conversations
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[
{
"from": "human",
"value": "Calculate the gradient on a linear section on a real life graph The cost of a taxi-ride is shown on the graph.\n\nWhat is the cost per mile? ![The graph is Cost (£) on the vertical axis and Distance (miles) on the horizontal axis. The graph is a straight line from (0, 2) to (5, 6)]() \\( £ 1.20 \\)"
},
{
"from": "gpt",
"value": "Believes change in y for gradient is always calculated from the origin, regardless of the y-intercept of the line"
}
] |
[
{
"from": "human",
"value": "Calculate the gradient on a linear section on a real life graph The cost of a taxi-ride is shown on the graph.\n\nWhat is the cost per mile? ![The graph is Cost (£) on the vertical axis and Distance (miles) on the horizontal axis. The graph is a straight line from (0, 2) to (5, 6)]() \\( £ 1 \\)"
},
{
"from": "gpt",
"value": "When reading graph, chooses nearest marked value on axis instead of reading accurately"
}
] |
[
{
"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, double it, subtract 5, and the answer is \\( 23 \\).\n\nWhich of the following should replace the star? ![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and has \"input\" written above it. The next 2 rectangles are empty and the final rectangle on the right has a purple star inside it and has \"output\" written above it.]() \\( n \\)"
},
{
"from": "gpt",
"value": "When using a function machine, confuses the input and the output."
}
] |
[
{
"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, double it, subtract 5, and the answer is \\( 23 \\).\n\nWhich of the following should replace the star? ![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and has \"input\" written above it. The next 2 rectangles are empty and the final rectangle on the right has a purple star inside it and has \"output\" written above it.]() \\( \\times 2 \\)"
},
{
"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, double it, subtract 5, and the answer is \\( 23 \\).\n\nWhich of the following should replace the star? ![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and has \"input\" written above it. The next 2 rectangles are empty and the final rectangle on the right has a purple star inside it and has \"output\" written above it.]() \\( -5 \\)"
},
{
"from": "gpt",
"value": "Does not understand where to place inputs/ operations/ outputs when drawing a function machine"
}
] |
[
{
"from": "human",
"value": "Use inequality notation to order fractions whose denominators are not multiples of the same number What sign would make this statement true?\n\\(\n\\frac{4}{6} ? \\frac{10}{15}\n\\) \\( < \\)"
},
{
"from": "gpt",
"value": "Believes that fractions with larger denominators are greater in size"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible\n\\(\n\\frac{5 m-10}{m^{2}+3 m-10}\n\\) \\( \\frac{5 m}{m^{2}+3 m} \\)"
},
{
"from": "gpt",
"value": "Simplifies a fraction by adding or subtracting the same amount from the numerator and denominator"
}
] |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising both the numerator and denominator Simplify the following, if possible\n\\(\n\\frac{5 m-10}{m^{2}+3 m-10}\n\\) Does not simplify"
},
{
"from": "gpt",
"value": "Does not know how to simplify algebraic fractions"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{2}{5} \\div 2\n\\) \\( \\frac{4}{5} \\)"
},
{
"from": "gpt",
"value": "when dividing a fraction by an integer, multiplies the numerator by the integer"
}
] |
[
{
"from": "human",
"value": "Divide proper fractions in the form: Fraction ÷ Integer Calculate:\n\\(\n\\frac{2}{5} \\div 2\n\\) \\( \\frac{4}{10} \\)"
},
{
"from": "gpt",
"value": "When dividing a fraction by an integer, multiplies both the numerator and denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Interpret the gradient on a linear section on a real life graph Jadon decides to go for a run.\nThe graph on the right shows Jadon's speed in metres per second \\( (s) \\) over time in seconds\n\\( (t) \\).\n\nThe gradient of the negative sloping section of the graph is \\( 0.8 \\).\n\nWhich of the following does that \\( 0.8 \\) best represent? ![A sketch of a graph with s on the y axis and t on the x axis. A straight line slopes upwards from the origin 2/3 of the way up the graph, 1/5 across the graph. It then becomes horizontal for the next 1/5 of the graph, before sloping downwards in a straight line for the remainder of the graph. ]() Jadon is travelling at a speed of \\( 0.8 \\mathrm{~m} / \\mathrm{s} \\)"
},
{
"from": "gpt",
"value": "Believes the gradient of a speed-time graph is the speed"
}
] |
[
{
"from": "human",
"value": "Interpret the gradient on a linear section on a real life graph Jadon decides to go for a run.\nThe graph on the right shows Jadon's speed in metres per second \\( (s) \\) over time in seconds\n\\( (t) \\).\n\nThe gradient of the negative sloping section of the graph is \\( 0.8 \\).\n\nWhich of the following does that \\( 0.8 \\) best represent? ![A sketch of a graph with s on the y axis and t on the x axis. A straight line slopes upwards from the origin 2/3 of the way up the graph, 1/5 across the graph. It then becomes horizontal for the next 1/5 of the graph, before sloping downwards in a straight line for the remainder of the graph. ]() Jadon is accelerating at a rate of \\( 0.8 \\mathrm{~m} / \\mathrm{s}^{2} \\)"
},
{
"from": "gpt",
"value": "Believes a downward slope on a speed-time graph shows positive acceleration"
}
] |
[
{
"from": "human",
"value": "Sketch curves in the form (x + a)(x + b) indicating where they cross the axes \\( y=(x-8)(x-6) \\) \\( y=(x-8)(x-6) \\) Where does this curve intercept the \\( y \\) axis? Where does this curve intercept the \\( y \\) axis? \\( (0,-14) \\) \\( (0,-14) \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiplying when expanding bracket"
}
] |
[
{
"from": "human",
"value": "Sketch curves in the form (x + a)(x + b) indicating where they cross the axes \\( y=(x-8)(x-6) \\) \\( y=(x-8)(x-6) \\) Where does this curve intercept the \\( y \\) axis? Where does this curve intercept the \\( y \\) axis? \\( \\begin{array}{c}(0,8) \\\\ \\text { and } \\\\ (0,6)\\end{array} \\) \\( \\begin{array}{c}(0,8) \\\\ \\text { and } \\\\ (0,6)\\end{array} \\)"
},
{
"from": "gpt",
"value": "Believes that the y intercept is where y = 0"
}
] |
[
{
"from": "human",
"value": "Sketch curves in the form (x + a)(x + b) indicating where they cross the axes \\( y=(x-8)(x-6) \\) \\( y=(x-8)(x-6) \\) Where does this curve intercept the \\( y \\) axis? Where does this curve intercept the \\( y \\) axis? \\( (0,-48) \\) \\( (0,-48) \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving roots Tom and Katie are discussing calculations involving square roots.\n\nTom says \\( \\sqrt{16}+\\sqrt{9}=5 \\)\n\nKatie says \\( \\sqrt{16+9}=5 \\)\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "When adding roots, adds the numbers under the roots"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving roots Tom and Katie are discussing calculations involving square roots.\n\nTom says \\( \\sqrt{16}+\\sqrt{9}=5 \\)\n\nKatie says \\( \\sqrt{16+9}=5 \\)\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not understand square root"
}
] |
[
{
"from": "human",
"value": "Find the nth term rule for an ascending fractional linear sequence \\( \\frac{1}{24}, \\frac{1}{12}, \\frac{1}{8}, \\frac{1}{6}, \\ldots \\) When calculating the nth-term rule of this sequence, what should replace the rectangle? ![nth-term rule:\n\\[\n\\frac{1}{24} n\n\\] followed by a purple rectangle. ]() \\( +\\frac{1}{24} \\)"
},
{
"from": "gpt",
"value": "Uses first term as numerical part of nth term rule"
}
] |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 Tom and Katie are trying to write calculations based on the diagram below.\n\nTom writes: \\( 15-20=-5 \\)\n\nKatie writes: \\( (-5)+20=15 \\)\n\nWho is correct? ![Number line with an arrow marked -20 going from 15 to -5]() Only Tom"
},
{
"from": "gpt",
"value": "Does not recognise that addition is the inverse operation of subtraction"
}
] |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 Tom and Katie are trying to write calculations based on the diagram below.\n\nTom writes: \\( 15-20=-5 \\)\n\nKatie writes: \\( (-5)+20=15 \\)\n\nWho is correct? ![Number line with an arrow marked -20 going from 15 to -5]() Only Katie"
},
{
"from": "gpt",
"value": "Does not recognise that subtracting a larger number from a smaller number will give a negative answer"
}
] |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 Tom and Katie are trying to write calculations based on the diagram below.\n\nTom writes: \\( 15-20=-5 \\)\n\nKatie writes: \\( (-5)+20=15 \\)\n\nWho is correct? ![Number line with an arrow marked -20 going from 15 to -5]() Neither is correct"
},
{
"from": "gpt",
"value": "Does not understand the diagram given in the question"
}
] |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence A sequence is formed using the rule\n\nSquare the position and add \\( 5 \\)\n\nWhat is the third term in the sequence? \\( 11 \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Given a description of an ascending sequence using quadratics in words, write some terms of that sequence A sequence is formed using the rule\n\nSquare the position and add \\( 5 \\)\n\nWhat is the third term in the sequence? \\( 6 \\)"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence gives the next term"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for the curve y = x3 + c This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\boldsymbol{x}^{\\mathbf{3}} \\) ![\\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 2 \\) \\\\\n\\hline\\( y \\) & W \\\\\n\\hline\n\\end{tabular}]() What should replace the star? \\( 5 \\)"
},
{
"from": "gpt",
"value": "Adds the index to the number"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for the curve y = x3 + c This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\boldsymbol{x}^{\\mathbf{3}} \\) ![\\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 2 \\) \\\\\n\\hline\\( y \\) & W \\\\\n\\hline\n\\end{tabular}]() What should replace the star? \\( 6 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Given a positive x value, find the corresponding y value for the curve y = x3 + c This is a part of the table of values for the equation \\( \\boldsymbol{y}=\\boldsymbol{x}^{\\mathbf{3}} \\) ![\\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( 2 \\) \\\\\n\\hline\\( y \\) & W \\\\\n\\hline\n\\end{tabular}]() What should replace the star? \\( 23 \\)"
},
{
"from": "gpt",
"value": "Writes the index as a digit on the end of a number"
}
] |
[
{
"from": "human",
"value": "Calculate distance where speed and time are in the appropriate units This displacement-time graph shows \\( 10 \\) seconds of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 15 \\mathrm{~m} / \\mathrm{s} \\).\n\nWhat distance should replace the star? ![The graph has its vertical axis labelled Distance (m) and it has no scale written except for a star three squares up.\nThe horizontal axis is labelled Time (secs) and has the scale 0, 2, 4, 6, 8, 10 in even steps.\nThe graph is a straight line sloping down from (0, star) to (10, 0).\n]() \\( 6 m \\)"
},
{
"from": "gpt",
"value": "Believes scales on graphs must match on both axes"
}
] |
[
{
"from": "human",
"value": "Calculate distance where speed and time are in the appropriate units This displacement-time graph shows \\( 10 \\) seconds of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 15 \\mathrm{~m} / \\mathrm{s} \\).\n\nWhat distance should replace the star? ![The graph has its vertical axis labelled Distance (m) and it has no scale written except for a star three squares up.\nThe horizontal axis is labelled Time (secs) and has the scale 0, 2, 4, 6, 8, 10 in even steps.\nThe graph is a straight line sloping down from (0, star) to (10, 0).\n]() \\( 30 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Makes an assumption about the squares on a scale representing either 1 or 10"
}
] |
[
{
"from": "human",
"value": "Calculate distance where speed and time are in the appropriate units This displacement-time graph shows \\( 10 \\) seconds of Mo's journey home.\n\nDuring that time he travelled at a speed of \\( 15 \\mathrm{~m} / \\mathrm{s} \\).\n\nWhat distance should replace the star? ![The graph has its vertical axis labelled Distance (m) and it has no scale written except for a star three squares up.\nThe horizontal axis is labelled Time (secs) and has the scale 0, 2, 4, 6, 8, 10 in even steps.\nThe graph is a straight line sloping down from (0, star) to (10, 0).\n]() \\( 1.5 \\mathrm{~m} \\)"
},
{
"from": "gpt",
"value": "Believes distance = speed/time"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.5=\\frac{1}{2}=? \\% \\) \\( 12 \\% \\)"
},
{
"from": "gpt",
"value": "Converts a fraction to a percentage by writing the numerator followed by the denominator"
}
] |
[
{
"from": "human",
"value": "Solve problems involving converting between fractions, decimals and percentages \\( 0.5=\\frac{1}{2}=? \\% \\) \\( 2 \\% \\)"
},
{
"from": "gpt",
"value": "Converts fraction to percentage by putting % sign after the denominator"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Simplify, if possible:\n\\(\na \\times 4\n\\) \\( a 4 \\)"
},
{
"from": "gpt",
"value": "Writes the variable before the coefficient in an algebraic term"
}
] |
[
{
"from": "human",
"value": "Write algebraic expressions with correct algebraic convention Simplify, if possible:\n\\(\na \\times 4\n\\) \\( a^{4} \\)"
},
{
"from": "gpt",
"value": "Thinks multiplying a variable by a number is the same as raising that variable to the power of that number"
}
] |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for the area of a triangle, \\( A \\), is ![Triangle with base labelled b and perpendicular height labelled h]() \\( A=\\frac{1}{2}(b \\times h) \\) Rearrange this to make the base, \\( b \\), the subject. \\( b=\\frac{1}{2}(h \\times A) \\)"
},
{
"from": "gpt",
"value": "Believes they can change the subject of a formula just by swapping two letters"
}
] |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for the area of a triangle, \\( A \\), is ![Triangle with base labelled b and perpendicular height labelled h]() \\( A=\\frac{1}{2}(b \\times h) \\) Rearrange this to make the base, \\( b \\), the subject. \\( b=\\frac{A}{2 h} \\)"
},
{
"from": "gpt",
"value": "Believes dividing by a unit fraction is equivalent to dividing by its reciprocal"
}
] |
[
{
"from": "human",
"value": "Given the distance travelled, complete missing values on a speed-time graph ![A speed-time graph. The vertical axis is labelled Speed (mph), with no scale labelled but 4 squares up is marked v.\nThe horizontal axis is labelled Time (hours) and the scale is 0, 1, 2, 3, 4 in even steps.\nThe graph first has a horizontal line from (0,v) to (2,v) and then a sloped line from (2,v) to (4,0).]() Work out the speed \\( v \\) if the distance travelled is \\( 90 \\) miles. \\( 22.5 \\mathrm{mph} \\)"
},
{
"from": "gpt",
"value": "Thinks the shape of the graph does not affect the area calculation"
}
] |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 4 \\) litres \\( = \\)_________ \\( \\mathrm{cm}^{3} \\) \\( 4 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 1 cubic centimetre"
}
] |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 4 \\) litres \\( = \\)_________ \\( \\mathrm{cm}^{3} \\) \\( 400 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 100 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Convert between l and cm³ Complete this statement:\n\\( 4 \\) litres \\( = \\)_________ \\( \\mathrm{cm}^{3} \\) \\( 40 \\)"
},
{
"from": "gpt",
"value": "Thinks 1l = 10 cubic centimetres"
}
] |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed The formula for finding the average speed is\n\n\\(\n\\text { speed }(S)=\\frac{\\text { distance }(D)}{\\text { time }(T)}\n\\)\n\nWhich of the following are not correct? \\( D=S T \\)"
},
{
"from": "gpt",
"value": "Does not know how to simplify algebraic fractions"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\( 2,2,4,7,10 \\) \\( 5 \\)"
},
{
"from": "gpt",
"value": "Finds the mean instead of the median"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\( 2,2,4,7,10 \\) \\( 2 \\)"
},
{
"from": "gpt",
"value": "Finds the mode instead of the median"
}
] |
[
{
"from": "human",
"value": "Calculate the median as an average from an odd numbered list of data What is the median of the following numbers?\n\\( 2,2,4,7,10 \\) \\( 5.5 \\)"
},
{
"from": "gpt",
"value": "When finding the median for an odd numbered data set, find the midpoint of two values rather than giving the middle value"
}
] |
[
{
"from": "human",
"value": "Identify when it is appropriate to use a line graph Which of the following situations would a line graph be the most appropriate to use? Showing the number of brothers and sisters children in a class have"
},
{
"from": "gpt",
"value": "Does not understand that a line graph shows a relationship between 2 variables"
}
] |
[
{
"from": "human",
"value": "Identify when it is appropriate to use a line graph Which of the following situations would a line graph be the most appropriate to use? Showing what time each member of a family went to bed last night"
},
{
"from": "gpt",
"value": "Does not understand that a line graph shows a relationship between 2 variables"
}
] |
[
{
"from": "human",
"value": "Identify when it is appropriate to use a line graph Which of the following situations would a line graph be the most appropriate to use? Showing the numbers of each type of animal in a zoo"
},
{
"from": "gpt",
"value": "Does not understand that a line graph shows a relationship between 2 variables"
}
] |
[
{
"from": "human",
"value": "Read values off a displacement-time graph This graph shows the displacement of a ball from a starting point at various times.\nHow far did the ball travel between \\( 1 \\) and \\( 2 \\) seconds? ![A displacement versus time graph]() This graph displacem from a start \\( 0.5 \\ \\text{m} \\)"
},
{
"from": "gpt",
"value": "When finding the difference between two points on a time series graph, only uses one of the points. "
}
] |
[
{
"from": "human",
"value": "Read values off a displacement-time graph This graph shows the displacement of a ball from a starting point at various times.\nHow far did the ball travel between \\( 1 \\) and \\( 2 \\) seconds? ![A displacement versus time graph]() This graph displacem from a start \\( 2 \\ \\text{m} \\)"
},
{
"from": "gpt",
"value": "When finding the difference between two points on a time series graph, only uses one of the points. "
}
] |
[
{
"from": "human",
"value": "Read values off a displacement-time graph This graph shows the displacement of a ball from a starting point at various times.\nHow far did the ball travel between \\( 1 \\) and \\( 2 \\) seconds? ![A displacement versus time graph]() This graph displacem from a start \\( 2.5 \\ \\text{m} \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts when asked to find the difference"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving negative integers Tom and Katie are arguing about a first step to solve this equation:\n\\(1-4 v=3-9 v\\)\n\nTom says you can write: \\( 1+5 v=3 \\)\n\nKatie says you can write: \\( -4 v=2-9 v \\)\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not realise that to maintain balance in an equation they must add or subtract the same amount from both sides"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 326 \\) rounded to the nearest \\( 10 \\) ? \\( 300 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 326 \\) rounded to the nearest \\( 10 \\) ? \\( 320 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round integers to the nearest 10 What is \\( 326 \\) rounded to the nearest \\( 10 \\) ? \\( 350 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too much)"
}
] |
[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units Paige, Kaci and David want to find the area of the school playground. They each do it a different way. Who is correct? ![A compound shape made up of two rectangles. Dimensions are 6 metres by 12 metres and also 4 metres by 8 metres. Two sides do not have measurements so need to be deduced]() Kaci: \\( 10 \\times 6+4 \\times 6 \\)"
},
{
"from": "gpt",
"value": "Cannot identify the correct side lengths to use when asked to find the area of a face"
}
] |
[
{
"from": "human",
"value": "Calculate compound area involving just rectangles and squares, where the dimensions are given in the same units Paige, Kaci and David want to find the area of the school playground. They each do it a different way. Who is correct? ![A compound shape made up of two rectangles. Dimensions are 6 metres by 12 metres and also 4 metres by 8 metres. Two sides do not have measurements so need to be deduced]() David: \\( 12 \\times 10-6 \\times 4 \\)"
},
{
"from": "gpt",
"value": "Does not know how to find missing lengths in a composite shape"
}
] |
[
{
"from": "human",
"value": "Carry out division problems involving one negative integer \\( 12 \\div(-4)= \\) \\( 3 \\)"
},
{
"from": "gpt",
"value": "Believes dividing a positive by a negative gives a positive answer"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n1,5,5,17,-6\n\\] \\( 5 \\)"
},
{
"from": "gpt",
"value": "Finds the mode rather than the range"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n1,5,5,17,-6\n\\] \\( 11 \\)"
},
{
"from": "gpt",
"value": "To find the range adds the biggest and smallest number rather than subtract"
}
] |
[
{
"from": "human",
"value": "Calculate the range from a list of data What is the range of the following numbers?\n\\[\n1,5,5,17,-6\n\\] \\( 16 \\)"
},
{
"from": "gpt",
"value": "Does not include negative numbers when calculating a range"
}
] |
[
{
"from": "human",
"value": "Describe an enlargement, with no centre of enlargement given, by a positive scale factor bigger than 1 Shape \\( Q \\) is an enlargement of shape \\( P \\).\nWhat calculation works out the constant of proportionality from shape \\( P \\) to shape \\( Q \\) ? ![To similar star shapes labelled P and Q. They have the same side labelled for P it is 3cm and for Q it is 11cm]() \\( 3 \\div 11 \\)"
},
{
"from": "gpt",
"value": "When calculating a scale factor, thinks the division is the other way around."
}
] |
[
{
"from": "human",
"value": "Describe an enlargement, with no centre of enlargement given, by a positive scale factor bigger than 1 Shape \\( Q \\) is an enlargement of shape \\( P \\).\nWhat calculation works out the constant of proportionality from shape \\( P \\) to shape \\( Q \\) ? ![To similar star shapes labelled P and Q. They have the same side labelled for P it is 3cm and for Q it is 11cm]() \\( 3 \\times 11 \\)"
},
{
"from": "gpt",
"value": "When calculating a scale factor, multiplies instead of dividing."
}
] |
[
{
"from": "human",
"value": "Describe an enlargement, with no centre of enlargement given, by a positive scale factor bigger than 1 Shape \\( Q \\) is an enlargement of shape \\( P \\).\nWhat calculation works out the constant of proportionality from shape \\( P \\) to shape \\( Q \\) ? ![To similar star shapes labelled P and Q. They have the same side labelled for P it is 3cm and for Q it is 11cm]() \\( 11-3 \\)"
},
{
"from": "gpt",
"value": "When calculating a scale factor, thinks they need to subtract rather than divide."
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division What does the following equal?\n\\[\n8-7+10 \\times 3\n\\] \\( -29 \\)"
},
{
"from": "gpt",
"value": "Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)"
}
] |
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving addition, subtraction, multiplication, and/or division What does the following equal?\n\\[\n8-7+10 \\times 3\n\\] \\( 33 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Distinguish between congruency and similarity Tom and Katie are discussing congruence and similarity. Who is correct? Tom says these two squares are congruent ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Katie says these two squares are similar ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Only\nTom"
},
{
"from": "gpt",
"value": "Thinks congruent shapes are the same shape but can be different sizes"
}
] |
[
{
"from": "human",
"value": "Distinguish between congruency and similarity Tom and Katie are discussing congruence and similarity. Who is correct? Tom says these two squares are congruent ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Katie says these two squares are similar ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Both Tom and Katie"
},
{
"from": "gpt",
"value": "Thinks congruent shapes are the same shape but can be different sizes"
}
] |
[
{
"from": "human",
"value": "Distinguish between congruency and similarity Tom and Katie are discussing congruence and similarity. Who is correct? Tom says these two squares are congruent ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Katie says these two squares are similar ![An image of two squares. A little one and a big one. They are enlargements of each other.]() Neither is correct"
},
{
"from": "gpt",
"value": "Thinks congruent shapes are the same shape but can be different sizes"
}
] |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Jo and Paul are arguing about how to fully describe the rotation from shape \\( P \\) to shape \\( Q \\)\n\nJo says: \"a rotation of \\( 90^{\\degree} \\) anticlockwise\"\n\nPaul says: \"a rotation of \\( +270^{\\degree} \\) about \\( (-1,1)^{\\prime \\prime} \\)\n\nWho is correct? ![A coordinate grid with two trapeziums drawn on it and a centre of rotation marked on, one space to the right and one space up from the origin. Trapezium P has the coordinates: (-4,4) (-2,4) (-2,3) and (-4,1). Trapezium Q has the coordinates: (-4,-2) (-4,0) (-3,0) and (-1,-2).]() Only\nJo"
},
{
"from": "gpt",
"value": "Forgets to give the centre of rotation"
}
] |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Jo and Paul are arguing about how to fully describe the rotation from shape \\( P \\) to shape \\( Q \\)\n\nJo says: \"a rotation of \\( 90^{\\degree} \\) anticlockwise\"\n\nPaul says: \"a rotation of \\( +270^{\\degree} \\) about \\( (-1,1)^{\\prime \\prime} \\)\n\nWho is correct? ![A coordinate grid with two trapeziums drawn on it and a centre of rotation marked on, one space to the right and one space up from the origin. Trapezium P has the coordinates: (-4,4) (-2,4) (-2,3) and (-4,1). Trapezium Q has the coordinates: (-4,-2) (-4,0) (-3,0) and (-1,-2).]() Both Jo and Paul"
},
{
"from": "gpt",
"value": "Forgets to give the centre of rotation"
}
] |
[
{
"from": "human",
"value": "Describe a 90° or 270° rotation giving the angle and direction of rotation, and the coordinates of the centre of rotation, where the centre of rotation lies on the edge or outside of the object Jo and Paul are arguing about how to fully describe the rotation from shape \\( P \\) to shape \\( Q \\)\n\nJo says: \"a rotation of \\( 90^{\\degree} \\) anticlockwise\"\n\nPaul says: \"a rotation of \\( +270^{\\degree} \\) about \\( (-1,1)^{\\prime \\prime} \\)\n\nWho is correct? ![A coordinate grid with two trapeziums drawn on it and a centre of rotation marked on, one space to the right and one space up from the origin. Trapezium P has the coordinates: (-4,4) (-2,4) (-2,3) and (-4,1). Trapezium Q has the coordinates: (-4,-2) (-4,0) (-3,0) and (-1,-2).]() Neither is correct"
},
{
"from": "gpt",
"value": "Does not know about the + notation for directions in rotations"
}
] |