Prompt:
Misconception:
Gives the vertex instead of the 3-letter angle notation

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

Options:
A. \( E \)
B. FEC
C. CGE
D. CEG

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


Prompt:
Misconception:
In 3 letter angle notation, gives a wider angle that contains the shaded angle

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

Options:
A. \( E \)
B. FEC
C. CGE
D. CEG

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


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

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

Options:
A. \( E \)
B. FEC
C. CGE
D. CEG

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Which multiplication will help factorise \( x^{2}+13 x+30 \) ?

Options:
A. \( 1 \times 30 \)
B. \( 2 \times 15 \)
C. \( 3 \times 10 \)
D. \( 5 \times 6 \)

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Which multiplication will help factorise \( x^{2}+13 x+30 \) ?

Options:
A. \( 1 \times 30 \)
B. \( 2 \times 15 \)
C. \( 3 \times 10 \)
D. \( 5 \times 6 \)

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Which multiplication will help factorise \( x^{2}+13 x+30 \) ?

Options:
A. \( 1 \times 30 \)
B. \( 2 \times 15 \)
C. \( 3 \times 10 \)
D. \( 5 \times 6 \)

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


Prompt:
Misconception:
Mixes up smallest and largest when ordering fractions

Question:
Which option shows the fractions in order from smallest to largest?

Options:
A. \( \begin{array}{llll}\frac{3}{4} & \frac{1}{2} & \frac{2}{6} & \frac{1}{12}\end{array} \)
B. \( \begin{array}{llll}\frac{1}{2} & \frac{3}{4} & \frac{2}{6} & \frac{1}{12}\end{array} \)
C. \( \frac{1}{12} \quad \frac{2}{6} \quad \frac{1}{2} \quad \frac{3}{4} \)
D. \( \begin{array}{llll}\frac{1}{2} & \frac{1}{12} & \frac{2}{6} & \frac{3}{4}\end{array} \)

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:
Ordered fractions by comparing denominators rather than using equivalent fractions.

Question:
Which option shows the fractions in order from smallest to largest?

Options:
A. \( \begin{array}{llll}\frac{3}{4} & \frac{1}{2} & \frac{2}{6} & \frac{1}{12}\end{array} \)
B. \( \begin{array}{llll}\frac{1}{2} & \frac{3}{4} & \frac{2}{6} & \frac{1}{12}\end{array} \)
C. \( \frac{1}{12} \quad \frac{2}{6} \quad \frac{1}{2} \quad \frac{3}{4} \)
D. \( \begin{array}{llll}\frac{1}{2} & \frac{1}{12} & \frac{2}{6} & \frac{3}{4}\end{array} \)

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


Prompt:
Misconception:
When comparing unit fractions believes that fractions with larger denominators are greater in size.

Question:
Which option shows the fractions in order from smallest to largest?

Options:
A. \( \begin{array}{llll}\frac{3}{4} & \frac{1}{2} & \frac{2}{6} & \frac{1}{12}\end{array} \)
B. \( \begin{array}{llll}\frac{1}{2} & \frac{3}{4} & \frac{2}{6} & \frac{1}{12}\end{array} \)
C. \( \frac{1}{12} \quad \frac{2}{6} \quad \frac{1}{2} \quad \frac{3}{4} \)
D. \( \begin{array}{llll}\frac{1}{2} & \frac{1}{12} & \frac{2}{6} & \frac{3}{4}\end{array} \)

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:
Finds the mean instead of the median

Question:
What is the median of the following numbers?
\[
3,5,6,18,18
\]

Options:
A. \( 10 \)
B. \( 12 \)
C. \( 6 \)
D. \( 18 \)

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


Prompt:
Misconception:
When finding the median for an odd numbered data set, find the midpoint of two values rather than giving the middle value

Question:
What is the median of the following numbers?
\[
3,5,6,18,18
\]

Options:
A. \( 10 \)
B. \( 12 \)
C. \( 6 \)
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:
Finds the mode instead of the median

Question:
What is the median of the following numbers?
\[
3,5,6,18,18
\]

Options:
A. \( 10 \)
B. \( 12 \)
C. \( 6 \)
D. \( 18 \)

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


Prompt:
Misconception:
Believes the first multiple of a is 2a

Question:
If you list the multiples of \( 15 \) in ascending order, what is the \( 5^{\text {th }} \) number in the list?

Options:
A. \( 60 \)
B. \( 45 \)
C. \( 90 \)
D. \( 75 \)

Solve the problem as a student with the misconception above.
You 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 sides of a rectangle must be horizontal and vertical, not diagonal

Question:
Here are \( 3 \) vertices of a rectangle:
\((0,3),(4,-1),(2,-3),\)

What are the coordinates of the \( 4^{\text {th }} \) vertex?

Options:
A. \( (0,1) \)
B. \( (4,1) \)
C. \( (-2,1) \)
D. \( (-2,-3) \)

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


Prompt:
Misconception:
Believes the sides of a rectangle must be horizontal and vertical, not diagonal

Question:
Here are \( 3 \) vertices of a rectangle:
\((0,3),(4,-1),(2,-3),\)

What are the coordinates of the \( 4^{\text {th }} \) vertex?

Options:
A. \( (0,1) \)
B. \( (4,1) \)
C. \( (-2,1) \)
D. \( (-2,-3) \)

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


Prompt:
Misconception:
Believes the sides of a rectangle must be horizontal and vertical, not diagonal

Question:
Here are \( 3 \) vertices of a rectangle:
\((0,3),(4,-1),(2,-3),\)

What are the coordinates of the \( 4^{\text {th }} \) vertex?

Options:
A. \( (0,1) \)
B. \( (4,1) \)
C. \( (-2,1) \)
D. \( (-2,-3) \)

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


Prompt:
Misconception:
When asked to multiply fractions, uses the method for adding instead

Question:
Write this as a single fraction as simply as possible:

\(
\frac{5}{x} \times \frac{2 y}{x^{2}}
\)

Options:
A. \( \frac{10 y}{x^{3}} \)
B. \( \frac{5 x+10 y}{x^{2}} \)
C. \( \frac{10 y}{3 x} \)
D. \( \frac{10 x y}{x^{2}} \)

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:
Believes cubing a number means you multiply it by 3

Question:
Write this as a single fraction as simply as possible:

\(
\frac{5}{x} \times \frac{2 y}{x^{2}}
\)

Options:
A. \( \frac{10 y}{x^{3}} \)
B. \( \frac{5 x+10 y}{x^{2}} \)
C. \( \frac{10 y}{3 x} \)
D. \( \frac{10 x y}{x^{2}} \)

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:
When subtracting a negative number, subtracts the absolute value rather than adding it

Question:
Isaac is trying to solve the pair of simultaneous equations on the right.

\[
6 g+h=12
\]
\[
6 g-3 h=-3
\]

He decides to subtract the bottom equation from the top equation.
What will he end up with?

Options:
A. \( -2 h=9 \)
B. \( -2 h=15 \)
C. \( 4 h=9 \)
D. \( 4 h=15 \)

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 subtracting a negative number, subtracts the absolute value rather than adding it

Question:
Isaac is trying to solve the pair of simultaneous equations on the right.

\[
6 g+h=12
\]
\[
6 g-3 h=-3
\]

He decides to subtract the bottom equation from the top equation.
What will he end up with?

Options:
A. \( -2 h=9 \)
B. \( -2 h=15 \)
C. \( 4 h=9 \)
D. \( 4 h=15 \)

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 subtracting a negative number, subtracts the absolute value rather than adding it

Question:
Isaac is trying to solve the pair of simultaneous equations on the right.

\[
6 g+h=12
\]
\[
6 g-3 h=-3
\]

He decides to subtract the bottom equation from the top equation.
What will he end up with?

Options:
A. \( -2 h=9 \)
B. \( -2 h=15 \)
C. \( 4 h=9 \)
D. \( 4 h=15 \)

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:
Ignores the negative sign

Question:
\( 3 \frac{4}{7}-1 \frac{3}{4}= \) Leave your answer as a mixed number

Options:
A. \( 2 \frac{5}{28} \)
B. \( 2 \frac{1}{3} \)
C. \( 1 \frac{23}{28} \)
D. \( \frac{51}{28} \)

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


Prompt:
Misconception:
Confused mixed numbers with improper fractions

Question:
\( 3 \frac{4}{7}-1 \frac{3}{4}= \) Leave your answer as a mixed number

Options:
A. \( 2 \frac{5}{28} \)
B. \( 2 \frac{1}{3} \)
C. \( 1 \frac{23}{28} \)
D. \( \frac{51}{28} \)

Solve the problem as a student with the misconception above.
You 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 sum of change in x and change in y gives the distance between points

Question:
Tom and Katie are arguing about distance and coordinates.

Tom says \( (3,-2) \) and \( (2,-3) \) are equidistant from the origin.
Katie says \( (4,1) \) and \( (7,-2) \) are equidistant from the origin.

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 negative and positive coordinates when working with graphs in four quadrants

Question:
Tom and Katie are arguing about distance and coordinates.

Tom says \( (3,-2) \) and \( (2,-3) \) are equidistant from the origin.
Katie says \( (4,1) \) and \( (7,-2) \) are equidistant from the origin.

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:
Rounds to the wrong degree of accuracy (rounds too much)

Question:
Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \( 505 \div 198 \)

Options:
A. \( 2.5505 \ldots \)
B. \( 2.243 \ldots \)
C. \( 5.136 \ldots \)
D. \( 3.1101 \ldots \)

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


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

Question:
Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \( 505 \div 198 \)

Options:
A. \( 2.5505 \ldots \)
B. \( 2.243 \ldots \)
C. \( 5.136 \ldots \)
D. \( 3.1101 \ldots \)

Solve the problem as a student with the misconception above.
You 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 every number up when estimating

Question:
Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct \( 505 \div 198 \)

Options:
A. \( 2.5505 \ldots \)
B. \( 2.243 \ldots \)
C. \( 5.136 \ldots \)
D. \( 3.1101 \ldots \)

Solve the problem as a student with the misconception above.
You 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 square root is found by dividing by 4

Question:
A shape is made up a square and regular pentagon.
The area of the square is \( 196 \mathrm{~cm}^{2} \).

What is the perimeter of the compound shape? ![A regular pentagon with a square joined along one edge]()

Options:
A. \( 14 \mathrm{~cm} \)
B. \( 343 \mathrm{~cm} \)
C. \( 112 \mathrm{~cm} \)
D. \( 98 \mathrm{~cm} \)

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:
Believes lines inside the shape are included when finding perimeter

Question:
A shape is made up a square and regular pentagon.
The area of the square is \( 196 \mathrm{~cm}^{2} \).

What is the perimeter of the compound shape? ![A regular pentagon with a square joined along one edge]()

Options:
A. \( 14 \mathrm{~cm} \)
B. \( 343 \mathrm{~cm} \)
C. \( 112 \mathrm{~cm} \)
D. \( 98 \mathrm{~cm} \)

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 given the perimeter of a regular polygon, subtracts instead of divides to find each side length

Question:
A regular octagon has a total perimeter of \( 12 \mathrm{~cm} \).
What is the length of each of its sides?

Options:
A. \( 1.5 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 96 \mathrm{~cm} \)
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 given the perimeter of a regular polygon, multiplies instead of divides to find each side length

Question:
A regular octagon has a total perimeter of \( 12 \mathrm{~cm} \).
What is the length of each of its sides?

Options:
A. \( 1.5 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 96 \mathrm{~cm} \)
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 know the meaning of the word regular

Question:
A regular octagon has a total perimeter of \( 12 \mathrm{~cm} \).
What is the length of each of its sides?

Options:
A. \( 1.5 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 96 \mathrm{~cm} \)
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:
Rounds too little when estimating

Question:
Estimate the value of
\(
\frac{3.24 \times 17.6}{0.224}
\)

Options:
A. \( 10.8 \)
B. \( 12 \)
C. \( 270 \)
D. \( 300 \)

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


Prompt:
Misconception:
Believes that dividing by a decimal is the same as dividing by its reciprocal

Question:
Estimate the value of
\(
\frac{3.24 \times 17.6}{0.224}
\)

Options:
A. \( 10.8 \)
B. \( 12 \)
C. \( 270 \)
D. \( 300 \)

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


Prompt:
Misconception:
Rounds to the nearest integer when estimating

Question:
Estimate the value of
\(
\frac{3.24 \times 17.6}{0.224}
\)

Options:
A. \( 10.8 \)
B. \( 12 \)
C. \( 270 \)
D. \( 300 \)

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


Prompt:
Misconception:
Mixes up greater than and less than symbols

Question:
What sign would make this statement true?
\(
\frac{5}{9} ? \frac{7}{12}
\)

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

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


Prompt:
Misconception:
Confuses an expression with a variable

Question:
Which of the following is the most appropriate word to describe: \( 6-3 g \)

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

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

Question:
Which of the following is the most appropriate word to describe: \( 6-3 g \)

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

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

Question:
Which of the following is the most appropriate word to describe: \( 6-3 g \)

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

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


Prompt:
Misconception:
Translates rather than reflects across a line of symmetry

Question:
![Squared paper with a horizontal line of reflection and a triangle. The horizontal base of the triangle is two squares above the line of reflection.]() Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![Tom does this: his reflected triangle is sitting upright the same as the original object. The base is 3 squares below the line of reflection.]() ![Katie does this: her reflected triangle is upside down compared to the original object. The base of the reflected triangle is on the line of reflection.]()

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:
Fails to reflect across mirror line

Question:
![Squared paper with a horizontal line of reflection and a triangle. The horizontal base of the triangle is two squares above the line of reflection.]() Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![Tom does this: his reflected triangle is sitting upright the same as the original object. The base is 3 squares below the line of reflection.]() ![Katie does this: her reflected triangle is upside down compared to the original object. The base of the reflected triangle is on the line of reflection.]()

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:
Cannot identify a line of symmetry in a simple shape

Question:
![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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:
Ignores colours or design on shape when looking for symmetry

Question:
![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
D. \( 4 \)

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


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

Question:
![A rectangle divided into 3 equal horizontal sections. The middle section is white and the other 2 sections are blue. In the centre of the white section are five 5-pointed blue stars in the same formation as the 5 dots on a dice. All the stars are in exactly the same orientation, with one point pointing directly upwards.]() How many lines of symmetry does this shape have?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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:
Gets the minutes and hours the wrong way around

Question:
Which clock shows ten to twelve at night?

Options:
A. 10:12
B. \( 12: 50 \)
C. 00:50
D. \( 23: 50 \)

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


Prompt:
Misconception:
Does not adjust the hour for “to” times

Question:
Which clock shows ten to twelve at night?

Options:
A. 10:12
B. \( 12: 50 \)
C. 00:50
D. \( 23: 50 \)

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


Prompt:
Misconception:
Does not adjust the hour for “to” times

Question:
Which clock shows ten to twelve at night?

Options:
A. 10:12
B. \( 12: 50 \)
C. 00:50
D. \( 23: 50 \)

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


Prompt:
Misconception:
Believes total frequency in a table is found by counting rows

Question:
Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\begin{tabular}{|c|c|}
\hline Goals scored & Frequency \\
\hline \( 0 \) & \( 6 \) \\
\hline \( 1 \) & \( 7 \) \\
\hline \( 2 \) & \( 4 \) \\
\hline \( 3 \) & \( 3 \) \\
\hline \( 4 \) & \( 1 \) \\
\hline
\end{tabular}]()

Options:
A. \( 21 \)
B. \( 5 \)
C. \( 28 \)
D. \( 10 \)

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


Prompt:
Misconception:
Believes the total frequency is the overall total in a grouped table

Question:
Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\begin{tabular}{|c|c|}
\hline Goals scored & Frequency \\
\hline \( 0 \) & \( 6 \) \\
\hline \( 1 \) & \( 7 \) \\
\hline \( 2 \) & \( 4 \) \\
\hline \( 3 \) & \( 3 \) \\
\hline \( 4 \) & \( 1 \) \\
\hline
\end{tabular}]()

Options:
A. \( 21 \)
B. \( 5 \)
C. \( 28 \)
D. \( 10 \)

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


Prompt:
Misconception:
Believes total frequency in a table is given by the sum of the categories given

Question:
Below is data from a Hockey team's matches over the course of a season, showing the number of goals scored. How many matches did the team play? ![\begin{tabular}{|c|c|}
\hline Goals scored & Frequency \\
\hline \( 0 \) & \( 6 \) \\
\hline \( 1 \) & \( 7 \) \\
\hline \( 2 \) & \( 4 \) \\
\hline \( 3 \) & \( 3 \) \\
\hline \( 4 \) & \( 1 \) \\
\hline
\end{tabular}]()

Options:
A. \( 21 \)
B. \( 5 \)
C. \( 28 \)
D. \( 10 \)

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


Prompt:
Misconception:
Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets

Question:
If
\(
m^{2}+5 m-14 \equiv(m+a)(m+b)
\)
then \( a \times b= \)

Options:
A. \( 5 \)
B. \( -5 \)
C. \( 14 \)
D. \( -14 \)

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


Prompt:
Misconception:
When factorising into double brackets, believes the product of the constants in the brackets is of the opposite sign to the constant in the expanded equation.

Question:
If
\(
m^{2}+5 m-14 \equiv(m+a)(m+b)
\)
then \( a \times b= \)

Options:
A. \( 5 \)
B. \( -5 \)
C. \( 14 \)
D. \( -14 \)

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


Prompt:
Misconception:
When writing a number as a percentage of another number gets them the wrong way around

Question:
What is \( 60 \mathrm{~m} \) as a percentage of \( 2 \mathrm{~km} \) ?

Options:
A. \( 333 \% \)
B. \( 30 \% \)
C. \( 3 \% \)
D. \( 60 \% \)

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


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

Question:
What is \( 60 \mathrm{~m} \) as a percentage of \( 2 \mathrm{~km} \) ?

Options:
A. \( 333 \% \)
B. \( 30 \% \)
C. \( 3 \% \)
D. \( 60 \% \)

Solve the problem as a student with the misconception above.
You 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 number to make it a percentage

Question:
What is \( 60 \mathrm{~m} \) as a percentage of \( 2 \mathrm{~km} \) ?

Options:
A. \( 333 \% \)
B. \( 30 \% \)
C. \( 3 \% \)
D. \( 60 \% \)

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


Prompt:
Misconception:
When writing ratio from diagram, writes total as one side

Question:
![A group of 8 squares and 5 circles]() What is the ratio of squares to circles?

Options:
A. \( 5: 13 \)
B. \( 8: 5 \)
C. \( 8: 13 \)
D. \( 5: 8 \)

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


Prompt:
Misconception:
When writing ratio from diagram, writes total as one side

Question:
![A group of 8 squares and 5 circles]() What is the ratio of squares to circles?

Options:
A. \( 5: 13 \)
B. \( 8: 5 \)
C. \( 8: 13 \)
D. \( 5: 8 \)

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


Prompt:
Misconception:
Mixes up sides of a ratio

Question:
![A group of 8 squares and 5 circles]() What is the ratio of squares to circles?

Options:
A. \( 5: 13 \)
B. \( 8: 5 \)
C. \( 8: 13 \)
D. \( 5: 8 \)

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


Prompt:
Misconception:
Performs addition ahead of multiplication

Question:
Tom and Katie are discussing the order of operations
Tom says: \( 3+2-1 \equiv 3-1+2 \)
Katie says: \( 3+2 \times 1 \equiv 2 \times 1+3 \)

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

Question:
Tom and Katie are discussing the order of operations
Tom says: \( 3+2-1 \equiv 3-1+2 \)
Katie says: \( 3+2 \times 1 \equiv 2 \times 1+3 \)

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 using a 180 degree protractor to measure reflex angles gives the value of the acute or obtuse angle that is a complement to 360

Question:
Jo and Paul are arguing about the size of the marked angle.
Jo says it is \( 120^{\circ} \)
Paul says it is \( 60^{\circ} \)
Who is correct? ![Angle with a protractor over it showing 240 degrees]()

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

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


Prompt:
Misconception:
Does not add on 180 degrees when using a protractor to measure a reflex angle

Question:
Jo and Paul are arguing about the size of the marked angle.
Jo says it is \( 120^{\circ} \)
Paul says it is \( 60^{\circ} \)
Who is correct? ![Angle with a protractor over it showing 240 degrees]()

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

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


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

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

Options:
A. \( t^{2}-16=0 \)
B. \( t^{2}-16 t=0 \)
C. \( t^{2}-8 t-16=0 \)
D. \( t^{2}-8 t+16=0 \)

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 how to interpret a fraction worded problem

Question:
Barry has two fraction cards.
\( \frac{3}{7} \quad \square\)
The product of the cards is \( \frac{2}{5} \) What is the other card?

Options:
A. \( \frac{29}{35} \)
B. \( \frac{14}{15} \)
C. \( \frac{1}{35} \)
D. \( \frac{6}{35} \)

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


Prompt:
Misconception:
Does not know how to interpret a fraction worded problem

Question:
Barry has two fraction cards.
\( \frac{3}{7} \quad \square\)
The product of the cards is \( \frac{2}{5} \) What is the other card?

Options:
A. \( \frac{29}{35} \)
B. \( \frac{14}{15} \)
C. \( \frac{1}{35} \)
D. \( \frac{6}{35} \)

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


Prompt:
Misconception:
Does not know how to interpret a fraction worded problem

Question:
Barry has two fraction cards.
\( \frac{3}{7} \quad \square\)
The product of the cards is \( \frac{2}{5} \) What is the other card?

Options:
A. \( \frac{29}{35} \)
B. \( \frac{14}{15} \)
C. \( \frac{1}{35} \)
D. \( \frac{6}{35} \)

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


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

Question:
If you were to write the equation of this line in the form \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x}+\boldsymbol{c} \), what is the value of \( \boldsymbol{m} \) ? ![Graph showing straight line with y intercept (0,0) and x intercept (0,0). Also goes through the point (6,-4)]()

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

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 gradient = change in x/change in y

Question:
If you were to write the equation of this line in the form \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x}+\boldsymbol{c} \), what is the value of \( \boldsymbol{m} \) ? ![Graph showing straight line with y intercept (0,0) and x intercept (0,0). Also goes through the point (6,-4)]()

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

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:
Confuses square rooting and halving the number

Question:
A square has an area \( 36 \mathrm{~mm}^{2} \) What is the length of one side of the square?

Options:
A. \( 6 \mathrm{~mm} \)
B. \( 1296 \mathrm{~mm} \)
C. \( 18 \mathrm{~mm} \)
D. \( 9 \mathrm{~mm} \)

Solve the problem as a student with the misconception above.
You 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 perimeter and area

Question:
A square has an area \( 36 \mathrm{~mm}^{2} \) What is the length of one side of the square?

Options:
A. \( 6 \mathrm{~mm} \)
B. \( 1296 \mathrm{~mm} \)
C. \( 18 \mathrm{~mm} \)
D. \( 9 \mathrm{~mm} \)

Solve the problem as a student with the misconception above.
You 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, adds instead of dividing

Question:
Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.

What operation should replace the star? ![A diagram showing the change from the equations 9y = to y = represented by a gold star]()

Options:
A. \( +9 \)
B. \( \times 9 \)
C. \( \div 9 \)
D. \( -9 \)

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


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

Question:
Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.

What operation should replace the star? ![A diagram showing the change from the equations 9y = to y = represented by a gold star]()

Options:
A. \( +9 \)
B. \( \times 9 \)
C. \( \div 9 \)
D. \( -9 \)

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


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

Question:
Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.

What operation should replace the star? ![A diagram showing the change from the equations 9y = to y = represented by a gold star]()

Options:
A. \( +9 \)
B. \( \times 9 \)
C. \( \div 9 \)
D. \( -9 \)

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


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

Question:
The bar chart shows the number of cups of tea and coffee sold in a café over \( 4 \) days.

How many cups of coffee were sold on Tuesday? ![A dual bar bar chart showing the number of cups of tea and coffee sold Monday to Thursday. The vertical scale showing the number of cups sold has 10 small boxes between 0 and 10.The bar for tea on Tuesday reaches 2 small boxes above 10. The bar for coffee on Tuesday reaches 5 small boxes above 40.]()

Options:
A. \( 50 \)
B. \( 38 \)
C. \( 12 \)
D. \( 45 \)

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


Prompt:
Misconception:
Incorrectly factorises a quadratic

Question:
Simplify the following, if possible: \( \frac{t^{2}+t-2}{t-1} \)

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

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


Prompt:
Misconception:
Incorrectly factorises a quadratic

Question:
Simplify the following, if possible: \( \frac{t^{2}+t-2}{t-1} \)

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

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


Prompt:
Misconception:
Does not recognise factorising a quadratic

Question:
Simplify the following, if possible: \( \frac{t^{2}+t-2}{t-1} \)

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

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


Prompt:
Misconception:
Does know know equilateral means the same as regular

Question:
An equilateral shape must have...

Options:
A. All sides equal
B. All sides and all angles equal
C. A right angle
D. All angles equal

Solve the problem as a student with the misconception above.
You 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 know know equilateral means the same as regular

Question:
An equilateral shape must have...

Options:
A. All sides equal
B. All sides and all angles equal
C. A right angle
D. All angles equal

Solve the problem as a student with the misconception above.
You 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 know know equilateral means the same as regular

Question:
An equilateral shape must have...

Options:
A. All sides equal
B. All sides and all angles equal
C. A right angle
D. All angles equal

Solve the problem as a student with the misconception above.
You 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 a difference of one part in a ratio means the quantities will differ by one unit

Question:
Jess and Heena share some sweets in the ratio \( 3\;: 5 \).
Jess gets \( 15 \) sweets.
How many sweets does Heena get?

Options:
A. \( 17 \)
B. \( 9 \)
C. \( 5 \)
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:
Believes f(x) - a translates the function up a units

Question:
What transformation maps the graph of
\(y=f(x)\)
to the graph of
\(y=f(x)+1\)

Options:
A. Translation by vector
\(\left[\begin{array}{l}
0 \\
1
\end{array}\right]\)
B. Translation by vector
\(\left[\begin{array}{l}
0 \\
-1
\end{array}\right]\)
C. Translation by vector
\(\left[\begin{array}{l}
1 \\
0
\end{array}\right]\)
D. Translation by vector
\(\left[\begin{array}{l}
-1 \\
0
\end{array}\right]\)

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
\(y=f(x)+1\)

Options:
A. Translation by vector
\(\left[\begin{array}{l}
0 \\
1
\end{array}\right]\)
B. Translation by vector
\(\left[\begin{array}{l}
0 \\
-1
\end{array}\right]\)
C. Translation by vector
\(\left[\begin{array}{l}
1 \\
0
\end{array}\right]\)
D. Translation by vector
\(\left[\begin{array}{l}
-1 \\
0
\end{array}\right]\)

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
\(y=f(x)+1\)

Options:
A. Translation by vector
\(\left[\begin{array}{l}
0 \\
1
\end{array}\right]\)
B. Translation by vector
\(\left[\begin{array}{l}
0 \\
-1
\end{array}\right]\)
C. Translation by vector
\(\left[\begin{array}{l}
1 \\
0
\end{array}\right]\)
D. Translation by vector
\(\left[\begin{array}{l}
-1 \\
0
\end{array}\right]\)

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:
Does not know how to calculate with exchange rates

Question:
\begin{tabular}{|l|}
\hline Exchange rates \\
\\
\( £ 1=€ 1.17 \) \\
\( £ 1=\$ 1.31 \)
\end{tabular} How much is \( \$ 5 \) worth in pounds ( \( £ \) )?

Options:
A. \( 6.55 \)
B. \( 4.27 \)
C. \( 5 \)
D. \( 3.82 \)

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:
Does not know how to calculate with exchange rates

Question:
\begin{tabular}{|l|}
\hline Exchange rates \\
\\
\( £ 1=€ 1.17 \) \\
\( £ 1=\$ 1.31 \)
\end{tabular} How much is \( \$ 5 \) worth in pounds ( \( £ \) )?

Options:
A. \( 6.55 \)
B. \( 4.27 \)
C. \( 5 \)
D. \( 3.82 \)

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:
Misunderstands order of operations in algebraic expressions

Question:
Rearrange the following equation to make \( r \) the subject
\[
p=3 r-5
\]

Options:
A. \( r=\frac{p+5}{3} \)
B. \( r=p+5 \div 3 \)
C. \( r=\frac{p-5}{3} \)
D. \( r=p-5 \div 3 \)

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:
Confuses the inverse operations of addition and subtraction when rearranging equations

Question:
Rearrange the following equation to make \( r \) the subject
\[
p=3 r-5
\]

Options:
A. \( r=\frac{p+5}{3} \)
B. \( r=p+5 \div 3 \)
C. \( r=\frac{p-5}{3} \)
D. \( r=p-5 \div 3 \)

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 multiplying a positive by a negative gives a positive answer

Question:
Multiply out the brackets: \( -5(m-7) \)

Options:
A. \( 5 m+35 \)
B. \( -5 m-35 \)
C. \( -5 m+35 \)
D. \( 5 m-35 \)

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


Prompt:
Misconception:
Believes multiplying two negatives gives a negative answer

Question:
Multiply out the brackets: \( -5(m-7) \)

Options:
A. \( 5 m+35 \)
B. \( -5 m-35 \)
C. \( -5 m+35 \)
D. \( 5 m-35 \)

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


Prompt:
Misconception:
Assumes they multiply by the numerator of fractional index

Question:
\( (16)^{\frac{5}{2}}=? \)

Options:
A. \( 1024 \)
B. \( \frac{80}{32} \)
C. \( 20 \)
D. \( 40 \)

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


Prompt:
Misconception:
Multiplies by the index

Question:
\( (16)^{\frac{5}{2}}=? \)

Options:
A. \( 1024 \)
B. \( \frac{80}{32} \)
C. \( 20 \)
D. \( 40 \)

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


Prompt:
Misconception:
Thinks that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression

Question:
Tom and Katie are discussing rearranging \( p=\sqrt{5-q} \) to make \( q \) the subject Tom says a correct first line of working could be: \( p^{2}=5-q \) Katie says a correct first line of working could be: \( p+\sqrt{q}=\sqrt{5} \)
Who is correct?

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

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


Prompt:
Misconception:
Thinks that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression

Question:
Tom and Katie are discussing rearranging \( p=\sqrt{5-q} \) to make \( q \) the subject Tom says a correct first line of working could be: \( p^{2}=5-q \) Katie says a correct first line of working could be: \( p+\sqrt{q}=\sqrt{5} \)
Who is correct?

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

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


Prompt:
Misconception:
Adds instead of multiplying when expanding bracket

Question:
James is expanding these two brackets.

What should he get when he multiplies the two terms indicated by the arrows? ![The brackets shown are (x-8)(x-2). The arrows are pointing at the x in the first bracket and the -2 in the second bracket.]()

Options:
A. \( x+2 \)
B. \( -2 x \)
C. \( x-2 \)
D. \( +2 x \)

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:
Ignores negative sign when expanding bracket

Question:
James is expanding these two brackets.

What should he get when he multiplies the two terms indicated by the arrows? ![The brackets shown are (x-8)(x-2). The arrows are pointing at the x in the first bracket and the -2 in the second bracket.]()

Options:
A. \( x+2 \)
B. \( -2 x \)
C. \( x-2 \)
D. \( +2 x \)

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:
Thinks finding a fraction of an amount means subtracting from that amount

Question:
\( \frac{1}{7} \) of \( 56= \)

Options:
A. \( 7 \)
B. \( 8 \)
C. \( 9 \)
D. \( 49 \)

Solve the problem as a student with the misconception above.
You 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 corresponding angles sum to 180 degrees

Question:
Calculate the missing angle: ![Two vertical lines marked with arrows are crossed by one diagonal line. Two angles are marked; they are both on the upper side of the diagonal line and to the right of the vertical lines. One is marked '70', the other '?'. ]()

Options:
A. \( 70^{\circ} \)
B. \( 110^{\circ} \)
C. \( 290^{\circ} \)
D. \( 220^{\circ} \)

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


Prompt:
Misconception:
Thinks corresponding angles sum to 360 degrees

Question:
Calculate the missing angle: ![Two vertical lines marked with arrows are crossed by one diagonal line. Two angles are marked; they are both on the upper side of the diagonal line and to the right of the vertical lines. One is marked '70', the other '?'. ]()

Options:
A. \( 70^{\circ} \)
B. \( 110^{\circ} \)
C. \( 290^{\circ} \)
D. \( 220^{\circ} \)

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


Prompt:
Misconception:
Believes the intersection in a prime factor venn diagram does not contribute to the size of the number represented by a circle

Question:
What number should replace \(\color{gold}\bigstar \) in the Venn diagram? ![A Venn diagram with two circles. The left hand one is labelled 'prime factors of \star\', the right hand circle is labelled 'prime factors of 60'. In the left hand circle, there is an 11, in the overlap there is a 2 and a 3, and in the right hand circle there is a 2 and a heart. ]()

Options:
A. \( 11 \)
B. \( 66 \)
C. \( 16 \)
D. \( 132 \)

Solve the problem as a student with the misconception above.
You 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 factors add to give a number

Question:
What number should replace \(\color{gold}\bigstar \) in the Venn diagram? ![A Venn diagram with two circles. The left hand one is labelled 'prime factors of \star\', the right hand circle is labelled 'prime factors of 60'. In the left hand circle, there is an 11, in the overlap there is a 2 and a 3, and in the right hand circle there is a 2 and a heart. ]()

Options:
A. \( 11 \)
B. \( 66 \)
C. \( 16 \)
D. \( 132 \)

Solve the problem as a student with the misconception above.
You 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 multiply all numbers in a prime factor venn diagram gives the value of one sets number

Question:
What number should replace \(\color{gold}\bigstar \) in the Venn diagram? ![A Venn diagram with two circles. The left hand one is labelled 'prime factors of \star\', the right hand circle is labelled 'prime factors of 60'. In the left hand circle, there is an 11, in the overlap there is a 2 and a 3, and in the right hand circle there is a 2 and a heart. ]()

Options:
A. \( 11 \)
B. \( 66 \)
C. \( 16 \)
D. \( 132 \)

Solve the problem as a student with the misconception above.
You 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 nearest 50 not 20

Question:
What is \( 646 \) rounded to the nearest \( 20 \) ?

Options:
A. \( 650 \)
B. \( 620 \)
C. \( 640 \)
D. \( 600 \)

Solve the problem as a student with the misconception above.
You 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 you can round to numbers other than powers of 10

Question:
What is \( 646 \) rounded to the nearest \( 20 \) ?

Options:
A. \( 650 \)
B. \( 620 \)
C. \( 640 \)
D. \( 600 \)

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


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

Question:
What is \( 623 \) rounded to the nearest \( 50 \) ?

Options:
A. \( 600 \)
B. \( 700 \)
C. \( 620 \)
D. \( 650 \)

Solve the problem as a student with the misconception above.
You 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 \( 623 \) rounded to the nearest \( 50 \) ?

Options:
A. \( 600 \)
B. \( 700 \)
C. \( 620 \)
D. \( 650 \)

Solve the problem as a student with the misconception above.
You 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 \( 623 \) rounded to the nearest \( 50 \) ?

Options:
A. \( 600 \)
B. \( 700 \)
C. \( 620 \)
D. \( 650 \)

Solve the problem as a student with the misconception above.
You 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 in the equation y=a, a is the gradient

Question:
Which of the following lines is perpendicular to
\(y=5 \text { ? }\)

Options:
A. \( x=-27 \)
B. \( y=-5 \)
C. \( y=\frac{1}{5} \)
D. \( y=-\frac{1}{5} \)

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


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

Question:
Which diagram is the net for a square based pyramid?

Options:
A. ![Net showing a square and four triangles]()
B. ![Net showing a square and four rectangles]()
C. ![Net showing two squares and four rectangles]()
D. ![Net showing three squares and two triangles]()

Solve the problem as a student with the misconception above.
You 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:
Which diagram is the net for a square based pyramid?

Options:
A. ![Net showing a square and four triangles]()
B. ![Net showing a square and four rectangles]()
C. ![Net showing two squares and four rectangles]()
D. ![Net showing three squares and two triangles]()

Solve the problem as a student with the misconception above.
You 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:
Which diagram is the net for a square based pyramid?

Options:
A. ![Net showing a square and four triangles]()
B. ![Net showing a square and four rectangles]()
C. ![Net showing two squares and four rectangles]()
D. ![Net showing three squares and two triangles]()

Solve the problem as a student with the misconception above.
You 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:
\(
\frac{3}{4}-\frac{1}{12}=\frac{2}{\bigstar}
\)

What should replace the star?

Options:
A. \( 12 \)
B. \( 48 \)
C. \( 8 \)
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:
Forgets to change the numerators when finding equivalent fractions

Question:
\(
\frac{3}{4}-\frac{1}{12}=\frac{2}{\bigstar}
\)

What should replace the star?

Options:
A. \( 12 \)
B. \( 48 \)
C. \( 8 \)
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:
Rounds down instead of up

Question:
\[
34590.8549
\]
What is this number rounded to \( 1 \) decimal place?

Options:
A. \( 34590.8 \)
B. \( 30000 \)
C. \( 34591.9 \)
D. \( 34590.9 \)

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


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

Question:
\[
34590.8549
\]
What is this number rounded to \( 1 \) decimal place?

Options:
A. \( 34590.8 \)
B. \( 30000 \)
C. \( 34591.9 \)
D. \( 34590.9 \)

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


Prompt:
Misconception:
Changes wrong place value column when rounding

Question:
\[
34590.8549
\]
What is this number rounded to \( 1 \) decimal place?

Options:
A. \( 34590.8 \)
B. \( 30000 \)
C. \( 34591.9 \)
D. \( 34590.9 \)

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


Prompt:
Misconception:
Does not know the definition of a rational number

Question:
Which of these two numbers are rational?
\(
\pi \text { and } \frac{1}{\pi}
\)

Options:
A. \( \pi \)
B. \( \frac{1}{\pi} \)
C. Both
D. Neither

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


Prompt:
Misconception:
Does not know the definition of a rational number

Question:
Which of these two numbers are rational?
\(
\pi \text { and } \frac{1}{\pi}
\)

Options:
A. \( \pi \)
B. \( \frac{1}{\pi} \)
C. Both
D. Neither

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


Prompt:
Misconception:
Does not know the definition of a rational number

Question:
Which of these two numbers are rational?
\(
\pi \text { and } \frac{1}{\pi}
\)

Options:
A. \( \pi \)
B. \( \frac{1}{\pi} \)
C. Both
D. Neither

Solve the problem as a student with the misconception above.
You 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 constant in an expanded quadratic comes from adding the two numbers in the brackets

Question:
Factorise this expression, if possible:
\(
p^{2}+2 p+3
\)

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

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Factorise this expression, if possible:
\(
p^{2}+2 p+3
\)

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

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


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

Question:
Factorise this expression, if possible:
\(
p^{2}+2 p+3
\)

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

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


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

Question:
The cost of journeys from two taxi companies is shown on the diagram.

After how many miles is Company P more expensive than Company Q? ![A graph showing Cost (£) on the y axis and Distance (miles) on the x axis. Y axis from 0 to 30, each square goes up by 5,  and x axis from 0 to 6, each square goes up by 1. A blue line slopes upwards from left to right, from (0, 10). It is labelled 'Company Q'. A red line slopes upwards from left to right, from (0,0). It is labelled 'Company P'. Both lines go through (5, 20)]()

Options:
A. \( 10 \)
B. \( 6 \)
C. \( 5 \)
D. \( 20 \)

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


Prompt:
Misconception:
Does not think that the compensation strategy for the multiplication of 2 numbers is valid.

Question:
Tom and Katie are discussing ways to calculate \( 59 \times 4 \) mentally
Tom doubles \( 59 \) and then doubles the answer
Katie does \( 60 \times 4 \) and then subtracts \( 4 \) from the answer
Who would get the correct answer?

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

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


Prompt:
Misconception:
Thinks that doubling and then doubling again is not the same as multiplying by 4

Question:
Tom and Katie are discussing ways to calculate \( 59 \times 4 \) mentally
Tom doubles \( 59 \) and then doubles the answer
Katie does \( 60 \times 4 \) and then subtracts \( 4 \) from the answer
Who would get the correct answer?

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

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


Prompt:
Misconception:
Does not know what a square number is

Question:
\[
1,8,27,64, \ldots
\]

What is the name given to this sequence of numbers?

Options:
A. The square numbers
B. The odd numbers
C. The cube numbers
D. The triangular numbers

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


Prompt:
Misconception:
Mixes up odd and even numbers

Question:
\[
1,8,27,64, \ldots
\]

What is the name given to this sequence of numbers?

Options:
A. The square numbers
B. The odd numbers
C. The cube numbers
D. The triangular numbers

Solve the problem as a student with the misconception above.
You 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 cube numbers are triangular numbers

Question:
\[
1,8,27,64, \ldots
\]

What is the name given to this sequence of numbers?

Options:
A. The square numbers
B. The odd numbers
C. The cube numbers
D. The triangular numbers

Solve the problem as a student with the misconception above.
You 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 out 2 or more brackets, does not multiply all the combinations of terms

Question:
When Aaron completes the square, what should replace the triangle?
\(
3 g^{2}-18 g-7 \equiv 3(g-3)^{2} \triangle
\)

Options:
A. \( \triangle=-34 \)
B. \( \triangle=-16 \)
C. \( \triangle=-25 \)
D. \( \triangle=-88 \)

Solve the problem as a student with the misconception above.
You 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:
When Aaron completes the square, what should replace the triangle?
\(
3 g^{2}-18 g-7 \equiv 3(g-3)^{2} \triangle
\)

Options:
A. \( \triangle=-34 \)
B. \( \triangle=-16 \)
C. \( \triangle=-25 \)
D. \( \triangle=-88 \)

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


Prompt:
Misconception:
When completing the square, believes a coefficient of x^2 does not affect the value of the constant inside the bracket

Question:
When Aaron completes the square, what should replace the triangle?
\(
3 g^{2}-18 g-7 \equiv 3(g-3)^{2} \triangle
\)

Options:
A. \( \triangle=-34 \)
B. \( \triangle=-16 \)
C. \( \triangle=-25 \)
D. \( \triangle=-88 \)

Solve the problem as a student with the misconception above.
You 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 10000mm in a metre

Question:
\( 4 m \) is the same as ___ \( mm \)

Options:
A. \( 4000 \)
B. \( 40000 \)
C. \( 40 \)
D. \( 400 \)

Solve the problem as a student with the misconception above.
You 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 account for scale on diagram

Question:
John is labelling the lengths of the sides of this shape. ![A hexagon with one side, length 3 squares, labelled 6cm. The side labelled with the gold star is 1 square in length.]() What should replace the star?

Options:
A. \( 1 \mathrm{~cm} \)
B. \( 2 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 0.5 \mathrm{~cm} \)

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:
Incorrect use of scale on a diagram

Question:
John is labelling the lengths of the sides of this shape. ![A hexagon with one side, length 3 squares, labelled 6cm. The side labelled with the gold star is 1 square in length.]() What should replace the star?

Options:
A. \( 1 \mathrm{~cm} \)
B. \( 2 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 0.5 \mathrm{~cm} \)

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 asked to solve simultaneous equations, believes they can just find values that work in one equation

Question:
What is a correct solution for the following pair of simultaneous equations:
\[4x+y=7\]
\[3x+2y=4\]

Options:
A. \( \begin{array}{l}x=2 \\ y=-1\end{array} \)
B. \( \begin{array}{l}x=3 \\ y=-5\end{array} \)
C. \( \begin{array}{l}x=0.6 \\ y=4.6\end{array} \)
D. \( \begin{array}{l}x=10 \\ y=-33\end{array} \)

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


Prompt:
Misconception:
When asked to solve simultaneous equations, believes they can just find values that work in one equation

Question:
What is a correct solution for the following pair of simultaneous equations:
\[4x+y=7\]
\[3x+2y=4\]

Options:
A. \( \begin{array}{l}x=2 \\ y=-1\end{array} \)
B. \( \begin{array}{l}x=3 \\ y=-5\end{array} \)
C. \( \begin{array}{l}x=0.6 \\ y=4.6\end{array} \)
D. \( \begin{array}{l}x=10 \\ y=-33\end{array} \)

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


Prompt:
Misconception:
When asked to solve simultaneous equations, believes they can just find values that work in one equation

Question:
What is a correct solution for the following pair of simultaneous equations:
\[4x+y=7\]
\[3x+2y=4\]

Options:
A. \( \begin{array}{l}x=2 \\ y=-1\end{array} \)
B. \( \begin{array}{l}x=3 \\ y=-5\end{array} \)
C. \( \begin{array}{l}x=0.6 \\ y=4.6\end{array} \)
D. \( \begin{array}{l}x=10 \\ y=-33\end{array} \)

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


Prompt:
Misconception:
When simplifying surds, does not square root the largest square number that goes into the number under the surd before putting it in front of the surd

Question:
Simplify \( \sqrt{48} \) as much as possible

Options:
A. \( 16 \sqrt{3} \)
B. \( 4 \sqrt{12} \)
C. \( 4 \sqrt{3} \)
D. \( 2 \sqrt{12} \)

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 simplifying surds, does not use the largest square number to simplify

Question:
Simplify \( \sqrt{48} \) as much as possible

Options:
A. \( 16 \sqrt{3} \)
B. \( 4 \sqrt{12} \)
C. \( 4 \sqrt{3} \)
D. \( 2 \sqrt{12} \)

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

Question:
Problem P: \( 6 \div 3+5= \)
Problem Q: \( 6 \div 3 \times 5= \)

Which calculation should you do first in each problem?

Options:
A. Problem P: \( 3+5 \)
Problem Q: \( 3 \times 5 \)
B. Problem P: \( 3+5 \)
Problem Q: \( 6 \div 3 \)
C. Problem P: \( 6 \div 3 \)
Problem Q: \( 3 \times 5 \)
D. Problem P: \( 6 \div 3 \)
Problem Q: \( 6 \div 3 \)

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:
Confuses the order of operations, believes addition comes before division

Question:
Problem P: \( 6 \div 3+5= \)
Problem Q: \( 6 \div 3 \times 5= \)

Which calculation should you do first in each problem?

Options:
A. Problem P: \( 3+5 \)
Problem Q: \( 3 \times 5 \)
B. Problem P: \( 3+5 \)
Problem Q: \( 6 \div 3 \)
C. Problem P: \( 6 \div 3 \)
Problem Q: \( 3 \times 5 \)
D. Problem P: \( 6 \div 3 \)
Problem Q: \( 6 \div 3 \)

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

Question:
Problem P: \( 6 \div 3+5= \)
Problem Q: \( 6 \div 3 \times 5= \)

Which calculation should you do first in each problem?

Options:
A. Problem P: \( 3+5 \)
Problem Q: \( 3 \times 5 \)
B. Problem P: \( 3+5 \)
Problem Q: \( 6 \div 3 \)
C. Problem P: \( 6 \div 3 \)
Problem Q: \( 3 \times 5 \)
D. Problem P: \( 6 \div 3 \)
Problem Q: \( 6 \div 3 \)

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

Question:
\( 0.2 \) hours \( = _______ \) minutes

Options:
A. \( 12 \)
B. \( 20 \)
C. \( 2 \)
D. \( 120 \)

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


Prompt:
Misconception:
Thinks there are 10 minutes in an hour

Question:
\( 0.2 \) hours \( = _______ \) minutes

Options:
A. \( 12 \)
B. \( 20 \)
C. \( 2 \)
D. \( 120 \)

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


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

Question:
What is the size of angle \( s \) ? ![4 angles on an irregular quadrilateral these are labelled s, 2s, 2s, and 3s]()

Options:
A. \( 45^{\circ} \)
B. \( 51.4^{\circ} \)
C. \( 60^{\circ} \)
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 word and/or does not know the function of a compass

Question:
What is the name of the mathematical instrument used to construct circles?

Options:
A. Callipers
B. Compass
C. Protractor
D. Slide rule

Solve the problem as a student with the misconception above.
You 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 word and/or does not know the function of a compass

Question:
What is the name of the mathematical instrument used to construct circles?

Options:
A. Callipers
B. Compass
C. Protractor
D. Slide rule

Solve the problem as a student with the misconception above.
You 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 word and/or does not know the function of a compass

Question:
What is the name of the mathematical instrument used to construct circles?

Options:
A. Callipers
B. Compass
C. Protractor
D. Slide rule

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


Prompt:
Misconception:
Cannot identify the correct side lengths to use when asked to find the area of a face

Question:
Which calculation would give you the area of the face of this cuboid labelled \( Q \) ('the top')? ![A cuboid with dimensions 6cm by 3cm by 4 cm. The top face Q is marked. It is a rectangle with dimensions 6cm by 3cm.]()

Options:
A. \( 6 \mathrm{~cm} \times 3 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \times 3 \mathrm{~cm} \)
C. \( 6 \mathrm{~cm} \times 4 \mathrm{~cm} \)
D. \( 6 \mathrm{~cm} \times 4 \mathrm{~cm} \times 3 \mathrm{~cm} \)

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


Prompt:
Misconception:
Cannot identify the correct side lengths to use when asked to find the area of a face

Question:
Which calculation would give you the area of the face of this cuboid labelled \( Q \) ('the top')? ![A cuboid with dimensions 6cm by 3cm by 4 cm. The top face Q is marked. It is a rectangle with dimensions 6cm by 3cm.]()

Options:
A. \( 6 \mathrm{~cm} \times 3 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \times 3 \mathrm{~cm} \)
C. \( 6 \mathrm{~cm} \times 4 \mathrm{~cm} \)
D. \( 6 \mathrm{~cm} \times 4 \mathrm{~cm} \times 3 \mathrm{~cm} \)

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


Prompt:
Misconception:
Finds volume when asked for surface area

Question:
Which calculation would give you the area of the face of this cuboid labelled \( Q \) ('the top')? ![A cuboid with dimensions 6cm by 3cm by 4 cm. The top face Q is marked. It is a rectangle with dimensions 6cm by 3cm.]()

Options:
A. \( 6 \mathrm{~cm} \times 3 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \times 3 \mathrm{~cm} \)
C. \( 6 \mathrm{~cm} \times 4 \mathrm{~cm} \)
D. \( 6 \mathrm{~cm} \times 4 \mathrm{~cm} \times 3 \mathrm{~cm} \)

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


Prompt:
Misconception:
Reads the wrong scale on the protractor when measuring reflex angles

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The outer scale goes from 0 to 360, clockwise. The angle is a reflex angle that is between the red line that is at 0 (outer scale) and 180 (inner scale) on the protractor and goes clockwise round to the red line that is half way between 200 and 210 (outer scale) and halfway between 340 and 330 (inner scale).]()

Options:
A. \( 345^{\circ} \)
B. \( 215^{\circ} \)
C. \( 335^{\circ} \)
D. \( 205^{\circ} \)

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


Prompt:
Misconception:
Correct scale but wrong value on protractor reading.

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The outer scale goes from 0 to 360, clockwise. The angle is a reflex angle that is between the red line that is at 0 (outer scale) and 180 (inner scale) on the protractor and goes clockwise round to the red line that is half way between 200 and 210 (outer scale) and halfway between 340 and 330 (inner scale).]()

Options:
A. \( 345^{\circ} \)
B. \( 215^{\circ} \)
C. \( 335^{\circ} \)
D. \( 205^{\circ} \)

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


Prompt:
Misconception:
Reads the wrong scale on the protractor when measuring reflex angles

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The outer scale goes from 0 to 360, clockwise. The angle is a reflex angle that is between the red line that is at 0 (outer scale) and 180 (inner scale) on the protractor and goes clockwise round to the red line that is half way between 200 and 210 (outer scale) and halfway between 340 and 330 (inner scale).]()

Options:
A. \( 345^{\circ} \)
B. \( 215^{\circ} \)
C. \( 335^{\circ} \)
D. \( 205^{\circ} \)

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


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line
What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant, coordinate grid with the reflection line y=-x drawn and a triangle. The triangle has coordinates: (-2,3) (-2,6) and (0,5). The point P is the coordinate (0,5)]()

Options:
A. \( (-5,0) \)
B. \( (-4,-1) \)
C. \( (-2,2) \)
D. \( (-4,5) \)

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


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line
What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant, coordinate grid with the reflection line y=-x drawn and a triangle. The triangle has coordinates: (-2,3) (-2,6) and (0,5). The point P is the coordinate (0,5)]()

Options:
A. \( (-5,0) \)
B. \( (-4,-1) \)
C. \( (-2,2) \)
D. \( (-4,5) \)

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


Prompt:
Misconception:
Reflects horizontally or vertically instead of across a diagonal line of symmetry

Question:
The triangle is reflected in the dashed line
What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant, coordinate grid with the reflection line y=-x drawn and a triangle. The triangle has coordinates: (-2,3) (-2,6) and (0,5). The point P is the coordinate (0,5)]()

Options:
A. \( (-5,0) \)
B. \( (-4,-1) \)
C. \( (-2,2) \)
D. \( (-4,5) \)

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


Prompt:
Misconception:
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}{|c|c|c|c|c|}
\hline & \( 4 \) & \( 2 \) & \(5\) & \(4\)\\
\hline+ & \( 2 \) & \(\bigstar\)  & \(7\) & \(1\) \\
\hline \(\space\) & \(6\) & \(3\) & \(2\) & \(5\)
\end{tabular}

Options:
A. \( 6 \)
B. \( 5 \)
C. \( 1 \)
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:
When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit

Question:
What number should replace the star? \begin{tabular}{|c|c|c|c|c|}
\hline & \( 4 \) & \( 2 \) & \(5\) & \(4\)\\
\hline+ & \( 2 \) & \(\bigstar\)  & \(7\) & \(1\) \\
\hline \(\space\) & \(6\) & \(3\) & \(2\) & \(5\)
\end{tabular}

Options:
A. \( 6 \)
B. \( 5 \)
C. \( 1 \)
D. \( 0 \)

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


Prompt:
Misconception:
Does not understand how to find percentages of an amount

Question:
Find \( 20 \% \) of \( 80 \)

Options:
A. \( 8 \)
B. \( 20 \)
C. \( 96 \)
D. \( 16 \)

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


Prompt:
Misconception:
Thinks you need to just add a % sign to a number to make it a percentage

Question:
Find \( 20 \% \) of \( 80 \)

Options:
A. \( 8 \)
B. \( 20 \)
C. \( 96 \)
D. \( 16 \)

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


Prompt:
Misconception:
Found the percentage but added it to 100%

Question:
Find \( 20 \% \) of \( 80 \)

Options:
A. \( 8 \)
B. \( 20 \)
C. \( 96 \)
D. \( 16 \)

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Write the following as simply as possible: \( \frac{q^{2}+q-12}{q^{2}-2 q-3} \)

Options:
A. \( \frac{q-4}{q-1} \)
B. \( \frac{q+4}{q+1} \)
C. \( \frac{q-4}{-2 q-1} \)
D. \( 4 \)

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


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

Question:
Write the following as simply as possible: \( \frac{q^{2}+q-12}{q^{2}-2 q-3} \)

Options:
A. \( \frac{q-4}{q-1} \)
B. \( \frac{q+4}{q+1} \)
C. \( \frac{q-4}{-2 q-1} \)
D. \( 4 \)

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


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

Question:
Calculate
\(
\frac{1}{6} \div 3
\)

Options:
A. \( 2 \)
B. \( \frac{1}{18} \)
C. \( 18 \)
D. \( \frac{1}{2} \)

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


Prompt:
Misconception:
Believes division is commutative

Question:
Calculate
\(
\frac{1}{6} \div 3
\)

Options:
A. \( 2 \)
B. \( \frac{1}{18} \)
C. \( 18 \)
D. \( \frac{1}{2} \)

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


Prompt:
Misconception:
When dividing a fraction by an integer, divides the denominator by the integer

Question:
Calculate
\(
\frac{1}{6} \div 3
\)

Options:
A. \( 2 \)
B. \( \frac{1}{18} \)
C. \( 18 \)
D. \( \frac{1}{2} \)

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


Prompt:
Misconception:
Thinks you need to just add a % sign to a decimal to convert to a percentage

Question:
Write \( 0.15 \) as a percentage.

Options:
A. \( 0.15 \% \)
B. \( \frac{15}{100} \)
C. \( 1.5 \% \)
D. \( 15 \% \)

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


Prompt:
Misconception:
Multiplies by 10 instead of 100 when converting decimal to percentage

Question:
Write \( 0.15 \) as a percentage.

Options:
A. \( 0.15 \% \)
B. \( \frac{15}{100} \)
C. \( 1.5 \% \)
D. \( 15 \% \)

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


Prompt:
Misconception:
When representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning.

Question:
Which inequality is represented by the diagram? ![A number line with a filled in circle above 1with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]()

Options:
A. \( x>1 \)
B. \( x \geq 1 \)
C. \( x<1 \)
D. \( x \leq 1 \)

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


Prompt:
Misconception:
Mixes up greater than and less than symbols

Question:
Which inequality is represented by the diagram? ![A number line with a filled in circle above 1with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]()

Options:
A. \( x>1 \)
B. \( x \geq 1 \)
C. \( x<1 \)
D. \( x \leq 1 \)

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


Prompt:
Misconception:
When solving an equation forgets to eliminate the coefficient in front of the variable in the last step

Question:
Chris orders \( 2 \) cups of tea and a cake, and his bill comes to £1.40

Amy orders \( 4 \) cups of tea and a cake, and her bill comes to £2.20.

How much does one cup of tea cost?

Options:
A. \( 80 p \)
B. \( 60 p \)
C. \( 40 p \)
D. \( 55 p \)

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


Prompt:
Misconception:
When asked to solve simultaneous equations, believes they can just find values that work in one equation

Question:
Chris orders \( 2 \) cups of tea and a cake, and his bill comes to £1.40

Amy orders \( 4 \) cups of tea and a cake, and her bill comes to £2.20.

How much does one cup of tea cost?

Options:
A. \( 80 p \)
B. \( 60 p \)
C. \( 40 p \)
D. \( 55 p \)

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


Prompt:
Misconception:
Does not know the term 'diameter'

Question:
The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]()

Options:
A. Diagram
B. Diameter
C. Diagonal
D. Diamond

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


Prompt:
Misconception:
Does not know the term 'diameter'

Question:
The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]()

Options:
A. Diagram
B. Diameter
C. Diagonal
D. Diamond

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


Prompt:
Misconception:
Does not know the term 'diameter'

Question:
The straight line across this circle is called a ....? ![A circle with a line across from edge to edge, passing through the centre]()

Options:
A. Diagram
B. Diameter
C. Diagonal
D. Diamond

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


Prompt:
Misconception:
Finds the unit fraction when asked to find a non-unit fraction of an amount

Question:
\( \frac{3}{5} \) of \( 30= \)

Options:
A. \( 6 \)
B. \( 50 \)
C. \( 12 \)
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:
Divides by the numerator and multiplies by the denominator when finding a fraction of an amount

Question:
\( \frac{3}{5} \) of \( 30= \)

Options:
A. \( 6 \)
B. \( 50 \)
C. \( 12 \)
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 total in a grouped table is found by counting rows

Question:
Bob recorded the number of cars he sold in one week.
How many cars did he sell altogether? \begin{tabular}{|c|c|}
\hline Colour & Frequency \\
\hline Blue & \( 3 \) \\
\hline Black & \( 2 \) \\
\hline Silver & \( 4 \) \\
\hline Red & \( 1 \) \\
\hline Other & \( 3 \) \\
\hline
\end{tabular}

Options:
A. \( 5 \)
B. \( 12 \)
C. \( 10 \)
D. \( 13 \)

Solve the problem as a student with the misconception above.
You 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 do not include an "other" category when finding a total frequency

Question:
Bob recorded the number of cars he sold in one week.
How many cars did he sell altogether? \begin{tabular}{|c|c|}
\hline Colour & Frequency \\
\hline Blue & \( 3 \) \\
\hline Black & \( 2 \) \\
\hline Silver & \( 4 \) \\
\hline Red & \( 1 \) \\
\hline Other & \( 3 \) \\
\hline
\end{tabular}

Options:
A. \( 5 \)
B. \( 12 \)
C. \( 10 \)
D. \( 13 \)

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


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

Question:
\( 0.4^{2}= \)

Options:
A. \( 0.08 \)
B. \( 0.8 \)
C. \( 1.6 \)
D. \( 0.16 \)

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


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

Question:
\( 0.4^{2}= \)

Options:
A. \( 0.08 \)
B. \( 0.8 \)
C. \( 1.6 \)
D. \( 0.16 \)

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


Prompt:
Misconception:
Misreads scale

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

Approximately how many Teas were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.
The Teas bar lower section is 1 tick below 50 on the vertical scale, and the whole bar's height is 2 ticks above 100 on the vertical scale.
]()

Options:
A. \( 62 \)
B. \( 80 \)
C. \( 120 \)
D. \( 40 \)

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


Prompt:
Misconception:
When reading a composite bar chart, just reads total height of bar

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

Approximately how many Teas were sold on Tuesday? ![Composite bar chart with four bars, labelled Tea, Coffee, Hot Choc and Cans. Each bar has two sections, the lower one shows how many sold on Monday and the upper one showing Tuesdays sales. The vertical scale has 5 ticks between 0 and 50, 50 and 100 etc.
The Teas bar lower section is 1 tick below 50 on the vertical scale, and the whole bar's height is 2 ticks above 100 on the vertical scale.
]()

Options:
A. \( 62 \)
B. \( 80 \)
C. \( 120 \)
D. \( 40 \)

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


Prompt:
Misconception:
Mixes up square rooting and fourth rooting

Question:
Which of the following is the square root of \( 81 \) ?

Options:
A. \( 3 \)
B. \( 9 \)
C. \( 162 \)
D. \( 6561 \)

Solve the problem as a student with the misconception above.
You 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 square rooting and multiplying by 2 or doubling

Question:
Which of the following is the square root of \( 81 \) ?

Options:
A. \( 3 \)
B. \( 9 \)
C. \( 162 \)
D. \( 6561 \)

Solve the problem as a student with the misconception above.
You 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:
Which of the following is the square root of \( 81 \) ?

Options:
A. \( 3 \)
B. \( 9 \)
C. \( 162 \)
D. \( 6561 \)

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


Prompt:
Misconception:
Believes that dividing by 100 gives 10%

Question:
Tom and Katie are arguing about working out percentages of amounts.

Tom says to find \( 40 \% \) you divide by \( 100 \) and multiply by \( 4 \).
Katie says to find \( 40 \% \) you divide by \( 5 \) and multiply by \( 2 \).
Who is correct?

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

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


Prompt:
Misconception:
Believes that dividing by 100 gives 10%

Question:
Tom and Katie are arguing about working out percentages of amounts.

Tom says to find \( 40 \% \) you divide by \( 100 \) and multiply by \( 4 \).
Katie says to find \( 40 \% \) you divide by \( 5 \) and multiply by \( 2 \).
Who is correct?

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

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


Prompt:
Misconception:
Unable to equate a division and multiplication to a single division

Question:
Tom and Katie are arguing about working out percentages of amounts.

Tom says to find \( 40 \% \) you divide by \( 100 \) and multiply by \( 4 \).
Katie says to find \( 40 \% \) you divide by \( 5 \) and multiply by \( 2 \).
Who is correct?

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

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


Prompt:
Misconception:
Thinks a Fibonacci sequence must start with 1, 1

Question:
Tom and Katie are discussing Fibonacci sequences.

Tom says this is a Fibonacci sequence: \( 1,1,2,3,5,8, \ldots \)

Katie says this is a Fibonacci sequence: \( 1,2,3,5,8,13, \ldots \)

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}.