conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "Use the order of operations to carry out calculations involving powers \\[\n3 \\times 2+4-5\n\\]\nWhere do the brackets need to go to make the answer equal \\( 13 \\) ? Does not need brackets"
},
{
"from": "gpt",
"value": "Confuses the order of operations, believes a... |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\) \\( m+1 \\)"
},
{
"from": "gpt",
"value": "Does not know that to factorise a quadratic expression, to find two numbers that add to give t... |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\) \\( m+2 \\)"
},
{
"from": "gpt",
"value": "Thinks that when you cancel identical terms from the numerator and denominator, they just disa... |
[
{
"from": "human",
"value": "Simplify an algebraic fraction by factorising the numerator Simplify the following, if possible: \\( \\frac{m^{2}+2 m-3}{m-3} \\) \\( m-1 \\)"
},
{
"from": "gpt",
"value": "Does not know that to factorise a quadratic expression, to find two numbers that add to give t... |
[
{
"from": "human",
"value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\( 24 \\mathrm{~cm}, 17 \\mathrm{~cm}, 42 \\mathrm{~cm}, 26 \\mathrm{~cm}, 13 \\mathrm{~cm} \\)\nTom says if all the plants were cut in half, the range wouldn't change... |
[
{
"from": "human",
"value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\( 24 \\mathrm{~cm}, 17 \\mathrm{~cm}, 42 \\mathrm{~cm}, 26 \\mathrm{~cm}, 13 \\mathrm{~cm} \\)\nTom says if all the plants were cut in half, the range wouldn't change... |
[
{
"from": "human",
"value": "Calculate the range from a list of data Tom and Katie are discussing the \\( 5 \\) plants with these heights:\n\\( 24 \\mathrm{~cm}, 17 \\mathrm{~cm}, 42 \\mathrm{~cm}, 26 \\mathrm{~cm}, 13 \\mathrm{~cm} \\)\nTom says if all the plants were cut in half, the range wouldn't change... |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rectangle The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle ... |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rectangle The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle ... |
[
{
"from": "human",
"value": "Recall and use the intersecting diagonals properties of a rectangle The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle ... |
[
{
"from": "human",
"value": "Substitute positive integer values into formulae involving powers or roots The equation \\( f=3 r^{2}+3 \\) is used to find values in the table below. What is the value covered by the star? \\begin{tabular}{|c|c|c|c|c|}\n\\hline\\( r \\) & \\( 1 \\) & \\( 2 \\) & \\( 3 \\) & \\(... |
[
{
"from": "human",
"value": "Identify a unit of area James has answered a question on the area of a trapezium and got an answer of \\( 54 \\).\n\nBehind the star he has written the units that he used.\n\n\\(\n54 \\, \\bigstar \n\\)\n\nWhich of the following units could be correct? \\( m \\)"
},
{
"f... |
[
{
"from": "human",
"value": "Identify a unit of area James has answered a question on the area of a trapezium and got an answer of \\( 54 \\).\n\nBehind the star he has written the units that he used.\n\n\\(\n54 \\, \\bigstar \n\\)\n\nWhich of the following units could be correct? \\( \\mathrm{cm} \\)"
},... |
[
{
"from": "human",
"value": "Identify a unit of area James has answered a question on the area of a trapezium and got an answer of \\( 54 \\).\n\nBehind the star he has written the units that he used.\n\n\\(\n54 \\, \\bigstar \n\\)\n\nWhich of the following units could be correct? \\( \\mathrm{km}^{3} \\)"
... |
[
{
"from": "human",
"value": "Convert two digit integer percentages to fractions Convert this percentage to a fraction\n\\( 62 \\% \\) \\( \\frac{62}{10} \\)"
},
{
"from": "gpt",
"value": "Does not understand a percentage is out of 100"
}
] |
[
{
"from": "human",
"value": "Convert two digit integer percentages to fractions Convert this percentage to a fraction\n\\( 62 \\% \\) \\( \\frac{6}{2} \\)"
},
{
"from": "gpt",
"value": "Thinks they can convert a 2 digit percentage to a fraction by writing one number over the other."
}
] |
[
{
"from": "human",
"value": "Convert two digit integer percentages to fractions Convert this percentage to a fraction\n\\( 62 \\% \\) None of these"
},
{
"from": "gpt",
"value": "Does not understand a percentage is out of 100"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 10 \\( 43.2 \\div 10= \\) \\( 0.432 \\)"
},
{
"from": "gpt",
"value": "Divided by 100 rather than 10"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 10 \\( 43.2 \\div 10= \\) \\( 33.2 \\)"
},
{
"from": "gpt",
"value": "Subtracts instead of divides"
}
] |
[
{
"from": "human",
"value": "Divide decimals by 10 \\( 43.2 \\div 10= \\) \\( 43.02 \\)"
},
{
"from": "gpt",
"value": "When dividing a decimal by a multiple of 10, just divides the fractional place values "
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star? \\( 5 \\)"
},
{
"from": "gpt",
"value": "Does not find a common denominator when adding/s... |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star? \\( 17 \\)"
},
{
"from": "gpt",
"value": "Adds instead of subtracts"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{4}{5}-\\frac{1}{3}=\\frac{\\bigstar}{15}\n\\)\nWhat should replace the star? \\( 3 \\)"
},
{
"from": "gpt",
"value": "Does not find a common denominator when adding/s... |
[
{
"from": "human",
"value": "Identify horizontal translations in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\) Translation by vector\n\\(\n\\left[\\begin{array}{l}\n0 \\\\\n3\n\\end{array}\\right]\n\\)"
},
{
... |
[
{
"from": "human",
"value": "Identify horizontal translations in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\) Translation by vector\n\\(\n\\left[\\begin{array}{c}\n0 \\\\\n-3\n\\end{array}\\right]\n\\)"
},
{
... |
[
{
"from": "human",
"value": "Identify horizontal translations in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\n\\)\nto the graph of\n\\(\ny=f(x-3)\n\\) Translation by vector\n\\(\n\\left[\\begin{array}{r}\n-3 \\\\\n0\n\\end{array}\\right]\n\\)"
},
{
... |
[
{
"from": "human",
"value": "Expand products of three binomials in the form (x + a)(x + b)(x + c) John is expanding these three brackets:\n\\(\n(x+5)(x-3)(x+6)\n\\)\n\nHe finds it helpful to split the first bracket and view the problem as follows:\n\\(\nx(x-3)(x+6)+5(x-3)(x+6)\n\\)\n\nHe expands the bracket... |
[
{
"from": "human",
"value": "Identify the net of a non-prism This is the net of a... ![A circle touching a sector]() Triangle"
},
{
"from": "gpt",
"value": "Struggles to visualise nets of 3D shapes"
}
] |
[
{
"from": "human",
"value": "Identify the net of a non-prism This is the net of a... ![A circle touching a sector]() Triangular prism"
},
{
"from": "gpt",
"value": "Struggles to visualise nets of 3D shapes"
}
] |
[
{
"from": "human",
"value": "Identify the net of a non-prism This is the net of a... ![A circle touching a sector]() Triangularbased pyramid"
},
{
"from": "gpt",
"value": "Struggles to visualise nets of 3D shapes"
}
] |
[
{
"from": "human",
"value": "Identify alternate angles Tom and Katie are arguing about alternate angles.\nTom says angles \\( p \\) and \\( q \\) are alternate.\n\nKatie says angles \\( p \\) and \\( q \\) are equal.\nWho is correct? ![Shows two non parallel lines that are intersected by another line. Angle... |
[
{
"from": "human",
"value": "Identify alternate angles Tom and Katie are arguing about alternate angles.\nTom says angles \\( p \\) and \\( q \\) are alternate.\n\nKatie says angles \\( p \\) and \\( q \\) are equal.\nWho is correct? ![Shows two non parallel lines that are intersected by another line. Angle... |
[
{
"from": "human",
"value": "Identify alternate angles Tom and Katie are arguing about alternate angles.\nTom says angles \\( p \\) and \\( q \\) are alternate.\n\nKatie says angles \\( p \\) and \\( q \\) are equal.\nWho is correct? ![Shows two non parallel lines that are intersected by another line. Angle... |
[
{
"from": "human",
"value": "Convert from hours to minutes Hannah's journey to camp is \\( 3 \\) hours and \\( 16 \\) minutes.\nTori's journey to camp is \\( 214 \\) minutes.\nWhat is the difference in their journeys in minutes? \\( 102 \\) minutes"
},
{
"from": "gpt",
"value": "Answers as if th... |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=5-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=2 \\), what is the solution to \\( x=5-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 4.78 \\)"
},
{
"from... |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=5-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=2 \\), what is the solution to \\( x=5-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 4.79128 \\ldots \\)"
},
... |
[
{
"from": "human",
"value": "Select the correct answer to an iteration question to the required degree of accuracy \\(\nx_{n+1}=5-\\frac{1}{x_{n}}\n\\)\n\nUsing a starting value of \\( x_{1}=2 \\), what is the solution to \\( x=5-\\frac{1}{x} \\) to \\( 2 \\) decimal places? \\( 4.8 \\)"
},
{
"from"... |
[
{
"from": "human",
"value": "Calculate the area of an equilateral triangle where the dimensions are given in the same units How would you calculate the area of this triangle? ![A triangle, base 12m. All three sides are equal.]() \\( \\frac{12 \\times 12}{2} \\)"
},
{
"from": "gpt",
"value": "Has... |
[
{
"from": "human",
"value": "Calculate the area of an equilateral triangle where the dimensions are given in the same units How would you calculate the area of this triangle? ![A triangle, base 12m. All three sides are equal.]() \\( \\frac{12 \\times 12 \\times 12}{2} \\)"
},
{
"from": "gpt",
"v... |
[
{
"from": "human",
"value": "Divide a quantity into two parts for a given a ratio, where each part is an integer In the diagram, AN : NB \\( =3: 5 \\) \nWhat is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]() ... |
[
{
"from": "human",
"value": "Divide a quantity into two parts for a given a ratio, where each part is an integer In the diagram, AN : NB \\( =3: 5 \\) \nWhat is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]() ... |
[
{
"from": "human",
"value": "Divide a quantity into two parts for a given a ratio, where each part is an integer In the diagram, AN : NB \\( =3: 5 \\) \nWhat is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]() ... |
[
{
"from": "human",
"value": "Prove statements involving odd and even numbers Which of these shows part of the proof that the sum of two odd numbers is even? \\( \\begin{array}{l}2 n+(2 m+1) \\\\ =2(n+m)+1\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not understand that 2n represents an ev... |
[
{
"from": "human",
"value": "Prove statements involving odd and even numbers Which of these shows part of the proof that the sum of two odd numbers is even? \\( \\begin{array}{l}(2 n-1)(2 m+1) \\\\ =4 m n+2 n-2 m-1 \\\\ =2(2 m n-n-m)+1\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not know... |
[
{
"from": "human",
"value": "Prove statements involving odd and even numbers Which of these shows part of the proof that the sum of two odd numbers is even? \\( \\begin{array}{l}\\text { Odd + Odd } \\\\ =\\text { even }\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not understand that 2n ... |
[
{
"from": "human",
"value": "Carry out missing number subtraction problems involving negative integers ![Number line with -12 and -7 marked. Starting at -12, follow an arrow pointing to the right labelled +10. Then there is an arrow labelled b pointing to the left, which ends at -7 on the number line.]() Wh... |
[
{
"from": "human",
"value": "Carry out missing number subtraction problems involving negative integers ![Number line with -12 and -7 marked. Starting at -12, follow an arrow pointing to the right labelled +10. Then there is an arrow labelled b pointing to the left, which ends at -7 on the number line.]() Wh... |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are single terms and are not multiples of each other Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\) \\( \\frac{1-t}{3 s} \\)"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are single terms and are not multiples of each other Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\) \\( \\frac{s-3 t}{3 s} \\)"
},
{
"from": "gpt... |
[
{
"from": "human",
"value": "Subtract algebraic fractions where the denominators are single terms and are not multiples of each other Express the following as a single fraction, writing your answer as simply as possible: \\( \\frac{1}{s}-\\frac{t}{3} \\) \\( \\frac{1-t}{s-3} \\)"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "Given the volume of a cuboid, work out missing information The volume of this cuboid is \\( 30 \\mathrm{~cm}^{3} \\)\n\nWhat length should replace the star? ![A cuboid, depth 2cm and height 3cm. The width is labelled with a star.]() \\( 25 \\mathrm{~cm} \\)"
},
{
"from":... |
[
{
"from": "human",
"value": "Factorise a quadratic expression in the form ax² + bx + c where a is prime Step 1: Factorise the following expression\n\n\\(\n3 x^{2}+5 x+2\n\\) \\( (3 x+2)(3 x+1) \\)"
},
{
"from": "gpt",
"value": "When factorising a quadratic with a non-unit coefficient of x square... |
[
{
"from": "human",
"value": "Given the solution to one problem, deduce the answer to a related problem using the same operation Tom and Katie are discussing related calculations\nTom says if you know that \\( 3748+426=4174 \\), then \\( 3748+427 \\) must equal \\( \\mathbf{4 1 7 5} \\)\n\nKatie says if you ... |
[
{
"from": "human",
"value": "Given the solution to one problem, deduce the answer to a related problem using the same operation Tom and Katie are discussing related calculations\nTom says if you know that \\( 3748+426=4174 \\), then \\( 3748+427 \\) must equal \\( \\mathbf{4 1 7 5} \\)\n\nKatie says if you ... |
[
{
"from": "human",
"value": "Interpret sloping linear sections of a displacement-time graph This graph shows how far Fido the dog is from his home.\nWhat might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at... |
[
{
"from": "human",
"value": "Interpret sloping linear sections of a displacement-time graph This graph shows how far Fido the dog is from his home.\nWhat might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at... |
[
{
"from": "human",
"value": "Interpret sloping linear sections of a displacement-time graph This graph shows how far Fido the dog is from his home.\nWhat might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at... |
[
{
"from": "human",
"value": "Solve missing number mental multiplication questions What should replace the star?\n\\[\n\\bigstar \\times 4=108\n\\] \\( 432 \\)"
},
{
"from": "gpt",
"value": "When solving a problem that requires an inverse operation (e.g. missing number problems), does the origina... |
[
{
"from": "human",
"value": "Solve missing number mental multiplication questions What should replace the star?\n\\[\n\\bigstar \\times 4=108\n\\] \\( 104 \\)"
},
{
"from": "gpt",
"value": "Adds instead of multiples"
}
] |
[
{
"from": "human",
"value": "Calculate speed where distance and time are in the appropriate units The formula for speed is\n\\(\n\\text { Speed }=\\frac{\\text { Distance }}{\\text { Time }}\n\\)\nA snail travels \\( 4 \\mathrm{~m} \\) in \\( 10 \\) hours. What was its speed? \\( 40 \\) metres per hour"
}... |
[
{
"from": "human",
"value": "Calculate speed where distance and time are in the appropriate units The formula for speed is\n\\(\n\\text { Speed }=\\frac{\\text { Distance }}{\\text { Time }}\n\\)\nA snail travels \\( 4 \\mathrm{~m} \\) in \\( 10 \\) hours. What was its speed? \\( 2.5 \\) metres per hour"
... |
[
{
"from": "human",
"value": "Given a sketch of a circle with centre at the origin, write its equation in the form x² + y² = r² What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]() \\( x^{2}+y^{2}=\\sqrt{4} \\)"
}... |
[
{
"from": "human",
"value": "Given a sketch of a circle with centre at the origin, write its equation in the form x² + y² = r² What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]() \\( x^{2}+y^{2}=8 \\)"
},
{
... |
[
{
"from": "human",
"value": "Given a sketch of a circle with centre at the origin, write its equation in the form x² + y² = r² What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]() \\( x^{2}+y^{2}=4 \\)"
},
{
... |
[
{
"from": "human",
"value": "Substitute negative integer values into expressions involving no powers or roots If \\( d=-2 \\) what is the value of \\( 10-2 d \\) ? \\( 6 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Count backwards in steps of of something other than one George is counting backwards in steps of \\( 5 \\).\nHe starts at the number \\( 19,103 \\) what is the next number he will say? \\( 19,102 \\)"
},
{
"from": "gpt",
"value": "Counts on by 1, when asked to count ... |
[
{
"from": "human",
"value": "Count backwards in steps of of something other than one George is counting backwards in steps of \\( 5 \\).\nHe starts at the number \\( 19,103 \\) what is the next number he will say? \\( 19,099 \\)"
},
{
"from": "gpt",
"value": "Counts the starting number when coun... |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n2 n+3 \\leq 3 n-7\n\\] \\( 2 \\leq n \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n2 n+3 \\leq 3 n-7\n\\] \\( n \\leq 10 \\)"
},
{
"from": "gpt",
"value": "Believes they can multiply/divide through by a negative number without changing the... |
[
{
"from": "human",
"value": "Solve linear inequalities in one variable where the unknown appears on boths sides of the equation Solve\n\\[\n2 n+3 \\leq 3 n-7\n\\] \\( -4 \\leq n \\)"
},
{
"from": "gpt",
"value": "When solving an equation, uses the same operation rather than the inverse."
}
] |
[
{
"from": "human",
"value": "Determine the function of a single function machine used to create an algebraic expression Tom and Katie are discussing this function machine ![A function machine with an input of m+2, no function labelled and an output of 3m+2]() Tom says the function could be \\( +2 m \\)\nKat... |
[
{
"from": "human",
"value": "Convert between cm and m \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \\( 45 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10cm in a metre"
}
] |
[
{
"from": "human",
"value": "Convert between cm and m \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \\( 5 \\)"
},
{
"from": "gpt",
"value": "Gives a rounded whole number instead of a decimal"
}
] |
[
{
"from": "human",
"value": "Convert between cm and m \\[450 \\mathrm{~cm}=\\] \\[\\square \\mathrm{~m}\\] \\( 45000 \\)"
},
{
"from": "gpt",
"value": "Multiplies when converting to a larger unit"
}
] |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\) \\( \\frac{2 r}{5}=5+r \\)"
},
{
"from": "gpt",
"value": "Adds or subtrac... |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\) \\( 10 r-15=10+5 r \\)"
},
{
"from": "gpt",
"value": "Incorrectly clears ... |
[
{
"from": "human",
"value": "Solve linear equations with the variable appearing on both sides, involving positive fractions Which of the following is a correct first step to solve this equation:\n\\(\\frac{2 r-3}{5}=2+r\\) \\( 2 r-3=10+r \\)"
},
{
"from": "gpt",
"value": "When solving an equatio... |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate real life graph Water is poured into a glass at a constant rate.\n\nThis graph shows how the depth \\( (d) \\) of water in a glass changes over time \\( (t) \\).\n\nWhich of the following glasses is this most likely to be the graph of? ![A... |
[
{
"from": "human",
"value": "Given a situation sketch an appropriate real life graph Water is poured into a glass at a constant rate.\n\nThis graph shows how the depth \\( (d) \\) of water in a glass changes over time \\( (t) \\).\n\nWhich of the following glasses is this most likely to be the graph of? ![A... |
[
{
"from": "human",
"value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 901,426 \\) ? \\( 801,426 \\)"
},
{
"from": "gpt",
"value": "When subtracting a power of 10, subtracts from the wrong column"
}
] |
[
{
"from": "human",
"value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 901,426 \\) ? \\( 911,426 \\)"
},
{
"from": "gpt",
"value": "Adds rather than subtracts when answering worded problems"
}
] |
[
{
"from": "human",
"value": "Find another power of 10 less than a given number What number is \\( 10,000 \\) less than \\( 901,426 \\) ? \\( 90.1426 \\)"
},
{
"from": "gpt",
"value": "Divides rather than subtracts when given the command 'less than'"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 1 decimal place to percentages Convert this decimal to a percentage\n\\[\n0.6\n\\] \\( 6 \\% \\)"
},
{
"from": "gpt",
"value": "Multiplies by 10 instead of 100 when converting decimal to percentage"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 1 decimal place to percentages Convert this decimal to a percentage\n\\[\n0.6\n\\] \\( 0.6 \\% \\)"
},
{
"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 1 decimal place to percentages Convert this decimal to a percentage\n\\[\n0.6\n\\] \\( 0.006 \\% \\)"
},
{
"from": "gpt",
"value": "Divides instead of multiplies when converting a decimal to a percentage"
}
] |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\] \\( 4 \\times d \\)"
},
{
"from": "gpt",
"value": "Does not realize we can omit the ... |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\] \\( d 4 \\)"
},
{
"from": "gpt",
"value": "Writes the variable before the coefficien... |
[
{
"from": "human",
"value": "Simplify algebraic expressions to maintain equivalence by collecting like terms involving just one linear variable Simplify the following by collecting like terms.\n\\[\nd+d+d+d\n\\] \\( d^{4} \\)"
},
{
"from": "gpt",
"value": "Confuses collecting like terms with mul... |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a unit fraction Write this fraction as simply as possible:\n\\(\n\\frac{9}{12}\n\\) \\( \\frac{3}{6} \\)"
},
{
"from": "gpt",
"value": "Believes when simplifying a fraction you can divide the numerator and denominator by different ... |
[
{
"from": "human",
"value": "Simplify fractions that simplify to a unit fraction Write this fraction as simply as possible:\n\\(\n\\frac{9}{12}\n\\) \\( \\frac{9}{12} \\)"
},
{
"from": "gpt",
"value": "Does not recognise when a fraction can be simplified"
}
] |
[
{
"from": "human",
"value": "Add algebraic fractions where one denominator is a multiple of the other Write this as a single fraction as simply as possible:\n\\(\n\\frac{3}{2 x}+\\frac{4}{x}\n\\) \\( \\frac{7}{3 x} \\)"
},
{
"from": "gpt",
"value": "When adding fractions, adds the numerators and... |
[
{
"from": "human",
"value": "Add algebraic fractions where one denominator is a multiple of the other Write this as a single fraction as simply as possible:\n\\(\n\\frac{3}{2 x}+\\frac{4}{x}\n\\) \\( \\frac{7}{2 x} \\)"
},
{
"from": "gpt",
"value": "Forgets to change the numerators when finding ... |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 598-1000= \\) \\( 402 \\)"
},
{
"from": "gpt",
"value": "Believes the smaller number is always subtracted from the larger, regardless of the order of the calculation"
}
] |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 598-1000= \\) \\( -412 \\)"
},
{
"from": "gpt",
"value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit"
}
] |
[
{
"from": "human",
"value": "Carry out a subtraction problem with positive integers where the answer is less than 0 \\( 598-1000= \\) This problem cannot be solved"
},
{
"from": "gpt",
"value": "Believes it is impossible to subtract a bigger number from a smaller number"
}
] |
[
{
"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 \\( 1000 \\) units of electricity? ![A g... |
[
{
"from": "human",
"value": "Write a missing term of an ascending integer linear sequence The \\( 1^{\\text {st }} \\) term in a linear sequence is \\( 7 \\).\n\nThe \\( 4^{\\text {th }} \\) term of the sequence is \\( 25 \\).\n\nWhat is the \\( 8^{\\text {th }} \\) term of the sequence? \\( 50 \\)"
},
... |
[
{
"from": "human",
"value": "Write a missing term of an ascending integer linear sequence The \\( 1^{\\text {st }} \\) term in a linear sequence is \\( 7 \\).\n\nThe \\( 4^{\\text {th }} \\) term of the sequence is \\( 25 \\).\n\nWhat is the \\( 8^{\\text {th }} \\) term of the sequence? \\( 56 \\)"
},
... |
[
{
"from": "human",
"value": "Given a gradient, state the gradient of a line parallel to it A line has a gradient of \\( 5 \\)\n\nA line parallel to this line would have a gradient of... \\( -5 \\)"
},
{
"from": "gpt",
"value": "Believes parallel lines have gradients of opposite signs"
}
] |
[
{
"from": "human",
"value": "Given a gradient, state the gradient of a line parallel to it A line has a gradient of \\( 5 \\)\n\nA line parallel to this line would have a gradient of... \\( -\\frac{1}{5} \\)"
},
{
"from": "gpt",
"value": "Believes parallel lines have gradients that multiply to g... |
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