Prompt:
Misconception:
Does not notice all changes in a sequence of visual patterns

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}.


Prompt:
Misconception:
Does not notice all changes in a sequence of visual patterns

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}.


Prompt:
Misconception:
Has found the total as a percentage of the amount being asked

Question:
What is \( 50 \mathrm{~m} \) as a percentage of \( 5 \mathrm{~km} \) ?

Options:
A. \( 100 \% \)
B. \( 1 \% \)
C. \( 50 \% \)
D. \( 10 \% \)

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


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

Question:
What is \( 50 \mathrm{~m} \) as a percentage of \( 5 \mathrm{~km} \) ?

Options:
A. \( 100 \% \)
B. \( 1 \% \)
C. \( 50 \% \)
D. \( 10 \% \)

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


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

Question:
What is \( 50 \mathrm{~m} \) as a percentage of \( 5 \mathrm{~km} \) ?

Options:
A. \( 100 \% \)
B. \( 1 \% \)
C. \( 50 \% \)
D. \( 10 \% \)

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


Prompt:
Misconception:
Believes that in y=mx+c, m is the y-intercept

Question:
Which of the following sketches could represent \( y=4-2 x \) ?

Options:
A. ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis above the origin.]()
B. ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis below the origin.]()
C. ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis above the origin.]()
D. ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis below the origin.]()

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

Question:
Which of the following sketches could represent \( y=4-2 x \) ?

Options:
A. ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis above the origin.]()
B. ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis below the origin.]()
C. ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis above the origin.]()
D. ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis below the origin.]()

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

Question:
Which of the following sketches could represent \( y=4-2 x \) ?

Options:
A. ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis above the origin.]()
B. ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis below the origin.]()
C. ![A straight line graph that crosses the x axis to the left of the origin and crosses the y axis above the origin.]()
D. ![A straight line graph that crosses the x axis to the right of the origin and crosses the y axis below the origin.]()

Solve the problem as a student with the misconception above.
You 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 identify common factors from algebraic terms

Question:
Tom and Katie are discussing factors

Tom says \( 3 \) is a common factor of \( 6 x \) and \( 9 y \)

Katie says \( x \) is a common factor of \( 6 x \) and \( 9 y \)

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 how to identify common factors from algebraic terms

Question:
Tom and Katie are discussing factors

Tom says \( 3 \) is a common factor of \( 6 x \) and \( 9 y \)

Katie says \( x \) is a common factor of \( 6 x \) and \( 9 y \)

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 how to identify common factors from algebraic terms

Question:
Tom and Katie are discussing factors

Tom says \( 3 \) is a common factor of \( 6 x \) and \( 9 y \)

Katie says \( x \) is a common factor of \( 6 x \) and \( 9 y \)

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

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
2 \div(3+a \times b)
\)

Options:
A. \( \frac{2}{3}+a b \)
B. \( \frac{2}{b(a+3)} \)
C. \( \frac{2}{a b+3} \)
D. \( \frac{2}{a \times b+3} \)

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:
Which answer shows the following calculation using the correct algebraic convention?
\(
2 \div(3+a \times b)
\)

Options:
A. \( \frac{2}{3}+a b \)
B. \( \frac{2}{b(a+3)} \)
C. \( \frac{2}{a b+3} \)
D. \( \frac{2}{a \times b+3} \)

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 realize we can omit the multiplication symbol in algebraic expressions

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
2 \div(3+a \times b)
\)

Options:
A. \( \frac{2}{3}+a b \)
B. \( \frac{2}{b(a+3)} \)
C. \( \frac{2}{a b+3} \)
D. \( \frac{2}{a \times b+3} \)

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 range does not need units

Question:
When finding the range of a data set, which step is never needed

Options:
A. Subtract the smallest number from the largest number.
B. Check the units of your answer
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:
When calculating the range does not reorder the data to find the largest number minus the smallest number

Question:
When finding the range of a data set, which step is never needed

Options:
A. Subtract the smallest number from the largest number.
B. Check the units of your answer
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:
Forgets the denominator in probability

Question:
A box contains \( 10 \) coloured counters.

\( 3 \) of the counters are pink

\( 3 \) of the counters are blue

The rest of the counters are green

What is the probability of choosing a green counter?

Options:
A. \( 4 \)
B. \( \frac{6}{10} \)
C. \( \frac{1}{3} \)
D. \( \frac{4}{10} \)

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


Prompt:
Misconception:
Thinks that probabilities of an event occurring or not occurring must be equal

Question:
A box contains \( 10 \) coloured counters.

\( 3 \) of the counters are pink

\( 3 \) of the counters are blue

The rest of the counters are green

What is the probability of choosing a green counter?

Options:
A. \( 4 \)
B. \( \frac{6}{10} \)
C. \( \frac{1}{3} \)
D. \( \frac{4}{10} \)

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


Prompt:
Misconception:
Does not convert measurements to have the same units before calculating area or volume

Question:
Which of the following calculations would give the volume of this cuboid? ![A cuboid with dimensions 60mm, 7cm and 5cm]()

Options:
A. \( 7 \times 5 \times 60 \)
B. \( 7 \times 5 \times 6 \)
C. \( 7+5+60 \)
D. \( 7+5+6 \)

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 when calculating volume instead of multiplying

Question:
Which of the following calculations would give the volume of this cuboid? ![A cuboid with dimensions 60mm, 7cm and 5cm]()

Options:
A. \( 7 \times 5 \times 60 \)
B. \( 7 \times 5 \times 6 \)
C. \( 7+5+60 \)
D. \( 7+5+6 \)

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 the constant in an expanded quadratic comes from adding the two numbers in the brackets

Question:
What should replace the circle when these two brackets are
expanded and simplified?

\(
(p-3)(p+3) \equiv p^{2} \color{purple}\triangle\) \(p\)\(\color{green}\bigcirc
\)

Options:
A. \(\color{green}\bigcirc\) = +6
B. \(\color{green}\bigcirc\) = +0
(no number term)
C. \(\color{green}\bigcirc\) = +9
D. \(\color{green}\bigcirc\) = -9

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


Prompt:
Misconception:
Believes multiplying a positive by a negative gives a positive answer

Question:
What should replace the circle when these two brackets are
expanded and simplified?

\(
(p-3)(p+3) \equiv p^{2} \color{purple}\triangle\) \(p\)\(\color{green}\bigcirc
\)

Options:
A. \(\color{green}\bigcirc\) = +6
B. \(\color{green}\bigcirc\) = +0
(no number term)
C. \(\color{green}\bigcirc\) = +9
D. \(\color{green}\bigcirc\) = -9

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


Prompt:
Misconception:
When adding column vectors, multiplies rather than adds

Question:
\( \left(\begin{array}{l}2 \\ 3\end{array}\right)+\left(\begin{array}{c}-1 \\ 0\end{array}\right)= \)

Options:
A. \( \left(\begin{array}{l}1 \\ 3\end{array}\right) \)
B. \( \left(\begin{array}{c}-2 \\ 3\end{array}\right) \)
C. \( \left(\begin{array}{c}-2 \\ 0\end{array}\right) \)
D. \( \left(\begin{array}{l}3 \\ 3\end{array}\right) \)

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


Prompt:
Misconception:
Only recognises the positive form of a quadratic graph

Question:
Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() Who is correct?

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

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


Prompt:
Misconception:
Only recognises the negative form of a quadratic graph

Question:
Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() 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 recognise a quadratic graph

Question:
Tom and Katie are discussing quadratic graphs Tom says this could be the graph of a quadratic function ![A graph showing a positive parabola in the shape of a u]() Katie says this could be the graph of a quadratic function ![A graph showing a negative parabola in the shape of an upside down u]() 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 divide by 2 when calculating the area of a trapezium

Question:
The area of this trapezium is \( 40 \mathrm{~cm}^{2} \).

What is the value of \( a \) ? ![A trapezium with the parallel sides labelled with 2cm and a and the height labelled with 8cm]()

Options:
A. \( 8 \mathrm{~cm} \)
B. \( 3 \mathrm{~cm} \)
C. \( 7 \mathrm{~cm} \)
D. \( 4 \mathrm{~cm} \)

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:
Can not square root a negative number

Question:
\( \sqrt{-16}=? \)

Options:
A. \( -4 \)
B. \( 4 \)
C. \( -8 \)
D. No real solutions

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


Prompt:
Misconception:
Can not square root a negative number

Question:
\( \sqrt{-16}=? \)

Options:
A. \( -4 \)
B. \( 4 \)
C. \( -8 \)
D. No real solutions

Solve the problem as a student with the misconception above.
You 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 go above an amount of money when finding how much of something you can buy

Question:
Alicia wants to buy some bottles of water.
Each bottle of water costs \( £ 1.65 \)
Alicia has \( £ 10 \) to spend.
What is the greatest number of bottles can she buy?

Options:
A. \( 10 \)
B. \( 6 \)
C. \( 16 \)
D. \( 7 \)

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


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

Question:
Solve
\[
3 n+2 \geq 4 n-5
\]

Options:
A. \( -3 \geq n \)
B. \( 1 \geq n \)
C. \( 7 \geq n \)
D. \( n \geq 7 \)

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


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

Question:
Solve
\[
3 n+2 \geq 4 n-5
\]

Options:
A. \( -3 \geq n \)
B. \( 1 \geq n \)
C. \( 7 \geq n \)
D. \( n \geq 7 \)

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


Prompt:
Misconception:
Believes they can multiply/divide through by a negative number without changing the direction of the inequality

Question:
Solve
\[
3 n+2 \geq 4 n-5
\]

Options:
A. \( -3 \geq n \)
B. \( 1 \geq n \)
C. \( 7 \geq n \)
D. \( n \geq 7 \)

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


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

Question:
A theme park charges \( £ 8 \) entry fee and then \( £ 3 \) for every ride you go on.
Heena goes on \( 5 \) rides.
How much does she pay in total?

Options:
A. \( £ 55 \)
B. \( £ 15 \)
C. \( £ 11 \)
D. \( £ 23 \)

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


Prompt:
Misconception:
Does not add on the constant in a worded substitution problem

Question:
A theme park charges \( £ 8 \) entry fee and then \( £ 3 \) for every ride you go on.
Heena goes on \( 5 \) rides.
How much does she pay in total?

Options:
A. \( £ 55 \)
B. \( £ 15 \)
C. \( £ 11 \)
D. \( £ 23 \)

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


Prompt:
Misconception:
Does not consider the variable when evaluating an expression that requires substitution.

Question:
A theme park charges \( £ 8 \) entry fee and then \( £ 3 \) for every ride you go on.
Heena goes on \( 5 \) rides.
How much does she pay in total?

Options:
A. \( £ 55 \)
B. \( £ 15 \)
C. \( £ 11 \)
D. \( £ 23 \)

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


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

Question:
Increase \( 160 \) by \( 30 \% \)

Options:
A. \( 208 \)
B. \( 190 \)
C. \( 48 \)
D. \( 4800 \)

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


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

Question:
Increase \( 160 \) by \( 30 \% \)

Options:
A. \( 208 \)
B. \( 190 \)
C. \( 48 \)
D. \( 4800 \)

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


Prompt:
Misconception:
Thinks when finding a percentage you multiply by the percentage being asked

Question:
Increase \( 160 \) by \( 30 \% \)

Options:
A. \( 208 \)
B. \( 190 \)
C. \( 48 \)
D. \( 4800 \)

Solve the problem as a student with the misconception above.
You 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 difference between triangle numbers decreases by 1 each time

Question:
Here are two consecutive triangle numbers: \( 153,171, \ldots \) What is the next triangle number in the sequence?

Options:
A. \( 188 \)
B. \( 189 \)
C. \( 190 \)
D. \( 324 \)

Solve the problem as a student with the misconception above.
You 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 difference between triangle numbers remains the same

Question:
Here are two consecutive triangle numbers: \( 153,171, \ldots \) What is the next triangle number in the sequence?

Options:
A. \( 188 \)
B. \( 189 \)
C. \( 190 \)
D. \( 324 \)

Solve the problem as a student with the misconception above.
You 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 to find the next traingle number you add the previous two numbers together i.e. Fibonacci

Question:
Here are two consecutive triangle numbers: \( 153,171, \ldots \) What is the next triangle number in the sequence?

Options:
A. \( 188 \)
B. \( 189 \)
C. \( 190 \)
D. \( 324 \)

Solve the problem as a student with the misconception above.
You 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 add all values in a worded problem, thereby not interpreting the problem correctly

Question:
At the start of the day, there was \( £ 1,456 \) in the till. \( £ 7,347 \) was taken and \( £ 4,377 \) was handed out. How much money was left?

Options:
A. \( £ 13,180 \)
B. \( £ 4,426 \)
C. \( £ 2,970 \)
D. \( £ 10,268 \)

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


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

Question:
At the start of the day, there was \( £ 1,456 \) in the till. \( £ 7,347 \) was taken and \( £ 4,377 \) was handed out. How much money was left?

Options:
A. \( £ 13,180 \)
B. \( £ 4,426 \)
C. \( £ 2,970 \)
D. \( £ 10,268 \)

Solve the problem as a student with the misconception above.
You 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 talking about money "taken" in a retail context, thinks that means take-away rather than add

Question:
At the start of the day, there was \( £ 1,456 \) in the till. \( £ 7,347 \) was taken and \( £ 4,377 \) was handed out. How much money was left?

Options:
A. \( £ 13,180 \)
B. \( £ 4,426 \)
C. \( £ 2,970 \)
D. \( £ 10,268 \)

Solve the problem as a student with the misconception above.
You 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 a quadratic graph

Question:
Which of the following is an example of a quadratic graph?

Options:
A. ![A graph showing a straight line from top left to bottom right.]()
B. ![A graph showing a curve that starts in the bottom left, moves steeply up and right, levels off briefly, then continues steeply up and right.]()
C. ![A graph with two curves. One curve is in the positive x, positive y quadrant. It starts at the top close to the y axis, as we move right it drops very quickly towards the x axis then levels off to travel almost parallel to the x axis.
The other curve is in the negative x, negative y quadrant. It starts at the top left close to the x axis, as we move right it drops very quickly towards the y axis then becomes almost vertical to travel almost parallel to the y axis. ]()
D. ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape.]()

Solve the problem as a student with the misconception above.
You 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 cubic and quadratic graphs

Question:
Which of the following is an example of a quadratic graph?

Options:
A. ![A graph showing a straight line from top left to bottom right.]()
B. ![A graph showing a curve that starts in the bottom left, moves steeply up and right, levels off briefly, then continues steeply up and right.]()
C. ![A graph with two curves. One curve is in the positive x, positive y quadrant. It starts at the top close to the y axis, as we move right it drops very quickly towards the x axis then levels off to travel almost parallel to the x axis.
The other curve is in the negative x, negative y quadrant. It starts at the top left close to the x axis, as we move right it drops very quickly towards the y axis then becomes almost vertical to travel almost parallel to the y axis. ]()
D. ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape.]()

Solve the problem as a student with the misconception above.
You 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 reciprocal and quadratic graphs

Question:
Which of the following is an example of a quadratic graph?

Options:
A. ![A graph showing a straight line from top left to bottom right.]()
B. ![A graph showing a curve that starts in the bottom left, moves steeply up and right, levels off briefly, then continues steeply up and right.]()
C. ![A graph with two curves. One curve is in the positive x, positive y quadrant. It starts at the top close to the y axis, as we move right it drops very quickly towards the x axis then levels off to travel almost parallel to the x axis.
The other curve is in the negative x, negative y quadrant. It starts at the top left close to the x axis, as we move right it drops very quickly towards the y axis then becomes almost vertical to travel almost parallel to the y axis. ]()
D. ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape.]()

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


Prompt:
Misconception:
Believes that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations.

Question:
Tom and Katie are discussing this pair of simultaneous equations: \( \begin{array}{l}3 x-2 y=8 \\ 3 x+y=14\end{array} \) Tom says if you add the two equations together you will eliminate a variable

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

Who is correct?

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

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


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

Question:
Tom and Katie are discussing this pair of simultaneous equations: \( \begin{array}{l}3 x-2 y=8 \\ 3 x+y=14\end{array} \) Tom says if you add the two equations together you will eliminate a variable

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

Who is correct?

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

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


Prompt:
Misconception:
Does not understand the first significant value is the first non-zero digit number

Question:
\(
180.5672
\)

What is the second significant figure in the number above?

Options:
A. \( 7 \)
B. \( 2 \)
C. \( 8 \)
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:
Does not understand the first significant value is the first non-zero digit number

Question:
\(
180.5672
\)

What is the second significant figure in the number above?

Options:
A. \( 7 \)
B. \( 2 \)
C. \( 8 \)
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:
Identifies second decimal place value when asked for the second significant figure

Question:
\(
180.5672
\)

What is the second significant figure in the number above?

Options:
A. \( 7 \)
B. \( 2 \)
C. \( 8 \)
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 that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations.

Question:
What do you need to do to eliminate the \( q \)s in each of these pairs of simultaneous equations?
\begin{array}{cc}
  Pair 1 & Pair 2 \\
\( 2p-4q=6 \) & \( 2p-4q=6 \)\\
\( 7p+4q=9 \) & \( 7p-4q=9 \)
\end{array}

Options:
A. Add Pair \( 1 \)
Subtract Pair \( 2 \)
B. Add Pair \( 1 \)
Add Pair \( 2 \)
C. Subtract Pair \( 1 \)
Add Pair \( 2 \)
D. Subtract Pair \( 1 \)
Subtract Pair \( 2 \)

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


Prompt:
Misconception:
Believes that when eliminating a variable, regardless of the signs of the terms with matching coefficients, we subtract the equations

Question:
What do you need to do to eliminate the \( q \)s in each of these pairs of simultaneous equations?
\begin{array}{cc}
  Pair 1 & Pair 2 \\
\( 2p-4q=6 \) & \( 2p-4q=6 \)\\
\( 7p+4q=9 \) & \( 7p-4q=9 \)
\end{array}

Options:
A. Add Pair \( 1 \)
Subtract Pair \( 2 \)
B. Add Pair \( 1 \)
Add Pair \( 2 \)
C. Subtract Pair \( 1 \)
Add Pair \( 2 \)
D. Subtract Pair \( 1 \)
Subtract Pair \( 2 \)

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 both the x and y co-ordinates of the x-intercept of a quadratic are derived from the constants in the factorised form.

Question:
\( y=(x-3)(x-5) \) Where does this curve intercept the \( x \) axis?

Options:
A. \( (3,5) \)
B. \( \begin{array}{c}(3,0) \\ \text { and } \\ (5,0)\end{array} \)
C. \( \begin{array}{c}(-3,0) \\ \text { and } \\ (-5,0)\end{array} \)
D. \( \begin{array}{c}(3,5) \\ \text { and } \\ (-3,-5)\end{array} \)

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

Question:
\( y=(x-3)(x-5) \) Where does this curve intercept the \( x \) axis?

Options:
A. \( (3,5) \)
B. \( \begin{array}{c}(3,0) \\ \text { and } \\ (5,0)\end{array} \)
C. \( \begin{array}{c}(-3,0) \\ \text { and } \\ (-5,0)\end{array} \)
D. \( \begin{array}{c}(3,5) \\ \text { and } \\ (-3,-5)\end{array} \)

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:
Believes both the x and y co-ordinates of the x-intercept of a quadratic are derived from the constants in the factorised form.

Question:
\( y=(x-3)(x-5) \) Where does this curve intercept the \( x \) axis?

Options:
A. \( (3,5) \)
B. \( \begin{array}{c}(3,0) \\ \text { and } \\ (5,0)\end{array} \)
C. \( \begin{array}{c}(-3,0) \\ \text { and } \\ (-5,0)\end{array} \)
D. \( \begin{array}{c}(3,5) \\ \text { and } \\ (-3,-5)\end{array} \)

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:
Confuses vertically opposite angles with angles on a straight line

Question:
What is the size of angle \( k \) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]()

Options:
A. \( 46^{\circ} \)
B. \( 65^{\circ} \)
C. \( 19^{\circ} \)
D. Not enough information

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


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

Question:
What is the size of angle \( k \) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]()

Options:
A. \( 46^{\circ} \)
B. \( 65^{\circ} \)
C. \( 19^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Does not know that angles on a straight line sum to 180 degrees

Question:
What is the size of angle \( k \) ? ![Three angles which meet to form a straight line. They are labelled 46 degrees, 115 degrees and k.]()

Options:
A. \( 46^{\circ} \)
B. \( 65^{\circ} \)
C. \( 19^{\circ} \)
D. Not enough information

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


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

Question:
When calculating the mean of the following numbers which calculation will give the correct answer?
\[
0,1,3,4,7
\]

Options:
A. \( \frac{1+3+4+7}{5} \)
B. \( 0+1+3+4+7 \div 5 \)
C. \( \frac{1+3+4+7}{4} \)
D. None of them

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


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

Question:
When calculating the mean of the following numbers which calculation will give the correct answer?
\[
0,1,3,4,7
\]

Options:
A. \( \frac{1+3+4+7}{5} \)
B. \( 0+1+3+4+7 \div 5 \)
C. \( \frac{1+3+4+7}{4} \)
D. None of them

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


Prompt:
Misconception:
Does not know how to calculate the mean

Question:
When calculating the mean of the following numbers which calculation will give the correct answer?
\[
0,1,3,4,7
\]

Options:
A. \( \frac{1+3+4+7}{5} \)
B. \( 0+1+3+4+7 \div 5 \)
C. \( \frac{1+3+4+7}{4} \)
D. None of them

Solve the problem as a student with the misconception above.
You 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 changing an improper fraction to a mixed number you divide the numerator by 10, regardless of the denominator

Question:
Convert this into a mixed number fraction:
\(
\frac{13}{5}
\)

Options:
A. \( 2 \frac{3}{5} \)
B. \( 1 \frac{3}{5} \)
C. \( 3 \frac{2}{5} \)
D. \( 13 \frac{1}{5} \)

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


Prompt:
Misconception:
Believes the whole and remainder are the other way when changing an improper fraction to a mixed number

Question:
Convert this into a mixed number fraction:
\(
\frac{13}{5}
\)

Options:
A. \( 2 \frac{3}{5} \)
B. \( 1 \frac{3}{5} \)
C. \( 3 \frac{2}{5} \)
D. \( 13 \frac{1}{5} \)

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


Prompt:
Misconception:
Believes the number of wholes in a mixed number multiplies by the fraction part

Question:
Convert this into a mixed number fraction:
\(
\frac{13}{5}
\)

Options:
A. \( 2 \frac{3}{5} \)
B. \( 1 \frac{3}{5} \)
C. \( 3 \frac{2}{5} \)
D. \( 13 \frac{1}{5} \)

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


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

Question:
The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]()

Options:
A. \( 12 x-8=10 x+4 \)
B. \( 12 x-2=10 x+2 \)
C. \( 8+6 x-4=4+10 x+4 \)
D. \( 4+3 x-2=2+5 x+2 \)

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:
Calculates perimeter when asked for area

Question:
The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]()

Options:
A. \( 12 x-8=10 x+4 \)
B. \( 12 x-2=10 x+2 \)
C. \( 8+6 x-4=4+10 x+4 \)
D. \( 4+3 x-2=2+5 x+2 \)

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:
Adds when calculating area instead of multiplying

Question:
The area of these shapes are equal. Which of these is correct? ![An image of two rectangles. The top one is blue and has the dimensions - side length: 4 and base 3x -2. The bottom one is yellow and has the dimensions - side length: 2 and base 5x + 2.]()

Options:
A. \( 12 x-8=10 x+4 \)
B. \( 12 x-2=10 x+2 \)
C. \( 8+6 x-4=4+10 x+4 \)
D. \( 4+3 x-2=2+5 x+2 \)

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:
Added rather than multiplied by a scale factor

Question:
\( 3 \) miles \( \approx 5 \mathrm{~km} \) \( 30 \mathrm{~km} \approx \square \) miles

Options:
A. \( 18 \)
B. \( 9 \)
C. \( 28 \)
D. \( 50 \)

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


Prompt:
Misconception:
Does not correctly apply the commutative property of multiplication

Question:
Tom and Katie are discussing mental multiplication strategies.
Tom says \( 15 \times 42=154 \times 2 \)
Katie says \( 15 \times 42=(15 \times 4)+(15 \times 2) \)
Who is correct?

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

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


Prompt:
Misconception:
Does not correctly apply the distributive property of multiplication

Question:
Tom and Katie are discussing mental multiplication strategies.
Tom says \( 15 \times 42=154 \times 2 \)
Katie says \( 15 \times 42=(15 \times 4)+(15 \times 2) \)
Who is correct?

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

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


Prompt:
Misconception:
Thinks there are 30 minutes in a hour

Question:
\( 3 \) hours is the same as ___________ minutes

Options:
A. \( 180 \)
B. \( 90 \)
C. \( 30 \)
D. \( 300 \)

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


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

Question:
\( 3 \) hours is the same as ___________ minutes

Options:
A. \( 180 \)
B. \( 90 \)
C. \( 30 \)
D. \( 300 \)

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


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

Question:
\( 3 \) hours is the same as ___________ minutes

Options:
A. \( 180 \)
B. \( 90 \)
C. \( 30 \)
D. \( 300 \)

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


Prompt:
Misconception:
Identifies the term-to-term rule rather than the next term

Question:
What is the next term in this sequence?

\[
18, \quad 11, \quad 4, \quad \ldots
\]

Options:
A. \( -3 \)
B. \( -2 \)
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?

\[
18, \quad 11, \quad 4, \quad \ldots
\]

Options:
A. \( -3 \)
B. \( -2 \)
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:
Thinks there are 10 minutes in an hour

Question:
\( 90 \) minutes is the same as _________ hours

Options:
A. \( 9 \)
B. \( 1.9 \)
C. \( 1.5 \)
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:
Answers as if there are 100 minutes in an hour when writing minutes as decimals

Question:
\( 90 \) minutes is the same as _________ hours

Options:
A. \( 9 \)
B. \( 1.9 \)
C. \( 1.5 \)
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 think a number can be a factor of itself

Question:
\[
1,2,4,8
\]
These are the only factors of...

Options:
A. \( 1 \)
B. \( 8 \)
C. \( 16 \)
D. \( 64 \)

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


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

Question:
\(
\frac{2}{3}-\frac{1}{10}=\frac{\bigstar}{30}
\)
What should replace the star?

Options:
A. \( 13 \)
B. \( 19 \)
C. \( 17 \)
D. \( 1 \)

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


Prompt:
Misconception:
When subtracting fractions, subtracts the numerators and denominators

Question:
\(
\frac{2}{3}-\frac{1}{10}=\frac{\bigstar}{30}
\)
What should replace the star?

Options:
A. \( 13 \)
B. \( 19 \)
C. \( 17 \)
D. \( 1 \)

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


Prompt:
Misconception:
When using inequality notation, thinks "greater than/less than or equal to" symbols are instead the "greater than/less than" symbols and vice versa

Question:
Which of the following shows " \( x \) is greater than or equal to \( 6 \) "?

Options:
A. \( x>6 \)
B. \( x \leq 6 \)
C. \( x<6 \)
D. \( x \geq 6 \)

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


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

Question:
Which of the following shows " \( x \) is greater than or equal to \( 6 \) "?

Options:
A. \( x>6 \)
B. \( x \leq 6 \)
C. \( x<6 \)
D. \( x \geq 6 \)

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 rearrange the Pythagoras' Theorem formula accurately

Question:
STEP \( 2 \)

Jessica is trying to work out the volume of this cone. ![A cone with the slant height labelled 9cm, the perpendicular height labelled h and half the cone's base (forming a right angled triangle with the slant and perpendicular heights) is labelled 6cm.]() First she needs the perpendicular height.

Which of the following equations is true?

Options:
A. \( h^{2}=9^{2}+6^{2} \)
B. \( h^{2}=9^{2}-6^{2} \)
C. \( h^{2}=12^{2}+9^{2} \)
D. \( h^{2}=12^{2}-9^{2} \)

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 using Pythagoras to find the height of an isosceles triangle, uses the whole base instead of half

Question:
STEP \( 2 \)

Jessica is trying to work out the volume of this cone. ![A cone with the slant height labelled 9cm, the perpendicular height labelled h and half the cone's base (forming a right angled triangle with the slant and perpendicular heights) is labelled 6cm.]() First she needs the perpendicular height.

Which of the following equations is true?

Options:
A. \( h^{2}=9^{2}+6^{2} \)
B. \( h^{2}=9^{2}-6^{2} \)
C. \( h^{2}=12^{2}+9^{2} \)
D. \( h^{2}=12^{2}-9^{2} \)

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 mixed numbers, forgets to multiply the fraction

Question:
\(
1 \frac{2}{3} \times 2
\)
Which of the following is a correct way to write the answer to this calculation?

Options:
A. \( 3 \frac{1}{3} \)
B. \( 2 \frac{2}{3} \)
C. \( 1 \frac{4}{3} \)
D. \( 2 \frac{4}{6} \)

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 multiplying a fraction by an integer, multiplies both numerator and denominator by the integer

Question:
\(
1 \frac{2}{3} \times 2
\)
Which of the following is a correct way to write the answer to this calculation?

Options:
A. \( 3 \frac{1}{3} \)
B. \( 2 \frac{2}{3} \)
C. \( 1 \frac{4}{3} \)
D. \( 2 \frac{4}{6} \)

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 added the powers rather than multiplying them

Question:
\( \left(5^{4}\right)^{3}= \)

Options:
A. \( 5^{12} \)
B. \( 5^{7} \)
C. \( 125^{12} \)
D. None of these options

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


Prompt:
Misconception:
Has cubed the base number and the power

Question:
\( \left(5^{4}\right)^{3}= \)

Options:
A. \( 5^{12} \)
B. \( 5^{7} \)
C. \( 125^{12} \)
D. None of these options

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


Prompt:
Misconception:
Does not understand laws of indices

Question:
\( \left(5^{4}\right)^{3}= \)

Options:
A. \( 5^{12} \)
B. \( 5^{7} \)
C. \( 125^{12} \)
D. None of these options

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


Prompt:
Misconception:
Confuses left and right

Question:
If you translate the star \( 2 \) squares left and \( 3 \) squares down, which letter do you land on? ![A set of axes: x-axis from 0 to 8, y-axis from 0 to 8. A yellow star is at point (4, 4). Point A is at (6, 1), Point B is at (2, 1), Point C is at (2, 2), Point D is at (1, 2). ]()

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

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


Prompt:
Misconception:
Counts the squares rather than the diagonals when reflecting in y=x or y=-x

Question:
If you translate the star \( 2 \) squares left and \( 3 \) squares down, which letter do you land on? ![A set of axes: x-axis from 0 to 8, y-axis from 0 to 8. A yellow star is at point (4, 4). Point A is at (6, 1), Point B is at (2, 1), Point C is at (2, 2), Point D is at (1, 2). ]()

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

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


Prompt:
Misconception:
Does not understand the value of zeros as placeholders

Question:
How do you write \( 0.909 \) as a percentage?

Options:
A. \( 99 \% \)
B. \( 909 \% \)
C. \( 90.9 \% \)
D. \( 9.9 \% \)

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


Prompt:
Misconception:
Thinks they just remove the decimal point when converting a decimal to a percentage

Question:
How do you write \( 0.909 \) as a percentage?

Options:
A. \( 99 \% \)
B. \( 909 \% \)
C. \( 90.9 \% \)
D. \( 9.9 \% \)

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


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

Question:
Which of the following is the correct solution to the inequality?

\(
x^{2}<16
\)

Options:
A. \( \{x<-4\} \cup\{x>4\} \)
B. \( \{-4<x<4\} \)
C. \( \{x<4\} \)
D. \( \{-8<x<8\} \)

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


Prompt:
Misconception:
Does not think a square root can be negative

Question:
Which of the following is the correct solution to the inequality?

\(
x^{2}<16
\)

Options:
A. \( \{x<-4\} \cup\{x>4\} \)
B. \( \{-4<x<4\} \)
C. \( \{x<4\} \)
D. \( \{-8<x<8\} \)

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


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

Question:
Which of the following is the correct solution to the inequality?

\(
x^{2}<16
\)

Options:
A. \( \{x<-4\} \cup\{x>4\} \)
B. \( \{-4<x<4\} \)
C. \( \{x<4\} \)
D. \( \{-8<x<8\} \)

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


Prompt:
Misconception:
Confuses triangular prism with pyramid

Question:
Tom and Katie are arguing about prisms.

Tom says this shape is a prism.                                                   Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() 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 definition of a prism

Question:
Tom and Katie are arguing about prisms.

Tom says this shape is a prism.                                                   Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() 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 definition of a prism

Question:
Tom and Katie are arguing about prisms.

Tom says this shape is a prism.                                                   Katie says this shape is a prism. ![A square based pyramid for Tom. A cone for Katie.]() 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 y=-f(x) is a reflection in the y-axis

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

Options:
A. Reflection in the
\[
x \text {-axis }
\]
B. Reflection in the
\[
y \text {-axis }
\]
C. Reflection in the line
\[
y=x
\]
D. Reflection in the line
\[
y=-x
\]

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:
Believes y=-f(x) is a reflection in y=x

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

Options:
A. Reflection in the
\[
x \text {-axis }
\]
B. Reflection in the
\[
y \text {-axis }
\]
C. Reflection in the line
\[
y=x
\]
D. Reflection in the line
\[
y=-x
\]

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:
Believes y=-f(x) is a reflection in y=-x

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

Options:
A. Reflection in the
\[
x \text {-axis }
\]
B. Reflection in the
\[
y \text {-axis }
\]
C. Reflection in the line
\[
y=x
\]
D. Reflection in the line
\[
y=-x
\]

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:
Believes angles on a straight line add to 360 degrees

Question:
![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true?

Options:
A. \( a+b=180^{\circ} \)
B. \( a+b=360^{\circ} \)
C. \( a=b \)
D. \( a+b=90^{\circ} \)

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


Prompt:
Misconception:
Student thinks that any two angles along a straight line are equal

Question:
![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true?

Options:
A. \( a+b=180^{\circ} \)
B. \( a+b=360^{\circ} \)
C. \( a=b \)
D. \( a+b=90^{\circ} \)

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


Prompt:
Misconception:
Thinks there are 180 degrees in a full turn

Question:
![Two angles meeting on a straight line, labelled a degrees and b degrees]() Which of the following is true?

Options:
A. \( a+b=180^{\circ} \)
B. \( a+b=360^{\circ} \)
C. \( a=b \)
D. \( a+b=90^{\circ} \)

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


Prompt:
Misconception:
Thinks terms in linear sequence are in direct proportion

Question:
Here are the first \( 4 \) terms of a linear sequence. ![A sequence of 4 patterns, that are the first 4 terms of a sequence. The first  pattern is a rectangle, made of 3 squares stacked vertically. The second  pattern is an L shape made of 4 squares, it is the same as the first pattern but with 1 square stuck to the right of the square that is at the bottom of the rectangle. The 3rd pattern is an L shape made of 5 squares. It is the same as the 2nd pattern but with 1 more square added to the right of the squares at the bottom. The 4th pattern is an L shape made of 6 squares. It is the same as the 3rd pattern but with 1 more square added to the right of the squares at the bottom ]() How many squares would be in the \( 10^{\text {th }} \) term?

Options:
A. \( 30 \)
B. \( 13 \)
C. \( 12 \)
D. \( 11 \)

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


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

Question:
\( 50.09-0.1= \)

Options:
A. \( 49.99 \)
B. \( 50.99 \)
C. \( 50.08 \)
D. \( 38.98 \)

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


Prompt:
Misconception:
When subtracting decimals with a different number of decimal places, lines up the digits incorrectly

Question:
\( 50.09-0.1= \)

Options:
A. \( 49.99 \)
B. \( 50.99 \)
C. \( 50.08 \)
D. \( 38.98 \)

Solve the problem as a student with the misconception above.
You 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 set notation for complement (eg. A')

Question:
Which element(s) is/are in \( P^{\prime} \) ? ![A diagram showing a Venn diagram of 2 circles. The left circle is for Set P and contains crisps in its left part, sweets in the intersection. The right circle is for set Q and contains pizza in its right part, sweets in the intersection. Outside of the circles it says chocolate.]()

Options:
A. crisps
B. crisps & sweets
C. pizza & chocolate
D. sweets, pizza & chocolate

Solve the problem as a student with the misconception above.
You 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 complement of a set includes any elements which are also in another set.

Question:
Which element(s) is/are in \( P^{\prime} \) ? ![A diagram showing a Venn diagram of 2 circles. The left circle is for Set P and contains crisps in its left part, sweets in the intersection. The right circle is for set Q and contains pizza in its right part, sweets in the intersection. Outside of the circles it says chocolate.]()

Options:
A. crisps
B. crisps & sweets
C. pizza & chocolate
D. sweets, pizza & chocolate

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


Prompt:
Misconception:
Does not reverse the order of operations when finding the input of a function machine

Question:
Look at the function machine. ![An image of two function machines. The first function machine has x as the input. The first function is divide by 3 and the second is +4. The output is 5. The second function machine is the reverse of the first so now 5 is the input but the two function boxes have been left blank.]() What would be the correct steps to solve this equation?
\(\frac{x}{3}+4=5\)

Options:
A. \( \begin{array}{l}\times 3 \\ -4\end{array} \)
B. \( \begin{array}{l}\div 3 \\ +4\end{array} \)
C. \( \begin{array}{r}+4 \\ \times 3\end{array} \)
D. \( \begin{array}{l}-4 \\ \times 3\end{array} \)

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:
Mixes up greater than and less than symbols

Question:
Which number line represents \( -3<x \leq 1 \) ?

Options:
A. ![A number line with a hollow circle above -3 and an arrow coming out of it over the numbers -4, -5 etc and a filled in circle above 1 with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]()
B. ![A number line with a hollow circle above -3 connected to a filled in circle above 1.]()
C. ![A number line with a filled in circle above -3 and an arrow coming out of it over the numbers -4, -5 etc and a hollow circle above 1 with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]()
D. ![A number line with a filled in circle above -3 connected to a hollow circle above 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 representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning.

Question:
Which number line represents \( -3<x \leq 1 \) ?

Options:
A. ![A number line with a hollow circle above -3 and an arrow coming out of it over the numbers -4, -5 etc and a filled in circle above 1 with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]()
B. ![A number line with a hollow circle above -3 connected to a filled in circle above 1.]()
C. ![A number line with a filled in circle above -3 and an arrow coming out of it over the numbers -4, -5 etc and a hollow circle above 1 with an arrow coming out of it over the numbers 2, 3, 4, 5 etc.]()
D. ![A number line with a filled in circle above -3 connected to a hollow circle above 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:
Reads the wrong scale on the protractor when measuring obtuse angles

Question:
Which diagram shows an angle of \( 325^{\circ} \) ?

Options:
A. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 160 and 150 (inner scale) and halfway between 20 and 30 (outer scale).]()
B. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 30 and 20 (inner scale) and halfway between 150 and 160 (outer scale).]()
C. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 150 and 140 (inner scale) and halfway between 30 and 40 (outer scale).]()
D. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 40 and 30 (inner scale) and halfway between 140 and 150 (outer scale).]()

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


Prompt:
Misconception:
Chooses the correct scale when measuring angles on a protractor but starts from the wrong number when the angle is in between two labelled dashes

Question:
Which diagram shows an angle of \( 325^{\circ} \) ?

Options:
A. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 160 and 150 (inner scale) and halfway between 20 and 30 (outer scale).]()
B. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 30 and 20 (inner scale) and halfway between 150 and 160 (outer scale).]()
C. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 150 and 140 (inner scale) and halfway between 30 and 40 (outer scale).]()
D. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 40 and 30 (inner scale) and halfway between 140 and 150 (outer scale).]()

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


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

Question:
Which diagram shows an angle of \( 325^{\circ} \) ?

Options:
A. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 160 and 150 (inner scale) and halfway between 20 and 30 (outer scale).]()
B. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 30 and 20 (inner scale) and halfway between 150 and 160 (outer scale).]()
C. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 150 and 140 (inner scale) and halfway between 30 and 40 (outer scale).]()
D. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out a reflex angle. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, clockwise around to the red line that is half way between 40 and 30 (inner scale) and halfway between 140 and 150 (outer scale).]()

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


Prompt:
Misconception:
Confuses the meaning of parallel and perpendicular

Question:
The two lines marked are... ![Trapezium with parallel sides labelled]()

Options:
A. Perpendicular
B. Vertical
C. Equal
D. Parallel

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


Prompt:
Misconception:
Does not recognise the notation for parallel sides

Question:
The two lines marked are... ![Trapezium with parallel sides labelled]()

Options:
A. Perpendicular
B. Vertical
C. Equal
D. Parallel

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


Prompt:
Misconception:
Does not recognise the notation for parallel sides

Question:
The two lines marked are... ![Trapezium with parallel sides labelled]()

Options:
A. Perpendicular
B. Vertical
C. Equal
D. Parallel

Solve the problem as a student with the misconception above.
You 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 subscript in iteration notation is the value to be substituted

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

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

If \( x_{0}=0 \), what does \( x_{1} \) equal? ![A rectangle with the base labelled x and the perpendicular height labelled x^2 + 9]()

Options:
A. \( \frac{8}{9} \)
B. \( \frac{7}{9} \)
C. \( 0 \)
D. \( \frac{1}{9} \)

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


Prompt:
Misconception:
Believes adjacent sides of a rhombus are always perpendicular

Question:
\( A B C D \) is a rhombus.
Which lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]()

Options:
A. \( A B \) and \( B C \)
B. \( A C \) and \( D B \)
C. \( A B \) and \( D C \)
D. None of them

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


Prompt:
Misconception:
Confuses the meaning of parallel and perpendicular

Question:
\( A B C D \) is a rhombus.
Which lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]()

Options:
A. \( A B \) and \( B C \)
B. \( A C \) and \( D B \)
C. \( A B \) and \( D C \)
D. None of them

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

Question:
\( A B C D \) is a rhombus.
Which lines must be perpendicular? ![Tilted rhombus with top left vertex labelled A, top right vertex labelled B, bottom left vertex labelled D and bottom right vertex labelled C.]()

Options:
A. \( A B \) and \( B C \)
B. \( A C \) and \( D B \)
C. \( A B \) and \( D C \)
D. None of them

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


Prompt:
Misconception:
Believes the gradient of a line is given by an intercept

Question:
What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the following points: (-3,-3) (-2,-2) (-1,-1) (0,0) (1,1) (2,2) and (3,3).]()

Options:
A. \( 0 \)
B. \( 2 \)
C. \( x \)
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 gradient of a line includes the variable x

Question:
What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the following points: (-3,-3) (-2,-2) (-1,-1) (0,0) (1,1) (2,2) and (3,3).]()

Options:
A. \( 0 \)
B. \( 2 \)
C. \( x \)
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:
Does not understand the value of zeros as placeholders

Question:
How do you write this number in words?

\( 60302 \)

Options:
A. Six hundred and thirty-two
B. Six thousand three hundred and two
C. Sixty thousand and thirty-two
D. Sixty thousand three hundred and two

Solve the problem as a student with the misconception above.
You 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 words?

\( 60302 \)

Options:
A. Six hundred and thirty-two
B. Six thousand three hundred and two
C. Sixty thousand and thirty-two
D. Sixty thousand three hundred and two

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


Prompt:
Misconception:
Confuses the hundreds and tens place value columns

Question:
How do you write this number in words?

\( 60302 \)

Options:
A. Six hundred and thirty-two
B. Six thousand three hundred and two
C. Sixty thousand and thirty-two
D. Sixty thousand three hundred and two

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


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

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

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

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


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

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

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

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


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

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

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

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


Prompt:
Misconception:
When the dividend is a mixed number and the divisor is an integer, thinks they only perform the calculation with the integers.

Question:
\(
2 \frac{2}{3} \div 2
\)
Which of the following is a correct way to write the answer to this calculation?

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

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 the dividend is a mixed number and the divisor is an integer, thinks they only divide the fraction by the integer.

Question:
\(
2 \frac{2}{3} \div 2
\)
Which of the following is a correct way to write the answer to this calculation?

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

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 division is commutative

Question:
\(
2 \frac{2}{3} \div 2
\)
Which of the following is a correct way to write the answer to this calculation?

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

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:
Mistakes unit of speed for unit of time

Question:
Tom and Katie are discussing units of time
Tom says days is a unit of time
Katie says \( \mathrm{km} / \mathrm{h} \) is a unit of time
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:
Mistakes unit of speed for unit of time

Question:
Tom and Katie are discussing units of time
Tom says days is a unit of time
Katie says \( \mathrm{km} / \mathrm{h} \) is a unit of time
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 recognise a unit of time

Question:
Tom and Katie are discussing units of time
Tom says days is a unit of time
Katie says \( \mathrm{km} / \mathrm{h} \) is a unit of time
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 a negative power results in a negative answer

Question:
\(
F=3^{a}
\)

What is the value of \( F \) when \( a=-5 \) ?

Options:
A. \( -243 \)
B. \( -\frac{1}{243} \)
C. \( -15 \)
D. \( \frac{1}{243} \)

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


Prompt:
Misconception:
Believes a negative power results in a negative answer

Question:
\(
F=3^{a}
\)

What is the value of \( F \) when \( a=-5 \) ?

Options:
A. \( -243 \)
B. \( -\frac{1}{243} \)
C. \( -15 \)
D. \( \frac{1}{243} \)

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


Prompt:
Misconception:
Has multiplied the base number and the power

Question:
\(
F=3^{a}
\)

What is the value of \( F \) when \( a=-5 \) ?

Options:
A. \( -243 \)
B. \( -\frac{1}{243} \)
C. \( -15 \)
D. \( \frac{1}{243} \)

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


Prompt:
Misconception:
Forgets to carry the tens when doing column multiplication

Question:
Charlotte is trying to solve this problem using long multiplication.

What should replace the star as the tens digit in her final answer? \( 538 \times 7 \) \begin{tabular}{r|r|r|r|}
\(\space\) & \( 5 \) & \( 3 \) & \( 8 \) \\
\( \times \) & \(\space\) & \(\space\) & \( 7 \) \\
\hline & \(\space\) & \(\bigstar\) & \\
\hline
\end{tabular}

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

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


Prompt:
Misconception:
Tries to multiply within place value columns during column multiplication

Question:
Charlotte is trying to solve this problem using long multiplication.

What should replace the star as the tens digit in her final answer? \( 538 \times 7 \) \begin{tabular}{r|r|r|r|}
\(\space\) & \( 5 \) & \( 3 \) & \( 8 \) \\
\( \times \) & \(\space\) & \(\space\) & \( 7 \) \\
\hline & \(\space\) & \(\bigstar\) & \\
\hline
\end{tabular}

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

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


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

Question:
Which of these could be used as a counter - example to disprove Katie's theory that \( 2 n^{2}-1 \) is positive?

Options:
A. \( 2\left(\frac{3}{4}\right)^{2}-1 \)
B. \( 2(0.5)^{2}-1 \)
C. \( 2(-2)^{2}-1 \)
D. \( 2(-1)^{2}-1 \)

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


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

Question:
Which of these could be used as a counter - example to disprove Katie's theory that \( 2 n^{2}-1 \) is positive?

Options:
A. \( 2\left(\frac{3}{4}\right)^{2}-1 \)
B. \( 2(0.5)^{2}-1 \)
C. \( 2(-2)^{2}-1 \)
D. \( 2(-1)^{2}-1 \)

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


Prompt:
Misconception:
Believes subtraction is commutative

Question:
What is the value of \( l \) in these simultaneous equations?
\(
\begin{array}{l}
2 l+3 m=13 \\
3 l+4 m=17
\end{array}
\)

Options:
A. \( l=-1 \)
B. \( l=5 \)
C. \( l=1 \)
D. \( l=4 \)

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 multiplying a fraction by an integer, multiplies the denominator instead of the numerator

Question:
\( \frac{1}{3} \times(-6)= \)

Options:
A. \( -18 \)
B. \( -\frac{6}{18} \)
C. \( -2 \)
D. \( -\frac{1}{18} \)

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
Tom and Katie are discussing bar models. Tom says this bar model represents \( 5 x \) \begin{tabular}{l|l}
\hline \( 5 \) & \( x \) \\
\hline
\end{tabular} Katie says this bar model represents \( 5 x \) \begin{tabular}{l|l|l|l|l|}
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) \\
\hline
\end{tabular} Who do you agree with?

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

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
Tom and Katie are discussing bar models. Tom says this bar model represents \( 5 x \) \begin{tabular}{l|l}
\hline \( 5 \) & \( x \) \\
\hline
\end{tabular} Katie says this bar model represents \( 5 x \) \begin{tabular}{l|l|l|l|l|}
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) \\
\hline
\end{tabular} Who do you agree with?

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

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
Tom and Katie are discussing bar models. Tom says this bar model represents \( 5 x \) \begin{tabular}{l|l}
\hline \( 5 \) & \( x \) \\
\hline
\end{tabular} Katie says this bar model represents \( 5 x \) \begin{tabular}{l|l|l|l|l|}
\( x \) & \( x \) & \( x \) & \( x \) & \( x \) \\
\hline
\end{tabular} Who do you agree with?

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

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


Prompt:
Misconception:
Thinks that only the sides need to be equal for a polygon to be regular

Question:
Tom and Katie are discussing regular polygons Tom says this is a regular polygon: ![A rhombus]() Katie says this is a regular polygon: ![A rectangle]() Who is correct?

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

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


Prompt:
Misconception:
Thinks that only the angles need to be the same for a polygon to be regular

Question:
Tom and Katie are discussing regular polygons Tom says this is a regular polygon: ![A rhombus]() Katie says this is a regular polygon: ![A rectangle]() Who is correct?

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

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


Prompt:
Misconception:
Does not understand that all angles and sides must be equal for regular shapes

Question:
Tom and Katie are discussing regular polygons Tom says this is a regular polygon: ![A rhombus]() Katie says this is a regular polygon: ![A rectangle]() 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:
Mixes up squaring and multiplying by 2 or doubling

Question:
This is a part of the table of values for the equation
\(
y=x^{2}-1
\) \begin{tabular}{|c|c|}
\hline\( x \) & \( 5 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 24 \)
B. \( 9 \)
C. \( 16 \)
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:
Believes order of operations does not affect the answer to a calculation

Question:
This is a part of the table of values for the equation
\(
y=x^{2}-1
\) \begin{tabular}{|c|c|}
\hline\( x \) & \( 5 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 24 \)
B. \( 9 \)
C. \( 16 \)
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 subtracting a negative number, adds the absolute values and then writes the answer with a negative sign

Question:
Mo wants to solve this equation using the quadratic formula.
\(
5 h^{2}-3 h-2=0
\)

What total should replace the square? \( \begin{array}{l} \frac{ ?\pm \sqrt{9-(-40)}}{?} \\ = \frac{ ?\pm \sqrt{\square}}{?} \end{array} \)

Options:
A. \( 31 \)
B. \( -49 \)
C. \( 49 \)
D. \( -31 \)

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


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

Question:
Mo wants to solve this equation using the quadratic formula.
\(
5 h^{2}-3 h-2=0
\)

What total should replace the square? \( \begin{array}{l} \frac{ ?\pm \sqrt{9-(-40)}}{?} \\ = \frac{ ?\pm \sqrt{\square}}{?} \end{array} \)

Options:
A. \( 31 \)
B. \( -49 \)
C. \( 49 \)
D. \( -31 \)

Solve the problem as a student with the misconception above.
You 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 a single letter labels a vertex

Question:
Which of the following is a correct way to describe the highlighted side of this shape? ![A  4 sided shape with two pairs of parallel sides. Each vertex (corner) is labelled with a letter. The bottom right is S, the bottom left is P, the top left is Q and the top right is R. The side joining P and Q is highlighted in red.]()

Options:
A. \( Q \)
B. P
C. QPRS
D. \( Q P \)

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


Prompt:
Misconception:
Does not know that a single letter labels a vertex

Question:
Which of the following is a correct way to describe the highlighted side of this shape? ![A  4 sided shape with two pairs of parallel sides. Each vertex (corner) is labelled with a letter. The bottom right is S, the bottom left is P, the top left is Q and the top right is R. The side joining P and Q is highlighted in red.]()

Options:
A. \( Q \)
B. P
C. QPRS
D. \( Q P \)

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


Prompt:
Misconception:
Does not know the correct notation for labelling a side length

Question:
Which of the following is a correct way to describe the highlighted side of this shape? ![A  4 sided shape with two pairs of parallel sides. Each vertex (corner) is labelled with a letter. The bottom right is S, the bottom left is P, the top left is Q and the top right is R. The side joining P and Q is highlighted in red.]()

Options:
A. \( Q \)
B. P
C. QPRS
D. \( Q P \)

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


Prompt:
Misconception:
Adds instead of multiplies when multiplying algebraic terms

Question:
\( 5 p^{2} \times 2 p q \equiv \)

Options:
A. \( 10 p q^{3} \)
B. \( 10 p^{3} q \)
C. \( 7 p^{3} q \)
D. Does not simplify

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


Prompt:
Misconception:
Does not understand how to multiply algebraic terms

Question:
\( 5 p^{2} \times 2 p q \equiv \)

Options:
A. \( 10 p q^{3} \)
B. \( 10 p^{3} q \)
C. \( 7 p^{3} q \)
D. Does not simplify

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


Prompt:
Misconception:
Does not know how to use a bar model to write division facts

Question:
Tom and Katie are discussing this bar model ![A comparison bar model showing 188 is the same as four lots of 47]() Tom uses the bar model to write:
\[
188 \div 4=47
\] Katie uses the bar model to write:
\[
188 \div 47=4
\] Who do you agree with?

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

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


Prompt:
Misconception:
Does not know how to use a bar model to write division facts

Question:
Tom and Katie are discussing this bar model ![A comparison bar model showing 188 is the same as four lots of 47]() Tom uses the bar model to write:
\[
188 \div 4=47
\] Katie uses the bar model to write:
\[
188 \div 47=4
\] Who do you agree with?

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

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


Prompt:
Misconception:
Does not know how to use a bar model to write division facts

Question:
Tom and Katie are discussing this bar model ![A comparison bar model showing 188 is the same as four lots of 47]() Tom uses the bar model to write:
\[
188 \div 4=47
\] Katie uses the bar model to write:
\[
188 \div 47=4
\] Who do you agree with?

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

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


Prompt:
Misconception:
Believes an outlier is a value that does not fit the same characteristics as the other values

Question:
\begin{tabular}{llllll}
\( \frac{2}{10} \) & \( \frac{9}{50} \) & \( \frac{9}{20} \) & \( 0.21 \) & \( \frac{1}{5} \) & \( \frac{19}{100} \) \\
\hline
\end{tabular} Which value is the outlier in this set of data?

Options:
A. \( \frac{2}{10} \)
B. \( \frac{19}{100} \)
C. \( 0.21 \)
D. \( \frac{9}{20} \)

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


Prompt:
Misconception:
Believes an outlier is the value in a data set with the biggest denominator, even if this value is close to the mean

Question:
\begin{tabular}{llllll}
\( \frac{2}{10} \) & \( \frac{9}{50} \) & \( \frac{9}{20} \) & \( 0.21 \) & \( \frac{1}{5} \) & \( \frac{19}{100} \) \\
\hline
\end{tabular} Which value is the outlier in this set of data?

Options:
A. \( \frac{2}{10} \)
B. \( \frac{19}{100} \)
C. \( 0.21 \)
D. \( \frac{9}{20} \)

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


Prompt:
Misconception:
Believes an outlier is a value that does not fit the same characteristics as the other values

Question:
\begin{tabular}{llllll}
\( \frac{2}{10} \) & \( \frac{9}{50} \) & \( \frac{9}{20} \) & \( 0.21 \) & \( \frac{1}{5} \) & \( \frac{19}{100} \) \\
\hline
\end{tabular} Which value is the outlier in this set of data?

Options:
A. \( \frac{2}{10} \)
B. \( \frac{19}{100} \)
C. \( 0.21 \)
D. \( \frac{9}{20} \)

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


Prompt:
Misconception:
Incorrectly identifies angles as vertically opposite

Question:
What is the size of angle \( x \) ? ![Angles around a point, split into 2 parts. One is labelled 310 degrees and the other x.]()

Options:
A. \( 310^{\circ} \)
B. \( 50^{\circ} \)
C. \( 90^{\circ} \)
D. \( 45^{\circ} \)

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


Prompt:
Misconception:
Does not know that angles around a point sum to 360

Question:
What is the size of angle \( x \) ? ![Angles around a point, split into 2 parts. One is labelled 310 degrees and the other x.]()

Options:
A. \( 310^{\circ} \)
B. \( 50^{\circ} \)
C. \( 90^{\circ} \)
D. \( 45^{\circ} \)

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


Prompt:
Misconception:
Estimates angle rather than calculating

Question:
What is the size of angle \( x \) ? ![Angles around a point, split into 2 parts. One is labelled 310 degrees and the other x.]()

Options:
A. \( 310^{\circ} \)
B. \( 50^{\circ} \)
C. \( 90^{\circ} \)
D. \( 45^{\circ} \)

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


Prompt:
Misconception:
Misunderstands the concept of common factors in algebra

Question:
Write the following as simply as possible:
\(
\frac{(x+3)(x+5)}{(x+3)(x+10)}
\)

Options:
A. \( \frac{x+1}{x+2} \)
B. \( \frac{x+5}{x+10} \)
C. \( \frac{x^{2}+8 x+15}{x^{2}+13 x+30} \)
D. \( \frac{1}{2} \)

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


Prompt:
Misconception:
Expands when asked to simplify

Question:
Write the following as simply as possible:
\(
\frac{(x+3)(x+5)}{(x+3)(x+10)}
\)

Options:
A. \( \frac{x+1}{x+2} \)
B. \( \frac{x+5}{x+10} \)
C. \( \frac{x^{2}+8 x+15}{x^{2}+13 x+30} \)
D. \( \frac{1}{2} \)

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