Prompt:
Misconception:
Uses slant heights instead of parallel sides to find area of a trapezium

Question:
When calculating the area of this trapezium, what are the values of \( a \) and \( b \) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \( =\left(\frac{a+b}{2}\right) h \)

Options:
A. \( 7+7.5 \)
B. \( 9+10 \)
C. \( 7+6 \)
D. \( 6+7.5 \)

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:
Uses slant heights instead of parallel sides to find area of a trapezium

Question:
When calculating the area of this trapezium, what are the values of \( a \) and \( b \) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \( =\left(\frac{a+b}{2}\right) h \)

Options:
A. \( 7+7.5 \)
B. \( 9+10 \)
C. \( 7+6 \)
D. \( 6+7.5 \)

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:
Simplifies integers when simplifying a mixed number

Question:
Write the following fraction in its simplest form: \( 6 \frac{3}{18} \)

Options:
A. \( 3 \frac{1}{2} \)
B. \( 6 \frac{1}{6} \)
C. \( 2 \frac{1}{6} \)
D. Cannot be simplified

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


Prompt:
Misconception:
Does not understand how to simplify fractions

Question:
Write the following fraction in its simplest form: \( 6 \frac{3}{18} \)

Options:
A. \( 3 \frac{1}{2} \)
B. \( 6 \frac{1}{6} \)
C. \( 2 \frac{1}{6} \)
D. Cannot be simplified

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


Prompt:
Misconception:
In algebra, thinks it's ok to write (for example) 0x rather than just 0

Question:
Simplify the following by collecting like terms.
\[
5 s-6 s+12 s-11 s
\]

Options:
A. \( 0 \)
B. \( 0 s \)
C. \( 1 s \)
D. \( S \)

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


Prompt:
Misconception:
Finds the median instead of the range

Question:
When finding the range of a data set, what is the first step?

Options:
A. Subtract the smallest number from the largest number.
B. Write the numbers in ascending order.
C. Add all the numbers together.
D. Write the numbers in ascending or descending order.

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

Question:
When finding the range of a data set, what is the first step?

Options:
A. Subtract the smallest number from the largest number.
B. Write the numbers in ascending order.
C. Add all the numbers together.
D. Write the numbers in ascending or descending order.

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


Prompt:
Misconception:
Finds the median instead of the range

Question:
When finding the range of a data set, what is the first step?

Options:
A. Subtract the smallest number from the largest number.
B. Write the numbers in ascending order.
C. Add all the numbers together.
D. Write the numbers in ascending or descending order.

Solve the problem as a student with the misconception above.
You 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 solutions of a quadratic equation are the absolute values of the constants in the factorised form

Question:
This is the final stage of Lucy's solution to a quadratic equation.
What should replace the star?
\[
(h+4)(h-3)=0
\] \( h=\bigstar \) or \( h=3 \)

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

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


Prompt:
Misconception:
Believes all quadratic equations have a solution of 0

Question:
This is the final stage of Lucy's solution to a quadratic equation.
What should replace the star?
\[
(h+4)(h-3)=0
\] \( h=\bigstar \) or \( h=3 \)

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

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


Prompt:
Misconception:
Believes the solutions of a quadratic equation are the constants in the factorised form

Question:
The area of the trapezium on the right is \( 40 \mathrm{~cm}^{2} \). ![A trapezium with the parallel sides a and b labelled with x+2 and x+4 and the perpendicular height x.]() Based on the information given, Adam writes this formula:
\(x^{2}+3 x=40\)

What are the two solutions to this equation?

Options:
A. \( \begin{array}{c}x=-8 \\ \text { and } \\ x=-5\end{array} \)
B. \( \begin{array}{c}x=-8 \\ \text { and } \\ x=5\end{array} \)
C. \( \begin{array}{c}x=8 \\ \text { and } \\ x=-5\end{array} \)
D. \( \begin{array}{c}x=8 \\ \text { and } \\ x=5\end{array} \)

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:
Has multiplied the value of the first term by the the term being asked

Question:
Without drawing any more terms, how many circles do you predict will be in the \( 7 \) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()

Options:
A. \( 42 \)
B. \( 26 \)
C. \( 34 \)
D. \( 30 \)

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


Prompt:
Misconception:
When asked for a specific term in a sequence gives the term before

Question:
Without drawing any more terms, how many circles do you predict will be in the \( 7 \) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()

Options:
A. \( 42 \)
B. \( 26 \)
C. \( 34 \)
D. \( 30 \)

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


Prompt:
Misconception:
When asked for a specific term in a sequence gives the term after

Question:
Without drawing any more terms, how many circles do you predict will be in the \( 7 \) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()

Options:
A. \( 42 \)
B. \( 26 \)
C. \( 34 \)
D. \( 30 \)

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


Prompt:
Misconception:
Believes you don't need to numerically order the data before calculating the median

Question:
What is the median of the following numbers?
\[
3,5,6,18,18,-4
\]

Options:
A. \( 5.5 \)
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 from a even dataset does not understand we must find the midpoint of the two values in the middle

Question:
What is the median of the following numbers?
\[
3,5,6,18,18,-4
\]

Options:
A. \( 5.5 \)
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?
\[
3,5,6,18,18,-4
\]

Options:
A. \( 5.5 \)
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:
Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term

Question:
When factorising \( x^{2}+5 x+6 \) we need two numbers that:

Options:
A. Add to give \( 6 \) and multiply to give \( 5 \)
B. Add to give \( 6 x \) and multiply to give \( 5 \)
C. Add to give \( 5 \) and multiply to give \( 6 \)
D. Add to give \( 5 x \) and multiply to give \( 6 \)

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


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

Question:
When factorising \( x^{2}+5 x+6 \) we need two numbers that:

Options:
A. Add to give \( 6 \) and multiply to give \( 5 \)
B. Add to give \( 6 x \) and multiply to give \( 5 \)
C. Add to give \( 5 \) and multiply to give \( 6 \)
D. Add to give \( 5 x \) and multiply to give \( 6 \)

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


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

Question:
When factorising \( x^{2}+5 x+6 \) we need two numbers that:

Options:
A. Add to give \( 6 \) and multiply to give \( 5 \)
B. Add to give \( 6 x \) and multiply to give \( 5 \)
C. Add to give \( 5 \) and multiply to give \( 6 \)
D. Add to give \( 5 x \) and multiply to give \( 6 \)

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


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

Question:
What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]()

Options:
A. \( 88 \mathrm{~cm}^{2} \)
B. \( 71.5 \mathrm{~cm}^{2} \)
C. \( 1144 \mathrm{~cm}^{2} \)
D. \( 44 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Has used slant height and base to find area of a triangle rather than perpendicular height and base

Question:
What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]()

Options:
A. \( 88 \mathrm{~cm}^{2} \)
B. \( 71.5 \mathrm{~cm}^{2} \)
C. \( 1144 \mathrm{~cm}^{2} \)
D. \( 44 \mathrm{~cm}^{2} \)

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


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

Question:
What is the area of this triangle? ![A right angled triangle with base length 11cm, slant height, 13 cm and perpendicular height 8cm.]()

Options:
A. \( 88 \mathrm{~cm}^{2} \)
B. \( 71.5 \mathrm{~cm}^{2} \)
C. \( 1144 \mathrm{~cm}^{2} \)
D. \( 44 \mathrm{~cm}^{2} \)

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


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

Question:
If you triple \( 8 \) you get...

Options:
A. \( 38 \)
B. \( 11 \)
C. \( 888 \)
D. \( 24 \)

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


Prompt:
Misconception:
Adds instead of multiples

Question:
If you triple \( 8 \) you get...

Options:
A. \( 38 \)
B. \( 11 \)
C. \( 888 \)
D. \( 24 \)

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


Prompt:
Misconception:
When asked to triple, writes the digit out three times

Question:
If you triple \( 8 \) you get...

Options:
A. \( 38 \)
B. \( 11 \)
C. \( 888 \)
D. \( 24 \)

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


Prompt:
Misconception:
Answers order of operations questions with brackets as if the brackets are not there

Question:
STEP \( 2 \)
Which of the options is a correct second step to express the following as a single fraction?

\(
\begin{aligned}
& \frac{x-1}{6} \div \frac{x^{2}-1}{9} \\
= & \frac{x-1}{6} \times \frac{9}{x^{2}-1}
\end{aligned}
\)

Options:
A. \( \frac{9 x-1}{6 x^{2}-1} \)
B. \( \frac{-1}{6} \times \frac{9}{x-1} \)
C. \( \frac{x-1}{6} \times \frac{9}{(x-1)(x-1)} \)
D. \( \frac{x-1}{6} \times \frac{9}{(x+1)(x-1)} \)

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


Prompt:
Misconception:
Incorrectly cancels what they believe is a factor in algebraic fractions

Question:
STEP \( 2 \)
Which of the options is a correct second step to express the following as a single fraction?

\(
\begin{aligned}
& \frac{x-1}{6} \div \frac{x^{2}-1}{9} \\
= & \frac{x-1}{6} \times \frac{9}{x^{2}-1}
\end{aligned}
\)

Options:
A. \( \frac{9 x-1}{6 x^{2}-1} \)
B. \( \frac{-1}{6} \times \frac{9}{x-1} \)
C. \( \frac{x-1}{6} \times \frac{9}{(x-1)(x-1)} \)
D. \( \frac{x-1}{6} \times \frac{9}{(x+1)(x-1)} \)

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


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

Question:
STEP \( 2 \)
Which of the options is a correct second step to express the following as a single fraction?

\(
\begin{aligned}
& \frac{x-1}{6} \div \frac{x^{2}-1}{9} \\
= & \frac{x-1}{6} \times \frac{9}{x^{2}-1}
\end{aligned}
\)

Options:
A. \( \frac{9 x-1}{6 x^{2}-1} \)
B. \( \frac{-1}{6} \times \frac{9}{x-1} \)
C. \( \frac{x-1}{6} \times \frac{9}{(x-1)(x-1)} \)
D. \( \frac{x-1}{6} \times \frac{9}{(x+1)(x-1)} \)

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


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 1

Question:
What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. "-10" next to the bottom dash and "2" next to the top dash are the only numbers marked on the line. An arrow, labelled "B" is pointing at the middle dash. ]()

Options:
A. \( -7 \)
B. \( -1 \)
C. \( -4 \)
D. \( 8 \)

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


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 1

Question:
What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. "-10" next to the bottom dash and "2" next to the top dash are the only numbers marked on the line. An arrow, labelled "B" is pointing at the middle dash. ]()

Options:
A. \( -7 \)
B. \( -1 \)
C. \( -4 \)
D. \( 8 \)

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


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

Question:
What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. "-10" next to the bottom dash and "2" next to the top dash are the only numbers marked on the line. An arrow, labelled "B" is pointing at the middle dash. ]()

Options:
A. \( -7 \)
B. \( -1 \)
C. \( -4 \)
D. \( 8 \)

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


Prompt:
Misconception:
Does not know you can find the mean from a pictogram

Question:
The pictogram shows how many people came to watch a netball match.
What is the mean number of people at each game? ![A pictogram with a key showing a smiley face represents 12 people. Game 1 has 4 smiley faces, Game 2 has 2 smiley faces, Game 3 has 3 smiley faces and Game 4 has 1 smiley face.]()

Options:
A. \( 30 \)
B. \( 12 \)
C. \( 2.5 \)
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:
When interpreting a pictogram, thinks each symbol stands for 1

Question:
The pictogram shows how many people came to watch a netball match.
What is the mean number of people at each game? ![A pictogram with a key showing a smiley face represents 12 people. Game 1 has 4 smiley faces, Game 2 has 2 smiley faces, Game 3 has 3 smiley faces and Game 4 has 1 smiley face.]()

Options:
A. \( 30 \)
B. \( 12 \)
C. \( 2.5 \)
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:
When calculating the mean from a list of data, adds up the numbers but does not divide

Question:
The pictogram shows how many people came to watch a netball match.
What is the mean number of people at each game? ![A pictogram with a key showing a smiley face represents 12 people. Game 1 has 4 smiley faces, Game 2 has 2 smiley faces, Game 3 has 3 smiley faces and Game 4 has 1 smiley face.]()

Options:
A. \( 30 \)
B. \( 12 \)
C. \( 2.5 \)
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 add on the constant in a worded substitution problem

Question:
Sally the electrician charges a call-out fee of \( £ 40 \) and then \( £ 15 \) per hour that the job takes.

If a job takes \( n \) hours, which formula would help work out the cost \( (C) \) of hiring Sally?

Options:
A. \( C=15 n \)
B. \( C=55 n \)
C. \( C=40+15 n \)
D. \( C=40 n+15 \)

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:
Combines variables with constants when writing a formula from a given situation

Question:
Sally the electrician charges a call-out fee of \( £ 40 \) and then \( £ 15 \) per hour that the job takes.

If a job takes \( n \) hours, which formula would help work out the cost \( (C) \) of hiring Sally?

Options:
A. \( C=15 n \)
B. \( C=55 n \)
C. \( C=40+15 n \)
D. \( C=40 n+15 \)

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:
Gets their constants and coefficients the wrong way around when writing a formula from a given situation

Question:
Sally the electrician charges a call-out fee of \( £ 40 \) and then \( £ 15 \) per hour that the job takes.

If a job takes \( n \) hours, which formula would help work out the cost \( (C) \) of hiring Sally?

Options:
A. \( C=15 n \)
B. \( C=55 n \)
C. \( C=40+15 n \)
D. \( C=40 n+15 \)

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

Question:
If the \( 3^{\text {rd }} \) term of a sequence is \( 8 \)
and the term-to-term rule is \( -2 \),
what is the \( 7^{\text {th }} \) term in this sequence?

Options:
A. \( 0 \)
B. \( -2 \)
C. \( -4 \)
D. \( 6 \)

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


Prompt:
Misconception:
When asked for a specific term in a sequence just gives the next term

Question:
If the \( 3^{\text {rd }} \) term of a sequence is \( 8 \)
and the term-to-term rule is \( -2 \),
what is the \( 7^{\text {th }} \) term in this sequence?

Options:
A. \( 0 \)
B. \( -2 \)
C. \( -4 \)
D. \( 6 \)

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


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

Question:
What is a correct way to set up this problem to solve it using long multiplication?
\[
426 \times 82
\]

Options:
A. ![426 multiplied by 82 set out to perform long multiplication. 426 is written in 3 columns with 400 in the first column, 20 in the second column and 6 in the third column. 82 is written underneath this, with 80 under 400 and 2 under 20.]()
B. ![426 multiplied by 82 set out to perform long multiplication. 82 is written under 426. The 8 of 82 is under the 4 of 426 and the 2 of 82 is under the 2 of 426.]()
C. ![426 multiplied by 82 set out to perform long multiplication. 82 is written under 426. The 8 of 82 is under the 2 of 426 and the 2 of 82 is under the 6 of 426]()
D. ![426 multiplied by 82 set out to perform long multiplication. 426 is written in 3 columns with 400 in the first column, 20 in the second column and 6 in the third column. 82 is written underneath this, with 80 under 20 and 2 under 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:
Has partitioned the digits when doing long multiplication

Question:
What is a correct way to set up this problem to solve it using long multiplication?
\[
426 \times 82
\]

Options:
A. ![426 multiplied by 82 set out to perform long multiplication. 426 is written in 3 columns with 400 in the first column, 20 in the second column and 6 in the third column. 82 is written underneath this, with 80 under 400 and 2 under 20.]()
B. ![426 multiplied by 82 set out to perform long multiplication. 82 is written under 426. The 8 of 82 is under the 4 of 426 and the 2 of 82 is under the 2 of 426.]()
C. ![426 multiplied by 82 set out to perform long multiplication. 82 is written under 426. The 8 of 82 is under the 2 of 426 and the 2 of 82 is under the 6 of 426]()
D. ![426 multiplied by 82 set out to perform long multiplication. 426 is written in 3 columns with 400 in the first column, 20 in the second column and 6 in the third column. 82 is written underneath this, with 80 under 20 and 2 under 6.]()

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


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

Question:
What is the first term of the sequence with the nth-term rule:
\[
5 n-7
\]

Options:
A. \( -2 \)
B. \( 5 \)
C. \( -7 \)
D. \( 1 \)

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


Prompt:
Misconception:
Thinks the first term in a sequence is the term before the sequence begins (0th term)

Question:
What is the first term of the sequence with the nth-term rule:
\[
5 n-7
\]

Options:
A. \( -2 \)
B. \( 5 \)
C. \( -7 \)
D. \( 1 \)

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


Prompt:
Misconception:
Thinks the first term of a sequence must be 1

Question:
What is the first term of the sequence with the nth-term rule:
\[
5 n-7
\]

Options:
A. \( -2 \)
B. \( 5 \)
C. \( -7 \)
D. \( 1 \)

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


Prompt:
Misconception:
Attempts to simplify ratio by subtracting from both sides

Question:
Kate and Isaac share some sweets in the ratio \( 3: 2 \)
What is this ratio in the form \( 1: n \) ?

Options:
A. \( 1: 1.5 \)
B. \( 1: \frac{2}{3} \)
C. \( 1: 0 \)
D. \( 1: 6 \)

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


Prompt:
Misconception:
When simplifying a ratio, divides one side of the ratio but multiplies the other side.

Question:
Kate and Isaac share some sweets in the ratio \( 3: 2 \)
What is this ratio in the form \( 1: n \) ?

Options:
A. \( 1: 1.5 \)
B. \( 1: \frac{2}{3} \)
C. \( 1: 0 \)
D. \( 1: 6 \)

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


Prompt:
Misconception:
Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c

Question:
Which of the following lines is not parallel to
\(y=3 x+5 \text { ? }\)

Options:
A. \( 2 y=6 x-5 \)
B. \( y=3 x-2 \)
C. \( y=4-3 x \)
D. \( y=3(1+x) \)

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


Prompt:
Misconception:
Believes lines are parallel if they have the same y intercept

Question:
Which of the following lines is not parallel to
\(y=3 x+5 \text { ? }\)

Options:
A. \( 2 y=6 x-5 \)
B. \( y=3 x-2 \)
C. \( y=4-3 x \)
D. \( y=3(1+x) \)

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


Prompt:
Misconception:
Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c

Question:
Which of the following lines is not parallel to
\(y=3 x+5 \text { ? }\)

Options:
A. \( 2 y=6 x-5 \)
B. \( y=3 x-2 \)
C. \( y=4-3 x \)
D. \( y=3(1+x) \)

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


Prompt:
Misconception:
Believes a kite has bisecting diagonals

Question:
Tom and Katie are arguing about the diagonals of quadrilaterals.
Tom says a kite has bisecting diagonals.
Katie says a rhombus has bisecting diagonals.
Who is correct? ![A pair of intersecting lines]()

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

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


Prompt:
Misconception:
Believes a kite has bisecting diagonals

Question:
Tom and Katie are arguing about the diagonals of quadrilaterals.
Tom says a kite has bisecting diagonals.
Katie says a rhombus has bisecting diagonals.
Who is correct? ![A pair of intersecting lines]()

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

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


Prompt:
Misconception:
Does not know the meaning of bisect

Question:
Tom and Katie are arguing about the diagonals of quadrilaterals.
Tom says a kite has bisecting diagonals.
Katie says a rhombus has bisecting diagonals.
Who is correct? ![A pair of intersecting lines]()

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 the square of a negative will also be negative

Question:
This is part of a table of values for
\(y=x^{2}-2 x+1\)

What should replace the star? \begin{tabular}{|c|c|}
\hline\( x \) & \( -3 \) \\
\hline\( y \) & \(\bigstar\) \\
\hline
\end{tabular}

Options:
A. \( 14 \)
B. \( 16 \)
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:
Believes inequalities can only include integers

Question:
How should you write the solution to the following inequality?
\(2 x>7\)

Options:
A. \( x>4 \)
B. \( x=3.5 \)
C. \( x<3.5 \)
D. \( x>3.5 \)

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


Prompt:
Misconception:
Believes solving an inequality gives a single value as a solution

Question:
How should you write the solution to the following inequality?
\(2 x>7\)

Options:
A. \( x>4 \)
B. \( x=3.5 \)
C. \( x<3.5 \)
D. \( x>3.5 \)

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


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

Question:
\( \frac{1}{6} \) of \( 24= \)

Options:
A. \( 18 \)
B. \( 4 \)
C. \( 144 \)
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:
Multiplies by the denominator instead of dividing when finding a fraction of an amount

Question:
\( \frac{1}{6} \) of \( 24= \)

Options:
A. \( 18 \)
B. \( 4 \)
C. \( 144 \)
D. \( 3 \)

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


Prompt:
Misconception:
Does not understand the place value of answers from a Napier's bones calculation

Question:
Dave is trying to solve this problem using Napier's bones
What number does the circled digit represent? \( 356 \times 93 \) ![A Napier's bones grid, with 356 along the top and 93 down the side. From left to right on the top row, with / representing a diagonal line through through the box, the boxes read 2/7, 4/5, 5/4.  From left to right on the bottom row, the boxes read 0/9, 1/5, 1/8. The digit 5 is circled in the second box of the top row, which is in the column under the 5 of 356 and the row along from the 9 of 93.]()

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

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


Prompt:
Misconception:
Does not understand the place value of answers from a Napier's bones calculation

Question:
Dave is trying to solve this problem using Napier's bones
What number does the circled digit represent? \( 356 \times 93 \) ![A Napier's bones grid, with 356 along the top and 93 down the side. From left to right on the top row, with / representing a diagonal line through through the box, the boxes read 2/7, 4/5, 5/4.  From left to right on the bottom row, the boxes read 0/9, 1/5, 1/8. The digit 5 is circled in the second box of the top row, which is in the column under the 5 of 356 and the row along from the 9 of 93.]()

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

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


Prompt:
Misconception:
Does not understand the place value of answers from a Napier's bones calculation

Question:
Dave is trying to solve this problem using Napier's bones
What number does the circled digit represent? \( 356 \times 93 \) ![A Napier's bones grid, with 356 along the top and 93 down the side. From left to right on the top row, with / representing a diagonal line through through the box, the boxes read 2/7, 4/5, 5/4.  From left to right on the bottom row, the boxes read 0/9, 1/5, 1/8. The digit 5 is circled in the second box of the top row, which is in the column under the 5 of 356 and the row along from the 9 of 93.]()

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

Solve the problem as a student with the misconception above.
You 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:
Which image completes a symmetric figure using the red line of symmetry? ![A figure drawn in the upper half of a box with a red dotted line immediately below. ]()

Options:
A. ![The correct completion of the figure given in the question. ]()
B. ![An incorrect completion of the figure given in the question. ]()
C. ![An incorrect completion of the figure given in the question. ]()
D. ![An incorrect completion of the figure given in the question. ]()

Solve the problem as a student with the misconception above.
You 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:
Which image completes a symmetric figure using the red line of symmetry? ![A figure drawn in the upper half of a box with a red dotted line immediately below. ]()

Options:
A. ![The correct completion of the figure given in the question. ]()
B. ![An incorrect completion of the figure given in the question. ]()
C. ![An incorrect completion of the figure given in the question. ]()
D. ![An incorrect completion of the figure given in the question. ]()

Solve the problem as a student with the misconception above.
You 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:
Which image completes a symmetric figure using the red line of symmetry? ![A figure drawn in the upper half of a box with a red dotted line immediately below. ]()

Options:
A. ![The correct completion of the figure given in the question. ]()
B. ![An incorrect completion of the figure given in the question. ]()
C. ![An incorrect completion of the figure given in the question. ]()
D. ![An incorrect completion of the figure given in the question. ]()

Solve the problem as a student with the misconception above.
You 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 one point on a time series graph instead of all the values from a given time period

Question:
This graph shows the amount of potatoes consumed by a restaurant in a week.

How many more potatoes were consumed on Sunday compared to Saturday? ![Chart of potatoes consumed with kilos against day of week]()

Options:
A. \( 35 \mathrm{~kg} \)
B. \( 25 \mathrm{~kg} \)
C. \( 2 \mathrm{~kg} \)
D. \( 10 \mathrm{~kg} \)

Solve the problem as a student with the misconception above.
You 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 one point on a time series graph instead of all the values from a given time period

Question:
This graph shows the amount of potatoes consumed by a restaurant in a week.

How many more potatoes were consumed on Sunday compared to Saturday? ![Chart of potatoes consumed with kilos against day of week]()

Options:
A. \( 35 \mathrm{~kg} \)
B. \( 25 \mathrm{~kg} \)
C. \( 2 \mathrm{~kg} \)
D. \( 10 \mathrm{~kg} \)

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


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

Question:
Factorise this expression, if possible:
\(
p^{2}-16
\)

Options:
A. \( (p-4)(p-4) \)
B. \( (p+4)(p-4) \)
C. \( p(p-16) \)
D. Does not factorise

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


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

Question:
Factorise this expression, if possible:
\(
p^{2}-16
\)

Options:
A. \( (p-4)(p-4) \)
B. \( (p+4)(p-4) \)
C. \( p(p-16) \)
D. Does not factorise

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Factorise this expression, if possible:
\(
p^{2}-16
\)

Options:
A. \( (p-4)(p-4) \)
B. \( (p+4)(p-4) \)
C. \( p(p-16) \)
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:
Doesn't know the area of a triangle formula

Question:
Which of the following triangles have the same area as this rectangle? ![Rectangle with base 7 and height 3]()

Options:
A. ![Triangle with base 6 and perpendicular height 7]()
B. ![Right-angled triangle with height 6, base 5 and hypotenuse length the square root of 61]()
C. ![Triangle with base 6, perpendicular height 8 and slant length 13]()
D. They are all equal to the rectangle

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


Prompt:
Misconception:
Doesn't know the area of a triangle formula

Question:
Which of the following triangles have the same area as this rectangle? ![Rectangle with base 7 and height 3]()

Options:
A. ![Triangle with base 6 and perpendicular height 7]()
B. ![Right-angled triangle with height 6, base 5 and hypotenuse length the square root of 61]()
C. ![Triangle with base 6, perpendicular height 8 and slant length 13]()
D. They are all equal to the rectangle

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


Prompt:
Misconception:
Doesn't know the area of a triangle formula

Question:
Which of the following triangles have the same area as this rectangle? ![Rectangle with base 7 and height 3]()

Options:
A. ![Triangle with base 6 and perpendicular height 7]()
B. ![Right-angled triangle with height 6, base 5 and hypotenuse length the square root of 61]()
C. ![Triangle with base 6, perpendicular height 8 and slant length 13]()
D. They are all equal to the rectangle

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


Prompt:
Misconception:
Miscounts when subtracting over zero

Question:
What is the next term in this sequence?

\[
23, \quad 13, \quad 3, \quad \ldots
\]

Options:
A. \( -3 \)
B. \( -10 \)
C. \( -7 \)
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:
Identifies the term-to-term rule rather than the next term

Question:
What is the next term in this sequence?

\[
23, \quad 13, \quad 3, \quad \ldots
\]

Options:
A. \( -3 \)
B. \( -10 \)
C. \( -7 \)
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 how to find the next term in a sequence

Question:
What is the next term in this sequence?

\[
23, \quad 13, \quad 3, \quad \ldots
\]

Options:
A. \( -3 \)
B. \( -10 \)
C. \( -7 \)
D. Not enough information

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


Prompt:
Misconception:
Believes the mean is total frequency divided by sum of categories given

Question:
The table below is a summary of the number of spots counted on \( 25 \) ladybirds. Calculate the mean number of spots per ladybird. ![\begin{tabular}{|c|c|}
Number of spots\\ & Frequency
\hline \( 5 \) & \( 4 \) \\
\hline \( 6 \) & \( 9 \) \\
\hline \( 7 \) & \( 9 \) \\
\hline \( 8 \) & \( 3 \) \\
\hline
\end{tabular}]()

Options:
A. \( 0.96(2 d p) \)
B. \( 40.25 \)
C. \( 0.16 \) (2dp)
D. \( 6.44 \)

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


Prompt:
Misconception:
Believes mean is total divided by number of groups

Question:
The table below is a summary of the number of spots counted on \( 25 \) ladybirds. Calculate the mean number of spots per ladybird. ![\begin{tabular}{|c|c|}
Number of spots\\ & Frequency
\hline \( 5 \) & \( 4 \) \\
\hline \( 6 \) & \( 9 \) \\
\hline \( 7 \) & \( 9 \) \\
\hline \( 8 \) & \( 3 \) \\
\hline
\end{tabular}]()

Options:
A. \( 0.96(2 d p) \)
B. \( 40.25 \)
C. \( 0.16 \) (2dp)
D. \( 6.44 \)

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


Prompt:
Misconception:
Believes the mean is total frequency divided by something

Question:
The table below is a summary of the number of spots counted on \( 25 \) ladybirds. Calculate the mean number of spots per ladybird. ![\begin{tabular}{|c|c|}
Number of spots\\ & Frequency
\hline \( 5 \) & \( 4 \) \\
\hline \( 6 \) & \( 9 \) \\
\hline \( 7 \) & \( 9 \) \\
\hline \( 8 \) & \( 3 \) \\
\hline
\end{tabular}]()

Options:
A. \( 0.96(2 d p) \)
B. \( 40.25 \)
C. \( 0.16 \) (2dp)
D. \( 6.44 \)

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


Prompt:
Misconception:
Believes that they only need to write non-zero digits when giving a number in digits

Question:
How do you write this number in digits?
Fifty-six thousand and thirteen

Options:
A. \( 5613 \)
B. \( 56030 \)
C. \( 56013 \)
D. \( 560013 \)

Solve the problem as a student with the misconception above.
You 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 written 'teen' numbers with their corresponding multiples of 10

Question:
How do you write this number in digits?
Fifty-six thousand and thirteen

Options:
A. \( 5613 \)
B. \( 56030 \)
C. \( 56013 \)
D. \( 560013 \)

Solve the problem as a student with the misconception above.
You 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 ten thousands and thousands place value columns

Question:
How do you write this number in digits?
Fifty-six thousand and thirteen

Options:
A. \( 5613 \)
B. \( 56030 \)
C. \( 56013 \)
D. \( 560013 \)

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


Prompt:
Misconception:
Thinks the remainder is the difference between the dividend and the next biggest multiple

Question:
Sarah has some apples.
She shares them into \( 6 \) equal groups and there is one left over.
How many apples could she have?

Options:
A. \( 66 \)
B. \( 30 \)
C. \( 35 \)
D. \( 43 \)

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


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![A grid with a left-leaning parallelogram drawn in the upper half and a blue line across the middle, marked 'line of reflection'. ]() ![Tom does this: an image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn immediately below. ]() ![Katie does this: An image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn one line down from the blue line. ]()

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:
Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![A grid with a left-leaning parallelogram drawn in the upper half and a blue line across the middle, marked 'line of reflection'. ]() ![Tom does this: an image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn immediately below. ]() ![Katie does this: An image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn one line down from the blue line. ]()

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:
Tom and Katie are arguing about how to reflect the object in the line of reflection. Who reflects it correctly? ![A grid with a left-leaning parallelogram drawn in the upper half and a blue line across the middle, marked 'line of reflection'. ]() ![Tom does this: an image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn immediately below. ]() ![Katie does this: An image of a grid with a left-leaning parallelogram drawn in the upper half, a blue line across the middle and a left-leaning parallelogram drawn one line down from the blue line. ]()

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

Question:
What is the \( 15 \) th term of this sequence? \( u_{n}=1-3 n \)

Options:
A. \( -44 \)
B. \( -46 \)
C. \( -14 \)
D. \( -30 \)

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


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

Question:
What is the \( 15 \) th term of this sequence? \( u_{n}=1-3 n \)

Options:
A. \( -44 \)
B. \( -46 \)
C. \( -14 \)
D. \( -30 \)

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


Prompt:
Misconception:
Thinks ratios are written as 1:total

Question:
![A straight line on squared paper. Points P, Q and R lie on this line. The leftmost end of the line is labelled P. If you travel right 4 squares and up 1 square you get to point Q. If you then travel 8 squares right and 2 squares up from Q you reach point R.]() What is the ratio of \( P Q: P R \) ?

Options:
A. \( 1: 12 \)
B. \( 1: 4 \)
C. \( 1: 2 \)
D. \( 1: 3 \)

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:
May have estimated when using ratios with geometry

Question:
![A straight line on squared paper. Points P, Q and R lie on this line. The leftmost end of the line is labelled P. If you travel right 4 squares and up 1 square you get to point Q. If you then travel 8 squares right and 2 squares up from Q you reach point R.]() What is the ratio of \( P Q: P R \) ?

Options:
A. \( 1: 12 \)
B. \( 1: 4 \)
C. \( 1: 2 \)
D. \( 1: 3 \)

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:
May have estimated when using ratios with geometry

Question:
![A straight line on squared paper. Points P, Q and R lie on this line. The leftmost end of the line is labelled P. If you travel right 4 squares and up 1 square you get to point Q. If you then travel 8 squares right and 2 squares up from Q you reach point R.]() What is the ratio of \( P Q: P R \) ?

Options:
A. \( 1: 12 \)
B. \( 1: 4 \)
C. \( 1: 2 \)
D. \( 1: 3 \)

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


Prompt:
Misconception:
Does not know how to compare decimal numbers

Question:
Which number is closest to zero?

Options:
A. \( -2.1 \)
B. \( -2.01 \)
C. \( -2.105 \)
D. \( -3 \)

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


Prompt:
Misconception:
Does not know how to compare decimal numbers

Question:
Which number is closest to zero?

Options:
A. \( -2.1 \)
B. \( -2.01 \)
C. \( -2.105 \)
D. \( -3 \)

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


Prompt:
Misconception:
When rounding up from a 9, does not add one on to the digit to the left

Question:
\[
\text { 2426. } 951
\]
What is this number rounded to \( 1 \) decimal place?

Options:
A. \( 2426.0 \)
B. \( 2427.0 \)
C. \( 2426.9 \)
D. \( 2000 \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
\[
\text { 2426. } 951
\]
What is this number rounded to \( 1 \) decimal place?

Options:
A. \( 2426.0 \)
B. \( 2427.0 \)
C. \( 2426.9 \)
D. \( 2000 \)

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


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

Question:
\[
\text { 2426. } 951
\]
What is this number rounded to \( 1 \) decimal place?

Options:
A. \( 2426.0 \)
B. \( 2427.0 \)
C. \( 2426.9 \)
D. \( 2000 \)

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


Prompt:
Misconception:
Multiplies by the index

Question:
\( (27)^{\frac{4}{3}}=? \)

Options:
A. \( 36 \)
B. \( 20.25 \)
C. \( 12 \)
D. \( 81 \)

Solve the problem as a student with the misconception above.
You 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 the fractional index denotes the root and power the other way around

Question:
\( (27)^{\frac{4}{3}}=? \)

Options:
A. \( 36 \)
B. \( 20.25 \)
C. \( 12 \)
D. \( 81 \)

Solve the problem as a student with the misconception above.
You 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:
\( (27)^{\frac{4}{3}}=? \)

Options:
A. \( 36 \)
B. \( 20.25 \)
C. \( 12 \)
D. \( 81 \)

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


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

Question:
What is the mean of the following numbers?

\[
1,4,7,9,9
\]

Options:
A. \( 7 \)
B. \( 9 \)
C. \( 30 \)
D. \( 6 \)

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


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

Question:
What is the mean of the following numbers?

\[
1,4,7,9,9
\]

Options:
A. \( 7 \)
B. \( 9 \)
C. \( 30 \)
D. \( 6 \)

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


Prompt:
Misconception:
When calculating the mean from a list of data, adds up the numbers but does not divide

Question:
What is the mean of the following numbers?

\[
1,4,7,9,9
\]

Options:
A. \( 7 \)
B. \( 9 \)
C. \( 30 \)
D. \( 6 \)

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


Prompt:
Misconception:
Adds or subtracts from numerator first when solving an equation with a fraction

Question:
Solve the equation:
\(
\frac{t-3}{2}=\frac{1}{8}
\)

Options:
A. \( t=6 \frac{1}{4} \)
B. \( t=1 \)
C. \( t=3 \frac{1}{16} \)
D. \( t=3 \frac{1}{4} \)

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


Prompt:
Misconception:
When adding an integer to a fraction, thinks you add the integer to the numerator

Question:
Solve the equation:
\(
\frac{t-3}{2}=\frac{1}{8}
\)

Options:
A. \( t=6 \frac{1}{4} \)
B. \( t=1 \)
C. \( t=3 \frac{1}{16} \)
D. \( t=3 \frac{1}{4} \)

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


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

Question:
Solve the equation:
\(
\frac{t-3}{2}=\frac{1}{8}
\)

Options:
A. \( t=6 \frac{1}{4} \)
B. \( t=1 \)
C. \( t=3 \frac{1}{16} \)
D. \( t=3 \frac{1}{4} \)

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


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

Question:
Rearrange the following equation to make \( r \) the subject
\(g=2 r+3\)

Options:
A. \( r=\frac{g+3}{2} \)
B. \( r=g+3 \div 2 \)
C. \( r=\frac{g-3}{2} \)
D. \( r=g-\frac{3}{2} \)

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:
Misunderstands order of operations in algebraic expressions

Question:
Rearrange the following equation to make \( r \) the subject
\(g=2 r+3\)

Options:
A. \( r=\frac{g+3}{2} \)
B. \( r=g+3 \div 2 \)
C. \( r=\frac{g-3}{2} \)
D. \( r=g-\frac{3}{2} \)

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 parallelogram is the term used to describe two lines at right angles

Question:
These two lines are ... ![Two lines on a graph meeting at a right angle]()

Options:
A. parallelogram
B. perpendicular
C. parallel
D. particular

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


Prompt:
Misconception:
Believes parallel is the term used to describe two lines at right angles

Question:
These two lines are ... ![Two lines on a graph meeting at a right angle]()

Options:
A. parallelogram
B. perpendicular
C. parallel
D. particular

Solve the problem as a student with the misconception above.
You 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 particular is the term used to describe two lines at right angles

Question:
These two lines are ... ![Two lines on a graph meeting at a right angle]()

Options:
A. parallelogram
B. perpendicular
C. parallel
D. particular

Solve the problem as a student with the misconception above.
You 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 square the conversion factor when converting squared units

Question:
\( 2 \mathrm{~km}^{2} \) is the same as _____ \( m^{2} \)

Options:
A. \( 2000 \)
B. \( 2000000 \)
C. \( 20000 \)
D. \( 2000000000 \)

Solve the problem as a student with the misconception above.
You 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:
\( 2 \mathrm{~km}^{2} \) is the same as _____ \( m^{2} \)

Options:
A. \( 2000 \)
B. \( 2000000 \)
C. \( 20000 \)
D. \( 2000000000 \)

Solve the problem as a student with the misconception above.
You 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 cube the conversion factor when dealing with squared units

Question:
\( 2 \mathrm{~km}^{2} \) is the same as _____ \( m^{2} \)

Options:
A. \( 2000 \)
B. \( 2000000 \)
C. \( 20000 \)
D. \( 2000000000 \)

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


Prompt:
Misconception:
Does not understand that a surd is a rational number if the number under the root is a square number

Question:
Which of these two numbers are rational?

\( \sqrt{36} \) and \( \sqrt{12} \)

Options:
A. \( \sqrt{36} \)
B. \( \sqrt{12} \)
C. Neither
D. Both

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


Prompt:
Misconception:
Does not understand that a surd is a rational number if the number under the root is a square number

Question:
Which of these two numbers are rational?

\( \sqrt{36} \) and \( \sqrt{12} \)

Options:
A. \( \sqrt{36} \)
B. \( \sqrt{12} \)
C. Neither
D. Both

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


Prompt:
Misconception:
Does not understand the definition of a rational number when it is a surd

Question:
Which of these two numbers are rational?

\( \sqrt{36} \) and \( \sqrt{12} \)

Options:
A. \( \sqrt{36} \)
B. \( \sqrt{12} \)
C. Neither
D. Both

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


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

Question:
What should replace the circle when this expression is fully factorised? \( 3 a^{2}+2 a \equiv \bigstar(\triangle a+\bigcirc) \)

Options:
A. \( \bigcirc=2 \)
B. \( \bigcirc=a \)
C. \( \bigcirc=2 a \)
D. \( \bigcirc=6 \)

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:
Confuses the equations of vertical and horizontal lines

Question:
Use a graphing program (e.g. Desmos) to plot the following pairs of functions.
\[
y=3 \text { and } y=-2
\]

Tom says both functions are linear

Katie says both functions are vertical lines

Who is correct?

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

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


Prompt:
Misconception:
Does not know the properties of a linear graph

Question:
Use a graphing program (e.g. Desmos) to plot the following pairs of functions.
\[
y=3 \text { and } y=-2
\]

Tom says both functions are linear

Katie says both functions are vertical lines

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:
Confused mixed numbers with improper fractions

Question:
\( 2 \frac{1}{5}+1 \frac{2}{5}= \) Leave your answer as a mixed number

Options:
A. \( 3 \frac{3}{5} \)
B. \( \frac{18}{5} \)
C. \( \frac{18}{10} \)
D. \( 3 \frac{3}{10} \)

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


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

Question:
\( 2 \frac{1}{5}+1 \frac{2}{5}= \) Leave your answer as a mixed number

Options:
A. \( 3 \frac{3}{5} \)
B. \( \frac{18}{5} \)
C. \( \frac{18}{10} \)
D. \( 3 \frac{3}{10} \)

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


Prompt:
Misconception:
Does not link Pythagoras Theorem to finding distance between two points

Question:
Mark is working out the distance between these two points. What type of triangle would help him? ![Axes with not scales drawn on. Two points are marked, (4,10) and (9,2)]()

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

Solve the problem as a student with the misconception above.
You 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 link Pythagoras Theorem to finding distance between two points

Question:
Mark is working out the distance between these two points. What type of triangle would help him? ![Axes with not scales drawn on. Two points are marked, (4,10) and (9,2)]()

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

Solve the problem as a student with the misconception above.
You 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 link Pythagoras Theorem to finding distance between two points

Question:
Mark is working out the distance between these two points. What type of triangle would help him? ![Axes with not scales drawn on. Two points are marked, (4,10) and (9,2)]()

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

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


Prompt:
Misconception:
Mistakes the place value column of hundred thousands with millions

Question:
How do you write this number in words?
\(
204050
\)

Options:
A. Two million and four thousand and fifty
B. Two hundred and four thousand and fifty
C. Two hundred and four and fifty
D. Two hundred and forty thousand and fifty

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


Prompt:
Misconception:
Does not understand that a space can be used to separate the thousands column from the hundreds column

Question:
How do you write this number in words?
\(
204050
\)

Options:
A. Two million and four thousand and fifty
B. Two hundred and four thousand and fifty
C. Two hundred and four and fifty
D. Two hundred and forty thousand and fifty

Solve the problem as a student with the misconception above.
You 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, treats digits in other columns as if they are units

Question:
What does the product of the two circled numbers represent? ![3847 times 28 written as a long multiplication question. The 8 in 3847 and the 2 in 28 are circled.]()

Options:
A. \( 16000 \)
B. \( 1600 \)
C. \( 160 \)
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:
Does not understand place value within a number

Question:
What does the product of the two circled numbers represent? ![3847 times 28 written as a long multiplication question. The 8 in 3847 and the 2 in 28 are circled.]()

Options:
A. \( 16000 \)
B. \( 1600 \)
C. \( 160 \)
D. \( 16 \)

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


Prompt:
Misconception:
When multiplying, treats digits in other columns as if they are units

Question:
What does the product of the two circled numbers represent? ![3847 times 28 written as a long multiplication question. The 8 in 3847 and the 2 in 28 are circled.]()

Options:
A. \( 16000 \)
B. \( 1600 \)
C. \( 160 \)
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:
Does not use the associative property of multiplication to find other factors of a number

Question:
If you can connect dots to draw a regular octagon in a ring of equally spaced dots, which other regular shape can you definitely draw?

Options:
A. Equilateral triangle
B. Square
C. Pentagon
D. Hexagon

Solve the problem as a student with the misconception above.
You 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 use the associative property of multiplication to find other factors of a number

Question:
If you can connect dots to draw a regular octagon in a ring of equally spaced dots, which other regular shape can you definitely draw?

Options:
A. Equilateral triangle
B. Square
C. Pentagon
D. Hexagon

Solve the problem as a student with the misconception above.
You 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 use the associative property of multiplication to find other factors of a number

Question:
If you can connect dots to draw a regular octagon in a ring of equally spaced dots, which other regular shape can you definitely draw?

Options:
A. Equilateral triangle
B. Square
C. Pentagon
D. Hexagon

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


Prompt:
Misconception:
Believes you can add or subtract from inside brackets without expanding when solving an equation

Question:
\(
x(3 x-5)+6(2 x-3) \equiv P x^{2}+Q x+R
\)

What is the value of \( R \) ?

Options:
A. \( -23 \)
B. \( -18 \)
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:
Believes you can add or subtract from inside brackets without expanding when solving an equation

Question:
\(
x(3 x-5)+6(2 x-3) \equiv P x^{2}+Q x+R
\)

What is the value of \( R \) ?

Options:
A. \( -23 \)
B. \( -18 \)
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:
Only multiplies the first term in the expansion of a bracket

Question:
\(
x(3 x-5)+6(2 x-3) \equiv P x^{2}+Q x+R
\)

What is the value of \( R \) ?

Options:
A. \( -23 \)
B. \( -18 \)
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:
Subtracts rather than divides when scaling down in direct proportion problems

Question:
Twelve rulers cost \( 96 p \).
How much do five rulers cost?

Options:
A. \( 89 p \)
B. \( 40 p \)
C. \( 8 p \)
D. \( £ 4.80 \)

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


Prompt:
Misconception:
Finds unit price but doesn't multiply up for number in question

Question:
Twelve rulers cost \( 96 p \).
How much do five rulers cost?

Options:
A. \( 89 p \)
B. \( 40 p \)
C. \( 8 p \)
D. \( £ 4.80 \)

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


Prompt:
Misconception:
Multiplies up without finding unit price in proportion question

Question:
Twelve rulers cost \( 96 p \).
How much do five rulers cost?

Options:
A. \( 89 p \)
B. \( 40 p \)
C. \( 8 p \)
D. \( £ 4.80 \)

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


Prompt:
Misconception:
Mixes up shortest and longest when ordering times

Question:
Order the times from shortest to longest.
A:  8 minutes
B:  8 minutes 40 seconds
C:  8 \(
\frac{1}{2}
\) minutes
D:  500 seconds

Options:
A. \( A, B, C, D \)
B. \( D, C, A, B \)
C. \( A, D, C, B \)
D. \( B, D, C, A \)

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


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

Question:
Round this number to \( 1 \) significant figure:
\( 0.8532 \)

Options:
A. \( 1 \)
B. \( 0 \)
C. \( 0.9 \)
D. \( 0.8 \)

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:
Rounds down instead of up

Question:
Round this number to \( 1 \) significant figure:
\( 0.8532 \)

Options:
A. \( 1 \)
B. \( 0 \)
C. \( 0.9 \)
D. \( 0.8 \)

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

Question:
\( 0.6=\frac{3}{5}=? \% \)

Options:
A. \( 50 \% \)
B. \( 35 \% \)
C. \( 60 \% \)
D. \( 6 \% \)

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


Prompt:
Misconception:
Believes a decimal with one significant figure is a multiple of 10 when converted to a percentage, regardless of place value

Question:
\( 0.6=\frac{3}{5}=? \% \)

Options:
A. \( 50 \% \)
B. \( 35 \% \)
C. \( 60 \% \)
D. \( 6 \% \)

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


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

Question:
Which of the following diagrams represents \( x<-1 \) or \( x \geq 2 \) ?

Options:
A. ![Number line from -5 to 5. Open circle at -1 with arrow to the left. Open circle at 2 with arrow to the right. ]()
B. ![Number line from -5 to 5. Closed circle at -1 with arrow to the left. Closed circle at 2 with arrow to the right. ]()
C. ![Number line from -5 to 5. Open circle at -1 with arrow to the left. Closed circle at 2 with arrow to the right. ]()
D. ![Number line from -5 to 5. Closed circle at -1 with arrow to the left. Open circle at 2 with arrow to the 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:
Has an incorrect assumption about the definition of a reciprocal

Question:
What is the reciprocal of \( -\frac{1}{3} \) ?

Options:
A. \( -3 \)
B. \( -0.333 \ldots \)
C. \( 3 \)
D. \( \frac{1}{3} \)

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:
Correctly finds the reciprocal of a number, but believes it should be opposite in sign to the original number.

Question:
What is the reciprocal of \( -\frac{1}{3} \) ?

Options:
A. \( -3 \)
B. \( -0.333 \ldots \)
C. \( 3 \)
D. \( \frac{1}{3} \)

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:
Makes the number negative when asked to find the reciprocal

Question:
What is the reciprocal of \( -\frac{1}{3} \) ?

Options:
A. \( -3 \)
B. \( -0.333 \ldots \)
C. \( 3 \)
D. \( \frac{1}{3} \)

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


Prompt:
Misconception:
Does not understand when like terms can be collected

Question:
Which answer shows the following calculation using the correct algebraic convention?

\(
a+6+a+j+5+j+j
\)

Options:
A. \( 11+2 a+3 j \)
B. \( 6+5+2 a+3 j \)
C. \( 6+2 a+5+3 j \)
D. \( 11+a^{2}+j^{3} \)

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


Prompt:
Misconception:
Does not understand when like terms can be collected

Question:
Which answer shows the following calculation using the correct algebraic convention?

\(
a+6+a+j+5+j+j
\)

Options:
A. \( 11+2 a+3 j \)
B. \( 6+5+2 a+3 j \)
C. \( 6+2 a+5+3 j \)
D. \( 11+a^{2}+j^{3} \)

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 collecting like terms with multiplication

Question:
Which answer shows the following calculation using the correct algebraic convention?

\(
a+6+a+j+5+j+j
\)

Options:
A. \( 11+2 a+3 j \)
B. \( 6+5+2 a+3 j \)
C. \( 6+2 a+5+3 j \)
D. \( 11+a^{2}+j^{3} \)

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


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 1

Question:
What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. "-8" next to the bottom dash and "4" next to the top dash are the only numbers marked on the line. An arrow, labelled "B" is pointing at the dash that is 2 below the "4" label and 4 above the "-8" label. ]()

Options:
A. \( 0 \)
B. \( 2 \)
C. \( -12 \)
D. \( -4 \)

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


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 1

Question:
What is the value of B? ![A vertical number-line with 7 horizontal, equally spaced, dashes representing the position of numbers. "-8" next to the bottom dash and "4" next to the top dash are the only numbers marked on the line. An arrow, labelled "B" is pointing at the dash that is 2 below the "4" label and 4 above the "-8" label. ]()

Options:
A. \( 0 \)
B. \( 2 \)
C. \( -12 \)
D. \( -4 \)

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


Prompt:
Misconception:
Believes switching the gradient and y-intercept gives a parallel line

Question:
Tom and Katie are arguing about parallel lines.

Tom says \( \boldsymbol{y}=\mathbf{2 x}+\mathbf{3} \) and \( \boldsymbol{y}=\mathbf{3 x}+\mathbf{2} \) are parallel.

Katie says \( \boldsymbol{y}=\mathbf{2 x}+\mathbf{3} \) and \( \boldsymbol{y}=\mathbf{2 x}-\mathbf{3} \) are parallel.

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 switching the gradient and y-intercept gives a parallel line

Question:
Tom and Katie are arguing about parallel lines.

Tom says \( \boldsymbol{y}=\mathbf{2 x}+\mathbf{3} \) and \( \boldsymbol{y}=\mathbf{3 x}+\mathbf{2} \) are parallel.

Katie says \( \boldsymbol{y}=\mathbf{2 x}+\mathbf{3} \) and \( \boldsymbol{y}=\mathbf{2 x}-\mathbf{3} \) are parallel.

Who is correct?

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

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


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

Question:
Solve the equation:
\(
0.15=0.5 p
\)

Options:
A. \( p=-0.35 \)
B. \( p=\frac{10}{3} \)
C. \( p=0.3 \)
D. \( p=0.75 \)

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 division is commutative

Question:
Solve the equation:
\(
0.15=0.5 p
\)

Options:
A. \( p=-0.35 \)
B. \( p=\frac{10}{3} \)
C. \( p=0.3 \)
D. \( p=0.75 \)

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:
Thinks the faster you travel the longer the time it will take

Question:
Which of the following graphs is most likely to represent the change in journey time against average speed?

Options:
A. ![A straight line graph starting at the origin and travelling right with a positive gradient.]()
B. ![A curved graph that starts at the origin. As you move right it travels steeply up, then levels off]()
C. ![A curved graph that starts up and right of the origin. As you move right it travels steeply down, then levels off. but never reaches the x-axis.]()
D. ![A straight line graph starting partway up the y-axis and travelling right with a negative gradient until it hits the x-axis.]()

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


Prompt:
Misconception:
Thinks the faster you travel the longer the time it will take

Question:
Which of the following graphs is most likely to represent the change in journey time against average speed?

Options:
A. ![A straight line graph starting at the origin and travelling right with a positive gradient.]()
B. ![A curved graph that starts at the origin. As you move right it travels steeply up, then levels off]()
C. ![A curved graph that starts up and right of the origin. As you move right it travels steeply down, then levels off. but never reaches the x-axis.]()
D. ![A straight line graph starting partway up the y-axis and travelling right with a negative gradient until it hits the x-axis.]()

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


Prompt:
Misconception:
Believes a reciprocal graph can be a straight line

Question:
Which of the following graphs is most likely to represent the change in journey time against average speed?

Options:
A. ![A straight line graph starting at the origin and travelling right with a positive gradient.]()
B. ![A curved graph that starts at the origin. As you move right it travels steeply up, then levels off]()
C. ![A curved graph that starts up and right of the origin. As you move right it travels steeply down, then levels off. but never reaches the x-axis.]()
D. ![A straight line graph starting partway up the y-axis and travelling right with a negative gradient until it hits the x-axis.]()

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


Prompt:
Misconception:
Finds the median instead of the mode

Question:
This table shows the number of pets a group of students owns.

What is the modal number of pets owned? \begin{tabular}{|c|c|}
\hline Number of pets & Frequency \\
\hline \( 0 \) & \( 9 \) \\
\hline \( 1 \) & \( 6 \) \\
\hline \( 2 \) & \( 3 \) \\
\hline \( 3 \) & \( 2 \) \\
\hline \( 4 \) & \( 3 \) \\
\hline
\end{tabular}

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

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


Prompt:
Misconception:
Believes the mode is the frequency rather than the value/group

Question:
This table shows the number of pets a group of students owns.

What is the modal number of pets owned? \begin{tabular}{|c|c|}
\hline Number of pets & Frequency \\
\hline \( 0 \) & \( 9 \) \\
\hline \( 1 \) & \( 6 \) \\
\hline \( 2 \) & \( 3 \) \\
\hline \( 3 \) & \( 2 \) \\
\hline \( 4 \) & \( 3 \) \\
\hline
\end{tabular}

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

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


Prompt:
Misconception:
Believes when identifying the mode you look at all values, not just frequencies, for the highest number

Question:
This table shows the number of pets a group of students owns.

What is the modal number of pets owned? \begin{tabular}{|c|c|}
\hline Number of pets & Frequency \\
\hline \( 0 \) & \( 9 \) \\
\hline \( 1 \) & \( 6 \) \\
\hline \( 2 \) & \( 3 \) \\
\hline \( 3 \) & \( 2 \) \\
\hline \( 4 \) & \( 3 \) \\
\hline
\end{tabular}

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

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


Prompt:
Misconception:
Added rather than multiplied by a scale factor

Question:
The triangle is enlarged by scale factor \( 3 \), with the centre of enlargement at \( (1,0) \).
What are the new coordinates of the point marked \( T \) ? ![A coordinate grid with the x-axis going from -1 to 10 and the y-axis going from -1 to 7.
3 points are plotted and joined with straight lines to form a triangle. The points are (1,1), (1,4) and (3,1). Point (3,1) is labelled as T.
Point (1,0) is also plotted.]()

Options:
A. \( (7,3) \)
B. \( (1,3) \)
C. \( (6,4) \)
D. \( (9,3) \)

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:
Enlarges by the wrong centre of enlargement

Question:
The triangle is enlarged by scale factor \( 3 \), with the centre of enlargement at \( (1,0) \).
What are the new coordinates of the point marked \( T \) ? ![A coordinate grid with the x-axis going from -1 to 10 and the y-axis going from -1 to 7.
3 points are plotted and joined with straight lines to form a triangle. The points are (1,1), (1,4) and (3,1). Point (3,1) is labelled as T.
Point (1,0) is also plotted.]()

Options:
A. \( (7,3) \)
B. \( (1,3) \)
C. \( (6,4) \)
D. \( (9,3) \)

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:
Identifies the biggest value for the range

Question:
What is the range of this set of data?
\[
5 \mathrm{~cm}, 19 \mathrm{~cm}, 6 \mathrm{~cm}, 2 \mathrm{~cm}
\]

Options:
A. \( 17 \mathrm{~cm} \)
B. \( 19 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 21 \mathrm{~cm} \)

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:
Thinks the range is just the first value subtracted from the last value, without ordering

Question:
What is the range of this set of data?
\[
5 \mathrm{~cm}, 19 \mathrm{~cm}, 6 \mathrm{~cm}, 2 \mathrm{~cm}
\]

Options:
A. \( 17 \mathrm{~cm} \)
B. \( 19 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 21 \mathrm{~cm} \)

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:
To find the range adds the biggest and smallest number rather than subtract

Question:
What is the range of this set of data?
\[
5 \mathrm{~cm}, 19 \mathrm{~cm}, 6 \mathrm{~cm}, 2 \mathrm{~cm}
\]

Options:
A. \( 17 \mathrm{~cm} \)
B. \( 19 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 21 \mathrm{~cm} \)

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


Prompt:
Misconception:
Confuses the lines y=x and y=-x

Question:
Which inequality is represented by the shaded region? ![Graph showing four quadrants with a straight line going from the top left to the bottom right. The line goes through (-4, 4) (-3, 3) (-2, 2) and so on]()

Options:
A. \( y>x \)
B. \( y<x \)
C. \( y>-x \)
D. \( y<-x \)

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:
Mixes up greater than and less than symbols

Question:
Which inequality is represented by the shaded region? ![Graph showing four quadrants with a straight line going from the top left to the bottom right. The line goes through (-4, 4) (-3, 3) (-2, 2) and so on]()

Options:
A. \( y>x \)
B. \( y<x \)
C. \( y>-x \)
D. \( y<-x \)

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

Question:
Here is a function machine
\( input\Rightarrow +2 \Rightarrow \times 3 \Rightarrow output\)
The input is \( 5 \).
Which calculation gives the correct output?

Options:
A. \( 5 \times 3+2 \)
B. \( 3(5+2) \)
C. \( 5(3+2) \)
D. \( 5+2 \times 3 \)

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:
In a function machine, confuses an operation with the input

Question:
Here is a function machine
\( input\Rightarrow +2 \Rightarrow \times 3 \Rightarrow output\)
The input is \( 5 \).
Which calculation gives the correct output?

Options:
A. \( 5 \times 3+2 \)
B. \( 3(5+2) \)
C. \( 5(3+2) \)
D. \( 5+2 \times 3 \)

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 order of operations does not affect the answer to a calculation

Question:
Here is a function machine
\( input\Rightarrow +2 \Rightarrow \times 3 \Rightarrow output\)
The input is \( 5 \).
Which calculation gives the correct output?

Options:
A. \( 5 \times 3+2 \)
B. \( 3(5+2) \)
C. \( 5(3+2) \)
D. \( 5+2 \times 3 \)

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:
Calculates perimeter when asked for area

Question:
A square has an area \( 64 \mathrm{~mm}^{2} \)

What is the length of one side of the square?

Options:
A. \( 16 \mathrm{~mm} \)
B. \( 32 \mathrm{~mm} \)
C. \( 8 \mathrm{~mm} \)
D. \( 4096 \mathrm{~mm} \)

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:
Adds when calculating area instead of multiplying

Question:
A square has an area \( 64 \mathrm{~mm}^{2} \)

What is the length of one side of the square?

Options:
A. \( 16 \mathrm{~mm} \)
B. \( 32 \mathrm{~mm} \)
C. \( 8 \mathrm{~mm} \)
D. \( 4096 \mathrm{~mm} \)

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:
Thinks the number in the ratio is the total

Question:
The ratio of cars to bikes in a housing estate is \( 5: 2 \)
If there are \( \mathbf{7 0} \) cars, how many vehicles (cars and bikes) are there in total?

Options:
A. \( 72 \)
B. \( 98 \)
C. \( 90 \)
D. \( 28 \)

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:
Thinks they solve mx + c = a, by substituting in the value of a for x and therefore calculating ma + c

Question:
This is the graph of
\[
y=0.5 x-2
\]

According to the graph, what is the solution to:
\[
0.5 x-2=1
\] ![Graph showing straight line with y intercept (0,-2) and x intercept (4,0)]()

Options:
A. \( x=6 \)
B. \( x=-1.5 \)
C. \( x=4 \)
D. \( x=2 \)

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 the solution to mx + c = a is the x intercept of y = mx +c

Question:
This is the graph of
\[
y=0.5 x-2
\]

According to the graph, what is the solution to:
\[
0.5 x-2=1
\] ![Graph showing straight line with y intercept (0,-2) and x intercept (4,0)]()

Options:
A. \( x=6 \)
B. \( x=-1.5 \)
C. \( x=4 \)
D. \( x=2 \)

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


Prompt:
Misconception:
Does not understand inequality notation

Question:
One of these pairs of numbers does not fit
the inequality \( d \leq h \)

Can you find which pair?

Options:
A. \( \begin{array}{l}d=4 \\ h=4\end{array} \)
B. \( \begin{array}{c}d=-4\\h=4\end{array} \)
C. \( \begin{array}{c}d=2 \\ h=-4\end{array} \)
D. \( \begin{array}{c}d=-2 \\ h=2\end{array} \)

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


Prompt:
Misconception:
Does not understand inequality notation

Question:
One of these pairs of numbers does not fit
the inequality \( d \leq h \)

Can you find which pair?

Options:
A. \( \begin{array}{l}d=4 \\ h=4\end{array} \)
B. \( \begin{array}{c}d=-4\\h=4\end{array} \)
C. \( \begin{array}{c}d=2 \\ h=-4\end{array} \)
D. \( \begin{array}{c}d=-2 \\ h=2\end{array} \)

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


Prompt:
Misconception:
Does not understand inequality notation

Question:
One of these pairs of numbers does not fit
the inequality \( d \leq h \)

Can you find which pair?

Options:
A. \( \begin{array}{l}d=4 \\ h=4\end{array} \)
B. \( \begin{array}{c}d=-4\\h=4\end{array} \)
C. \( \begin{array}{c}d=2 \\ h=-4\end{array} \)
D. \( \begin{array}{c}d=-2 \\ h=2\end{array} \)

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


Prompt:
Misconception:
Believes there is more than one line which passes through a given pair of points

Question:
Tom and Katie are arguing about midpoints.
\( M \) is the midpoint between points \( P \) and \( Q \).

Tom says if you know the location of \( M \) only, then there is more than one possible location for \( \mathrm{P} \) and \( \mathrm{Q} \).

Katie says if you only know the locations of \( M \) and \( Q \), then there is more than one possible location for \( \mathrm{P} \).
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 one point is enough to specify a line

Question:
Tom and Katie are arguing about midpoints.
\( M \) is the midpoint between points \( P \) and \( Q \).

Tom says if you know the location of \( M \) only, then there is more than one possible location for \( \mathrm{P} \) and \( \mathrm{Q} \).

Katie says if you only know the locations of \( M \) and \( Q \), then there is more than one possible location for \( \mathrm{P} \).
Who is correct?

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

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


Prompt:
Misconception:
When asked for the next term in the sequence adds one to the last term given, despite the sequence not going up in ones.

Question:
How many squares will the next term in this sequence have? ![A diagram showing the first 3 patterns in a sequence.
Pattern 1 contains 3 squares in this arrangement :.
Pattern 2 contains 5 squares in this arrangement ::.
Pattern 3 contains 7 squares in this arrangement :::.]()

Options:
A. \( 9 \)
B. \( 8 \)
C. \( 10 \)
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}.