Prompt:
Misconception:
Confuses the order of operations, believes addition comes before multiplication

Question:
\[
3 \times 2+4-5
\]
Where do the brackets need to go to make the answer equal \( 13 \) ?

Options:
A. \( 3 \times(2+4)-5 \)
B. \( 3 \times 2+(4-5) \)
C. \( 3 \times(2+4-5) \)
D. Does not need brackets

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


Prompt:
Misconception:
Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term

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

Options:
A. \( m+1 \)
B. \( m+2 \)
C. \( m-1 \)
D. Does not simplify

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


Prompt:
Misconception:
Thinks that when you cancel identical terms from the numerator and denominator, they just disappear

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

Options:
A. \( m+1 \)
B. \( m+2 \)
C. \( m-1 \)
D. Does not simplify

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


Prompt:
Misconception:
Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term

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

Options:
A. \( m+1 \)
B. \( m+2 \)
C. \( m-1 \)
D. Does not simplify

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


Prompt:
Misconception:
Believes if you changed all values by the same proportion the range would not change

Question:
Tom and Katie are discussing the \( 5 \) plants with these heights:
\( 24 \mathrm{~cm}, 17 \mathrm{~cm}, 42 \mathrm{~cm}, 26 \mathrm{~cm}, 13 \mathrm{~cm} \)
Tom says if all the plants were cut in half, the range wouldn't change.
Katie says if all the plants grew by \( 3 \mathrm{~cm} \) each, the range wouldn't change.
Who do you agree with?

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

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


Prompt:
Misconception:
Believes if you changed all values by the same proportion the range would not change

Question:
Tom and Katie are discussing the \( 5 \) plants with these heights:
\( 24 \mathrm{~cm}, 17 \mathrm{~cm}, 42 \mathrm{~cm}, 26 \mathrm{~cm}, 13 \mathrm{~cm} \)
Tom says if all the plants were cut in half, the range wouldn't change.
Katie says if all the plants grew by \( 3 \mathrm{~cm} \) each, the range wouldn't change.
Who do you agree with?

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

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


Prompt:
Misconception:
Believes if you add the same value to all numbers in the dataset the range will change

Question:
Tom and Katie are discussing the \( 5 \) plants with these heights:
\( 24 \mathrm{~cm}, 17 \mathrm{~cm}, 42 \mathrm{~cm}, 26 \mathrm{~cm}, 13 \mathrm{~cm} \)
Tom says if all the plants were cut in half, the range wouldn't change.
Katie says if all the plants grew by \( 3 \mathrm{~cm} \) each, the range wouldn't change.
Who do you agree with?

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

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


Prompt:
Misconception:
Does not know the properties of a rectangle

Question:
The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle at the bottom at the centre is highlighted in yellow.]()

Options:
A. acute
B. obtuse
C. \( 90^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Does not know the properties of a rectangle

Question:
The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle at the bottom at the centre is highlighted in yellow.]()

Options:
A. acute
B. obtuse
C. \( 90^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Does not know the properties of a rectangle

Question:
The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle at the bottom at the centre is highlighted in yellow.]()

Options:
A. acute
B. obtuse
C. \( 90^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Thinks you can find missing values in a given table by treating the row as linear and adding on the difference between the first two values given.

Question:
The equation \( f=3 r^{2}+3 \) is used to find values in the table below. What is the value covered by the star? \begin{tabular}{|c|c|c|c|c|}
\hline\( r \) & \( 1 \) & \( 2 \) & \( 3 \) & \( 4 \) \\
\hline\( f \) & \( 6 \) & \( 15 \) & \( \color{gold}\bigstar \) & \\
\hline
\end{tabular}

Options:
A. \( 30 \)
B. \( 27 \)
C. \( 51 \)
D. \( 24 \)

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


Prompt:
Misconception:
Does not know units of area should be squared

Question:
James has answered a question on the area of a trapezium and got an answer of \( 54 \).

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

\(
54 \, \bigstar
\)

Which of the following units could be correct?

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

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


Prompt:
Misconception:
Does not know units of area should be squared

Question:
James has answered a question on the area of a trapezium and got an answer of \( 54 \).

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

\(
54 \, \bigstar
\)

Which of the following units could be correct?

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

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


Prompt:
Misconception:
Does not know units of area should be squared

Question:
James has answered a question on the area of a trapezium and got an answer of \( 54 \).

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

\(
54 \, \bigstar
\)

Which of the following units could be correct?

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

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


Prompt:
Misconception:
Does not understand a percentage is out of 100

Question:
Convert this percentage to a fraction
\( 62 \% \)

Options:
A. \( \frac{62}{10} \)
B. \( \frac{31}{50} \)
C. \( \frac{6}{2} \)
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:
Thinks they can convert a 2 digit percentage to a fraction by writing one number over the other.

Question:
Convert this percentage to a fraction
\( 62 \% \)

Options:
A. \( \frac{62}{10} \)
B. \( \frac{31}{50} \)
C. \( \frac{6}{2} \)
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:
Does not understand a percentage is out of 100

Question:
Convert this percentage to a fraction
\( 62 \% \)

Options:
A. \( \frac{62}{10} \)
B. \( \frac{31}{50} \)
C. \( \frac{6}{2} \)
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:
Divided by 100 rather than 10

Question:
\( 43.2 \div 10= \)

Options:
A. \( 4.32 \)
B. \( 0.432 \)
C. \( 33.2 \)
D. \( 43.02 \)

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


Prompt:
Misconception:
Subtracts instead of divides

Question:
\( 43.2 \div 10= \)

Options:
A. \( 4.32 \)
B. \( 0.432 \)
C. \( 33.2 \)
D. \( 43.02 \)

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


Prompt:
Misconception:
When dividing a decimal by a multiple of 10, just divides the fractional place values

Question:
\( 43.2 \div 10= \)

Options:
A. \( 4.32 \)
B. \( 0.432 \)
C. \( 33.2 \)
D. \( 43.02 \)

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


Prompt:
Misconception:
Does not find a common denominator when adding/subtracting fractions

Question:
\(
\frac{4}{5}-\frac{1}{3}=\frac{\bigstar}{15}
\)
What should replace the star?

Options:
A. \( 7 \)
B. \( 5 \)
C. \( 17 \)
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:
Adds instead of subtracts

Question:
\(
\frac{4}{5}-\frac{1}{3}=\frac{\bigstar}{15}
\)
What should replace the star?

Options:
A. \( 7 \)
B. \( 5 \)
C. \( 17 \)
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:
Does not find a common denominator when adding/subtracting fractions

Question:
\(
\frac{4}{5}-\frac{1}{3}=\frac{\bigstar}{15}
\)
What should replace the star?

Options:
A. \( 7 \)
B. \( 5 \)
C. \( 17 \)
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:
Believes f(x - a) translates the function up a units

Question:
What transformation maps the graph of
\(y=f(x)
\)
to the graph of
\(
y=f(x-3)
\)

Options:
A. Translation by vector
\(
\left[\begin{array}{l}
0 \\
3
\end{array}\right]
\)
B. Translation by vector
\(
\left[\begin{array}{c}
0 \\
-3
\end{array}\right]
\)
C. Translation by vector
\(
\left[\begin{array}{l}
3 \\
0
\end{array}\right]
\)
D. Translation by vector
\(
\left[\begin{array}{r}
-3 \\
0
\end{array}\right]
\)

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


Prompt:
Misconception:
Believes f(x + a) translates the function up a units

Question:
What transformation maps the graph of
\(y=f(x)
\)
to the graph of
\(
y=f(x-3)
\)

Options:
A. Translation by vector
\(
\left[\begin{array}{l}
0 \\
3
\end{array}\right]
\)
B. Translation by vector
\(
\left[\begin{array}{c}
0 \\
-3
\end{array}\right]
\)
C. Translation by vector
\(
\left[\begin{array}{l}
3 \\
0
\end{array}\right]
\)
D. Translation by vector
\(
\left[\begin{array}{r}
-3 \\
0
\end{array}\right]
\)

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


Prompt:
Misconception:
Believes f(x) + a translates the function right a units

Question:
What transformation maps the graph of
\(y=f(x)
\)
to the graph of
\(
y=f(x-3)
\)

Options:
A. Translation by vector
\(
\left[\begin{array}{l}
0 \\
3
\end{array}\right]
\)
B. Translation by vector
\(
\left[\begin{array}{c}
0 \\
-3
\end{array}\right]
\)
C. Translation by vector
\(
\left[\begin{array}{l}
3 \\
0
\end{array}\right]
\)
D. Translation by vector
\(
\left[\begin{array}{r}
-3 \\
0
\end{array}\right]
\)

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


Prompt:
Misconception:
Ignores negative sign when expanding bracket

Question:
John is expanding these three brackets:
\(
(x+5)(x-3)(x+6)
\)

He finds it helpful to split the first bracket and view the problem as follows:
\(
x(x-3)(x+6)+5(x-3)(x+6)
\)

He expands the brackets further. Before he simplifies, what are the terms than contain an \( \boldsymbol{x}^{2} \) ?

Options:
A. \( +6 x^{2} \)
B. \( \begin{array}{l}+6 x^{2} \\ -3 x^{2} \\ +5 x^{2}\end{array} \)
C. \( \begin{array}{l}+6 x^{2} \\ +3 x^{2} \\ +5 x^{2}\end{array} \)
D. \( \begin{array}{l}+6 x^{2} \\ -3 x^{2} \\ -5 x^{2}\end{array} \)

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


Prompt:
Misconception:
Struggles to visualise nets of 3D shapes

Question:
This is the net of a... ![A circle touching a sector]()

Options:
A. Triangle
B. Triangular prism
C. Triangularbased pyramid
D. Cone

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


Prompt:
Misconception:
Struggles to visualise nets of 3D shapes

Question:
This is the net of a... ![A circle touching a sector]()

Options:
A. Triangle
B. Triangular prism
C. Triangularbased pyramid
D. Cone

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


Prompt:
Misconception:
Struggles to visualise nets of 3D shapes

Question:
This is the net of a... ![A circle touching a sector]()

Options:
A. Triangle
B. Triangular prism
C. Triangularbased pyramid
D. Cone

Solve the problem as a student with the misconception above.
You 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 alternate angles are always equal

Question:
Tom and Katie are arguing about alternate angles.
Tom says angles \( p \) and \( q \) are alternate.

Katie says angles \( p \) and \( q \) are equal.
Who is correct? ![Shows two non parallel lines that are intersected by another line. Angles P and Q are both on the outside of the lines and on opposite sides of the transversal.]()

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 alternate angles are always equal

Question:
Tom and Katie are arguing about alternate angles.
Tom says angles \( p \) and \( q \) are alternate.

Katie says angles \( p \) and \( q \) are equal.
Who is correct? ![Shows two non parallel lines that are intersected by another line. Angles P and Q are both on the outside of the lines and on opposite sides of the transversal.]()

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 only angles on parallel lines can be alternate

Question:
Tom and Katie are arguing about alternate angles.
Tom says angles \( p \) and \( q \) are alternate.

Katie says angles \( p \) and \( q \) are equal.
Who is correct? ![Shows two non parallel lines that are intersected by another line. Angles P and Q are both on the outside of the lines and on opposite sides of the transversal.]()

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:
Answers as if there are 100 minutes in an hour when changing from hours to minutes

Question:
Hannah's journey to camp is \( 3 \) hours and \( 16 \) minutes.
Tori's journey to camp is \( 214 \) minutes.
What is the difference in their journeys in minutes?

Options:
A. \( 196 \) minutes
B. \( 18 \) minutes
C. \( 102 \) minutes
D. \( 12 \) minutes

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


Prompt:
Misconception:
Stops iteration too early when solving equations

Question:
\(
x_{n+1}=5-\frac{1}{x_{n}}
\)

Using a starting value of \( x_{1}=2 \), what is the solution to \( x=5-\frac{1}{x} \) to \( 2 \) decimal places?

Options:
A. \( 4.78 \)
B. \( 4.79128 \ldots \)
C. \( 4.8 \)
D. \( 4.79 \)

Solve the problem as a student with the misconception above.
You 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:
\(
x_{n+1}=5-\frac{1}{x_{n}}
\)

Using a starting value of \( x_{1}=2 \), what is the solution to \( x=5-\frac{1}{x} \) to \( 2 \) decimal places?

Options:
A. \( 4.78 \)
B. \( 4.79128 \ldots \)
C. \( 4.8 \)
D. \( 4.79 \)

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


Prompt:
Misconception:
Rounds to the wrong degree of accuracy (significant figures rather than decimal places)

Question:
\(
x_{n+1}=5-\frac{1}{x_{n}}
\)

Using a starting value of \( x_{1}=2 \), what is the solution to \( x=5-\frac{1}{x} \) to \( 2 \) decimal places?

Options:
A. \( 4.78 \)
B. \( 4.79128 \ldots \)
C. \( 4.8 \)
D. \( 4.79 \)

Solve the problem as a student with the misconception above.
You 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 used slant height and base to find area of a triangle rather than perpendicular height and base

Question:
How would you calculate the area of this triangle? ![A triangle, base 12m. All three sides are equal.]()

Options:
A. \( \frac{6 \times 12}{2} \)
B. \( \frac{12 \times 12}{2} \)
C. \( \frac{12 \times 12 \times 12}{2} \)
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:
Multiplies all given dimensions when calculating an area

Question:
How would you calculate the area of this triangle? ![A triangle, base 12m. All three sides are equal.]()

Options:
A. \( \frac{6 \times 12}{2} \)
B. \( \frac{12 \times 12}{2} \)
C. \( \frac{12 \times 12 \times 12}{2} \)
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:
Divides total amount by each side of the ratio instead of dividing by the sum of the parts

Question:
In the diagram, AN : NB \( =3: 5 \)
What is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]()

Options:
A. \( 16 \mathrm{~m} \)
B. \( 30 \mathrm{~m} \)
C. \( 6 \mathrm{~m} \)
D. \( 18 \mathrm{~m} \)

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:
Mixes up sides of a ratio

Question:
In the diagram, AN : NB \( =3: 5 \)
What is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]()

Options:
A. \( 16 \mathrm{~m} \)
B. \( 30 \mathrm{~m} \)
C. \( 6 \mathrm{~m} \)
D. \( 18 \mathrm{~m} \)

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:
Finds one part of a ratio but doesn't multiply that by the number of parts needed

Question:
In the diagram, AN : NB \( =3: 5 \)
What is the distance AN? ![A line that begins with point A, ends with point B, and has point N in between. The entire length of the line measures 48 m.]()

Options:
A. \( 16 \mathrm{~m} \)
B. \( 30 \mathrm{~m} \)
C. \( 6 \mathrm{~m} \)
D. \( 18 \mathrm{~m} \)

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:
Does not understand that 2n represents an even number

Question:
Which of these shows part of the proof that the sum of two odd numbers is even?

Options:
A. \( \begin{array}{l}2 n+(2 m+1) \\ =2(n+m)+1\end{array} \)
B. \( \begin{array}{l}(2 n-1)(2 m+1) \\ =4 m n+2 n-2 m-1 \\ =2(2 m n-n-m)+1\end{array} \)
C. \( \begin{array}{l}\text { Odd + Odd } \\ =\text { even }\end{array} \)
D. \( \begin{array}{l}(2 n-1)+(2 m+1) \\ =2 n+2 m \\ =2(n+m)\end{array} \)

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


Prompt:
Misconception:
Does not know the meaning of the word "sum"

Question:
Which of these shows part of the proof that the sum of two odd numbers is even?

Options:
A. \( \begin{array}{l}2 n+(2 m+1) \\ =2(n+m)+1\end{array} \)
B. \( \begin{array}{l}(2 n-1)(2 m+1) \\ =4 m n+2 n-2 m-1 \\ =2(2 m n-n-m)+1\end{array} \)
C. \( \begin{array}{l}\text { Odd + Odd } \\ =\text { even }\end{array} \)
D. \( \begin{array}{l}(2 n-1)+(2 m+1) \\ =2 n+2 m \\ =2(n+m)\end{array} \)

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


Prompt:
Misconception:
Does not understand that 2n represents an even number

Question:
Which of these shows part of the proof that the sum of two odd numbers is even?

Options:
A. \( \begin{array}{l}2 n+(2 m+1) \\ =2(n+m)+1\end{array} \)
B. \( \begin{array}{l}(2 n-1)(2 m+1) \\ =4 m n+2 n-2 m-1 \\ =2(2 m n-n-m)+1\end{array} \)
C. \( \begin{array}{l}\text { Odd + Odd } \\ =\text { even }\end{array} \)
D. \( \begin{array}{l}(2 n-1)+(2 m+1) \\ =2 n+2 m \\ =2(n+m)\end{array} \)

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


Prompt:
Misconception:
Assumes that an arrow on a number line starts at zero

Question:
![Number line with -12 and -7 marked. Starting at -12, follow an arrow pointing to the right labelled +10. Then there is an arrow labelled b pointing to the left, which ends at -7 on the number line.]() What is the value of \( b \) ?

Options:
A. \( -7 \)
B. \( -5 \)
C. \( -2 \)
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 the starting number when counting backwards

Question:
![Number line with -12 and -7 marked. Starting at -12, follow an arrow pointing to the right labelled +10. Then there is an arrow labelled b pointing to the left, which ends at -7 on the number line.]() What is the value of \( b \) ?

Options:
A. \( -7 \)
B. \( -5 \)
C. \( -2 \)
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 subtracting fractions, subtracts the numerators and multiplies the denominators

Question:
Express the following as a single fraction, writing your answer as simply as possible: \( \frac{1}{s}-\frac{t}{3} \)

Options:
A. \( \frac{1-t}{3 s} \)
B. \( \frac{s-3 t}{3 s} \)
C. \( \frac{3-s t}{3 s} \)
D. \( \frac{1-t}{s-3} \)

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 they should multiply each numerator by its original denominator when adding/subtracting fractions

Question:
Express the following as a single fraction, writing your answer as simply as possible: \( \frac{1}{s}-\frac{t}{3} \)

Options:
A. \( \frac{1-t}{3 s} \)
B. \( \frac{s-3 t}{3 s} \)
C. \( \frac{3-s t}{3 s} \)
D. \( \frac{1-t}{s-3} \)

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 find a common denominator when adding/subtracting fractions

Question:
Express the following as a single fraction, writing your answer as simply as possible: \( \frac{1}{s}-\frac{t}{3} \)

Options:
A. \( \frac{1-t}{3 s} \)
B. \( \frac{s-3 t}{3 s} \)
C. \( \frac{3-s t}{3 s} \)
D. \( \frac{1-t}{s-3} \)

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:
Adds when calculating volume instead of multiplying

Question:
The volume of this cuboid is \( 30 \mathrm{~cm}^{3} \)

What length should replace the star? ![A cuboid, depth 2cm and height 3cm. The width is labelled with a star.]()

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 4 \mathrm{~cm} \)
D. \( 25 \mathrm{~cm} \)

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


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

Question:
Step 1: Factorise the following expression

\(
3 x^{2}+5 x+2
\)

Options:
A. \( (3 x+2)(3 x+1) \)
B. \( (3 x+2)(x+1) \)
C. Cannot be factorised
D. \( (3 x+1)(x+2) \)

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


Prompt:
Misconception:
Does not realise that adding a larger number gives a larger answer

Question:
Tom and Katie are discussing related calculations
Tom says if you know that \( 3748+426=4174 \), then \( 3748+427 \) must equal \( \mathbf{4 1 7 5} \)

Katie says if you know that \( 3748-426=3322 \), then \( 3748 \) - \( 427 \) must equal \( \mathbf{3 3 2 3} \)
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 realise that subtracting a larger number will give a smaller answer

Question:
Tom and Katie are discussing related calculations
Tom says if you know that \( 3748+426=4174 \), then \( 3748+427 \) must equal \( \mathbf{4 1 7 5} \)

Katie says if you know that \( 3748-426=3322 \), then \( 3748 \) - \( 427 \) must equal \( \mathbf{3 3 2 3} \)
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 rest and movement on a distance time graph

Question:
This graph shows how far Fido the dog is from his home.
What might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis. ]()

Options:
A. Fido is walking home
B. Fido has fallen asleep
C. Fido is accelerating
D. Fido is walking away from home

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


Prompt:
Misconception:
Believes the gradient of a distance-time graph is the acceleration

Question:
This graph shows how far Fido the dog is from his home.
What might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis. ]()

Options:
A. Fido is walking home
B. Fido has fallen asleep
C. Fido is accelerating
D. Fido is walking away from home

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


Prompt:
Misconception:
Believes a downward slope on a distance-time graph means travelling away

Question:
This graph shows how far Fido the dog is from his home.
What might the negative-sloping section represent? ![A graph with time (secs) on the horizontal axis and distance (m) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis. ]()

Options:
A. Fido is walking home
B. Fido has fallen asleep
C. Fido is accelerating
D. Fido is walking away from home

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


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

Question:
What should replace the star?
\[
\bigstar \times 4=108
\]

Options:
A. \( 112 \)
B. \( 27 \)
C. \( 432 \)
D. \( 104 \)

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

Question:
What should replace the star?
\[
\bigstar \times 4=108
\]

Options:
A. \( 112 \)
B. \( 27 \)
C. \( 432 \)
D. \( 104 \)

Solve the problem as a student with the misconception above.
You 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 speed is distance multiplied by time

Question:
The formula for speed is
\(
\text { Speed }=\frac{\text { Distance }}{\text { Time }}
\)
A snail travels \( 4 \mathrm{~m} \) in \( 10 \) hours. What was its speed?

Options:
A. \( 0.4 \) metres per hour
B. \( 40 \) metres per hour
C. \( 2.5 \) metres per hour
D. \( 4 \) metres per hour

Solve the problem as a student with the misconception above.
You 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:
The formula for speed is
\(
\text { Speed }=\frac{\text { Distance }}{\text { Time }}
\)
A snail travels \( 4 \mathrm{~m} \) in \( 10 \) hours. What was its speed?

Options:
A. \( 0.4 \) metres per hour
B. \( 40 \) metres per hour
C. \( 2.5 \) metres per hour
D. \( 4 \) metres per hour

Solve the problem as a student with the misconception above.
You 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 square root of the radius with the radius squared in the equation of a circle

Question:
What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]()

Options:
A. \( x^{2}+y^{2}=16 \)
B. \( x^{2}+y^{2}=\sqrt{4} \)
C. \( x^{2}+y^{2}=8 \)
D. \( x^{2}+y^{2}=4 \)

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:
Mixes up squaring and multiplying by 2 or doubling

Question:
What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]()

Options:
A. \( x^{2}+y^{2}=16 \)
B. \( x^{2}+y^{2}=\sqrt{4} \)
C. \( x^{2}+y^{2}=8 \)
D. \( x^{2}+y^{2}=4 \)

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:
Confuses the radius with the radius squared in the equation of a circle

Question:
What is the equation of this circle? ![A set of axes with a circle drawn. The circle goes through the points (4,0), (0, -4), (-4,0) and (0,4). ]()

Options:
A. \( x^{2}+y^{2}=16 \)
B. \( x^{2}+y^{2}=\sqrt{4} \)
C. \( x^{2}+y^{2}=8 \)
D. \( x^{2}+y^{2}=4 \)

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:
Believes multiplying two negatives gives a negative answer

Question:
If \( d=-2 \) what is the value of \( 10-2 d \) ?

Options:
A. \( -12 \)
B. \( 6 \)
C. \( 14 \)
D. \( 32 \)

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


Prompt:
Misconception:
Counts on by 1, when asked to count forward/backwards in a step other than 1

Question:
George is counting backwards in steps of \( 5 \).
He starts at the number \( 19,103 \) what is the next number he will say?

Options:
A. \( 19,102 \)
B. \( 19,099 \)
C. \( 19,098 \)
D. \( 19,097 \)

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

Question:
George is counting backwards in steps of \( 5 \).
He starts at the number \( 19,103 \) what is the next number he will say?

Options:
A. \( 19,102 \)
B. \( 19,099 \)
C. \( 19,098 \)
D. \( 19,097 \)

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


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

Question:
Solve
\[
2 n+3 \leq 3 n-7
\]

Options:
A. \( 2 \leq n \)
B. \( 10 \leq n \)
C. \( n \leq 10 \)
D. \( -4 \leq n \)

Solve the problem as a student with the misconception above.
You 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 they can multiply/divide through by a negative number without changing the direction of the inequality

Question:
Solve
\[
2 n+3 \leq 3 n-7
\]

Options:
A. \( 2 \leq n \)
B. \( 10 \leq n \)
C. \( n \leq 10 \)
D. \( -4 \leq n \)

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


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

Question:
Solve
\[
2 n+3 \leq 3 n-7
\]

Options:
A. \( 2 \leq n \)
B. \( 10 \leq n \)
C. \( n \leq 10 \)
D. \( -4 \leq n \)

Solve the problem as a student with the misconception above.
You 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 this function machine ![A function machine with an input of m+2, no function labelled and an output of 3m+2]() Tom says the function could be \( +2 m \)
Katie says the function could be \( \times 3 \)
Who do you agree with?

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

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


Prompt:
Misconception:
Thinks there are 10cm in a metre

Question:
\[450 \mathrm{~cm}=\] \[\square \mathrm{~m}\]

Options:
A. \( 4.5 \)
B. \( 45 \)
C. \( 5 \)
D. \( 45000 \)

Solve the problem as a student with the misconception above.
You 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 a rounded whole number instead of a decimal

Question:
\[450 \mathrm{~cm}=\] \[\square \mathrm{~m}\]

Options:
A. \( 4.5 \)
B. \( 45 \)
C. \( 5 \)
D. \( 45000 \)

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


Prompt:
Misconception:
Multiplies when converting to a larger unit

Question:
\[450 \mathrm{~cm}=\] \[\square \mathrm{~m}\]

Options:
A. \( 4.5 \)
B. \( 45 \)
C. \( 5 \)
D. \( 45000 \)

Solve the problem as a student with the misconception above.
You 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 or subtracts from numerator first when solving an equation with a fraction

Question:
Which of the following is a correct first step to solve this equation:
\(\frac{2 r-3}{5}=2+r\)

Options:
A. \( \frac{2 r}{5}=5+r \)
B. \( 10 r-15=10+5 r \)
C. \( 2 r-3=10+r \)
D. \( 2 r-3=10+5 r \)

Solve the problem as a student with the misconception above.
You 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 clears fractions from equations

Question:
Which of the following is a correct first step to solve this equation:
\(\frac{2 r-3}{5}=2+r\)

Options:
A. \( \frac{2 r}{5}=5+r \)
B. \( 10 r-15=10+5 r \)
C. \( 2 r-3=10+r \)
D. \( 2 r-3=10+5 r \)

Solve the problem as a student with the misconception above.
You 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 with a fraction, thinks you don't need to multiply every term on both sides when multiplying by the denominator

Question:
Which of the following is a correct first step to solve this equation:
\(\frac{2 r-3}{5}=2+r\)

Options:
A. \( \frac{2 r}{5}=5+r \)
B. \( 10 r-15=10+5 r \)
C. \( 2 r-3=10+r \)
D. \( 2 r-3=10+5 r \)

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


Prompt:
Misconception:
Does not interpret a sloping gradient as a change in rate

Question:
Water is poured into a glass at a constant rate.

This graph shows how the depth \( (d) \) of water in a glass changes over time \( (t) \).

Which of the following glasses is this most likely to be the graph of? ![A depth-time graph which is a curve starting at (0, 0), with a steep gradient to begin with but then the gradient decreases and the graph levels off to almost horizontal.]()

Options:
A. ![A cylinder sitting on one of its circular faces.]()
B. ![A wide cylinder with a narrow cylinder on top.]()
C. ![A narrow cylinder with a wide cylinder on top.]()
D. ![A shape that looks like a beaker. It has a circular base, with sloped edges up to a larger circular face at the top.]()

Solve the problem as a student with the misconception above.
You 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 spot the difference between a gradual change of gradient and 2 distinct line segments with different constant gradients

Question:
Water is poured into a glass at a constant rate.

This graph shows how the depth \( (d) \) of water in a glass changes over time \( (t) \).

Which of the following glasses is this most likely to be the graph of? ![A depth-time graph which is a curve starting at (0, 0), with a steep gradient to begin with but then the gradient decreases and the graph levels off to almost horizontal.]()

Options:
A. ![A cylinder sitting on one of its circular faces.]()
B. ![A wide cylinder with a narrow cylinder on top.]()
C. ![A narrow cylinder with a wide cylinder on top.]()
D. ![A shape that looks like a beaker. It has a circular base, with sloped edges up to a larger circular face at the top.]()

Solve the problem as a student with the misconception above.
You 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 power of 10, subtracts from the wrong column

Question:
What number is \( 10,000 \) less than \( 901,426 \) ?

Options:
A. \( 801,426 \)
B. \( 911,426 \)
C. \( 891,426 \)
D. \( 90.1426 \)

Solve the problem as a student with the misconception above.
You 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 rather than subtracts when answering worded problems

Question:
What number is \( 10,000 \) less than \( 901,426 \) ?

Options:
A. \( 801,426 \)
B. \( 911,426 \)
C. \( 891,426 \)
D. \( 90.1426 \)

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


Prompt:
Misconception:
Divides rather than subtracts when given the command 'less than'

Question:
What number is \( 10,000 \) less than \( 901,426 \) ?

Options:
A. \( 801,426 \)
B. \( 911,426 \)
C. \( 891,426 \)
D. \( 90.1426 \)

Solve the problem as a student with the misconception above.
You 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 10 instead of 100 when converting decimal to percentage

Question:
Convert this decimal to a percentage
\[
0.6
\]

Options:
A. \( 60 \% \)
B. \( 6 \% \)
C. \( 0.6 \% \)
D. \( 0.006 \% \)

Solve the problem as a student with the misconception above.
You 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 need to just add a % sign to a decimal to convert to a percentage

Question:
Convert this decimal to a percentage
\[
0.6
\]

Options:
A. \( 60 \% \)
B. \( 6 \% \)
C. \( 0.6 \% \)
D. \( 0.006 \% \)

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


Prompt:
Misconception:
Divides instead of multiplies when converting a decimal to a percentage

Question:
Convert this decimal to a percentage
\[
0.6
\]

Options:
A. \( 60 \% \)
B. \( 6 \% \)
C. \( 0.6 \% \)
D. \( 0.006 \% \)

Solve the problem as a student with the misconception above.
You 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 realize we can omit the multiplication symbol in algebraic expressions

Question:
Simplify the following by collecting like terms.
\[
d+d+d+d
\]

Options:
A. \( 4 \times d \)
B. \( d 4 \)
C. \( 4 d \)
D. \( d^{4} \)

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:
Writes the variable before the coefficient in an algebraic term

Question:
Simplify the following by collecting like terms.
\[
d+d+d+d
\]

Options:
A. \( 4 \times d \)
B. \( d 4 \)
C. \( 4 d \)
D. \( d^{4} \)

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:
Confuses collecting like terms with multiplication

Question:
Simplify the following by collecting like terms.
\[
d+d+d+d
\]

Options:
A. \( 4 \times d \)
B. \( d 4 \)
C. \( 4 d \)
D. \( d^{4} \)

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:
Believes when simplifying a fraction you can divide the numerator and denominator by different values

Question:
Write this fraction as simply as possible:
\(
\frac{9}{12}
\)

Options:
A. \( \frac{3}{6} \)
B. \( \frac{2}{6} \)
C. \( \frac{3}{4} \)
D. \( \frac{9}{12} \)

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


Prompt:
Misconception:
Does not recognise when a fraction can be simplified

Question:
Write this fraction as simply as possible:
\(
\frac{9}{12}
\)

Options:
A. \( \frac{3}{6} \)
B. \( \frac{2}{6} \)
C. \( \frac{3}{4} \)
D. \( \frac{9}{12} \)

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


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

Question:
Write this as a single fraction as simply as possible:
\(
\frac{3}{2 x}+\frac{4}{x}
\)

Options:
A. \( \frac{11}{2 x} \)
B. \( \frac{7}{3 x} \)
C. \( \frac{11}{x} \)
D. \( \frac{7}{2 x} \)

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


Prompt:
Misconception:
Forgets to change the numerators when finding equivalent fractions

Question:
Write this as a single fraction as simply as possible:
\(
\frac{3}{2 x}+\frac{4}{x}
\)

Options:
A. \( \frac{11}{2 x} \)
B. \( \frac{7}{3 x} \)
C. \( \frac{11}{x} \)
D. \( \frac{7}{2 x} \)

Solve the problem as a student with the misconception above.
You 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 smaller number is always subtracted from the larger, regardless of the order of the calculation

Question:
\( 598-1000= \)

Options:
A. \( 402 \)
B. \( -402 \)
C. \( -412 \)
D. This problem cannot be solved

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


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

Question:
\( 598-1000= \)

Options:
A. \( 402 \)
B. \( -402 \)
C. \( -412 \)
D. This problem cannot be solved

Solve the problem as a student with the misconception above.
You 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 it is impossible to subtract a bigger number from a smaller number

Question:
\( 598-1000= \)

Options:
A. \( 402 \)
B. \( -402 \)
C. \( -412 \)
D. This problem cannot be solved

Solve the problem as a student with the misconception above.
You 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 terms in linear sequence are in direct proportion

Question:
Lethna pays at one rate for the first \( 100 \) units of electricity she uses. She pays at a different rate for all the other units of electricity she uses.

How much must she pay for using a total of \( 1000 \) units of electricity? ![A graph showing how the cost changes for different numbers of units. The first 100 units cost £0.25 per unit. Then the rate changes to £0.10 per unit.]()

Options:
A. \( £ 130 \)
B. \( £ 250 \)
C. \( £ 115 \)
D. \( £ 175 \)

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


Prompt:
Misconception:
Believes there is a multiplicative relationship between values of terms in a linear sequence e.g. 10th term is double 5th term

Question:
The \( 1^{\text {st }} \) term in a linear sequence is \( 7 \).

The \( 4^{\text {th }} \) term of the sequence is \( 25 \).

What is the \( 8^{\text {th }} \) term of the sequence?

Options:
A. \( 49 \)
B. \( 50 \)
C. \( 42 \)
D. \( 56 \)

Solve the problem as a student with the misconception above.
You 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 multiply the constant difference by the term number to get the term value

Question:
The \( 1^{\text {st }} \) term in a linear sequence is \( 7 \).

The \( 4^{\text {th }} \) term of the sequence is \( 25 \).

What is the \( 8^{\text {th }} \) term of the sequence?

Options:
A. \( 49 \)
B. \( 50 \)
C. \( 42 \)
D. \( 56 \)

Solve the problem as a student with the misconception above.
You 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 parallel lines have gradients of opposite signs

Question:
A line has a gradient of \( 5 \)

A line parallel to this line would have a gradient of...

Options:
A. \( -5 \)
B. \( -\frac{1}{5} \)
C. \( 5 \)
D. Not enough information

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


Prompt:
Misconception:
Believes parallel lines have gradients that multiply to give -1

Question:
A line has a gradient of \( 5 \)

A line parallel to this line would have a gradient of...

Options:
A. \( -5 \)
B. \( -\frac{1}{5} \)
C. \( 5 \)
D. Not enough information

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


Prompt:
Misconception:
Does not know parallel lines have equal gradients

Question:
A line has a gradient of \( 5 \)

A line parallel to this line would have a gradient of...

Options:
A. \( -5 \)
B. \( -\frac{1}{5} \)
C. \( 5 \)
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:
When dividing a fraction by an integer, divides both the numerator and denominator by the integer

Question:
Calculate: \( \frac{4}{8} \div 2 \)

Options:
A. \( \frac{2}{4} \)
B. \( \frac{2}{8} \)
C. \( \frac{2}{16} \)
D. \( \frac{4}{4} \)

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 dividing a fraction by an integer, divides the denominator by the integer

Question:
Calculate: \( \frac{4}{8} \div 2 \)

Options:
A. \( \frac{2}{4} \)
B. \( \frac{2}{8} \)
C. \( \frac{2}{16} \)
D. \( \frac{4}{4} \)

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:
Confuses scalene and right angle triangles

Question:
\( A B C D \) is a rectangle.
What type of triangle is triangle \( \mathrm{BCD} \) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]()

Options:
A. Scalene
B. Isosceles
C. Right-angled
D. Equilateral

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


Prompt:
Misconception:
Confuses isosceles and right angle triangles

Question:
\( A B C D \) is a rectangle.
What type of triangle is triangle \( \mathrm{BCD} \) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]()

Options:
A. Scalene
B. Isosceles
C. Right-angled
D. Equilateral

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


Prompt:
Misconception:
Confuses isosceles and right angle triangles

Question:
\( A B C D \) is a rectangle.
What type of triangle is triangle \( \mathrm{BCD} \) ? ![Rectangle ABCD with the diagonal shown using a red dotted line]()

Options:
A. Scalene
B. Isosceles
C. Right-angled
D. Equilateral

Solve the problem as a student with the misconception above.
You 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:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "5a + 2" written inside it. The middle rectangle has "✕ 2" written inside it and the final rectangle is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 10 a+2 \)
B. \( 5 a+4 \)
C. \( 7 a+4 \)
D. \( 10 a+4 \)

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


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

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "5a + 2" written inside it. The middle rectangle has "✕ 2" written inside it and the final rectangle is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 10 a+2 \)
B. \( 5 a+4 \)
C. \( 7 a+4 \)
D. \( 10 a+4 \)

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:
Adds instead of multiplies when multiplying algebraic terms

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "5a + 2" written inside it. The middle rectangle has "✕ 2" written inside it and the final rectangle is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 10 a+2 \)
B. \( 5 a+4 \)
C. \( 7 a+4 \)
D. \( 10 a+4 \)

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
![Tom and Katie are discussing bar models.]() Tom says this bar model represents \( 2 x \) \begin{tabular}{|l|l|}
\hline \( 2 \) & \( x \) \\
\hline
\end{tabular} Katie says this bar model represents \( 2 x \) \begin{tabular}{|l|l|}
\hline\( x \) & \( x \) \\
\hline
\end{tabular} Who do you agree with?

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

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
![Tom and Katie are discussing bar models.]() Tom says this bar model represents \( 2 x \) \begin{tabular}{|l|l|}
\hline \( 2 \) & \( x \) \\
\hline
\end{tabular} Katie says this bar model represents \( 2 x \) \begin{tabular}{|l|l|}
\hline\( x \) & \( x \) \\
\hline
\end{tabular} Who do you agree with?

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

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
![Tom and Katie are discussing bar models.]() Tom says this bar model represents \( 2 x \) \begin{tabular}{|l|l|}
\hline \( 2 \) & \( x \) \\
\hline
\end{tabular} Katie says this bar model represents \( 2 x \) \begin{tabular}{|l|l|}
\hline\( x \) & \( x \) \\
\hline
\end{tabular} Who do you agree with?

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

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


Prompt:
Misconception:
When two digits multiply to 10 or more during a multiplication problem, does not add carried value to the preceding digit

Question:
What should replace the star?
\(
\frac{1}{3} \text { of } \color{yellow}\bigstar\)\(=27
\)

Options:
A. \( 61 \)
B. \( 9 \)
C. \( 81 \)
D. \( 30 \)

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


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

Question:
What should replace the star?
\(
\frac{1}{3} \text { of } \color{yellow}\bigstar\)\(=27
\)

Options:
A. \( 61 \)
B. \( 9 \)
C. \( 81 \)
D. \( 30 \)

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


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

Question:
input \(\Rightarrow-3 \Rightarrow \times 3 \Rightarrow 9a-21 \) What is the input of this function machine?

Options:
A. \( 3 a-18 \)
B. \( 3 a-4 \)
C. \( 3 a-21 \)
D. \( 3 a-7 \)

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


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

Question:
input \(\Rightarrow-3 \Rightarrow \times 3 \Rightarrow 9a-21 \) What is the input of this function machine?

Options:
A. \( 3 a-18 \)
B. \( 3 a-4 \)
C. \( 3 a-21 \)
D. \( 3 a-7 \)

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


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

Question:
input \(\Rightarrow-3 \Rightarrow \times 3 \Rightarrow 9a-21 \) What is the input of this function machine?

Options:
A. \( 3 a-18 \)
B. \( 3 a-4 \)
C. \( 3 a-21 \)
D. \( 3 a-7 \)

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


Prompt:
Misconception:
Does not know how many days are in a leap year

Question:
\( 2 \) leap years \( =\square \) days

Options:
A. \( 728 \)
B. \( 730 \)
C. \( 366 \)
D. \( 732 \)

Solve the problem as a student with the misconception above.
You 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 many days are in a leap year

Question:
\( 2 \) leap years \( =\square \) days

Options:
A. \( 728 \)
B. \( 730 \)
C. \( 366 \)
D. \( 732 \)

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


Prompt:
Misconception:
When dividing involving a power of 10, gives an answer 10 times bigger than it should be

Question:
What is the value of:
\[
23.04 \div 1000
\]

Options:
A. \( 0.02304 \)
B. \( 0.2304 \)
C. \( 0.0002304 \)
D. \( 0.002304 \)

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


Prompt:
Misconception:
When dividing a decimal by a power of 10 adds zeroes to start of the number ignoring the placement of the initial decimal point

Question:
What is the value of:
\[
23.04 \div 1000
\]

Options:
A. \( 0.02304 \)
B. \( 0.2304 \)
C. \( 0.0002304 \)
D. \( 0.002304 \)

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


Prompt:
Misconception:
When dividing involving a power of 10, gives an answer 10 times smaller than it should be

Question:
What is the value of:
\[
23.04 \div 1000
\]

Options:
A. \( 0.02304 \)
B. \( 0.2304 \)
C. \( 0.0002304 \)
D. \( 0.002304 \)

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


Prompt:
Misconception:
When multiplying multiples of ten and the answer requires an extra digit, leaves off that extra digit

Question:
\( 427 \times 6= \)

Options:
A. \( 240+120+42 \)
B. \( 2400+120+47 \)
C. \( 400+20+7 \)
D. \( 2400+120+42 \)

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


Prompt:
Misconception:
Believes division is commutative

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
b \div a
\)

Options:
A. \( \frac{b}{a} \)
B. \( a \div b \)
C. \( \frac{a}{b} \)
D. \( a b \)

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


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

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
b \div a
\)

Options:
A. \( \frac{b}{a} \)
B. \( a \div b \)
C. \( \frac{a}{b} \)
D. \( a b \)

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


Prompt:
Misconception:
Thinks that we can remove a division symbol and just write the variables next to each other

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
b \div a
\)

Options:
A. \( \frac{b}{a} \)
B. \( a \div b \)
C. \( \frac{a}{b} \)
D. \( a b \)

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


Prompt:
Misconception:
Thinks rectangles have rotational symmetry or order 4

Question:
In which region would a rectangle belong? ![Venn diagram with two circles labelled with 'exactly two lines of symmetry' and 'rotational symmetry of order 2'. A is in the only exactly two lines of symmetry region, B is in the intersection, C is in the only rotational symmetry of order 2 region and D is outside the two circles.]()

Options:
A. A
B. B
C. C
D. D

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


Prompt:
Misconception:
Thinks rectangles have line symmetry in the diagonals

Question:
In which region would a rectangle belong? ![Venn diagram with two circles labelled with 'exactly two lines of symmetry' and 'rotational symmetry of order 2'. A is in the only exactly two lines of symmetry region, B is in the intersection, C is in the only rotational symmetry of order 2 region and D is outside the two circles.]()

Options:
A. A
B. B
C. C
D. D

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


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

Question:
What fraction of the rectangle is shaded? ![A rectangle split into 10 equal parts with 3 parts shaded in yellow]()

Options:
A. \( \frac{7}{10} \)
B. \( 3 \)
C. \( \frac{3}{7} \)
D. \( \frac{3}{10} \)

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


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

Question:
What fraction of the rectangle is shaded? ![A rectangle split into 10 equal parts with 3 parts shaded in yellow]()

Options:
A. \( \frac{7}{10} \)
B. \( 3 \)
C. \( \frac{3}{7} \)
D. \( \frac{3}{10} \)

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


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

Question:
What should replace the star? \( \bigstar-37=38 \)

Options:
A. \( 75 \)
B. \( 1 \)
C. \( -1 \)
D. \( 65 \)

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


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

Question:
What should replace the star? \( \bigstar-37=38 \)

Options:
A. \( 75 \)
B. \( 1 \)
C. \( -1 \)
D. \( 65 \)

Solve the problem as a student with the misconception above.
You 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 an addition problem, does not add one to the preceding digit

Question:
What should replace the star? \( \bigstar-37=38 \)

Options:
A. \( 75 \)
B. \( 1 \)
C. \( -1 \)
D. \( 65 \)

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


Prompt:
Misconception:
Does not realise ratio in worded problem can be simplified

Question:
For every \( 5 \) marbles Karen has, Marty has three times as many.

Write the number of marbles Karen and Marty have as a ratio, with Karen's part first.

Options:
A. \( 1: 3 \)
B. \( 5: 3 \)
C. \( 5: 8 \)
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 sin when tan is required

Question:
Which ratio would you use to find the value of \( p \) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]()

Options:
A. \( \operatorname{Sin} \)
B. Cos
C. Tan
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 tan is required

Question:
Which ratio would you use to find the value of \( p \) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]()

Options:
A. \( \operatorname{Sin} \)
B. Cos
C. Tan
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:
Does not understand how to apply sohcahtoa

Question:
Which ratio would you use to find the value of \( p \) ? ![A right-angled triangle where the angle is 52 degrees, the side next to this is p and the side opposite is 6cm.]()

Options:
A. \( \operatorname{Sin} \)
B. Cos
C. Tan
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:
Mixes up greater than and less than symbols

Question:
Which of the following diagrams represents \( x>-1 \) ?

Options:
A. ![Image of a number line. At -1 there is an open, unfilled circle drawn, with a arrow pointing to the left, towards the negative numbers in the number line.]()
B. ![Image of a number line. At -1 there is a red, filled circle drawn, with a arrow pointing to the left, towards the negative numbers in the number line.]()
C. ![Image of a number line. At -1 there is an open, unfilled circle drawn, with a arrow pointing to the right, towards the higher positive numbers in the number line.]()
D. ![Image of a number line. At -1 there is a red, filled circle drawn, with a arrow pointing to the right, towards the higher positive numbers in the number line.]()

Solve the problem as a student with the misconception above.
You 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 representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning.

Question:
Which of the following diagrams represents \( x>-1 \) ?

Options:
A. ![Image of a number line. At -1 there is an open, unfilled circle drawn, with a arrow pointing to the left, towards the negative numbers in the number line.]()
B. ![Image of a number line. At -1 there is a red, filled circle drawn, with a arrow pointing to the left, towards the negative numbers in the number line.]()
C. ![Image of a number line. At -1 there is an open, unfilled circle drawn, with a arrow pointing to the right, towards the higher positive numbers in the number line.]()
D. ![Image of a number line. At -1 there is a red, filled circle drawn, with a arrow pointing to the right, towards the higher positive numbers in the number line.]()

Solve the problem as a student with the misconception above.
You 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:
\( 130 \% \) of \( 40= \)

Options:
A. \( 12 \)
B. \( 52 \)
C. \( 170 \)
D. Impossible as you cannot have a percentage 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:
\( 130 \% \) of \( 40= \)

Options:
A. \( 12 \)
B. \( 52 \)
C. \( 170 \)
D. Impossible as you cannot have a percentage 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:
\( 130 \% \) of \( 40= \)

Options:
A. \( 12 \)
B. \( 52 \)
C. \( 170 \)
D. Impossible as you cannot have a percentage 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:
Simplifies integers when simplifying a mixed number

Question:
Write the following fraction in its simplest form: \( 3 \frac{7}{21} \)

Options:
A. \( 1 \frac{16}{21} \)
B. \( 1 \frac{1}{3} \)
C. \( 3 \frac{1}{3} \)
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:
Believes mixed numbers cannot be simplified

Question:
Write the following fraction in its simplest form: \( 3 \frac{7}{21} \)

Options:
A. \( 1 \frac{16}{21} \)
B. \( 1 \frac{1}{3} \)
C. \( 3 \frac{1}{3} \)
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:
Does not realise you can use equivalent fractions to break fractions up into smaller divisions

Question:
What fraction should replace the star? ![A number line marked with 1/4, 2/4, 3/4, 4/4, 5/4. The star is halfway between 2/4 and 3/4.]()

Options:
A. \( \frac{3}{8} \)
B. \( \frac{5}{8} \)
C. \( \frac{1}{2} \)
D. None of these

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


Prompt:
Misconception:
Believes the fx column for calculating mean is value + frequency

Question:
This table shows the number of pets a group of students owns.
If calculating the mean number of pets owned, what would replace the star? \begin{tabular}{|c|c|c|}
\hline Number of pets & Frequency & \\
\hline \( 0 \) & \( 9 \) & \\
\hline \( 1 \) & \( 5 \) & \\
\hline \( 2 \) & \( 4 \) & \( \color{gold}\bigstar \)
\hline \( 3 \) & \( 2 \) & \\
\hline \( 4 \) & \( 3 \) & \\
\hline
\end{tabular}

Options:
A. \( 2+4=6 \)
B. \( 2-4=(-2) \)
C. \( 2 \times 4=8 \)
D. \( 2 \div 4=0.5 \)

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:
Believes the fx column for calculating mean is value - frequency

Question:
This table shows the number of pets a group of students owns.
If calculating the mean number of pets owned, what would replace the star? \begin{tabular}{|c|c|c|}
\hline Number of pets & Frequency & \\
\hline \( 0 \) & \( 9 \) & \\
\hline \( 1 \) & \( 5 \) & \\
\hline \( 2 \) & \( 4 \) & \( \color{gold}\bigstar \)
\hline \( 3 \) & \( 2 \) & \\
\hline \( 4 \) & \( 3 \) & \\
\hline
\end{tabular}

Options:
A. \( 2+4=6 \)
B. \( 2-4=(-2) \)
C. \( 2 \times 4=8 \)
D. \( 2 \div 4=0.5 \)

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:
Believes the fx column for calculating mean is value/frequency

Question:
This table shows the number of pets a group of students owns.
If calculating the mean number of pets owned, what would replace the star? \begin{tabular}{|c|c|c|}
\hline Number of pets & Frequency & \\
\hline \( 0 \) & \( 9 \) & \\
\hline \( 1 \) & \( 5 \) & \\
\hline \( 2 \) & \( 4 \) & \( \color{gold}\bigstar \)
\hline \( 3 \) & \( 2 \) & \\
\hline \( 4 \) & \( 3 \) & \\
\hline
\end{tabular}

Options:
A. \( 2+4=6 \)
B. \( 2-4=(-2) \)
C. \( 2 \times 4=8 \)
D. \( 2 \div 4=0.5 \)

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

Question:
What number should replace the star? \begin{tabular}{cccc}
\(\space\) & \( 9 \) & \( 3 \) & \( 5 \) & \( 2 \) \\
\(-\) & \(4\) & \(5\) & \(7\) & \(\bigstar\)\\
\(\space\) & \(4\) & \(7\) & \(7\) & \(3\)\\
\end{tabular}

Options:
A. \( 9 \)
B. \( 1 \)
C. \( 5 \)
D. It is not possible

Solve the problem as a student with the misconception above.
You 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 missing number subtraction problems

Question:
What number should replace the star? \begin{tabular}{cccc}
\(\space\) & \( 9 \) & \( 3 \) & \( 5 \) & \( 2 \) \\
\(-\) & \(4\) & \(5\) & \(7\) & \(\bigstar\)\\
\(\space\) & \(4\) & \(7\) & \(7\) & \(3\)\\
\end{tabular}

Options:
A. \( 9 \)
B. \( 1 \)
C. \( 5 \)
D. It is not possible

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


Prompt:
Misconception:
Does not realise we can borrow from the preceding digit in a subtraction problem

Question:
What number should replace the star? \begin{tabular}{cccc}
\(\space\) & \( 9 \) & \( 3 \) & \( 5 \) & \( 2 \) \\
\(-\) & \(4\) & \(5\) & \(7\) & \(\bigstar\)\\
\(\space\) & \(4\) & \(7\) & \(7\) & \(3\)\\
\end{tabular}

Options:
A. \( 9 \)
B. \( 1 \)
C. \( 5 \)
D. It is not possible

Solve the problem as a student with the misconception above.
You 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:
Solve the equation:
\[
0.45=0.3 p
\]

Options:
A. \( p=\frac{2}{3} \)
B. \( p=1.5 \)
C. \( p=0.135 \)
D. \( p=0.15 \)

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


Prompt:
Misconception:
When solving an equation, multiplies instead of dividing

Question:
Solve the equation:
\[
0.45=0.3 p
\]

Options:
A. \( p=\frac{2}{3} \)
B. \( p=1.5 \)
C. \( p=0.135 \)
D. \( p=0.15 \)

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


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

Question:
Vera wants to solve this equation using the quadratic formula.
\(
h^{2}+4=5 h
\)

What should replace the triangle? ![The image shows the structure of the quadratic formula. It says plus or minus the square root, and the triangle is the first thing after the square root sign, with a minus sign after it.]()

Options:
A. \( 8 \)
B. \( -10 \)
C. \( 16 \)
D. \( 25 \)

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


Prompt:
Misconception:
When using the formula to solve a quadratic equation, believes that a, b and c are always taken from the 1st, 2nd and 3rd terms, respectively, of the quadratic.

Question:
Vera wants to solve this equation using the quadratic formula.
\(
h^{2}+4=5 h
\)

What should replace the triangle? ![The image shows the structure of the quadratic formula. It says plus or minus the square root, and the triangle is the first thing after the square root sign, with a minus sign after it.]()

Options:
A. \( 8 \)
B. \( -10 \)
C. \( 16 \)
D. \( 25 \)

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


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

Question:
\( 4.72-3.1 \) What should replace the star?

Options:
A. \( 4.41 \)
B. \( 1.71 \)
C. \( 1.62 \)
D. \( 7.82 \)

Solve the problem as a student with the misconception above.
You 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:
\( 4.72-3.1 \) What should replace the star?

Options:
A. \( 4.41 \)
B. \( 1.71 \)
C. \( 1.62 \)
D. \( 7.82 \)

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


Prompt:
Misconception:
Adds instead of subtracts

Question:
\( 4.72-3.1 \) What should replace the star?

Options:
A. \( 4.41 \)
B. \( 1.71 \)
C. \( 1.62 \)
D. \( 7.82 \)

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


Prompt:
Misconception:
Halves when asked to find the square root

Question:
What is the square root of nine?

Options:
A. \( 3 \)
B. \( 4.5 \)
C. \( 81 \)
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:
Squares when asked to find the square root

Question:
What is the square root of nine?

Options:
A. \( 3 \)
B. \( 4.5 \)
C. \( 81 \)
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:
Mixes up squaring and multiplying by 2 or doubling

Question:
What is the square root of nine?

Options:
A. \( 3 \)
B. \( 4.5 \)
C. \( 81 \)
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 0 has no square root

Question:
One of these equations has no real solutions
Which is it?

Options:
A. \( (w-4)^{2}-16=0 \)
B. \( (w-4)^{2}+16=0 \)
C. \( (w-4)^{2}=0 \)
D. \( (w-4)^{2}-4=0 \)

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


Prompt:
Misconception:
Does not know that sample size affects reliability

Question:
A vegetarian restaurant wants to know people's eating habits
\( 50 \) people in Town \( A \) are asked if they eat meat. \begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Town A } \\
\hline Do you eat meat? & Frequency \\
\hline Yes & \( 39 \) \\
\hline No & \( 11 \) \\
\hline
\end{tabular} \( 200 \) people in Town B are asked if they eat meat. \begin{tabular}{|cc|}
\hline \multicolumn{2}{|c|}{ Town B } \\
\hline Do you eat meat? & Frequency \\
\hline Yes & \( 143 \) \\
\hline No & \( 57 \) \\
\hline
\end{tabular} Which results are more reliable?

Options:
A. Town A
B. Town B
C. They are the same
D. Impossible to say

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


Prompt:
Misconception:
Does not know that sample size affects reliability

Question:
A vegetarian restaurant wants to know people's eating habits
\( 50 \) people in Town \( A \) are asked if they eat meat. \begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Town A } \\
\hline Do you eat meat? & Frequency \\
\hline Yes & \( 39 \) \\
\hline No & \( 11 \) \\
\hline
\end{tabular} \( 200 \) people in Town B are asked if they eat meat. \begin{tabular}{|cc|}
\hline \multicolumn{2}{|c|}{ Town B } \\
\hline Do you eat meat? & Frequency \\
\hline Yes & \( 143 \) \\
\hline No & \( 57 \) \\
\hline
\end{tabular} Which results are more reliable?

Options:
A. Town A
B. Town B
C. They are the same
D. Impossible to say

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


Prompt:
Misconception:
Does not know that sample size affects reliability

Question:
A vegetarian restaurant wants to know people's eating habits
\( 50 \) people in Town \( A \) are asked if they eat meat. \begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Town A } \\
\hline Do you eat meat? & Frequency \\
\hline Yes & \( 39 \) \\
\hline No & \( 11 \) \\
\hline
\end{tabular} \( 200 \) people in Town B are asked if they eat meat. \begin{tabular}{|cc|}
\hline \multicolumn{2}{|c|}{ Town B } \\
\hline Do you eat meat? & Frequency \\
\hline Yes & \( 143 \) \\
\hline No & \( 57 \) \\
\hline
\end{tabular} Which results are more reliable?

Options:
A. Town A
B. Town B
C. They are the same
D. Impossible to say

Solve the problem as a student with the misconception above.
You 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 when finding a percentage you divide by the percentage being asked

Question:
What should replace the star? ![A percentage number line representing the value 630 with a star above the 84% mark]() Use your calculator, if needed, and give your answer to \( 1 \) decimal place.

Options:
A. \( 750 \)
B. \( 529.2 \)
C. \( 546 \)
D. \( 614 \)

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


Prompt:
Misconception:
Adds instead of subtracts when asked to find the difference

Question:
![A line graph with title "Height of rocket".
The x-axis is titled "Time in seconds" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.
The y-axis is titled "Height in metres" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).
]() How many metres did the rocket travel between \( 20 \) and \( 50 \) seconds?

Options:
A. \( 25 \)
B. \( 85 \)
C. \( 30 \)
D. \( 55 \)

Solve the problem as a student with the misconception above.
You 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 difference between two points on a time series graph, only uses one of the points.

Question:
![A line graph with title "Height of rocket".
The x-axis is titled "Time in seconds" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.
The y-axis is titled "Height in metres" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).
]() How many metres did the rocket travel between \( 20 \) and \( 50 \) seconds?

Options:
A. \( 25 \)
B. \( 85 \)
C. \( 30 \)
D. \( 55 \)

Solve the problem as a student with the misconception above.
You 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 difference between two points on a time series graph, only uses one of the points.

Question:
![A line graph with title "Height of rocket".
The x-axis is titled "Time in seconds" and the scale is labelled from 0 to 90 seconds in steps of 10 seconds.
The y-axis is titled "Height in metres" and the scale is labelled from 0 to 60 in steps of 10 metres. The following points are plotted and joined together: (0, 0), (10, 10), (20, 30),(30, 40), (40, 50), (60, 60).
]() How many metres did the rocket travel between \( 20 \) and \( 50 \) seconds?

Options:
A. \( 25 \)
B. \( 85 \)
C. \( 30 \)
D. \( 55 \)

Solve the problem as a student with the misconception above.
You 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 y =1 is the y axis

Question:
What is the equation of the \( y \) axis?

Options:
A. \( y=1 \)
B. \( y=0 \)
C. \( y=x \)
D. \( x=0 \)

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:
Confuses the equations of vertical and horizontal lines

Question:
What is the equation of the \( y \) axis?

Options:
A. \( y=1 \)
B. \( y=0 \)
C. \( y=x \)
D. \( x=0 \)

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:
Thinks x = y is an axis

Question:
What is the equation of the \( y \) axis?

Options:
A. \( y=1 \)
B. \( y=0 \)
C. \( y=x \)
D. \( x=0 \)

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:
Rounds up instead of down

Question:
What is \( 326 \) rounded to the nearest \( 1000 \) ?

Options:
A. \( 1000 \)
B. \( 3000 \)
C. \( 500 \)
D. \( 0 \)

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


Prompt:
Misconception:
Rounds to the wrong degree of accuracy (rounds too little)

Question:
What is \( 326 \) rounded to the nearest \( 1000 \) ?

Options:
A. \( 1000 \)
B. \( 3000 \)
C. \( 500 \)
D. \( 0 \)

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


Prompt:
Misconception:
Believes 0 is not a real solution to an equation

Question:
One of these equations has no real solutions.
Which is it?

Options:
A. \( t^{2}-45=0 \)
B. \( t^{2}-45=-45 \)
C. \( t^{3}=-45 \)
D. \( t^{2}=-45 \)

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


Prompt:
Misconception:
Believes a number raised to a power will always give a positive answer

Question:
One of these equations has no real solutions.
Which is it?

Options:
A. \( t^{2}-45=0 \)
B. \( t^{2}-45=-45 \)
C. \( t^{3}=-45 \)
D. \( t^{2}=-45 \)

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


Prompt:
Misconception:
Stops iteration too early when solving equations

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

To find the value of \( x \), Sally uses:
\(x_{n+1}=\frac{8}{9}-\frac{x^{3}{ }_{n}}{9}\)

If \( x_{0}=0 \), what is the value of \( x \) to \( 3 \) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]()

Options:
A. \( 0.826 \)
B. \( 0.830 \)
C. \( 0.825 \)
D. \( 0.8101 \)

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


Prompt:
Misconception:
Stops iteration too early when solving equations

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

To find the value of \( x \), Sally uses:
\(x_{n+1}=\frac{8}{9}-\frac{x^{3}{ }_{n}}{9}\)

If \( x_{0}=0 \), what is the value of \( x \) to \( 3 \) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]()

Options:
A. \( 0.826 \)
B. \( 0.830 \)
C. \( 0.825 \)
D. \( 0.8101 \)

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


Prompt:
Misconception:
Stops iteration too early when solving equations

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

To find the value of \( x \), Sally uses:
\(x_{n+1}=\frac{8}{9}-\frac{x^{3}{ }_{n}}{9}\)

If \( x_{0}=0 \), what is the value of \( x \) to \( 3 \) decimal places? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]()

Options:
A. \( 0.826 \)
B. \( 0.830 \)
C. \( 0.825 \)
D. \( 0.8101 \)

Solve the problem as a student with the misconception above.
You 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:
The diagonals of a rectangle with different length sides \(_____________\) intersect at right-angles ![A rectangle]()

Options:
A. always
B. sometimes
C. never
D. I don't know

Solve the problem as a student with the misconception above.
You 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:
The diagonals of a rectangle with different length sides \(_____________\) intersect at right-angles ![A rectangle]()

Options:
A. always
B. sometimes
C. never
D. I don't know

Solve the problem as a student with the misconception above.
You 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:
The diagonals of a rectangle with different length sides \(_____________\) intersect at right-angles ![A rectangle]()

Options:
A. always
B. sometimes
C. never
D. I don't know

Solve the problem as a student with the misconception above.
You 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 gradients of perpendicular lines are reciprocals of the same sign

Question:
Which of the following lines is perpendicular to
\[
y=3 x-2 ?
\]

Options:
A. \( y=\frac{1}{3} x+1 \)
B. \( y=5-\frac{1}{3} x \)
C. \( y=3 x+7 \)
D. \( x=3 y-4 \)

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:
Confuses the meaning of parallel and perpendicular

Question:
Which of the following lines is perpendicular to
\[
y=3 x-2 ?
\]

Options:
A. \( y=\frac{1}{3} x+1 \)
B. \( y=5-\frac{1}{3} x \)
C. \( y=3 x+7 \)
D. \( x=3 y-4 \)

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 finding a missing side of a parallelogram given the area completes an extra step of dividing by 2

Question:
The area of this parallelogram is \( 24 \mathrm{~cm}^{2} \)

What measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 2 \mathrm{~cm} \)
C. \( 8 \mathrm{~cm} \)
D. Not enough information

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


Prompt:
Misconception:
When finding the area of a parallelogram finds base x perpendicular height but divides the answer by 2

Question:
The area of this parallelogram is \( 24 \mathrm{~cm}^{2} \)

What measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 2 \mathrm{~cm} \)
C. \( 8 \mathrm{~cm} \)
D. Not enough information

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


Prompt:
Misconception:
Does not realise we can find a missing length if we know the base of a parallelogram and its area.

Question:
The area of this parallelogram is \( 24 \mathrm{~cm}^{2} \)

What measurement should replace the star? ![Parallelogram with base length 6cm and the perpendicular height has a star symbol.]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 2 \mathrm{~cm} \)
C. \( 8 \mathrm{~cm} \)
D. Not enough information

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