Prompt:
Misconception:
When collecting like terms, assigns positivity or negativity incorrectly.

Question:
Simplify the following expression by collecting
like terms
\(6 x-2 y-x+3 y\)

Options:
A. \( 5 x+5 y \)
B. \( 5 x+y \)
C. \( 7 x+5 y \)
D. \( 7 x+y \)

Solve the problem as a student with the misconception above.
You 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 collecting like terms, treats subtractions as if they are additions

Question:
Simplify the following expression by collecting
like terms
\(6 x-2 y-x+3 y\)

Options:
A. \( 5 x+5 y \)
B. \( 5 x+y \)
C. \( 7 x+5 y \)
D. \( 7 x+y \)

Solve the problem as a student with the misconception above.
You 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 collecting like terms, assigns positivity or negativity incorrectly.

Question:
Simplify the following expression by collecting
like terms
\(6 x-2 y-x+3 y\)

Options:
A. \( 5 x+5 y \)
B. \( 5 x+y \)
C. \( 7 x+5 y \)
D. \( 7 x+y \)

Solve the problem as a student with the misconception above.
You 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 collecting like terms, assigns positivity or negativity incorrectly.

Question:
Simplify the following by collecting like terms. \( \frac{2}{3} k^{2}+\frac{1}{6} k^{2}-\frac{1}{3} k^{2}+\frac{5}{6} k^{2} \)

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

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


Prompt:
Misconception:
Does not think that a variable with no coefficient has a coefficient of 1.

Question:
Simplify the following by collecting like terms. \( \frac{2}{3} k^{2}+\frac{1}{6} k^{2}-\frac{1}{3} k^{2}+\frac{5}{6} k^{2} \)

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

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


Prompt:
Misconception:
When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle

Question:
What is the median of the following numbers?
\[
2, \quad 0.2, \quad 0.02, \quad 0.002
\]

Options:
A. \( 0.22 \)
B. \( 0.11 \)
C. \( 0.44 \)
D. \( 0.011 \)

Solve the problem as a student with the misconception above.
You 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:
What is the median of the following numbers?
\[
2, \quad 0.2, \quad 0.02, \quad 0.002
\]

Options:
A. \( 0.22 \)
B. \( 0.11 \)
C. \( 0.44 \)
D. \( 0.011 \)

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


Prompt:
Misconception:
Finds the median instead of the mode

Question:
This table shows the ages of people on a university running team.

What is the modal age? \begin{tabular}{|c|c|l|}
\hline Age & Frequency & \\
\hline \( 18 \) & \( 7 \) & \\
\hline \( 19 \) & \( 3 \) & \\
\hline \( 20 \) & \( 1 \) & \\
\hline \( 21 \) & \( 2 \) & \\
\hline
\end{tabular}

Options:
A. \( 18 \)
B. \( 19.5 \)
C. \( 7 \)
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:
Believes the mode is the frequency rather than the value/group

Question:
This table shows the ages of people on a university running team.

What is the modal age? \begin{tabular}{|c|c|l|}
\hline Age & Frequency & \\
\hline \( 18 \) & \( 7 \) & \\
\hline \( 19 \) & \( 3 \) & \\
\hline \( 20 \) & \( 1 \) & \\
\hline \( 21 \) & \( 2 \) & \\
\hline
\end{tabular}

Options:
A. \( 18 \)
B. \( 19.5 \)
C. \( 7 \)
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:
Believes when identifying the mode you look at all values, not just frequencies, for the highest number

Question:
This table shows the ages of people on a university running team.

What is the modal age? \begin{tabular}{|c|c|l|}
\hline Age & Frequency & \\
\hline \( 18 \) & \( 7 \) & \\
\hline \( 19 \) & \( 3 \) & \\
\hline \( 20 \) & \( 1 \) & \\
\hline \( 21 \) & \( 2 \) & \\
\hline
\end{tabular}

Options:
A. \( 18 \)
B. \( 19.5 \)
C. \( 7 \)
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:
Has treated this like an addition problem and added the ones column.

Question:
\( \begin{array}{r}\quad58 \\ \times 22 \\ \hline\end{array} \) What number will be in the ones/units column of the final answer?

Options:
A. \( 6 \)
B. \( 0 \)
C. \( 1 \)
D. \( 16 \)

Solve the problem as a student with the misconception above.
You 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 written the value of the 'ones' column as the answer, withiut using the numbers in the question.

Question:
\( \begin{array}{r}\quad58 \\ \times 22 \\ \hline\end{array} \) What number will be in the ones/units column of the final answer?

Options:
A. \( 6 \)
B. \( 0 \)
C. \( 1 \)
D. \( 16 \)

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


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

Question:
\[
300200
\]
Write this number using standard form

Options:
A. \( 3.002 \times 10^{5} \)
B. \( 3.2 \times 10^{5} \)
C. \( 3.002 \times 10^{6} \)
D. \( 3.2 \times 10^{6} \)

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 writing standard form does not give the correct power of ten

Question:
\[
300200
\]
Write this number using standard form

Options:
A. \( 3.002 \times 10^{5} \)
B. \( 3.2 \times 10^{5} \)
C. \( 3.002 \times 10^{6} \)
D. \( 3.2 \times 10^{6} \)

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 changing a number to standard form omits zero's of significance

Question:
\[
300200
\]
Write this number using standard form

Options:
A. \( 3.002 \times 10^{5} \)
B. \( 3.2 \times 10^{5} \)
C. \( 3.002 \times 10^{6} \)
D. \( 3.2 \times 10^{6} \)

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:
Does not divide by 2 when finding midpoint

Question:
What is the midpoint of \( (4,3) \) and \( (1,-5) \) ?

Options:
A. \( (2.5,-1) \)
B. \( (5,-2) \)
C. \( (2.5,-4) \)
D. Impossible as you can't have a decimal coordinate

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


Prompt:
Misconception:
Does not understand that coordinates can be decimals

Question:
What is the midpoint of \( (4,3) \) and \( (1,-5) \) ?

Options:
A. \( (2.5,-1) \)
B. \( (5,-2) \)
C. \( (2.5,-4) \)
D. Impossible as you can't have a decimal coordinate

Solve the problem as a student with the misconception above.
You 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:
What is the first term of the sequence given by this rule:
\[
4 n+3
\]

Options:
A. \( 4 \)
B. \( 7 \)
C. \( 3 \)
D. \( 43 \)

Solve the problem as a student with the misconception above.
You 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 first term in a sequence is the term before the sequence begins (0th term)

Question:
What is the first term of the sequence given by this rule:
\[
4 n+3
\]

Options:
A. \( 4 \)
B. \( 7 \)
C. \( 3 \)
D. \( 43 \)

Solve the problem as a student with the misconception above.
You 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 applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction

Question:
STEP \( 3 \)

Which of the options is the final answer, expressed as simply as possible?
\(
\begin{aligned}
& \frac{3 x+1}{3} \div \frac{9 x^{2}-1}{12} \\
= & \frac{3 x+1}{3} \times \frac{12}{9 x^{2}-1} \\
= & \frac{3 x+1}{3} \times \frac{12}{(3 x-1)(3 x+1)}
\end{aligned}
\)

Options:
A. \( \frac{12}{9 x-1} \)
B. \( \frac{4(3 x+1)}{(3 x-1)(3 x+1)} \)
C. \( \frac{5}{3 x} \)
D. \( \frac{4}{3 x-1} \)

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


Prompt:
Misconception:
When simplifying an algebraic fraction, only looks for number factors

Question:
STEP \( 3 \)

Which of the options is the final answer, expressed as simply as possible?
\(
\begin{aligned}
& \frac{3 x+1}{3} \div \frac{9 x^{2}-1}{12} \\
= & \frac{3 x+1}{3} \times \frac{12}{9 x^{2}-1} \\
= & \frac{3 x+1}{3} \times \frac{12}{(3 x-1)(3 x+1)}
\end{aligned}
\)

Options:
A. \( \frac{12}{9 x-1} \)
B. \( \frac{4(3 x+1)}{(3 x-1)(3 x+1)} \)
C. \( \frac{5}{3 x} \)
D. \( \frac{4}{3 x-1} \)

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

Question:
STEP \( 3 \)

Which of the options is the final answer, expressed as simply as possible?
\(
\begin{aligned}
& \frac{3 x+1}{3} \div \frac{9 x^{2}-1}{12} \\
= & \frac{3 x+1}{3} \times \frac{12}{9 x^{2}-1} \\
= & \frac{3 x+1}{3} \times \frac{12}{(3 x-1)(3 x+1)}
\end{aligned}
\)

Options:
A. \( \frac{12}{9 x-1} \)
B. \( \frac{4(3 x+1)}{(3 x-1)(3 x+1)} \)
C. \( \frac{5}{3 x} \)
D. \( \frac{4}{3 x-1} \)

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:
Rounded to wrong degree of accuracy (2sf not 1sf)

Question:
Julie wants to estimate the answer to this calculation by rounding each number to \( 1 \) significant figure.

\[
87.4 \times 0.3727
\]

What number should replace \( \mathbf{8 7 . 4} \) in her estimation?

Options:
A. \( 90 \)
B. \( 87 \)
C. \( 88 \)
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:
Rounds to the wrong degree of accuracy (rounds too little)

Question:
Julie wants to estimate the answer to this calculation by rounding each number to \( 1 \) significant figure.

\[
87.4 \times 0.3727
\]

What number should replace \( \mathbf{8 7 . 4} \) in her estimation?

Options:
A. \( 90 \)
B. \( 87 \)
C. \( 88 \)
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:
Rounds down instead of up

Question:
Julie wants to estimate the answer to this calculation by rounding each number to \( 1 \) significant figure.

\[
87.4 \times 0.3727
\]

What number should replace \( \mathbf{8 7 . 4} \) in her estimation?

Options:
A. \( 90 \)
B. \( 87 \)
C. \( 88 \)
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:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Factorise this expression, if possible:
\(
p^{2}+5 p+6
\)

Options:
A. \( (p+2)(p+3) \)
B. \( (p+6)(p+1) \)
C. \( (p+6)(p-1) \)
D. Does not factorise

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x

Question:
Factorise this expression, if possible:
\(
p^{2}+5 p+6
\)

Options:
A. \( (p+2)(p+3) \)
B. \( (p+6)(p+1) \)
C. \( (p+6)(p-1) \)
D. Does not factorise

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


Prompt:
Misconception:
In ratio question where one side of ratio is given, treats that as the total

Question:
Josh and Lucy share some money in the ratio \( 3: 7 \)

Josh receives \( £ 84 \).

How much money does Lucy receive?

Options:
A. \( £ 196 \)
B. \( £ 58.80 \)
C. \( £ 28 \)
D. \( £ 36 \)

Solve the problem as a student with the misconception above.
You 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 one part of a ratio but doesn't multiply that by the number of parts needed

Question:
Josh and Lucy share some money in the ratio \( 3: 7 \)

Josh receives \( £ 84 \).

How much money does Lucy receive?

Options:
A. \( £ 196 \)
B. \( £ 58.80 \)
C. \( £ 28 \)
D. \( £ 36 \)

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


Prompt:
Misconception:
Gets order of ratio wrong

Question:
Josh and Lucy share some money in the ratio \( 3: 7 \)

Josh receives \( £ 84 \).

How much money does Lucy receive?

Options:
A. \( £ 196 \)
B. \( £ 58.80 \)
C. \( £ 28 \)
D. \( £ 36 \)

Solve the problem as a student with the misconception above.
You 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 more digits a number has the greater it is, regardless of place value

Question:
Here are the depths below sea level of \( 3 \) creatures:
Tuna: \( -2.6 m \)
Ray: \( -6 m \)
Ling: \( -1.5 \mathrm{~m} \)
Arrange their depths in ascending order, starting with the deepest

Options:
A. \( 1^{\text {st }} \) Tuna
\( 2^{\text {nd }} \) Ling
\( 3^{\text {rd }} \) Ray
B. \( 1^{\text {st }} \) Ling
\( 2^{\text {nd }} \) Ray
\( 3^{\text {rd }} \) Tuna
C. \( \begin{array}{l}1^{\text {st }} \text { Ling } \\ 2^{\text {nd }} \text { Tuna } \\ 3^{\text {rd }} \text { Ray }\end{array} \)
D. \( 1^{\text {st }} \) Ray \( 2^{\text {nd }} \) Tuna \( 3^{\text {rd }} \) Ling

Solve the problem as a student with the misconception above.
You 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 negative numbers with a larger absolute value are greater

Question:
Here are the depths below sea level of \( 3 \) creatures:
Tuna: \( -2.6 m \)
Ray: \( -6 m \)
Ling: \( -1.5 \mathrm{~m} \)
Arrange their depths in ascending order, starting with the deepest

Options:
A. \( 1^{\text {st }} \) Tuna
\( 2^{\text {nd }} \) Ling
\( 3^{\text {rd }} \) Ray
B. \( 1^{\text {st }} \) Ling
\( 2^{\text {nd }} \) Ray
\( 3^{\text {rd }} \) Tuna
C. \( \begin{array}{l}1^{\text {st }} \text { Ling } \\ 2^{\text {nd }} \text { Tuna } \\ 3^{\text {rd }} \text { Ray }\end{array} \)
D. \( 1^{\text {st }} \) Ray \( 2^{\text {nd }} \) Tuna \( 3^{\text {rd }} \) Ling

Solve the problem as a student with the misconception above.
You 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:
Amy is trying to work out the distance between these two points: \( (2,-5) \) and \( (-7,1) \) She labels them like this: \( \begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\ (2, & -5) & (-7, & 1)\end{array} \) And then decides to use this formula: \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \) What does the first bracket equal?

Options:
A. \( (-9)^{2} \)
B. \( (-5)^{2} \)
C. \( (9)^{2} \)
D. \( (5)^{2} \)

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


Prompt:
Misconception:
Believes subtraction is commutative

Question:
Amy is trying to work out the distance between these two points: \( (2,-5) \) and \( (-7,1) \) She labels them like this: \( \begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\ (2, & -5) & (-7, & 1)\end{array} \) And then decides to use this formula: \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \) What does the first bracket equal?

Options:
A. \( (-9)^{2} \)
B. \( (-5)^{2} \)
C. \( (9)^{2} \)
D. \( (5)^{2} \)

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


Prompt:
Misconception:
When asked for the mean of a list of data, gives the mode

Question:
What is the mean of this set of data?
\[
5, \quad 2, \quad 0, \quad 2, \quad 3
\]

Options:
A. \( 2 \)
B. \( 3 \)
C. \( 2.4 \)
D. \( 2.5 \)

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


Prompt:
Misconception:
When asked for the mean of a list of data, does not count any zeros in the data when working out what to divide by

Question:
What is the mean of this set of data?
\[
5, \quad 2, \quad 0, \quad 2, \quad 3
\]

Options:
A. \( 2 \)
B. \( 3 \)
C. \( 2.4 \)
D. \( 2.5 \)

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 follow the arrows through a function machine, changes the order of the operations asked.

Question:
Which of the following pairs of function machines are correct?

Options:
A. \(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2a-5\)

\(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2(a-5)\)
B. \(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2a-5\)

\(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2(a-5)\)
C. \(a \Rightarrow -5 \Rightarrow \times2 \Rightarrow 2a-5\)

\(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2(a-5)\)
D. \(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2a-5\)

\(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2(a-5)\)

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 follow the arrows through a function machine, changes the order of the operations asked.

Question:
Which of the following pairs of function machines are correct?

Options:
A. \(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2a-5\)

\(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2(a-5)\)
B. \(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2a-5\)

\(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2(a-5)\)
C. \(a \Rightarrow -5 \Rightarrow \times2 \Rightarrow 2a-5\)

\(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2(a-5)\)
D. \(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2a-5\)

\(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2(a-5)\)

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 follow the arrows through a function machine, changes the order of the operations asked.

Question:
Which of the following pairs of function machines are correct?

Options:
A. \(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2a-5\)

\(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2(a-5)\)
B. \(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2a-5\)

\(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2(a-5)\)
C. \(a \Rightarrow -5 \Rightarrow \times2 \Rightarrow 2a-5\)

\(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2(a-5)\)
D. \(a \Rightarrow \times2  \Rightarrow -5\Rightarrow 2a-5\)

\(a \Rightarrow -5  \Rightarrow \times2\Rightarrow 2(a-5)\)

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:
Confuses order of sides in a trigonometric ratio

Question:
\(
\bigstar=\frac{\text { Hypotenuse }}{\text { Opposite }}
\)

What should replace the star?

Options:
A. \( \sin (\theta) \)
B. \( \cos (\theta) \)
C. \( \tan (\theta) \)
D. None of these

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


Prompt:
Misconception:
Uses cos when sin is required

Question:
\(
\bigstar=\frac{\text { Hypotenuse }}{\text { Opposite }}
\)

What should replace the star?

Options:
A. \( \sin (\theta) \)
B. \( \cos (\theta) \)
C. \( \tan (\theta) \)
D. None of these

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


Prompt:
Misconception:
Uses tan when sin is required

Question:
\(
\bigstar=\frac{\text { Hypotenuse }}{\text { Opposite }}
\)

What should replace the star?

Options:
A. \( \sin (\theta) \)
B. \( \cos (\theta) \)
C. \( \tan (\theta) \)
D. None of these

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


Prompt:
Misconception:
Subtracts simultaneous equations when addition is required

Question:
Tom and Katie are discussing this pair of simultaneous equations: \( \begin{array}{l}3 x-2 y=15 \\ x+2 y=20\end{array} \) Tom says if you add the two equations together you will eliminate a variable

Katie says if you subtract the two equations together you will eliminate a variable

Who is correct?

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

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


Prompt:
Misconception:
When solving simultaneous equations thinks that identical terms in given equations can be eliminated by either adding or subtracting.

Question:
Tom and Katie are discussing this pair of simultaneous equations: \( \begin{array}{l}3 x-2 y=15 \\ x+2 y=20\end{array} \) Tom says if you add the two equations together you will eliminate a variable

Katie says if you subtract the two equations together you will eliminate a variable

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:
Confuses the part and the whole in fraction of an amount problems

Question:
Here is a number card
\( \frac{1}{6} \) of \( A \) is \( 12 \)
What is \( \frac{1}{8} \) of \( A \) ? ![A pink rounded rectangle with a capital A typed inside]()

Options:
A. \( 0.25 \)
B. \( 4 \)
C. \( 72 \)
D. \( 9 \)

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


Prompt:
Misconception:
Confuses the part and the whole in fraction of an amount problems

Question:
Here is a number card
\( \frac{1}{6} \) of \( A \) is \( 12 \)
What is \( \frac{1}{8} \) of \( A \) ? ![A pink rounded rectangle with a capital A typed inside]()

Options:
A. \( 0.25 \)
B. \( 4 \)
C. \( 72 \)
D. \( 9 \)

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


Prompt:
Misconception:
In a worded problem, does not complete all calculations

Question:
Here is a number card
\( \frac{1}{6} \) of \( A \) is \( 12 \)
What is \( \frac{1}{8} \) of \( A \) ? ![A pink rounded rectangle with a capital A typed inside]()

Options:
A. \( 0.25 \)
B. \( 4 \)
C. \( 72 \)
D. \( 9 \)

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


Prompt:
Misconception:
When given a linear sequence, cannot match it to a visual pattern

Question:
\[
1,3,6,10, \ldots \text { ? }
\]

Which pattern matches the sequence above?

Options:
A. ![The square numbers represented by green circles arranged into squares.]()
B. ![The cube numbers represented by small, pale, blue cubes arranged into larger cubes]()
C. ![The triangle numbers represented by dark blue circles arranged into triangles.]()
D. ![A sequence represented using red circles arranged in a pattern so that the first term has one red dot and then an additional two dots are added underneath this one red dot for the second term. For the third term another two red dots are added underneath and for the fourth term, two more added underneath the previous pattern.]()

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


Prompt:
Misconception:
When given a linear sequence, cannot match it to a visual pattern

Question:
\[
1,3,6,10, \ldots \text { ? }
\]

Which pattern matches the sequence above?

Options:
A. ![The square numbers represented by green circles arranged into squares.]()
B. ![The cube numbers represented by small, pale, blue cubes arranged into larger cubes]()
C. ![The triangle numbers represented by dark blue circles arranged into triangles.]()
D. ![A sequence represented using red circles arranged in a pattern so that the first term has one red dot and then an additional two dots are added underneath this one red dot for the second term. For the third term another two red dots are added underneath and for the fourth term, two more added underneath the previous pattern.]()

Solve the problem as a student with the misconception above.
You 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 first two terms of a sequence to work out a term-to-term rule

Question:
\[
1,3,6,10, \ldots \text { ? }
\]

Which pattern matches the sequence above?

Options:
A. ![The square numbers represented by green circles arranged into squares.]()
B. ![The cube numbers represented by small, pale, blue cubes arranged into larger cubes]()
C. ![The triangle numbers represented by dark blue circles arranged into triangles.]()
D. ![A sequence represented using red circles arranged in a pattern so that the first term has one red dot and then an additional two dots are added underneath this one red dot for the second term. For the third term another two red dots are added underneath and for the fourth term, two more added underneath the previous pattern.]()

Solve the problem as a student with the misconception above.
You 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 a fact without considering enough examples

Question:
Tom and Katie are arguing about powers.
\( m \) and \( n \) are integers

Tom says there is no value of \( m \) that means \( 2^{m} \) ends in \( 0 \).
Katie says there is no value of \( n \) that means \( 5^{n} \) ends in \( 0 \).
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:
Assumes a fact without considering enough examples

Question:
Tom and Katie are arguing about powers.
\( m \) and \( n \) are integers

Tom says there is no value of \( m \) that means \( 2^{m} \) ends in \( 0 \).
Katie says there is no value of \( n \) that means \( 5^{n} \) ends in \( 0 \).
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:
Assumes a fact without considering enough examples

Question:
Tom and Katie are arguing about powers.
\( m \) and \( n \) are integers

Tom says there is no value of \( m \) that means \( 2^{m} \) ends in \( 0 \).
Katie says there is no value of \( n \) that means \( 5^{n} \) ends in \( 0 \).
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:
Multiplies up without finding unit price in proportion question

Question:
Eight bottles of water cost \( £ 3.60 \).

How much does one bottle of water cost?

Options:
A. \( £ 28.80 \)
B. \( 30 p \)
C. \( 45 p \)
D. \( £ 3.53 \)

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


Prompt:
Misconception:
Subtracts rather than dividing to find unit price

Question:
Eight bottles of water cost \( £ 3.60 \).

How much does one bottle of water cost?

Options:
A. \( £ 28.80 \)
B. \( 30 p \)
C. \( 45 p \)
D. \( £ 3.53 \)

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


Prompt:
Misconception:
Found the percentage but forgot to add to 100%

Question:
What is \( 120 \% \) of \( 50 \) ?

Options:
A. \( 10 \)
B. \( 60 \)
C. \( 70 \)
D. You cannot have percentages greater than \( 100 \)

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


Prompt:
Misconception:
Added the values together instead of finding the percentage

Question:
What is \( 120 \% \) of \( 50 \) ?

Options:
A. \( 10 \)
B. \( 60 \)
C. \( 70 \)
D. You cannot have percentages greater than \( 100 \)

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


Prompt:
Misconception:
Does not understand that you can have percentages greater than 100%

Question:
What is \( 120 \% \) of \( 50 \) ?

Options:
A. \( 10 \)
B. \( 60 \)
C. \( 70 \)
D. You cannot have percentages greater than \( 100 \)

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


Prompt:
Misconception:
Believes dividing a negative by a negative gives a negative answer

Question:
\( (-3) \div(-5)= \)

Options:
A. \( 8 \)
B. \( -8 \)
C. \( 0.6 \)
D. \( -0.6 \)

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:
Believes gradient is the difference between the change in x and the change in y

Question:
Max is working out the gradient between these two points. He has worked out the lengths of the triangle.
What is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]()

Options:
A. \( \frac{1}{2} \)
B. \( 3 \)
C. \( 2 \)
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:
Believes gradient = change in x/change in y

Question:
Max is working out the gradient between these two points. He has worked out the lengths of the triangle.
What is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]()

Options:
A. \( \frac{1}{2} \)
B. \( 3 \)
C. \( 2 \)
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:
Believes gradient = change in y multiplied by change in x

Question:
Max is working out the gradient between these two points. He has worked out the lengths of the triangle.
What is the gradient? ![A coordinate grid with a right angled triangle drawn on it. The hypotenuse of the triangle is between the coordinates (1,2) and (7,5). The base of the triangle is labelled with 6 and the perpendicular height of the triangle is labelled with 3.]()

Options:
A. \( \frac{1}{2} \)
B. \( 3 \)
C. \( 2 \)
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:
Believes the discriminant must be a perfect square for an equation to have real solutions

Question:
One of these quadratic equations will give no real solutions.
Which one?

Options:
A. \( \frac{-6 \pm \sqrt{-12}}{3} \)
B. \( \frac{-6 \pm \sqrt{12}}{-3} \)
C. \( \frac{-6 \pm \sqrt{1200}}{3} \)
D. \( \frac{-6 \pm \sqrt{0}}{3} \)

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


Prompt:
Misconception:
Believes the discriminant must be a perfect square for an equation to have real solutions

Question:
One of these quadratic equations will give no real solutions.
Which one?

Options:
A. \( \frac{-6 \pm \sqrt{-12}}{3} \)
B. \( \frac{-6 \pm \sqrt{12}}{-3} \)
C. \( \frac{-6 \pm \sqrt{1200}}{3} \)
D. \( \frac{-6 \pm \sqrt{0}}{3} \)

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


Prompt:
Misconception:
Believes that a discriminant of 0 means there are no real solutions

Question:
One of these quadratic equations will give no real solutions.
Which one?

Options:
A. \( \frac{-6 \pm \sqrt{-12}}{3} \)
B. \( \frac{-6 \pm \sqrt{12}}{-3} \)
C. \( \frac{-6 \pm \sqrt{1200}}{3} \)
D. \( \frac{-6 \pm \sqrt{0}}{3} \)

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


Prompt:
Misconception:
Does not follow the arrows through a function machine, changes the order of the operations asked.

Question:
Which of the following pairs of function machines are correct?

Options:
A. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.
]()
B. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "−3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()
C. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "−3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()
D. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "−3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "−3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()

Solve the problem as a student with the misconception above.
You 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 follow the arrows through a function machine, changes the order of the operations asked.

Question:
Which of the following pairs of function machines are correct?

Options:
A. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.
]()
B. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "−3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()
C. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "−3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()
D. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "−3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "−3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()

Solve the problem as a student with the misconception above.
You 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 follow the arrows through a function machine, changes the order of the operations asked.

Question:
Which of the following pairs of function machines are correct?

Options:
A. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.
]()
B. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "−3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()
C. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "−3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "−3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()
D. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "−3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2p − 3" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "−3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(p − 3)" written inside it.]()

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


Prompt:
Misconception:
Identifies the wrong part of a fraction model as the whole

Question:
What should replace the star? ![A number line from 0% to 100% with 20% labelled with 90 and a star above the 100%]()

Options:
A. \( 450 \)
B. \( 1800 \)
C. \( 70 \)
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 understand that similar shapes sides must all have the same scale factor

Question:
Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]()

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

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


Prompt:
Misconception:
Thinks adding the same value to each side makes shapes similar

Question:
Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]()

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

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


Prompt:
Misconception:
Does not understand that similar shapes sides must all have the same scale factor

Question:
Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 2cm and height 3cm. The other rectangle has width 4cm and height 9cm. ]() Katie says these two rectangles are similar ![Two rectangles of different sizes. One rectangle has width 4cm and height 6cm. The other rectangle has width 7cm and height 9cm. ]()

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:
Incorrectly converted cm to m

Question:
How should you write \( 5 \) kilometres and \( 7 \) centimetres in metres?

Options:
A. \( 5070 \mathrm{~m} \)
B. \( 5000.07 \mathrm{~m} \)
C. \( 5007 \mathrm{~m} \)
D. \( 5700 \mathrm{~m} \)

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


Prompt:
Misconception:
Has forgotten to convert cm to m

Question:
How should you write \( 5 \) kilometres and \( 7 \) centimetres in metres?

Options:
A. \( 5070 \mathrm{~m} \)
B. \( 5000.07 \mathrm{~m} \)
C. \( 5007 \mathrm{~m} \)
D. \( 5700 \mathrm{~m} \)

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


Prompt:
Misconception:
Incorrectly converted cm to m

Question:
How should you write \( 5 \) kilometres and \( 7 \) centimetres in metres?

Options:
A. \( 5070 \mathrm{~m} \)
B. \( 5000.07 \mathrm{~m} \)
C. \( 5007 \mathrm{~m} \)
D. \( 5700 \mathrm{~m} \)

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


Prompt:
Misconception:
Adds instead of multiplying when expanding bracket

Question:
Multiply out the brackets: \( m(2 m-7) \)

Options:
A. \( 3 m-7 \)
B. \( 2 m^{2}-7 \)
C. \( 3 m-7 m \)
D. \( 2 m^{2}-7 m \)

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


Prompt:
Misconception:
Only multiplies the first term in the expansion of a bracket

Question:
Multiply out the brackets: \( m(2 m-7) \)

Options:
A. \( 3 m-7 \)
B. \( 2 m^{2}-7 \)
C. \( 3 m-7 m \)
D. \( 2 m^{2}-7 m \)

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


Prompt:
Misconception:
Believes you add the terms together when multiplying like terms.

Question:
Multiply out the brackets: \( m(2 m-7) \)

Options:
A. \( 3 m-7 \)
B. \( 2 m^{2}-7 \)
C. \( 3 m-7 m \)
D. \( 2 m^{2}-7 m \)

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


Prompt:
Misconception:
When adding decimals, just adds the digits and ignores place value

Question:
\( 0.8+0.2= \)

Options:
A. \( 10 \)
B. \( 0.10 \)
C. \( 0.1 \)
D. \( 1 \)

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


Prompt:
Misconception:
When adding, just writes the digit to the right of the number without considering place value

Question:
\( 0.8+0.2= \)

Options:
A. \( 10 \)
B. \( 0.10 \)
C. \( 0.1 \)
D. \( 1 \)

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


Prompt:
Misconception:
When two digits sum to 10 or more during addition of decimals, does not carry across decimal point to preceding digit.

Question:
\( 0.8+0.2= \)

Options:
A. \( 10 \)
B. \( 0.10 \)
C. \( 0.1 \)
D. \( 1 \)

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


Prompt:
Misconception:
Confuses the terms faces and edges

Question:
How many faces does this shape have? ![\( \theta \)]()

Options:
A. \( 1 \)
B. \( 2 \)
C. \( 3 \)
D. \( 4 \)

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


Prompt:
Misconception:
When reading graph, chooses nearest marked value on axis instead of reading accurately

Question:
![A bar chart with blue vertical bars. The x-axis is titled "Fruits" and the y-axis is titled "Number of Children" and its scale is from 0 to 50 in steps of 10. The bars represent the following numbers of children: Banana, 30; Apple, 20; Kiwi Fruits, 30; Orange, 35; Pineapple, 10.]() \begin{tabular}{|c|c|}
\hline
Type of Fruit & Number of Children\\
\hline Banana & \(  \) \\
\hline Apple & \( 20 \) \\
\hline Kiwi & \( 30 \) \\
\hline Orange & \(  \) \\
\hline Pineapple & \( 10 \) \\
\hline
\end{tabular} Using the bar chart, what two numbers are missing from the table?

Options:
A. \( 30 \) and \( 35 \)
B. \( 30 \) and \( 40 \)
C. Banana and orange
D. \( 35 \) and \( 40 \)

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

Question:
Here is a function machine Input \( \longrightarrow \times 5 \longrightarrow-1 \quad \longrightarrow \) Output What is the output when the input is \( 9 ? \)

Options:
A. \( 2 \)
B. \( 40 \)
C. \( 36 \)
D. \( 44 \)

Solve the problem as a student with the misconception above.
You 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 follow the arrows through a function machine, changes the order of the operations asked.

Question:
Here is a function machine Input \( \longrightarrow \times 5 \longrightarrow-1 \quad \longrightarrow \) Output What is the output when the input is \( 9 ? \)

Options:
A. \( 2 \)
B. \( 40 \)
C. \( 36 \)
D. \( 44 \)

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


Prompt:
Misconception:
In a function machine, confuses the first operation and the input

Question:
Here is a function machine Input \( \longrightarrow \times 5 \longrightarrow-1 \quad \longrightarrow \) Output What is the output when the input is \( 9 ? \)

Options:
A. \( 2 \)
B. \( 40 \)
C. \( 36 \)
D. \( 44 \)

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


Prompt:
Misconception:
Hasn't lined up the place value columns when writing out the calculation

Question:
What is a correct way to set up this problem to solve it using long multiplication?
\[
128 \times 26
\]

Options:
A. ![128 multiplied by 26 set out to perform long multiplication. 26 is written under 128. The 2 of 26 is under the 1 of 128 and the 6 of 26 is under the 2 of 128.]()
B. ![128 multiplied by 26 set out to perform long multiplication. 128 is written in 3 columns with 100 in the first column, 20 in the second column and 8 in the third column. 26 is written underneath this, with 20 under 100 and 6 under 20.]()
C. ![128 multiplied by 26 set out to perform long multiplication. 128 is written in 3 columns with 100 in the first column, 20 in the second column and 8 in the third column. 26 is written underneath this, with 20 under 20 and 6 under 8.]()
D. ![128 multiplied by 26 set out to perform long multiplication. 26 is written under 128. The 2 of 26 is under the 2 of 128 and the 6 of 26 is under the 8 of 128.]()

Solve the problem as a student with the misconception above.
You 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 partitioned the digits when doing long multiplication

Question:
What is a correct way to set up this problem to solve it using long multiplication?
\[
128 \times 26
\]

Options:
A. ![128 multiplied by 26 set out to perform long multiplication. 26 is written under 128. The 2 of 26 is under the 1 of 128 and the 6 of 26 is under the 2 of 128.]()
B. ![128 multiplied by 26 set out to perform long multiplication. 128 is written in 3 columns with 100 in the first column, 20 in the second column and 8 in the third column. 26 is written underneath this, with 20 under 100 and 6 under 20.]()
C. ![128 multiplied by 26 set out to perform long multiplication. 128 is written in 3 columns with 100 in the first column, 20 in the second column and 8 in the third column. 26 is written underneath this, with 20 under 20 and 6 under 8.]()
D. ![128 multiplied by 26 set out to perform long multiplication. 26 is written under 128. The 2 of 26 is under the 2 of 128 and the 6 of 26 is under the 8 of 128.]()

Solve the problem as a student with the misconception above.
You 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:
Jane is trying to find the angles \( x \) and \( y \). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]()

Options:
A. \[
x=103\degree\]
as alternate angles
B. \[
y=65\degree
\]
as alternate angles
C. Both steps are correct
D. Both steps are incorrect

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


Prompt:
Misconception:
Does not know the meaning of alternate

Question:
Jane is trying to find the angles \( x \) and \( y \). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]()

Options:
A. \[
x=103\degree\]
as alternate angles
B. \[
y=65\degree
\]
as alternate angles
C. Both steps are correct
D. Both steps are incorrect

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


Prompt:
Misconception:
Does not know the meaning of alternate

Question:
Jane is trying to find the angles \( x \) and \( y \). Here are her workings. Which step is incorrect? ![A diagram showing parallel lines and two transversals. Some angles are given and one is labelled x]()

Options:
A. \[
x=103\degree\]
as alternate angles
B. \[
y=65\degree
\]
as alternate angles
C. Both steps are correct
D. Both steps are incorrect

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


Prompt:
Misconception:
When simplifying an algebraic fraction, only looks for number factors

Question:
Write the following as a single fraction, giving your answer as simply as possible: \( \frac{4 t^{2}-4 t-48}{8} \times \frac{2}{t-4} \)

Options:
A. \( \frac{4 t^{2}-4 t-48}{4(t-4)} \)
B. \( t+3 \)
C. \( \frac{t^{2}-t-12}{t-4} \)
D. \( t-3 \)

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


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

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

Options:
A. \( -1.5 \)
B. \( -0.5 \)
C. \( -1 \)
D. \( -0.25 \)

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:
Believes a quarter of 2 is 0.25

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

Options:
A. \( -1.5 \)
B. \( -0.5 \)
C. \( -1 \)
D. \( -0.25 \)

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

Question:
![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer?

Options:
A. \( -3+9=6 \)
B. \( 3+6=9 \)
C. \( 6+9=-3 \)
D. \( -3+6=9 \)

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


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

Question:
![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer?

Options:
A. \( -3+9=6 \)
B. \( 3+6=9 \)
C. \( 6+9=-3 \)
D. \( -3+6=9 \)

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


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

Question:
![Diagram of a thermometer showing positive and negative temperatures, with an arrow labelled +9 going from -3 up to 6]() Which of the following calculations is represented on the thermometer?

Options:
A. \( -3+9=6 \)
B. \( 3+6=9 \)
C. \( 6+9=-3 \)
D. \( -3+6=9 \)

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


Prompt:
Misconception:
Believes angles in a triangle sum to 360 degrees

Question:
Find the value of \( x \). ![A triangle with the angles labelled: 4x, 2x - 12 and 4x + 42]()

Options:
A. \( x=15^{\circ} \)
B. \( x=12.6^{\circ} \)
C. \( x=33^{\circ} \)
D. \( x=21^{\circ} \)

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 solving an equation, uses the same operation rather than the inverse.

Question:
Find the value of \( x \). ![A triangle with the angles labelled: 4x, 2x - 12 and 4x + 42]()

Options:
A. \( x=15^{\circ} \)
B. \( x=12.6^{\circ} \)
C. \( x=33^{\circ} \)
D. \( x=21^{\circ} \)

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 division is commutative

Question:
Miran says the following:

"It doesn't matter if you do \( \mathbf{7} \div \mathbf{1 4 0} \) or \( \mathbf{1 4 0} \div \mathbf{7} \), you get the same answer"

What do you think?

Options:
A. Miran is correct because division is commutative
B. Miran is incorrect because division is commutative
C. Miran is correct because division is not commutative
D. Miran is incorrect because division is not commutative

Solve the problem as a student with the misconception above.
You 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:
Miran says the following:

"It doesn't matter if you do \( \mathbf{7} \div \mathbf{1 4 0} \) or \( \mathbf{1 4 0} \div \mathbf{7} \), you get the same answer"

What do you think?

Options:
A. Miran is correct because division is commutative
B. Miran is incorrect because division is commutative
C. Miran is correct because division is not commutative
D. Miran is incorrect because division is not commutative

Solve the problem as a student with the misconception above.
You 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:
Miran says the following:

"It doesn't matter if you do \( \mathbf{7} \div \mathbf{1 4 0} \) or \( \mathbf{1 4 0} \div \mathbf{7} \), you get the same answer"

What do you think?

Options:
A. Miran is correct because division is commutative
B. Miran is incorrect because division is commutative
C. Miran is correct because division is not commutative
D. Miran is incorrect because division is not commutative

Solve the problem as a student with the misconception above.
You 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 units of area should be squared

Question:
Tom and Katie are discussing units of area
Tom says centimetres is a unit of area
Katie says \( \mathrm{mm}^{2} \) is a unit of area
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 units of area should be squared

Question:
Tom and Katie are discussing units of area
Tom says centimetres is a unit of area
Katie says \( \mathrm{mm}^{2} \) is a unit of area
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 units of area should be squared

Question:
Tom and Katie are discussing units of area
Tom says centimetres is a unit of area
Katie says \( \mathrm{mm}^{2} \) is a unit of area
Who is correct?

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

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


Prompt:
Misconception:
When counting partial symbols on pictogram, uses the fraction rather than the amount it represents

Question:
This pictogram shows the different types of music Bob has in his music collection.

How many more Pop CDs does Bob have than Rock CDs? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]()

Options:
A. \( 4.5 \)
B. \( 5 \)
C. \( 1.5 \)
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 interpreting a pictogram, thinks each symbol stands for 1

Question:
This pictogram shows the different types of music Bob has in his music collection.

How many more Pop CDs does Bob have than Rock CDs? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]()

Options:
A. \( 4.5 \)
B. \( 5 \)
C. \( 1.5 \)
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:
Counts on in the wrong direction on a number line

Question:
What number belongs in the box?
\(
(-11)+7=
\square\)

Options:
A. \( -18 \)
B. \( -4 \)
C. \( -5 \)
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:
Counts the starting number when counting on

Question:
What number belongs in the box?
\(
(-11)+7=
\square\)

Options:
A. \( -18 \)
B. \( -4 \)
C. \( -5 \)
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:
Believes subtraction is commutative

Question:
This is a part of the table of values for the equation
\[
y=6-x
\] \begin{tabular}{|l|l|}
\hline\( x \) & \( \bigstar \) \\
\hline\( y \) & \( 8 \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( -8 \)
B. \( 14 \)
C. \( 2 \)
D. \( -2 \)

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:
Answers as if there are 100 minutes in an hour

Question:
\( \frac{1}{8} \) th of an hour \( = _______ \) minutes

Options:
A. \( 7.5 \)
B. \( 8 \)
C. \( 0.8 \)
D. \( 12.5 \)

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:
Chooses the wrong 3 letters to describe an angle

Question:
Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it.  The marked angle is between the lines CE and BC.]()

Options:
A. BCA
B. CDB
C. ECB
D. None of these options

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


Prompt:
Misconception:
Gives 3-letter angle notation in the wrong order

Question:
Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it.  The marked angle is between the lines CE and BC.]()

Options:
A. BCA
B. CDB
C. ECB
D. None of these options

Solve the problem as a student with the misconception above.
You 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 3-letter angle notation has to use the nearest vertex on each side of the angle

Question:
Which of the following correctly describes the marked angle? ![An image of square ABCE with various triangles attached to it.  The marked angle is between the lines CE and BC.]()

Options:
A. BCA
B. CDB
C. ECB
D. None of these options

Solve the problem as a student with the misconception above.
You 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 fully simplify fraction

Question:
Simplify the following: \( \frac{9 y^{3}}{6 y^{2}+3 y} \)

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

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


Prompt:
Misconception:
Thinks you can divide terms by different factors when simplifying an algebraic fraction

Question:
Simplify the following: \( \frac{9 y^{3}}{6 y^{2}+3 y} \)

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

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


Prompt:
Misconception:
Thinks you can divide terms by different factors when simplifying an algebraic fraction

Question:
Simplify the following: \( \frac{9 y^{3}}{6 y^{2}+3 y} \)

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

Solve the problem as a student with the misconception above.
You 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 half-squares as full squares when calculating area on a square grid

Question:
What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]()

Options:
A. The blue square has a larger area
B. The red square has a larger area
C. The areas are the same
D. It is impossible to say without measuring

Solve the problem as a student with the misconception above.
You 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 diagonal of a square is the same length as the side of the square

Question:
What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]()

Options:
A. The blue square has a larger area
B. The red square has a larger area
C. The areas are the same
D. It is impossible to say without measuring

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


Prompt:
Misconception:
Does not know how to find area by counting squares on a grid

Question:
What can you say about the areas of the two squares? ![Two squares drawn on a grid. The blue square is three grid squares wide, and the three grid squares long. The red square is drawn diagonally, so that each side goes through two grid squares from corner to corner.]()

Options:
A. The blue square has a larger area
B. The red square has a larger area
C. The areas are the same
D. It is impossible to say without measuring

Solve the problem as a student with the misconception above.
You 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:
What is the area of this rectangle? ![A rectangle, 5cm by 12cm]()

Options:
A. \( 17 \mathrm{~cm}^{2} \)
B. \( 60 \mathrm{~cm}^{2} \)
C. \( 34 \mathrm{~cm}^{2} \)
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:
Calculates perimeter when asked for area

Question:
What is the area of this rectangle? ![A rectangle, 5cm by 12cm]()

Options:
A. \( 17 \mathrm{~cm}^{2} \)
B. \( 60 \mathrm{~cm}^{2} \)
C. \( 34 \mathrm{~cm}^{2} \)
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 recall rectangle side length property

Question:
What is the area of this rectangle? ![A rectangle, 5cm by 12cm]()

Options:
A. \( 17 \mathrm{~cm}^{2} \)
B. \( 60 \mathrm{~cm}^{2} \)
C. \( 34 \mathrm{~cm}^{2} \)
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:
Assumes that converting a decimal percentage to a fraction, they can just convert the decimal to a fraction, instead of writing the decimal over 100.

Question:
How do you write \( 0.5 \% \) as a fraction?

Options:
A. \( \frac{1}{2} \)
B. \( \frac{1}{20} \)
C. \( \frac{1}{200} \)
D. \( \frac{1}{2000} \)

Solve the problem as a student with the misconception above.
You 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 decimal point can be ignored when given a decimal percentage to convert to a fraction

Question:
How do you write \( 0.5 \% \) as a fraction?

Options:
A. \( \frac{1}{2} \)
B. \( \frac{1}{20} \)
C. \( \frac{1}{200} \)
D. \( \frac{1}{2000} \)

Solve the problem as a student with the misconception above.
You 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 completing the square, believes the constant in the bracket is double the coefficient of x

Question:
When Aaron completes the square, what should replace the star? \( p^{2}-p-1 \equiv(p \bigstar )^{2} \triangle \)

Options:
A. \(\bigstar =-2 \)
B. \(\bigstar =-1 \)
C. \(\bigstar =+0 \)
(just \( \mathrm{p} \) inside brackets)
D. \(\bigstar =-0.5 \)

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


Prompt:
Misconception:
When completing the square, believes the constant in the bracket is the coefficient of x

Question:
When Aaron completes the square, what should replace the star? \( p^{2}-p-1 \equiv(p \bigstar )^{2} \triangle \)

Options:
A. \(\bigstar =-2 \)
B. \(\bigstar =-1 \)
C. \(\bigstar =+0 \)
(just \( \mathrm{p} \) inside brackets)
D. \(\bigstar =-0.5 \)

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:
Confuses octagon and pentagon

Question:
If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]()

Options:
A. An octagon
B. A hexagon
C. A pentagon
D. A circle

Solve the problem as a student with the misconception above.
You 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 pentagon and hexagon

Question:
If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]()

Options:
A. An octagon
B. A hexagon
C. A pentagon
D. A circle

Solve the problem as a student with the misconception above.
You 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 regular

Question:
If you continue to join up the intersections of the curves with straight lines, which of the following regular polygons could you have constructed? ![A circle has been intersected by curves at 5 equally spaced intervals about its circumference]()

Options:
A. An octagon
B. A hexagon
C. A pentagon
D. A circle

Solve the problem as a student with the misconception above.
You 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:
When \( h=5 \)
\(
h^{2}=
\)

Options:
A. \( 25 \)
B. \( 10 \)
C. \( 7 \)
D. \( 52 \)

Solve the problem as a student with the misconception above.
You 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 squaring is the same as adding two

Question:
When \( h=5 \)
\(
h^{2}=
\)

Options:
A. \( 25 \)
B. \( 10 \)
C. \( 7 \)
D. \( 52 \)

Solve the problem as a student with the misconception above.
You 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:
When \( h=5 \)
\(
h^{2}=
\)

Options:
A. \( 25 \)
B. \( 10 \)
C. \( 7 \)
D. \( 52 \)

Solve the problem as a student with the misconception above.
You 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 or subtracting surds, simplifies the surds correctly but puts the digits in the answer the wrong way round

Question:
\(
\sqrt{3}+\sqrt{5}
\)

Simplify, if possible.

Options:
A. \( 3 \sqrt{5} \)
B. \( \sqrt{8} \)
C. \( \sqrt{15} \)
D. Cannot be simplified

Solve the problem as a student with the misconception above.
You 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 or subtracting surds, just adds or subtracts the numbers under the surd rather than first trying to simplifying to find like surds

Question:
\(
\sqrt{3}+\sqrt{5}
\)

Simplify, if possible.

Options:
A. \( 3 \sqrt{5} \)
B. \( \sqrt{8} \)
C. \( \sqrt{15} \)
D. Cannot be simplified

Solve the problem as a student with the misconception above.
You 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 surds, just multiplies the numbers under the surd rather than first trying to simplifying to find like surds

Question:
\(
\sqrt{3}+\sqrt{5}
\)

Simplify, if possible.

Options:
A. \( 3 \sqrt{5} \)
B. \( \sqrt{8} \)
C. \( \sqrt{15} \)
D. Cannot be simplified

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


Prompt:
Misconception:
Only multiplies the first term in the expansion of a bracket

Question:
The area of the rectangle on the right is \( 8 \mathrm{~cm}^{2} \).

Which of the following equations can we write from the information given? ![A rectangle with the short side labelled \(x\) and the opposite side labelled \(x^2 + 9\).]()

Options:
A. \( x^{3}+9=8 \)
B. \( x^{2}+x+9=8 \)
C. \( 2 x^{2}+2 x+18=8 \)
D. \( x^{3}+9 x=8 \)

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 when calculating area instead of multiplying

Question:
The area of the rectangle on the right is \( 8 \mathrm{~cm}^{2} \).

Which of the following equations can we write from the information given? ![A rectangle with the short side labelled \(x\) and the opposite side labelled \(x^2 + 9\).]()

Options:
A. \( x^{3}+9=8 \)
B. \( x^{2}+x+9=8 \)
C. \( 2 x^{2}+2 x+18=8 \)
D. \( x^{3}+9 x=8 \)

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:
Calculates perimeter when asked for area

Question:
The area of the rectangle on the right is \( 8 \mathrm{~cm}^{2} \).

Which of the following equations can we write from the information given? ![A rectangle with the short side labelled \(x\) and the opposite side labelled \(x^2 + 9\).]()

Options:
A. \( x^{3}+9=8 \)
B. \( x^{2}+x+9=8 \)
C. \( 2 x^{2}+2 x+18=8 \)
D. \( x^{3}+9 x=8 \)

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:
Misremembers the exact values of trigonometric functions at standard angles

Question:
What is the exact value of \( \tan (30) \) ?

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

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


Prompt:
Misconception:
Misremembers the exact values of trigonometric functions at standard angles

Question:
What is the exact value of \( \tan (30) \) ?

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

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


Prompt:
Misconception:
Misremembers the exact values of trigonometric functions at standard angles

Question:
What is the exact value of \( \tan (30) \) ?

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

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


Prompt:
Misconception:
Believes the square of a negative will also be negative

Question:
Amy is trying to work out the distance between these two points: \( (2,-5) \) and \( (-7,1) \) She labels them like this: \( \begin{array}{cccc}x_{1} & y_{1} & x_{2} & y_{2} \\ (2, & -5) & (-7, & 1)\end{array} \) And then decides to use this formula: \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \) \( \sqrt{(-9)^{2}+(6)^{2}} \) What is the distance between the points?

Options:
A. \( \sqrt{6} \)
B. \( \sqrt{30} \)
C. \( -\sqrt{45} \)
D. \( \sqrt{117} \)

Solve the problem as a student with the misconception above.
You 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 a formula with an equation

Question:
Which of the following is the most appropriate word to describe: \( V=\frac{1}{3} \pi r^{2} h \) ![A cone, with the dimensions labelled h and r]()

Options:
A. Equation
B. Formula
C. Variable
D. Expression

Solve the problem as a student with the misconception above.
You 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 a variable with a formula

Question:
Which of the following is the most appropriate word to describe: \( V=\frac{1}{3} \pi r^{2} h \) ![A cone, with the dimensions labelled h and r]()

Options:
A. Equation
B. Formula
C. Variable
D. Expression

Solve the problem as a student with the misconception above.
You 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 a formula with an expression

Question:
Which of the following is the most appropriate word to describe: \( V=\frac{1}{3} \pi r^{2} h \) ![A cone, with the dimensions labelled h and r]()

Options:
A. Equation
B. Formula
C. Variable
D. Expression

Solve the problem as a student with the misconception above.
You 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:
Rearrange the following equation to make \( v \) the subject
\(F=\frac{v^{2}}{r}\)

Options:
A. \( v=r F^{2} \)
B. \( v=\sqrt{\frac{F}{r}} \)
C. \( v=\sqrt{r F} \)
D. \( v=r \sqrt{F} \)

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


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

Question:
Rearrange the following equation to make \( v \) the subject
\(F=\frac{v^{2}}{r}\)

Options:
A. \( v=r F^{2} \)
B. \( v=\sqrt{\frac{F}{r}} \)
C. \( v=\sqrt{r F} \)
D. \( v=r \sqrt{F} \)

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


Prompt:
Misconception:
Does not reverse the order of operations when solving an equation

Question:
Rearrange the following equation to make \( v \) the subject
\(F=\frac{v^{2}}{r}\)

Options:
A. \( v=r F^{2} \)
B. \( v=\sqrt{\frac{F}{r}} \)
C. \( v=\sqrt{r F} \)
D. \( v=r \sqrt{F} \)

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


Prompt:
Misconception:
Thinks there are 10 centimetres in 1 mm.

Question:
How many millimetres are there in \( 1 \) centimetre?

Options:
A. \( 0.1 \)
B. \( 10 \)
C. \( 100 \)
D. \( 1000 \)

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


Prompt:
Misconception:
Thinks there are 100mm in a centimetre

Question:
How many millimetres are there in \( 1 \) centimetre?

Options:
A. \( 0.1 \)
B. \( 10 \)
C. \( 100 \)
D. \( 1000 \)

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


Prompt:
Misconception:
Thinks there are 1000mm in a centimetre

Question:
How many millimetres are there in \( 1 \) centimetre?

Options:
A. \( 0.1 \)
B. \( 10 \)
C. \( 100 \)
D. \( 1000 \)

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


Prompt:
Misconception:
Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)

Question:
Tom and Katie are discussing the order of operations
Tom says: \( 6+4-2 \equiv 4-2+6 \)
Katie says: \( 6+4 \times 2 \equiv 6 \times 4+2 \)
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 consider that all three angles in a triangle sum to 180 degrees

Question:
Tom and Katie are arguing about triangles.
Tom says a triangle can have two right angles.
Katie says only a scalene triangle can have a right angle.
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 the properties of an isosceles triangle

Question:
Tom and Katie are arguing about triangles.
Tom says a triangle can have two right angles.
Katie says only a scalene triangle can have a right angle.
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:
Only multiplies the first term in the expansion of a bracket

Question:
Tom and Katie are discussing calculations involving brackets
Tom says \( a(b+c) \equiv(b+c) \times a \)
Katie says \( a(b+c) \equiv a b+c \)
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 the meaning of the identity symbol

Question:
Tom and Katie are discussing calculations involving brackets
Tom says \( a(b+c) \equiv(b+c) \times a \)
Katie says \( a(b+c) \equiv a b+c \)
Who is correct?

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

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


Prompt:
Misconception:
When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right.

Question:
What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. "-4" below the 2nd dash and "5" below the last dash are the only numbers marked on the line. An arrow, labelled "A" is pointing halfway between the 5th and 6th dashes. ]()

Options:
A. \( 0.5 \)
B. \( -7.5 \)
C. \( -0.5 \)
D. \( 3 \)

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


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 2

Question:
What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. "-4" below the 2nd dash and "5" below the last dash are the only numbers marked on the line. An arrow, labelled "A" is pointing halfway between the 5th and 6th dashes. ]()

Options:
A. \( 0.5 \)
B. \( -7.5 \)
C. \( -0.5 \)
D. \( 3 \)

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


Prompt:
Misconception:
Converts a fraction to a percentage by writing the numerator followed by the denominator

Question:
What is \( 8 \) out of \( 20 \) as a percentage?

Options:
A. \( 82 \% \)
B. \( 32 \% \)
C. \( 16 \% \)
D. \( 40 \% \)

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:
Thinks they double the numerator to turn a fraction into a percentage

Question:
What is \( 8 \) out of \( 20 \) as a percentage?

Options:
A. \( 82 \% \)
B. \( 32 \% \)
C. \( 16 \% \)
D. \( 40 \% \)

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:
Does not know the properties of a rectangle

Question:
![A blue, rectangle with each side labelled. The left side is labelled x and the right side 8. The top side is labelled 2x + 4 and the base 3x - 4.]() Which of the following statements is incorrect?

Options:
A. Area \( =3 x^{2}-4 \)
B. Perimeter \( =6 x+8 \)
C. \( 2 x+4=3 x-4 \)
D. \( x=8 \)

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 know the properties of a rectangle

Question:
![A blue, rectangle with each side labelled. The left side is labelled x and the right side 8. The top side is labelled 2x + 4 and the base 3x - 4.]() Which of the following statements is incorrect?

Options:
A. Area \( =3 x^{2}-4 \)
B. Perimeter \( =6 x+8 \)
C. \( 2 x+4=3 x-4 \)
D. \( x=8 \)

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

Question:
One of these equations has exactly one solution.
Which is it?

Options:
A. \( t^{2}-9 t=0 \)
B. \( t^{2}+6 t+9=0 \)
C. \( t^{2}-6 t-9=0 \)
D. \( t^{2}-9=0 \)

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 given a term to term sequence with multiple steps, applies one step per term

Question:
![Square and then subtract \( 4 \)]() The first three terms of which sequence below is produced by this term-to-term rule?

Options:
A. \( -3,9,5 \)
B. \( -3,-13,-173 \)
C. \( -3,5,21 \)
D. \( -3,0,5 \)

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


Prompt:
Misconception:
When given a term to term sequence with multiple steps, applies one step per term

Question:
![Square and then subtract \( 4 \)]() The first three terms of which sequence below is produced by this term-to-term rule?

Options:
A. \( -3,9,5 \)
B. \( -3,-13,-173 \)
C. \( -3,5,21 \)
D. \( -3,0,5 \)

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}.