conversations
listlengths 2
2
|
|---|
[
{
"from": "human",
"value": "Interpret a pictogram involving full symbols The pictogram shows how many people came to watch a netball match.\nWhat is the mean number of people at each game? ![A pictogram with a key showing a smiley face represents 12 people. Game 1 has 4 smiley faces, Game 2 has 2 smiley faces, Game 3 has 3 smiley faces and Game 4 has 1 smiley face.]() \\( 2.5 \\)"
},
{
"from": "gpt",
"value": "When interpreting a pictogram, thinks each symbol stands for 1"
}
] |
[
{
"from": "human",
"value": "Interpret a pictogram involving full symbols The pictogram shows how many people came to watch a netball match.\nWhat is the mean number of people at each game? ![A pictogram with a key showing a smiley face represents 12 people. Game 1 has 4 smiley faces, Game 2 has 2 smiley faces, Game 3 has 3 smiley faces and Game 4 has 1 smiley face.]() \\( 120 \\)"
},
{
"from": "gpt",
"value": "When calculating the mean from a list of data, adds up the numbers but does not divide"
}
] |
[
{
"from": "human",
"value": "Write a formula to describe a situation Sally the electrician charges a call-out fee of \\( £ 40 \\) and then \\( £ 15 \\) per hour that the job takes.\n\nIf a job takes \\( n \\) hours, which formula would help work out the cost \\( (C) \\) of hiring Sally? \\( C=15 n \\)"
},
{
"from": "gpt",
"value": "Does not add on the constant in a worded substitution problem"
}
] |
[
{
"from": "human",
"value": "Write a formula to describe a situation Sally the electrician charges a call-out fee of \\( £ 40 \\) and then \\( £ 15 \\) per hour that the job takes.\n\nIf a job takes \\( n \\) hours, which formula would help work out the cost \\( (C) \\) of hiring Sally? \\( C=55 n \\)"
},
{
"from": "gpt",
"value": "Combines variables with constants when writing a formula from a given situation"
}
] |
[
{
"from": "human",
"value": "Write a formula to describe a situation Sally the electrician charges a call-out fee of \\( £ 40 \\) and then \\( £ 15 \\) per hour that the job takes.\n\nIf a job takes \\( n \\) hours, which formula would help work out the cost \\( (C) \\) of hiring Sally? \\( C=40 n+15 \\)"
},
{
"from": "gpt",
"value": "Gets their constants and coefficients the wrong way around when writing a formula from a given situation"
}
] |
[
{
"from": "human",
"value": "Given a description of a descending linear sequence in words, write some terms of that sequence If the \\( 3^{\\text {rd }} \\) term of a sequence is \\( 8 \\) \nand the term-to-term rule is \\( -2 \\), \nwhat is the \\( 7^{\\text {th }} \\) term in this sequence? \\( -2 \\)"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence gives the term after"
}
] |
[
{
"from": "human",
"value": "Given a description of a descending linear sequence in words, write some terms of that sequence If the \\( 3^{\\text {rd }} \\) term of a sequence is \\( 8 \\) \nand the term-to-term rule is \\( -2 \\), \nwhat is the \\( 7^{\\text {th }} \\) term in this sequence? \\( 6 \\)"
},
{
"from": "gpt",
"value": "When asked for a specific term in a sequence just gives the next term"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 2 digit integers using long multiplication What is a correct way to set up this problem to solve it using long multiplication?\n\\[\n426 \\times 82\n\\] ![426 multiplied by 82 set out to perform long multiplication. 82 is written under 426. The 8 of 82 is under the 4 of 426 and the 2 of 82 is under the 2 of 426.]()"
},
{
"from": "gpt",
"value": "Hasn't lined up the place value columns when writing out the calculation"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 2 digit integers using long multiplication What is a correct way to set up this problem to solve it using long multiplication?\n\\[\n426 \\times 82\n\\] ![426 multiplied by 82 set out to perform long multiplication. 426 is written in 3 columns with 400 in the first column, 20 in the second column and 6 in the third column. 82 is written underneath this, with 80 under 20 and 2 under 6.]()"
},
{
"from": "gpt",
"value": "Has partitioned the digits when doing long multiplication"
}
] |
[
{
"from": "human",
"value": "Generate an ascending integer linear sequence from the nth term rule What is the first term of the sequence with the nth-term rule:\n\\[\n5 n-7\n\\] \\( 5 \\)"
},
{
"from": "gpt",
"value": "When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n."
}
] |
[
{
"from": "human",
"value": "Generate an ascending integer linear sequence from the nth term rule What is the first term of the sequence with the nth-term rule:\n\\[\n5 n-7\n\\] \\( -7 \\)"
},
{
"from": "gpt",
"value": "Thinks the first term in a sequence is the term before the sequence begins (0th term)"
}
] |
[
{
"from": "human",
"value": "Generate an ascending integer linear sequence from the nth term rule What is the first term of the sequence with the nth-term rule:\n\\[\n5 n-7\n\\] \\( 1 \\)"
},
{
"from": "gpt",
"value": "Thinks the first term of a sequence must be 1"
}
] |
[
{
"from": "human",
"value": "Write a given ratio in the form 1:n Kate and Isaac share some sweets in the ratio \\( 3: 2 \\)\nWhat is this ratio in the form \\( 1: n \\) ? \\( 1: 0 \\)"
},
{
"from": "gpt",
"value": "Attempts to simplify ratio by subtracting from both sides"
}
] |
[
{
"from": "human",
"value": "Write a given ratio in the form 1:n Kate and Isaac share some sweets in the ratio \\( 3: 2 \\)\nWhat is this ratio in the form \\( 1: n \\) ? \\( 1: 6 \\)"
},
{
"from": "gpt",
"value": "When simplifying a ratio, divides one side of the ratio but multiplies the other side."
}
] |
[
{
"from": "human",
"value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\(y=3 x+5 \\text { ? }\\) \\( 2 y=6 x-5 \\)"
},
{
"from": "gpt",
"value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c"
}
] |
[
{
"from": "human",
"value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\(y=3 x+5 \\text { ? }\\) \\( y=3 x-2 \\)"
},
{
"from": "gpt",
"value": "Believes lines are parallel if they have the same y intercept "
}
] |
[
{
"from": "human",
"value": "Identify parallel lines with at least one equation written in another form Which of the following lines is not parallel to\n\\(y=3 x+5 \\text { ? }\\) \\( y=3(1+x) \\)"
},
{
"from": "gpt",
"value": "Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c"
}
] |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rhombus Tom and Katie are arguing about the diagonals of quadrilaterals.\nTom says a kite has bisecting diagonals.\nKatie says a rhombus has bisecting diagonals.\nWho is correct? ![A pair of intersecting lines]() Only\nTom"
},
{
"from": "gpt",
"value": "Believes a kite has bisecting diagonals"
}
] |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rhombus Tom and Katie are arguing about the diagonals of quadrilaterals.\nTom says a kite has bisecting diagonals.\nKatie says a rhombus has bisecting diagonals.\nWho is correct? ![A pair of intersecting lines]() Both Tom and Katie"
},
{
"from": "gpt",
"value": "Believes a kite has bisecting diagonals"
}
] |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rhombus Tom and Katie are arguing about the diagonals of quadrilaterals.\nTom says a kite has bisecting diagonals.\nKatie says a rhombus has bisecting diagonals.\nWho is correct? ![A pair of intersecting lines]() Neither is correct"
},
{
"from": "gpt",
"value": "Does not know the meaning of bisect"
}
] |
[
{
"from": "human",
"value": "Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c This is part of a table of values for\n\\(y=x^{2}-2 x+1\\)\n\nWhat should replace the star? \\begin{tabular}{|c|c|}\n\\hline\\( x \\) & \\( -3 \\) \\\\\n\\hline\\( y \\) & \\(\\bigstar\\) \\\\\n\\hline\n\\end{tabular} \\( -2 \\)"
},
{
"from": "gpt",
"value": "Believes the square of a negative will also be negative"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear inequalities in one variable where the variable appears on one side of the equation How should you write the solution to the following inequality?\n\\(2 x>7\\) \\( x>4 \\)"
},
{
"from": "gpt",
"value": "Believes inequalities can only include integers"
}
] |
[
{
"from": "human",
"value": "Solve one-step linear inequalities in one variable where the variable appears on one side of the equation How should you write the solution to the following inequality?\n\\(2 x>7\\) \\( x=3.5 \\)"
},
{
"from": "gpt",
"value": "Believes solving an inequality gives a single value as a solution"
}
] |
[
{
"from": "human",
"value": "Calculate unit fractions of an amount \\( \\frac{1}{6} \\) of \\( 24= \\) \\( 18 \\)"
},
{
"from": "gpt",
"value": "Thinks finding a fraction of an amount means subtracting from that amount"
}
] |
[
{
"from": "human",
"value": "Calculate unit fractions of an amount \\( \\frac{1}{6} \\) of \\( 24= \\) \\( 144 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the denominator instead of dividing when finding a fraction of an amount"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 2 digit integers using Napier’s bones Dave is trying to solve this problem using Napier's bones\nWhat number does the circled digit represent? \\( 356 \\times 93 \\) ![A Napier's bones grid, with 356 along the top and 93 down the side. From left to right on the top row, with / representing a diagonal line through through the box, the boxes read 2/7, 4/5, 5/4. From left to right on the bottom row, the boxes read 0/9, 1/5, 1/8. The digit 5 is circled in the second box of the top row, which is in the column under the 5 of 356 and the row along from the 9 of 93.]() \\( 5 \\)"
},
{
"from": "gpt",
"value": "Does not understand the place value of answers from a Napier's bones calculation"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 2 digit integers using Napier’s bones Dave is trying to solve this problem using Napier's bones\nWhat number does the circled digit represent? \\( 356 \\times 93 \\) ![A Napier's bones grid, with 356 along the top and 93 down the side. From left to right on the top row, with / representing a diagonal line through through the box, the boxes read 2/7, 4/5, 5/4. From left to right on the bottom row, the boxes read 0/9, 1/5, 1/8. The digit 5 is circled in the second box of the top row, which is in the column under the 5 of 356 and the row along from the 9 of 93.]() \\( 50 \\)"
},
{
"from": "gpt",
"value": "Does not understand the place value of answers from a Napier's bones calculation"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 2 digit integers using Napier’s bones Dave is trying to solve this problem using Napier's bones\nWhat number does the circled digit represent? \\( 356 \\times 93 \\) ![A Napier's bones grid, with 356 along the top and 93 down the side. From left to right on the top row, with / representing a diagonal line through through the box, the boxes read 2/7, 4/5, 5/4. From left to right on the bottom row, the boxes read 0/9, 1/5, 1/8. The digit 5 is circled in the second box of the top row, which is in the column under the 5 of 356 and the row along from the 9 of 93.]() \\( 5000 \\)"
},
{
"from": "gpt",
"value": "Does not understand the place value of answers from a Napier's bones calculation"
}
] |
[
{
"from": "human",
"value": "Complete a symmetric figure with respect to a specific line of symmetry Which image completes a symmetric figure using the red line of symmetry? ![A figure drawn in the upper half of a box with a red dotted line immediately below. ]() ![An incorrect completion of the figure given in the question. ]()"
},
{
"from": "gpt",
"value": "Translates rather than reflects across a line of symmetry"
}
] |
[
{
"from": "human",
"value": "Complete a symmetric figure with respect to a specific line of symmetry Which image completes a symmetric figure using the red line of symmetry? ![A figure drawn in the upper half of a box with a red dotted line immediately below. ]() ![An incorrect completion of the figure given in the question. ]()"
},
{
"from": "gpt",
"value": "Fails to reflect across mirror line"
}
] |
[
{
"from": "human",
"value": "Complete a symmetric figure with respect to a specific line of symmetry Which image completes a symmetric figure using the red line of symmetry? ![A figure drawn in the upper half of a box with a red dotted line immediately below. ]() ![An incorrect completion of the figure given in the question. ]()"
},
{
"from": "gpt",
"value": "Fails to reflect across mirror line"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph This graph shows the amount of potatoes consumed by a restaurant in a week.\n\nHow many more potatoes were consumed on Sunday compared to Saturday? ![Chart of potatoes consumed with kilos against day of week]() \\( 35 \\mathrm{~kg} \\)"
},
{
"from": "gpt",
"value": "Reads one point on a time series graph instead of all the values from a given time period"
}
] |
[
{
"from": "human",
"value": "Interpret continuous data using a line graph This graph shows the amount of potatoes consumed by a restaurant in a week.\n\nHow many more potatoes were consumed on Sunday compared to Saturday? ![Chart of potatoes consumed with kilos against day of week]() \\( 25 \\mathrm{~kg} \\)"
},
{
"from": "gpt",
"value": "Reads one point on a time series graph instead of all the values from a given time period"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible:\n\\(\np^{2}-16\n\\) \\( (p-4)(p-4) \\)"
},
{
"from": "gpt",
"value": "Factorises difference of two squares with the same sign in both brackets"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible:\n\\(\np^{2}-16\n\\) \\( p(p-16) \\)"
},
{
"from": "gpt",
"value": "Believes only the first term needs to be divided when factorising an expression"
}
] |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form x² - c Factorise this expression, if possible:\n\\(\np^{2}-16\n\\) Does not factorise"
},
{
"from": "gpt",
"value": "Does not recognise difference of two squares"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a scalene triangle where the dimensions are given in the same units Which of the following triangles have the same area as this rectangle? ![Rectangle with base 7 and height 3]() ![Right-angled triangle with height 6, base 5 and hypotenuse length the square root of 61]()"
},
{
"from": "gpt",
"value": "Doesn't know the area of a triangle formula"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a scalene triangle where the dimensions are given in the same units Which of the following triangles have the same area as this rectangle? ![Rectangle with base 7 and height 3]() ![Triangle with base 6, perpendicular height 8 and slant length 13]()"
},
{
"from": "gpt",
"value": "Doesn't know the area of a triangle formula"
}
] |
[
{
"from": "human",
"value": "Calculate the area of a scalene triangle where the dimensions are given in the same units Which of the following triangles have the same area as this rectangle? ![Rectangle with base 7 and height 3]() They are all equal to the rectangle"
},
{
"from": "gpt",
"value": "Doesn't know the area of a triangle formula"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n23, \\quad 13, \\quad 3, \\quad \\ldots\n\\] \\( -3 \\)"
},
{
"from": "gpt",
"value": "Miscounts when subtracting over zero"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n23, \\quad 13, \\quad 3, \\quad \\ldots\n\\] \\( -10 \\)"
},
{
"from": "gpt",
"value": "Identifies the term-to-term rule rather than the next term"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n23, \\quad 13, \\quad 3, \\quad \\ldots\n\\] Not enough information"
},
{
"from": "gpt",
"value": "Does not know how to find the next term in a sequence"
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 25 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\nNumber of spots\\\\ & Frequency \n\\hline \\( 5 \\) & \\( 4 \\) \\\\\n\\hline \\( 6 \\) & \\( 9 \\) \\\\\n\\hline \\( 7 \\) & \\( 9 \\) \\\\\n\\hline \\( 8 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 0.96(2 d p) \\)"
},
{
"from": "gpt",
"value": "Believes the mean is total frequency divided by sum of categories given"
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 25 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\nNumber of spots\\\\ & Frequency \n\\hline \\( 5 \\) & \\( 4 \\) \\\\\n\\hline \\( 6 \\) & \\( 9 \\) \\\\\n\\hline \\( 7 \\) & \\( 9 \\) \\\\\n\\hline \\( 8 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 40.25 \\)"
},
{
"from": "gpt",
"value": "Believes mean is total divided by number of groups"
}
] |
[
{
"from": "human",
"value": "Calculate the mean from a frequency table The table below is a summary of the number of spots counted on \\( 25 \\) ladybirds. Calculate the mean number of spots per ladybird. ![\\begin{tabular}{|c|c|}\nNumber of spots\\\\ & Frequency \n\\hline \\( 5 \\) & \\( 4 \\) \\\\\n\\hline \\( 6 \\) & \\( 9 \\) \\\\\n\\hline \\( 7 \\) & \\( 9 \\) \\\\\n\\hline \\( 8 \\) & \\( 3 \\) \\\\\n\\hline\n\\end{tabular}]() \\( 0.16 \\) (2dp)"
},
{
"from": "gpt",
"value": "Believes the mean is total frequency divided by something"
}
] |
[
{
"from": "human",
"value": "Express words as 5 digit numbers and above How do you write this number in digits?\nFifty-six thousand and thirteen \\( 5613 \\)"
},
{
"from": "gpt",
"value": "Believes that they only need to write non-zero digits when giving a number in digits"
}
] |
[
{
"from": "human",
"value": "Express words as 5 digit numbers and above How do you write this number in digits?\nFifty-six thousand and thirteen \\( 56030 \\)"
},
{
"from": "gpt",
"value": "Confuses written 'teen' numbers with their corresponding multiples of 10"
}
] |
[
{
"from": "human",
"value": "Express words as 5 digit numbers and above How do you write this number in digits?\nFifty-six thousand and thirteen \\( 560013 \\)"
},
{
"from": "gpt",
"value": "Confuses the ten thousands and thousands place value columns"
}
] |
[
{
"from": "human",
"value": "Carry out mental divisions when the answer leaves a remainder Sarah has some apples.\nShe shares them into \\( 6 \\) equal groups and there is one left over.\nHow many apples could she have? \\( 35 \\)"
},
{
"from": "gpt",
"value": "Thinks the remainder is the difference between the dividend and the next biggest multiple"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![A grid with a left-leaning parallelogram drawn in the upper half and a blue line across the middle, marked 'line of reflection'. ]() ![Tom does this: an image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn immediately below. ]() ![Katie does this: An image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn one line down from the blue line. ]() Only\nTom"
},
{
"from": "gpt",
"value": "Fails to reflect across mirror line"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![A grid with a left-leaning parallelogram drawn in the upper half and a blue line across the middle, marked 'line of reflection'. ]() ![Tom does this: an image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn immediately below. ]() ![Katie does this: An image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn one line down from the blue line. ]() Only Katie"
},
{
"from": "gpt",
"value": "Fails to reflect across mirror line"
}
] |
[
{
"from": "human",
"value": "Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![A grid with a left-leaning parallelogram drawn in the upper half and a blue line across the middle, marked 'line of reflection'. ]() ![Tom does this: an image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn immediately below. ]() ![Katie does this: An image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn one line down from the blue line. ]() Both Tom and Katie"
},
{
"from": "gpt",
"value": "Fails to reflect across mirror line"
}
] |
[
{
"from": "human",
"value": "Use the nth term rule for descending integer linear sequences to find another term in a the sequence What is the \\( 15 \\) th term of this sequence? \\( u_{n}=1-3 n \\) \\( -46 \\)"
},
{
"from": "gpt",
"value": "When subtracting past zero, adds the absolute values and then writes the answer with a negative sign"
}
] |
[
{
"from": "human",
"value": "Use the nth term rule for descending integer linear sequences to find another term in a the sequence What is the \\( 15 \\) th term of this sequence? \\( u_{n}=1-3 n \\) \\( -30 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Solve coordinate geometry questions involving ratio ![A straight line on squared paper. Points P, Q and R lie on this line. The leftmost end of the line is labelled P. If you travel right 4 squares and up 1 square you get to point Q. If you then travel 8 squares right and 2 squares up from Q you reach point R.]() What is the ratio of \\( P Q: P R \\) ? \\( 1: 12 \\)"
},
{
"from": "gpt",
"value": "Thinks ratios are written as 1:total"
}
] |
[
{
"from": "human",
"value": "Solve coordinate geometry questions involving ratio ![A straight line on squared paper. Points P, Q and R lie on this line. The leftmost end of the line is labelled P. If you travel right 4 squares and up 1 square you get to point Q. If you then travel 8 squares right and 2 squares up from Q you reach point R.]() What is the ratio of \\( P Q: P R \\) ? \\( 1: 4 \\)"
},
{
"from": "gpt",
"value": "May have estimated when using ratios with geometry"
}
] |
[
{
"from": "human",
"value": "Solve coordinate geometry questions involving ratio ![A straight line on squared paper. Points P, Q and R lie on this line. The leftmost end of the line is labelled P. If you travel right 4 squares and up 1 square you get to point Q. If you then travel 8 squares right and 2 squares up from Q you reach point R.]() What is the ratio of \\( P Q: P R \\) ? \\( 1: 2 \\)"
},
{
"from": "gpt",
"value": "May have estimated when using ratios with geometry"
}
] |
[
{
"from": "human",
"value": "Order negative decimals with a different number of digits Which number is closest to zero? \\( -2.1 \\)"
},
{
"from": "gpt",
"value": "Does not know how to compare decimal numbers"
}
] |
[
{
"from": "human",
"value": "Order negative decimals with a different number of digits Which number is closest to zero? \\( -2.105 \\)"
},
{
"from": "gpt",
"value": "Does not know how to compare decimal numbers"
}
] |
[
{
"from": "human",
"value": "Round numbers to one decimal place \\[\n\\text { 2426. } 951\n\\]\nWhat is this number rounded to \\( 1 \\) decimal place? \\( 2426.0 \\)"
},
{
"from": "gpt",
"value": "When rounding up from a 9, does not add one on to the digit to the left"
}
] |
[
{
"from": "human",
"value": "Round numbers to one decimal place \\[\n\\text { 2426. } 951\n\\]\nWhat is this number rounded to \\( 1 \\) decimal place? \\( 2426.9 \\)"
},
{
"from": "gpt",
"value": "Rounds down instead of up"
}
] |
[
{
"from": "human",
"value": "Round numbers to one decimal place \\[\n\\text { 2426. } 951\n\\]\nWhat is this number rounded to \\( 1 \\) decimal place? \\( 2000 \\)"
},
{
"from": "gpt",
"value": "Rounds to the wrong degree of accuracy (rounds too little)"
}
] |
[
{
"from": "human",
"value": "Raise an integer to a positive non-unit fraction power \\( (27)^{\\frac{4}{3}}=? \\) \\( 36 \\)"
},
{
"from": "gpt",
"value": "Multiplies by the index"
}
] |
[
{
"from": "human",
"value": "Raise an integer to a positive non-unit fraction power \\( (27)^{\\frac{4}{3}}=? \\) \\( 20.25 \\)"
},
{
"from": "gpt",
"value": "Assumes the fractional index denotes the root and power the other way around"
}
] |
[
{
"from": "human",
"value": "Raise an integer to a positive non-unit fraction power \\( (27)^{\\frac{4}{3}}=? \\) \\( 12 \\)"
},
{
"from": "gpt",
"value": "Assumes they multiply by the numerator of fractional index"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data What is the mean of the following numbers?\n\n\\[\n1,4,7,9,9\n\\] \\( 7 \\)"
},
{
"from": "gpt",
"value": "When asked for the mean of a list of data, gives the median"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data What is the mean of the following numbers?\n\n\\[\n1,4,7,9,9\n\\] \\( 9 \\)"
},
{
"from": "gpt",
"value": "When asked for the mean of a list of data, gives the mode"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data What is the mean of the following numbers?\n\n\\[\n1,4,7,9,9\n\\] \\( 30 \\)"
},
{
"from": "gpt",
"value": "When calculating the mean from a list of data, adds up the numbers but does not divide"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n\\frac{t-3}{2}=\\frac{1}{8}\n\\) \\( t=6 \\frac{1}{4} \\)"
},
{
"from": "gpt",
"value": "Adds or subtracts from numerator first when solving an equation with a fraction"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n\\frac{t-3}{2}=\\frac{1}{8}\n\\) \\( t=1 \\)"
},
{
"from": "gpt",
"value": "When adding an integer to a fraction, thinks you add the integer to the numerator"
}
] |
[
{
"from": "human",
"value": "Solve two-step linear equations, with the variable on one side, involving positive fractions Solve the equation:\n\\(\n\\frac{t-3}{2}=\\frac{1}{8}\n\\) \\( t=3 \\frac{1}{16} \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed Rearrange the following equation to make \\( r \\) the subject\n\\(g=2 r+3\\) \\( r=\\frac{g+3}{2} \\)"
},
{
"from": "gpt",
"value": "Confuses the inverse operations of addition and subtraction when rearranging equations"
}
] |
[
{
"from": "human",
"value": "Rearrange formulae to change the subject where the subject appears once and two steps are needed Rearrange the following equation to make \\( r \\) the subject\n\\(g=2 r+3\\) \\( r=g+3 \\div 2 \\)"
},
{
"from": "gpt",
"value": "Misunderstands order of operations in algebraic expressions"
}
] |
[
{
"from": "human",
"value": "Recognise perpendicular lines These two lines are ... ![Two lines on a graph meeting at a right angle]() parallelogram"
},
{
"from": "gpt",
"value": "Believes parallelogram is the term used to describe two lines at right angles"
}
] |
[
{
"from": "human",
"value": "Recognise perpendicular lines These two lines are ... ![Two lines on a graph meeting at a right angle]() parallel"
},
{
"from": "gpt",
"value": "Believes parallel is the term used to describe two lines at right angles"
}
] |
[
{
"from": "human",
"value": "Recognise perpendicular lines These two lines are ... ![Two lines on a graph meeting at a right angle]() particular"
},
{
"from": "gpt",
"value": "Believes particular is the term used to describe two lines at right angles"
}
] |
[
{
"from": "human",
"value": "Convert from km² to m² \\( 2 \\mathrm{~km}^{2} \\) is the same as _____ \\( m^{2} \\) \\( 2000 \\)"
},
{
"from": "gpt",
"value": "Does not square the conversion factor when converting squared units"
}
] |
[
{
"from": "human",
"value": "Convert from km² to m² \\( 2 \\mathrm{~km}^{2} \\) is the same as _____ \\( m^{2} \\) \\( 20000 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 100m and a km"
}
] |
[
{
"from": "human",
"value": "Convert from km² to m² \\( 2 \\mathrm{~km}^{2} \\) is the same as _____ \\( m^{2} \\) \\( 2000000000 \\)"
},
{
"from": "gpt",
"value": "Believes you cube the conversion factor when dealing with squared units"
}
] |
[
{
"from": "human",
"value": "Identify rational and irrational numbers Which of these two numbers are rational?\n\n\\( \\sqrt{36} \\) and \\( \\sqrt{12} \\) \\( \\sqrt{12} \\)"
},
{
"from": "gpt",
"value": "Does not understand that a surd is a rational number if the number under the root is a square number"
}
] |
[
{
"from": "human",
"value": "Identify rational and irrational numbers Which of these two numbers are rational?\n\n\\( \\sqrt{36} \\) and \\( \\sqrt{12} \\) Neither"
},
{
"from": "gpt",
"value": "Does not understand that a surd is a rational number if the number under the root is a square number"
}
] |
[
{
"from": "human",
"value": "Identify rational and irrational numbers Which of these two numbers are rational?\n\n\\( \\sqrt{36} \\) and \\( \\sqrt{12} \\) Both"
},
{
"from": "gpt",
"value": "Does not understand the definition of a rational number when it is a surd"
}
] |
[
{
"from": "human",
"value": "Factorise a single bracket containing a non-linear expression by taking out a single algebraic common factor (e.g. a) What should replace the circle when this expression is fully factorised? \\( 3 a^{2}+2 a \\equiv \\bigstar(\\triangle a+\\bigcirc) \\) \\( \\bigcirc=2 a \\)"
},
{
"from": "gpt",
"value": "Believes only the first term needs to be divided when factorising an expression"
}
] |
[
{
"from": "human",
"value": "Recognise a linear graph from its shape Use a graphing program (e.g. Desmos) to plot the following pairs of functions.\n\\[\ny=3 \\text { and } y=-2\n\\]\n\nTom says both functions are linear\n\nKatie says both functions are vertical lines\n\nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Confuses the equations of vertical and horizontal lines"
}
] |
[
{
"from": "human",
"value": "Recognise a linear graph from its shape Use a graphing program (e.g. Desmos) to plot the following pairs of functions.\n\\[\ny=3 \\text { and } y=-2\n\\]\n\nTom says both functions are linear\n\nKatie says both functions are vertical lines\n\nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not know the properties of a linear graph"
}
] |
[
{
"from": "human",
"value": "Add fractions involving mixed number fractions with the same denominator \\( 2 \\frac{1}{5}+1 \\frac{2}{5}= \\) Leave your answer as a mixed number \\( \\frac{18}{5} \\)"
},
{
"from": "gpt",
"value": "Confused mixed numbers with improper fractions"
}
] |
[
{
"from": "human",
"value": "Add fractions involving mixed number fractions with the same denominator \\( 2 \\frac{1}{5}+1 \\frac{2}{5}= \\) Leave your answer as a mixed number \\( 3 \\frac{3}{10} \\)"
},
{
"from": "gpt",
"value": "When adding fractions, adds the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Calculate the distance between two coordinates in 2D, where all the values are positive integers Mark is working out the distance between these two points. What type of triangle would help him? ![Axes with not scales drawn on. Two points are marked, (4,10) and (9,2)]() Isosceles"
},
{
"from": "gpt",
"value": "Does not link Pythagoras Theorem to finding distance between two points"
}
] |
[
{
"from": "human",
"value": "Calculate the distance between two coordinates in 2D, where all the values are positive integers Mark is working out the distance between these two points. What type of triangle would help him? ![Axes with not scales drawn on. Two points are marked, (4,10) and (9,2)]() Equilateral"
},
{
"from": "gpt",
"value": "Does not link Pythagoras Theorem to finding distance between two points"
}
] |
[
{
"from": "human",
"value": "Calculate the distance between two coordinates in 2D, where all the values are positive integers Mark is working out the distance between these two points. What type of triangle would help him? ![Axes with not scales drawn on. Two points are marked, (4,10) and (9,2)]() Scalene"
},
{
"from": "gpt",
"value": "Does not link Pythagoras Theorem to finding distance between two points"
}
] |
[
{
"from": "human",
"value": "Write 5 digit numbers and above as words How do you write this number in words?\n\\(\n204050\n\\) Two million and four thousand and fifty"
},
{
"from": "gpt",
"value": "Mistakes the place value column of hundred thousands with millions"
}
] |
[
{
"from": "human",
"value": "Write 5 digit numbers and above as words How do you write this number in words?\n\\(\n204050\n\\) Two hundred and four and fifty"
},
{
"from": "gpt",
"value": "Does not understand that a space can be used to separate the thousands column from the hundreds column"
}
] |
[
{
"from": "human",
"value": "Interpret the value of digits in multiplication calculations using long multiplication What does the product of the two circled numbers represent? ![3847 times 28 written as a long multiplication question. The 8 in 3847 and the 2 in 28 are circled.]() \\( 1600 \\)"
},
{
"from": "gpt",
"value": "When multiplying, treats digits in other columns as if they are units"
}
] |
[
{
"from": "human",
"value": "Interpret the value of digits in multiplication calculations using long multiplication What does the product of the two circled numbers represent? ![3847 times 28 written as a long multiplication question. The 8 in 3847 and the 2 in 28 are circled.]() \\( 160 \\)"
},
{
"from": "gpt",
"value": "Does not understand place value within a number"
}
] |
[
{
"from": "human",
"value": "Interpret the value of digits in multiplication calculations using long multiplication What does the product of the two circled numbers represent? ![3847 times 28 written as a long multiplication question. The 8 in 3847 and the 2 in 28 are circled.]() \\( 16 \\)"
},
{
"from": "gpt",
"value": "When multiplying, treats digits in other columns as if they are units"
}
] |
[
{
"from": "human",
"value": "Understand the relationship between different factors of a number If you can connect dots to draw a regular octagon in a ring of equally spaced dots, which other regular shape can you definitely draw? Equilateral triangle"
},
{
"from": "gpt",
"value": "Does not use the associative property of multiplication to find other factors of a number"
}
] |
[
{
"from": "human",
"value": "Understand the relationship between different factors of a number If you can connect dots to draw a regular octagon in a ring of equally spaced dots, which other regular shape can you definitely draw? Pentagon"
},
{
"from": "gpt",
"value": "Does not use the associative property of multiplication to find other factors of a number"
}
] |
[
{
"from": "human",
"value": "Understand the relationship between different factors of a number If you can connect dots to draw a regular octagon in a ring of equally spaced dots, which other regular shape can you definitely draw? Hexagon"
},
{
"from": "gpt",
"value": "Does not use the associative property of multiplication to find other factors of a number"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables \\(\nx(3 x-5)+6(2 x-3) \\equiv P x^{2}+Q x+R\n\\)\n\nWhat is the value of \\( R \\) ? \\( -23 \\)"
},
{
"from": "gpt",
"value": "Believes you can add or subtract from inside brackets without expanding when solving an equation"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving non-linear variables \\(\nx(3 x-5)+6(2 x-3) \\equiv P x^{2}+Q x+R\n\\)\n\nWhat is the value of \\( R \\) ? \\( -8 \\)"
},
{
"from": "gpt",
"value": "Believes you can add or subtract from inside brackets without expanding when solving an equation"
}
] |