Prompt:
Misconception:
Ignores numbers written as words in worded questions, and just calculates using those written in digits

Question:
There are \( 8 \) shelves of plates. Four of the shelves hold \( 15 \) plates each. Two of the shelves hold \( 23 \) plates each. The other shelves hold \( 17 \) plates each.
How many plates are there in total?

Options:
A. \( 123 \)
B. \( 55 \)
C. \( 63 \)
D. \( 140 \)

Solve the problem as a student with the misconception above.
You 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 numbers written as words in worded questions, and just calculates using those written in digits

Question:
There are \( 8 \) shelves of plates. Four of the shelves hold \( 15 \) plates each. Two of the shelves hold \( 23 \) plates each. The other shelves hold \( 17 \) plates each.
How many plates are there in total?

Options:
A. \( 123 \)
B. \( 55 \)
C. \( 63 \)
D. \( 140 \)

Solve the problem as a student with the misconception above.
You 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 believe you can scale up a proportional statement

Question:
For every \( 3 \) green squares there are \( 1 \) red squares.

How many squares should be coloured green in the grid on the right? \begin{tabular}{|l|l|l|l|}
\hline \(\;\) & \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) & \(\;\) \\
\hline
\end{tabular}

Options:
A. \( 3 \)
B. \( 8 \)
C. \( 12 \)
D. \( 4 \)

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


Prompt:
Misconception:
Shares equally instead of in given ratio

Question:
For every \( 3 \) green squares there are \( 1 \) red squares.

How many squares should be coloured green in the grid on the right? \begin{tabular}{|l|l|l|l|}
\hline \(\;\) & \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) & \(\;\) \\
\hline
\end{tabular}

Options:
A. \( 3 \)
B. \( 8 \)
C. \( 12 \)
D. \( 4 \)

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


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

Question:
\[
6-3+2
\]
Tom and Katie are trying to make the calculation above equal to \( 5 \).
Tom says you can write it like this: \( (6-3)+2 \)
Katie says you can leave it like this: \( 6-3+2 \)
Who is correct?

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

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


Prompt:
Misconception:
Does not divide by 2 when finding midpoint

Question:
What is the median of the following numbers?
\( 1, \quad 0.1, \quad 0.01,\quad 0.001 \)

Options:
A. \( 0.055 \)
B. \( 0.22 \)
C. \( 0.55 \)
D. \( 0.11 \)

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


Prompt:
Misconception:
When finding the median from a even dataset does not understand we must find the midpoint of the two values in the middle

Question:
What is the median of the following numbers?
\( 1, \quad 0.1, \quad 0.01,\quad 0.001 \)

Options:
A. \( 0.055 \)
B. \( 0.22 \)
C. \( 0.55 \)
D. \( 0.11 \)

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


Prompt:
Misconception:
Does not recognise that a linear sequence must increase or decrease by same amount

Question:
Which of the following is the best way to describe this sequence: ![A pattern with 6 terms made of green and red dots. The first term is a green dot, the second a red dot, the third is one red and one green dot. The fourth term is made of one green and two red dots. The fifth term is made from two green dots and three red dots. The sixth term is made of five red dots and three green dots. ]()

Options:
A. Linear
B. Quadratic
C. Geometric
D. Fibonacci

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

Question:
Which of the following is the best way to describe this sequence: ![A pattern with 6 terms made of green and red dots. The first term is a green dot, the second a red dot, the third is one red and one green dot. The fourth term is made of one green and two red dots. The fifth term is made from two green dots and three red dots. The sixth term is made of five red dots and three green dots. ]()

Options:
A. Linear
B. Quadratic
C. Geometric
D. Fibonacci

Solve the problem as a student with the misconception above.
You 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 Fibonacci sequence is

Question:
Which of the following is the best way to describe this sequence: ![A pattern with 6 terms made of green and red dots. The first term is a green dot, the second a red dot, the third is one red and one green dot. The fourth term is made of one green and two red dots. The fifth term is made from two green dots and three red dots. The sixth term is made of five red dots and three green dots. ]()

Options:
A. Linear
B. Quadratic
C. Geometric
D. Fibonacci

Solve the problem as a student with the misconception above.
You 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 letter describes the region where \( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{3} \) and \( \boldsymbol{y} \leq \mathbf{1} \) ? ![A set of axes with two straight lines drawn on. The line x+y=3 goes through points (3,0) and (0,3). The line y=1 is a horizontal line going through (0,1). The lines intersect one another at (2,1).
A is the region below x+y=3 and above y=1.
B is the region above both lines.
C is the region below y=1 but above x+y=3.
D is the region below both lines. ]()

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:
Confuses negative and positive coordinates when working with graphs in four quadrants

Question:
Describe the movements to get from

\[
(5,-2) \text { to }(0,1)
\]

Options:
A. Left \( 5 \) squares, up \( 3 \) squares
B. Left \( 5 \) squares, down \( 1 \) square
C. Right \( 5 \) squares, down \( 3 \) squares
D. Left \( 5 \) squares, up \( 4 \) squares

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


Prompt:
Misconception:
When finding the distance between coordinates, includes the starting number

Question:
Describe the movements to get from

\[
(5,-2) \text { to }(0,1)
\]

Options:
A. Left \( 5 \) squares, up \( 3 \) squares
B. Left \( 5 \) squares, down \( 1 \) square
C. Right \( 5 \) squares, down \( 3 \) squares
D. Left \( 5 \) squares, up \( 4 \) squares

Solve the problem as a student with the misconception above.
You 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 10g in a kilogram

Question:
\( 4000 \mathrm{~g} \) is the same as \( k g \)

Options:
A. \( 400 \)
B. \( 4000000 \)
C. \( 4 \)
D. \( 40 \)

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


Prompt:
Misconception:
Multiplies rather than divides

Question:
\( 4000 \mathrm{~g} \) is the same as \( k g \)

Options:
A. \( 400 \)
B. \( 4000000 \)
C. \( 4 \)
D. \( 40 \)

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


Prompt:
Misconception:
Thinks there are 100g in a kilogram

Question:
\( 4000 \mathrm{~g} \) is the same as \( k g \)

Options:
A. \( 400 \)
B. \( 4000000 \)
C. \( 4 \)
D. \( 40 \)

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


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

Question:
\( 3.06 \div 100= \)

Options:
A. \( 0.36 \)
B. \( 0.0306 \)
C. \( 0.036 \)
D. \( 0.00306 \)

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


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

Question:
\( 3.06 \div 100= \)

Options:
A. \( 0.36 \)
B. \( 0.0306 \)
C. \( 0.036 \)
D. \( 0.00306 \)

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


Prompt:
Misconception:
Divided by 100 rather than 10

Question:
\( 3.06 \div 100= \)

Options:
A. \( 0.36 \)
B. \( 0.0306 \)
C. \( 0.036 \)
D. \( 0.00306 \)

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


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

Question:
\( 0.7^{2}= \)

Options:
A. \( 0.49 \)
B. \( 1.4 \)
C. \( 0.14 \)
D. \( 4.9 \)

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


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

Question:
\( 0.7^{2}= \)

Options:
A. \( 0.49 \)
B. \( 1.4 \)
C. \( 0.14 \)
D. \( 4.9 \)

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


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

Question:
\( 0.7^{2}= \)

Options:
A. \( 0.49 \)
B. \( 1.4 \)
C. \( 0.14 \)
D. \( 4.9 \)

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


Prompt:
Misconception:
Believes vertically opposite angles sum to 180 degrees

Question:
What is the size of angle \( y \) ? ![A diagram showing 3 lines crossing at a point to form 6 angles. One angle is marked as 43 degrees. Another angle is marked as y. There are two blank angles between each marked angle.]()

Options:
A. \( 43^{\circ} \)
B. \( 137^{\circ} \)
C. \( 47^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Believes vertically opposite angles sum to 90 degrees

Question:
What is the size of angle \( y \) ? ![A diagram showing 3 lines crossing at a point to form 6 angles. One angle is marked as 43 degrees. Another angle is marked as y. There are two blank angles between each marked angle.]()

Options:
A. \( 43^{\circ} \)
B. \( 137^{\circ} \)
C. \( 47^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Does not know that vertically opposite angles are equal

Question:
What is the size of angle \( y \) ? ![A diagram showing 3 lines crossing at a point to form 6 angles. One angle is marked as 43 degrees. Another angle is marked as y. There are two blank angles between each marked angle.]()

Options:
A. \( 43^{\circ} \)
B. \( 137^{\circ} \)
C. \( 47^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Does not understand a denominator represents equal parts

Question:
What fraction of the shape is shaded? ![A rectangle split in half. One half is split in half again, and one half of that is split in half again, with one of those parts shaded.]()

Options:
A. \( \frac{1}{3} \)
B. \( 1 \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{8} \)

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


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

Question:
What fraction of the shape is shaded? ![A rectangle split in half. One half is split in half again, and one half of that is split in half again, with one of those parts shaded.]()

Options:
A. \( \frac{1}{3} \)
B. \( 1 \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{8} \)

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


Prompt:
Misconception:
Does not understand a denominator represents equal parts

Question:
What fraction of the shape is shaded? ![A rectangle split in half. One half is split in half again, and one half of that is split in half again, with one of those parts shaded.]()

Options:
A. \( \frac{1}{3} \)
B. \( 1 \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{8} \)

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


Prompt:
Misconception:
Mixes up square numbers and cube numbers

Question:
What is the value of "\( 3 \) cubed"?

Options:
A. \( 9 \)
B. \( 27 \)
C. \( 33 \)
D. \( 333 \)

Solve the problem as a student with the misconception above.
You 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 the index to the number

Question:
What is the value of "\( 3 \) cubed"?

Options:
A. \( 9 \)
B. \( 27 \)
C. \( 33 \)
D. \( 333 \)

Solve the problem as a student with the misconception above.
You 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 three times when cubing a number

Question:
What is the value of "\( 3 \) cubed"?

Options:
A. \( 9 \)
B. \( 27 \)
C. \( 33 \)
D. \( 333 \)

Solve the problem as a student with the misconception above.
You 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:
Amy is trying to work out the distance between these two points: \( (1,-6) \) and \( (-5,2) \) She labels them like this: \( \begin{array}{rrrr}x_{1} & y_{1} & x_{2} & y_{2} \\ (1, & -6) & (-5, & 2)\end{array} \) And then decides to use this formula: \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \) What does the second bracket equal?

Options:
A. \( (-8)^{2} \)
B. \( (-4)^{2} \)
C. \( (8)^{2} \)
D. \( (4)^{2} \)

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


Prompt:
Misconception:
When subtracting a negative number from a positive number, uses a method which assumes one of the negative signs can be ignored

Question:
Amy is trying to work out the distance between these two points: \( (1,-6) \) and \( (-5,2) \) She labels them like this: \( \begin{array}{rrrr}x_{1} & y_{1} & x_{2} & y_{2} \\ (1, & -6) & (-5, & 2)\end{array} \) And then decides to use this formula: \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \) What does the second bracket equal?

Options:
A. \( (-8)^{2} \)
B. \( (-4)^{2} \)
C. \( (8)^{2} \)
D. \( (4)^{2} \)

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


Prompt:
Misconception:
Thinks that when adding decimals with a different number of decimal places, you should line up the digits to the right

Question:
How should you line up the digits to calculate \( 0.7+0.54 \) ?

Options:
A. ![A column addition of 0.7 + 0.54. The 0 of 0.7 is directly above the decimal point of 0.54, the decimal point of 0.7 is directly above the 5 of 0.54 and the 7 of 0.7 is directly above the 4 of 0.54.]()
B. ![A column addition of 0.07 + 0.54 with the decimal points lined up.]()
C. ![A column addition of 0.7 + 5.4 with the decimal points lined up.]()
D. ![A column addition of 0.70 + 0.54 with the decimal points lined up.]()

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


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

Question:
How should you line up the digits to calculate \( 0.7+0.54 \) ?

Options:
A. ![A column addition of 0.7 + 0.54. The 0 of 0.7 is directly above the decimal point of 0.54, the decimal point of 0.7 is directly above the 5 of 0.54 and the 7 of 0.7 is directly above the 4 of 0.54.]()
B. ![A column addition of 0.07 + 0.54 with the decimal points lined up.]()
C. ![A column addition of 0.7 + 5.4 with the decimal points lined up.]()
D. ![A column addition of 0.70 + 0.54 with the decimal points lined up.]()

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


Prompt:
Misconception:
Does not know that units of volume are usually cubed

Question:
Tom and Katie are discussing units of volume
Tom says litres is a unit of volume
Katie says \( m^{3} \) is a unit of volume
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 litres as a unit of volume

Question:
Tom and Katie are discussing units of volume
Tom says litres is a unit of volume
Katie says \( m^{3} \) is a unit of volume
Who is correct?

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

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


Prompt:
Misconception:
Does not recognise a unit of volume

Question:
Tom and Katie are discussing units of volume
Tom says litres is a unit of volume
Katie says \( m^{3} \) is a unit of volume
Who is correct?

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

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


Prompt:
Misconception:
Mixes up squaring and addition

Question:
To calculate \( 53^{2} \) you need to do...

Options:
A. \( 53+2 \)
B. \( 53 \times 2 \)
C. \( 53 \times 53 \)
D. \( 532 \times 1 \)

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


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

Question:
To calculate \( 53^{2} \) you need to do...

Options:
A. \( 53+2 \)
B. \( 53 \times 2 \)
C. \( 53 \times 53 \)
D. \( 532 \times 1 \)

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 recognise a unit of length

Question:
Sally has answered a question on perimeter and got an answer of \( 500 \).

Behind the star she has written the units that she used.
Which of the following units is definitely wrong? \( 500 \bigstar \)

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

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


Prompt:
Misconception:
Does not recognise a unit of length

Question:
Sally has answered a question on perimeter and got an answer of \( 500 \).

Behind the star she has written the units that she used.
Which of the following units is definitely wrong? \( 500 \bigstar \)

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

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


Prompt:
Misconception:
Does not recognise a unit of length

Question:
Sally has answered a question on perimeter and got an answer of \( 500 \).

Behind the star she has written the units that she used.
Which of the following units is definitely wrong? \( 500 \bigstar \)

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

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


Prompt:
Misconception:
Believes a steeper downwards line on a graph means a slower decrease

Question:
This graph shows the temperature in Dan's garden in a \( 24 \) hour period.

In which \( 4 \) hour period did the temperature fall the most? ![A graph showing the temperature in Dan's house over a 24 hours period. At 00:00 the temperature is -2 degrees, at 04:00 it is -4 degrees, at 08:00 it is 0 degrees, at 12:00 it is 5 degrees, at 16:00 it is 8 degrees, at 20:00 it is 3 degrees and at 00:00 it is 0 degrees.]()

Options:
A. \( \begin{array}{c}00: 00 \text { to } \\ 04: 00\end{array} \)
B. \( \begin{array}{c}08: 00 \text { to } \\ 12: 00\end{array} \)
C. \( \begin{array}{c}16: 00 \text { to } \\ 20: 00\end{array} \)
D. \( \begin{aligned} 20 & : 00 \text { to } \\ 00 & : 00\end{aligned} \)

Solve the problem as a student with the misconception above.
You 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:
This graph shows the temperature in Dan's garden in a \( 24 \) hour period.

In which \( 4 \) hour period did the temperature fall the most? ![A graph showing the temperature in Dan's house over a 24 hours period. At 00:00 the temperature is -2 degrees, at 04:00 it is -4 degrees, at 08:00 it is 0 degrees, at 12:00 it is 5 degrees, at 16:00 it is 8 degrees, at 20:00 it is 3 degrees and at 00:00 it is 0 degrees.]()

Options:
A. \( \begin{array}{c}00: 00 \text { to } \\ 04: 00\end{array} \)
B. \( \begin{array}{c}08: 00 \text { to } \\ 12: 00\end{array} \)
C. \( \begin{array}{c}16: 00 \text { to } \\ 20: 00\end{array} \)
D. \( \begin{aligned} 20 & : 00 \text { to } \\ 00 & : 00\end{aligned} \)

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


Prompt:
Misconception:
Believes a steeper downwards line on a graph means a slower decrease

Question:
This graph shows the temperature in Dan's garden in a \( 24 \) hour period.

In which \( 4 \) hour period did the temperature fall the most? ![A graph showing the temperature in Dan's house over a 24 hours period. At 00:00 the temperature is -2 degrees, at 04:00 it is -4 degrees, at 08:00 it is 0 degrees, at 12:00 it is 5 degrees, at 16:00 it is 8 degrees, at 20:00 it is 3 degrees and at 00:00 it is 0 degrees.]()

Options:
A. \( \begin{array}{c}00: 00 \text { to } \\ 04: 00\end{array} \)
B. \( \begin{array}{c}08: 00 \text { to } \\ 12: 00\end{array} \)
C. \( \begin{array}{c}16: 00 \text { to } \\ 20: 00\end{array} \)
D. \( \begin{aligned} 20 & : 00 \text { to } \\ 00 & : 00\end{aligned} \)

Solve the problem as a student with the misconception above.
You 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:
\( (-2)^{4}= \)

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

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


Prompt:
Misconception:
Multiplies by the index

Question:
\( (-2)^{4}= \)

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

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


Prompt:
Misconception:
Does not understand that a probability of 0 represents something that is impossible

Question:
The probability of an event occurring is \( 0 \).

Which of the following most accurately describes the likelihood of the event occurring?

Options:
A. Certain
B. Unlikely
C. Even chance
D. Impossible

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


Prompt:
Misconception:
Does not understand that a probability of 0 represents something that is impossible

Question:
The probability of an event occurring is \( 0 \).

Which of the following most accurately describes the likelihood of the event occurring?

Options:
A. Certain
B. Unlikely
C. Even chance
D. Impossible

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


Prompt:
Misconception:
Does not understand that a probability of 0 represents something that is impossible

Question:
The probability of an event occurring is \( 0 \).

Which of the following most accurately describes the likelihood of the event occurring?

Options:
A. Certain
B. Unlikely
C. Even chance
D. Impossible

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


Prompt:
Misconception:
Believes division is carried out before a power

Question:
\( 8-7 \div 6^{3}= \) Which calculation should you do first?

Options:
A. \( 6^{3} \)
B. \( 7 \div 6 \)
C. \( 8-7 \)
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:
\( 8-7 \div 6^{3}= \) Which calculation should you do first?

Options:
A. \( 6^{3} \)
B. \( 7 \div 6 \)
C. \( 8-7 \)
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:
\( 8-7 \div 6^{3}= \) Which calculation should you do first?

Options:
A. \( 6^{3} \)
B. \( 7 \div 6 \)
C. \( 8-7 \)
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:
Subtracts from left to right, ignoring the word ‘from’

Question:
Which expression correctly represents the following description?
"Subtract five from \( \mathrm{h} \) and then multiply by six."

Options:
A. \( 6(h-5) \)
B. \( 6(5-h) \)
C. \( (5-h) \times 6 \)
D. \( (h-5) \times 6 \)

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


Prompt:
Misconception:
Subtracts from left to right, ignoring the word ‘from’

Question:
Which expression correctly represents the following description?
"Subtract five from \( \mathrm{h} \) and then multiply by six."

Options:
A. \( 6(h-5) \)
B. \( 6(5-h) \)
C. \( (5-h) \times 6 \)
D. \( (h-5) \times 6 \)

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


Prompt:
Misconception:
Does not realize we can omit the multiplication symbol in algebraic expressions

Question:
Which expression correctly represents the following description?
"Subtract five from \( \mathrm{h} \) and then multiply by six."

Options:
A. \( 6(h-5) \)
B. \( 6(5-h) \)
C. \( (5-h) \times 6 \)
D. \( (h-5) \times 6 \)

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


Prompt:
Misconception:
Assumes an addition pyramid works in a different way to how it actually does

Question:
Tom and Katie are arguing about what term could replace the star in this addition pyramid.
Tom says it could be: \( f \)
Katie says it could be: \( 2 f \)
Who is correct? ![A diagram showing 3 rows of boxes. the bottom row has 3 boxes, containing a star, 3g and 2g from left to right. The next row up contains two boxes, overlapping the joins of the boxes below. Both are empty. The top row is one box, centered over the join of the two below, containing 2f + 8g.]()

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:
Assumes an addition pyramid works in a different way to how it actually does

Question:
Tom and Katie are arguing about what term could replace the star in this addition pyramid.
Tom says it could be: \( f \)
Katie says it could be: \( 2 f \)
Who is correct? ![A diagram showing 3 rows of boxes. the bottom row has 3 boxes, containing a star, 3g and 2g from left to right. The next row up contains two boxes, overlapping the joins of the boxes below. Both are empty. The top row is one box, centered over the join of the two below, containing 2f + 8g.]()

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}{|c|c|}
\hline\( x \) & \( 4 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 8 \)
B. \( 16 \)
C. \( 4 \)
D. \( -16 \)

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


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

Question:
Using the graph of
\(
y=x^{2}-3 x-10
\)

What is the correct way to write the solution to
\(
x^{2}-3 x-10 \leq 0 ?
\) ![A quadratic parabola which crosses the x axis at (-2,0) and (5,0) and crosses the y axis at (0, -10)]()

Options:
A. \( \{x \leq-2\} \cup\{x \geq 5\} \)
B. \( \{-2 \leq x \leq 5\} \)
C. \( \{-2 \geq x \geq 5\} \)
D. \( \{x \geq-2\} \cup\{x \leq 5\} \)

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:
Does not understand inequality notation

Question:
Using the graph of
\(
y=x^{2}-3 x-10
\)

What is the correct way to write the solution to
\(
x^{2}-3 x-10 \leq 0 ?
\) ![A quadratic parabola which crosses the x axis at (-2,0) and (5,0) and crosses the y axis at (0, -10)]()

Options:
A. \( \{x \leq-2\} \cup\{x \geq 5\} \)
B. \( \{-2 \leq x \leq 5\} \)
C. \( \{-2 \geq x \geq 5\} \)
D. \( \{x \geq-2\} \cup\{x \leq 5\} \)

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 inequalities cannot be combined

Question:
Using the graph of
\(
y=x^{2}-3 x-10
\)

What is the correct way to write the solution to
\(
x^{2}-3 x-10 \leq 0 ?
\) ![A quadratic parabola which crosses the x axis at (-2,0) and (5,0) and crosses the y axis at (0, -10)]()

Options:
A. \( \{x \leq-2\} \cup\{x \geq 5\} \)
B. \( \{-2 \leq x \leq 5\} \)
C. \( \{-2 \geq x \geq 5\} \)
D. \( \{x \geq-2\} \cup\{x \leq 5\} \)

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:
Mixes up clockwise and anticlockwise

Question:
I am facing East. \( \mathrm{E} \longrightarrow \) How many degrees anti-clockwise will I need to turn so I am facing South?

Options:
A. \( 90^{\circ} \)
B. \( 180^{\circ} \)
C. \( 270^{\circ} \)
D. \( 360^{\circ} \)

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:
When subtracting fractions, subtracts the numerators and denominators

Question:
Calculate:
\( \frac{5}{9}-\frac{1}{3} \)

Options:
A. \( \frac{4}{6} \)
B. \( \frac{4}{9} \)
C. \( \frac{8}{9} \)
D. \( \frac{2}{9} \)

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


Prompt:
Misconception:
Does not consider the denominator when adding/ subtracting fractions. Adds/subtracts the numerator and makes the denominator the one with the highest value.

Question:
Calculate:
\( \frac{5}{9}-\frac{1}{3} \)

Options:
A. \( \frac{4}{6} \)
B. \( \frac{4}{9} \)
C. \( \frac{8}{9} \)
D. \( \frac{2}{9} \)

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


Prompt:
Misconception:
Adds instead of subtracts

Question:
Calculate:
\( \frac{5}{9}-\frac{1}{3} \)

Options:
A. \( \frac{4}{6} \)
B. \( \frac{4}{9} \)
C. \( \frac{8}{9} \)
D. \( \frac{2}{9} \)

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


Prompt:
Misconception:
Rounds incorrectly by changing multiple place values

Question:
What is \( 29.156828 \) rounded to \( 3 \) decimal places?

Options:
A. \( 29.267 \)
B. \( 29.16 \)
C. \( 29.156 \)
D. \( 29.157 \)

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


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

Question:
What is \( 29.156828 \) rounded to \( 3 \) decimal places?

Options:
A. \( 29.267 \)
B. \( 29.16 \)
C. \( 29.156 \)
D. \( 29.157 \)

Solve the problem as a student with the misconception above.
You 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:
What is \( 29.156828 \) rounded to \( 3 \) decimal places?

Options:
A. \( 29.267 \)
B. \( 29.16 \)
C. \( 29.156 \)
D. \( 29.157 \)

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


Prompt:
Misconception:
Believes the difference of 2 squares method of factorising also works for the addition of 2 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:
Thinks you can divide terms by different factors when simplifying an algebraic fraction

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:
Counts squares instead of the correct scale when plotting coordinates

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

How many potatoes were consumed on Friday? ![Graph of potatoes consumed with kilos against day of week]()

Options:
A. \( 3 \mathrm{~kg} \)
B. \( 10 \mathrm{~kg} \)
C. \( 15 \mathrm{~kg} \)
D. \( 25 \mathrm{~kg} \)

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


Prompt:
Misconception:
Rounds down instead of up when next digit is 5

Question:
Two different numbers are equal to \( 7.46 \) to two decimal places.
The numbers could be....

Options:
A. \( 7.4651 \)
and
\( 7.4559 \)
B. \( 7.4628 \)
and
\( 7.4528 \)
C. \( 7.463 \)
and
\( 6.461 \)
D. \( 7.4608 \)
and
\( 7.4551 \)

Solve the problem as a student with the misconception above.
You 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:
Two different numbers are equal to \( 7.46 \) to two decimal places.
The numbers could be....

Options:
A. \( 7.4651 \)
and
\( 7.4559 \)
B. \( 7.4628 \)
and
\( 7.4528 \)
C. \( 7.463 \)
and
\( 6.461 \)
D. \( 7.4608 \)
and
\( 7.4551 \)

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

Question:
Which of the following is a power of \( 4 \) ?

Options:
A. \( 44 \)
B. \( 64 \)
C. \( 400 \)
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 powers and multiples

Question:
Which of the following is a power of \( 4 \) ?

Options:
A. \( 44 \)
B. \( 64 \)
C. \( 400 \)
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 powers and multiples

Question:
Which of the following is a power of \( 4 \) ?

Options:
A. \( 44 \)
B. \( 64 \)
C. \( 400 \)
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:
Draws both angles at the same end of the line when constructing a triangle

Question:
Which of the following best describes how to construct a triangle with side length \( 7 \mathrm{~cm} \) with angles of \( 40^{\degree} \) and \( 50^{\degree} \) either side?

Options:
A. - Draw a line \( 7 \mathrm{~cm} \) long
- Place a protractor at one end of the line, measure \( 40^{\degree} \) and place a dot
- Draw a line \( 50 \mathrm{~cm} \) long that starts at the same end of the line and goes through the dot.
- Join up the end of this line with the other end of the \( 7 \mathrm{~cm} \) line.
B. - Draw a line \( 7 \mathrm{~cm} \) long
- Set the compass width to \( 40 \mathrm{~cm} \) and draw an arc from one end of the line
- Set the compass width to \( 50 \mathrm{~cm} \) and draw an arc from the other end of the line
- Join up the ends of the line to the intersection of the arcs with straight lines
C. - Draw a line \( 7 \mathrm{~cm} \) long
- Place a protractor at one end of the line, measure \( 40^{\degree} \) and place a dot
- Place a protractor at the same end of the line, measure \( 50^{\degree} \) and place a dot
- Draw straight lines through the end of the lines through the dots
- Where these lines cross completes the triangle
D. - Draw a line \( 7 \mathrm{~cm} \) long
- Place a protractor at one end of the line, measure \( 40^{\degree} \) and place a dot
- Place a protractor at the other end of the line, measure \( 50^{\degree} \) and place a dot
- Draw straight lines through the end of the lines through the dots
- Where these lines cross completes the triangle

Solve the problem as a student with the misconception above.
You 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:
Which option gives a correct substitution into the quadratic formula to solve the quadratic equation? \( 2 x^{2}-8 x+7=0 \)

Options:
A. \( -8 \pm \frac{\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
B. \( 8 \pm \frac{\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
C. \( \frac{-8 \pm \sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
D. \( \frac{8 \pm \sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)

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:
Misremembers the quadratic formula

Question:
Which option gives a correct substitution into the quadratic formula to solve the quadratic equation? \( 2 x^{2}-8 x+7=0 \)

Options:
A. \( -8 \pm \frac{\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
B. \( 8 \pm \frac{\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
C. \( \frac{-8 \pm \sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
D. \( \frac{8 \pm \sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)

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:
Misremembers the quadratic formula

Question:
Which option gives a correct substitution into the quadratic formula to solve the quadratic equation? \( 2 x^{2}-8 x+7=0 \)

Options:
A. \( -8 \pm \frac{\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
B. \( 8 \pm \frac{\sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
C. \( \frac{-8 \pm \sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)
D. \( \frac{8 \pm \sqrt{(-8)^{2}-4(2)(7)}}{2(2)} \)

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:
Thinks they double the numerator to turn a fraction into a percentage

Question:
What is \( 6 \) out of \( 25 \) as a percentage?

Options:
A. \( 12 \% \)
B. \( 30 \% \)
C. \( 62.5 \% \)
D. \( 24 \% \)

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


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

Question:
What is \( 6 \) out of \( 25 \) as a percentage?

Options:
A. \( 12 \% \)
B. \( 30 \% \)
C. \( 62.5 \% \)
D. \( 24 \% \)

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


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

Question:
\( 3+6 \div 2+1= \)

Options:
A. \( 7 \)
B. \( 3 \)
C. \( 5.5 \)
D. \( 5 \)

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


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

Question:
\( 3+6 \div 2+1= \)

Options:
A. \( 7 \)
B. \( 3 \)
C. \( 5.5 \)
D. \( 5 \)

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


Prompt:
Misconception:
When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value

Question:
Find \( d \) in the following equation \( \frac{5 d-2}{3}=2 d-1 \)

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

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


Prompt:
Misconception:
When multiplying a decimal less than 1 by an integer, gives an answer 10 times bigger than it should be

Question:
Work out:
\[
0.04 \times 21
\]

Options:
A. \( 8.4 \)
B. \( 8.04 \)
C. \( 0.84 \)
D. \( 0.084 \)

Solve the problem as a student with the misconception above.
You 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, does not realize that the order and position of the digits (relative to each other) has to remain constant.

Question:
Work out:
\[
0.04 \times 21
\]

Options:
A. \( 8.4 \)
B. \( 8.04 \)
C. \( 0.84 \)
D. \( 0.084 \)

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


Prompt:
Misconception:
When multiplying a decimal less than 1 by an integer, gives an answer 10 times smaller than it should be

Question:
Work out:
\[
0.04 \times 21
\]

Options:
A. \( 8.4 \)
B. \( 8.04 \)
C. \( 0.84 \)
D. \( 0.084 \)

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


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

Question:
Tom has correctly drawn the graph of the following function:
\(
y=\left\{\begin{array}{c}
P \text { for } 0 \leq x<Q \\
2.5 \text { for } 2 \leq x<4 \\
1 \text { for } 4 \leq x \leq 6
\end{array}\right.
\)

What are the values of \( P \) and Q? ![The graph is three separate horizontal lines. It goes from (0,3.5) to (2, 3.5), then (2, 2.5) to (4, 2.5) and the last section is from (4, 1) to (6, 1)]()

Options:
A. \( \begin{array}{c}P=3.5 \\ Q=2\end{array} \)
B. \( \begin{array}{c}P=2 \\ Q=3.5\end{array} \)
C. \( \begin{array}{l}P=0 \\ Q=2\end{array} \)
D. \( \begin{array}{c}P=0 \\ Q=3.5\end{array} \)

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


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

Question:
\( \sqrt{8^{2}}= \)

Options:
A. \( 8 \)
B. \( 64 \)
C. \( 4 \)
D. \( 16 \)

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


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

Question:
\( \sqrt{8^{2}}= \)

Options:
A. \( 8 \)
B. \( 64 \)
C. \( 4 \)
D. \( 16 \)

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


Prompt:
Misconception:
Mixes up squaring and multiplying by 2 or doubling, and not square rooted

Question:
\( \sqrt{8^{2}}= \)

Options:
A. \( 8 \)
B. \( 64 \)
C. \( 4 \)
D. \( 16 \)

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


Prompt:
Misconception:
Does not find a common denominator when comparing fractions

Question:
In a bakery \( \frac{2}{5} \) of the cakes are chocolate, \( \frac{3}{8} \) of the cakes are vanilla and \( \frac{13}{40} \) are lemon.
Which flavour cake is there more of?

Options:
A. Chocolate
B. Vanilla
C. Lemon
D. There is the same amount of each.

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


Prompt:
Misconception:
Does not find a common denominator when comparing fractions

Question:
In a bakery \( \frac{2}{5} \) of the cakes are chocolate, \( \frac{3}{8} \) of the cakes are vanilla and \( \frac{13}{40} \) are lemon.
Which flavour cake is there more of?

Options:
A. Chocolate
B. Vanilla
C. Lemon
D. There is the same amount of each.

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


Prompt:
Misconception:
Does not find a common denominator when comparing fractions

Question:
In a bakery \( \frac{2}{5} \) of the cakes are chocolate, \( \frac{3}{8} \) of the cakes are vanilla and \( \frac{13}{40} \) are lemon.
Which flavour cake is there more of?

Options:
A. Chocolate
B. Vanilla
C. Lemon
D. There is the same amount of each.

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


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

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

Tom says to find \( 30 \% \) you divide by \( 3 \).

Katie says to find \( 30 \% \) you divide by \( 100 \) and multiply by \( 3 \).

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:
Error finding percentage value after finding 1%

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

Tom says to find \( 30 \% \) you divide by \( 3 \).

Katie says to find \( 30 \% \) you divide by \( 100 \) and multiply by \( 3 \).

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 understand a percentage is out of 100

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

Tom says to find \( 30 \% \) you divide by \( 3 \).

Katie says to find \( 30 \% \) you divide by \( 100 \) and multiply by \( 3 \).

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:
Believes a less steep gradient corresponds to a faster speed

Question:
John walks from home at a constant speed to a bench, stops for a rest, and then runs home at a constant speed. Which of the following displacement \( (d) \) time \( (t) \) graphs is most likely to illustrate John's journey?

Options:
A. ![The graph has three sections.
The first section is a horizontal line, then a sloped line with negative gradient. The last section is a horizontal line.]()
B. ![The graph has three sections.
The first section starts at (0, 0) and is a sloped line with steep, positive, uphill gradient, then a horizontal line. The third section is a sloped line with gentle, negative gradient that ends when it touches the horizontal axis.]()
C. ![The graph has three sections.
The first section starts at (0, 0) and is a sloped line with positive, uphill gradient, then a horizontal line. The third section is another sloped line with a steeper positive gradient.]()
D. ![The graph has three sections.
The first section starts at (0, 0) and is a sloped line with gentle, positive, uphill gradient, then a horizontal line. The third section is a sloped line with very steep negative gradient that ends when it touches the horizontal axis.]()

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


Prompt:
Misconception:
Believes displacement continues to increase even when returning to starting point

Question:
John walks from home at a constant speed to a bench, stops for a rest, and then runs home at a constant speed. Which of the following displacement \( (d) \) time \( (t) \) graphs is most likely to illustrate John's journey?

Options:
A. ![The graph has three sections.
The first section is a horizontal line, then a sloped line with negative gradient. The last section is a horizontal line.]()
B. ![The graph has three sections.
The first section starts at (0, 0) and is a sloped line with steep, positive, uphill gradient, then a horizontal line. The third section is a sloped line with gentle, negative gradient that ends when it touches the horizontal axis.]()
C. ![The graph has three sections.
The first section starts at (0, 0) and is a sloped line with positive, uphill gradient, then a horizontal line. The third section is another sloped line with a steeper positive gradient.]()
D. ![The graph has three sections.
The first section starts at (0, 0) and is a sloped line with gentle, positive, uphill gradient, then a horizontal line. The third section is a sloped line with very steep negative gradient that ends when it touches the horizontal axis.]()

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


Prompt:
Misconception:
Thinks there are 1000mm in a km

Question:
How many millimetres in \( 100 \) kilometres?

Options:
A. One hundred thousand
B. One million
C. One hundred million
D. One billion

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


Prompt:
Misconception:
Thinks there are 10000mm in a km

Question:
How many millimetres in \( 100 \) kilometres?

Options:
A. One hundred thousand
B. One million
C. One hundred million
D. One billion

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


Prompt:
Misconception:
Thinks there are 10 million mm in 1 km

Question:
How many millimetres in \( 100 \) kilometres?

Options:
A. One hundred thousand
B. One million
C. One hundred million
D. One billion

Solve the problem as a student with the misconception above.
You 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 collecting like terms, treats subtractions as if they are additions

Question:
Which of the following is a correct simplification of: \( 4 x^{2}+2 x-x \)

Options:
A. \( 5 x^{3} \)
B. \( 4 x^{2}+x \)
C. \( 4 x^{2}+3 x \)
D. Cannot be simplified

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


Prompt:
Misconception:
Confuses pyramid with prism

Question:
Which is the correct net for this shape? ![A 3D image of a triangular prism]()

Options:
A. ![Net showing 3 rectangles and two triangles]()
B. ![\( \theta \)]()
C. ![Net showing four triangles]()
D. ![None of the above]()

Solve the problem as a student with the misconception above.
You 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 is the correct net for this shape? ![A 3D image of a triangular prism]()

Options:
A. ![Net showing 3 rectangles and two triangles]()
B. ![\( \theta \)]()
C. ![Net showing four triangles]()
D. ![None of the above]()

Solve the problem as a student with the misconception above.
You 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 is the correct net for this shape? ![A 3D image of a triangular prism]()

Options:
A. ![Net showing 3 rectangles and two triangles]()
B. ![\( \theta \)]()
C. ![Net showing four triangles]()
D. ![None of the above]()

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


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

Question:
Tom and Katie are discussing this sequence. ![3 consecutive patterns of a sequence are shown. The first pattern is a green triangle inside a square shape that is made from 4 separate red sticks. The second term is Pattern 1 but with 1 more green triangle and 3 more red sticks so that the 2 triangles are enclosed by squares made from red sticks. The third term is Pattern 2 but with 1 more green triangle and 3 more red sticks so that the 3 triangles are enclosed by squares made from red sticks.]() Tom says the number of triangles in the \( 6^{\text {th }} \) term will be
double the number of triangles in the \( 3^{\text {rd }} \) term.

Katie says the number of sticks in the \( 6^{\text {th }} \) term will be
double the number of sticks in the \( 3^{\text {rd }} \) term.

Who do you agree with?

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

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


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

Question:
What transformation maps the graph of
\(y=3 x-7\)
to the graph of
\(y=7-3 x\)

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

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


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

Question:
What transformation maps the graph of
\(y=3 x-7\)
to the graph of
\(y=7-3 x\)

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

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


Prompt:
Misconception:
Believes y=-f(x) is a reflection in the y-axis

Question:
What transformation maps the graph of
\(y=3 x-7\)
to the graph of
\(y=7-3 x\)

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

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


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

Question:
What length replaces the \( \color{green}\bigstar \) ? ![A diagram showing a compound shape. It is an L shape rotated 90 degrees clockwise. The top full width is 3x+4, the partial width to the right is x+4. The left full height is 5, the partial height on the right is 3. There is a green star on the left partial width at the bottom of the diagram.]()

Options:
A. \( 3 \)
B. \( 2 x \)
C. \( 4 x+16 \)
D. Not enough information

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


Prompt:
Misconception:
Does not know how to find missing lengths in a composite shape

Question:
What length replaces the \( \color{green}\bigstar \) ? ![A diagram showing a compound shape. It is an L shape rotated 90 degrees clockwise. The top full width is 3x+4, the partial width to the right is x+4. The left full height is 5, the partial height on the right is 3. There is a green star on the left partial width at the bottom of the diagram.]()

Options:
A. \( 3 \)
B. \( 2 x \)
C. \( 4 x+16 \)
D. Not enough information

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


Prompt:
Misconception:
Thinks the smallest bar in a bar chart is the mode

Question:
![A bar chart with blue bars. The x-axis is labelled with fruits and the y-axis is titled "Number of Children" and its scale is from 0 to 60 in steps of 10. The bars represent the following numbers of children: Banana, 20; Apple, 40; Kiwi Fruits, 50; Orange, 30; Pineapple, 25.]() Which of the following statements is true?

Options:
A. Banana is the most popular fruit
B. Only pineapple is liked less than oranges
C. Kiwi is the most popular fruit
D. Apple is the third most popular fruit

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


Prompt:
Misconception:
When solving simultaneous equations, believes the terms must be of opposite signs in order to be eliminated.

Question:
Tom and Katie are discussing whether simultaneous equations are in an appropriate form to be added or subtracted, or whether they need transforming first. Tom says these equations are in an appropriate form
\(
\begin{array}{l}
2 x-3 y=10 \\
5 x+3 y=18
\end{array}
\) Katie says these equations are in an appropriate form
\(
\begin{array}{l}
2 x-3 y=10 \\
2 x+y=4
\end{array}
\) Who is correct?

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

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


Prompt:
Misconception:
When solving simultaneous equations, believes the terms must have the same sign in order to be eliminated.

Question:
Tom and Katie are discussing whether simultaneous equations are in an appropriate form to be added or subtracted, or whether they need transforming first. Tom says these equations are in an appropriate form
\(
\begin{array}{l}
2 x-3 y=10 \\
5 x+3 y=18
\end{array}
\) Katie says these equations are in an appropriate form
\(
\begin{array}{l}
2 x-3 y=10 \\
2 x+y=4
\end{array}
\) Who is correct?

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

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


Prompt:
Misconception:
Believes a less steep gradient corresponds to a faster speed

Question:
\( p \) increases slowly at first, then quickly, then slowly again
Which of the following sketches best shows this?

Options:
A. ![A graph with time on the horizontal axis and p on the vertical axis. The graph starts at the origin and curves right and upwards, gradually getting more steep as you move right.]()
B. ![A graph with time on the horizontal axis and p on the vertical axis. The graph starts at the origin and curves right and upwards very steeply, then begins to level off.]()
C. ![A graph with time on the horizontal axis and p on the vertical axis. The graph starts at the origin and curves right and upwards very steeply, then begins to level off slightly, then travels more steeply again.]()
D. ![A graph with time on the horizontal axis and p on the vertical axis. The graph starts at the origin and curves right and upwards very steeply, then begins to level off slightly, then travels more steeply again.]()

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


Prompt:
Misconception:
Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets

Question:
When \( x^{2}-x-12 \) is factorised, what will appear in the box below ![\( (x+3) \)]()

Options:
A. \( (x+9) \)
B. \( (x-4) \)
C. \( (x+4) \)
D. \( (x-15) \)

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


Prompt:
Misconception:
Subtracts instead of adds

Question:
The fractions in the two circles below add to give the fraction in the circle above.

What should replace the question mark? ![Two circles containing the fractions 3/5 and 2/7, both linked to a third circle above]()

Options:
A. \( \frac{11}{35} \)
B. \( \frac{31}{35} \)
C. \( \frac{5}{12} \)
D. \( \frac{5}{35} \)

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


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

Question:
The fractions in the two circles below add to give the fraction in the circle above.

What should replace the question mark? ![Two circles containing the fractions 3/5 and 2/7, both linked to a third circle above]()

Options:
A. \( \frac{11}{35} \)
B. \( \frac{31}{35} \)
C. \( \frac{5}{12} \)
D. \( \frac{5}{35} \)

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:
Forgets to change the numerators when finding equivalent fractions

Question:
The fractions in the two circles below add to give the fraction in the circle above.

What should replace the question mark? ![Two circles containing the fractions 3/5 and 2/7, both linked to a third circle above]()

Options:
A. \( \frac{11}{35} \)
B. \( \frac{31}{35} \)
C. \( \frac{5}{12} \)
D. \( \frac{5}{35} \)

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:
Uses more than 3 letters to describe an angle

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

Options:
A. EGCE
B. HCE
C. \( \mathrm{EGH} \)
D. CGE

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


Prompt:
Misconception:
Chooses the wrong 3 letters to describe an angle

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

Options:
A. EGCE
B. HCE
C. \( \mathrm{EGH} \)
D. CGE

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


Prompt:
Misconception:
Chooses the wrong 3 letters to describe an angle

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

Options:
A. EGCE
B. HCE
C. \( \mathrm{EGH} \)
D. CGE

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


Prompt:
Misconception:
When simplifying, thinks they write 0 in front of a negative number in the final answer, instead of just writing the negative number

Question:
Simplify the following by collecting like terms.
\[
10 t-4 h-15 t+4 h
\]

Options:
A. \( -5 t \)
B. \( 0-5 t \)
C. \( 0 h-5 t \)
D. \( h-5 t \)

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

Question:
Simplify the following by collecting like terms.
\[
10 t-4 h-15 t+4 h
\]

Options:
A. \( -5 t \)
B. \( 0-5 t \)
C. \( 0 h-5 t \)
D. \( h-5 t \)

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:
Believes subtraction is commutative

Question:
\( 0.4-\frac{1}{5} \times 3= \)

Options:
A. \( 0.2 \)
B. \( 0.6 \)
C. \( -0.2 \)
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:
Carries out operations from left to right regardless of priority order

Question:
\( 0.4-\frac{1}{5} \times 3= \)

Options:
A. \( 0.2 \)
B. \( 0.6 \)
C. \( -0.2 \)
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:
When multiplying just writes the numbers next to each other

Question:
What is the answer to \( 4 c \times 5 d \) ?

Options:
A. \( 20 c d \)
B. \( 45 c d \)
C. \( 20 c d^{2} \)
D. \( 9 c d \)

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


Prompt:
Misconception:
Thinks any 2 values multiplied together can be denoted with a squared symbol

Question:
What is the answer to \( 4 c \times 5 d \) ?

Options:
A. \( 20 c d \)
B. \( 45 c d \)
C. \( 20 c d^{2} \)
D. \( 9 c d \)

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:
Adds instead of multiplies when multiplying algebraic terms

Question:
What is the answer to \( 4 c \times 5 d \) ?

Options:
A. \( 20 c d \)
B. \( 45 c d \)
C. \( 20 c d^{2} \)
D. \( 9 c d \)

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:
Doubles side length for similar shape instead of using correct scale factor

Question:
These two shapes are similar (not drawn to scale).
What should replace the star? ![Two scalene triangles. The bigger one has sides 9 cm and 7.5 cm. On the smaller triangle, the side corresponding to the 9 cm is 6 cm, and the side corresponding to the 7.5 cm is marked with a star.]()

Options:
A. \( 3.75 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 4.5 \mathrm{~cm} \)
D. Not enough information

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


Prompt:
Misconception:
Thinks adding the same value to each side makes shapes similar

Question:
These two shapes are similar (not drawn to scale).
What should replace the star? ![Two scalene triangles. The bigger one has sides 9 cm and 7.5 cm. On the smaller triangle, the side corresponding to the 9 cm is 6 cm, and the side corresponding to the 7.5 cm is marked with a star.]()

Options:
A. \( 3.75 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 4.5 \mathrm{~cm} \)
D. Not enough information

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


Prompt:
Misconception:
Does not understand how to find a scale factor

Question:
These two shapes are similar (not drawn to scale).
What should replace the star? ![Two scalene triangles. The bigger one has sides 9 cm and 7.5 cm. On the smaller triangle, the side corresponding to the 9 cm is 6 cm, and the side corresponding to the 7.5 cm is marked with a star.]()

Options:
A. \( 3.75 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 4.5 \mathrm{~cm} \)
D. Not enough information

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


Prompt:
Misconception:
Does not copy a given method accurately

Question:
This is how Ron calculates the answer to \( 46+28 \) mentally ![Cartoon picture of a boy's head with 2 thought bubbles:
First thought bubble says: "46+20 is equal to 66"
Second thought bubble says: "Then I am going to add on the 8.  66+8=74"]() Ron uses the same method to calculate \( 38+45 \).
Which of the following shows how he would do this?

Options:
A. \( \begin{array}{c}38+5=43 \\ 43+40=83\end{array} \)
B. \( \begin{array}{c}30+40=70 \\ 8+5=13 \\ 70+13=83\end{array} \)
C. \( \begin{array}{c}38+40=78 \\ 78+5=83\end{array} \)
D. \( \begin{array}{c}8+5=13 \\ 30+13=43 \\ 43+40=83\end{array} \)

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 ![Cartoon picture of a boy's head with 2 thought bubbles:
First thought bubble says: "46+20 is equal to 66"
Second thought bubble says: "Then I am going to add on the 8.  66+8=74"]() Ron uses the same method to calculate \( 38+45 \).
Which of the following shows how he would do this?

Options:
A. \( \begin{array}{c}38+5=43 \\ 43+40=83\end{array} \)
B. \( \begin{array}{c}30+40=70 \\ 8+5=13 \\ 70+13=83\end{array} \)
C. \( \begin{array}{c}38+40=78 \\ 78+5=83\end{array} \)
D. \( \begin{array}{c}8+5=13 \\ 30+13=43 \\ 43+40=83\end{array} \)

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 ![Cartoon picture of a boy's head with 2 thought bubbles:
First thought bubble says: "46+20 is equal to 66"
Second thought bubble says: "Then I am going to add on the 8.  66+8=74"]() Ron uses the same method to calculate \( 38+45 \).
Which of the following shows how he would do this?

Options:
A. \( \begin{array}{c}38+5=43 \\ 43+40=83\end{array} \)
B. \( \begin{array}{c}30+40=70 \\ 8+5=13 \\ 70+13=83\end{array} \)
C. \( \begin{array}{c}38+40=78 \\ 78+5=83\end{array} \)
D. \( \begin{array}{c}8+5=13 \\ 30+13=43 \\ 43+40=83\end{array} \)

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 link Pythagoras Theorem to finding distance between two points

Question:
Natalie is working out the distance between these two points. She has worked out the lengths of the triangle.
What is the distance? ![The image is of two points (-7, -3) and (4,2) joined by a sloped straight line, and then a horizontal and vertical line to create a right-angled triangle. The horizontal line is marked 11 and the vertical line is marked 5.]()

Options:
A. \( \sqrt{146} \)
B. \( 55 \)
C. \( \sqrt{32} \)
D. \( \sqrt{96} \)

Solve the problem as a student with the misconception above.
You 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:
Natalie is working out the distance between these two points. She has worked out the lengths of the triangle.
What is the distance? ![The image is of two points (-7, -3) and (4,2) joined by a sloped straight line, and then a horizontal and vertical line to create a right-angled triangle. The horizontal line is marked 11 and the vertical line is marked 5.]()

Options:
A. \( \sqrt{146} \)
B. \( 55 \)
C. \( \sqrt{32} \)
D. \( \sqrt{96} \)

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


Prompt:
Misconception:
Does not rearrange the Pythagoras' Theorem formula accurately

Question:
Natalie is working out the distance between these two points. She has worked out the lengths of the triangle.
What is the distance? ![The image is of two points (-7, -3) and (4,2) joined by a sloped straight line, and then a horizontal and vertical line to create a right-angled triangle. The horizontal line is marked 11 and the vertical line is marked 5.]()

Options:
A. \( \sqrt{146} \)
B. \( 55 \)
C. \( \sqrt{32} \)
D. \( \sqrt{96} \)

Solve the problem as a student with the misconception above.
You 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, ignores any remainders

Question:
When using long-division to solve this problem, what digit should replace the rectangle to give the correct answer (quotient)? ![Division sum written out in Bus Stop format with dividend = 771, divisor = 3, the digits of the quotient are represented by a yellow star, a purple triangle and a blue rectangle.]()

Options:
A. \( 7 \)
B. \( 2 \)
C. \( 0 \)
D. \( 1 \)

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


Prompt:
Misconception:
Does not understand that an acute angle is between 0 and 90 degrees

Question:
An angle measures \( 192^{\degree} \).
This means it is...

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:
An angle measures \( 192^{\degree} \).
This means it is...

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 know that a right angle is 90 degrees

Question:
An angle measures \( 192^{\degree} \).
This means it is...

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

Question:
What is the mean of the following numbers?

\[
2,2,3,5,8
\]

Options:
A. \( 20 \)
B. \( 4 \)
C. \( 3 \)
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 mean of a list of data, gives the median

Question:
What is the mean of the following numbers?

\[
2,2,3,5,8
\]

Options:
A. \( 20 \)
B. \( 4 \)
C. \( 3 \)
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 mean of a list of data, gives the mode

Question:
What is the mean of the following numbers?

\[
2,2,3,5,8
\]

Options:
A. \( 20 \)
B. \( 4 \)
C. \( 3 \)
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:
Thinks the more digits a number has the greater it is, regardless of place value

Question:
Tom and Katie are discussing how to order decimals
Tom says \( 0.06 \) is greater than \( 0.006 \)
Katie says \( 0.5 \) is greater than \( 0.6087 \)
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 ordering integers, orders from the digits at the end of the number instead of the digits at the start

Question:
Tom and Katie are discussing how to order decimals
Tom says \( 0.06 \) is greater than \( 0.006 \)
Katie says \( 0.5 \) is greater than \( 0.6087 \)
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:
Counts half-squares as full squares when calculating area on a square grid

Question:
What is the area of this shape? ![A parallelogram drawn on a square grid in purple with an area of 9 square units. The base is length 3 squares and the perpendicular height is also length 3 squares.]()

Options:
A. \( 12 \)
B. \( 8 \)
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:
Underestimates the area of shapes when counting squares when some squares are neither wholes nor halves

Question:
What is the area of this shape? ![A parallelogram drawn on a square grid in purple with an area of 9 square units. The base is length 3 squares and the perpendicular height is also length 3 squares.]()

Options:
A. \( 12 \)
B. \( 8 \)
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:
Only includes fully shaded squares when counting area

Question:
What is the area of this shape? ![A parallelogram drawn on a square grid in purple with an area of 9 square units. The base is length 3 squares and the perpendicular height is also length 3 squares.]()

Options:
A. \( 12 \)
B. \( 8 \)
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:
Believes you can make assumptions about size of pie chart sectors without enough information

Question:
People from Iceland were asked to pick their favourite from: lamb, fish and hotdog. A pie chart was made and \( 90 \) degrees represented fish.
What does this mean?

Options:
A. Fish are the least preferred food from the list
B. \( 25 \% \) of the people picked fish as their favourite food
C. Lamb is the most preferred food from the list
D. \( 90 \% \) of the people prefer fish

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


Prompt:
Misconception:
Believes you can make assumptions about size of pie chart sectors without enough information

Question:
People from Iceland were asked to pick their favourite from: lamb, fish and hotdog. A pie chart was made and \( 90 \) degrees represented fish.
What does this mean?

Options:
A. Fish are the least preferred food from the list
B. \( 25 \% \) of the people picked fish as their favourite food
C. Lamb is the most preferred food from the list
D. \( 90 \% \) of the people prefer fish

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


Prompt:
Misconception:
Believes a pie chart makes 360% not 360 degrees

Question:
People from Iceland were asked to pick their favourite from: lamb, fish and hotdog. A pie chart was made and \( 90 \) degrees represented fish.
What does this mean?

Options:
A. Fish are the least preferred food from the list
B. \( 25 \% \) of the people picked fish as their favourite food
C. Lamb is the most preferred food from the list
D. \( 90 \% \) of the people prefer fish

Solve the problem as a student with the misconception above.
You 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:
This is part of a table of values for
\[y=x^{2} -2 x+1\] \begin{tabular}{|c|c|}
\hline\( x \) & \( -1 \) \\
\hline\( y \) & \(\bigstar\) \\
\hline
\end{tabular} What should replace the star?

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

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


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

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

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

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


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

Question:
One of these quadratic equations will give exactly one solution.
Which one?

Options:
A. \( \frac{-3 \pm \sqrt{11}}{5} \)
B. \( \frac{-3 \pm \sqrt{0}}{5} \)
C. \( \frac{-3 \pm \sqrt{-16}}{5} \)
D. \( \frac{-3 \pm \sqrt{16}}{-5} \)

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 you can square root a negative number

Question:
One of these quadratic equations will give exactly one solution.
Which one?

Options:
A. \( \frac{-3 \pm \sqrt{11}}{5} \)
B. \( \frac{-3 \pm \sqrt{0}}{5} \)
C. \( \frac{-3 \pm \sqrt{-16}}{5} \)
D. \( \frac{-3 \pm \sqrt{16}}{-5} \)

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:
Does not think a square root can be negative

Question:
One of these quadratic equations will give exactly one solution.
Which one?

Options:
A. \( \frac{-3 \pm \sqrt{11}}{5} \)
B. \( \frac{-3 \pm \sqrt{0}}{5} \)
C. \( \frac{-3 \pm \sqrt{-16}}{5} \)
D. \( \frac{-3 \pm \sqrt{16}}{-5} \)

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:
Divides by the index

Question:
To calculate \( 47^{2} \) you need to do...

Options:
A. \( 47 \div 2 \)
B. \( 47 \times 47 \)
C. \( 47+2 \)
D. \( 47 \times 2 \)

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 the index to the number

Question:
To calculate \( 47^{2} \) you need to do...

Options:
A. \( 47 \div 2 \)
B. \( 47 \times 47 \)
C. \( 47+2 \)
D. \( 47 \times 2 \)

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


Prompt:
Misconception:
Multiplies by the index

Question:
To calculate \( 47^{2} \) you need to do...

Options:
A. \( 47 \div 2 \)
B. \( 47 \times 47 \)
C. \( 47+2 \)
D. \( 47 \times 2 \)

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


Prompt:
Misconception:
Does not know how to find missing lengths in a composite shape

Question:
What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form upside down step structure.  The base of the shape is horizontal and is 12m long. The vertical height of the whole shape is 27m. The horizontal width of the top part of the shape is 32m. The horizontal width of the top step is 15m. The vertical height of the top rectangle is 9m. The vertical height of the bottom rectangle is 10m. ]()

Options:
A. \( 118 \mathrm{~m} \)
B. \( 121 \mathrm{~m} \)
C. \( 130 \mathrm{~m} \)
D. \( 105 \mathrm{~m} \)

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


Prompt:
Misconception:
Does not know how to find missing lengths in a composite shape

Question:
What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form upside down step structure.  The base of the shape is horizontal and is 12m long. The vertical height of the whole shape is 27m. The horizontal width of the top part of the shape is 32m. The horizontal width of the top step is 15m. The vertical height of the top rectangle is 9m. The vertical height of the bottom rectangle is 10m. ]()

Options:
A. \( 118 \mathrm{~m} \)
B. \( 121 \mathrm{~m} \)
C. \( 130 \mathrm{~m} \)
D. \( 105 \mathrm{~m} \)

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


Prompt:
Misconception:
When calculating perimeter, only adds the marked lengths

Question:
What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form upside down step structure.  The base of the shape is horizontal and is 12m long. The vertical height of the whole shape is 27m. The horizontal width of the top part of the shape is 32m. The horizontal width of the top step is 15m. The vertical height of the top rectangle is 9m. The vertical height of the bottom rectangle is 10m. ]()

Options:
A. \( 118 \mathrm{~m} \)
B. \( 121 \mathrm{~m} \)
C. \( 130 \mathrm{~m} \)
D. \( 105 \mathrm{~m} \)

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


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

Question:
Kate and Isaac share some sweets in the ratio \( 3: 2 \)

Kate receives \( 60 \) sweets.

How many sweets does Isaac receive?

Options:
A. \( 20 \)
B. \( 24 \)
C. \( 40 \)
D. \( 90 \)

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


Prompt:
Misconception:
In ratio question where one side of ratio is given, treats that as the total

Question:
Kate and Isaac share some sweets in the ratio \( 3: 2 \)

Kate receives \( 60 \) sweets.

How many sweets does Isaac receive?

Options:
A. \( 20 \)
B. \( 24 \)
C. \( 40 \)
D. \( 90 \)

Solve the problem as a student with the misconception above.
You 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:
\[
8+12 \div 4 \square(8+12) \div 4
\]
Which symbol belongs in the box?

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

Solve the problem as a student with the misconception above.
You 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:
\[
8+12 \div 4 \square(8+12) \div 4
\]
Which symbol belongs in the box?

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

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


Prompt:
Misconception:
Does not understand inequality notation

Question:
\[
8+12 \div 4 \square(8+12) \div 4
\]
Which symbol belongs in the box?

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

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


Prompt:
Misconception:
Assumes an angle has been split into equal parts

Question:
What is value of the shaded angle in this diagram? ![[not to scale]]()

Options:
A. \( 80^{\circ} \)
B. \( 140^{\circ} \)
C. \( 70^{\circ} \)
D. \( 110^{\circ} \)

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:
Assumes an angle has been split into equal parts

Question:
What is value of the shaded angle in this diagram? ![[not to scale]]()

Options:
A. \( 80^{\circ} \)
B. \( 140^{\circ} \)
C. \( 70^{\circ} \)
D. \( 110^{\circ} \)

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:
Mixes up squaring and multiplying by 2 or doubling

Question:
Which of the following means the same as
\(a^{2} b\)

Options:
A. \( a \times b \times b \)
B. \( 2 \times a \times b \)
C. \( a \times b \times a \times b \)
D. \( a \times a \times b \)

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


Prompt:
Misconception:
When a variable in an expression has a power, thinks the power applies to the whole expression

Question:
Which of the following means the same as
\(a^{2} b\)

Options:
A. \( a \times b \times b \)
B. \( 2 \times a \times b \)
C. \( a \times b \times a \times b \)
D. \( a \times a \times b \)

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


Prompt:
Misconception:
Thinks that a larger shaded area represents a larger fraction

Question:
Which diagram represents the largest fraction?

Options:
A. ![An equilateral triangle divided into 4 smaller equilateral triangles that are identical to each other in size and shape. 2 of the smaller triangles are shaded orange, the rest are white.]()
B. ![A rectangle divided horizontally into 3 smaller rectangles that are identical to each other in size and shape. The top rectangle, of the 3, is shaded orange, the rest are white.]()
C. ![A rectangle divided into a grid of 30 smaller rectangles (5 high by 6 wide) that are identical to each other in size and shape. 8 of these smaller rectangles are shaded orange, the rest are white.]()
D. ![A rectangle divided horizontally into 3 smaller rectangles that are identical to each other in size and shape. The top 2 rectangles, of the 3, are shaded orange, the other is white.]()

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