conversations
listlengths 2
2
|
|---|
[
{
"from": "human",
"value": "Round numbers greater than 1 to two significant figures \\(\n180.5672\n\\)\n\nWhat is the second significant figure in the number above? \\( 2 \\)"
},
{
"from": "gpt",
"value": "Does not understand the first significant value is the first non-zero digit number"
}
] |
[
{
"from": "human",
"value": "Round numbers greater than 1 to two significant figures \\(\n180.5672\n\\)\n\nWhat is the second significant figure in the number above? \\( 6 \\)"
},
{
"from": "gpt",
"value": "Identifies second decimal place value when asked for the second significant figure"
}
] |
[
{
"from": "human",
"value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable What do you need to do to eliminate the \\( q \\)s in each of these pairs of simultaneous equations?\n\\begin{array}{cc}\n Pair 1 & Pair 2 \\\\\n\\( 2p-4q=6 \\) & \\( 2p-4q=6 \\)\\\\\n\\( 7p+4q=9 \\) & \\( 7p-4q=9 \\)\n\\end{array}\n Add Pair \\( 1 \\)\nAdd Pair \\( 2 \\)"
},
{
"from": "gpt",
"value": "Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations."
}
] |
[
{
"from": "human",
"value": "Recognise whether you need to add or subtract linear equations in order to eliminate a variable What do you need to do to eliminate the \\( q \\)s in each of these pairs of simultaneous equations?\n\\begin{array}{cc}\n Pair 1 & Pair 2 \\\\\n\\( 2p-4q=6 \\) & \\( 2p-4q=6 \\)\\\\\n\\( 7p+4q=9 \\) & \\( 7p-4q=9 \\)\n\\end{array}\n Subtract Pair \\( 1 \\)\nSubtract Pair \\( 2 \\)"
},
{
"from": "gpt",
"value": "Believes that when eliminating a variable, regardless of the signs of the terms with matching coefficients, we subtract the equations"
}
] |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis? \\( (3,5) \\)"
},
{
"from": "gpt",
"value": "Believes both the x and y co-ordinates of the x-intercept of a quadratic are derived from the constants in the factorised form."
}
] |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis? \\( \\begin{array}{c}(-3,0) \\\\ \\text { and } \\\\ (-5,0)\\end{array} \\)"
},
{
"from": "gpt",
"value": "Believes the solutions of a quadratic equation are the constants in the factorised form"
}
] |
[
{
"from": "human",
"value": "Know that the factorised form of a quadratic is useful for finding where the curve crosses the x-axis \\( y=(x-3)(x-5) \\) Where does this curve intercept the \\( x \\) axis? \\( \\begin{array}{c}(3,5) \\\\ \\text { and } \\\\ (-3,-5)\\end{array} \\)"
},
{
"from": "gpt",
"value": "Believes both the x and y co-ordinates of the x-intercept of a quadratic are derived from the constants in the factorised form."
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]() \\( 46^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Confuses vertically opposite angles with angles on a straight line"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]() \\( 65^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Misinterprets the meaning of angles on a straight line angle fact"
}
] |
[
{
"from": "human",
"value": "Find missing angles using angles on a straight line What is the size of angle \\( k \\) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]() Not enough information"
},
{
"from": "gpt",
"value": "Does not know that angles on a straight line sum to 180 degrees"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\] \\( 0+1+3+4+7 \\div 5 \\)"
},
{
"from": "gpt",
"value": "Carries out operations from left to right regardless of priority order"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\] \\( \\frac{1+3+4+7}{4} \\)"
},
{
"from": "gpt",
"value": "When asked for the mean of a list of data, does not count any zeros in the data when working out what to divide by"
}
] |
[
{
"from": "human",
"value": "Calculate the mean as an average from a list of data When calculating the mean of the following numbers which calculation will give the correct answer?\n\\[\n0,1,3,4,7\n\\] None of them"
},
{
"from": "gpt",
"value": "Does not know how to calculate the mean"
}
] |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\) \\( 1 \\frac{3}{5} \\)"
},
{
"from": "gpt",
"value": "Believes when changing an improper fraction to a mixed number you divide the numerator by 10, regardless of the denominator"
}
] |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\) \\( 3 \\frac{2}{5} \\)"
},
{
"from": "gpt",
"value": "Believes the whole and remainder are the other way when changing an improper fraction to a mixed number"
}
] |
[
{
"from": "human",
"value": "Convert from improper fractions to mixed number fractions Convert this into a mixed number fraction:\n\\(\n\\frac{13}{5}\n\\) \\( 13 \\frac{1}{5} \\)"
},
{
"from": "gpt",
"value": "Believes the number of wholes in a mixed number multiplies by the fraction part"
}
] |
[
{
"from": "human",
"value": "Use area to write algebraic expressions The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]() \\( 12 x-2=10 x+2 \\)"
},
{
"from": "gpt",
"value": "Only multiplies the first term in the expansion of a bracket"
}
] |
[
{
"from": "human",
"value": "Use area to write algebraic expressions The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]() \\( 8+6 x-4=4+10 x+4 \\)"
},
{
"from": "gpt",
"value": "Calculates perimeter when asked for area"
}
] |
[
{
"from": "human",
"value": "Use area to write algebraic expressions The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]() \\( 4+3 x-2=2+5 x+2 \\)"
},
{
"from": "gpt",
"value": "Adds when calculating area instead of multiplying"
}
] |
[
{
"from": "human",
"value": "Convert from kilometers to miles \\( 3 \\) miles \\( \\approx 5 \\mathrm{~km} \\) \\( 30 \\mathrm{~km} \\approx \\square \\) miles \\( 28 \\)"
},
{
"from": "gpt",
"value": "Added rather than multiplied by a scale factor"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing mental multiplication strategies.\nTom says \\( 15 \\times 42=154 \\times 2 \\)\nKatie says \\( 15 \\times 42=(15 \\times 4)+(15 \\times 2) \\)\nWho is correct? Only Tom"
},
{
"from": "gpt",
"value": "Does not correctly apply the commutative property of multiplication"
}
] |
[
{
"from": "human",
"value": "Recognise and use efficient methods for mental multiplication Tom and Katie are discussing mental multiplication strategies.\nTom says \\( 15 \\times 42=154 \\times 2 \\)\nKatie says \\( 15 \\times 42=(15 \\times 4)+(15 \\times 2) \\)\nWho is correct? Only Katie"
},
{
"from": "gpt",
"value": "Does not correctly apply the distributive property of multiplication"
}
] |
[
{
"from": "human",
"value": "Convert from hours to minutes \\( 3 \\) hours is the same as ___________ minutes \\( 90 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 30 minutes in a hour"
}
] |
[
{
"from": "human",
"value": "Convert from hours to minutes \\( 3 \\) hours is the same as ___________ minutes \\( 30 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10 minutes in an hour"
}
] |
[
{
"from": "human",
"value": "Convert from hours to minutes \\( 3 \\) hours is the same as ___________ minutes \\( 300 \\)"
},
{
"from": "gpt",
"value": "Answers as if there are 100 minutes in an hour when changing from hours to minutes"
}
] |
[
{
"from": "human",
"value": "Write the next term of a descending integer linear sequence What is the next term in this sequence?\n\n\n\\[\n18, \\quad 11, \\quad 4, \\quad \\ldots\n\\] \\( -7 \\)"
},
{
"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\\[\n18, \\quad 11, \\quad 4, \\quad \\ldots\n\\] Not enough information"
},
{
"from": "gpt",
"value": "Does not know how to find the next term in a sequence"
}
] |
[
{
"from": "human",
"value": "Change minutes into decimals of hours (e.g. 90 minutes = 1.5 hours) \\( 90 \\) minutes is the same as _________ hours \\( 9 \\)"
},
{
"from": "gpt",
"value": "Thinks there are 10 minutes in an hour"
}
] |
[
{
"from": "human",
"value": "Change minutes into decimals of hours (e.g. 90 minutes = 1.5 hours) \\( 90 \\) minutes is the same as _________ hours \\( 1.3 \\)"
},
{
"from": "gpt",
"value": "Answers as if there are 100 minutes in an hour when writing minutes as decimals"
}
] |
[
{
"from": "human",
"value": "Identify factors of a number \\[\n1,2,4,8\n\\]\nThese are the only factors of... \\( 16 \\)"
},
{
"from": "gpt",
"value": "Does not think a number can be a factor of itself"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{2}{3}-\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star? \\( 19 \\)"
},
{
"from": "gpt",
"value": "Forgets to change the numerators when finding equivalent fractions"
}
] |
[
{
"from": "human",
"value": "Subtract proper fractions with different denominators which do not share a common factor \\(\n\\frac{2}{3}-\\frac{1}{10}=\\frac{\\bigstar}{30}\n\\)\nWhat should replace the star? \\( 1 \\)"
},
{
"from": "gpt",
"value": "When subtracting fractions, subtracts the numerators and denominators"
}
] |
[
{
"from": "human",
"value": "Understand inequality notation Which of the following shows \" \\( x \\) is greater than or equal to \\( 6 \\) \"? \\( x>6 \\)"
},
{
"from": "gpt",
"value": "When using inequality notation, thinks \"greater than/less than or equal to\" symbols are instead the \"greater than/less than\" symbols and vice versa"
}
] |
[
{
"from": "human",
"value": "Understand inequality notation Which of the following shows \" \\( x \\) is greater than or equal to \\( 6 \\) \"? \\( x \\leq 6 \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cone where the dimensions are all given in the same units STEP \\( 2 \\)\n\nJessica is trying to work out the volume of this cone. ![A cone with the slant height labelled 9cm, the perpendicular height labelled h and half the cone's base (forming a right angled triangle with the slant and perpendicular heights) is labelled 6cm.]() First she needs the perpendicular height.\n\nWhich of the following equations is true? \\( h^{2}=9^{2}+6^{2} \\)"
},
{
"from": "gpt",
"value": "Does not rearrange the Pythagoras' Theorem formula accurately"
}
] |
[
{
"from": "human",
"value": "Calculate the volume of a cone where the dimensions are all given in the same units STEP \\( 2 \\)\n\nJessica is trying to work out the volume of this cone. ![A cone with the slant height labelled 9cm, the perpendicular height labelled h and half the cone's base (forming a right angled triangle with the slant and perpendicular heights) is labelled 6cm.]() First she needs the perpendicular height.\n\nWhich of the following equations is true? \\( h^{2}=12^{2}-9^{2} \\)"
},
{
"from": "gpt",
"value": "When using Pythagoras to find the height of an isosceles triangle, uses the whole base instead of half"
}
] |
[
{
"from": "human",
"value": "Multiply mixed number fractions in the form: Fraction × Integer \\(\n1 \\frac{2}{3} \\times 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 2 \\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "When multiplying mixed numbers, forgets to multiply the fraction"
}
] |
[
{
"from": "human",
"value": "Multiply mixed number fractions in the form: Fraction × Integer \\(\n1 \\frac{2}{3} \\times 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 2 \\frac{4}{6} \\)"
},
{
"from": "gpt",
"value": "When multiplying a fraction by an integer, multiplies both numerator and denominator by the integer"
}
] |
[
{
"from": "human",
"value": "Calculate questions involving the power law of indices with positive integer powers \\( \\left(5^{4}\\right)^{3}= \\) \\( 5^{7} \\)"
},
{
"from": "gpt",
"value": "Has added the powers rather than multiplying them"
}
] |
[
{
"from": "human",
"value": "Calculate questions involving the power law of indices with positive integer powers \\( \\left(5^{4}\\right)^{3}= \\) \\( 125^{12} \\)"
},
{
"from": "gpt",
"value": "Has cubed the base number and the power"
}
] |
[
{
"from": "human",
"value": "Calculate questions involving the power law of indices with positive integer powers \\( \\left(5^{4}\\right)^{3}= \\) None of these options"
},
{
"from": "gpt",
"value": "Does not understand laws of indices"
}
] |
[
{
"from": "human",
"value": "Follow simple directions to translate a shape or object using words not vectors If you translate the star \\( 2 \\) squares left and \\( 3 \\) squares down, which letter do you land on? ![A set of axes: x-axis from 0 to 8, y-axis from 0 to 8. A yellow star is at point (4, 4). Point A is at (6, 1), Point B is at (2, 1), Point C is at (2, 2), Point D is at (1, 2). ]() A"
},
{
"from": "gpt",
"value": "Confuses left and right"
}
] |
[
{
"from": "human",
"value": "Follow simple directions to translate a shape or object using words not vectors If you translate the star \\( 2 \\) squares left and \\( 3 \\) squares down, which letter do you land on? ![A set of axes: x-axis from 0 to 8, y-axis from 0 to 8. A yellow star is at point (4, 4). Point A is at (6, 1), Point B is at (2, 1), Point C is at (2, 2), Point D is at (1, 2). ]() D"
},
{
"from": "gpt",
"value": "Counts the squares rather than the diagonals when reflecting in y=x or y=-x "
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 3 or more decimal place to percentages How do you write \\( 0.909 \\) as a percentage? \\( 99 \\% \\)"
},
{
"from": "gpt",
"value": "Does not understand the value of zeros as placeholders"
}
] |
[
{
"from": "human",
"value": "Convert decimals less than 1 with 3 or more decimal place to percentages How do you write \\( 0.909 \\) as a percentage? \\( 909 \\% \\)"
},
{
"from": "gpt",
"value": "Thinks they just remove the decimal point when converting a decimal to a percentage"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\) \\( \\{x<-4\\} \\cup\\{x>4\\} \\)"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\) \\( \\{x<4\\} \\)"
},
{
"from": "gpt",
"value": "Does not think a square root can be negative"
}
] |
[
{
"from": "human",
"value": "Solve positive quadratic inequalities by balancing e.g x² ≤ a Which of the following is the correct solution to the inequality?\n\n\\(\nx^{2}<16\n\\) \\( \\{-8<x<8\\} \\)"
},
{
"from": "gpt",
"value": "Mixes up squaring and multiplying by 2 or doubling"
}
] |
[
{
"from": "human",
"value": "Identify a prism from a diagram Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct? Only Tom"
},
{
"from": "gpt",
"value": "Confuses triangular prism with pyramid"
}
] |
[
{
"from": "human",
"value": "Identify a prism from a diagram Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct? Only Katie"
},
{
"from": "gpt",
"value": "Does not know the definition of a prism"
}
] |
[
{
"from": "human",
"value": "Identify a prism from a diagram Tom and Katie are arguing about prisms.\n\nTom says this shape is a prism. Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() Who is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not know the definition of a prism"
}
] |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\) Reflection in the\n\\[\ny \\text {-axis }\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a reflection in the y-axis"
}
] |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\) Reflection in the line\n\\[\ny=x\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a reflection in y=x"
}
] |
[
{
"from": "human",
"value": "Identify vertical reflections in the form f(x) = for non-trigonometric functions What transformation maps the graph of\n\\(y=f(x)\\)\nto the graph of\n\\(y=-f(x)\\) Reflection in the line\n\\[\ny=-x\n\\]"
},
{
"from": "gpt",
"value": "Believes y=-f(x) is a reflection in y=-x"
}
] |
[
{
"from": "human",
"value": "Recognise the angles on a straight line relationship ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true? \\( a+b=360^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Believes angles on a straight line add to 360 degrees"
}
] |
[
{
"from": "human",
"value": "Recognise the angles on a straight line relationship ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true? \\( a=b \\)"
},
{
"from": "gpt",
"value": "Student thinks that any two angles along a straight line are equal"
}
] |
[
{
"from": "human",
"value": "Recognise the angles on a straight line relationship ![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true? \\( a+b=90^{\\circ} \\)"
},
{
"from": "gpt",
"value": "Thinks there are 180 degrees in a full turn"
}
] |
[
{
"from": "human",
"value": "Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Here are the first \\( 4 \\) terms of a linear sequence. ![A sequence of 4 patterns, that are the first 4 terms of a sequence. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is an L shape made of 4 squares, it is the same as the first pattern but with 1 square stuck to the right of the square that is at the bottom of the rectangle. The 3rd pattern is an L shape made of 5 squares. It is the same as the 2nd pattern but with 1 more square added to the right of the squares at the bottom. The 4th pattern is an L shape made of 6 squares. It is the same as the 3rd pattern but with 1 more square added to the right of the squares at the bottom ]() How many squares would be in the \\( 10^{\\text {th }} \\) term? \\( 30 \\)"
},
{
"from": "gpt",
"value": "Thinks terms in linear sequence are in direct proportion"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 50.09-0.1= \\) \\( 50.99 \\)"
},
{
"from": "gpt",
"value": "When “borrowing” during a subtraction problem, does not subtract one from the preceding digit"
}
] |
[
{
"from": "human",
"value": "Subtract decimals where the numbers involved have a different number of decimal places \\( 50.09-0.1= \\) \\( 50.08 \\)"
},
{
"from": "gpt",
"value": "When subtracting decimals with a different number of decimal places, lines up the digits incorrectly"
}
] |
[
{
"from": "human",
"value": "Identify the regions on a double Venn diagram given in set notation Which element(s) is/are in \\( P^{\\prime} \\) ? ![A diagram showing a Venn diagram of 2 circles. The left circle is for Set P and contains crisps in its left part, sweets in the intersection. The right circle is for set Q and contains pizza in its right part, sweets in the intersection. Outside of the circles it says chocolate.]() crisps"
},
{
"from": "gpt",
"value": "Does not understand set notation for complement (eg. A')"
}
] |
[
{
"from": "human",
"value": "Identify the regions on a double Venn diagram given in set notation Which element(s) is/are in \\( P^{\\prime} \\) ? ![A diagram showing a Venn diagram of 2 circles. The left circle is for Set P and contains crisps in its left part, sweets in the intersection. The right circle is for set Q and contains pizza in its right part, sweets in the intersection. Outside of the circles it says chocolate.]() sweets, pizza & chocolate"
},
{
"from": "gpt",
"value": "Believes that the complement of a set includes any elements which are also in another set."
}
] |
[
{
"from": "human",
"value": "Solve a linear equation using a function machine Look at the function machine. ![An image of two function machines. The first function machine has x as the input. The first function is divide by 3 and the second is +4. The output is 5. The second function machine is the reverse of the first so now 5 is the input but the two function boxes have been left blank.]() What would be the correct steps to solve this equation?\n\\(\\frac{x}{3}+4=5\\) \\( \\begin{array}{l}\\times 3 \\\\ -4\\end{array} \\)"
},
{
"from": "gpt",
"value": "Does not reverse the order of operations when finding the input of a function machine"
}
] |
[
{
"from": "human",
"value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -3<x \\leq 1 \\) ? ![A number line with a hollow circle above -3 and an arrow coming out of it over the numbers -4, -5 etc and a filled in circle above 1 with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]()"
},
{
"from": "gpt",
"value": "Mixes up greater than and less than symbols"
}
] |
[
{
"from": "human",
"value": "Represent a linear inequality in the form a ≤ x ≤ b (and other sign arrangements) on a numberline Which number line represents \\( -3<x \\leq 1 \\) ? ![A number line with a filled in circle above -3 connected to a hollow circle above 1.]()"
},
{
"from": "gpt",
"value": "When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning."
}
] |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° Which diagram shows an angle of \\( 325^{\\circ} \\) ? ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 160 and 150 (inner scale) and halfway between 20 and 30 (outer scale).]()"
},
{
"from": "gpt",
"value": "Reads the wrong scale on the protractor when measuring obtuse angles"
}
] |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° Which diagram shows an angle of \\( 325^{\\circ} \\) ? ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 30 and 20 (inner scale) and halfway between 150 and 160 (outer scale).]()"
},
{
"from": "gpt",
"value": "Chooses the correct scale when measuring angles on a protractor but starts from the wrong number when the angle is in between two labelled dashes"
}
] |
[
{
"from": "human",
"value": "Use a protractor to measure angles between 270° and 360° Which diagram shows an angle of \\( 325^{\\circ} \\) ? ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 150 and 140 (inner scale) and halfway between 30 and 40 (outer scale).]()"
},
{
"from": "gpt",
"value": "Reads the wrong scale on the protractor when measuring obtuse angles"
}
] |
[
{
"from": "human",
"value": "Recognise the notation for parallel lines The two lines marked are... ![Trapezium with parallel sides labelled]() Perpendicular"
},
{
"from": "gpt",
"value": "Confuses the meaning of parallel and perpendicular"
}
] |
[
{
"from": "human",
"value": "Recognise the notation for parallel lines The two lines marked are... ![Trapezium with parallel sides labelled]() Vertical"
},
{
"from": "gpt",
"value": "Does not recognise the notation for parallel sides"
}
] |
[
{
"from": "human",
"value": "Recognise the notation for parallel lines The two lines marked are... ![Trapezium with parallel sides labelled]() Equal"
},
{
"from": "gpt",
"value": "Does not recognise the notation for parallel sides"
}
] |
[
{
"from": "human",
"value": "Carry out the first stage in an iteration solution The area of the rectangle on the right is \\( 8 \\mathrm{~cm}^{2} \\).\n\nTo find the value of \\( x \\), Sally uses:\n\\(x_{n+1}=\\frac{8}{9}-\\frac{x_{n}{ }^{3}}{9}\\)\n\nIf \\( x_{0}=0 \\), what does \\( x_{1} \\) equal? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]() \\( \\frac{7}{9} \\)"
},
{
"from": "gpt",
"value": "Believes the subscript in iteration notation is the value to be substituted"
}
] |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]() \\( A B \\) and \\( B C \\)"
},
{
"from": "gpt",
"value": "Believes adjacent sides of a rhombus are always perpendicular"
}
] |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]() \\( A B \\) and \\( D C \\)"
},
{
"from": "gpt",
"value": "Confuses the meaning of parallel and perpendicular"
}
] |
[
{
"from": "human",
"value": "Describe the properties of a rhombus \\( A B C D \\) is a rhombus.\nWhich lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]() None of them"
},
{
"from": "gpt",
"value": "Does not know the properties of a rhombus"
}
] |
[
{
"from": "human",
"value": "Given a line segment, calculate the gradient where the gradient is a positive integer What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the following points: (-3,-3) (-2,-2) (-1,-1) (0,0) (1,1) (2,2) and (3,3).]() \\( 0 \\)"
},
{
"from": "gpt",
"value": "Believes the gradient of a line is given by an intercept"
}
] |
[
{
"from": "human",
"value": "Given a line segment, calculate the gradient where the gradient is a positive integer What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the following points: (-3,-3) (-2,-2) (-1,-1) (0,0) (1,1) (2,2) and (3,3).]() \\( x \\)"
},
{
"from": "gpt",
"value": "Thinks the gradient of a line includes the variable x"
}
] |
[
{
"from": "human",
"value": "Write 5 digit numbers and above as words How do you write this number in words?\n\n\\( 60302 \\) Six hundred and thirty-two"
},
{
"from": "gpt",
"value": "Does not understand the value of zeros as placeholders"
}
] |
[
{
"from": "human",
"value": "Write 5 digit numbers and above as words How do you write this number in words?\n\n\\( 60302 \\) Six thousand three hundred and two"
},
{
"from": "gpt",
"value": "Confuses the ten thousands and thousands place value columns"
}
] |
[
{
"from": "human",
"value": "Write 5 digit numbers and above as words How do you write this number in words?\n\n\\( 60302 \\) Sixty thousand and thirty-two"
},
{
"from": "gpt",
"value": "Confuses the hundreds and tens place value columns"
}
] |
[
{
"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 \\( \\omega \\) the subject \\( F=r \\omega^{2} \\) \\( \\omega=r F^{2} \\)"
},
{
"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 \\( \\omega \\) the subject \\( F=r \\omega^{2} \\) \\( \\omega=\\sqrt{r F} \\)"
},
{
"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 \\( \\omega \\) the subject \\( F=r \\omega^{2} \\) \\( \\omega=\\frac{\\sqrt{F}}{r} \\)"
},
{
"from": "gpt",
"value": "Does not reverse the order of operations when solving an equation"
}
] |
[
{
"from": "human",
"value": "Divide mixed number fractions in the form: Fraction ÷ Integer \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 1 \\frac{2}{3} \\)"
},
{
"from": "gpt",
"value": "When the dividend is a mixed number and the divisor is an integer, thinks they only perform the calculation with the integers."
}
] |
[
{
"from": "human",
"value": "Divide mixed number fractions in the form: Fraction ÷ Integer \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( 2 \\frac{1}{3} \\)"
},
{
"from": "gpt",
"value": "When the dividend is a mixed number and the divisor is an integer, thinks they only divide the fraction by the integer."
}
] |
[
{
"from": "human",
"value": "Divide mixed number fractions in the form: Fraction ÷ Integer \\(\n2 \\frac{2}{3} \\div 2\n\\)\nWhich of the following is a correct way to write the answer to this calculation? \\( \\frac{3}{4} \\)"
},
{
"from": "gpt",
"value": "Believes division is commutative "
}
] |
[
{
"from": "human",
"value": "Identify a unit of time Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct? Only\nKatie"
},
{
"from": "gpt",
"value": "Mistakes unit of speed for unit of time"
}
] |
[
{
"from": "human",
"value": "Identify a unit of time Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Mistakes unit of speed for unit of time"
}
] |
[
{
"from": "human",
"value": "Identify a unit of time Tom and Katie are discussing units of time \nTom says days is a unit of time \nKatie says \\( \\mathrm{km} / \\mathrm{h} \\) is a unit of time \nWho is correct? Neither is correct"
},
{
"from": "gpt",
"value": "Does not recognise a unit of time"
}
] |
[
{
"from": "human",
"value": "Substitute negative integer values into formulae involving powers or roots \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ? \\( -243 \\)"
},
{
"from": "gpt",
"value": "Believes a negative power results in a negative answer"
}
] |
[
{
"from": "human",
"value": "Substitute negative integer values into formulae involving powers or roots \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ? \\( -\\frac{1}{243} \\)"
},
{
"from": "gpt",
"value": "Believes a negative power results in a negative answer"
}
] |
[
{
"from": "human",
"value": "Substitute negative integer values into formulae involving powers or roots \\(\nF=3^{a}\n\\)\n\nWhat is the value of \\( F \\) when \\( a=-5 \\) ? \\( -15 \\)"
},
{
"from": "gpt",
"value": "Has multiplied the base number and the power"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 1 digit integers using long multiplication Charlotte is trying to solve this problem using long multiplication.\n\nWhat should replace the star as the tens digit in her final answer? \\( 538 \\times 7 \\) \\begin{tabular}{r|r|r|r|}\n\\(\\space\\) & \\( 5 \\) & \\( 3 \\) & \\( 8 \\) \\\\\n\\( \\times \\) & \\(\\space\\) & \\(\\space\\) & \\( 7 \\) \\\\\n\\hline & \\(\\space\\) & \\(\\bigstar\\) & \\\\\n\\hline\n\\end{tabular} \\( 1 \\)"
},
{
"from": "gpt",
"value": "Forgets to carry the tens when doing column multiplication"
}
] |
[
{
"from": "human",
"value": "Multiply 3 digit integers by 1 digit integers using long multiplication Charlotte is trying to solve this problem using long multiplication.\n\nWhat should replace the star as the tens digit in her final answer? \\( 538 \\times 7 \\) \\begin{tabular}{r|r|r|r|}\n\\(\\space\\) & \\( 5 \\) & \\( 3 \\) & \\( 8 \\) \\\\\n\\( \\times \\) & \\(\\space\\) & \\(\\space\\) & \\( 7 \\) \\\\\n\\hline & \\(\\space\\) & \\(\\bigstar\\) & \\\\\n\\hline\n\\end{tabular} \\( 0 \\)"
},
{
"from": "gpt",
"value": "Tries to multiply within place value columns during column multiplication"
}
] |
[
{
"from": "human",
"value": "Prove statements involving positive and negative numbers Which of these could be used as a counter - example to disprove Katie's theory that \\( 2 n^{2}-1 \\) is positive? \\( 2(-2)^{2}-1 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Prove statements involving positive and negative numbers Which of these could be used as a counter - example to disprove Katie's theory that \\( 2 n^{2}-1 \\) is positive? \\( 2(-1)^{2}-1 \\)"
},
{
"from": "gpt",
"value": "Believes multiplying two negatives gives a negative answer"
}
] |
[
{
"from": "human",
"value": "Solve linear simultaneous equations requiring a scaling of both expressions What is the value of \\( l \\) in these simultaneous equations?\n\\(\n\\begin{array}{l}\n2 l+3 m=13 \\\\\n3 l+4 m=17\n\\end{array}\n\\) \\( l=1 \\)"
},
{
"from": "gpt",
"value": "Believes subtraction is commutative "
}
] |
[
{
"from": "human",
"value": "Multiply proper fractions in the form: Fraction × Integer \\( \\frac{1}{3} \\times(-6)= \\) \\( -\\frac{1}{18} \\)"
},
{
"from": "gpt",
"value": "When multiplying a fraction by an integer, multiplies the denominator instead of the numerator"
}
] |
[
{
"from": "human",
"value": "Represent an equation using a bar model Tom and Katie are discussing bar models. Tom says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l}\n\\hline \\( 5 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l|l|l|l|}\n\\( x \\) & \\( x \\) & \\( x \\) & \\( x \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Who do you agree with? Only Tom"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |
[
{
"from": "human",
"value": "Represent an equation using a bar model Tom and Katie are discussing bar models. Tom says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l}\n\\hline \\( 5 \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Katie says this bar model represents \\( 5 x \\) \\begin{tabular}{l|l|l|l|l|}\n\\( x \\) & \\( x \\) & \\( x \\) & \\( x \\) & \\( x \\) \\\\\n\\hline\n\\end{tabular} Who do you agree with? Both Tom and Katie"
},
{
"from": "gpt",
"value": "Does not understand bar modelling in algebra"
}
] |