Prompt:
Misconception:
Rounds too early in calculation

Question:
This is a part of the table of values for the equation
\[
y=3 x
\] ![A table with two rows and two columns. The top left box has 'x', top right has a star, the bottom left box has 'y', bottom right has '-1'. ]() What should replace the star?

Options:
A. \( -3 \)
B. \( -0.3 \)
C. \( -\frac{1}{3} \)
D. There is no possible solution

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


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

Question:
\( \frac{1}{5} \) of \( 35= \)

Options:
A. \( 7 \)
B. \( 5 \)
C. \( 3 \)
D. \( 30 \)

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


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

Question:
What is the first cube number greater than \( 100 ? \)

Options:
A. \( 103 \)
B. \( 125 \)
C. \( 121 \)
D. \( 102 \)

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


Prompt:
Misconception:
Mixes up square numbers and cube numbers

Question:
What is the first cube number greater than \( 100 ? \)

Options:
A. \( 103 \)
B. \( 125 \)
C. \( 121 \)
D. \( 102 \)

Solve the problem as a student with the misconception above.
You 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 cube numbers are just multiples of 3

Question:
What is the first cube number greater than \( 100 ? \)

Options:
A. \( 103 \)
B. \( 125 \)
C. \( 121 \)
D. \( 102 \)

Solve the problem as a student with the misconception above.
You 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 fractions multiplies by the reciprocal of the 2nd fraction instead

Question:
Write this as a single fraction as simply as possible: \( \frac{5}{x-3} \times \frac{x^{2}}{2 y} \)

Options:
A. \( \frac{10 y}{x^{2}(x-3)} \)
B. \( \frac{5 x^{2}}{2 y(x-3)} \)
C. \( \frac{5 x^{2}}{x-6 y} \)
D. \( \frac{5 x^{2}}{2 x y-3} \)

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 second term in the expansion of a bracket

Question:
Write this as a single fraction as simply as possible: \( \frac{5}{x-3} \times \frac{x^{2}}{2 y} \)

Options:
A. \( \frac{10 y}{x^{2}(x-3)} \)
B. \( \frac{5 x^{2}}{2 y(x-3)} \)
C. \( \frac{5 x^{2}}{x-6 y} \)
D. \( \frac{5 x^{2}}{2 x y-3} \)

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:
Write this as a single fraction as simply as possible: \( \frac{5}{x-3} \times \frac{x^{2}}{2 y} \)

Options:
A. \( \frac{10 y}{x^{2}(x-3)} \)
B. \( \frac{5 x^{2}}{2 y(x-3)} \)
C. \( \frac{5 x^{2}}{x-6 y} \)
D. \( \frac{5 x^{2}}{2 x y-3} \)

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


Prompt:
Misconception:
Confuses the terms faces and edges

Question:
![Line drawing of a triangular prism]() How many faces does this prism have?

Options:
A. \( 5 \)
B. \( 9 \)
C. \( 6 \)
D. \( 3 \)

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


Prompt:
Misconception:
Confuses the terms faces and vertices

Question:
![Line drawing of a triangular prism]() How many faces does this prism have?

Options:
A. \( 5 \)
B. \( 9 \)
C. \( 6 \)
D. \( 3 \)

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


Prompt:
Misconception:
Does not know the definition of a prism

Question:
![Line drawing of a triangular prism]() How many faces does this prism have?

Options:
A. \( 5 \)
B. \( 9 \)
C. \( 6 \)
D. \( 3 \)

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


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

Question:
What is the next term of this linear sequence?
\[
3,9,15,21, \ldots
\]

Options:
A. \( 22 \)
B. \( 27 \)
C. \( 24 \)
D. \( 28 \)

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


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

Question:
Problem P: \( (4+5)^{2}= \)
Problem Q: \( 4+5^{2}= \)

Which calculation should you do first in each problem?

Options:
A. Problem P: \( 4+5 \)
Problem Q: \( 4+5 \)
B. Problem P: \( 4+5 \)
Problem Q: \( 5^{2} \)
C. Problem P: \( 5^{2} \)
Problem Q: \( 4+5 \)
D. Problem P: \( 5^{2} \)
Problem Q: \( 5^{2} \)

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


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

Question:
Problem P: \( (4+5)^{2}= \)
Problem Q: \( 4+5^{2}= \)

Which calculation should you do first in each problem?

Options:
A. Problem P: \( 4+5 \)
Problem Q: \( 4+5 \)
B. Problem P: \( 4+5 \)
Problem Q: \( 5^{2} \)
C. Problem P: \( 5^{2} \)
Problem Q: \( 4+5 \)
D. Problem P: \( 5^{2} \)
Problem Q: \( 5^{2} \)

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


Prompt:
Misconception:
Believes that a number divided by itself equals 0

Question:
Solve the equation:
\(12 d-3=6 d+3\)

Options:
A. \( d=0 \)
B. \( d=1 \)
C. \( d=-1 \)
D. \( d=\frac{1}{3} \)

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


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

Question:
Solve the equation:
\(12 d-3=6 d+3\)

Options:
A. \( d=0 \)
B. \( d=1 \)
C. \( d=-1 \)
D. \( d=\frac{1}{3} \)

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


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

Question:
Solve the equation:
\(12 d-3=6 d+3\)

Options:
A. \( d=0 \)
B. \( d=1 \)
C. \( d=-1 \)
D. \( d=\frac{1}{3} \)

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


Prompt:
Misconception:
When subtracting from a negative thinks the answer must be positive

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

Options:
A. \( 2 \)
B. \( -2 \)
C. \( 8 \)
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 from a negative thinks the answer must be positive

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

Options:
A. \( 2 \)
B. \( -2 \)
C. \( 8 \)
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:
Confuses the variable and frequency columns in a frequency table

Question:
\begin{tabular}{|c|c|c|}
\hline TVs & Frequency & TVs \( \times \) Frequency \\
\hline \( 0 \) & \( 5 \) & \( 0 \) \\
\hline \( 1 \) & \( 8 \) & \( 8 \) \\
\hline \( 2 \) & \( 7 \) & \( 14 \) \\
\hline \( 3 \) & \( 4 \) & \( 12 \) \\
\hline \( 4 \) & \( 4 \) & \( 16 \) \\
\hline
\end{tabular} The table shows the numbers of TVs in the households of students in a class.

What does the "14" represent?

Options:
A. How many people who live in the \( 7 \) households
B. The total number of TVs in the \( 2 \) households
C. The mean number of TVs in the \( 7 \) households
D. The total number of TVs in the \( 7 \) households

Solve the problem as a student with the misconception above.
You 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 interpretation of the fx column in a frequency table

Question:
\begin{tabular}{|c|c|c|}
\hline TVs & Frequency & TVs \( \times \) Frequency \\
\hline \( 0 \) & \( 5 \) & \( 0 \) \\
\hline \( 1 \) & \( 8 \) & \( 8 \) \\
\hline \( 2 \) & \( 7 \) & \( 14 \) \\
\hline \( 3 \) & \( 4 \) & \( 12 \) \\
\hline \( 4 \) & \( 4 \) & \( 16 \) \\
\hline
\end{tabular} The table shows the numbers of TVs in the households of students in a class.

What does the "14" represent?

Options:
A. How many people who live in the \( 7 \) households
B. The total number of TVs in the \( 2 \) households
C. The mean number of TVs in the \( 7 \) households
D. The total number of TVs in the \( 7 \) households

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


Prompt:
Misconception:
Believes the solution to mx + c = a is the x intercept of y = mx +c

Question:
This is a graph of
\(y=4 x-1\) ![A set of axes with y=4x-1 drawn on.]() Use the graph to solve
\(4 x-1=-3\)

Options:
A. \( x=0.25 \)
B. \( x=-3 \)
C. \( x=-0.5 \)
D. No 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 the solution of mx + c = a is x =a

Question:
This is a graph of
\(y=4 x-1\) ![A set of axes with y=4x-1 drawn on.]() Use the graph to solve
\(4 x-1=-3\)

Options:
A. \( x=0.25 \)
B. \( x=-3 \)
C. \( x=-0.5 \)
D. No 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:
Adds instead of multiplies

Question:
\( \frac{1}{2} \times 3= \)

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

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


Prompt:
Misconception:
When multiplying fractions, multiplies both the numerator and denominator

Question:
\( \frac{1}{2} \times 3= \)

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

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


Prompt:
Misconception:
When multiplying fractions, multiplies the denominator

Question:
\( \frac{1}{2} \times 3= \)

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

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


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

Question:
This is the graph of \( y=5-0.5 x \) According to the graph, what is the solution to: \( 5-0.5 x=6 \) ![Graph showing straight line with y intercept (0,5) and x intercept (10,0)]()

Options:
A. \( x=-2 \)
B. \( x=2 \)
C. \( x=5 \)
D. \( x=10 \)

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


Prompt:
Misconception:
Believes the solution to mx + c = a is the y intercept of y = mx +c

Question:
This is the graph of \( y=5-0.5 x \) According to the graph, what is the solution to: \( 5-0.5 x=6 \) ![Graph showing straight line with y intercept (0,5) and x intercept (10,0)]()

Options:
A. \( x=-2 \)
B. \( x=2 \)
C. \( x=5 \)
D. \( x=10 \)

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


Prompt:
Misconception:
Believes the solution to mx + c = a is the x intercept of y = mx +c

Question:
This is the graph of \( y=5-0.5 x \) According to the graph, what is the solution to: \( 5-0.5 x=6 \) ![Graph showing straight line with y intercept (0,5) and x intercept (10,0)]()

Options:
A. \( x=-2 \)
B. \( x=2 \)
C. \( x=5 \)
D. \( x=10 \)

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 multiplying two negatives gives a negative answer

Question:
Which of the following could be the equation of the curve? ![A negative  quadratic graph that crosses the x-axis at (-5,0) and (1,0).]()

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

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 that a positive x squared coefficient in a quadratic equation results in an n shaped graph

Question:
Which of the following could be the equation of the curve? ![A negative  quadratic graph that crosses the x-axis at (-5,0) and (1,0).]()

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

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 that a positive x squared coefficient in a quadratic equation results in an n shaped graph

Question:
Which of the following could be the equation of the curve? ![A negative  quadratic graph that crosses the x-axis at (-5,0) and (1,0).]()

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

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:
Counts the starting number when counting backwards

Question:
![A number line going from -8 up to 7]() Asha's office is on level \( 7 \).
Her car is parked in the basement on level \( -2 \).

How many floors does Asha need to go down to get from the office to her car?

Options:
A. \( 10 \)
B. \( 5 \)
C. \( 9 \)
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:
Thinks the difference between a positive number and a negative number is equal to the positive number

Question:
![A number line going from -8 up to 7]() Asha's office is on level \( 7 \).
Her car is parked in the basement on level \( -2 \).

How many floors does Asha need to go down to get from the office to her car?

Options:
A. \( 10 \)
B. \( 5 \)
C. \( 9 \)
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:
Believes they only need to multiply the first and last pairs of terms when expanding double brackets

Question:
Which of the following answers shows a correct expansion and simplification of the expression below? \( (x-4)^{2} \)

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

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


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

Question:
Which of the following answers shows a correct expansion and simplification of the expression below? \( (x-4)^{2} \)

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

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


Prompt:
Misconception:
Does not copy a given method accurately

Question:
This is how Ron calculates the answer to \( 46+28 \) mentally "\( 46+20 \) is equal to \( 66 \). Then I am going to add on the \( 8\). \(66+8=74 \)" Ron uses the same method to calculate \( 37+56 \). Which of the following shows how he would do this?

Options:
A. \( \begin{array}{c}37+6=43 \\ 43+50=93\end{array} \)
B. \( \begin{array}{c}37+50=87 \\ 87+6=93\end{array} \)
C. \( \begin{array}{c}30+50=80 \\ 7+6=13 \\ 80+13=93\end{array} \)
D. \( \begin{array}{c}7+6=13 \\ 30+13=43 \\ 43+50=93\end{array} \)

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


Prompt:
Misconception:
Does not copy a given method accurately

Question:
This is how Ron calculates the answer to \( 46+28 \) mentally "\( 46+20 \) is equal to \( 66 \). Then I am going to add on the \( 8\). \(66+8=74 \)" Ron uses the same method to calculate \( 37+56 \). Which of the following shows how he would do this?

Options:
A. \( \begin{array}{c}37+6=43 \\ 43+50=93\end{array} \)
B. \( \begin{array}{c}37+50=87 \\ 87+6=93\end{array} \)
C. \( \begin{array}{c}30+50=80 \\ 7+6=13 \\ 80+13=93\end{array} \)
D. \( \begin{array}{c}7+6=13 \\ 30+13=43 \\ 43+50=93\end{array} \)

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


Prompt:
Misconception:
Does not copy a given method accurately

Question:
This is how Ron calculates the answer to \( 46+28 \) mentally "\( 46+20 \) is equal to \( 66 \). Then I am going to add on the \( 8\). \(66+8=74 \)" Ron uses the same method to calculate \( 37+56 \). Which of the following shows how he would do this?

Options:
A. \( \begin{array}{c}37+6=43 \\ 43+50=93\end{array} \)
B. \( \begin{array}{c}37+50=87 \\ 87+6=93\end{array} \)
C. \( \begin{array}{c}30+50=80 \\ 7+6=13 \\ 80+13=93\end{array} \)
D. \( \begin{array}{c}7+6=13 \\ 30+13=43 \\ 43+50=93\end{array} \)

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 mean is total divided by sum of categories given

Question:
What is the mean shoe size? \begin{tabular}{|c|c|}
\hline Shoe Size \( (\mathrm{s}) \) & Frequency \( (f) \) \\
\hline \( 2 \) & \( 5 \) \\
\hline \( 3 \) & \( 8 \) \\
\hline \( 4 \) & \( 9 \) \\
\hline \( 5 \) & \( 5 \) \\
\hline \( 6 \) & \( 3 \) \\
\hline
\end{tabular}

Options:
A. A \( \quad 3.77 \)
B. B \( \quad 5.65 \)
C. C \( \quad \mathbf{1 . 5 0} \)
D. D \( \quad 22.6 \)

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 mean is total frequency divided by sum of categories given

Question:
What is the mean shoe size? \begin{tabular}{|c|c|}
\hline Shoe Size \( (\mathrm{s}) \) & Frequency \( (f) \) \\
\hline \( 2 \) & \( 5 \) \\
\hline \( 3 \) & \( 8 \) \\
\hline \( 4 \) & \( 9 \) \\
\hline \( 5 \) & \( 5 \) \\
\hline \( 6 \) & \( 3 \) \\
\hline
\end{tabular}

Options:
A. A \( \quad 3.77 \)
B. B \( \quad 5.65 \)
C. C \( \quad \mathbf{1 . 5 0} \)
D. D \( \quad 22.6 \)

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 mean is total divided by number of groups

Question:
What is the mean shoe size? \begin{tabular}{|c|c|}
\hline Shoe Size \( (\mathrm{s}) \) & Frequency \( (f) \) \\
\hline \( 2 \) & \( 5 \) \\
\hline \( 3 \) & \( 8 \) \\
\hline \( 4 \) & \( 9 \) \\
\hline \( 5 \) & \( 5 \) \\
\hline \( 6 \) & \( 3 \) \\
\hline
\end{tabular}

Options:
A. A \( \quad 3.77 \)
B. B \( \quad 5.65 \)
C. C \( \quad \mathbf{1 . 5 0} \)
D. D \( \quad 22.6 \)

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 given a linear sequence, cannot match it to a visual pattern

Question:
\[
1,3,5,7, \ldots ?
\]

Which pattern matches the sequence above?

Options:
A. ![A sequence of 4 patterns. The first pattern is 1 green dot. The second pattern is green dots arranged in a 2 by 2 square shape. The third pattern is green dots arranged in a 3 by 3 square shape. The fourth pattern is green dots arranged in a 4 by 4 square shape. ]()
B. ![A sequence of 4 patterns. The first pattern is one small cube. The other patterns are larger cubes made from small cubes like the one in the first pattern: Pattern 2 is a cube of width 2; Pattern 3 is a cube of width 3; Pattern 4 is a cube of width 4.]()
C. ![A sequence of 4 patterns. The first pattern is one blue dot. The other patterns are triangles, made from blue dots like the one in the first pattern: Pattern 2 has 2 dots on the bottom and 1 dot above these; Pattern 3 is the same as Pattern 2 but with 3 extra dots that form a 3rd row at the bottom; Pattern 4 is the same as Pattern 3 but with 4 extra dots forming a 4th row at the bottom.]()
D. ![A sequence of 4 patterns. The first pattern is one red dot. The other patterns are made from multiple red dots: Pattern 2 is like a 2 by 2 square of dots but with the top left dot missing; Pattern 3 is like a 2 (width) by 3 rectangle of dots but with the top left dot missing; Pattern 4 is like a 2 (width) by 4 rectangle of dots but with the top left dot missing;]()

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


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

Question:
\[
1,3,5,7, \ldots ?
\]

Which pattern matches the sequence above?

Options:
A. ![A sequence of 4 patterns. The first pattern is 1 green dot. The second pattern is green dots arranged in a 2 by 2 square shape. The third pattern is green dots arranged in a 3 by 3 square shape. The fourth pattern is green dots arranged in a 4 by 4 square shape. ]()
B. ![A sequence of 4 patterns. The first pattern is one small cube. The other patterns are larger cubes made from small cubes like the one in the first pattern: Pattern 2 is a cube of width 2; Pattern 3 is a cube of width 3; Pattern 4 is a cube of width 4.]()
C. ![A sequence of 4 patterns. The first pattern is one blue dot. The other patterns are triangles, made from blue dots like the one in the first pattern: Pattern 2 has 2 dots on the bottom and 1 dot above these; Pattern 3 is the same as Pattern 2 but with 3 extra dots that form a 3rd row at the bottom; Pattern 4 is the same as Pattern 3 but with 4 extra dots forming a 4th row at the bottom.]()
D. ![A sequence of 4 patterns. The first pattern is one red dot. The other patterns are made from multiple red dots: Pattern 2 is like a 2 by 2 square of dots but with the top left dot missing; Pattern 3 is like a 2 (width) by 3 rectangle of dots but with the top left dot missing; Pattern 4 is like a 2 (width) by 4 rectangle of dots but with the top left dot missing;]()

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


Prompt:
Misconception:
Uses only the first two terms of a sequence to work out a term-to-term rule

Question:
\[
1,3,5,7, \ldots ?
\]

Which pattern matches the sequence above?

Options:
A. ![A sequence of 4 patterns. The first pattern is 1 green dot. The second pattern is green dots arranged in a 2 by 2 square shape. The third pattern is green dots arranged in a 3 by 3 square shape. The fourth pattern is green dots arranged in a 4 by 4 square shape. ]()
B. ![A sequence of 4 patterns. The first pattern is one small cube. The other patterns are larger cubes made from small cubes like the one in the first pattern: Pattern 2 is a cube of width 2; Pattern 3 is a cube of width 3; Pattern 4 is a cube of width 4.]()
C. ![A sequence of 4 patterns. The first pattern is one blue dot. The other patterns are triangles, made from blue dots like the one in the first pattern: Pattern 2 has 2 dots on the bottom and 1 dot above these; Pattern 3 is the same as Pattern 2 but with 3 extra dots that form a 3rd row at the bottom; Pattern 4 is the same as Pattern 3 but with 4 extra dots forming a 4th row at the bottom.]()
D. ![A sequence of 4 patterns. The first pattern is one red dot. The other patterns are made from multiple red dots: Pattern 2 is like a 2 by 2 square of dots but with the top left dot missing; Pattern 3 is like a 2 (width) by 3 rectangle of dots but with the top left dot missing; Pattern 4 is like a 2 (width) by 4 rectangle of dots but with the top left dot missing;]()

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


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

Question:
Paige, Kaci and David want to find the area of the school playground. They each do it a different way. Who is correct? ![A compound shape making an L shape. The full width across the bottom is 9m, the partial width on the top is 5m. The full height on the left is 10m, the partial height on the right is 6m.]()

Options:
A. Paige: \( 10 \times 6+5 \times 4 \)
B. Kaci: \( 10 \times 5+9 \times 6 \)
C. David: \( 9 \times 10-6 \times 4 \)
D. They are all 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 find missing lengths in a composite shape

Question:
Paige, Kaci and David want to find the area of the school playground. They each do it a different way. Who is correct? ![A compound shape making an L shape. The full width across the bottom is 9m, the partial width on the top is 5m. The full height on the left is 10m, the partial height on the right is 6m.]()

Options:
A. Paige: \( 10 \times 6+5 \times 4 \)
B. Kaci: \( 10 \times 5+9 \times 6 \)
C. David: \( 9 \times 10-6 \times 4 \)
D. They are all 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:
Repeats the digits twice when squaring a number

Question:
\( 11^{2}= \)

Options:
A. \( 1111 \)
B. \( 121 \)
C. \( 22 \)
D. \( 112 \)

Solve the problem as a student with the misconception above.
You 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:
\( 11^{2}= \)

Options:
A. \( 1111 \)
B. \( 121 \)
C. \( 22 \)
D. \( 112 \)

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


Prompt:
Misconception:
Writes the index as a digit on the end of a number

Question:
\( 11^{2}= \)

Options:
A. \( 1111 \)
B. \( 121 \)
C. \( 22 \)
D. \( 112 \)

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Simplify the following, if possible: \( \frac{4 t^{2}-1}{4 t+2} \)

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

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


Prompt:
Misconception:
Uses sin when tan is required

Question:
Which ratio would you use to find the value of \( \theta \) ? ![A right angled triangle with the two shorter sides marked as 7cm and 10cm. The angle opposite the 10 cm side is labelled with θ. The longest side of the triangle has no label.]()

Options:
A. Sin
B. Cos
C. Tan
D. None of these

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


Prompt:
Misconception:
Uses cos when tan is required

Question:
Which ratio would you use to find the value of \( \theta \) ? ![A right angled triangle with the two shorter sides marked as 7cm and 10cm. The angle opposite the 10 cm side is labelled with θ. The longest side of the triangle has no label.]()

Options:
A. Sin
B. Cos
C. Tan
D. None of these

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


Prompt:
Misconception:
Does not understand how to apply sohcahtoa

Question:
Which ratio would you use to find the value of \( \theta \) ? ![A right angled triangle with the two shorter sides marked as 7cm and 10cm. The angle opposite the 10 cm side is labelled with θ. The longest side of the triangle has no label.]()

Options:
A. Sin
B. Cos
C. Tan
D. None of these

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


Prompt:
Misconception:
Rounds down instead of up

Question:
Round \( 27.48 \) to one decimal place

Options:
A. \( 27.4 \)
B. \( 27 \)
C. \( 27.5 \)
D. \( 28.0 \)

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


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

Question:
Round \( 27.48 \) to one decimal place

Options:
A. \( 27.4 \)
B. \( 27 \)
C. \( 27.5 \)
D. \( 28.0 \)

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


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

Question:
Sophie is organising a charity hot dog sale.
There are \( 18 \) bread rolls in each packet.
There are \( 15 \) hot dogs in each packet.
Sophie buys exactly the same number of bread rolls as hot dogs.
What is the smallest number of each packet that Sophie can buy?

To solve this problem you need to work out the \( ___ \) of \( 18 \) and \( 15 \)

Options:
A. Product
B. Sum
C. Lowest Common Multiple
D. Highest Common Factor

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


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

Question:
Sophie is organising a charity hot dog sale.
There are \( 18 \) bread rolls in each packet.
There are \( 15 \) hot dogs in each packet.
Sophie buys exactly the same number of bread rolls as hot dogs.
What is the smallest number of each packet that Sophie can buy?

To solve this problem you need to work out the \( ___ \) of \( 18 \) and \( 15 \)

Options:
A. Product
B. Sum
C. Lowest Common Multiple
D. Highest Common Factor

Solve the problem as a student with the misconception above.
You 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 use of LCM and HCF in real life examples

Question:
Sophie is organising a charity hot dog sale.
There are \( 18 \) bread rolls in each packet.
There are \( 15 \) hot dogs in each packet.
Sophie buys exactly the same number of bread rolls as hot dogs.
What is the smallest number of each packet that Sophie can buy?

To solve this problem you need to work out the \( ___ \) of \( 18 \) and \( 15 \)

Options:
A. Product
B. Sum
C. Lowest Common Multiple
D. Highest Common Factor

Solve the problem as a student with the misconception above.
You 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 millilitres as a unit of volume

Question:
Tom and Katie are discussing units of length
Tom says miles is a unit of length
Katie says \( m l \) is a unit of length
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 millilitres as a unit of volume

Question:
Tom and Katie are discussing units of length
Tom says miles is a unit of length
Katie says \( m l \) is a unit of length
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 miles as a unit of length

Question:
Tom and Katie are discussing units of length
Tom says miles is a unit of length
Katie says \( m l \) is a unit of length
Who is correct?

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

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


Prompt:
Misconception:
When asked for the value of a digit, gives an answer 10 times too big

Question:
What is the value of the \( 2 \) in the number below?
\(
12030
\)

Options:
A. \( 20000 \)
B. \( 2000 \)
C. \( 200 \)
D. \( 2 \)

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


Prompt:
Misconception:
When asked for the value of a digit, gives an answer 10 times too small

Question:
What is the value of the \( 2 \) in the number below?
\(
12030
\)

Options:
A. \( 20000 \)
B. \( 2000 \)
C. \( 200 \)
D. \( 2 \)

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


Prompt:
Misconception:
When asked for the value of a digit, just gives the digit

Question:
What is the value of the \( 2 \) in the number below?
\(
12030
\)

Options:
A. \( 20000 \)
B. \( 2000 \)
C. \( 200 \)
D. \( 2 \)

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


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

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

Options:
A. \( -2 \)
B. \( -1 \)
C. \( -1.5 \)
D. \( -0.5 \)

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


Prompt:
Misconception:
Believes gradient = change in x/change in y

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

Options:
A. \( -2 \)
B. \( -1 \)
C. \( -1.5 \)
D. \( -0.5 \)

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


Prompt:
Misconception:
Writes times in the afternoon as if they are morning on a 24 hour clock

Question:
What time is \( 30 \) minutes before midnight?

Options:
A. \( 11: 30 \)
B. 11:30 am
C. 11:30 pm
D. None of these answers 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 times just before midnight are "am" times

Question:
What time is \( 30 \) minutes before midnight?

Options:
A. \( 11: 30 \)
B. 11:30 am
C. 11:30 pm
D. None of these answers 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 terms in linear sequence are in direct proportion

Question:
Here are the first five terms of a sequence ![\( \begin{array}{llllll}3 & 5 & 7 & 9 & 11 & \ldots\end{array} \)]() Find an expression for the \( n \)th term of this sequence.

Options:
A. \( 2 n \)
B. Double, add \( 1 \)
C. \( 2 n+1 \)
D. Add \( 2 \) each time

Solve the problem as a student with the misconception above.
You 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 nth term rule can be given in words

Question:
Here are the first five terms of a sequence ![\( \begin{array}{llllll}3 & 5 & 7 & 9 & 11 & \ldots\end{array} \)]() Find an expression for the \( n \)th term of this sequence.

Options:
A. \( 2 n \)
B. Double, add \( 1 \)
C. \( 2 n+1 \)
D. Add \( 2 \) each time

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


Prompt:
Misconception:
Counts the starting number when counting backwards

Question:
![Number line with -7 and -5 marked on it. From the -7 there is an arrow to the right labelled +5. Then there is an arrow pointing to the left labelled b and ending at -5.]() What is the value of \( b \) ?

Options:
A. \( -7 \)
B. \( -4 \)
C. \( -2 \)
D. \( -3 \)

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


Prompt:
Misconception:
Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount

Question:
Tom and Katie are discussing how to solve:
\(\frac{5 x}{3}-1=-2.4\)

Tom says a correct next line of working could be: \( 5 x-3=-7.2 \)

Katie says a correct next line of working could be: \( \frac{5 x}{3}=-3.4 \)

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 multiplying fractions, adds the numerators and the denominators

Question:
Calculate: \( \frac{1}{8} \times \frac{1}{3} \)

Options:
A. \( \frac{2}{11} \)
B. \( \frac{3}{8} \)
C. \( \frac{1}{11} \)
D. \( \frac{1}{24} \)

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


Prompt:
Misconception:
Divides rather than multiplies

Question:
Calculate: \( \frac{1}{8} \times \frac{1}{3} \)

Options:
A. \( \frac{2}{11} \)
B. \( \frac{3}{8} \)
C. \( \frac{1}{11} \)
D. \( \frac{1}{24} \)

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


Prompt:
Misconception:
When multiplying fractions, multiplies the numerator and adds the denominator

Question:
Calculate: \( \frac{1}{8} \times \frac{1}{3} \)

Options:
A. \( \frac{2}{11} \)
B. \( \frac{3}{8} \)
C. \( \frac{1}{11} \)
D. \( \frac{1}{24} \)

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


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

Question:
Which shape has rotational symmetry order \( 4 \) ?

Options:
A. ![Rectangle]()
B. ![Square]()
C. ![Trapezium]()
D. ![Hexagon]()

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


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
Which shape has rotational symmetry order \( 4 \) ?

Options:
A. ![Rectangle]()
B. ![Square]()
C. ![Trapezium]()
D. ![Hexagon]()

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


Prompt:
Misconception:
Does not connect rotational symmetry to number of sides/vertices

Question:
Which shape has rotational symmetry order \( 4 \) ?

Options:
A. ![Rectangle]()
B. ![Square]()
C. ![Trapezium]()
D. ![Hexagon]()

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


Prompt:
Misconception:
Rounds down instead of up

Question:
Round \( 0.0572 \) to \( 1 \) significant figure

Options:
A. \( 0.05 \)
B. \( 0.1 \)
C. \( 0 \)
D. \( 0.06 \)

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


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

Question:
Round \( 0.0572 \) to \( 1 \) significant figure

Options:
A. \( 0.05 \)
B. \( 0.1 \)
C. \( 0 \)
D. \( 0.06 \)

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


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

Question:
Round \( 0.0572 \) to \( 1 \) significant figure

Options:
A. \( 0.05 \)
B. \( 0.1 \)
C. \( 0 \)
D. \( 0.06 \)

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


Prompt:
Misconception:
Multiplies by the index

Question:
Tom and Katie are arguing about powers.
Tom says \( 2^{6}=4^{3} \)
Katie says \( 2^{6}=8^{2} \)
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 powers with different bases cannot be equal

Question:
Tom and Katie are arguing about powers.
Tom says \( 2^{6}=4^{3} \)
Katie says \( 2^{6}=8^{2} \)
Who is correct?

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

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


Prompt:
Misconception:
Believes adding two negatives gives a positive answer

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

Options:
A. \( m^{2}-2 m-35 \)
B. \( m^{2}-12 m+35 \)
C. \( m^{2}+12 m+35 \)
D. \( m^{2}-12 m-35 \)

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


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

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

Options:
A. \( m^{2}-2 m-35 \)
B. \( m^{2}-12 m+35 \)
C. \( m^{2}+12 m+35 \)
D. \( m^{2}-12 m-35 \)

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


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

Question:
Tom and Katie are arguing about the solution to this inequality:
\[
20 \geq 8 m
\]

Tom says \( m \) could be \( 2.5 \)

Katie says \( m \) could be \( 3 \)

Who is correct?

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

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


Prompt:
Misconception:
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:
Tom and Katie are arguing about the solution to this inequality:
\[
20 \geq 8 m
\]

Tom says \( m \) could be \( 2.5 \)

Katie says \( m \) could be \( 3 \)

Who is correct?

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

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


Prompt:
Misconception:
Does not realise multiplying a variable by itself results in a power of that variable

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

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

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

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

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

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


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

Question:
Which of the following triangles have the same area as this rectangle? ![A rectangle with height of 4 and width of 8]()

Options:
A. ![An isosceles triangle with base of 4 and perpendicular height of 8]()
B. ![A right angled triangle with base of 4, perpendicular height of 8 and hypotenuse of root 80]()
C. ![A triangle with a base of 8, perpendicular height of 8 and slant height of 10.]()
D. They are all equal to the rectangle

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


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

Question:
Which of the following triangles have the same area as this rectangle? ![A rectangle with height of 4 and width of 8]()

Options:
A. ![An isosceles triangle with base of 4 and perpendicular height of 8]()
B. ![A right angled triangle with base of 4, perpendicular height of 8 and hypotenuse of root 80]()
C. ![A triangle with a base of 8, perpendicular height of 8 and slant height of 10.]()
D. They are all equal to the rectangle

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


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

Question:
Which of the following triangles have the same area as this rectangle? ![A rectangle with height of 4 and width of 8]()

Options:
A. ![An isosceles triangle with base of 4 and perpendicular height of 8]()
B. ![A right angled triangle with base of 4, perpendicular height of 8 and hypotenuse of root 80]()
C. ![A triangle with a base of 8, perpendicular height of 8 and slant height of 10.]()
D. They are all equal to the rectangle

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


Prompt:
Misconception:
Does not compensate when subtracting

Question:
\( 204-36= \)

Options:
A. \( 156 \)
B. \( 178 \)
C. \( 240 \)
D. \( 168 \)

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


Prompt:
Misconception:
Adds instead of subtracts

Question:
\( 204-36= \)

Options:
A. \( 156 \)
B. \( 178 \)
C. \( 240 \)
D. \( 168 \)

Solve the problem as a student with the misconception above.
You 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 grams and tonnes are the same

Question:
How should you write \( 5 \) kilograms and \( 7 \) grams in tonnes?

Options:
A. \( 5007 t \)
B. \( 0.05007 t \)
C. \( 5.007 t \)
D. \( 0.005007 t \)

Solve the problem as a student with the misconception above.
You 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 100kg in a tonne

Question:
How should you write \( 5 \) kilograms and \( 7 \) grams in tonnes?

Options:
A. \( 5007 t \)
B. \( 0.05007 t \)
C. \( 5.007 t \)
D. \( 0.005007 t \)

Solve the problem as a student with the misconception above.
You 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 formulae for area of triangle and area of rectangle

Question:
This triangle has an area of \( 36 \mathrm{~cm}^{2} \).

What is the value of \( p \) ? ![A triangle with base labelled p and the perpendicular height labelled 12cm.]()

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 12 \mathrm{~cm} \)

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


Prompt:
Misconception:
Confuses perimeter and area

Question:
This triangle has an area of \( 36 \mathrm{~cm}^{2} \).

What is the value of \( p \) ? ![A triangle with base labelled p and the perpendicular height labelled 12cm.]()

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 12 \mathrm{~cm} \)

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

Question:
\[
9-8+5
\]
Jo and Paul are trying to make the calculation above equal to \( 6 \).
Jo says you can write it like this: \( 9-(8+5) \)
Paul says you can leave it like this: \( 9-8+5 \)
Who is correct?

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

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


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

Question:
\[
9-8+5
\]
Jo and Paul are trying to make the calculation above equal to \( 6 \).
Jo says you can write it like this: \( 9-(8+5) \)
Paul says you can leave it like this: \( 9-8+5 \)
Who is correct?

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

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


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

Question:
\[
9-8+5
\]
Jo and Paul are trying to make the calculation above equal to \( 6 \).
Jo says you can write it like this: \( 9-(8+5) \)
Paul says you can leave it like this: \( 9-8+5 \)
Who is correct?

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

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


Prompt:
Misconception:
Does not understand that when multiplying both sides of an equation by an amount every term must be multiplied by the same amount

Question:
Tom and Katie are discussing this equation:
\[
x+y=12
\] Tom uses the equation to write:
\[
3 x+3 y=36
\] Katie uses the equation to write:
\[
x+2 y=24
\] Who has written a related linear equation?

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 when multiplying both sides of an equation by an amount every term must be multiplied by the same amount

Question:
Tom and Katie are discussing this equation:
\[
x+y=12
\] Tom uses the equation to write:
\[
3 x+3 y=36
\] Katie uses the equation to write:
\[
x+2 y=24
\] Who has written a related linear equation?

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 how to create a multiple of an equation

Question:
Tom and Katie are discussing this equation:
\[
x+y=12
\] Tom uses the equation to write:
\[
3 x+3 y=36
\] Katie uses the equation to write:
\[
x+2 y=24
\] Who has written a related linear equation?

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
\(
y=x^{2}
\) \begin{tabular}{|l|l|}
\hline\( x \) & \( -9 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( -18 \)
B. \( -9 \)
C. \( 81 \)
D. \( -81 \)

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


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

Question:
This is a part of the table of values for the equation
\(
y=x^{2}
\) \begin{tabular}{|l|l|}
\hline\( x \) & \( -9 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( -18 \)
B. \( -9 \)
C. \( 81 \)
D. \( -81 \)

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


Prompt:
Misconception:
Ignores the negative sign

Question:
Which statement about the temperatures \( -5^{\circ} \mathrm{C} \) and \( 2^{\circ} \mathrm{C} \) is true?

Options:
A. \( 2^{\circ} \mathrm{C} \) is \( 3^{\circ} \mathrm{C} \)
hotter than
\[
-5^{\circ} \mathrm{C}
\]
B. \( 2^{\circ} \mathrm{C} \) is \( 7^{\circ} \mathrm{C} \) hotter than \( -5^{\circ} \mathrm{C} \)
C. \( 2^{\circ} \mathrm{C} \) is \( 3^{\circ} \mathrm{C} \) colder than \( -5^{\circ} \mathrm{C} \)
D. \( 2^{\circ} \mathrm{C} \) is \( 7^{\circ} \mathrm{C} \) colder than
\[
-5^{\circ} \mathrm{C}
\]

Solve the problem as a student with the misconception above.
You 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 colder and hotter when comparing temperatures

Question:
Which statement about the temperatures \( -5^{\circ} \mathrm{C} \) and \( 2^{\circ} \mathrm{C} \) is true?

Options:
A. \( 2^{\circ} \mathrm{C} \) is \( 3^{\circ} \mathrm{C} \)
hotter than
\[
-5^{\circ} \mathrm{C}
\]
B. \( 2^{\circ} \mathrm{C} \) is \( 7^{\circ} \mathrm{C} \) hotter than \( -5^{\circ} \mathrm{C} \)
C. \( 2^{\circ} \mathrm{C} \) is \( 3^{\circ} \mathrm{C} \) colder than \( -5^{\circ} \mathrm{C} \)
D. \( 2^{\circ} \mathrm{C} \) is \( 7^{\circ} \mathrm{C} \) colder than
\[
-5^{\circ} \mathrm{C}
\]

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


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

Question:
\[
10-8 \times 7+6=
\]

Which calculation should you do first?

Options:
A. \( 7+6 \)
B. \( 10-8 \)
C. \( 8 \times 7 \)
D. It doesn't matter: you get the same answer

Solve the problem as a student with the misconception above.
You 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:
\[
10-8 \times 7+6=
\]

Which calculation should you do first?

Options:
A. \( 7+6 \)
B. \( 10-8 \)
C. \( 8 \times 7 \)
D. It doesn't matter: you get the same answer

Solve the problem as a student with the misconception above.
You 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:
\[
10-8 \times 7+6=
\]

Which calculation should you do first?

Options:
A. \( 7+6 \)
B. \( 10-8 \)
C. \( 8 \times 7 \)
D. It doesn't matter: you get the same answer

Solve the problem as a student with the misconception above.
You 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 1l = 10 000 cubic centimetres

Question:
\( 500000 \mathrm{~cm}^{3} \) is the same as ______ litres

Options:
A. \( 0.5 \)
B. \( 5 \)
C. \( 500 \)
D. \( 5000 \)

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


Prompt:
Misconception:
Thinks 1l = 100 cubic centimetres

Question:
\( 500000 \mathrm{~cm}^{3} \) is the same as ______ litres

Options:
A. \( 0.5 \)
B. \( 5 \)
C. \( 500 \)
D. \( 5000 \)

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


Prompt:
Misconception:
Confuses a variable with an equation

Question:
Which of the following is the most appropriate word to describe \( p \) in this:
\(
3 p+7
\)

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

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


Prompt:
Misconception:
Confuses a term with a variable

Question:
Which of the following is the most appropriate word to describe \( p \) in this:
\(
3 p+7
\)

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

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


Prompt:
Misconception:
Confuses an expression with a variable

Question:
Which of the following is the most appropriate word to describe \( p \) in this:
\(
3 p+7
\)

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

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


Prompt:
Misconception:
Does not realise that two letters together, or a number and letter together, are multiplying

Question:
Simplify, if possible:
\[
z+5
\]

Options:
A. \( 5 z \)
B. \( z^{5} \)
C. \( z 5 \)
D. Does not simplify

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


Prompt:
Misconception:
Believes addition of terms and powers of terms are equivalent e.g. a + c = a^c

Question:
Simplify, if possible:
\[
z+5
\]

Options:
A. \( 5 z \)
B. \( z^{5} \)
C. \( z 5 \)
D. Does not simplify

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


Prompt:
Misconception:
Believes lines of symmetry must be vertical or horizontal

Question:
Which shape has a line of symmetry? ![A Trapezium above the label "A"; A shape which is a circle with a 90 degree sector removed above the label "B"; A crescent (moon) shape above the label "C"; the words "All of them" above the label "D".]()

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

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).
]()

Options:
A. \( 255^{\circ} \)
B. \( 285^{\circ} \)
C. \( 180^{\circ} \)
D. \( 295^{\circ} \)

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


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

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).
]()

Options:
A. \( 255^{\circ} \)
B. \( 285^{\circ} \)
C. \( 180^{\circ} \)
D. \( 295^{\circ} \)

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


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

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out an angle being measured by the protractor. The inner scale goes from 0 to 360 anti-clockwise. The angle is a reflex angle that is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, anti-clockwise to the red line that is half way between 280 and 290 (inner scale) and halfway between 260 and 250 (outer scale).
]()

Options:
A. \( 255^{\circ} \)
B. \( 285^{\circ} \)
C. \( 180^{\circ} \)
D. \( 295^{\circ} \)

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:
Confuses obtuse and acute angles

Question:
This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]()

Options:
A. Acute
B. Obtuse
C. Reflex
D. A right angle

Solve the problem as a student with the misconception above.
You 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 an obtuse angle is between 90 and 180 degrees

Question:
This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]()

Options:
A. Acute
B. Obtuse
C. Reflex
D. A right angle

Solve the problem as a student with the misconception above.
You 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 an obtuse angle is between 90 and 180 degrees

Question:
This angle is... ![An image of an angle that is larger than 90 degrees but smaller than 180 degrees.]()

Options:
A. Acute
B. Obtuse
C. Reflex
D. A right angle

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


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (0,1) (0,3) and (-3,2). The point P is the coordinate (0,3)]()

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

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

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (0,1) (0,3) and (-3,2). The point P is the coordinate (0,3)]()

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

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

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (0,1) (0,3) and (-3,2). The point P is the coordinate (0,3)]()

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

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:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "-4" written inside it and the final rectangle has "output" written above it and "11" written inside it.]() What is the input of this function machine?

Options:
A. \( 15 \)
B. \( -7 \)
C. \( 4 \)
D. \( 44 \)

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


Prompt:
Misconception:
Thinks the inverse of subtraction is multiplication

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "-4" written inside it and the final rectangle has "output" written above it and "11" written inside it.]() What is the input of this function machine?

Options:
A. \( 15 \)
B. \( -7 \)
C. \( 4 \)
D. \( 44 \)

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


Prompt:
Misconception:
Believes the solution of mx + c = 0 is x =0

Question:
This is a graph of
\(y=1-0.4 x\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve
\(1-0.4 x=0\)

Options:
A. \( x=2.5 \)
B. \( x=0 \)
C. \( x=1 \)
D. \( x=-0.4 \)

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 they solve mx + c = 0 by substituting in x = 0

Question:
This is a graph of
\(y=1-0.4 x\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve
\(1-0.4 x=0\)

Options:
A. \( x=2.5 \)
B. \( x=0 \)
C. \( x=1 \)
D. \( x=-0.4 \)

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


Prompt:
Misconception:
Believes the solution of mx + c = 0 is x = m

Question:
This is a graph of
\(y=1-0.4 x\) ![A set of axes with y=1-0.4x drawn on.]() Use the graph to solve
\(1-0.4 x=0\)

Options:
A. \( x=2.5 \)
B. \( x=0 \)
C. \( x=1 \)
D. \( x=-0.4 \)

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


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

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

Options:
A. ![Number line with numbers from -5 to 5. Above the -1 is an open, unfilled circle with an arrow to the left. Above the 3 is a red, filled circle with an arrow to the right.]()
B. ![Number line with numbers from -5 to 5. Above the -1 is a blue, filled circle with an arrow to the left. Above the 3 is an open, unfilled circle with an arrow to the right.]()
C. ![Number line with numbers from -5 to 5. Above the -1 is an open,  unfilled circle and above the 3 is a green, filled circle. The two circles are joined by a horizontal line.]()
D. ![Number line with numbers from -5 to 5. Above the -1 is a purple, filled circle and above the 3 is an open, unfilled circle. The two circles are joined by a horizontal line.]()

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


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

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

Options:
A. ![Number line with numbers from -5 to 5. Above the -1 is an open, unfilled circle with an arrow to the left. Above the 3 is a red, filled circle with an arrow to the right.]()
B. ![Number line with numbers from -5 to 5. Above the -1 is a blue, filled circle with an arrow to the left. Above the 3 is an open, unfilled circle with an arrow to the right.]()
C. ![Number line with numbers from -5 to 5. Above the -1 is an open,  unfilled circle and above the 3 is a green, filled circle. The two circles are joined by a horizontal line.]()
D. ![Number line with numbers from -5 to 5. Above the -1 is a purple, filled circle and above the 3 is an open, unfilled circle. The two circles are joined by a horizontal line.]()

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


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

Question:
Expand:
\[
3(p-1)
\]

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

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:
Only multiplies second term in the expansion of a bracket

Question:
Expand:
\[
3(p-1)
\]

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

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 expanding brackets, multiplies out the first term correctly but adds together the number outside the bracket with the second term inside the bracket.

Question:
Expand:
\[
3(p-1)
\]

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

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:
Only multiplies second term in the expansion of a bracket

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "3m + 1" written inside it. The middle rectangle has "✕ 2" written inside it and the final rectangle is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 6 m+2 \)
B. \( 3 m+2 \)
C. \( 6 m+1 \)
D. \( 6 m+3 \)

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:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "3m + 1" written inside it. The middle rectangle has "✕ 2" written inside it and the final rectangle is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 6 m+2 \)
B. \( 3 m+2 \)
C. \( 6 m+1 \)
D. \( 6 m+3 \)

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


Prompt:
Misconception:
Adds instead of multiplies

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "3m + 1" written inside it. The middle rectangle has "✕ 2" written inside it and the final rectangle is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 6 m+2 \)
B. \( 3 m+2 \)
C. \( 6 m+1 \)
D. \( 6 m+3 \)

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


Prompt:
Misconception:
Does not understand the effect of consecutive operations

Question:
Nick wants to subtract \( 199 \) from a number.
Which one of the following methods would give him the correct answer?

Options:
A. \( +200 \) then \( +1 \)
B. \( -200 \) then \( +1 \)
C. \( -200 \) then \( -1 \)
D. \( +200 \) then \( -1 \)

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 effect of consecutive operations

Question:
Nick wants to subtract \( 199 \) from a number.
Which one of the following methods would give him the correct answer?

Options:
A. \( +200 \) then \( +1 \)
B. \( -200 \) then \( +1 \)
C. \( -200 \) then \( -1 \)
D. \( +200 \) then \( -1 \)

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 effect of consecutive operations

Question:
Nick wants to subtract \( 199 \) from a number.
Which one of the following methods would give him the correct answer?

Options:
A. \( +200 \) then \( +1 \)
B. \( -200 \) then \( +1 \)
C. \( -200 \) then \( -1 \)
D. \( +200 \) then \( -1 \)

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 interpretation of the fx column in a frequency table

Question:
\begin{tabular}{|c|c|c|}
\hline TVs & Frequency & TVs \( \times \) Frequency \\
\hline \( 0 \) & \( 3 \) & \( 0 \) \\
\hline \( 1 \) & \( 8 \) & \( 8 \) \\
\hline \( 2 \) & \( 8 \) & \( 16 \) \\
\hline \( 3 \) & \( 4 \) & \( 12 \) \\
\hline \( 4 \) & \( 2 \) & \( 8 \) \\
\hline
\end{tabular} The table shows the numbers of TVs in the households of students in a class.

What does the "16" represent?

Options:
A. How many people who live in the \( 7 \) households
B. The mean number of TVs in the \( 8 \) households
C. The total number of TVs in the \( 8 \) households
D. The total number of TVs in the \( 2 \) households

Solve the problem as a student with the misconception above.
You 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 variable and frequency columns in a frequency table

Question:
\begin{tabular}{|c|c|c|}
\hline TVs & Frequency & TVs \( \times \) Frequency \\
\hline \( 0 \) & \( 3 \) & \( 0 \) \\
\hline \( 1 \) & \( 8 \) & \( 8 \) \\
\hline \( 2 \) & \( 8 \) & \( 16 \) \\
\hline \( 3 \) & \( 4 \) & \( 12 \) \\
\hline \( 4 \) & \( 2 \) & \( 8 \) \\
\hline
\end{tabular} The table shows the numbers of TVs in the households of students in a class.

What does the "16" represent?

Options:
A. How many people who live in the \( 7 \) households
B. The mean number of TVs in the \( 8 \) households
C. The total number of TVs in the \( 8 \) households
D. The total number of TVs in the \( 2 \) households

Solve the problem as a student with the misconception above.
You 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 diameter and radius

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

Options:
A. Radius
B. Arc
C. Diameter
D. Circumference

Solve the problem as a student with the misconception above.
You 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 arc and diameter

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

Options:
A. Radius
B. Arc
C. Diameter
D. Circumference

Solve the problem as a student with the misconception above.
You 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 circumference and diameter

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

Options:
A. Radius
B. Arc
C. Diameter
D. Circumference

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


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

Question:
What is the ratio of tables to chairs? ![tables
chairs]()

Options:
A. \( 3: 1 \)
B. \( 3: 4 \)
C. \( \frac{3}{4} \)
D. \( \frac{270}{360} \)

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


Prompt:
Misconception:
When writing fraction from diagram, writes total as denominator

Question:
What is the ratio of tables to chairs? ![tables
chairs]()

Options:
A. \( 3: 1 \)
B. \( 3: 4 \)
C. \( \frac{3}{4} \)
D. \( \frac{270}{360} \)

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


Prompt:
Misconception:
When writing fraction from diagram, writes total as denominator

Question:
What is the ratio of tables to chairs? ![tables
chairs]()

Options:
A. \( 3: 1 \)
B. \( 3: 4 \)
C. \( \frac{3}{4} \)
D. \( \frac{270}{360} \)

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


Prompt:
Misconception:
When rounding to decimal places and the only digits after the decimal point will be zeros, just gives the integer as the answer.

Question:
Jo and Paul are arguing about rounding.

Jo says \( \mathbf{9 9 . 9 6} \) rounded to \( 1 \) significant figure is \( \mathbf{1 0 0} \)

Paul says \( \mathbf{9 9 . 9 6} \) rounded to \( 1 \) decimal place is \( \mathbf{1 0 0} \)
Who is correct?

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

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


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

Question:
Tom and Katie are discussing rearranging \( t=\sqrt{u+9} \) to make \( u \) the subject
Tom says a correct first line of working could be: \( t=\sqrt{u}+3 \)
Katie says a correct first line of working could be: \( t^{2}=u+9 \)
Who is correct?

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

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


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

Question:
Tom and Katie are discussing rearranging \( t=\sqrt{u+9} \) to make \( u \) the subject
Tom says a correct first line of working could be: \( t=\sqrt{u}+3 \)
Katie says a correct first line of working could be: \( t^{2}=u+9 \)
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:
Subtracts instead of divides

Question:
\( 0.5 \div 2= \)

Options:
A. \( 0.3 \)
B. \( 0.025 \)
C. \( 1 \)
D. \( 0.25 \)

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


Prompt:
Misconception:
When dividing a decimal by an integer, divides by the wrong power of 10 when reinserting the decimal.

Question:
\( 0.5 \div 2= \)

Options:
A. \( 0.3 \)
B. \( 0.025 \)
C. \( 1 \)
D. \( 0.25 \)

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


Prompt:
Misconception:
Multiplies rather than divides

Question:
\( 0.5 \div 2= \)

Options:
A. \( 0.3 \)
B. \( 0.025 \)
C. \( 1 \)
D. \( 0.25 \)

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


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

Question:
This is a part of the table of values for the equation
\[y=3 x^{2}\] \begin{tabular}{|l|l|}
\hline\( x \) & \( 0.3 \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 0.81 \)
B. \( 0.27 \)
C. \( 1.8 \)
D. \( 2.7 \)

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:
Mixes up squaring and multiplying by 2 or doubling

Question:
This is a part of the table of values for the equation
\[y=3 x^{2}\] \begin{tabular}{|l|l|}
\hline\( x \) & \( 0.3 \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 0.81 \)
B. \( 0.27 \)
C. \( 1.8 \)
D. \( 2.7 \)

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 multiplying decimals, divides by the wrong power of 10 when reinserting the decimal

Question:
This is a part of the table of values for the equation
\[y=3 x^{2}\] \begin{tabular}{|l|l|}
\hline\( x \) & \( 0.3 \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 0.81 \)
B. \( 0.27 \)
C. \( 1.8 \)
D. \( 2.7 \)

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 rounding up from a 9, does not add one on to the digit to the left

Question:
Round this number to \( 1 \) significant figure:
\( 95365 \)

Options:
A. \( 10000 \)
B. \( 90000 \)
C. \( 100000 \)
D. \( 95365 \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
Round this number to \( 1 \) significant figure:
\( 95365 \)

Options:
A. \( 10000 \)
B. \( 90000 \)
C. \( 100000 \)
D. \( 95365 \)

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


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

Question:
What is \( 20.15349 \) rounded to \( 3 \) decimal places?

Options:
A. \( 20.153 \)
B. \( 20.15 \)
C. \( 20.154 \)
D. \( 20.253 \)

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


Prompt:
Misconception:
Rounds up instead of down

Question:
What is \( 20.15349 \) rounded to \( 3 \) decimal places?

Options:
A. \( 20.153 \)
B. \( 20.15 \)
C. \( 20.154 \)
D. \( 20.253 \)

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


Prompt:
Misconception:
Rounds incorrectly by changing multiple place values

Question:
What is \( 20.15349 \) rounded to \( 3 \) decimal places?

Options:
A. \( 20.153 \)
B. \( 20.15 \)
C. \( 20.154 \)
D. \( 20.253 \)

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

Question:
\( 1 \mathrm{~cm}^{3} \) is the same as _______ \( \mathrm{mm}^{3} \)

Options:
A. \( 10 \)
B. \( 100 \)
C. \( 1000 \)
D. \( 10000 \)

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

Question:
\( 1 \mathrm{~cm}^{3} \) is the same as _______ \( \mathrm{mm}^{3} \)

Options:
A. \( 10 \)
B. \( 100 \)
C. \( 1000 \)
D. \( 10000 \)

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


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

Question:
What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]()

Options:
A. \( 0.64 \mathrm{~m}^{2} \)
B. \( 1.12 \mathrm{~m}^{2} \)
C. \( 0.064 \mathrm{~m}^{2} \)
D. \( 0.56 \mathrm{~m}^{2} \)

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:
What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]()

Options:
A. \( 0.64 \mathrm{~m}^{2} \)
B. \( 1.12 \mathrm{~m}^{2} \)
C. \( 0.064 \mathrm{~m}^{2} \)
D. \( 0.56 \mathrm{~m}^{2} \)

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:
What is the area of this rectangle? ![Rectangle with base 0.4 m and height 0.16 m]()

Options:
A. \( 0.64 \mathrm{~m}^{2} \)
B. \( 1.12 \mathrm{~m}^{2} \)
C. \( 0.064 \mathrm{~m}^{2} \)
D. \( 0.56 \mathrm{~m}^{2} \)

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:
Confuses pyramid with prism

Question:
Which of the following collections of shapes would allow you to draw the net of a hexagonal prism?

Options:
A. \( 1 \) hexagon
\( 6 \) triangles
B. \( 2 \) hexagons \( 6 \) rectangles
C. \( 1 \) hexagon
\( 6 \) rectangles
D. \( 2 \) hexagons
\( 6 \) triangles

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


Prompt:
Misconception:
Confuses pyramid with prism

Question:
Which of the following collections of shapes would allow you to draw the net of a hexagonal prism?

Options:
A. \( 1 \) hexagon
\( 6 \) triangles
B. \( 2 \) hexagons \( 6 \) rectangles
C. \( 1 \) hexagon
\( 6 \) rectangles
D. \( 2 \) hexagons
\( 6 \) triangles

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


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

Question:
Which of the following collections of shapes would allow you to draw the net of a hexagonal prism?

Options:
A. \( 1 \) hexagon
\( 6 \) triangles
B. \( 2 \) hexagons \( 6 \) rectangles
C. \( 1 \) hexagon
\( 6 \) rectangles
D. \( 2 \) hexagons
\( 6 \) triangles

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


Prompt:
Misconception:
Misremembers the quadratic formula

Question:
Vera wants to solve this equation using the quadratic formula.
\(
3 h^{2}-10 h+4=0
\)

What should replace the circle? \( \frac{? \pm \sqrt{?-?}}{\bigcirc} \)

Options:
A. \( 3 \)
B. \( 5 \)
C. \( 9 \)
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:
Thinks a variable next to a number means addition rather than multiplication

Question:
Vera wants to solve this equation using the quadratic formula.
\(
3 h^{2}-10 h+4=0
\)

What should replace the circle? \( \frac{? \pm \sqrt{?-?}}{\bigcirc} \)

Options:
A. \( 3 \)
B. \( 5 \)
C. \( 9 \)
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:
Mixes up squaring and multiplying by 2 or doubling

Question:
Vera wants to solve this equation using the quadratic formula.
\(
3 h^{2}-10 h+4=0
\)

What should replace the circle? \( \frac{? \pm \sqrt{?-?}}{\bigcirc} \)

Options:
A. \( 3 \)
B. \( 5 \)
C. \( 9 \)
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 recognise when to find a factor from a worded question

Question:
Emma has \( 24 \) cakes to give away to her friends.
To work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \( 24 \)

Options:
A. factors
B. digits
C. multiples
D. reciprocal

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

Question:
Emma has \( 24 \) cakes to give away to her friends.
To work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \( 24 \)

Options:
A. factors
B. digits
C. multiples
D. reciprocal

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


Prompt:
Misconception:
Does not recognise when to find a factor from a worded question

Question:
Emma has \( 24 \) cakes to give away to her friends.
To work out what numbers of friends Emma could give equal amounts of cake to without having any cakes left over, Emma needs to know the ___ of \( 24 \)

Options:
A. factors
B. digits
C. multiples
D. reciprocal

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


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

Question:
The table below is a summary of the number of spots counted on \( 20 \) ladybirds. Calculate the mean number of spots per ladybird. ![\begin{tabular}{|c|c|}

Number of Spots & Frequency \\
\hline \( 5 \) & \( 3 \) \\
\hline \( 6 \) & \( 4 \) \\
\hline \( 7 \) & \( 12 \) \\
\hline \( 8 \) & \( 1 \) \\
\hline
\end{tabular}]()

Options:
A. \( 0.2(1 \mathrm{dp}) \)
B. \( 32.75 \)
C. \( 6.6(1 \mathrm{dp}) \)
D. \( 6.5(1 \mathrm{dp}) \)

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


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

Question:
The table below is a summary of the number of spots counted on \( 20 \) ladybirds. Calculate the mean number of spots per ladybird. ![\begin{tabular}{|c|c|}

Number of Spots & Frequency \\
\hline \( 5 \) & \( 3 \) \\
\hline \( 6 \) & \( 4 \) \\
\hline \( 7 \) & \( 12 \) \\
\hline \( 8 \) & \( 1 \) \\
\hline
\end{tabular}]()

Options:
A. \( 0.2(1 \mathrm{dp}) \)
B. \( 32.75 \)
C. \( 6.6(1 \mathrm{dp}) \)
D. \( 6.5(1 \mathrm{dp}) \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
The table below is a summary of the number of spots counted on \( 20 \) ladybirds. Calculate the mean number of spots per ladybird. ![\begin{tabular}{|c|c|}

Number of Spots & Frequency \\
\hline \( 5 \) & \( 3 \) \\
\hline \( 6 \) & \( 4 \) \\
\hline \( 7 \) & \( 12 \) \\
\hline \( 8 \) & \( 1 \) \\
\hline
\end{tabular}]()

Options:
A. \( 0.2(1 \mathrm{dp}) \)
B. \( 32.75 \)
C. \( 6.6(1 \mathrm{dp}) \)
D. \( 6.5(1 \mathrm{dp}) \)

Solve the problem as a student with the misconception above.
You 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 describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.

Question:
How would you describe the movement to get from the star to the triangle? ![Positive coordinate grid from 0 to 5 in the x and y directions with a gold star at (1,4) and a purple triangle at (4,3)]()

Options:
A. \( 1 \) square left,
\( 3 \) squares up
B. \( 3 \) squares right,
\( 1 \) square down
C. \( 4 \) squares right,
\( 1 \) square down
D. \( 3 \) squares down,
\( 1 \) square 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}.