Prompt:
Misconception:
Confuses the number of regions in a Venn diagram as the total number of entries in the diagram

Question:
All the students in a class were asked if they have a brother, sister, both or none.

The Venn Diagram shows the results. ![A Venn diagram with two sets, one labelled Brother and one labelled Sister. The number 10 is written in Brother without the intersection , number 5 is in Sister without the intersection, the number 7 is in the intersection of Brother and Sister. The number 9 is outside the circles.]() How many students are in the class?

Options:
A. \( 24 \)
B. \( 31 \)
C. \( 4 \)
D. \( 21 \)

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:
Forgets to include values outside of the Venn diagram when finding the total

Question:
All the students in a class were asked if they have a brother, sister, both or none.

The Venn Diagram shows the results. ![A Venn diagram with two sets, one labelled Brother and one labelled Sister. The number 10 is written in Brother without the intersection , number 5 is in Sister without the intersection, the number 7 is in the intersection of Brother and Sister. The number 9 is outside the circles.]() How many students are in the class?

Options:
A. \( 24 \)
B. \( 31 \)
C. \( 4 \)
D. \( 21 \)

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:
When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation

Question:
What number belongs in the box to make the calculation correct?

\[
6 \times \square=108
\]

Options:
A. \( 648 \)
B. \( 11 \)
C. \( 102 \)
D. \( 18 \)

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 a problem that requires an inverse operation (e.g. missing number problems), does subtraction when division is required

Question:
What number belongs in the box to make the calculation correct?

\[
6 \times \square=108
\]

Options:
A. \( 648 \)
B. \( 11 \)
C. \( 102 \)
D. \( 18 \)

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 the height of a trapezium as the perpendicular length between the parallel sides

Question:
Sally wants to calculate the area of this trapezium using the formula: Area \( =\left(\frac{a+b}{2}\right) h \) ![A trapezium with the parallel sides labelled 5cm and 1cm, the slant height labelled 6cm and the perpendicular height labelled 4cm.]() What is the values of \( h \) ?

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 6 \mathrm{~cm} \)
D. \( 1 \mathrm{~cm} \)

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 slant height instead of perpendicular height to find area of a trapezium

Question:
Sally wants to calculate the area of this trapezium using the formula: Area \( =\left(\frac{a+b}{2}\right) h \) ![A trapezium with the parallel sides labelled 5cm and 1cm, the slant height labelled 6cm and the perpendicular height labelled 4cm.]() What is the values of \( h \) ?

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 6 \mathrm{~cm} \)
D. \( 1 \mathrm{~cm} \)

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 the height of a trapezium as the perpendicular length between the parallel sides

Question:
Sally wants to calculate the area of this trapezium using the formula: Area \( =\left(\frac{a+b}{2}\right) h \) ![A trapezium with the parallel sides labelled 5cm and 1cm, the slant height labelled 6cm and the perpendicular height labelled 4cm.]() What is the values of \( h \) ?

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 6 \mathrm{~cm} \)
D. \( 1 \mathrm{~cm} \)

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 terms faces and vertices

Question:
How many vertices does this shape have? ![cuboid]()

Options:
A. \( 6 \)
B. \( 8 \)
C. \( 4 \)
D. \( 7 \)

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 vertices on a 3D shape match those of the 2D cross section

Question:
How many vertices does this shape have? ![cuboid]()

Options:
A. \( 6 \)
B. \( 8 \)
C. \( 4 \)
D. \( 7 \)

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 vertices

Question:
How many vertices does this shape have? ![cuboid]()

Options:
A. \( 6 \)
B. \( 8 \)
C. \( 4 \)
D. \( 7 \)

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 difference in a coordinate pair rather than the midpoint

Question:
Millie is working out the midpoint of these two points. What should replace the triangle? ![An x and y axis showing 3 points. (1,8) (star, triangle) and (7,3)]()

Options:
A. ![\( \triangle=6 \)]()
B. ![\( \triangle=5 \)]()
C. ![\( \triangle=5.5 \)]()
D. ![\( \triangle=11 \)]()

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 divide by 2 when finding midpoint

Question:
Millie is working out the midpoint of these two points. What should replace the triangle? ![An x and y axis showing 3 points. (1,8) (star, triangle) and (7,3)]()

Options:
A. ![\( \triangle=6 \)]()
B. ![\( \triangle=5 \)]()
C. ![\( \triangle=5.5 \)]()
D. ![\( \triangle=11 \)]()

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

Question:
What could go in the missing gaps? \begin{tabular}{|l|l|l|l|}
\hline \multicolumn{4}{|c|}{\( 8 a+7 \)} \\
\hline \( 3 a \) & \( -3 \) & \( ? \) & \( ? \) \\
\hline
\end{tabular}

Options:
A. \( 5 a \) and \( 10 \)
B. \( 5 a+10 \)
C. \( 5 a \) and \( 4 \)
D. \( 6 a \) and \( 4-a \)

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 that angles on a straight line sum to 180 degrees

Question:
Which calculation is a correct procedure to find the angle marked [?]
A
\( 360-(54 \times 2) \)
B
\( 180-54 \) ![Two intersecting lines and one adjacent line. One line is marked with the angle 54 degrees. Between the two adjacent lines there is a box with a question mark in it [?]]()

Options:
A. A
B. B
C. Both \( A \) and \( B \)
D. Neither A nor B

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:
\( 0.8^{2}= \)

Options:
A. \( 6.4 \)
B. \( 1.6 \)
C. \( 0.16 \)
D. \( 0.64 \)

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:
\( 0.8^{2}= \)

Options:
A. \( 6.4 \)
B. \( 1.6 \)
C. \( 0.16 \)
D. \( 0.64 \)

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:
\( 0.8^{2}= \)

Options:
A. \( 6.4 \)
B. \( 1.6 \)
C. \( 0.16 \)
D. \( 0.64 \)

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 h in the formula for area of a trapezium stands for half the sum of the parallel sides

Question:
The area of this trapezium is \( 40 \mathrm{~cm}^{2} \). What would the perpendicular height, \( h \), of the trapezium be? ![Trapezium with parallel sides of lengths 6cm and 10cm]()

Options:
A. \( h=8 \mathrm{~cm} \)
B. \( h=2.5 \mathrm{~cm} \)
C. \( h=5 \mathrm{~cm} \)
D. \( h=13.3 \mathrm{~cm} \)

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 calculating the area of a trapezium

Question:
The area of this trapezium is \( 40 \mathrm{~cm}^{2} \). What would the perpendicular height, \( h \), of the trapezium be? ![Trapezium with parallel sides of lengths 6cm and 10cm]()

Options:
A. \( h=8 \mathrm{~cm} \)
B. \( h=2.5 \mathrm{~cm} \)
C. \( h=5 \mathrm{~cm} \)
D. \( h=13.3 \mathrm{~cm} \)

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 only the base and perpendicular height when calculating the area of a trapezium

Question:
The area of this trapezium is \( 40 \mathrm{~cm}^{2} \). What would the perpendicular height, \( h \), of the trapezium be? ![Trapezium with parallel sides of lengths 6cm and 10cm]()

Options:
A. \( h=8 \mathrm{~cm} \)
B. \( h=2.5 \mathrm{~cm} \)
C. \( h=5 \mathrm{~cm} \)
D. \( h=13.3 \mathrm{~cm} \)

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:
What is \( 875,599 \) rounded to the nearest \( 10,000 \) ?

Options:
A. \( 870,000 \)
B. \( 900,000 \)
C. \( 880,000 \)
D. \( 876,000 \)

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 wrong degree of accuracy (rounds too much)

Question:
What is \( 875,599 \) rounded to the nearest \( 10,000 \) ?

Options:
A. \( 870,000 \)
B. \( 900,000 \)
C. \( 880,000 \)
D. \( 876,000 \)

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 wrong degree of accuracy (rounds too little)

Question:
What is \( 875,599 \) rounded to the nearest \( 10,000 \) ?

Options:
A. \( 870,000 \)
B. \( 900,000 \)
C. \( 880,000 \)
D. \( 876,000 \)

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 composite bar chart, just reads total height of bar

Question:
The bar chart shows the drinks sold in Caroline's Café on Monday and Tuesday last week.

Approximately how many Hot Chocs were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.
The Hot Chocs bar's lower section is 5 ticks high, and the whole bar is 2 ticks above 100 on the vertical scale.]()

Options:
A. \( 60 \)
B. \( 110 \)
C. \( 50 \)
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:
Misreads scale

Question:
The bar chart shows the drinks sold in Caroline's Café on Monday and Tuesday last week.

Approximately how many Hot Chocs were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.
The Hot Chocs bar's lower section is 5 ticks high, and the whole bar is 2 ticks above 100 on the vertical scale.]()

Options:
A. \( 60 \)
B. \( 110 \)
C. \( 50 \)
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:
Believes infinite gradient is not possible in real life.

Question:
Imran slept really well until a car alarm woke him up and he couldn't get back to sleep.

Which of the following sketches best shows Imran's sleep?

Options:
A. ![This graph shows depth of sleep increasing quickly and then maintaining a consistent level until it starts to gradually decrease until the end of the night when it reaches 0.]()
B. ![This graph shows depth of sleep increasing quickly and then maintaining a consistent level until it suddenly drops all the way to 0 and stays there for the rest of the night.]()
C. ![This graph shows depth of sleep staying around 0 for some time before gradually increasing, maintaining a consistent level for a short period and then gradually decreasing until the end of the night.]()
D. ![This graph shows depth of sleep staying at 0 for some time before gradually increasing, maintaining a consistent level for a short period and then gradually decreasing until the end of the night.]()

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 the meaning of "value"

Question:
What is the value of the \( 3 \) in the number
\[
7,359,250 \text { ? }
\]

Options:
A. \( 3 \)
B. \( 300,000 \)
C. \( 30,000 \)
D. \( 300 \)

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 hundred thousands column is the ten thousands column

Question:
What is the value of the \( 3 \) in the number
\[
7,359,250 \text { ? }
\]

Options:
A. \( 3 \)
B. \( 300,000 \)
C. \( 30,000 \)
D. \( 300 \)

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 hundreds and hundred thousands place value columns

Question:
What is the value of the \( 3 \) in the number
\[
7,359,250 \text { ? }
\]

Options:
A. \( 3 \)
B. \( 300,000 \)
C. \( 30,000 \)
D. \( 300 \)

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:
\(
(-20) \times(-5)=2 \times(-10) \times(-5)
\)
Is this...

Options:
A. true because of distributivity
B. true because of associativity
C. true because of commutativity
D. false

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 the meaning of the word commutative

Question:
\(
(-20) \times(-5)=2 \times(-10) \times(-5)
\)
Is this...

Options:
A. true because of distributivity
B. true because of associativity
C. true because of commutativity
D. false

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 area of this shape? ![A square cm grid showing a shape made up of 3 small squares.]()

Options:
A. \( 3 \)
B. \( 8 \)
C. \( 20 \)
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:
Finds the area of the whole grid instead of the shaded shape

Question:
What is the area of this shape? ![A square cm grid showing a shape made up of 3 small squares.]()

Options:
A. \( 3 \)
B. \( 8 \)
C. \( 20 \)
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:
When calculating the area of a rectilinear compound shape, calculates the are of the surrounding rectangle

Question:
What is the area of this shape? ![A square cm grid showing a shape made up of 3 small squares.]()

Options:
A. \( 3 \)
B. \( 8 \)
C. \( 20 \)
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:
Does not understand bar modelling in algebra

Question:
\(k<\frac{m}{3} +1\)
Using the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()

Options:
A. always true
B. sometimes true
C. never true
D. Need more 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 understand bar modelling in algebra

Question:
\(k<\frac{m}{3} +1\)
Using the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()

Options:
A. always true
B. sometimes true
C. never true
D. Need more 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 understand bar modelling in algebra

Question:
\(k<\frac{m}{3} +1\)
Using the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()

Options:
A. always true
B. sometimes true
C. never true
D. Need more 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:
When calculating perimeter, only adds the marked lengths

Question:
What is the perimeter of this rectangle? ![A rectangle with a base length of 8 cm and a perpendicular height of 5 cm.]()

Options:
A. \( 26 \mathrm{~cm} \)
B. \( 13 \mathrm{~cm} \)
C. \( 40 \mathrm{~cm} \)
D. Not enough information in the diagram

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 area when asked for perimeter

Question:
What is the perimeter of this rectangle? ![A rectangle with a base length of 8 cm and a perpendicular height of 5 cm.]()

Options:
A. \( 26 \mathrm{~cm} \)
B. \( 13 \mathrm{~cm} \)
C. \( 40 \mathrm{~cm} \)
D. Not enough information in the diagram

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 recall rectangle side length property

Question:
What is the perimeter of this rectangle? ![A rectangle with a base length of 8 cm and a perpendicular height of 5 cm.]()

Options:
A. \( 26 \mathrm{~cm} \)
B. \( 13 \mathrm{~cm} \)
C. \( 40 \mathrm{~cm} \)
D. Not enough information in the diagram

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:
Goes the wrong direction in the sequence when identifying term-to-term rule

Question:
\[
20,14,8,2,-4, \ldots
\]

When calculating the nth-term rule of this sequence, what should replace the star? nth-term rule: \(\color{gold}\bigstar\)n  \(\square\)

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 20 \)
D. \( -6 \)

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:
\[
20,14,8,2,-4, \ldots
\]

When calculating the nth-term rule of this sequence, what should replace the star? nth-term rule: \(\color{gold}\bigstar\)n  \(\square\)

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 20 \)
D. \( -6 \)

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:
Converts a fraction to a decimal by using only the numerator after the decimal point

Question:
Convert \( \frac{7}{40} \) into a decimal

Options:
A. \( 0.175 \)
B. \( 0.7 \)
C. \( 0.1 \)
D. \( 7.40 \)

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:
Converts a fraction to a decimal by placing a decimal point between the numerator and denominator

Question:
Convert \( \frac{7}{40} \) into a decimal

Options:
A. \( 0.175 \)
B. \( 0.7 \)
C. \( 0.1 \)
D. \( 7.40 \)

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 fractions, subtracts the numerators and denominators

Question:
\( \frac{7}{8}-\frac{1}{4}= \)

Options:
A. \( \frac{5}{8} \)
B. \( \frac{6}{4} \)
C. \( \frac{9}{8} \)
D. \( \frac{6}{8} \)

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 subtracts

Question:
\( \frac{7}{8}-\frac{1}{4}= \)

Options:
A. \( \frac{5}{8} \)
B. \( \frac{6}{4} \)
C. \( \frac{9}{8} \)
D. \( \frac{6}{8} \)

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 how to maintain equivalence in fractions

Question:
\( \frac{7}{8}-\frac{1}{4}= \)

Options:
A. \( \frac{5}{8} \)
B. \( \frac{6}{4} \)
C. \( \frac{9}{8} \)
D. \( \frac{6}{8} \)

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 an angle is the size that it looks in the (not to scale) diagram

Question:
What is the size of angle \( k \) ? ![A triangle with two labelled interior angles. One angle is 65 degrees. One angle is k degrees. The third angle has no label.]()

Options:
A. \( 50\degree\)
B. \( 65\degree\)
C. \( 90\degree\)
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 angles which look the same on diagram will be equal

Question:
What is the size of angle \( k \) ? ![A triangle with two labelled interior angles. One angle is 65 degrees. One angle is k degrees. The third angle has no label.]()

Options:
A. \( 50\degree\)
B. \( 65\degree\)
C. \( 90\degree\)
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 all triangles have a right angle

Question:
What is the size of angle \( k \) ? ![A triangle with two labelled interior angles. One angle is 65 degrees. One angle is k degrees. The third angle has no label.]()

Options:
A. \( 50\degree\)
B. \( 65\degree\)
C. \( 90\degree\)
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 know that units of volume are usually cubed

Question:
Sally has answered a question on volume. Her answer is \( 500 \).
Behind the star she has written the units that she used.
Which of the following units is definitely wrong?

\( 500 \,\bigstar \)

Options:
A. \( \mathrm{cm}^{2} \)
B. \( \mathrm{mm}^{3} \)
C. \( m^{3} \)
D. \( l \)

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 that units of volume are usually cubed

Question:
Sally has answered a question on volume. Her answer is \( 500 \).
Behind the star she has written the units that she used.
Which of the following units is definitely wrong?

\( 500 \,\bigstar \)

Options:
A. \( \mathrm{cm}^{2} \)
B. \( \mathrm{mm}^{3} \)
C. \( m^{3} \)
D. \( l \)

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 litres as a unit of volume

Question:
Sally has answered a question on volume. Her answer is \( 500 \).
Behind the star she has written the units that she used.
Which of the following units is definitely wrong?

\( 500 \,\bigstar \)

Options:
A. \( \mathrm{cm}^{2} \)
B. \( \mathrm{mm}^{3} \)
C. \( m^{3} \)
D. \( l \)

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 a reflection line drawn and a triangle. The reflection line passes through the coordinates: (-1,-1) (0,0) (1,1) (2,2) etc. The triangle has coordinates: (2,2) (3,3) and (4,2). P is the coordinate (4,2).]()

Options:
A. \( (2,2) \)
B. \( (2,0) \)
C. \( (2,4) \)
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:
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 a reflection line drawn and a triangle. The reflection line passes through the coordinates: (-1,-1) (0,0) (1,1) (2,2) etc. The triangle has coordinates: (2,2) (3,3) and (4,2). P is the coordinate (4,2).]()

Options:
A. \( (2,2) \)
B. \( (2,0) \)
C. \( (2,4) \)
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:
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 a reflection line drawn and a triangle. The reflection line passes through the coordinates: (-1,-1) (0,0) (1,1) (2,2) etc. The triangle has coordinates: (2,2) (3,3) and (4,2). P is the coordinate (4,2).]()

Options:
A. \( (2,2) \)
B. \( (2,0) \)
C. \( (2,4) \)
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:
Rounds to the wrong degree of accuracy (significant figures rather than decimal places)

Question:
\( 0.009753 \)
What is this number rounded to \( 2 \) decimal places?

Options:
A. \( 0.0098 \)
B. \( 0.0097 \)
C. \( 0.01 \)
D. \( 0.00 \)

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 wrong degree of accuracy (significant figures rather than decimal places)

Question:
\( 0.009753 \)
What is this number rounded to \( 2 \) decimal places?

Options:
A. \( 0.0098 \)
B. \( 0.0097 \)
C. \( 0.01 \)
D. \( 0.00 \)

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:
\( 0.009753 \)
What is this number rounded to \( 2 \) decimal places?

Options:
A. \( 0.0098 \)
B. \( 0.0097 \)
C. \( 0.01 \)
D. \( 0.00 \)

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 decimals with a different number of decimals, subtracts one digit from more than one column

Question:
\( 0.55-0.2= \)

Options:
A. \( 0.552 \)
B. \( 0.33 \)
C. \( 0.53 \)
D. \( 0.35 \)

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 decimals with a different number of decimal places, lines up the digits incorrectly

Question:
\( 0.55-0.2= \)

Options:
A. \( 0.552 \)
B. \( 0.33 \)
C. \( 0.53 \)
D. \( 0.35 \)

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:
What is the solution to the following inequality?
\(
-5<2 x+1<5
\)

Options:
A. \( -9<x<11 \)
B. \( -3<x<2 \)
C. \( -2<x<2 \)
D. \( -3.5<x<1.5 \)

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 subtracting a positive number from a negative number makes the answer less negative

Question:
What is the solution to the following inequality?
\(
-5<2 x+1<5
\)

Options:
A. \( -9<x<11 \)
B. \( -3<x<2 \)
C. \( -2<x<2 \)
D. \( -3.5<x<1.5 \)

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 reverse the order of operations when solving an equation

Question:
What is the solution to the following inequality?
\(
-5<2 x+1<5
\)

Options:
A. \( -9<x<11 \)
B. \( -3<x<2 \)
C. \( -2<x<2 \)
D. \( -3.5<x<1.5 \)

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 find a common denominator when comparing fractions

Question:
In a bakery \( \frac{3}{7} \) of the cakes are chocolate, \( \frac{5}{14} \) of the cakes are vanilla and \( \frac{6}{28} \) are lemon.
Which flavour cake is there more of?

Options:
A. Chocolate
B. Vanilla
C. Lemon
D. There is the same amount of each.

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 find a common denominator when comparing fractions

Question:
In a bakery \( \frac{3}{7} \) of the cakes are chocolate, \( \frac{5}{14} \) of the cakes are vanilla and \( \frac{6}{28} \) are lemon.
Which flavour cake is there more of?

Options:
A. Chocolate
B. Vanilla
C. Lemon
D. There is the same amount of each.

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:
Estimates angle without using knowledge of degrees in quarter turns

Question:
Which of the following is the best estimate of the size of this angle? ![An obtuse angle]()

Options:
A. \( 60^{\circ} \)
B. \( 90^{\circ} \)
C. \( 120^{\circ} \)
D. \( 160^{\circ} \)

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:
Estimates angle without using knowledge of degrees in quarter turns

Question:
Which of the following is the best estimate of the size of this angle? ![An obtuse angle]()

Options:
A. \( 60^{\circ} \)
B. \( 90^{\circ} \)
C. \( 120^{\circ} \)
D. \( 160^{\circ} \)

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:
Estimates angle without using knowledge of degrees in quarter turns

Question:
Which of the following is the best estimate of the size of this angle? ![An obtuse angle]()

Options:
A. \( 60^{\circ} \)
B. \( 90^{\circ} \)
C. \( 120^{\circ} \)
D. \( 160^{\circ} \)

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 substituting a value into a non-linear term with a coefficient, multiplies by the coefficient then calculates the power.

Question:
This is a part of the table of values for the equation
\(y=\frac{1}{2} x^{2}\) \begin{tabular}{|c|c|}
\hline\( x \) & \( \frac{2}{3} \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( \frac{1}{9} \)
B. \( \frac{2}{9} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{6} \)

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:
This is a part of the table of values for the equation
\(y=\frac{1}{2} x^{2}\) \begin{tabular}{|c|c|}
\hline\( x \) & \( \frac{2}{3} \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( \frac{1}{9} \)
B. \( \frac{2}{9} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{6} \)

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 numbers are a multiple of their index

Question:
What is the smallest odd cube number?

Options:
A. \( 1 \)
B. \( 3 \)
C. \( 8 \)
D. \( 27 \)

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 odd and even numbers

Question:
What is the smallest odd cube number?

Options:
A. \( 1 \)
B. \( 3 \)
C. \( 8 \)
D. \( 27 \)

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:
Write the following using correct algebraic notation \( p \) multiplied by three lots of \( q \)

Options:
A. \( 3 p+q \)
B. \( p q^{3} \)
C. \( p q+3 \)
D. \( 3 p q \)

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 4

Question:
What is the value of \( 3^{2} \) ?

Options:
A. \( 12 \)
B. \( 6 \)
C. \( 9 \)
D. \( 5 \)

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:
Multiplies by the index

Question:
What is the value of \( 3^{2} \) ?

Options:
A. \( 12 \)
B. \( 6 \)
C. \( 9 \)
D. \( 5 \)

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:
Adds the index to the number

Question:
What is the value of \( 3^{2} \) ?

Options:
A. \( 12 \)
B. \( 6 \)
C. \( 9 \)
D. \( 5 \)

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:
Multiplies by the index

Question:
Simplify, if possible:
\(
m^{2} \times m^{2}
\)

Options:
A. \( m^{4} \)
B. \( 4 m \)
C. \( 2 m^{2} \)
D. Does not simplify

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 collecting like terms with multiplication

Question:
Simplify, if possible:
\(
m^{2} \times m^{2}
\)

Options:
A. \( m^{4} \)
B. \( 4 m \)
C. \( 2 m^{2} \)
D. Does not simplify

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 multiplying a positive by a negative gives a positive answer

Question:
What should replace the circle when these two brackets are expanded and simplified?
\(
(p-3)(p+1) \equiv p^{2} \triangle p \bigcirc
\)

Options:
A. \( \bigcirc=-3 \)
B. \( \bigcirc=+3 \)
C. \( \bigcirc=-4 \)
D. \( \bigcirc=-2 \)

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:
Adds instead of multiplying when expanding bracket

Question:
What should replace the circle when these two brackets are expanded and simplified?
\(
(p-3)(p+1) \equiv p^{2} \triangle p \bigcirc
\)

Options:
A. \( \bigcirc=-3 \)
B. \( \bigcirc=+3 \)
C. \( \bigcirc=-4 \)
D. \( \bigcirc=-2 \)

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:
Finds total instead of difference when asked 'How many more'

Question:
The bar chart shows the number of students in each year group who study French, Spanish and Chinese.

How many more Year 8s than Year 7s study French? ![An image of a vertical bar chart with bars striped red and white for French, solid blue for Spanish and solid white for Chinese (a key shows this). The x-axis is titled 'year group' with labels for Years 7 to 11. The y-axis is titled 'number of children' and its scale is from 0 to 80 in steps of 10. The following data is shown on the bar chart.
Year 7: French 42, Spanish 35, Chinese 60; Year 8: French 80, Spanish 27, Chinese 25; Year 9: French 35, Spanish 70, Chinese 12; Year 10: French 12, Spanish 35, Chinese 0; Year 11: French 33, Spanish 26, Chinese 0.]()

Options:
A. \( 42 \)
B. \( 122 \)
C. \( 38 \)
D. \( 80 \)

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:
Estimates a measurement on a diagram rather than working it out

Question:
What is the length of the side marked \( q \) ? ![Two, intersecting circles drawn with a compass and used to construct a triangle with one side labelled with q]()

Options:
A. \( 2 \mathrm{~cm} \)
B. \( 2.5 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
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:
Given a line segment with a midpoint that is not the origin, assumes that the two end points will still have the same absolute value

Question:
Here are two points and their midpoint. What should replace the star? ![A set of axis showing all four quadrants. Three points are marked in a straight line with a negative gradient. One lilac circle marks a point in the 1st quadrant and is labelled (-5, 5). One red circle marks a point in the 1st quadrant and is labelled (-2,1). Another lilac circle marks a point in the 4th quadrant and is labelled (gold star icon, green triangle icon) as the coordinates are unknown. ]()

Options:
A. \(\color{gold}\bigstar\) = 5
B. \(\color{gold}\bigstar\) = -7
C. \(\color{gold}\bigstar\) = -3.5
D. \(\color{gold}\bigstar\) = 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 adding coordinates of endpoint and midpoint of a line will give the other endpoint

Question:
Here are two points and their midpoint. What should replace the star? ![A set of axis showing all four quadrants. Three points are marked in a straight line with a negative gradient. One lilac circle marks a point in the 1st quadrant and is labelled (-5, 5). One red circle marks a point in the 1st quadrant and is labelled (-2,1). Another lilac circle marks a point in the 4th quadrant and is labelled (gold star icon, green triangle icon) as the coordinates are unknown. ]()

Options:
A. \(\color{gold}\bigstar\) = 5
B. \(\color{gold}\bigstar\) = -7
C. \(\color{gold}\bigstar\) = -3.5
D. \(\color{gold}\bigstar\) = 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:
Underestimates the area of shapes when counting squares when some squares are neither wholes nor halves

Question:
Each square is \( 1 \mathrm{~cm} \) by \( 1 \mathrm{~cm} \)

What is the area of this shape? ![A 6 by 5 centimetre squared grid. A purple right angled triangle is drawn on the grid with a base of 3cm and a perpendicular height of 3cm.]()

Options:
A. \( 5 \mathrm{~cm}^{2} \)
B. \( 3 \mathrm{~cm}^{2} \)
C. \( 9 \mathrm{~cm}^{2} \)
D. \( 4.5 \mathrm{~cm}^{2} \)

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:
Adds when calculating area instead of multiplying

Question:
Each square is \( 1 \mathrm{~cm} \) by \( 1 \mathrm{~cm} \)

What is the area of this shape? ![A 6 by 5 centimetre squared grid. A purple right angled triangle is drawn on the grid with a base of 3cm and a perpendicular height of 3cm.]()

Options:
A. \( 5 \mathrm{~cm}^{2} \)
B. \( 3 \mathrm{~cm}^{2} \)
C. \( 9 \mathrm{~cm}^{2} \)
D. \( 4.5 \mathrm{~cm}^{2} \)

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:
Does not divide by 2 when calculating the area of a triangle

Question:
Each square is \( 1 \mathrm{~cm} \) by \( 1 \mathrm{~cm} \)

What is the area of this shape? ![A 6 by 5 centimetre squared grid. A purple right angled triangle is drawn on the grid with a base of 3cm and a perpendicular height of 3cm.]()

Options:
A. \( 5 \mathrm{~cm}^{2} \)
B. \( 3 \mathrm{~cm}^{2} \)
C. \( 9 \mathrm{~cm}^{2} \)
D. \( 4.5 \mathrm{~cm}^{2} \)

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:
Believes that the compensation strategy for the multiplication of 2 numbers can only be used one way round.

Question:
Tom and Katie are discussing ways to calculate \( 49 \times 9 \) mentally
Tom multiplies \( 49 \) by \( 10 \) and then subtracts \( 49 \) from the answer.
Katie does \( 50 \times 9 \) and then subtracts \( 9 \) from the answer
Who would get the correct answer?

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 that the compensation strategy for the multiplication of 2 numbers can only be used one way round.

Question:
Tom and Katie are discussing ways to calculate \( 49 \times 9 \) mentally
Tom multiplies \( 49 \) by \( 10 \) and then subtracts \( 49 \) from the answer.
Katie does \( 50 \times 9 \) and then subtracts \( 9 \) from the answer
Who would get the correct answer?

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 think that the compensation strategy for the multiplication of 2 numbers is valid.

Question:
Tom and Katie are discussing ways to calculate \( 49 \times 9 \) mentally
Tom multiplies \( 49 \) by \( 10 \) and then subtracts \( 49 \) from the answer.
Katie does \( 50 \times 9 \) and then subtracts \( 9 \) from the answer
Who would get the correct answer?

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:
Forgotten that anything to the power of 0 equals 1

Question:
\( (16)^{0}=? \)

Options:
A. \( 16 \)
B. \( 0 \)
C. \( 1 \)
D. You cannot have a power of \( 0 \)

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:
Forgotten that anything to the power of 0 equals 1

Question:
\( (16)^{0}=? \)

Options:
A. \( 16 \)
B. \( 0 \)
C. \( 1 \)
D. You cannot have a power of \( 0 \)

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:
Forgotten that anything to the power of 0 equals 1

Question:
\( (16)^{0}=? \)

Options:
A. \( 16 \)
B. \( 0 \)
C. \( 1 \)
D. You cannot have a power of \( 0 \)

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:
When reading integers on a number line, assumes each dash is 10

Question:
What number is the arrow pointing to? ![Number line from 100 to 200 with an arrow pointing to the value 145]()

Options:
A. \( 145 \)
B. \( 140 \)
C. \( 149 \)
D. \( 148 \)

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 integers on a number line, assumes each dash is 1

Question:
What number is the arrow pointing to? ![Number line from 100 to 200 with an arrow pointing to the value 145]()

Options:
A. \( 145 \)
B. \( 140 \)
C. \( 149 \)
D. \( 148 \)

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 integers on a number line, assumes each dash is 2

Question:
What number is the arrow pointing to? ![Number line from 100 to 200 with an arrow pointing to the value 145]()

Options:
A. \( 145 \)
B. \( 140 \)
C. \( 149 \)
D. \( 148 \)

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:
\( 0.01^{3}= \)

Options:
A. \( 0.0001 \)
B. \( 0.000001 \)
C. \( 0.03 \)
D. \( 0.00001 \)

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 cubing a number means you multiply it by 3

Question:
\( 0.01^{3}= \)

Options:
A. \( 0.0001 \)
B. \( 0.000001 \)
C. \( 0.03 \)
D. \( 0.00001 \)

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:
\( 0.01^{3}= \)

Options:
A. \( 0.0001 \)
B. \( 0.000001 \)
C. \( 0.03 \)
D. \( 0.00001 \)

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 can have decimals in a simplified fraction

Question:
Tom and Katie are arguing about how to leave answers to some fractions questions they are working on.

Tom says he is going to leave one of his answers as \( \frac{143}{2} \)

Katie says she is going to leave one of her answers as \( \frac{4.2}{9} \)

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:
Believes you can have decimals in a simplified fraction

Question:
Tom and Katie are arguing about how to leave answers to some fractions questions they are working on.

Tom says he is going to leave one of his answers as \( \frac{143}{2} \)

Katie says she is going to leave one of her answers as \( \frac{4.2}{9} \)

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:
Does not know that you can leave a fraction in improper form

Question:
Tom and Katie are arguing about how to leave answers to some fractions questions they are working on.

Tom says he is going to leave one of his answers as \( \frac{143}{2} \)

Katie says she is going to leave one of her answers as \( \frac{4.2}{9} \)

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:
Divides by the order of the root

Question:
\( \sqrt[3]{27}=? \)

Options:
A. \( 3 \)
B. \( 9 \)
C. \( 81 \)
D. \( 327 \)

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:
\( \sqrt[3]{27}=? \)

Options:
A. \( 3 \)
B. \( 9 \)
C. \( 81 \)
D. \( 327 \)

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 \( R S \).
Which angle is corresponding to angle QMY? ![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 QMY is marked in red.]()

Options:
A. XMP
B. SNY
C. SNX
D. XNR

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 \( R S \).
Which angle is corresponding to angle QMY? ![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 QMY is marked in red.]()

Options:
A. XMP
B. SNY
C. SNX
D. XNR

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 \( R S \).
Which angle is corresponding to angle QMY? ![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 QMY is marked in red.]()

Options:
A. XMP
B. SNY
C. SNX
D. XNR

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 factors and multiples

Question:
A common factor of \( 8 \) and \( 20 \) is...

Options:
A. \( 40 \)
B. \( 20 \)
C. \( 8 \)
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:
Does not know the meaning of common, eg. common factor

Question:
A common factor of \( 8 \) and \( 20 \) is...

Options:
A. \( 40 \)
B. \( 20 \)
C. \( 8 \)
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:
Does not know the meaning of common, eg. common factor

Question:
A common factor of \( 8 \) and \( 20 \) is...

Options:
A. \( 40 \)
B. \( 20 \)
C. \( 8 \)
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:
Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round

Question:
Which vector correctly describes the translation that maps object \( P \) onto object \( Q \)? ![The image shows a pair of axes and two congruent trapezia labelled P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (3, 3), (4, 5), (6, 5), (7, 3).]()

Options:
A. \( \left(\begin{array}{c}2 \\ -4\end{array}\right) \)
B. \( \left(\begin{array}{c}-4 \\ 2\end{array}\right) \)
C. \( \left(\begin{array}{c}4 \\ -2\end{array}\right) \)
D. \( \left(\begin{array}{c}-2 \\ 4\end{array}\right) \)

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 vector correctly describes the translation that maps object \( P \) onto object \( Q \)? ![The image shows a pair of axes and two congruent trapezia labelled P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (3, 3), (4, 5), (6, 5), (7, 3).]()

Options:
A. \( \left(\begin{array}{c}2 \\ -4\end{array}\right) \)
B. \( \left(\begin{array}{c}-4 \\ 2\end{array}\right) \)
C. \( \left(\begin{array}{c}4 \\ -2\end{array}\right) \)
D. \( \left(\begin{array}{c}-2 \\ 4\end{array}\right) \)

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 meaning of perpendicular

Question:
![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a vertical line measuring 2 units. EF is a diagonal line with a positive gradient of 4. GH is a diagonal line with a negative gradient of -4. IJ is a horizontal line measuring 3 units. KL is a diagonal line with a negative gradient of -1. MN is a diagonal line with a positive gradient of 1. OP is a diagonal line with a positive gradient of 4.]() Which line segment is perpendicular to \( \mathrm{MN} \) ?

Options:
A. \( \mathrm{GH} \)
B. \( C D \)
C. OP
D. \( \mathrm{KL} \)

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 meaning of perpendicular and vertical

Question:
![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a vertical line measuring 2 units. EF is a diagonal line with a positive gradient of 4. GH is a diagonal line with a negative gradient of -4. IJ is a horizontal line measuring 3 units. KL is a diagonal line with a negative gradient of -1. MN is a diagonal line with a positive gradient of 1. OP is a diagonal line with a positive gradient of 4.]() Which line segment is perpendicular to \( \mathrm{MN} \) ?

Options:
A. \( \mathrm{GH} \)
B. \( C D \)
C. OP
D. \( \mathrm{KL} \)

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 meaning of perpendicular

Question:
![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a vertical line measuring 2 units. EF is a diagonal line with a positive gradient of 4. GH is a diagonal line with a negative gradient of -4. IJ is a horizontal line measuring 3 units. KL is a diagonal line with a negative gradient of -1. MN is a diagonal line with a positive gradient of 1. OP is a diagonal line with a positive gradient of 4.]() Which line segment is perpendicular to \( \mathrm{MN} \) ?

Options:
A. \( \mathrm{GH} \)
B. \( C D \)
C. OP
D. \( \mathrm{KL} \)

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 total instead of difference when asked 'How many more'

Question:
The bar chart shows the number of students in each year group who study French, Spanish and Chinese.

How many more Year \( 7 s \) than Year 8s study Chinese? ![An image of a bar chart with bars striped red and white for French, blue for Spanish and white for Chinese. The x-axis is marked 'year group' with options 7-11, and the y-axis is marked 'number of children'. ]()

Options:
A. \( 60 \)
B. \( 35 \)
C. \( 85 \)
D. \( 25 \)

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 if two lines do not intersect on a diagram then they will never intersect and are therefore parallel

Question:
Tom and Katie are discussing this pair of lines
Tom says they are parallel
Katie says they are perpendicular
Who do you agree with? ![Two blue lines, each with a small red line marked across them about halfway up. The two blue lines do not touch, but they are closer together at one end.]()

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 any lines that cross are perpendicular

Question:
Tom and Katie are discussing this pair of lines
Tom says they are parallel
Katie says they are perpendicular
Who do you agree with? ![Two blue lines, each with a small red line marked across them about halfway up. The two blue lines do not touch, but they are closer together at one end.]()

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 negative power results in a negative answer

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{2}^{\boldsymbol{x}} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( -5 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( -32 \)
B. \( -\frac{1}{32} \)
C. \( -10 \)
D. \( \frac{1}{32} \)

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 power results in a negative answer

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{2}^{\boldsymbol{x}} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( -5 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( -32 \)
B. \( -\frac{1}{32} \)
C. \( -10 \)
D. \( \frac{1}{32} \)

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:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{2}^{\boldsymbol{x}} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( -5 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( -32 \)
B. \( -\frac{1}{32} \)
C. \( -10 \)
D. \( \frac{1}{32} \)

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 asked for the next term in the sequence subtracts one from the last term given, despite the sequence not going down in ones.

Question:
\( \begin{array}{llll}7.5, & 6.6, & 5.7, & ?\end{array} \)

What is the next term in this linear sequence?

Options:
A. \( 5.8 \)
B. \( 4.7 \)
C. \( 4.9 \)
D. \( 4.8 \)

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 a linear sequence must increase or decrease by same amount

Question:
\( \begin{array}{llll}7.5, & 6.6, & 5.7, & ?\end{array} \)

What is the next term in this linear sequence?

Options:
A. \( 5.8 \)
B. \( 4.7 \)
C. \( 4.9 \)
D. \( 4.8 \)

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:
Misinterprets the meaning of angles on a straight line angle fact

Question:
What is the value of the angle marked \( \mathbf{\square} \) ? ![Image showing three vertices of a polygon. We do not see how many sides the polygon has. The angles shown are marked 20 degrees, 120 degrees and the third is marked with a square.]()

Options:
A. \( 60^{\circ} \)
B. Impossible to say
C. \( 120^{\circ} \)
D. \( 40^{\circ} \)

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:
Thinks angles which look the same on diagram will be equal

Question:
What is the value of the angle marked \( \mathbf{\square} \) ? ![Image showing three vertices of a polygon. We do not see how many sides the polygon has. The angles shown are marked 20 degrees, 120 degrees and the third is marked with a square.]()

Options:
A. \( 60^{\circ} \)
B. Impossible to say
C. \( 120^{\circ} \)
D. \( 40^{\circ} \)

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:
Misinterprets the meaning of angles on a straight line angle fact

Question:
What is the value of the angle marked \( \mathbf{\square} \) ? ![Image showing three vertices of a polygon. We do not see how many sides the polygon has. The angles shown are marked 20 degrees, 120 degrees and the third is marked with a square.]()

Options:
A. \( 60^{\circ} \)
B. Impossible to say
C. \( 120^{\circ} \)
D. \( 40^{\circ} \)

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 that dividing by a decimal is the same as dividing by its reciprocal

Question:
Estimate the value of
\(
\frac{4.12 \times 18.3}{0.226}
\)

Options:
A. \( 14.4 \)
B. \( 16 \)
C. \( 400 \)
D. \( 360 \)

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 when estimating

Question:
Estimate the value of
\(
\frac{4.12 \times 18.3}{0.226}
\)

Options:
A. \( 14.4 \)
B. \( 16 \)
C. \( 400 \)
D. \( 360 \)

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 meaning of the word parallel

Question:
What is the name given to the red line that intersects the two dashed lines? ![Shows two straight horizontal dashed lines that are converging and are both intersected by a solid red line]()

Options:
A. Parallel
B. Corresponding
C. Alternate
D. Transversal

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 meaning of corresponding

Question:
What is the name given to the red line that intersects the two dashed lines? ![Shows two straight horizontal dashed lines that are converging and are both intersected by a solid red line]()

Options:
A. Parallel
B. Corresponding
C. Alternate
D. Transversal

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 meaning of alternate

Question:
What is the name given to the red line that intersects the two dashed lines? ![Shows two straight horizontal dashed lines that are converging and are both intersected by a solid red line]()

Options:
A. Parallel
B. Corresponding
C. Alternate
D. Transversal

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 1 cubic metre = 1000 cubic centimetres

Question:
\(
1 m^3 =\bigstar cm^3
\)

What should replace the star?

Options:
A. \( 1000000 \)
B. \( 1000 \)
C. \( 100 \)
D. \( 10000 \)

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 cube the conversion factor when converting cubed units

Question:
\(
1 m^3 =\bigstar cm^3
\)

What should replace the star?

Options:
A. \( 1000000 \)
B. \( 1000 \)
C. \( 100 \)
D. \( 10000 \)

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 cube the conversion factor when converting cubed units

Question:
\(
1 m^3 =\bigstar cm^3
\)

What should replace the star?

Options:
A. \( 1000000 \)
B. \( 1000 \)
C. \( 100 \)
D. \( 10000 \)

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 isosceles and equilateral triangles

Question:
An isosceles triangle must have ...

Options:
A. three \( 60^{\circ} \) angles.
B. a right angle.
C. three equal side lengths.
D. two sides of equal length and two equal angles.

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 isosceles and right angle triangles

Question:
An isosceles triangle must have ...

Options:
A. three \( 60^{\circ} \) angles.
B. a right angle.
C. three equal side lengths.
D. two sides of equal length and two equal angles.

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 isosceles and equilateral triangles

Question:
An isosceles triangle must have ...

Options:
A. three \( 60^{\circ} \) angles.
B. a right angle.
C. three equal side lengths.
D. two sides of equal length and two equal angles.

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 that two letters together, or a number and letter together, are multiplying

Question:
Tom and Katie are discussing this function machine ![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 "m" written inside it. The middle rectangle is empty and the final rectangle has "output" written above it and "4m" written inside it.]() Tom says the function could be \( +3 m \)

Katie says the function could be \( \times 4 \)

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:
Does not understand when like terms can be collected

Question:
Tom and Katie are discussing this function machine ![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 "m" written inside it. The middle rectangle is empty and the final rectangle has "output" written above it and "4m" written inside it.]() Tom says the function could be \( +3 m \)

Katie says the function could be \( \times 4 \)

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:
Does not realise that two letters together, or a number and letter together, are multiplying

Question:
Tom and Katie are discussing this function machine ![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 "m" written inside it. The middle rectangle is empty and the final rectangle has "output" written above it and "4m" written inside it.]() Tom says the function could be \( +3 m \)

Katie says the function could be \( \times 4 \)

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:
When ordering integers, orders from the digits at the end of the number instead of the digits at the start

Question:
Which symbol makes the following statement correct?
\[
1,959,909 \quad
 \square \quad
1,995,902
\]

Options:
A. \( > \)
B. \( = \)
C. None of these
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 understand inequality notation

Question:
Which symbol makes the following statement correct?
\[
1,959,909 \quad
 \square \quad
1,995,902
\]

Options:
A. \( > \)
B. \( = \)
C. None of these
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 understand inequality notation

Question:
Which symbol makes the following statement correct?
\[
1,959,909 \quad
 \square \quad
1,995,902
\]

Options:
A. \( > \)
B. \( = \)
C. None of these
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:
Believes a direct proportion graph is a horizontal line

Question:
\( £ 1 \) is \( 1.5 \) US dollars.
Which of these graphs shows the value of up to \( £ 10 \) in US dollars?

Options:
A. ![A straight line graph from the origin. Y axis labelled US dollars extending to 10, x axis labelled pounds extending to 15]()
B. ![A straight horizontal line graph from 15 on the y axis. Y axis labelled US dollars extending to 15, x axis labelled pounds extending to 10]()
C. ![A straight line graph from the origin. Y axis labelled US dollars extending to 15, x axis labelled pounds extending to 10]()
D. ![A straight line graph from approx 5 on the y axis. Y axis labelled US dollars extending to 15, x axis labelled pounds extending to 10]()

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 direct proportion graph does not have to start at the origin

Question:
\( £ 1 \) is \( 1.5 \) US dollars.
Which of these graphs shows the value of up to \( £ 10 \) in US dollars?

Options:
A. ![A straight line graph from the origin. Y axis labelled US dollars extending to 10, x axis labelled pounds extending to 15]()
B. ![A straight horizontal line graph from 15 on the y axis. Y axis labelled US dollars extending to 15, x axis labelled pounds extending to 10]()
C. ![A straight line graph from the origin. Y axis labelled US dollars extending to 15, x axis labelled pounds extending to 10]()
D. ![A straight line graph from approx 5 on the y axis. Y axis labelled US dollars extending to 15, x axis labelled pounds extending to 10]()

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 work out all possibilites when given an 'at least' question in probability

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. The balls are all the same size.]() Kate picks out two balls at the same time.

What is the probability at least one ball is red?

Options:
A. \( \frac{12}{42} \)
B. \( \frac{36}{42} \)
C. \( \frac{24}{42} \)
D. \( \frac{37}{42} \)

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 work out all possibilites when given an 'at least' question in probability

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. The balls are all the same size.]() Kate picks out two balls at the same time.

What is the probability at least one ball is red?

Options:
A. \( \frac{12}{42} \)
B. \( \frac{36}{42} \)
C. \( \frac{24}{42} \)
D. \( \frac{37}{42} \)

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 numerators when working out a combined probability

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup ![A cup with 4 red and 3 yellow balls in it. The balls are all the same size.]() Kate picks out two balls at the same time.

What is the probability at least one ball is red?

Options:
A. \( \frac{12}{42} \)
B. \( \frac{36}{42} \)
C. \( \frac{24}{42} \)
D. \( \frac{37}{42} \)

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 negative of a positive squared (where there are no brackets) gives a positive answer

Question:
What answer would your calculator give if you typed in \(-5^{2}\) ![A scientific calculator]()

Options:
A. \( 25 \)
B. \( -25 \)
C. \( 10 \)
D. \( -10 \)

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 the base number and the power

Question:
What answer would your calculator give if you typed in \(-5^{2}\) ![A scientific calculator]()

Options:
A. \( 25 \)
B. \( -25 \)
C. \( 10 \)
D. \( -10 \)

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 change in y for gradient is always calculated from the origin, regardless of the y-intercept of the line

Question:
The cost of a taxi-ride is shown on the graph.

What is the cost per mile? ![The graph is Cost (£) on the vertical axis and Distance (miles) on the horizontal axis. The graph is a straight line from (0, 2) to (5, 6)]()

Options:
A. £6
B. \( £ 1.20 \)
C. \( £ 1 \)
D. \( £ 0.80 \)

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 graph, chooses nearest marked value on axis instead of reading accurately

Question:
The cost of a taxi-ride is shown on the graph.

What is the cost per mile? ![The graph is Cost (£) on the vertical axis and Distance (miles) on the horizontal axis. The graph is a straight line from (0, 2) to (5, 6)]()

Options:
A. £6
B. \( £ 1.20 \)
C. \( £ 1 \)
D. \( £ 0.80 \)

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 using a function machine, confuses the input and the output.

Question:
Cally wants to use the function machine below to solve this problem:

I think of a number, double it, subtract 5, and the answer is \( 23 \).

Which of the following should replace the star? ![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and has "input" written above it. The next 2 rectangles are empty and the final rectangle on the right has a purple star inside it and has "output" written above it.]()

Options:
A. \( n \)
B. \( \times 2 \)
C. \( -5 \)
D. \( 23 \)

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 where to place inputs/ operations/ outputs when drawing a function machine

Question:
Cally wants to use the function machine below to solve this problem:

I think of a number, double it, subtract 5, and the answer is \( 23 \).

Which of the following should replace the star? ![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and has "input" written above it. The next 2 rectangles are empty and the final rectangle on the right has a purple star inside it and has "output" written above it.]()

Options:
A. \( n \)
B. \( \times 2 \)
C. \( -5 \)
D. \( 23 \)

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 where to place inputs/ operations/ outputs when drawing a function machine

Question:
Cally wants to use the function machine below to solve this problem:

I think of a number, double it, subtract 5, and the answer is \( 23 \).

Which of the following should replace the star? ![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and has "input" written above it. The next 2 rectangles are empty and the final rectangle on the right has a purple star inside it and has "output" written above it.]()

Options:
A. \( n \)
B. \( \times 2 \)
C. \( -5 \)
D. \( 23 \)

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 fractions with larger denominators are greater in size

Question:
What sign would make this statement true?
\(
\frac{4}{6} ? \frac{10}{15}
\)

Options:
A. \( > \)
B. \( < \)
C. \( = \)
D. \( \approx \)

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:
Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator

Question:
Simplify the following, if possible
\(
\frac{5 m-10}{m^{2}+3 m-10}
\)

Options:
A. \( \frac{5}{m+3} \)
B. \( \frac{5 m}{m^{2}+3 m} \)
C. \( \frac{5}{m+5} \)
D. Does not simplify

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 simplify algebraic fractions

Question:
Simplify the following, if possible
\(
\frac{5 m-10}{m^{2}+3 m-10}
\)

Options:
A. \( \frac{5}{m+3} \)
B. \( \frac{5 m}{m^{2}+3 m} \)
C. \( \frac{5}{m+5} \)
D. Does not simplify

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:
\(
\frac{2}{5} \div 2
\)

Options:
A. \( \frac{1}{5} \)
B. \( \frac{1}{10} \)
C. \( \frac{4}{5} \)
D. \( \frac{4}{10} \)

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:
\(
\frac{2}{5} \div 2
\)

Options:
A. \( \frac{1}{5} \)
B. \( \frac{1}{10} \)
C. \( \frac{4}{5} \)
D. \( \frac{4}{10} \)

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 gradient of a speed-time graph is the speed

Question:
Jadon decides to go for a run.
The graph on the right shows Jadon's speed in metres per second \( (s) \) over time in seconds
\( (t) \).

The gradient of the negative sloping section of the graph is \( 0.8 \).

Which of the following does that \( 0.8 \) best represent? ![A sketch of a graph with s on the y axis and t on the x axis. A straight line slopes upwards from the origin 2/3 of the way up the graph, 1/5 across the graph. It then becomes horizontal for the next 1/5 of the graph, before sloping downwards in a straight line for the remainder of the graph. ]()

Options:
A. Jadon is travelling at a speed of \( 0.8 \mathrm{~m} / \mathrm{s} \)
B. Jadon is decelerating at a rate of \( 0.8 \mathrm{~m} / \mathrm{s}^{2} \)
C. Jadon is resting for \( 0.8 \) seconds
D. Jadon is accelerating at a rate of \( 0.8 \mathrm{~m} / \mathrm{s}^{2} \)

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 a downward slope on a speed-time graph shows positive acceleration

Question:
Jadon decides to go for a run.
The graph on the right shows Jadon's speed in metres per second \( (s) \) over time in seconds
\( (t) \).

The gradient of the negative sloping section of the graph is \( 0.8 \).

Which of the following does that \( 0.8 \) best represent? ![A sketch of a graph with s on the y axis and t on the x axis. A straight line slopes upwards from the origin 2/3 of the way up the graph, 1/5 across the graph. It then becomes horizontal for the next 1/5 of the graph, before sloping downwards in a straight line for the remainder of the graph. ]()

Options:
A. Jadon is travelling at a speed of \( 0.8 \mathrm{~m} / \mathrm{s} \)
B. Jadon is decelerating at a rate of \( 0.8 \mathrm{~m} / \mathrm{s}^{2} \)
C. Jadon is resting for \( 0.8 \) seconds
D. Jadon is accelerating at a rate of \( 0.8 \mathrm{~m} / \mathrm{s}^{2} \)

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:
Adds instead of multiplying when expanding bracket

Question:
\( y=(x-8)(x-6) \) \( y=(x-8)(x-6) \) Where does this curve intercept the \( y \) axis? Where does this curve intercept the \( y \) axis?

Options:
A. \( (0,-14) \) \( (0,-14) \)
B. \( \begin{array}{c}(0,8) \\ \text { and } \\ (0,6)\end{array} \) \( \begin{array}{c}(0,8) \\ \text { and } \\ (0,6)\end{array} \)
C. \( (0,48) \) \( (0,48) \)
D. \( (0,-48) \) \( (0,-48) \)

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:
Believes that the y intercept is where y = 0

Question:
\( y=(x-8)(x-6) \) \( y=(x-8)(x-6) \) Where does this curve intercept the \( y \) axis? Where does this curve intercept the \( y \) axis?

Options:
A. \( (0,-14) \) \( (0,-14) \)
B. \( \begin{array}{c}(0,8) \\ \text { and } \\ (0,6)\end{array} \) \( \begin{array}{c}(0,8) \\ \text { and } \\ (0,6)\end{array} \)
C. \( (0,48) \) \( (0,48) \)
D. \( (0,-48) \) \( (0,-48) \)

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:
Believes multiplying two negatives gives a negative answer

Question:
\( y=(x-8)(x-6) \) \( y=(x-8)(x-6) \) Where does this curve intercept the \( y \) axis? Where does this curve intercept the \( y \) axis?

Options:
A. \( (0,-14) \) \( (0,-14) \)
B. \( \begin{array}{c}(0,8) \\ \text { and } \\ (0,6)\end{array} \) \( \begin{array}{c}(0,8) \\ \text { and } \\ (0,6)\end{array} \)
C. \( (0,48) \) \( (0,48) \)
D. \( (0,-48) \) \( (0,-48) \)

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 adding roots, adds the numbers under the roots

Question:
Tom and Katie are discussing calculations involving square roots.

Tom says \( \sqrt{16}+\sqrt{9}=5 \)

Katie says \( \sqrt{16+9}=5 \)

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 square root

Question:
Tom and Katie are discussing calculations involving square roots.

Tom says \( \sqrt{16}+\sqrt{9}=5 \)

Katie says \( \sqrt{16+9}=5 \)

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:
Uses first term as numerical part of nth term rule

Question:
\( \frac{1}{24}, \frac{1}{12}, \frac{1}{8}, \frac{1}{6}, \ldots \) When calculating the nth-term rule of this sequence, what should replace the rectangle? ![nth-term rule:
\[
\frac{1}{24} n
\] followed by a purple rectangle. ]()

Options:
A. \( +\frac{1}{24} \)
B. \( +\frac{1}{36} \)
C. \( +\frac{1}{48} \)
D. \( +0 \)

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:
Does not recognise that addition is the inverse operation of subtraction

Question:
Tom and Katie are trying to write calculations based on the diagram below.

Tom writes: \( 15-20=-5 \)

Katie writes: \( (-5)+20=15 \)

Who is correct? ![Number line with an arrow marked -20 going from 15 to -5]()

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 that subtracting a larger number from a smaller number will give a negative answer

Question:
Tom and Katie are trying to write calculations based on the diagram below.

Tom writes: \( 15-20=-5 \)

Katie writes: \( (-5)+20=15 \)

Who is correct? ![Number line with an arrow marked -20 going from 15 to -5]()

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 the diagram given in the question

Question:
Tom and Katie are trying to write calculations based on the diagram below.

Tom writes: \( 15-20=-5 \)

Katie writes: \( (-5)+20=15 \)

Who is correct? ![Number line with an arrow marked -20 going from 15 to -5]()

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:
Mixes up squaring and multiplying by 2 or doubling

Question:
A sequence is formed using the rule

Square the position and add \( 5 \)

What is the third term in the sequence?

Options:
A. \( 14 \)
B. \( 11 \)
C. \( 6 \)
D. \( 8 \)

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 asked for a specific term in a sequence gives the next term

Question:
A sequence is formed using the rule

Square the position and add \( 5 \)

What is the third term in the sequence?

Options:
A. \( 14 \)
B. \( 11 \)
C. \( 6 \)
D. \( 8 \)

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:
This is a part of the table of values for the equation \( \boldsymbol{y}=\boldsymbol{x}^{\mathbf{3}} \) ![\begin{tabular}{|c|c|}
\hline\( x \) & \( 2 \) \\
\hline\( y \) & W \\
\hline
\end{tabular}]() What should replace the star?

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 8 \)
D. \( 23 \)

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:
This is a part of the table of values for the equation \( \boldsymbol{y}=\boldsymbol{x}^{\mathbf{3}} \) ![\begin{tabular}{|c|c|}
\hline\( x \) & \( 2 \) \\
\hline\( y \) & W \\
\hline
\end{tabular}]() What should replace the star?

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 8 \)
D. \( 23 \)

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:
This is a part of the table of values for the equation \( \boldsymbol{y}=\boldsymbol{x}^{\mathbf{3}} \) ![\begin{tabular}{|c|c|}
\hline\( x \) & \( 2 \) \\
\hline\( y \) & W \\
\hline
\end{tabular}]() What should replace the star?

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 8 \)
D. \( 23 \)

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 scales on graphs must match on both axes

Question:
This displacement-time graph shows \( 10 \) seconds of Mo's journey home.

During that time he travelled at a speed of \( 15 \mathrm{~m} / \mathrm{s} \).

What distance should replace the star? ![The graph has its vertical axis labelled Distance (m) and it has no scale written except for a star three squares up.
The horizontal axis is labelled Time (secs) and has the scale 0, 2, 4, 6, 8, 10 in even steps.
The graph is a straight line sloping down from (0, star) to (10, 0).
]()

Options:
A. \( 6 m \)
B. \( 30 \mathrm{~m} \)
C. \( 1.5 \mathrm{~m} \)
D. \( 150 \mathrm{~m} \)

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}.