value": "Convert between any other time periods To work out how many hours in a year you could do... \\( 365 \\times 12 \\)" }, { "from": "gpt", "value": "Thinks there are 12 hours in 1 day" } ]
[ { "from": "human", "value": "Solve quadratic equations using completing the square in the form (x + q)² + r One of these equations has no real solutions\nWhich is it? \\( (w+5)^{2}-5=0 \\)" }, { "from": "gpt", "value": "Believes we can only take the square root of a perfect square" } ]
[ { "from": "human", "value": "Solve quadratic equations using completing the square in the form (x + q)² + r One of these equations has no real solutions\nWhich is it? \\( (w+5)^{2}=0 \\)" }, { "from": "gpt", "value": "Believes 0 is not a real solution to an equation" } ]
[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{2}{7} \\times 3=3 \\div K \\times L \\) \\( \\begin{array}{l}K=2 \\\\ L=7\\end{array} \\)" }, { "from": "gpt", "value": "When multiplying a fraction by an integer, multiplies the denominator instead of the numerator" } ]
[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{2}{7} \\times 3=3 \\div K \\times L \\) Not possible" }, { "from": "gpt", "value": "Does not realize we can write a division as a fraction" } ]
[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places What should replace the star? \\( \\bigstar \\div 0.3=1.5 \\) \\( 0.5 \\)" }, { "from": "gpt", "value": "When solving an equation thinks they divide when in fact they need to multiply" } ]
[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places What should replace the star? \\( \\bigstar \\div 0.3=1.5 \\) \\( 1.8 \\)" }, { "from": "gpt", "value": "When solving an equation thinks they add when in fact they need to multiply" } ]
[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places What should replace the star? \\( \\bigstar \\div 0.3=1.5 \\) \\( 0.2 \\)" }, { "from": "gpt", "value": "When solving an equation thinks they divide when in fact they need to multiply" } ]
[ { "from": "human", "value": "Represent written scenarios as ratios For every \\( 2 \\) marbles Karen has, Marty has \\( 3 \\).\nWrite the number of marbles Karen and Marty have as a ratio, with Karen's part first. \\( 3\\; : 2 \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]
[ { "from": "human", "value": "Represent written scenarios as ratios For every \\( 2 \\) marbles Karen has, Marty has \\( 3 \\).\nWrite the number of marbles Karen and Marty have as a ratio, with Karen's part first. \\( 2\\; : 3\\; : 5 \\)" }, { "from": "gpt", "value": "Thinks you need to include the total as well as the individual parts when asked to write a ratio" } ]
[ { "from": "human", "value": "Represent written scenarios as ratios For every \\( 2 \\) marbles Karen has, Marty has \\( 3 \\).\nWrite the number of marbles Karen and Marty have as a ratio, with Karen's part first. \\( 2\\; : 5 \\)" }, { "from": "gpt", "value": "When writing ratio, writes total as one side" } ]
[ { "from": "human", "value": "Solve quadratic inequalities from the graph of the quadratic Use the graph to approximate the solution to \\( x^{2}<5 \\) ![A set of axes with the quadratic graph y=x^2 drawn on.]() \\( x<-2.2, x>2.2 \\)" }, { "from": "gpt", "value": "Selects y>a solutions instead of y<a solutions for a quadratic inequality" } ]
[ { "from": "human", "value": "Given information about one part, work out the whole The ratio of cars to vans in a car park is \\( 5: 3 \\)\n\nIf there are \\( 80 \\) cars, how many vehicles (cars and vans) are there in total? \\( 83 \\)" }, { "from": "gpt", "value": "Thinks the number in the ratio is the total" } ]
[ { "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 Without drawing any more terms, how many circles do you predict will be in the \\( 5 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 30 \\)" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]
[ { "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 Without drawing any more terms, how many circles do you predict will be in the \\( 5 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 18 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the term before" } ]
[ { "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 Without drawing any more terms, how many circles do you predict will be in the \\( 5 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 24 \\)" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]
[ { "from": "human", "value": "Identify non-unit fractions when part of a shape What should replace the question mark? ![A bar split into 8 equal parts. 3 of the parts are shaded, and the total length of these 3 parts is labelled 3/4. The total length of 6 parts is labelled with a question mark.]() \\( \\frac{6}{8} \\)" }, { "from": "gpt", "value": "When multiplying a fraction by an integer, multiplies both numerator and denominator by the integer" } ]
[ { "from": "human", "value": "Identify non-unit fractions when part of a shape What should replace the question mark? ![A bar split into 8 equal parts. 3 of the parts are shaded, and the total length of these 3 parts is labelled 3/4. The total length of 6 parts is labelled with a question mark.]() \\( 6 \\)" }, { "from": "gpt", "value": "Believes that 1 part of a bar model will always have a value of 1" } ]
[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{13}{40} \\) written as a percentage? \\( 13 \\% \\)" }, { "from": "gpt", "value": "Thinks you just add a % sign to the numerator to make a fraction into a percentage" } ]
[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{13}{40} \\) written as a percentage? \\( 26 \\% \\)" }, { "from": "gpt", "value": "Believes a fraction out of a number other than 100 represents a percentage" } ]
[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{13}{40} \\) written as a percentage? \\( 52 \\% \\)" }, { "from": "gpt", "value": "Believes a fraction out of a number other than 100 represents a percentage" } ]
[ { "from": "human", "value": "Recognise when to find a factor to solve a problem A Zumba teacher wants to split her group of \\( 60 \\) clients into equal sized classes.\nTo do this she needs to know the _________ of \\( 60 \\)\nWhich word best fills in the gap? Remainders" }, { "from": "gpt", "value": "Does not understand that factors are divisors which split the number into equal groups" } ]
[ { "from": "human", "value": "Recognise when to find a factor to solve a problem A Zumba teacher wants to split her group of \\( 60 \\) clients into equal sized classes.\nTo do this she needs to know the _________ of \\( 60 \\)\nWhich word best fills in the gap? Fractions" }, { "from": "gpt", "value": "Does not understand that factors are divisors which split the number into equal groups" } ]
[ { "from": "human", "value": "Recognise when to find a factor to solve a problem A Zumba teacher wants to split her group of \\( 60 \\) clients into equal sized classes.\nTo do this she needs to know the _________ of \\( 60 \\)\nWhich word best fills in the gap? Multiples" }, { "from": "gpt", "value": "Confuses factors and multiples" } ]
[ { "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 This triangle is reflected in the line \\( x= \\) 4. What will the coordinate of the point marked \\( \\mathrm{C} \\) on the reflected shape be? ![A positive quadrant graph showing a triangle ABC plotted]() \\( (6,3) \\)" }, { "from": "gpt", "value": "Thinks x = ? is a horizontal line through ? " } ]
[ { "from": "human", "value": "Solve problems involving adding a period of time on to a given start time A coach takes \\( 3 \\) hours \\( 50 \\) minutes to complete a journey from Manchester to London.\n\nIf the coach leaves Manchester at 09:25, what time does it arrive in London? \\( 12: 75 \\)" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour" } ]
[ { "from": "human", "value": "Solve problems involving adding a period of time on to a given start time A coach takes \\( 3 \\) hours \\( 50 \\) minutes to complete a journey from Manchester to London.\n\nIf the coach leaves Manchester at 09:25, what time does it arrive in London? 01:15" }, { "from": "gpt", "value": "Writes times in the afternoon as if they are morning on a 24 hour clock" } ]
[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Fraction Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 3 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]() \\( \\frac{3}{6} \\times \\frac{1}{3} \\)" }, { "from": "gpt", "value": "Does not understand parts must be equal in a fraction diagram" } ]
[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Fraction Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 3 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]() \\( \\frac{1}{4} \\div \\frac{1}{3} \\)" }, { "from": "gpt", "value": "Believes that dividing by a decimal is the same as dividing by its reciprocal" } ]
[ { "from": "human", "value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, subtract 2, triple it, and the answer is \\( 12 \\).\n\nWhich of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]() \\( x \\)" }, { "from": "gpt", "value": "Does not understand where to place inputs/ operations/ outputs when drawing a function machine" } ]
[ { "from": "human", "value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, subtract 2, triple it, and the answer is \\( 12 \\).\n\nWhich of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]() \\( -2 \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]
[ { "from": "human", "value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, subtract 2, triple it, and the answer is \\( 12 \\).\n\nWhich of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]() \\( 12 \\)" }, { "from": "gpt", "value": "Does not understand where to place inputs/ operations/ outputs when drawing a function machine" } ]
[ { "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\\(\n467+\\square=1253\n\\)\nWhat is the \\( 3^{\\text {rd }} \\) digit of the number that belongs in the box? \\( 4 \\)" }, { "from": "gpt", "value": "Subtracts the smallest digit from the largest digit" } ]
[ { "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\\(\n467+\\square=1253\n\\)\nWhat is the \\( 3^{\\text {rd }} \\) digit of the number that belongs in the box? \\( 0 \\)" }, { "from": "gpt", "value": "Adds instead of subtracts" } ]
[ { "from": "human", "value": "Convert single digit integer percentages to fractions \\( 4 \\% \\) as a fraction is.... \\( \\frac{2}{5} \\)" }, { "from": "gpt", "value": "Divided by 10 rather than 100" } ]
[ { "from": "human", "value": "Convert single digit integer percentages to fractions \\( 4 \\% \\) as a fraction is.... \\( \\frac{4}{10} \\)" }, { "from": "gpt", "value": "Divided by 10 rather than 100" } ]
[ { "from": "human", "value": "Convert single digit integer percentages to fractions \\( 4 \\% \\) as a fraction is.... \\( \\frac{1}{4} \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]
[ { "from": "human", "value": "Given the area of a square, calculate a missing dimension A shape is made up a square and regular pentagon.\nThe area of the square is \\( 144 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![Pentagon and square joined along one edge]() \\( 108 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Believes lines inside the shape are included when finding perimeter" } ]
[ { "from": "human", "value": "Given the area of a square, calculate a missing dimension A shape is made up a square and regular pentagon.\nThe area of the square is \\( 144 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![Pentagon and square joined along one edge]() \\( 252 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]
[ { "from": "human", "value": "Substitute negative non-integer values into expressions involving no powers or roots What is the value of\n\\( a b \\)\nwhen \\( a=9 \\) and \\( b=-0.5 \\) ? \\( -45 \\)" }, { "from": "gpt", "value": "When multiplying decimals, ignores place value and just multiplies the digits" } ]
[ { "from": "human", "value": "Substitute negative non-integer values into expressions involving no powers or roots What is the value of\n\\( a b \\)\nwhen \\( a=9 \\) and \\( b=-0.5 \\) ? \\( 8.5 \\)" }, { "from": "gpt", "value": "Thinks two variables next to each other represent addition" } ]
[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card\n\n \\( \\frac{1}{3} \\) of \\( \\mathrm{A} \\) is \\( 12 \\)\n\n What is \\( \\frac{1}{2} \\) of \\( A \\) ?\n ![\\( A \\)]() \\( 2 \\)" }, { "from": "gpt", "value": "Confuses the part and the whole in fraction of an amount problems" } ]
[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card\n\n \\( \\frac{1}{3} \\) of \\( \\mathrm{A} \\) is \\( 12 \\)\n\n What is \\( \\frac{1}{2} \\) of \\( A \\) ?\n ![\\( A \\)]() \\( 8 \\)" }, { "from": "gpt", "value": "Confuses the part and the whole in fraction of an amount problems" } ]
[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card\n\n \\( \\frac{1}{3} \\) of \\( \\mathrm{A} \\) is \\( 12 \\)\n\n What is \\( \\frac{1}{2} \\) of \\( A \\) ?\n ![\\( A \\)]() \\( 36 \\)" }, { "from": "gpt", "value": "In a worded problem, does not complete all calculations" } ]
[ { "from": "human", "value": "Solve problems involving converting between fractions, decimals and percentages Tom and Katie are arguing about percentages.\nTom says \\( 45 \\%>0.059 \\)\nKatie says \\( 45 \\%>\\frac{16}{31} \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Divides by 1000 instead of 100 when converting a percentage to a decimal" } ]
[ { "from": "human", "value": "Calculate the area of an isosceles triangle where the dimensions are given in the same units What is the area of the triangle? ![Triangle with base the square root of 144 cm and height 6cm.]() \\( 144 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Thinks they double rather than halve when finding the area of a triangle" } ]
[ { "from": "human", "value": "Calculate the area of an isosceles triangle where the dimensions are given in the same units What is the area of the triangle? ![Triangle with base the square root of 144 cm and height 6cm.]() \\( 72 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Does not have when calculating the area of a triangle" } ]
[ { "from": "human", "value": "Raise a positive integer to a positive integer power Jo and Paul are arguing about powers.\n\nJo says there is no value of \\( m \\) that means \\( 3^{m} \\) is even.\n\nPaul says there is no value of \\( n \\) that means \\( 4^{n} \\) ends in \\( 0 \\).\nWho is correct? Only\nJo" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Raise a positive integer to a positive integer power Jo and Paul are arguing about powers.\n\nJo says there is no value of \\( m \\) that means \\( 3^{m} \\) is even.\n\nPaul says there is no value of \\( n \\) that means \\( 4^{n} \\) ends in \\( 0 \\).\nWho is correct? Only\nPaul" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Raise a positive integer to a positive integer power Jo and Paul are arguing about powers.\n\nJo says there is no value of \\( m \\) that means \\( 3^{m} \\) is even.\n\nPaul says there is no value of \\( n \\) that means \\( 4^{n} \\) ends in \\( 0 \\).\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]
[ { "from": "human", "value": "Read values off a real life graph Lethna pays at one rate for the first \\( 100 \\) units of electricity she uses. She pays at a different rate for all the other units of electricity she uses.\n\nHow much must she pay for using a total of \\( 800 \\) units of electricity? ![A graph showing how the cost changes for different numbers of units. The first 100 units cost £0.25 per unit. Then the rate changes to £0.10 per unit.]() \\( £ 110 \\)" }, { "from": "gpt", "value": "Thinks terms in linear sequence are in direct proportion" } ]
[ { "from": "human", "value": "Solve quadratic equations using balancing A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d+3)^{2}-25=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d+3)^{2}=25\n\\) \\( d+3=5 \\)" }, { "from": "gpt", "value": "Only considers the positive solution when calculating a square root" } ]
[ { "from": "human", "value": "Solve quadratic equations using balancing A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d+3)^{2}-25=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d+3)^{2}=25\n\\) \\( d+3=12.5 \\)" }, { "from": "gpt", "value": "Believes the inverse of square rooting is halving" } ]
[ { "from": "human", "value": "Solve quadratic equations using balancing A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d+3)^{2}-25=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d+3)^{2}=25\n\\) \\( d^{2}=22 \\)" }, { "from": "gpt", "value": "Believes you can subtract from inside brackets without expanding when solving an equation" } ]
[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Mo wants to solve this equation using the quadratic formula.\n\\(\n5 h^{2}-3 h-2=0\n\\)\n\nWhat should replace the star? \\( \\bigstar \\pm \\sqrt{ ? - ? } \\) \\( 2 \\)" }, { "from": "gpt", "value": "Misremembers the quadratic formula" } ]
[ { "from": "human", "value": "Estimate the size of obtuse angles using bearings An exam question asks students to estimate the size of the bearing on the right\nTom writes his answer as: \\( 110\\degree\\)\nKatie writes her answer as: \\( 190\\degree\\)\n\nWho would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]() Only Katie" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]
[ { "from": "human", "value": "Estimate the size of obtuse angles using bearings An exam question asks students to estimate the size of the bearing on the right\nTom writes his answer as: \\( 110\\degree\\)\nKatie writes her answer as: \\( 190\\degree\\)\n\nWho would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]() Both Tom and Katie" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]
[ { "from": "human", "value": "Estimate the size of obtuse angles using bearings An exam question asks students to estimate the size of the bearing on the right\nTom writes his answer as: \\( 110\\degree\\)\nKatie writes her answer as: \\( 190\\degree\\)\n\nWho would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]() Neither is correct" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]
[ { "from": "human", "value": "Round numbers greater than 1 to two significant figures Tom and Katie are arguing about rounding.\n\nTom says \\( \\mathbf{6 0 5 . 7 6} \\) rounded to \\( 1 \\) significant figure is \\( \\mathbf{6 0 0} \\)\n\nKatie says \\( \\mathbf{6 0 5 . 7 6} \\) rounded to \\( 2 \\) significant figures is \\( \\mathbf{6 0 0} \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Rounds down instead of up when next digit is 5" } ]
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.15 \\times 0.2= \\) \\( 3 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]
[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.15 \\times 0.2= \\) \\( 0.3 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]

[ { "from": "human", "value": "Reflect an object or a point in a diagonal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object The triangle is reflected in the dashed line\nWhat are the new coordinates of point \\( \\mathrm{P} \\) ? ![Four quadrant, coordinate grid with the reflection line y=-x drawn and a triangle. The triangle has coordinates: (-2,3) (-2,6) and (0,5). The point P is the coordinate (0,5)]() \\( (-4,5) \\)" }, { "from": "gpt", "value": "Reflects horizontally or vertically instead of across a diagonal line of symmetry" } ]

[ { "from": "human", "value": "Add integers up to 4 digits using a written method where carrying is needed What number should replace the star? \\begin{tabular}{|c|c|c|c|c|}\n\\hline & \\( 4 \\) & \\( 2 \\) & \\(5\\) & \\(4\\)\\\\\n\\hline+ & \\( 2 \\) & \\(\\bigstar\\) & \\(7\\) & \\(1\\) \\\\\n\\hline \\(\\space\\) & \\(6\\) & \\(3\\) & \\(2\\) & \\(5\\)\n\\end{tabular} \\( 6 \\)" }, { "from": "gpt", "value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation" } ]

[ { "from": "human", "value": "Add integers up to 4 digits using a written method where carrying is needed What number should replace the star? \\begin{tabular}{|c|c|c|c|c|}\n\\hline & \\( 4 \\) & \\( 2 \\) & \\(5\\) & \\(4\\)\\\\\n\\hline+ & \\( 2 \\) & \\(\\bigstar\\) & \\(7\\) & \\(1\\) \\\\\n\\hline \\(\\space\\) & \\(6\\) & \\(3\\) & \\(2\\) & \\(5\\)\n\\end{tabular} \\( 1 \\)" }, { "from": "gpt", "value": "When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Find \\( 20 \\% \\) of \\( 80 \\) \\( 8 \\)" }, { "from": "gpt", "value": "Does not understand how to find percentages of an amount" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Find \\( 20 \\% \\) of \\( 80 \\) \\( 20 \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a number to make it a percentage" } ]

[ { "from": "human", "value": "Calculate percentage of an amount mentally where the percent is a multiple of 10 Find \\( 20 \\% \\) of \\( 80 \\) \\( 96 \\)" }, { "from": "gpt", "value": "Found the percentage but added it to 100%" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as simply as possible: \\( \\frac{q^{2}+q-12}{q^{2}-2 q-3} \\) \\( \\frac{q-4}{q-1} \\)" }, { "from": "gpt", "value": "Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant" } ]

[ { "from": "human", "value": "Simplify an algebraic fraction by factorising both the numerator and denominator Write the following as simply as possible: \\( \\frac{q^{2}+q-12}{q^{2}-2 q-3} \\) \\( \\frac{q-4}{-2 q-1} \\)" }, { "from": "gpt", "value": "Thinks that when you cancel identical terms from the numerator and denominator, they just disappear" } ]

[ { "from": "human", "value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate\n\\(\n\\frac{1}{6} \\div 3\n\\) \\( 2 \\)" }, { "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: Fraction ÷ Integer Calculate\n\\(\n\\frac{1}{6} \\div 3\n\\) \\( 18 \\)" }, { "from": "gpt", "value": "Believes division is commutative " } ]

[ { "from": "human", "value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate\n\\(\n\\frac{1}{6} \\div 3\n\\) \\( \\frac{1}{2} \\)" }, { "from": "gpt", "value": "When dividing a fraction by an integer, divides the denominator by the integer" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages Write \\( 0.15 \\) as a percentage. \\( 0.15 \\% \\)" }, { "from": "gpt", "value": "Thinks you need to just add a % sign to a decimal to convert to a percentage" } ]

[ { "from": "human", "value": "Convert decimals less than 1 with 2 decimal place to percentages Write \\( 0.15 \\) as a percentage. \\( 1.5 \\% \\)" }, { "from": "gpt", "value": "Multiplies by 10 instead of 100 when converting decimal to percentage" } ]

[ { "from": "human", "value": "Represent a linear inequality with a single tail on a numberline Which inequality is represented by the diagram? ![A number line with a filled in circle above 1with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]() \\( x>1 \\)" }, { "from": "gpt", "value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning." } ]

[ { "from": "human", "value": "Represent a linear inequality with a single tail on a numberline Which inequality is represented by the diagram? ![A number line with a filled in circle above 1with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]() \\( x \\leq 1 \\)" }, { "from": "gpt", "value": "Mixes up greater than and less than symbols" } ]

[ { "from": "human", "value": "Solve basic introduction simultaneous equation problems, often involving shapes and symbols Chris orders \\( 2 \\) cups of tea and a cake, and his bill comes to £1.40\n\nAmy orders \\( 4 \\) cups of tea and a cake, and her bill comes to £2.20.\n\nHow much does one cup of tea cost? \\( 80 p \\)" }, { "from": "gpt", "value": "When solving an equation forgets to eliminate the coefficient in front of the variable in the last step" } ]

[ { "from": "human", "value": "Solve basic introduction simultaneous equation problems, often involving shapes and symbols Chris orders \\( 2 \\) cups of tea and a cake, and his bill comes to £1.40\n\nAmy orders \\( 4 \\) cups of tea and a cake, and her bill comes to £2.20.\n\nHow much does one cup of tea cost? \\( 55 p \\)" }, { "from": "gpt", "value": "When asked to solve simultaneous equations, believes they can just find values that work in one equation" } ]

[ { "from": "human", "value": "Identify a diameter The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]() Diagram" }, { "from": "gpt", "value": "Does not know the term 'diameter'" } ]

[ { "from": "human", "value": "Identify a diameter The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]() Diagonal" }, { "from": "gpt", "value": "Does not know the term 'diameter'" } ]

[ { "from": "human", "value": "Identify a diameter The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]() Diamond" }, { "from": "gpt", "value": "Does not know the term 'diameter'" } ]

[ { "from": "human", "value": "Calculate non-unit fractions of an amount \\( \\frac{3}{5} \\) of \\( 30= \\) \\( 6 \\)" }, { "from": "gpt", "value": "Finds the unit fraction when asked to find a non-unit fraction of an amount" } ]

[ { "from": "human", "value": "Calculate non-unit fractions of an amount \\( \\frac{3}{5} \\) of \\( 30= \\) \\( 50 \\)" }, { "from": "gpt", "value": "Divides by the numerator and multiplies by the denominator when finding a fraction of an amount" } ]

[ { "from": "human", "value": "Interpret numbers in a frequency table Bob recorded the number of cars he sold in one week.\nHow many cars did he sell altogether? \\begin{tabular}{|c|c|}\n\\hline Colour & Frequency \\\\\n\\hline Blue & \\( 3 \\) \\\\\n\\hline Black & \\( 2 \\) \\\\\n\\hline Silver & \\( 4 \\) \\\\\n\\hline Red & \\( 1 \\) \\\\\n\\hline Other & \\( 3 \\) \\\\\n\\hline\n\\end{tabular} \\( 5 \\)" }, { "from": "gpt", "value": "Believes total in a grouped table is found by counting rows" } ]

[ { "from": "human", "value": "Interpret numbers in a frequency table Bob recorded the number of cars he sold in one week.\nHow many cars did he sell altogether? \\begin{tabular}{|c|c|}\n\\hline Colour & Frequency \\\\\n\\hline Blue & \\( 3 \\) \\\\\n\\hline Black & \\( 2 \\) \\\\\n\\hline Silver & \\( 4 \\) \\\\\n\\hline Red & \\( 1 \\) \\\\\n\\hline Other & \\( 3 \\) \\\\\n\\hline\n\\end{tabular} \\( 10 \\)" }, { "from": "gpt", "value": "Believes you do not include an \"other\" category when finding a total frequency" } ]

[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places \\( 0.4^{2}= \\) \\( 0.8 \\)" }, { "from": "gpt", "value": "Mixes up squaring and multiplying by 2 or doubling" } ]

[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places \\( 0.4^{2}= \\) \\( 1.6 \\)" }, { "from": "gpt", "value": "When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal" } ]

[ { "from": "human", "value": "Interpret a bar chart The bar chart shows the drinks sold in Caroline's Café on Monday and Tuesday last week.\n\nApproximately how many Teas were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.\nThe Teas bar lower section is 1 tick below 50 on the vertical scale, and the whole bar's height is 2 ticks above 100 on the vertical scale.\n]() \\( 62 \\)" }, { "from": "gpt", "value": "Misreads scale" } ]

[ { "from": "human", "value": "Interpret a bar chart The bar chart shows the drinks sold in Caroline's Café on Monday and Tuesday last week.\n\nApproximately how many Teas were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.\nThe Teas bar lower section is 1 tick below 50 on the vertical scale, and the whole bar's height is 2 ticks above 100 on the vertical scale.\n]() \\( 120 \\)" }, { "from": "gpt", "value": "When reading a composite bar chart, just reads total height of bar" } ]

[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 81 \\) ? \\( 3 \\)" }, { "from": "gpt", "value": "Mixes up square rooting and fourth rooting" } ]

[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 81 \\) ? \\( 162 \\)" }, { "from": "gpt", "value": "Mixes up square rooting and multiplying by 2 or doubling" } ]

[ { "from": "human", "value": "Recognise square roots Which of the following is the square root of \\( 81 \\) ? \\( 6561 \\)" }, { "from": "gpt", "value": "Squares when asked to find the square root" } ]

[ { "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 \\( 40 \\% \\) you divide by \\( 100 \\) and multiply by \\( 4 \\). \nKatie says to find \\( 40 \\% \\) you divide by \\( 5 \\) and multiply by \\( 2 \\).\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Believes that dividing by 100 gives 10%" } ]

[ { "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 \\( 40 \\% \\) you divide by \\( 100 \\) and multiply by \\( 4 \\). \nKatie says to find \\( 40 \\% \\) you divide by \\( 5 \\) and multiply by \\( 2 \\).\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Believes that dividing by 100 gives 10%" } ]

[ { "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 \\( 40 \\% \\) you divide by \\( 100 \\) and multiply by \\( 4 \\). \nKatie says to find \\( 40 \\% \\) you divide by \\( 5 \\) and multiply by \\( 2 \\).\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Unable to equate a division and multiplication to a single division" } ]

[ { "from": "human", "value": "Recognise a Fibonacci sequence Tom and Katie are discussing Fibonacci sequences.\n\nTom says this is a Fibonacci sequence: \\( 1,1,2,3,5,8, \\ldots \\)\n\nKatie says this is a Fibonacci sequence: \\( 1,2,3,5,8,13, \\ldots \\)\n\nWho is correct? Only Tom" }, { "from": "gpt", "value": "Thinks a Fibonacci sequence must start with 1, 1" } ]

[ { "from": "human", "value": "Recognise a Fibonacci sequence Tom and Katie are discussing Fibonacci sequences.\n\nTom says this is a Fibonacci sequence: \\( 1,1,2,3,5,8, \\ldots \\)\n\nKatie says this is a Fibonacci sequence: \\( 1,2,3,5,8,13, \\ldots \\)\n\nWho is correct? Only Katie" }, { "from": "gpt", "value": "Thinks it can't be called a sequence with a repeated number at the start" } ]

[ { "from": "human", "value": "Recognise a Fibonacci sequence Tom and Katie are discussing Fibonacci sequences.\n\nTom says this is a Fibonacci sequence: \\( 1,1,2,3,5,8, \\ldots \\)\n\nKatie says this is a Fibonacci sequence: \\( 1,2,3,5,8,13, \\ldots \\)\n\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Does not know what a Fibonacci sequence is" } ]

[ { "from": "human", "value": "Convert between any other time periods To work out how many hours in a year you could do... \\( 365 \\times 7 \\)" }, { "from": "gpt", "value": "Thinks there are 7 hours in 1 day" } ]

[ { "from": "human", "value": "Convert between any other time periods To work out how many hours in a year you could do... \\( 365 \\times 60 \\)" }, { "from": "gpt", "value": "Answers as if there are 60 hours in a day" } ]

[ { "from": "human", "value": "Convert between any other time periods To work out how many hours in a year you could do... \\( 365 \\times 12 \\)" }, { "from": "gpt", "value": "Thinks there are 12 hours in 1 day" } ]

[ { "from": "human", "value": "Solve quadratic equations using completing the square in the form (x + q)² + r One of these equations has no real solutions\nWhich is it? \\( (w+5)^{2}-5=0 \\)" }, { "from": "gpt", "value": "Believes we can only take the square root of a perfect square" } ]

[ { "from": "human", "value": "Solve quadratic equations using completing the square in the form (x + q)² + r One of these equations has no real solutions\nWhich is it? \\( (w+5)^{2}=0 \\)" }, { "from": "gpt", "value": "Believes 0 is not a real solution to an equation" } ]

[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{2}{7} \\times 3=3 \\div K \\times L \\) \\( \\begin{array}{l}K=2 \\\\ L=7\\end{array} \\)" }, { "from": "gpt", "value": "When multiplying a fraction by an integer, multiplies the denominator instead of the numerator" } ]

[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{2}{7} \\times 3=3 \\div K \\times L \\) Not possible" }, { "from": "gpt", "value": "Does not realize we can write a division as a fraction" } ]

[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places What should replace the star? \\( \\bigstar \\div 0.3=1.5 \\) \\( 0.5 \\)" }, { "from": "gpt", "value": "When solving an equation thinks they divide when in fact they need to multiply" } ]

[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places What should replace the star? \\( \\bigstar \\div 0.3=1.5 \\) \\( 1.8 \\)" }, { "from": "gpt", "value": "When solving an equation thinks they add when in fact they need to multiply" } ]

[ { "from": "human", "value": "Multiply two decimals together with the same number of decimal places What should replace the star? \\( \\bigstar \\div 0.3=1.5 \\) \\( 0.2 \\)" }, { "from": "gpt", "value": "When solving an equation thinks they divide when in fact they need to multiply" } ]

[ { "from": "human", "value": "Represent written scenarios as ratios For every \\( 2 \\) marbles Karen has, Marty has \\( 3 \\).\nWrite the number of marbles Karen and Marty have as a ratio, with Karen's part first. \\( 3\\; : 2 \\)" }, { "from": "gpt", "value": "Mixes up sides of a ratio" } ]

[ { "from": "human", "value": "Represent written scenarios as ratios For every \\( 2 \\) marbles Karen has, Marty has \\( 3 \\).\nWrite the number of marbles Karen and Marty have as a ratio, with Karen's part first. \\( 2\\; : 3\\; : 5 \\)" }, { "from": "gpt", "value": "Thinks you need to include the total as well as the individual parts when asked to write a ratio" } ]

[ { "from": "human", "value": "Represent written scenarios as ratios For every \\( 2 \\) marbles Karen has, Marty has \\( 3 \\).\nWrite the number of marbles Karen and Marty have as a ratio, with Karen's part first. \\( 2\\; : 5 \\)" }, { "from": "gpt", "value": "When writing ratio, writes total as one side" } ]

[ { "from": "human", "value": "Solve quadratic inequalities from the graph of the quadratic Use the graph to approximate the solution to \\( x^{2}<5 \\) ![A set of axes with the quadratic graph y=x^2 drawn on.]() \\( x<-2.2, x>2.2 \\)" }, { "from": "gpt", "value": "Selects y>a solutions instead of y<a solutions for a quadratic inequality" } ]

[ { "from": "human", "value": "Given information about one part, work out the whole The ratio of cars to vans in a car park is \\( 5: 3 \\)\n\nIf there are \\( 80 \\) cars, how many vehicles (cars and vans) are there in total? \\( 83 \\)" }, { "from": "gpt", "value": "Thinks the number in the ratio is the total" } ]

[ { "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 Without drawing any more terms, how many circles do you predict will be in the \\( 5 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 30 \\)" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]

[ { "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 Without drawing any more terms, how many circles do you predict will be in the \\( 5 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 18 \\)" }, { "from": "gpt", "value": "When asked for a specific term in a sequence gives the term before" } ]

[ { "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 Without drawing any more terms, how many circles do you predict will be in the \\( 5 \\) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]() \\( 24 \\)" }, { "from": "gpt", "value": "Does not notice all changes in a sequence of visual patterns" } ]

[ { "from": "human", "value": "Identify non-unit fractions when part of a shape What should replace the question mark? ![A bar split into 8 equal parts. 3 of the parts are shaded, and the total length of these 3 parts is labelled 3/4. The total length of 6 parts is labelled with a question mark.]() \\( \\frac{6}{8} \\)" }, { "from": "gpt", "value": "When multiplying a fraction by an integer, multiplies both numerator and denominator by the integer" } ]

[ { "from": "human", "value": "Identify non-unit fractions when part of a shape What should replace the question mark? ![A bar split into 8 equal parts. 3 of the parts are shaded, and the total length of these 3 parts is labelled 3/4. The total length of 6 parts is labelled with a question mark.]() \\( 6 \\)" }, { "from": "gpt", "value": "Believes that 1 part of a bar model will always have a value of 1" } ]

[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{13}{40} \\) written as a percentage? \\( 13 \\% \\)" }, { "from": "gpt", "value": "Thinks you just add a % sign to the numerator to make a fraction into a percentage" } ]

[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{13}{40} \\) written as a percentage? \\( 26 \\% \\)" }, { "from": "gpt", "value": "Believes a fraction out of a number other than 100 represents a percentage" } ]

[ { "from": "human", "value": "Convert fractions to percentages containing 1 decimal place What is \\( \\frac{13}{40} \\) written as a percentage? \\( 52 \\% \\)" }, { "from": "gpt", "value": "Believes a fraction out of a number other than 100 represents a percentage" } ]

[ { "from": "human", "value": "Recognise when to find a factor to solve a problem A Zumba teacher wants to split her group of \\( 60 \\) clients into equal sized classes.\nTo do this she needs to know the _________ of \\( 60 \\)\nWhich word best fills in the gap? Remainders" }, { "from": "gpt", "value": "Does not understand that factors are divisors which split the number into equal groups" } ]

[ { "from": "human", "value": "Recognise when to find a factor to solve a problem A Zumba teacher wants to split her group of \\( 60 \\) clients into equal sized classes.\nTo do this she needs to know the _________ of \\( 60 \\)\nWhich word best fills in the gap? Fractions" }, { "from": "gpt", "value": "Does not understand that factors are divisors which split the number into equal groups" } ]

[ { "from": "human", "value": "Recognise when to find a factor to solve a problem A Zumba teacher wants to split her group of \\( 60 \\) clients into equal sized classes.\nTo do this she needs to know the _________ of \\( 60 \\)\nWhich word best fills in the gap? Multiples" }, { "from": "gpt", "value": "Confuses factors and multiples" } ]

[ { "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 This triangle is reflected in the line \\( x= \\) 4. What will the coordinate of the point marked \\( \\mathrm{C} \\) on the reflected shape be? ![A positive quadrant graph showing a triangle ABC plotted]() \\( (6,3) \\)" }, { "from": "gpt", "value": "Thinks x = ? is a horizontal line through ? " } ]

[ { "from": "human", "value": "Solve problems involving adding a period of time on to a given start time A coach takes \\( 3 \\) hours \\( 50 \\) minutes to complete a journey from Manchester to London.\n\nIf the coach leaves Manchester at 09:25, what time does it arrive in London? \\( 12: 75 \\)" }, { "from": "gpt", "value": "Answers as if there are 100 minutes in an hour" } ]

[ { "from": "human", "value": "Solve problems involving adding a period of time on to a given start time A coach takes \\( 3 \\) hours \\( 50 \\) minutes to complete a journey from Manchester to London.\n\nIf the coach leaves Manchester at 09:25, what time does it arrive in London? 01:15" }, { "from": "gpt", "value": "Writes times in the afternoon as if they are morning on a 24 hour clock" } ]

[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Fraction Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 3 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]() \\( \\frac{3}{6} \\times \\frac{1}{3} \\)" }, { "from": "gpt", "value": "Does not understand parts must be equal in a fraction diagram" } ]

[ { "from": "human", "value": "Multiply proper fractions in the form: Fraction × Fraction Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 3 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]() \\( \\frac{1}{4} \\div \\frac{1}{3} \\)" }, { "from": "gpt", "value": "Believes that dividing by a decimal is the same as dividing by its reciprocal" } ]

[ { "from": "human", "value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, subtract 2, triple it, and the answer is \\( 12 \\).\n\nWhich of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]() \\( x \\)" }, { "from": "gpt", "value": "Does not understand where to place inputs/ operations/ outputs when drawing a function machine" } ]

[ { "from": "human", "value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, subtract 2, triple it, and the answer is \\( 12 \\).\n\nWhich of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]() \\( -2 \\)" }, { "from": "gpt", "value": "Does not follow the arrows through a function machine, changes the order of the operations asked." } ]

[ { "from": "human", "value": "For a given input find the output of a function machine Cally wants to use the function machine below to solve this problem:\n\nI think of a number, subtract 2, triple it, and the answer is \\( 12 \\).\n\nWhich of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]() \\( 12 \\)" }, { "from": "gpt", "value": "Does not understand where to place inputs/ operations/ outputs when drawing a function machine" } ]

[ { "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\\(\n467+\\square=1253\n\\)\nWhat is the \\( 3^{\\text {rd }} \\) digit of the number that belongs in the box? \\( 4 \\)" }, { "from": "gpt", "value": "Subtracts the smallest digit from the largest digit" } ]

[ { "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\\(\n467+\\square=1253\n\\)\nWhat is the \\( 3^{\\text {rd }} \\) digit of the number that belongs in the box? \\( 0 \\)" }, { "from": "gpt", "value": "Adds instead of subtracts" } ]

[ { "from": "human", "value": "Convert single digit integer percentages to fractions \\( 4 \\% \\) as a fraction is.... \\( \\frac{2}{5} \\)" }, { "from": "gpt", "value": "Divided by 10 rather than 100" } ]

[ { "from": "human", "value": "Convert single digit integer percentages to fractions \\( 4 \\% \\) as a fraction is.... \\( \\frac{4}{10} \\)" }, { "from": "gpt", "value": "Divided by 10 rather than 100" } ]

[ { "from": "human", "value": "Convert single digit integer percentages to fractions \\( 4 \\% \\) as a fraction is.... \\( \\frac{1}{4} \\)" }, { "from": "gpt", "value": "Does not understand a percentage is out of 100" } ]

[ { "from": "human", "value": "Given the area of a square, calculate a missing dimension A shape is made up a square and regular pentagon.\nThe area of the square is \\( 144 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![Pentagon and square joined along one edge]() \\( 108 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Believes lines inside the shape are included when finding perimeter" } ]

[ { "from": "human", "value": "Given the area of a square, calculate a missing dimension A shape is made up a square and regular pentagon.\nThe area of the square is \\( 144 \\mathrm{~cm}^{2} \\).\n\nWhat is the perimeter of the compound shape? ![Pentagon and square joined along one edge]() \\( 252 \\mathrm{~cm} \\)" }, { "from": "gpt", "value": "Adds when calculating area instead of multiplying" } ]

[ { "from": "human", "value": "Substitute negative non-integer values into expressions involving no powers or roots What is the value of\n\\( a b \\)\nwhen \\( a=9 \\) and \\( b=-0.5 \\) ? \\( -45 \\)" }, { "from": "gpt", "value": "When multiplying decimals, ignores place value and just multiplies the digits" } ]

[ { "from": "human", "value": "Substitute negative non-integer values into expressions involving no powers or roots What is the value of\n\\( a b \\)\nwhen \\( a=9 \\) and \\( b=-0.5 \\) ? \\( 8.5 \\)" }, { "from": "gpt", "value": "Thinks two variables next to each other represent addition" } ]

[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card\n\n \\( \\frac{1}{3} \\) of \\( \\mathrm{A} \\) is \\( 12 \\)\n\n What is \\( \\frac{1}{2} \\) of \\( A \\) ?\n ![\\( A \\)]() \\( 2 \\)" }, { "from": "gpt", "value": "Confuses the part and the whole in fraction of an amount problems" } ]

[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card\n\n \\( \\frac{1}{3} \\) of \\( \\mathrm{A} \\) is \\( 12 \\)\n\n What is \\( \\frac{1}{2} \\) of \\( A \\) ?\n ![\\( A \\)]() \\( 8 \\)" }, { "from": "gpt", "value": "Confuses the part and the whole in fraction of an amount problems" } ]

[ { "from": "human", "value": "Calculate the whole amount, given a fraction of the amount Here is a number card\n\n \\( \\frac{1}{3} \\) of \\( \\mathrm{A} \\) is \\( 12 \\)\n\n What is \\( \\frac{1}{2} \\) of \\( A \\) ?\n ![\\( A \\)]() \\( 36 \\)" }, { "from": "gpt", "value": "In a worded problem, does not complete all calculations" } ]

[ { "from": "human", "value": "Solve problems involving converting between fractions, decimals and percentages Tom and Katie are arguing about percentages.\nTom says \\( 45 \\%>0.059 \\)\nKatie says \\( 45 \\%>\\frac{16}{31} \\)\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Divides by 1000 instead of 100 when converting a percentage to a decimal" } ]

[ { "from": "human", "value": "Calculate the area of an isosceles triangle where the dimensions are given in the same units What is the area of the triangle? ![Triangle with base the square root of 144 cm and height 6cm.]() \\( 144 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Thinks they double rather than halve when finding the area of a triangle" } ]

[ { "from": "human", "value": "Calculate the area of an isosceles triangle where the dimensions are given in the same units What is the area of the triangle? ![Triangle with base the square root of 144 cm and height 6cm.]() \\( 72 \\mathrm{~cm}^{2} \\)" }, { "from": "gpt", "value": "Does not have when calculating the area of a triangle" } ]

[ { "from": "human", "value": "Raise a positive integer to a positive integer power Jo and Paul are arguing about powers.\n\nJo says there is no value of \\( m \\) that means \\( 3^{m} \\) is even.\n\nPaul says there is no value of \\( n \\) that means \\( 4^{n} \\) ends in \\( 0 \\).\nWho is correct? Only\nJo" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Raise a positive integer to a positive integer power Jo and Paul are arguing about powers.\n\nJo says there is no value of \\( m \\) that means \\( 3^{m} \\) is even.\n\nPaul says there is no value of \\( n \\) that means \\( 4^{n} \\) ends in \\( 0 \\).\nWho is correct? Only\nPaul" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Raise a positive integer to a positive integer power Jo and Paul are arguing about powers.\n\nJo says there is no value of \\( m \\) that means \\( 3^{m} \\) is even.\n\nPaul says there is no value of \\( n \\) that means \\( 4^{n} \\) ends in \\( 0 \\).\nWho is correct? Neither is correct" }, { "from": "gpt", "value": "Assumes a fact without considering enough examples" } ]

[ { "from": "human", "value": "Read values off a real life graph Lethna pays at one rate for the first \\( 100 \\) units of electricity she uses. She pays at a different rate for all the other units of electricity she uses.\n\nHow much must she pay for using a total of \\( 800 \\) units of electricity? ![A graph showing how the cost changes for different numbers of units. The first 100 units cost £0.25 per unit. Then the rate changes to £0.10 per unit.]() \\( £ 110 \\)" }, { "from": "gpt", "value": "Thinks terms in linear sequence are in direct proportion" } ]

[ { "from": "human", "value": "Solve quadratic equations using balancing A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d+3)^{2}-25=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d+3)^{2}=25\n\\) \\( d+3=5 \\)" }, { "from": "gpt", "value": "Only considers the positive solution when calculating a square root" } ]

[ { "from": "human", "value": "Solve quadratic equations using balancing A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d+3)^{2}-25=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d+3)^{2}=25\n\\) \\( d+3=12.5 \\)" }, { "from": "gpt", "value": "Believes the inverse of square rooting is halving" } ]

[ { "from": "human", "value": "Solve quadratic equations using balancing A student wishes to solve the equation below.\n\nWhich of the following is a correct next step?\n\\(\n(d+3)^{2}-25=0\n\\)\n\nStep \\( 1 \\)\n\\(\n(d+3)^{2}=25\n\\) \\( d^{2}=22 \\)" }, { "from": "gpt", "value": "Believes you can subtract from inside brackets without expanding when solving an equation" } ]

[ { "from": "human", "value": "Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Mo wants to solve this equation using the quadratic formula.\n\\(\n5 h^{2}-3 h-2=0\n\\)\n\nWhat should replace the star? \\( \\bigstar \\pm \\sqrt{ ? - ? } \\) \\( 2 \\)" }, { "from": "gpt", "value": "Misremembers the quadratic formula" } ]

[ { "from": "human", "value": "Estimate the size of obtuse angles using bearings An exam question asks students to estimate the size of the bearing on the right\nTom writes his answer as: \\( 110\\degree\\)\nKatie writes her answer as: \\( 190\\degree\\)\n\nWho would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]() Only Katie" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]

[ { "from": "human", "value": "Estimate the size of obtuse angles using bearings An exam question asks students to estimate the size of the bearing on the right\nTom writes his answer as: \\( 110\\degree\\)\nKatie writes her answer as: \\( 190\\degree\\)\n\nWho would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]() Both Tom and Katie" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]

[ { "from": "human", "value": "Estimate the size of obtuse angles using bearings An exam question asks students to estimate the size of the bearing on the right\nTom writes his answer as: \\( 110\\degree\\)\nKatie writes her answer as: \\( 190\\degree\\)\n\nWho would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]() Neither is correct" }, { "from": "gpt", "value": "Does not understand that an obtuse angle is between 90 and 180 degrees" } ]

[ { "from": "human", "value": "Round numbers greater than 1 to two significant figures Tom and Katie are arguing about rounding.\n\nTom says \\( \\mathbf{6 0 5 . 7 6} \\) rounded to \\( 1 \\) significant figure is \\( \\mathbf{6 0 0} \\)\n\nKatie says \\( \\mathbf{6 0 5 . 7 6} \\) rounded to \\( 2 \\) significant figures is \\( \\mathbf{6 0 0} \\)\n\nWho is correct? Both Tom and Katie" }, { "from": "gpt", "value": "Rounds down instead of up when next digit is 5" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.15 \\times 0.2= \\) \\( 3 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]

[ { "from": "human", "value": "Multiply two decimals together with a different number of decimal places \\( 0.15 \\times 0.2= \\) \\( 0.3 \\)" }, { "from": "gpt", "value": "Does not understand place value within a number" } ]