Prompt:
Misconception:
Thinks a greater number of shaded parts represents a greater fraction

Question:
Which diagram represents the largest fraction?

Options:
A. ![An equilateral triangle divided into 4 smaller equilateral triangles that are identical to each other in size and shape. 2 of the smaller triangles are shaded orange, the rest are white.]()
B. ![A rectangle divided horizontally into 3 smaller rectangles that are identical to each other in size and shape. The top rectangle, of the 3, is shaded orange, the rest are white.]()
C. ![A rectangle divided into a grid of 30 smaller rectangles (5 high by 6 wide) that are identical to each other in size and shape. 8 of these smaller rectangles are shaded orange, the rest are white.]()
D. ![A rectangle divided horizontally into 3 smaller rectangles that are identical to each other in size and shape. The top 2 rectangles, of the 3, are shaded orange, the other is white.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that the smaller a divisor is, the smaller the answer will be

Question:
Jo and Paul are discussing how to estimate the answer to
\[
188.945 \div 15.3382
\]

Jo says \( 200 \div 15.3382 \) would give an overestimate.

Paul says \( 188.945 \div 15 \) would give an overestimate.

Who is correct?

Options:
A. Only Jo
B. Only Paul
C. Both Jo and Paul
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that the larger the dividend, the smaller the answer.

Question:
Jo and Paul are discussing how to estimate the answer to
\[
188.945 \div 15.3382
\]

Jo says \( 200 \div 15.3382 \) would give an overestimate.

Paul says \( 188.945 \div 15 \) would give an overestimate.

Who is correct?

Options:
A. Only Jo
B. Only Paul
C. Both Jo and Paul
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When multiplying numbers with different bases, multiplies the powers and multiplies the base numbers.

Question:
Tom and Katie are arguing about \( 4^{2} \times 2^{2} \)
Tom says \( 4^{2} \times 2^{2}=64 \)
Katie says \( 4^{2} \times 2^{2}=8^{4} \)
Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Subtracts instead of divides

Question:
A quick way to change approximately from miles to kilometers is to divide the number of miles by \( 3 \) and then multiply by \( 5 \).
Using this method, how many kilometres are equal to \( 15 \) miles?

Options:
A. \( 25 \)
B. \( 9 \)
C. \( 17 \)
D. \( 15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Think 1km = 1 mile

Question:
A quick way to change approximately from miles to kilometers is to divide the number of miles by \( 3 \) and then multiply by \( 5 \).
Using this method, how many kilometres are equal to \( 15 \) miles?

Options:
A. \( 25 \)
B. \( 9 \)
C. \( 17 \)
D. \( 15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When ordering numbers in standard form just looks at the decimal without multiplying by a power of 10

Question:
Tom and Katie are discussing standard form.

Tom says \( 9.3 \times 10^{5}>2.3 \times 10^{6} \)

Katie says \( 9.3 \times 10^{-5}>2.3 \times 10^{-6} \)

Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes there is only one orientation for the isosceles triangle base angles

Question:
This is an isosceles triangle.
Calculate the size of angle \( p \). ![An isosceles triangle with one angle labelled 56 degrees and one angle labelled p [not to scale]]()

Options:
A. \( 56^{\circ} \)
B. \( 68^{\circ} \)
C. \( 124^{\circ} \)
D. Not enough information

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes there is only one orientation for the isosceles triangle base angles

Question:
This is an isosceles triangle.
Calculate the size of angle \( p \). ![An isosceles triangle with one angle labelled 56 degrees and one angle labelled p [not to scale]]()

Options:
A. \( 56^{\circ} \)
B. \( 68^{\circ} \)
C. \( 124^{\circ} \)
D. Not enough information

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Forgets to subtract sum of angles we know from 180 to find missing angle in a triangle

Question:
This is an isosceles triangle.
Calculate the size of angle \( p \). ![An isosceles triangle with one angle labelled 56 degrees and one angle labelled p [not to scale]]()

Options:
A. \( 56^{\circ} \)
B. \( 68^{\circ} \)
C. \( 124^{\circ} \)
D. Not enough information

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks 1l = 1 cubic centimetre

Question:
Complete this statement:
\( 5 \) litres \( = \) ________\( \mathrm{cm}^{3} \)

Options:
A. \( 5 \)
B. \( 500 \)
C. \( 5000 \)
D. \( 50 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks 1l = 100 cubic centimetres

Question:
Complete this statement:
\( 5 \) litres \( = \) ________\( \mathrm{cm}^{3} \)

Options:
A. \( 5 \)
B. \( 500 \)
C. \( 5000 \)
D. \( 50 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks 1l = 10 cubic centimetres

Question:
Complete this statement:
\( 5 \) litres \( = \) ________\( \mathrm{cm}^{3} \)

Options:
A. \( 5 \)
B. \( 500 \)
C. \( 5000 \)
D. \( 50 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes division is commutative

Question:
Tom and Katie want to share £2 between \( 4 \) people.
Tom says you would calculate the amount each person gets by doing \( 4 \div 2 \)
Katie says you would calculate the amount each person gets by doing \( 2 \div 4 \)
Who do you agree with?

Options:
A. Only Tom
B. Only Katie
C. Both of them
D. Neither of them

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes division is commutative

Question:
Tom and Katie want to share £2 between \( 4 \) people.
Tom says you would calculate the amount each person gets by doing \( 4 \div 2 \)
Katie says you would calculate the amount each person gets by doing \( 2 \div 4 \)
Who do you agree with?

Options:
A. Only Tom
B. Only Katie
C. Both of them
D. Neither of them

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Uses an incorrect side length when splitting a composite shape into parts

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that makes a backwards "L" shape from 2 rectangles.  The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The left handed rectangle is shaded blue.]()

Options:
A. \( 44 \mathrm{~cm}^{2} \)
B. \( 22 \mathrm{~cm}^{2} \)
C. \( 28 \mathrm{~cm}^{2} \)
D. \( 24 \mathrm{~cm}^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Uses an incorrect side length when splitting a composite shape into parts

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that makes a backwards "L" shape from 2 rectangles.  The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The left handed rectangle is shaded blue.]()

Options:
A. \( 44 \mathrm{~cm}^{2} \)
B. \( 22 \mathrm{~cm}^{2} \)
C. \( 28 \mathrm{~cm}^{2} \)
D. \( 24 \mathrm{~cm}^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Uses an incorrect side length when splitting a composite shape into parts

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that makes a backwards "L" shape from 2 rectangles.  The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The left handed rectangle is shaded blue.]()

Options:
A. \( 44 \mathrm{~cm}^{2} \)
B. \( 22 \mathrm{~cm}^{2} \)
C. \( 28 \mathrm{~cm}^{2} \)
D. \( 24 \mathrm{~cm}^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks x = 0 is the x axis

Question:
Which is the correct point for \( \mathrm{E} \) when reflected in the line \( x=0 \) ? ![A 4 quadrant, coordinate grid with a triangle drawn on it with the coordinates (-4,1) (-1,1) and (-2,3). E is the point (-2,3)]()

Options:
A. A is the coordinate (2,3)
B. B is the coordinate (-2,-3)
C. C is the coordinate (2,-3)
D. None of these

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rotates instead of reflects

Question:
Which is the correct point for \( \mathrm{E} \) when reflected in the line \( x=0 \) ? ![A 4 quadrant, coordinate grid with a triangle drawn on it with the coordinates (-4,1) (-1,1) and (-2,3). E is the point (-2,3)]()

Options:
A. A is the coordinate (2,3)
B. B is the coordinate (-2,-3)
C. C is the coordinate (2,-3)
D. None of these

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a rectangle has four equal sides

Question:
Tom and Katie have been asked to give the name of a quadrilateral with four equal sides
Tom says rectangle
Katie says rhombus
Who do you agree with?

Options:
A. Only
Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a rectangle has four equal sides

Question:
Tom and Katie have been asked to give the name of a quadrilateral with four equal sides
Tom says rectangle
Katie says rhombus
Who do you agree with?

Options:
A. Only
Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a rectangle has four equal sides

Question:
Tom and Katie have been asked to give the name of a quadrilateral with four equal sides
Tom says rectangle
Katie says rhombus
Who do you agree with?

Options:
A. Only
Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks congruent shapes are the same shape but can be different sizes

Question:
Tom and Katie are discussing congruent shapes Tom says these two shapes are congruent ![Two identical 6-sided "L shape" polygons. One of the polygons has been rotated through 90 degrees.]() Katie says these two shapes are congruent ![Two 6-sided "L shape" polygons. One of the polygons has a wider upright section than the other.]() Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks congruent shapes are the same shape but can be different sizes

Question:
Tom and Katie are discussing congruent shapes Tom says these two shapes are congruent ![Two identical 6-sided "L shape" polygons. One of the polygons has been rotated through 90 degrees.]() Katie says these two shapes are congruent ![Two 6-sided "L shape" polygons. One of the polygons has a wider upright section than the other.]() Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand that shapes are congruent if they have the same size and shape

Question:
Tom and Katie are discussing congruent shapes Tom says these two shapes are congruent ![Two identical 6-sided "L shape" polygons. One of the polygons has been rotated through 90 degrees.]() Katie says these two shapes are congruent ![Two 6-sided "L shape" polygons. One of the polygons has a wider upright section than the other.]() Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not recognise metres as a unit of length

Question:
Sally has answered a question on perimeter and worked out an answer of \( 120 \).

Behind the star she has written the units that she used.

Which of the following units is definitely wrong? \( 120 \color{yellow}\bigstar \)

Options:
A. \( m \)
B. \( \mathrm{km} \)
C. \( 11 \)
D. \( m g \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not recognise km as a unit of length

Question:
Sally has answered a question on perimeter and worked out an answer of \( 120 \).

Behind the star she has written the units that she used.

Which of the following units is definitely wrong? \( 120 \color{yellow}\bigstar \)

Options:
A. \( m \)
B. \( \mathrm{km} \)
C. \( 11 \)
D. \( m g \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not recognise inches (") as a unit of length

Question:
Sally has answered a question on perimeter and worked out an answer of \( 120 \).

Behind the star she has written the units that she used.

Which of the following units is definitely wrong? \( 120 \color{yellow}\bigstar \)

Options:
A. \( m \)
B. \( \mathrm{km} \)
C. \( 11 \)
D. \( m g \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Swaps the dividend and divisor in order to get an integer answer

Question:
Solve the equation:
\(20 t-5=0\)

Options:
A. \( t=\frac{1}{4} \)
B. \( t=4 \)
C. \( t=-4 \)
D. \( t=-\frac{1}{4} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When solving an equation, uses the same operation rather than the inverse.

Question:
Solve the equation:
\(20 t-5=0\)

Options:
A. \( t=\frac{1}{4} \)
B. \( t=4 \)
C. \( t=-4 \)
D. \( t=-\frac{1}{4} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplies rather than divides

Question:
What is the value of:
\(
\frac{54+58}{2}
\)

Options:
A. \( 56 \)
B. \( 224 \)
C. \( 85 \)
D. \( 51 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not interpret the correct order of operations in a fraction when there is an addition on the numerator

Question:
What is the value of:
\(
\frac{54+58}{2}
\)

Options:
A. \( 56 \)
B. \( 224 \)
C. \( 85 \)
D. \( 51 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not divide by 2 when finding midpoint

Question:
Cara is trying to work out the midpoint of these two points: \( (-5,7) \) and \( (-2,-1) \) She labels them like this: \( \left.\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\ (-5, & 7) & (-2, & -1) \end{array}\right.\) And then decides to use this formula: \( \left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right) \) What is the \( \boldsymbol{y} \) value of the midpoint?

Options:
A. \( 6 \)
B. \( 4 \)
C. \( 3 \)
D. \( 3.5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that adding a negative will increase the value of the original number

Question:
Cara is trying to work out the midpoint of these two points: \( (-5,7) \) and \( (-2,-1) \) She labels them like this: \( \left.\begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\ (-5, & 7) & (-2, & -1) \end{array}\right.\) And then decides to use this formula: \( \left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right) \) What is the \( \boldsymbol{y} \) value of the midpoint?

Options:
A. \( 6 \)
B. \( 4 \)
C. \( 3 \)
D. \( 3.5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Student thinks that any two angles along a straight line are equal

Question:
What is the size of angle \( q \) ? ![Two angles on a straight line, one is labelled 62 degrees and the other is q]()

Options:
A. \( 62^{\circ} \)
B. \( 128^{\circ} \)
C. \( 298^{\circ} \)
D. \( 118^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When “borrowing” during a subtraction problem, does not subtract one from the preceding digit

Question:
What is the size of angle \( q \) ? ![Two angles on a straight line, one is labelled 62 degrees and the other is q]()

Options:
A. \( 62^{\circ} \)
B. \( 128^{\circ} \)
C. \( 298^{\circ} \)
D. \( 118^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes angles on a straight line add to 360 degrees

Question:
What is the size of angle \( q \) ? ![Two angles on a straight line, one is labelled 62 degrees and the other is q]()

Options:
A. \( 62^{\circ} \)
B. \( 128^{\circ} \)
C. \( 298^{\circ} \)
D. \( 118^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes angles on a straight line add to 90 degrees

Question:
Adjacent angles on a straight line sum to...

Options:
A. \( 90^{\circ} \)
B. \( 100^{\circ} \)
C. \( 180^{\circ} \)
D. \( 360^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes angles on a straight line add to 100 degrees

Question:
Adjacent angles on a straight line sum to...

Options:
A. \( 90^{\circ} \)
B. \( 100^{\circ} \)
C. \( 180^{\circ} \)
D. \( 360^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes angles on a straight line add to 360 degrees

Question:
Adjacent angles on a straight line sum to...

Options:
A. \( 90^{\circ} \)
B. \( 100^{\circ} \)
C. \( 180^{\circ} \)
D. \( 360^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses additive and multiplicative relationships

Question:
The shape below has a perimeter of \( p \). If the length of all the sides are doubled, what is the perimeter of the enlarged shape? ![A trapezium]()

Options:
A. \( 2 p \)
B. \( p+2 \)
C. \( 8 p \)
D. Not enough information

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not realise we can scale the perimeter as a whole, rather than finding individual side lengths

Question:
The shape below has a perimeter of \( p \). If the length of all the sides are doubled, what is the perimeter of the enlarged shape? ![A trapezium]()

Options:
A. \( 2 p \)
B. \( p+2 \)
C. \( 8 p \)
D. Not enough information

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Factorises difference of two squares with the same sign in both brackets

Question:
Factorise this expression, if possible:
\(
p^{2}-9
\)

Options:
A. \( (p-3)(p-3) \)
B. \( p(p-9) \)
C. \( (p+3)(p-3) \)
D. Does not factorise

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes only the first term needs to be divided when factorising an expression

Question:
Factorise this expression, if possible:
\(
p^{2}-9
\)

Options:
A. \( (p-3)(p-3) \)
B. \( p(p-9) \)
C. \( (p+3)(p-3) \)
D. Does not factorise

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Factorise this expression, if possible:
\(
p^{2}-9
\)

Options:
A. \( (p-3)(p-3) \)
B. \( p(p-9) \)
C. \( (p+3)(p-3) \)
D. Does not factorise

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Finds the median instead of the mean

Question:
What is the mean of the following numbers?
\[
2, \quad 0.2, \quad 0.02
\]

Options:
A. \( 0.66 \)
B. \( 0.74 \)
C. \( 0.666 \)
D. \( 0.2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When a variable in an expression has a power, thinks the power applies to the whole expression

Question:
\( s=u t+\frac{1}{2} a t^{2} \) What is the value of \( s \) when
a=6
u=3
t=4

Options:
A. \( 60 \)
B. \( 156 \)
C. \( 576 \)
D. \( 24 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When a variable in an expression has a power, thinks the power applies to the whole expression

Question:
\( s=u t+\frac{1}{2} a t^{2} \) What is the value of \( s \) when
a=6
u=3
t=4

Options:
A. \( 60 \)
B. \( 156 \)
C. \( 576 \)
D. \( 24 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks you apply one inverse operation to one term and the other inverse operation to the other term

Question:
![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The next rectangle has "− 4" written inside it, the next rectangle has "✕ 4" written inside it and the final rectangle on the right has "output" written above it and "8m − 20" written inside it.]() What is the input of this function machine?

Options:
A. \( 2 m-16 \)
B. \( 2 m-1 \)
C. \( 2 m-20 \)
D. \( 2 m-5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not apply the inverse function to every term in an expression

Question:
![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The next rectangle has "− 4" written inside it, the next rectangle has "✕ 4" written inside it and the final rectangle on the right has "output" written above it and "8m − 20" written inside it.]() What is the input of this function machine?

Options:
A. \( 2 m-16 \)
B. \( 2 m-1 \)
C. \( 2 m-20 \)
D. \( 2 m-5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Has completed only one of the two operations.

Question:
![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The next rectangle has "− 4" written inside it, the next rectangle has "✕ 4" written inside it and the final rectangle on the right has "output" written above it and "8m − 20" written inside it.]() What is the input of this function machine?

Options:
A. \( 2 m-16 \)
B. \( 2 m-1 \)
C. \( 2 m-20 \)
D. \( 2 m-5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored

Question:
Jo and Paul are arguing about points on the line
\(4 x-5 y=20\)

Jo says \( (10,-4) \) lies on the line \( \mathbf{4 x}-\mathbf{5 y}=\mathbf{2 0} \)

Paul says \( (-4,10) \) lies on the line \( \mathbf{4} \boldsymbol{x}-\mathbf{5 y}=\mathbf{2 0} \)

Who is correct?

Options:
A. Only
Jo
B. Only
Paul
C. Both Jo and Paul
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Counts the squares rather than the diagonals when reflecting in y=x or y=-x

Question:
The triangle is reflected in the dashed line
What are the new coordinates of point \( \mathrm{P} \) ? ![A coordinate grid with the reflection line y=-x drawn and a triangle with the coordinates (-2,3) (-1,4) and (0,3). P is the point (0,3)]()

Options:
A. \( (-6,3) \)
B. \( (-3,6) \)
C. \( (-3,3) \)
D. \( (-3,0) \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line
What are the new coordinates of point \( \mathrm{P} \) ? ![A coordinate grid with the reflection line y=-x drawn and a triangle with the coordinates (-2,3) (-1,4) and (0,3). P is the point (0,3)]()

Options:
A. \( (-6,3) \)
B. \( (-3,6) \)
C. \( (-3,3) \)
D. \( (-3,0) \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line
What are the new coordinates of point \( \mathrm{P} \) ? ![A coordinate grid with the reflection line y=-x drawn and a triangle with the coordinates (-2,3) (-1,4) and (0,3). P is the point (0,3)]()

Options:
A. \( (-6,3) \)
B. \( (-3,6) \)
C. \( (-3,3) \)
D. \( (-3,0) \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Forgets you need a ruler to measure lengths

Question:
Which combination of mathematical instruments has been used to construct this triangle? ![A triangle construction with one angle and two sides labelled ]()

Options:
A. Protractor
Compass
B. Ruler
Compass
C. Ruler
Protractor
Compass
D. Ruler
Protractor

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Forgets you need a protractor to measure angles

Question:
Which combination of mathematical instruments has been used to construct this triangle? ![A triangle construction with one angle and two sides labelled ]()

Options:
A. Protractor
Compass
B. Ruler
Compass
C. Ruler
Protractor
Compass
D. Ruler
Protractor

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Forgets you need a compass to draw arcs

Question:
Which combination of mathematical instruments has been used to construct this triangle? ![A triangle construction with one angle and two sides labelled ]()

Options:
A. Protractor
Compass
B. Ruler
Compass
C. Ruler
Protractor
Compass
D. Ruler
Protractor

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Forgets to multiply up for the correct time frame in a worded question

Question:
Every week for \( 4 \) weeks, Cara buys a magazine for \( £ 6 \) and gets her nails painted for \( £ 28 \).

How much money does Cara spend altogether?

Options:
A. \( £ 34 \)
B. \( £ 52 \)
C. \( £ 118 \)
D. \( £ 136 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not interpret the correct order of operations from a worded problem

Question:
Every week for \( 4 \) weeks, Cara buys a magazine for \( £ 6 \) and gets her nails painted for \( £ 28 \).

How much money does Cara spend altogether?

Options:
A. \( £ 34 \)
B. \( £ 52 \)
C. \( £ 118 \)
D. \( £ 136 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not interpret the correct order of operations from a worded problem

Question:
Every week for \( 4 \) weeks, Cara buys a magazine for \( £ 6 \) and gets her nails painted for \( £ 28 \).

How much money does Cara spend altogether?

Options:
A. \( £ 34 \)
B. \( £ 52 \)
C. \( £ 118 \)
D. \( £ 136 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Divides by the order of the root

Question:
\( \sqrt[3]{125}= \)

Options:
A. \( 5 \)
B. \( 25 \)
C. \( \frac{125}{3} \)
D. \( 375 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Has multiplied by the root power

Question:
\( \sqrt[3]{125}= \)

Options:
A. \( 5 \)
B. \( 25 \)
C. \( \frac{125}{3} \)
D. \( 375 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses corresponding and vertically opposite angles

Question:
\( \mathrm{M} \) and \( \mathrm{N} \) are the intersections of the line \( X Y \) with the lines \( P Q \) and RS.
Which angle is corresponding to angle MNS? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.
A red straight line, XY, crosses the parallel lines. X is on the left of the diagram.
Line XY crosses line PQ at a point marked M.
Line XY crosses line RS at a point marked N.
The angle MNS is marked in red.]()

Options:
A. YNR
B. QMX
C. QMN
D. NMP

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses co-interior and corresponding angles

Question:
\( \mathrm{M} \) and \( \mathrm{N} \) are the intersections of the line \( X Y \) with the lines \( P Q \) and RS.
Which angle is corresponding to angle MNS? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.
A red straight line, XY, crosses the parallel lines. X is on the left of the diagram.
Line XY crosses line PQ at a point marked M.
Line XY crosses line RS at a point marked N.
The angle MNS is marked in red.]()

Options:
A. YNR
B. QMX
C. QMN
D. NMP

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses corresponding and alternate angles

Question:
\( \mathrm{M} \) and \( \mathrm{N} \) are the intersections of the line \( X Y \) with the lines \( P Q \) and RS.
Which angle is corresponding to angle MNS? ![A pair of parallel lines pointing up to the left. PQ and RS are the ends of the parallel lines. PQ is on the left of the diagram with Q being the top left.
A red straight line, XY, crosses the parallel lines. X is on the left of the diagram.
Line XY crosses line PQ at a point marked M.
Line XY crosses line RS at a point marked N.
The angle MNS is marked in red.]()

Options:
A. YNR
B. QMX
C. QMN
D. NMP

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplies when converting to a larger unit

Question:
\[
30 \text { centilitres }=\bigstar \text { litres }
\]
What should replace the star?

Options:
A. \( 3000 \)
B. \( 3 \)
C. \( 0.3 \)
D. \( 0.03 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks there are 10cl in a litre

Question:
\[
30 \text { centilitres }=\bigstar \text { litres }
\]
What should replace the star?

Options:
A. \( 3000 \)
B. \( 3 \)
C. \( 0.3 \)
D. \( 0.03 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses cl and ml

Question:
\[
30 \text { centilitres }=\bigstar \text { litres }
\]
What should replace the star?

Options:
A. \( 3000 \)
B. \( 3 \)
C. \( 0.3 \)
D. \( 0.03 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we do the operation matching the sign (+ if positive, - if negative)

Question:
What do you need to do to eliminate the \( q s \) in each of these pairs of simultaneous equations?
 Pair \( 1 \)
\(
\begin{array}{l}
5 p+2 q=12 \\
3 p+2 q=8
\end{array}
\) Pair \( 2 \)
\(
\begin{array}{l}
5 p-2 q=12 \\
3 p-2 q=8
\end{array}
\)

Options:
A. Add Pair \( 1 \)
Subtract Pair \( 2 \)
B. Add Pair \( 1 \)
Add Pair \( 2 \)
C. Subtract Pair \( 1 \)
Add Pair \( 2 \)
D. Subtract Pair \( 1 \)
Subtract Pair \( 2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations.

Question:
What do you need to do to eliminate the \( q s \) in each of these pairs of simultaneous equations?
 Pair \( 1 \)
\(
\begin{array}{l}
5 p+2 q=12 \\
3 p+2 q=8
\end{array}
\) Pair \( 2 \)
\(
\begin{array}{l}
5 p-2 q=12 \\
3 p-2 q=8
\end{array}
\)

Options:
A. Add Pair \( 1 \)
Subtract Pair \( 2 \)
B. Add Pair \( 1 \)
Add Pair \( 2 \)
C. Subtract Pair \( 1 \)
Add Pair \( 2 \)
D. Subtract Pair \( 1 \)
Subtract Pair \( 2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we do the operation inverse to the sign (- if positive, + if negative)

Question:
What do you need to do to eliminate the \( q s \) in each of these pairs of simultaneous equations?
 Pair \( 1 \)
\(
\begin{array}{l}
5 p+2 q=12 \\
3 p+2 q=8
\end{array}
\) Pair \( 2 \)
\(
\begin{array}{l}
5 p-2 q=12 \\
3 p-2 q=8
\end{array}
\)

Options:
A. Add Pair \( 1 \)
Subtract Pair \( 2 \)
B. Add Pair \( 1 \)
Add Pair \( 2 \)
C. Subtract Pair \( 1 \)
Add Pair \( 2 \)
D. Subtract Pair \( 1 \)
Subtract Pair \( 2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When reading values from graphs, writes down the wrong units

Question:
How far away from home was Rachel at 10:15? ![A line graph with title "A graph to show the distance Rachel travels from her home on her daily run."
The x-axis is titled "Time" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.
The y-axis is titled "Distance from home (Km)" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0).    ]()

Options:
A. \( 6.5 \mathrm{~m} \)
B. \( 650 \mathrm{~m} \)
C. \( 6500 \mathrm{~m} \)
D. \( 7 \mathrm{~km} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks there are 100m and a km

Question:
How far away from home was Rachel at 10:15? ![A line graph with title "A graph to show the distance Rachel travels from her home on her daily run."
The x-axis is titled "Time" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.
The y-axis is titled "Distance from home (Km)" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0).    ]()

Options:
A. \( 6.5 \mathrm{~m} \)
B. \( 650 \mathrm{~m} \)
C. \( 6500 \mathrm{~m} \)
D. \( 7 \mathrm{~km} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Misreads scale

Question:
How far away from home was Rachel at 10:15? ![A line graph with title "A graph to show the distance Rachel travels from her home on her daily run."
The x-axis is titled "Time" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.
The y-axis is titled "Distance from home (Km)" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0).    ]()

Options:
A. \( 6.5 \mathrm{~m} \)
B. \( 650 \mathrm{~m} \)
C. \( 6500 \mathrm{~m} \)
D. \( 7 \mathrm{~km} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When reading value from graph, reads from the wrong axes.

Question:
Johan wants to plot a graph to show the distance a ball travels over time.

After \( 2 \) seconds the ball has travelled \( 3 \) metres.

Where on the graph should Johan plot this?

Options:
A. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. A is plotted above 2 on the horizontal axis and right of 3 on the vertical axis.]()
B. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. B is plotted above 3 on the horizontal axis and right of 2 on the vertical axis.]()
C. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. C is plotted below 3 on the horizontal axis and right of -2 on the vertical axis.]()
D. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. D is plotted below 2 on the horizontal axis and right of -3 on the vertical axis.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When reading value from graph, reads from the wrong axes.

Question:
Johan wants to plot a graph to show the distance a ball travels over time.

After \( 2 \) seconds the ball has travelled \( 3 \) metres.

Where on the graph should Johan plot this?

Options:
A. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. A is plotted above 2 on the horizontal axis and right of 3 on the vertical axis.]()
B. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. B is plotted above 3 on the horizontal axis and right of 2 on the vertical axis.]()
C. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. C is plotted below 3 on the horizontal axis and right of -2 on the vertical axis.]()
D. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. D is plotted below 2 on the horizontal axis and right of -3 on the vertical axis.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses negative and positive coordinates when working with graphs in four quadrants

Question:
Johan wants to plot a graph to show the distance a ball travels over time.

After \( 2 \) seconds the ball has travelled \( 3 \) metres.

Where on the graph should Johan plot this?

Options:
A. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. A is plotted above 2 on the horizontal axis and right of 3 on the vertical axis.]()
B. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. B is plotted above 3 on the horizontal axis and right of 2 on the vertical axis.]()
C. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. C is plotted below 3 on the horizontal axis and right of -2 on the vertical axis.]()
D. ![A graph with time (sec) on the horizontal axis and distance (m) on the vertical axis. D is plotted below 2 on the horizontal axis and right of -3 on the vertical axis.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Calculates perimeter when asked for area

Question:
What is the volume of this cube? ![A cube with one side labelled 5 cm.]()

Options:
A. \( 120 \mathrm{~cm}^{3} \)
B. \( 100 \mathrm{~cm}^{3} \)
C. \( 125 \mathrm{~cm}^{3} \)
D. \( 150 \mathrm{~cm}^{3} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not recognise that all lengths on a cube are equal

Question:
What is the volume of this cube? ![A cube with one side labelled 5 cm.]()

Options:
A. \( 120 \mathrm{~cm}^{3} \)
B. \( 100 \mathrm{~cm}^{3} \)
C. \( 125 \mathrm{~cm}^{3} \)
D. \( 150 \mathrm{~cm}^{3} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Finds surface area when asked for volume

Question:
What is the volume of this cube? ![A cube with one side labelled 5 cm.]()

Options:
A. \( 120 \mathrm{~cm}^{3} \)
B. \( 100 \mathrm{~cm}^{3} \)
C. \( 125 \mathrm{~cm}^{3} \)
D. \( 150 \mathrm{~cm}^{3} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When multiplying fractions, adds the numerators and the denominators

Question:
Calculate:
\(
\frac{1}{9} \times \frac{1}{5}
\)

Options:
A. \( \frac{1}{45} \)
B. \( \frac{2}{14} \)
C. \( \frac{5}{9} \)
D. \( \frac{1}{14} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
when multiplying fractions multiplies by the reciprocal of the 2nd fraction instead

Question:
Calculate:
\(
\frac{1}{9} \times \frac{1}{5}
\)

Options:
A. \( \frac{1}{45} \)
B. \( \frac{2}{14} \)
C. \( \frac{5}{9} \)
D. \( \frac{1}{14} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When multiplying fractions, multiplies the numerator and adds the denominator

Question:
Calculate:
\(
\frac{1}{9} \times \frac{1}{5}
\)

Options:
A. \( \frac{1}{45} \)
B. \( \frac{2}{14} \)
C. \( \frac{5}{9} \)
D. \( \frac{1}{14} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mixes up squaring and multiplying by 2 or doubling

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "30" written inside it. The middle rectangle has "squared" written inside it and the final rectangle is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 60 \)
B. \( 900 \)
C. \( 22 \)
D. \( 15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mixes up squaring and halving

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "30" written inside it. The middle rectangle has "squared" written inside it and the final rectangle is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 60 \)
B. \( 900 \)
C. \( 22 \)
D. \( 15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When dividing an integer by a fraction, thinks they can just multiply instead.

Question:
Calculate
\(
2 \div \frac{1}{5}
\)

Options:
A. \( \frac{2}{5} \)
B. \( 10 \)
C. \( \frac{1}{10} \)
D. \( \frac{5}{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When dividing fractions, does the reciprocal of the first fraction instead of the second

Question:
Calculate
\(
2 \div \frac{1}{5}
\)

Options:
A. \( \frac{2}{5} \)
B. \( 10 \)
C. \( \frac{1}{10} \)
D. \( \frac{5}{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When dividing fractions, does the reciprocal of both fractions

Question:
Calculate
\(
2 \div \frac{1}{5}
\)

Options:
A. \( \frac{2}{5} \)
B. \( 10 \)
C. \( \frac{1}{10} \)
D. \( \frac{5}{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not think we can have negative powers in standard form

Question:
Write the following number in standard form:
\[
0.00506
\]

Options:
A. \( 5.06 \times 10^{3} \)
B. \( 5.6 \times 10^{-3} \)
C. \( 5.06 \times 10^{-5} \)
D. \( 5.06 \times 10^{-3} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When changing a number to standard form omits zero's of significance

Question:
Write the following number in standard form:
\[
0.00506
\]

Options:
A. \( 5.06 \times 10^{3} \)
B. \( 5.6 \times 10^{-3} \)
C. \( 5.06 \times 10^{-5} \)
D. \( 5.06 \times 10^{-3} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When changing a number to standard form omits zero's of significance

Question:
Write the following number in standard form:
\[
0.00506
\]

Options:
A. \( 5.06 \times 10^{3} \)
B. \( 5.6 \times 10^{-3} \)
C. \( 5.06 \times 10^{-5} \)
D. \( 5.06 \times 10^{-3} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When factorising a quadratic with a coefficient of x squared, believes the signs and/or positions of the constants are interchangeable

Question:
Factorise \( 9 x^{2}-24 x+16 \)

Options:
A. \( (3 x+4)^{2} \)
B. \( (9 x-4)^{2} \)
C. \( (3 x-4)^{2} \)
D. \( (3 x+8)^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When factorising a quadratic with a non-unit coefficient of x squared, believes that coefficient will be in front of both x terms in the factorised form

Question:
Factorise \( 9 x^{2}-24 x+16 \)

Options:
A. \( (3 x+4)^{2} \)
B. \( (9 x-4)^{2} \)
C. \( (3 x-4)^{2} \)
D. \( (3 x+8)^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not realise you can use equivalent fractions to break fractions up into smaller divisions

Question:
What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/5. On the rightmost dash is the number 3/5. An arrow points to the 4th dash from the left]()

Options:
A. \( \frac{1}{2} \)
B. \( \frac{2}{5} \)
C. \( \frac{3}{4} \)
D. There is no such fraction

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When reading a dash on a number line does not take into account the number at the start or the width of each division

Question:
What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/5. On the rightmost dash is the number 3/5. An arrow points to the 4th dash from the left]()

Options:
A. \( \frac{1}{2} \)
B. \( \frac{2}{5} \)
C. \( \frac{3}{4} \)
D. There is no such fraction

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not realise you can use equivalent fractions to break fractions up into smaller divisions

Question:
What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/5. On the rightmost dash is the number 3/5. An arrow points to the 4th dash from the left]()

Options:
A. \( \frac{1}{2} \)
B. \( \frac{2}{5} \)
C. \( \frac{3}{4} \)
D. There is no such fraction

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
Which shape has the lowest order of rotational symmetry?

Options:
A. ![Equilateral triangle]()
B. ![Circle]()
C. ![Square]()
D. ![Trapezium]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
Which shape has the lowest order of rotational symmetry?

Options:
A. ![Equilateral triangle]()
B. ![Circle]()
C. ![Square]()
D. ![Trapezium]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
Which shape has the lowest order of rotational symmetry?

Options:
A. ![Equilateral triangle]()
B. ![Circle]()
C. ![Square]()
D. ![Trapezium]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds to the nearest integer rather than one significant figure

Question:
When estimating the answer to a complicated problem involving \( 0.482 \), you should instead use...

Options:
A. \( 0 \)
B. \( 0.4 \)
C. \( 0.5 \)
D. \( 0.48 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds down instead of up

Question:
When estimating the answer to a complicated problem involving \( 0.482 \), you should instead use...

Options:
A. \( 0 \)
B. \( 0.4 \)
C. \( 0.5 \)
D. \( 0.48 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds to the nearest hundredth, rather than one significant figure

Question:
When estimating the answer to a complicated problem involving \( 0.482 \), you should instead use...

Options:
A. \( 0 \)
B. \( 0.4 \)
C. \( 0.5 \)
D. \( 0.48 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.

Question:
Which of the following describes how to get from point \( P \) to point \( Q \) ? ![Point P and Point Q are marked on a grid. Q is 4 squares to the right and 2 squares above P]()

Options:
A. \( 4 \) squares right \( 2 \) squares up
B. \( 5 \) squares right \( 3 \) squares up
C. \( 4 \) squares left \( 2 \) squares down
D. \( 5 \) squares right \( 2 \) squares up

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When describing a translation, goes from the image to the original

Question:
Which of the following describes how to get from point \( P \) to point \( Q \) ? ![Point P and Point Q are marked on a grid. Q is 4 squares to the right and 2 squares above P]()

Options:
A. \( 4 \) squares right \( 2 \) squares up
B. \( 5 \) squares right \( 3 \) squares up
C. \( 4 \) squares left \( 2 \) squares down
D. \( 5 \) squares right \( 2 \) squares up

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.

Question:
Which of the following describes how to get from point \( P \) to point \( Q \) ? ![Point P and Point Q are marked on a grid. Q is 4 squares to the right and 2 squares above P]()

Options:
A. \( 4 \) squares right \( 2 \) squares up
B. \( 5 \) squares right \( 3 \) squares up
C. \( 4 \) squares left \( 2 \) squares down
D. \( 5 \) squares right \( 2 \) squares up

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not half sum of parallel sides when finding area of a trapezium

Question:
What is the area of the shaded face? ![A prism of length 11mm. The cross-section, which is shaded, is a trapezium. The perpendicular height of the trapezium is 6mm. The two parallel sides of the trapezium are 6mm and 10mm.]()

Options:
A. \( 80 \mathrm{~mm}^{2} \)
B. \( 300 \mathrm{~mm}^{2} \)
C. \( 40 \mathrm{~mm}^{2} \)
D. \( 150 \mathrm{~mm}^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplies all given dimensions when calculating an area

Question:
What is the area of the shaded face? ![A prism of length 11mm. The cross-section, which is shaded, is a trapezium. The perpendicular height of the trapezium is 6mm. The two parallel sides of the trapezium are 6mm and 10mm.]()

Options:
A. \( 80 \mathrm{~mm}^{2} \)
B. \( 300 \mathrm{~mm}^{2} \)
C. \( 40 \mathrm{~mm}^{2} \)
D. \( 150 \mathrm{~mm}^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplies all given dimensions when calculating an area

Question:
What is the area of the shaded face? ![A prism of length 11mm. The cross-section, which is shaded, is a trapezium. The perpendicular height of the trapezium is 6mm. The two parallel sides of the trapezium are 6mm and 10mm.]()

Options:
A. \( 80 \mathrm{~mm}^{2} \)
B. \( 300 \mathrm{~mm}^{2} \)
C. \( 40 \mathrm{~mm}^{2} \)
D. \( 150 \mathrm{~mm}^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Denominator used for other parts rather than total parts

Question:
What fraction of the rectangle is shaded? ![Rectangle split into 100 equal parts with 27 parts shaded in yellow]()

Options:
A. \( \frac{27}{100} \)
B. \( \frac{27}{73} \)
C. \( 27 \)
D. \( \frac{73}{100} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to write a fraction - just given an integer answer

Question:
What fraction of the rectangle is shaded? ![Rectangle split into 100 equal parts with 27 parts shaded in yellow]()

Options:
A. \( \frac{27}{100} \)
B. \( \frac{27}{73} \)
C. \( 27 \)
D. \( \frac{73}{100} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know the term transversal

Question:
Line JK is.. ![A pair of parallel lines are drawn with the arrow on each pointing to the right.
A straight red line, KJ, is drawn so that diagonally crosses both parallel lines.]()

Options:
A. Parallel
B. A transversal
C. Skew
D. Perpendicular

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes any lines that cross are perpendicular

Question:
Line JK is.. ![A pair of parallel lines are drawn with the arrow on each pointing to the right.
A straight red line, KJ, is drawn so that diagonally crosses both parallel lines.]()

Options:
A. Parallel
B. A transversal
C. Skew
D. Perpendicular

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses the sign for parallel lines as being dashes

Question:
What do the dashes tell you about the sides of this polygon? ![A hexagon with a dash on each side.]()

Options:
A. They are parallel
B. They are straight
C. They are the midpoints
D. They are the same length

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses the signs for straight lines as being dashes

Question:
What do the dashes tell you about the sides of this polygon? ![A hexagon with a dash on each side.]()

Options:
A. They are parallel
B. They are straight
C. They are the midpoints
D. They are the same length

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Misunderstands dashed lines as being the midpoint

Question:
What do the dashes tell you about the sides of this polygon? ![A hexagon with a dash on each side.]()

Options:
A. They are parallel
B. They are straight
C. They are the midpoints
D. They are the same length

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Assumes that a graph always starts at the origin

Question:
This graph shows the position of a ball, relative to a fixed point, over time.

Approximately how far away from its starting point is the ball after \( 8 \) seconds? ![A graph showing time (secs) on the horizontal axis and position (m) on the vertical axis. The graph starts at (0,6) travels in a straight line to (8,15), then a straight line to (16,-15) then a straight line to (24,0). ]()

Options:
A. \( 2 m \)
B. \( 9 \mathrm{~m} \)
C. \( 14.5 \mathrm{~m} \)
D. \( 15 \mathrm{~m} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Answers as if there are 100 minutes in an hour

Question:
\( \frac{1}{12} \) of an hour \( = ____\) minutes

Options:
A. \( 12 \)
B. \( 8.3 \)
C. \( 5 \)
D. \( 1.2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks the fraction button on a calculator converts fractions to decimals

Question:
Which button would you press to raise a number to a power? Which button would you press to raise a number to a power? ![A scientific calculator]() ![A scientific calculator]()

Options:
A. ![Image of a calculator button. The symbol on the button is \(\frac{\square}{\square}\)]() ![Image of a calculator button. The symbol on the button is \(\frac{\square}{\square}\)]()
B. ![Image of a calculator button. The symbol on the button is \( x^{-1} \)]() ![Image of a calculator button. The symbol on the button is \( x^{-1} \)]()
C. ![Image of a calculator button. The symbol on the button is \( x^{\square} \)]() ![Image of a calculator button. The symbol on the button is \( x^{\square} \)]()
D. ![Image of a calculator button. The symbol on the button is \( S \Leftrightarrow D \)]() ![Image of a calculator button. The symbol on the button is \( S \Leftrightarrow D \)]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not recognise a reciprocal equation

Question:
Which button would you press to raise a number to a power? Which button would you press to raise a number to a power? ![A scientific calculator]() ![A scientific calculator]()

Options:
A. ![Image of a calculator button. The symbol on the button is \(\frac{\square}{\square}\)]() ![Image of a calculator button. The symbol on the button is \(\frac{\square}{\square}\)]()
B. ![Image of a calculator button. The symbol on the button is \( x^{-1} \)]() ![Image of a calculator button. The symbol on the button is \( x^{-1} \)]()
C. ![Image of a calculator button. The symbol on the button is \( x^{\square} \)]() ![Image of a calculator button. The symbol on the button is \( x^{\square} \)]()
D. ![Image of a calculator button. The symbol on the button is \( S \Leftrightarrow D \)]() ![Image of a calculator button. The symbol on the button is \( S \Leftrightarrow D \)]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks the fraction to decimal conversion button on a calculator can be used to raise to a power

Question:
Which button would you press to raise a number to a power? Which button would you press to raise a number to a power? ![A scientific calculator]() ![A scientific calculator]()

Options:
A. ![Image of a calculator button. The symbol on the button is \(\frac{\square}{\square}\)]() ![Image of a calculator button. The symbol on the button is \(\frac{\square}{\square}\)]()
B. ![Image of a calculator button. The symbol on the button is \( x^{-1} \)]() ![Image of a calculator button. The symbol on the button is \( x^{-1} \)]()
C. ![Image of a calculator button. The symbol on the button is \( x^{\square} \)]() ![Image of a calculator button. The symbol on the button is \( x^{\square} \)]()
D. ![Image of a calculator button. The symbol on the button is \( S \Leftrightarrow D \)]() ![Image of a calculator button. The symbol on the button is \( S \Leftrightarrow D \)]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Reads the position of a number from the space between the line marked, rather than the line marked

Question:
Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with "-6", the 3rd dash is labelled "-4", the 5th dash is labelled "-2", the 7th dash is labelled "0", the 9th dash is labelled "2", the 11th dash is labelled "4" and the 13th dash is labelled "6"    A red arrow, labelled with a question mark is pointing halfway between the 3rd and 4th dashes. ]() Which of the following numbers could be indicated by the arrow?

Options:
A. \( -3 \)
B. \( -2.75 \)
C. \( -4.5 \)
D. \( -3.5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a gap of 2 is a gap of 1 on a numberline

Question:
Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with "-6", the 3rd dash is labelled "-4", the 5th dash is labelled "-2", the 7th dash is labelled "0", the 9th dash is labelled "2", the 11th dash is labelled "4" and the 13th dash is labelled "6"    A red arrow, labelled with a question mark is pointing halfway between the 3rd and 4th dashes. ]() Which of the following numbers could be indicated by the arrow?

Options:
A. \( -3 \)
B. \( -2.75 \)
C. \( -4.5 \)
D. \( -3.5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Counts on in the wrong direction on a number line

Question:
Here is a number line: ![A horizontal number-line with 13 vertical, equally spaced, dashes representing the position of numbers. The 1st dash is labelled with "-6", the 3rd dash is labelled "-4", the 5th dash is labelled "-2", the 7th dash is labelled "0", the 9th dash is labelled "2", the 11th dash is labelled "4" and the 13th dash is labelled "6"    A red arrow, labelled with a question mark is pointing halfway between the 3rd and 4th dashes. ]() Which of the following numbers could be indicated by the arrow?

Options:
A. \( -3 \)
B. \( -2.75 \)
C. \( -4.5 \)
D. \( -3.5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not correctly apply the distributive property of multiplication

Question:
Which answer shows the following calculation using the correct algebraic convention? \( c \div(h+4) \)

Options:
A. \( \frac{c}{h+4} \)
B. \( \frac{c+4}{h+4} \)
C. \( \frac{c}{h}+4 \)
D. \( \frac{h+4}{c} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Carries out operations from left to right regardless of priority order

Question:
Which answer shows the following calculation using the correct algebraic convention? \( c \div(h+4) \)

Options:
A. \( \frac{c}{h+4} \)
B. \( \frac{c+4}{h+4} \)
C. \( \frac{c}{h}+4 \)
D. \( \frac{h+4}{c} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that a fraction means dividing the denominator by the numerator

Question:
Which answer shows the following calculation using the correct algebraic convention? \( c \div(h+4) \)

Options:
A. \( \frac{c}{h+4} \)
B. \( \frac{c+4}{h+4} \)
C. \( \frac{c}{h}+4 \)
D. \( \frac{h+4}{c} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Selects y>a solutions instead of y<a solutions for a quadratic inequality

Question:
Use the graph to approximate the solution to \( x^{2}<2 \) ![A set of axes with the quadratic graph y=x^2 drawn on.]()

Options:
A. \( x<4 \)
B. \( x<-1.4, x>1.4 \)
C. \( x \geq 0 \)
D. \( -1.4<x<1.4 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Only multiplies the numerical terms when expanding a bracket

Question:
\(
2(5 x+4)-4(x-7) \equiv A x+B
\)

What is the value of \( A \) ?

Options:
A. \( 4 \)
B. \( 6 \)
C. \( 14 \)
D. \( 3 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When factorising a quadratic without a non variable term, tries to double bracket factorise

Question:
Tom and Katie are arguing about factorising

Tom says \( p^{2}+9 p \equiv(p+3)(p+3) \)

Katie says \( p^{2}+9 p \equiv p(p+9) \)

Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n.

Question:
\[
7,10,13,16,19, \ldots
\]

When calculating the nth-term rule of this sequence, what should replace the star? nth-term rule: ![\( \hat{\omega}^{n} \)]()

Options:
A. \( 7 \)
B. \( 5 \)
C. \( 3 \)
D. \( 4 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplies by the index

Question:
What is the value of \( 1^{2} \) ?

Options:
A. \( 1 \)
B. \( 2 \)
C. \( 3 \)
D. \( 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Adds the index to the number

Question:
What is the value of \( 1^{2} \) ?

Options:
A. \( 1 \)
B. \( 2 \)
C. \( 3 \)
D. \( 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Writes the index as a digit on the end of a number

Question:
What is the value of \( 1^{2} \) ?

Options:
A. \( 1 \)
B. \( 2 \)
C. \( 3 \)
D. \( 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When multiplying just writes the numbers next to each other

Question:
\( 0.2 \times 0.8= \)

Options:
A. \( 0.28 \)
B. \( 1.6 \)
C. \( 0.16 \)
D. \( 1 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When multiplying decimals, divides by the wrong power of 10 when reinserting the decimal

Question:
\( 0.2 \times 0.8= \)

Options:
A. \( 0.28 \)
B. \( 1.6 \)
C. \( 0.16 \)
D. \( 1 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Adds instead of multiplies

Question:
\( 0.2 \times 0.8= \)

Options:
A. \( 0.28 \)
B. \( 1.6 \)
C. \( 0.16 \)
D. \( 1 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes raising a negative number to an odd power will give a positive answer

Question:
"If \( n \) is a positive integer, then \( (2 n-13)^{3} \) is negative"

Is the above statement always true, sometimes true, or never true?

Options:
A. Always true
B. Sometimes true
C. Never true
D. l'd just be guessing

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When solving an equation, uses the same operation rather than the inverse.

Question:
Isaac is trying to solve the equation on the right. \( 15=\frac{1+k}{4} \) Here are his steps. Step \( 1: \) \(
60=1+k
\)

Step \( 2: \) \(
61=k
\) Which steps, if any, are correct?

Options:
A. Only step \( 1 \)
B. Only ste.p \( 2 \)
C. Both steps are correct
D. Both step.s are incorrect

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When solving an equation, uses the same operation rather than the inverse.

Question:
Isaac is trying to solve the equation on the right. \( 15=\frac{1+k}{4} \) Here are his steps. Step \( 1: \) \(
60=1+k
\)

Step \( 2: \) \(
61=k
\) Which steps, if any, are correct?

Options:
A. Only step \( 1 \)
B. Only ste.p \( 2 \)
C. Both steps are correct
D. Both step.s are incorrect

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to solve linear equations involving fractions

Question:
Isaac is trying to solve the equation on the right. \( 15=\frac{1+k}{4} \) Here are his steps. Step \( 1: \) \(
60=1+k
\)

Step \( 2: \) \(
61=k
\) Which steps, if any, are correct?

Options:
A. Only step \( 1 \)
B. Only ste.p \( 2 \)
C. Both steps are correct
D. Both step.s are incorrect

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes we move down a number line when we add

Question:
![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +5 going from -1 up to 4]() Which of the following calculations is represented on the thermometer?

Options:
A. \( 4+5=-1 \)
B. \( -1+5=4 \)
C. \( -1+4=5 \)
D. \( 1+4=5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes the number of jumps between two numbers on a numberline represents the sum of those 2 numbers

Question:
![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +5 going from -1 up to 4]() Which of the following calculations is represented on the thermometer?

Options:
A. \( 4+5=-1 \)
B. \( -1+5=4 \)
C. \( -1+4=5 \)
D. \( 1+4=5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a negative number can be replaced with its positive equivalent when answering an addition problem from a numberline

Question:
![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +5 going from -1 up to 4]() Which of the following calculations is represented on the thermometer?

Options:
A. \( 4+5=-1 \)
B. \( -1+5=4 \)
C. \( -1+4=5 \)
D. \( 1+4=5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
![\( \nabla \)]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 3 \)
D. \( 9 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
![\( \nabla \)]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 3 \)
D. \( 9 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
![\( \nabla \)]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 3 \)
D. \( 9 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Writes four symbols after rather than one before in Roman numerals

Question:
Which of the following is the correct way to write \( 900 \) using Roman numerals?

Options:
A. \( \mathrm{CM} \)
B. DCCCC
C. IXOO
D. ССССССССС

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks that we can use O as zero for place value in Roman numerals

Question:
Which of the following is the correct way to write \( 900 \) using Roman numerals?

Options:
A. \( \mathrm{CM} \)
B. DCCCC
C. IXOO
D. ССССССССС

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to combine different symbols in Roman numerals

Question:
Which of the following is the correct way to write \( 900 \) using Roman numerals?

Options:
A. \( \mathrm{CM} \)
B. DCCCC
C. IXOO
D. ССССССССС

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds down instead of up

Question:
Jo and Paul are arguing about rounding.
Jo says \( \mathbf{1 2 0 6 . 9 7 8} \) rounded to the nearest hundred is \( \mathbf{1 2 0 0} \)
Paul says \( \mathbf{1 2 0 6 . 9 7 8} \) rounded to the nearest ten is \( \mathbf{1 2 0 0} \)
Who is correct?

Options:
A. Only
Jo
B. Only
Paul
C. Both Jo and Paul
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes subtraction is commutative

Question:
\( 0.51-0.202= \)

Options:
A. \( 0.151 \)
B. \( 0.312 \)
C. \( 0.308 \)
D. \( 0.318 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes you subtract the smaller digit from the larger digit in column subtraction, regardless of position

Question:
\( 0.51-0.202= \)

Options:
A. \( 0.151 \)
B. \( 0.312 \)
C. \( 0.308 \)
D. \( 0.318 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When “borrowing” during a subtraction problem, does not subtract one from the preceding digit

Question:
\( 0.51-0.202= \)

Options:
A. \( 0.151 \)
B. \( 0.312 \)
C. \( 0.308 \)
D. \( 0.318 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not think that -n + n = 0

Question:
Tom and Katie are discussing simultaneous equations Tom says you need to add these equations to eliminate \( y \)
\(\begin{array}{r}
4 x-3 y=12 \\
x+3 y=15
\end{array}\) Katie says you need to add these equations to eliminate \( y \)
\(\begin{array}{r}
4 x+3 y=12 \\
x-3 y=15
\end{array}\) Who is correct?

Options:
A. Only
Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When given the equation of a straight line, believes the first term always gives the gradient, even when the first term is actually c

Question:
Which of the following sketches could represent \( y=1-4 x ? \)

Options:
A. ![2 axes showing a positive gradient, crossing the y axis at a positive number]()
B. ![2 axes showing a positive gradient with a negative y intercept ]()
C. ![2 axes showing a negative gradient with a positive y intercept]()
D. ![2 axes with a negative gradient and a negative y intercept]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When given the equation of a straight line, believes the first term always gives the gradient, even when the first term is actually c

Question:
Which of the following sketches could represent \( y=1-4 x ? \)

Options:
A. ![2 axes showing a positive gradient, crossing the y axis at a positive number]()
B. ![2 axes showing a positive gradient with a negative y intercept ]()
C. ![2 axes showing a negative gradient with a positive y intercept]()
D. ![2 axes with a negative gradient and a negative y intercept]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that in y=mx+c, m is the y-intercept

Question:
Which of the following sketches could represent \( y=1-4 x ? \)

Options:
A. ![2 axes showing a positive gradient, crossing the y axis at a positive number]()
B. ![2 axes showing a positive gradient with a negative y intercept ]()
C. ![2 axes showing a negative gradient with a positive y intercept]()
D. ![2 axes with a negative gradient and a negative y intercept]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Carries out operations from left to right regardless of priority order

Question:
I think of a number. I take away six and then divide the result by three. The answer I get is \( 21 \).
Which of the following equations represents this?

Options:
A. \( \frac{n-6}{3}=21 \)
B. \( n-6 \div 3=21 \)
C. \( 3(n-6)=21 \)
D. \( \frac{n}{3}-6=21 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks that a number in front of a bracket means divide

Question:
I think of a number. I take away six and then divide the result by three. The answer I get is \( 21 \).
Which of the following equations represents this?

Options:
A. \( \frac{n-6}{3}=21 \)
B. \( n-6 \div 3=21 \)
C. \( 3(n-6)=21 \)
D. \( \frac{n}{3}-6=21 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that the order of a worded calculation should be changed to follow BIDMAS

Question:
I think of a number. I take away six and then divide the result by three. The answer I get is \( 21 \).
Which of the following equations represents this?

Options:
A. \( \frac{n-6}{3}=21 \)
B. \( n-6 \div 3=21 \)
C. \( 3(n-6)=21 \)
D. \( \frac{n}{3}-6=21 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes you find the frequency for a pie chart sector by calculating its angle divided by the total frequency

Question:
A class of students were surveyed about how many siblings they have.

A selection of results are shown in the table. \begin{tabular}{|c|c|c|}
\hline Number of siblings & Frequency & Angle on a pie chart \\
\hline  0  & \( 5 \) & \( \) \\
\hline 1  & \( \bigstar \) & \( 165 \degree \) \\
\hline 2  & \(  \) & \(  \) \\
\hline 3  & \( 2 \) & \(  \) \\
\hline 4 or more  & \(  \) & \(  \) \\
\hline  TOTAL  & 24  & \(  \) \\
\end{tabular} Jenny wants to draw a pie chart of the information.

Which of the following calculations would work out what replaces the star?

Options:
A. \( 165 \div 24 \)
B. \( \frac{165}{360} \times 24 \)
C. \( \frac{360}{24} \times 165 \)
D. \( \frac{165}{360} \div 24 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Divides rather than multiplies

Question:
A class of students were surveyed about how many siblings they have.

A selection of results are shown in the table. \begin{tabular}{|c|c|c|}
\hline Number of siblings & Frequency & Angle on a pie chart \\
\hline  0  & \( 5 \) & \( \) \\
\hline 1  & \( \bigstar \) & \( 165 \degree \) \\
\hline 2  & \(  \) & \(  \) \\
\hline 3  & \( 2 \) & \(  \) \\
\hline 4 or more  & \(  \) & \(  \) \\
\hline  TOTAL  & 24  & \(  \) \\
\end{tabular} Jenny wants to draw a pie chart of the information.

Which of the following calculations would work out what replaces the star?

Options:
A. \( 165 \div 24 \)
B. \( \frac{165}{360} \times 24 \)
C. \( \frac{360}{24} \times 165 \)
D. \( \frac{165}{360} \div 24 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
when dividing a fraction by an integer, multiplies the numerator by the integer

Question:
Calculate:
\(
\frac{3}{11} \div 3
\)

Options:
A. \( \frac{1}{33} \)
B. \( \frac{9}{11} \)
C. \( \frac{9}{33} \)
D. \( \frac{1}{11} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When dividing a fraction by an integer, multiplies both the numerator and denominator by the integer

Question:
Calculate:
\(
\frac{3}{11} \div 3
\)

Options:
A. \( \frac{1}{33} \)
B. \( \frac{9}{11} \)
C. \( \frac{9}{33} \)
D. \( \frac{1}{11} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know the definition of a prism

Question:
Which of the following is a correct name of this shape? ![A 3D shape with 1 square face and 4 triangular faces. 1 triangular face is attached to each side of the square face.]()

Options:
A. Square-based pyramid
B. Triangular prism
C. Cone
D. Triangular-based pyramid

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know the definition of a cone

Question:
Which of the following is a correct name of this shape? ![A 3D shape with 1 square face and 4 triangular faces. 1 triangular face is attached to each side of the square face.]()

Options:
A. Square-based pyramid
B. Triangular prism
C. Cone
D. Triangular-based pyramid

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Only counts visible faces

Question:
Which of the following is a correct name of this shape? ![A 3D shape with 1 square face and 4 triangular faces. 1 triangular face is attached to each side of the square face.]()

Options:
A. Square-based pyramid
B. Triangular prism
C. Cone
D. Triangular-based pyramid

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not realise addition is commutative

Question:
When \( h=15 \) and \( j=3 \)
Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}h(j+2)=75 \\ h(2+j)=-75\end{array} \)
B. \( \begin{array}{l}h(j+2)=23 \\ h(2+j)=32\end{array} \)
C. \( \begin{array}{l}h(j+2)=32 \\ h(2+j)=23\end{array} \)
D. \( \begin{array}{l}h(j+2)=75 \\ h(2+j)=75\end{array} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not realise addition is commutative

Question:
When \( h=15 \) and \( j=3 \)
Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}h(j+2)=75 \\ h(2+j)=-75\end{array} \)
B. \( \begin{array}{l}h(j+2)=23 \\ h(2+j)=32\end{array} \)
C. \( \begin{array}{l}h(j+2)=32 \\ h(2+j)=23\end{array} \)
D. \( \begin{array}{l}h(j+2)=75 \\ h(2+j)=75\end{array} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not realise addition is commutative

Question:
When \( h=15 \) and \( j=3 \)
Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}h(j+2)=75 \\ h(2+j)=-75\end{array} \)
B. \( \begin{array}{l}h(j+2)=23 \\ h(2+j)=32\end{array} \)
C. \( \begin{array}{l}h(j+2)=32 \\ h(2+j)=23\end{array} \)
D. \( \begin{array}{l}h(j+2)=75 \\ h(2+j)=75\end{array} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When subtracting past zero, adds the absolute values and then writes the answer with a negative sign

Question:
What is the 11th term of this sequence? \( u_{n}=2-5 n \)

Options:
A. \( -9 \)
B. \( -53 \)
C. \( -57 \)
D. \( -45 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mistakes lines as parallel

Question:
Which of the following are corresponding angles on this diagram? ![Three almost horizontal lines, two marked with arrows. One almost vertical line crossing them. The twelve angles created are marked a-l. ]()

Options:
A. \( c \) and \( g \)
B. \( c \) and \( k \)
C. \( d \) and \( j \)
D. \( b \) and \( f \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses co-interior and corresponding angles

Question:
Which of the following are corresponding angles on this diagram? ![Three almost horizontal lines, two marked with arrows. One almost vertical line crossing them. The twelve angles created are marked a-l. ]()

Options:
A. \( c \) and \( g \)
B. \( c \) and \( k \)
C. \( d \) and \( j \)
D. \( b \) and \( f \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.