Prompt:
Misconception:
Mixes up square rooting and multiplying by 2 or doubling

Question:
Which of the following is the square root of \( 36 \) ?

Options:
A. \( 18 \)
B. \( 1296 \)
C. \( 6 \)
D. \( 72 \)

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


Prompt:
Misconception:
Adds instead of multiplies

Question:
\( 0.32 \times 0.8= \)

Options:
A. \( 0.4 \)
B. \( 0.0256 \)
C. \( 2.56 \)
D. \( 0.256 \)

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


Prompt:
Misconception:
Does not understand place value within a number

Question:
\( 0.32 \times 0.8= \)

Options:
A. \( 0.4 \)
B. \( 0.0256 \)
C. \( 2.56 \)
D. \( 0.256 \)

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


Prompt:
Misconception:
Does not understand place value within a number

Question:
\( 0.32 \times 0.8= \)

Options:
A. \( 0.4 \)
B. \( 0.0256 \)
C. \( 2.56 \)
D. \( 0.256 \)

Solve the problem as a student with the misconception above.
You 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 angle in a pie chart sector is equal to the frequency

Question:
The pie chart shows the favourite subjects of children at a school.

If \( 12 \) students chose Science, how many chose French? ![A pie chart split into four parts, labelled with school subjects. The part for Mathematics is 144 degrees, Science is 36 degrees, English is 72 degrees and French is 108 degrees.]()

Options:
A. \( 36 \)
B. \( 108 \)
C. \( 87 \)
D. \( 45 \)

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


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

Question:
Which of the following term-to-term rule describes this sequence?
\[
2, \quad 5, \quad 14, \quad 41 \ldots
\]

Options:
A. To get the next term you add \( 3 \) to the previous term
B. To get the next term you double the previous term and add \( 1 \)
C. To get the next term you square the previous term and add \( 1 \)
D. To get the next term you multiply the previous term by \( 3 \) and subtract \( 1 \)

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

Question:
Which of the following term-to-term rule describes this sequence?
\[
2, \quad 5, \quad 14, \quad 41 \ldots
\]

Options:
A. To get the next term you add \( 3 \) to the previous term
B. To get the next term you double the previous term and add \( 1 \)
C. To get the next term you square the previous term and add \( 1 \)
D. To get the next term you multiply the previous term by \( 3 \) and subtract \( 1 \)

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

Question:
Which of the following term-to-term rule describes this sequence?
\[
2, \quad 5, \quad 14, \quad 41 \ldots
\]

Options:
A. To get the next term you add \( 3 \) to the previous term
B. To get the next term you double the previous term and add \( 1 \)
C. To get the next term you square the previous term and add \( 1 \)
D. To get the next term you multiply the previous term by \( 3 \) and subtract \( 1 \)

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

Question:
Tom shares some money with his brother in the ratio \( 5: 4 \) If Tom gets \( £180 \), how much does his brother get?

Options:
A. \( £ 100 \)
B. \( £ 80 \)
C. \( £ 144 \)
D. \( £ 720 \)

Solve the problem as a student with the misconception above.
You 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:
Tom shares some money with his brother in the ratio \( 5: 4 \) If Tom gets \( £180 \), how much does his brother get?

Options:
A. \( £ 100 \)
B. \( £ 80 \)
C. \( £ 144 \)
D. \( £ 720 \)

Solve the problem as a student with the misconception above.
You 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, uses that as one part in ratio without dividing

Question:
Tom shares some money with his brother in the ratio \( 5: 4 \) If Tom gets \( £180 \), how much does his brother get?

Options:
A. \( £ 100 \)
B. \( £ 80 \)
C. \( £ 144 \)
D. \( £ 720 \)

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


Prompt:
Misconception:
The student does not understand the place value of 3-digit numbers

Question:
How do you write this number in words?
\( 107 \)

Options:
A. Ten seven
B. One hundred and seven
C. One hundred and seventy
D. Seventeen

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


Prompt:
Misconception:
The student does not understand the place value of 3-digit numbers

Question:
How do you write this number in words?
\( 107 \)

Options:
A. Ten seven
B. One hundred and seven
C. One hundred and seventy
D. Seventeen

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


Prompt:
Misconception:
The student does not understand the place value of 3-digit numbers

Question:
How do you write this number in words?
\( 107 \)

Options:
A. Ten seven
B. One hundred and seven
C. One hundred and seventy
D. Seventeen

Solve the problem as a student with the misconception above.
You 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 reduce the denominator when an item is not replaced in a probability question

Question:
There are \( 5 \) red balls and \( 4 \) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks a yellow ball out and does not replace it.

She then has a second pick.

What is the probability the second pick is a red ball?

Options:
A. \( \frac{5}{9} \)
B. \( \frac{5}{8} \)
C. \( \frac{4}{9} \)
D. \( \frac{4}{8} \)

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


Prompt:
Misconception:
Believes a cubic expression should have three terms

Question:
When Nadia expands these brackets, how many terms should she get after she simplifies?
\(
(p+8)(p+2)(p+1)
\)

Options:
A. \( 5 \)
B. \( 8 \)
C. \( 3 \)
D. \( 4 \)

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


Prompt:
Misconception:
Believes the mean is the middle number

Question:
Without using a calculator, what is the mean of the following numbers?

\[
3,4,3,4,4
\]

Options:
A. \( 3 \)
B. A little more than \( 4 \)
C. \( 4 \)
D. A little less than \( 4 \)

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


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

Question:
Without using a calculator, what is the mean of the following numbers?

\[
3,4,3,4,4
\]

Options:
A. \( 3 \)
B. A little more than \( 4 \)
C. \( 4 \)
D. A little less than \( 4 \)

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:
Does not find a common denominator when adding/subtracting fractions

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

Options:
A. \( 13 \)
B. \( 2 \)
C. \( 4 \)
D. \( 11 \)

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


Prompt:
Misconception:
Does not find a common denominator when adding/subtracting fractions

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

Options:
A. \( 13 \)
B. \( 2 \)
C. \( 4 \)
D. \( 11 \)

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


Prompt:
Misconception:
Does not find a common denominator when adding/subtracting fractions

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

Options:
A. \( 13 \)
B. \( 2 \)
C. \( 4 \)
D. \( 11 \)

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


Prompt:
Misconception:
Believes you can only have one mode

Question:
What is the mode of the following numbers?
\[
1,1,4,6,7,7
\]

Options:
A. \( 1 \) and \( 7 \)
B. \( 7 \)
C. \( 4 \)
D. There is no mode

Solve the problem as a student with the misconception above.
You 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 there are two modes, finds the mean of these values and gives that as the mode

Question:
What is the mode of the following numbers?
\[
1,1,4,6,7,7
\]

Options:
A. \( 1 \) and \( 7 \)
B. \( 7 \)
C. \( 4 \)
D. There is no mode

Solve the problem as a student with the misconception above.
You 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 if there are two numbers with the same frequency, there isn't a mode

Question:
What is the mode of the following numbers?
\[
1,1,4,6,7,7
\]

Options:
A. \( 1 \) and \( 7 \)
B. \( 7 \)
C. \( 4 \)
D. There is no mode

Solve the problem as a student with the misconception above.
You 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:
Which is the best estimate for \( (4.2)^{2} \) ?

Options:
A. \( 25 \)
B. \( 16 \)
C. \( 8 \)
D. \( 10 \)

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


Prompt:
Misconception:
Multiplies by the index

Question:
Which is the best estimate for \( (4.2)^{2} \) ?

Options:
A. \( 25 \)
B. \( 16 \)
C. \( 8 \)
D. \( 10 \)

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


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

Question:
![Two angles meeting on a straight line labelled n and 48 degrees, one angle further down the straight line labelled 30 degrees]() What is the size of angle \( n \) ?

Options:
A. \( 132^{\circ} \)
B. \( 142^{\circ} \)
C. \( 102^{\circ} \)
D. \( 312^{\circ} \)

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


Prompt:
Misconception:
Thinks that all angles anywhere along a straight line add to 180

Question:
![Two angles meeting on a straight line labelled n and 48 degrees, one angle further down the straight line labelled 30 degrees]() What is the size of angle \( n \) ?

Options:
A. \( 132^{\circ} \)
B. \( 142^{\circ} \)
C. \( 102^{\circ} \)
D. \( 312^{\circ} \)

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


Prompt:
Misconception:
Believes angles on a straight line add to 360 degrees

Question:
![Two angles meeting on a straight line labelled n and 48 degrees, one angle further down the straight line labelled 30 degrees]() What is the size of angle \( n \) ?

Options:
A. \( 132^{\circ} \)
B. \( 142^{\circ} \)
C. \( 102^{\circ} \)
D. \( 312^{\circ} \)

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

Question:
Which of the following term-to-term rule describes this sequence? \( 2, \quad 9, \quad 11, \quad 20, \quad \ldots \)

Options:
A. To get the next term you add \( 7 \) to the previous term
B. To get the next term you add the previous two terms together
C. To get the next term you square the previous term and add \( 5 \)
D. To get the next term you multiply the previous term by \( 5 \) and subtract \( 1 \)

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

Question:
Which of the following term-to-term rule describes this sequence? \( 2, \quad 9, \quad 11, \quad 20, \quad \ldots \)

Options:
A. To get the next term you add \( 7 \) to the previous term
B. To get the next term you add the previous two terms together
C. To get the next term you square the previous term and add \( 5 \)
D. To get the next term you multiply the previous term by \( 5 \) and subtract \( 1 \)

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

Question:
Which of the following term-to-term rule describes this sequence? \( 2, \quad 9, \quad 11, \quad 20, \quad \ldots \)

Options:
A. To get the next term you add \( 7 \) to the previous term
B. To get the next term you add the previous two terms together
C. To get the next term you square the previous term and add \( 5 \)
D. To get the next term you multiply the previous term by \( 5 \) and subtract \( 1 \)

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:
Confuses pentagon and hexagon

Question:
Which of the following shapes is a hexagon?

Options:
A. ![An irregular, five sided shape]()
B. ![A regular, five sided shape]()
C. ![A regular, eight sided shape]()
D. None of these

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


Prompt:
Misconception:
Confuses pentagon and hexagon

Question:
Which of the following shapes is a hexagon?

Options:
A. ![An irregular, five sided shape]()
B. ![A regular, five sided shape]()
C. ![A regular, eight sided shape]()
D. None of these

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


Prompt:
Misconception:
Confuses octagon and hexagon

Question:
Which of the following shapes is a hexagon?

Options:
A. ![An irregular, five sided shape]()
B. ![A regular, five sided shape]()
C. ![A regular, eight sided shape]()
D. None of these

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


Prompt:
Misconception:
Forgot to simplify the fraction

Question:
Write \( 16 \) over \( 28 \) as a fraction in its simplest terms.

Options:
A. \( \frac{16}{28} \)
B. \( \frac{1}{13} \)
C. \( \frac{4}{6} \)
D. \( \frac{4}{7} \)

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


Prompt:
Misconception:
Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator

Question:
Write \( 16 \) over \( 28 \) as a fraction in its simplest terms.

Options:
A. \( \frac{16}{28} \)
B. \( \frac{1}{13} \)
C. \( \frac{4}{6} \)
D. \( \frac{4}{7} \)

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


Prompt:
Misconception:
When solving simultaneous equations, thinks they can't multiply each equation by a different number

Question:
Tom and Katie are discussing how to get this pair of simultaneous equations in a form where they can eliminate \( y \) \(( 1)\)  \(-2 x+6 y=4 \)
\( (2)\)  \( x+2 y=8 \) Tom says you need to multiply equation \( (2) \) by \( 3 \).

Katie says you need to multiply equation \( (1) \) by \( 2 \) and multiply equation \( (2) \) by \( 6 \).

Who is correct?

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

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


Prompt:
Misconception:
Does not realise that multiplication can be broken down into factors

Question:
Tom and Katie are discussing ways to calculate \( 28 \times 15 \) mentally Tom does \( 28 \times 5 \) and then multiplies his answer by \( 3 \) Katie does \( 14 \times 15 \) and then doubles her answer Who would get the correct answer?

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

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


Prompt:
Misconception:
Believes that fractions with larger denominators are greater in size

Question:
Which fraction is closest to \( 1 \) ?

Options:
A. \( 1 \frac{1}{3} \)
B. \( \frac{9}{10} \)
C. \( \frac{4}{5} \)
D. \( 1 \frac{1}{7} \)

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


Prompt:
Misconception:
Believes angles around a point sum to 180

Question:
Which of the following equations is true based on the diagram? ![Angles around a point made up of two angles labelled: f and f-20]()

Options:
A. \( 2 f-20=360 \)
B. \( 2 f-20=180 \)
C. \( f^{2}-20=360 \)
D. \( f-20=f \)

Solve the problem as a student with the misconception above.
You 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 index notation represents repeated addition rather than repeated multiplication

Question:
Which of the following equations is true based on the diagram? ![Angles around a point made up of two angles labelled: f and f-20]()

Options:
A. \( 2 f-20=360 \)
B. \( 2 f-20=180 \)
C. \( f^{2}-20=360 \)
D. \( f-20=f \)

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


Prompt:
Misconception:
Confuses vertically opposite angles and angles around a point

Question:
Which of the following equations is true based on the diagram? ![Angles around a point made up of two angles labelled: f and f-20]()

Options:
A. \( 2 f-20=360 \)
B. \( 2 f-20=180 \)
C. \( f^{2}-20=360 \)
D. \( f-20=f \)

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


Prompt:
Misconception:
Confuses perimeter and area

Question:
A square has an area of \( 100 \mathrm{~cm}^{2} \)
What is the length of each side of the square?

Options:
A. \( 25 \mathrm{~cm} \)
B. \( 10 \mathrm{~cm} \)
C. \( 50 \mathrm{~cm} \)
D. \( 100 \mathrm{~cm} \)

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


Prompt:
Misconception:
Confuses square rooting and halving the number

Question:
A square has an area of \( 100 \mathrm{~cm}^{2} \)
What is the length of each side of the square?

Options:
A. \( 25 \mathrm{~cm} \)
B. \( 10 \mathrm{~cm} \)
C. \( 50 \mathrm{~cm} \)
D. \( 100 \mathrm{~cm} \)

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


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

Question:
Which of the following correctly describes the marked angle? ![An image of square ABCE. D lies 1/3 from C on the line CE and is connected to A by a line. Attached to the square at line CE is a pentagon CEFGH. G is connected to C and E by lines. The angle highlighted is the interior angle at G.]()

Options:
A. HGC
B. \( \mathrm{GFH} \)
C. FGE
D. FGH

Solve the problem as a student with the misconception above.
You 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 point on the line of reflection will stay the same when reflected

Question:
A point, \( Q \), has coordinates \( (4,-4) \)

The point is reflected in the line \( y=-x \)

What are the new coordinates of point Q?

Options:
A. \( (4.4) \)
B. \( (-4,-4) \)
C. \( (-4,4) \)
D. \( (4,-4) \)

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:
Does not understand that a point on the line of reflection will stay the same when reflected

Question:
A point, \( Q \), has coordinates \( (4,-4) \)

The point is reflected in the line \( y=-x \)

What are the new coordinates of point Q?

Options:
A. \( (4.4) \)
B. \( (-4,-4) \)
C. \( (-4,4) \)
D. \( (4,-4) \)

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


Prompt:
Misconception:
Believes reflection in y = -x switches x and y coordinates

Question:
A point, \( Q \), has coordinates \( (4,-4) \)

The point is reflected in the line \( y=-x \)

What are the new coordinates of point Q?

Options:
A. \( (4.4) \)
B. \( (-4,-4) \)
C. \( (-4,4) \)
D. \( (4,-4) \)

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


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

Question:
\( 12 \div 2+1 \times 2= \)

Options:
A. \( 9 \)
B. \( 3 \)
C. \( 14 \)
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:
Carries out operations from left to right regardless of priority order

Question:
\( 12 \div 2+1 \times 2= \)

Options:
A. \( 9 \)
B. \( 3 \)
C. \( 14 \)
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:
Converts a fraction to a decimal by using the denominator after the decimal point

Question:
The probability of picking a green ball is \( \frac{1}{5} \)
Where is this value on the probability scale? ![A diagram showing a probability scale with 10 segments. The scale starts at 0.0, has 0.5 marked after 5 segments, and 1.0 marked at the end, after 10 segments. A is marked after 2 segments, B after 4, C after 5 and D after 7.]()

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

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


Prompt:
Misconception:
Does not find a common denominator when adding/subtracting fractions

Question:
\(
\frac{3}{4}-\frac{1}{3}=\frac{\bigstar}{12}
\)
What should replace the star?

Options:
A. \( 5 \)
B. \( 2 \)
C. \( 13 \)
D. \( 4 \)

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


Prompt:
Misconception:
Believes that the larger the divisor, the larger the answer.

Question:
Tom and Katie are discussing how to estimate the answer to
\[
38.8745 \div 7.9302
\]

Tom says \( 40 \div 7.9302 \) would give an overestimate.

Katie says \( 38.8745 \div 8 \) would give an overestimate.

Who is correct?

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

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


Prompt:
Misconception:
Believes that the larger the divisor, the larger the answer.

Question:
Tom and Katie are discussing how to estimate the answer to
\[
38.8745 \div 7.9302
\]

Tom says \( 40 \div 7.9302 \) would give an overestimate.

Katie says \( 38.8745 \div 8 \) would give an overestimate.

Who is correct?

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

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


Prompt:
Misconception:
Believes that the larger the dividend, the smaller the answer.

Question:
Tom and Katie are discussing how to estimate the answer to
\[
38.8745 \div 7.9302
\]

Tom says \( 40 \div 7.9302 \) would give an overestimate.

Katie says \( 38.8745 \div 8 \) would give an overestimate.

Who is correct?

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

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


Prompt:
Misconception:
Adds instead of multiplies

Question:
This table shows the ages of people on a university running team.
To calculate the mean age, what is the most sensible heading for the third column? \begin{tabular}{|c|c|l|}
\hline Age & Frequency & \\
\hline \( 18 \) & \( 7 \) & \\
\hline \( 19 \) & \( 3 \) & \\
\hline \( 20 \) & \( 1 \) & \\
\hline \( 21 \) & \( 2 \) & \\
\hline
\end{tabular}

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

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

Question:
This table shows the ages of people on a university running team.
To calculate the mean age, what is the most sensible heading for the third column? \begin{tabular}{|c|c|l|}
\hline Age & Frequency & \\
\hline \( 18 \) & \( 7 \) & \\
\hline \( 19 \) & \( 3 \) & \\
\hline \( 20 \) & \( 1 \) & \\
\hline \( 21 \) & \( 2 \) & \\
\hline
\end{tabular}

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

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


Prompt:
Misconception:
Divides rather than multiplies

Question:
This table shows the ages of people on a university running team.
To calculate the mean age, what is the most sensible heading for the third column? \begin{tabular}{|c|c|l|}
\hline Age & Frequency & \\
\hline \( 18 \) & \( 7 \) & \\
\hline \( 19 \) & \( 3 \) & \\
\hline \( 20 \) & \( 1 \) & \\
\hline \( 21 \) & \( 2 \) & \\
\hline
\end{tabular}

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

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


Prompt:
Misconception:
Thinks cube numbers are triangular numbers

Question:
\( 1,3,6,10,15,21,28 \ldots \) What is the name commonly given to this sequence of numbers?

Options:
A. The cube numbers
B. The Fibonacci numbers
C. The square numbers
D. The triangle numbers

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


Prompt:
Misconception:
Believes Fibonacci numbers are triangle numbers

Question:
\( 1,3,6,10,15,21,28 \ldots \) What is the name commonly given to this sequence of numbers?

Options:
A. The cube numbers
B. The Fibonacci numbers
C. The square numbers
D. The triangle numbers

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


Prompt:
Misconception:
Believes square numbers are triangle numbers

Question:
\( 1,3,6,10,15,21,28 \ldots \) What is the name commonly given to this sequence of numbers?

Options:
A. The cube numbers
B. The Fibonacci numbers
C. The square numbers
D. The triangle numbers

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


Prompt:
Misconception:
When solving simultaneous equations, thinks you only transform the algebraic terms, rather than the whole equation.

Question:
Sandeep wants to eliminate \( l \) from these simultaneous equations.
\(\begin{array}{l}
2 l+3 m=13 \\
3 l+4 m=17
\end{array}\)

First he will transform both of them to get them in an appropriate form.
Which of the following is a correct transformation?

Options:
A. \( \begin{array}{l}6 l+9 m=26 \\ 6 l+8 m=51\end{array} \)
B. \( \begin{array}{l}6 l+9 m=13 \\ 6 l+8 m=17\end{array} \)
C. \( \begin{array}{l}6 l+3 m=13 \\ 6 l+4 m=17\end{array} \)
D. \( \begin{array}{l}6 l+9 m=39 \\ 6 l+8 m=34\end{array} \)

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


Prompt:
Misconception:
When solving simultaneous equations, thinks you only transform the term that is being eliminated, rather than the whole equation.

Question:
Sandeep wants to eliminate \( l \) from these simultaneous equations.
\(\begin{array}{l}
2 l+3 m=13 \\
3 l+4 m=17
\end{array}\)

First he will transform both of them to get them in an appropriate form.
Which of the following is a correct transformation?

Options:
A. \( \begin{array}{l}6 l+9 m=26 \\ 6 l+8 m=51\end{array} \)
B. \( \begin{array}{l}6 l+9 m=13 \\ 6 l+8 m=17\end{array} \)
C. \( \begin{array}{l}6 l+3 m=13 \\ 6 l+4 m=17\end{array} \)
D. \( \begin{array}{l}6 l+9 m=39 \\ 6 l+8 m=34\end{array} \)

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:
Adds instead of multiplies

Question:
If you use the grid method to calculate \( 27 \times 42 \) what should replace the star? \begin{tabular}{|c|c|c|}
\hline\( \times \) & \( 20 \) & \( 7 \) \\
\hline \( 40 \) & \(\space\) & \(\color{gold}\bigstar\)\\
\hline \( 2 \) & \(\space\) & \\
\hline
\end{tabular}

Options:
A. \( 47 \)
B. \( 280 \)
C. \( 28 \)
D. \( 2800 \)

Solve the problem as a student with the misconception above.
You 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 involving a multiple of 10, gives an answer 10 times smaller than it should be

Question:
If you use the grid method to calculate \( 27 \times 42 \) what should replace the star? \begin{tabular}{|c|c|c|}
\hline\( \times \) & \( 20 \) & \( 7 \) \\
\hline \( 40 \) & \(\space\) & \(\color{gold}\bigstar\)\\
\hline \( 2 \) & \(\space\) & \\
\hline
\end{tabular}

Options:
A. \( 47 \)
B. \( 280 \)
C. \( 28 \)
D. \( 2800 \)

Solve the problem as a student with the misconception above.
You 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 by a multiple of 10, gives an answer 10 times bigger than it should be

Question:
If you use the grid method to calculate \( 27 \times 42 \) what should replace the star? \begin{tabular}{|c|c|c|}
\hline\( \times \) & \( 20 \) & \( 7 \) \\
\hline \( 40 \) & \(\space\) & \(\color{gold}\bigstar\)\\
\hline \( 2 \) & \(\space\) & \\
\hline
\end{tabular}

Options:
A. \( 47 \)
B. \( 280 \)
C. \( 28 \)
D. \( 2800 \)

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


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

Question:
Solve the equation:
\[
-3=p+12
\]

Options:
A. \( p=9 \)
B. \( p=-15 \)
C. \( p=-9 \)
D. \( p=15 \)

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:
Believes you write the carried value in the number rather than adding it to the next place value column

Question:
\( \begin{array}{r}\quad35 \\ \times 46 \\ \hline\end{array} \) What number will be in the ones/units column of the final answer?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 8 \)
D. \( 30 \)

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


Prompt:
Misconception:
Believes when dividing numbers with the same base you divide the powers, rather than subtracting

Question:
Simplify (if possible):
\(
6^{9} \div 6^{3}
\)

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

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


Prompt:
Misconception:
When dividing numbers with the same base divides the base numbers and the powers

Question:
Simplify (if possible):
\(
6^{9} \div 6^{3}
\)

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

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


Prompt:
Misconception:
When dividing numbers with the same base correctly subtracts the powers but divides the base numbers.

Question:
Simplify (if possible):
\(
6^{9} \div 6^{3}
\)

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

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


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

Question:
Which function machine will solve the equation \( x^{2}+5=14 ? \)

Options:
A. ![A function machine showing x as the input then +5 then squaring to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input square root and then -5]()
B. ![A function machine showing 14 as the input then squaring and +5 to give the output]()
C. ![A function machine showing x as the input then squaring then +5 to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input -5 and then square root]()
D. ![A function machine showing x as the input then x2 then +5 to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input  -5 and then divide by 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 solving an equation, uses the same operation rather than the inverse.

Question:
Which function machine will solve the equation \( x^{2}+5=14 ? \)

Options:
A. ![A function machine showing x as the input then +5 then squaring to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input square root and then -5]()
B. ![A function machine showing 14 as the input then squaring and +5 to give the output]()
C. ![A function machine showing x as the input then squaring then +5 to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input -5 and then square root]()
D. ![A function machine showing x as the input then x2 then +5 to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input  -5 and then divide by 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:
Mixes up squaring and multiplying by 2 or doubling

Question:
Which function machine will solve the equation \( x^{2}+5=14 ? \)

Options:
A. ![A function machine showing x as the input then +5 then squaring to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input square root and then -5]()
B. ![A function machine showing 14 as the input then squaring and +5 to give the output]()
C. ![A function machine showing x as the input then squaring then +5 to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input -5 and then square root]()
D. ![A function machine showing x as the input then x2 then +5 to give 14 as the output. Then a reverse function machine underneath showing 14 (the output) now as the input  -5 and then divide by 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:
Rounds to wrong degree of accuracy (decimal places rather than significant figures)

Question:
Tom and Katie are arguing about rounding.

Tom says \( \mathbf{0 . 0 3 4 5 6} \) rounded to \( 2 \) significant figures is \( \mathbf{0 . 0 3} \)

Katie says \( 0.03456 \) rounded to \( 2 \) decimal places is \( \mathbf{0 . 0 3} \)

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

Question:
Tom and Katie are arguing about rounding.

Tom says \( \mathbf{0 . 0 3 4 5 6} \) rounded to \( 2 \) significant figures is \( \mathbf{0 . 0 3} \)

Katie says \( 0.03456 \) rounded to \( 2 \) decimal places is \( \mathbf{0 . 0 3} \)

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:
Rounds up instead of down

Question:
What is \( \mathbf{1 . 5 1 6} \) rounded to the nearest \( \mathbf{0 . 0 5} \) ?

Options:
A. \( 1.50 \)
B. \( 1.51 \)
C. \( 1.55 \)
D. \( 1.52 \)

Solve the problem as a student with the misconception above.
You 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 \( \mathbf{1 . 5 1 6} \) rounded to the nearest \( \mathbf{0 . 0 5} \) ?

Options:
A. \( 1.50 \)
B. \( 1.51 \)
C. \( 1.55 \)
D. \( 1.52 \)

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


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

Question:
STEP \( 2 \)

Which of the options is a correct second step to express the following as a single fraction?
\(
\begin{array}{c}
\frac{9}{x+3}-\frac{2}{x} \\
=\frac{9 x}{x(x+3)}-\frac{2(x+3)}{x(x+3)}
\end{array}
\)

Options:
A. \( \frac{9 x-2(x+3)}{x(x+3)} \)
B. \( \frac{9}{3}-\frac{2(3)}{3} \)
C. \( \frac{9}{x+3}-\frac{2}{x} \)
D. \( \frac{9 x-2(x+3)}{x(x+3)-x(x+3)} \)

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


Prompt:
Misconception:
Does not understand how to subtract algebraic fractions

Question:
STEP \( 2 \)

Which of the options is a correct second step to express the following as a single fraction?
\(
\begin{array}{c}
\frac{9}{x+3}-\frac{2}{x} \\
=\frac{9 x}{x(x+3)}-\frac{2(x+3)}{x(x+3)}
\end{array}
\)

Options:
A. \( \frac{9 x-2(x+3)}{x(x+3)} \)
B. \( \frac{9}{3}-\frac{2(3)}{3} \)
C. \( \frac{9}{x+3}-\frac{2}{x} \)
D. \( \frac{9 x-2(x+3)}{x(x+3)-x(x+3)} \)

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


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

Question:
STEP \( 2 \)

Which of the options is a correct second step to express the following as a single fraction?
\(
\begin{array}{c}
\frac{9}{x+3}-\frac{2}{x} \\
=\frac{9 x}{x(x+3)}-\frac{2(x+3)}{x(x+3)}
\end{array}
\)

Options:
A. \( \frac{9 x-2(x+3)}{x(x+3)} \)
B. \( \frac{9}{3}-\frac{2(3)}{3} \)
C. \( \frac{9}{x+3}-\frac{2}{x} \)
D. \( \frac{9 x-2(x+3)}{x(x+3)-x(x+3)} \)

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


Prompt:
Misconception:
When converting ratio to fractions, puts the other side of the ratio as the denominator rather than the total

Question:
A lassi drink is made of yoghurt and water in the ratio 5:1. What fraction of the drink is water?

Options:
A. \( \frac{1}{5} \)
B. \( \frac{5}{6} \)
C. \( \frac{1}{6} \)
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:
Gets order of ratio wrong

Question:
A lassi drink is made of yoghurt and water in the ratio 5:1. What fraction of the drink is water?

Options:
A. \( \frac{1}{5} \)
B. \( \frac{5}{6} \)
C. \( \frac{1}{6} \)
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 the relationship between a ratio and fraction

Question:
A lassi drink is made of yoghurt and water in the ratio 5:1. What fraction of the drink is water?

Options:
A. \( \frac{1}{5} \)
B. \( \frac{5}{6} \)
C. \( \frac{1}{6} \)
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:
Confuses circumference and radius

Question:
Which of the following diagrams shows the circumference of a circle?

Options:
A. ![Circle with a line from the centre to the edge]()
B. ![Circle with its whole edge highlighted]()
C. ![Circle with a line below it, touching the circle in one place]()
D. ![Circle with a line across from edge to edge, not passing through the centre]()

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

Question:
Which of the following diagrams shows the circumference of a circle?

Options:
A. ![Circle with a line from the centre to the edge]()
B. ![Circle with its whole edge highlighted]()
C. ![Circle with a line below it, touching the circle in one place]()
D. ![Circle with a line across from edge to edge, not passing through the centre]()

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

Question:
Which of the following diagrams shows the circumference of a circle?

Options:
A. ![Circle with a line from the centre to the edge]()
B. ![Circle with its whole edge highlighted]()
C. ![Circle with a line below it, touching the circle in one place]()
D. ![Circle with a line across from edge to edge, not passing through the centre]()

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


Prompt:
Misconception:
Believes when simplifying a fraction you can divide the numerator and denominator by different values

Question:
Which of the following fractions is equivalent to \( \frac{9}{12} \) ?

Options:
A. \( \frac{12}{16} \)
B. \( \frac{2}{3} \)
C. \( \frac{12}{15} \)
D. None of these

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


Prompt:
Misconception:
Believes equivalent fractions are formed with addition not multiplication

Question:
Which of the following fractions is equivalent to \( \frac{9}{12} \) ?

Options:
A. \( \frac{12}{16} \)
B. \( \frac{2}{3} \)
C. \( \frac{12}{15} \)
D. None of these

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


Prompt:
Misconception:
Believes subtraction is commutative

Question:
Miran says the following:

“It doesn't matter if you do \( 81-53 \) or \( 53-81 \), you get the same answer."

What do you think?

Options:
A. Miran is correct because subtraction is commutative
B. Miran is incorrect because subtraction is commutative
C. Miran is correct because subtraction is not commutative
D. Miran is incorrect because subtraction is not commutative

Solve the problem as a student with the misconception above.
You 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 meaning of the word commutative

Question:
Miran says the following:

“It doesn't matter if you do \( 81-53 \) or \( 53-81 \), you get the same answer."

What do you think?

Options:
A. Miran is correct because subtraction is commutative
B. Miran is incorrect because subtraction is commutative
C. Miran is correct because subtraction is not commutative
D. Miran is incorrect because subtraction is not commutative

Solve the problem as a student with the misconception above.
You 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 meaning of the word commutative

Question:
Miran says the following:

“It doesn't matter if you do \( 81-53 \) or \( 53-81 \), you get the same answer."

What do you think?

Options:
A. Miran is correct because subtraction is commutative
B. Miran is incorrect because subtraction is commutative
C. Miran is correct because subtraction is not commutative
D. Miran is incorrect because subtraction is not commutative

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


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

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

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

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


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

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

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

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 the volume of an enlarged shape is the volume of the original multiplied by the cube of the scale factor of the lengths.

Question:
![Two cuboids. Cuboid P has width 5cm, and cuboid Q has width 15cm.]() Shape P and Shape Q are similar.

What is the volume scale factor to get from Shape \( P \) to Shape \( Q \) ?

Options:
A. \( \times 3 \)
B. \( \times 6 \)
C. \( \times 9 \)
D. \( \times 27 \)

Solve the problem as a student with the misconception above.
You 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 the volume of an enlarged shape is the volume of the original multiplied by the cube of the scale factor of the lengths.

Question:
![Two cuboids. Cuboid P has width 5cm, and cuboid Q has width 15cm.]() Shape P and Shape Q are similar.

What is the volume scale factor to get from Shape \( P \) to Shape \( Q \) ?

Options:
A. \( \times 3 \)
B. \( \times 6 \)
C. \( \times 9 \)
D. \( \times 27 \)

Solve the problem as a student with the misconception above.
You 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 the volume of an enlarged shape is the volume of the original multiplied by the cube of the scale factor of the lengths.

Question:
![Two cuboids. Cuboid P has width 5cm, and cuboid Q has width 15cm.]() Shape P and Shape Q are similar.

What is the volume scale factor to get from Shape \( P \) to Shape \( Q \) ?

Options:
A. \( \times 3 \)
B. \( \times 6 \)
C. \( \times 9 \)
D. \( \times 27 \)

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


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

Question:
\( A B C D \) is a rhombus.
Which lines must be perpendicular? ![Parallelogram with the vertices labelled A, B, C and D]()

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

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


Prompt:
Misconception:
Confuses the meaning of parallel and perpendicular

Question:
\( A B C D \) is a rhombus.
Which lines must be perpendicular? ![Parallelogram with the vertices labelled A, B, C and D]()

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

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


Prompt:
Misconception:
Does not know the properties of a rhombus

Question:
\( A B C D \) is a rhombus.
Which lines must be perpendicular? ![Parallelogram with the vertices labelled A, B, C and D]()

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

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


Prompt:
Misconception:
Does not understand that you can have percentages greater than 100%

Question:
\( 300 \% \) of \( 25= \)

Options:
A. \( 7.5 \)
B. \( 30.25 \)
C. \( 75 \)
D. You cannot have
a percentage
greater than \( 100 \)

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


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

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

Options:
A. \( 2 \)
B. \( 1 \)
C. \( 0 \)
D. \( 1.5 \)

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


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

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

Options:
A. \( 2 \)
B. \( 1 \)
C. \( 0 \)
D. \( 1.5 \)

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


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

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

Options:
A. \( 2 \)
B. \( 1 \)
C. \( 0 \)
D. \( 1.5 \)

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


Prompt:
Misconception:
Writes digits in the order of the pictorial representation rather than using place value columns

Question:
What number is represented below? ![An image showing four rods, each cut into ten squares, three individual squares and one large square cut into ten rows and ten columns. ]()

Options:
A. \( 431 \)
B. \( 341 \)
C. \( 143 \)
D. \( 134 \)

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


Prompt:
Misconception:
Writes digits in the order of the pictorial representation rather than using place value columns

Question:
What number is represented below? ![An image showing four rods, each cut into ten squares, three individual squares and one large square cut into ten rows and ten columns. ]()

Options:
A. \( 431 \)
B. \( 341 \)
C. \( 143 \)
D. \( 134 \)

Solve the problem as a student with the misconception above.
You 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 gives 1 value of x for a given value of y, when reading from a parabolic graph

Question:
What is the value of \( x \) when \( y=1 \) ?

Give your answer(s) to \( 1 \) decimal place ![A curved U shaped graph. There are 5 boxes between 0 and 1 on both axes. The graph goes through (-2, 1), (0,0), (2,1) and (4,4).]()

Options:
A. \( x=1.3 \)
B. \( x=2 \)
C. \( \begin{array}{c}x=-1.3 \\ \text { and } x=1.3\end{array} \)
D. \( \begin{array}{c}x=-2 \\ \text { and } x=2\end{array} \)

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


Prompt:
Misconception:
Gives the probability out of the number of non-successes rather than the total

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() What is the probability of picking a red ball?

Options:
A. \( \frac{4}{3} \)
B. \( \frac{7}{4} \)
C. \( \frac{3}{7} \)
D. \( \frac{4}{7} \)

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


Prompt:
Misconception:
Writes the numerator and the denominator the wrong way round in a probability

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() What is the probability of picking a red ball?

Options:
A. \( \frac{4}{3} \)
B. \( \frac{7}{4} \)
C. \( \frac{3}{7} \)
D. \( \frac{4}{7} \)

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


Prompt:
Misconception:
Believes linear graphs can be curved

Question:
Which of the following is most likely to be the graph of a linear function?

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

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


Prompt:
Misconception:
Believes linear graphs can be curved

Question:
Which of the following is most likely to be the graph of a linear function?

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

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


Prompt:
Misconception:
Confuses linear and reciprocal graphs

Question:
Which of the following is most likely to be the graph of a linear function?

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

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


Prompt:
Misconception:
Believes negative numbers with a larger absolute value are greater

Question:
Tom and Katie are discussing negative numbers.

Tom says \( -12>-9 \)

Katie says \( -0.401>-0.41 \)

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:
Added the values together instead of finding the percentage

Question:
What is \( 80 \% \) of \( 300 \) ?

Options:
A. \( 380 \)
B. \( 240 \)
C. \( 80 \)
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:
Does not understand a percentage can be applied to something not out of 100

Question:
What is \( 80 \% \) of \( 300 \) ?

Options:
A. \( 380 \)
B. \( 240 \)
C. \( 80 \)
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:
Believes that dividing by 100 gives 10%

Question:
What is \( 80 \% \) of \( 300 \) ?

Options:
A. \( 380 \)
B. \( 240 \)
C. \( 80 \)
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:
Believes multiplying a positive by a negative gives a positive answer

Question:
Multiply out the brackets: \( -3(m-2) \)

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

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 multiplying two negatives gives a negative answer

Question:
Multiply out the brackets: \( -3(m-2) \)

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

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


Prompt:
Misconception:
When completing the square, believes the constant in the bracket is the coefficient of x

Question:
\[
x^{2}-5 x+8 \equiv(x-b)^{2}+1.75
\]
What is the value of \( b \) ?

Options:
A. \( 5 \)
B. \( 6.25 \)
C. \( 3 \)
D. \( \frac{5}{2} \)

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


Prompt:
Misconception:
When completing the square in the form (x - a)^2 + b, believes b is the difference between a and the constant of the original quadratic

Question:
\[
x^{2}-5 x+8 \equiv(x-b)^{2}+1.75
\]
What is the value of \( b \) ?

Options:
A. \( 5 \)
B. \( 6.25 \)
C. \( 3 \)
D. \( \frac{5}{2} \)

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


Prompt:
Misconception:
Rounds every number up when estimating

Question:
Jane measures the length and width of her rectangular classroom as \( 9.1 \mathrm{~m} \) and \( 11.7 \mathrm{~m} \).
Which calculation will give the best estimate of the area?

Options:
A. \( 10 \times 12 \)
B. \( 9 \times 11 \)
C. \( 9 \times 12 \)
D. \( 10 \times 11 \)

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:
Rounds down instead of up

Question:
Jane measures the length and width of her rectangular classroom as \( 9.1 \mathrm{~m} \) and \( 11.7 \mathrm{~m} \).
Which calculation will give the best estimate of the area?

Options:
A. \( 10 \times 12 \)
B. \( 9 \times 11 \)
C. \( 9 \times 12 \)
D. \( 10 \times 11 \)

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:
Assumed each part of a fraction diagram is worth 10%

Question:
What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]()

Options:
A. \( 30 \% \)
B. \( 60 \% \)
C. \( 3 \% \)
D. \( 55 \% \)

Solve the problem as a student with the misconception above.
You 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:
What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]()

Options:
A. \( 30 \% \)
B. \( 60 \% \)
C. \( 3 \% \)
D. \( 55 \% \)

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


Prompt:
Misconception:
Estimated when not appropriate

Question:
What percentage of this shape is shaded? ![A bar split into 5 equal parts. 3 parts are shaded.]()

Options:
A. \( 30 \% \)
B. \( 60 \% \)
C. \( 3 \% \)
D. \( 55 \% \)

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


Prompt:
Misconception:
Thinks you need to include the total as well as the individual parts when asked to write a ratio

Question:
What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]()

Options:
A. \( 5: 4: 9 \)
B. \( 4: 5 \)
C. \( 5: 4 \)
D. \( 5: 9 \)

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 sides of a ratio

Question:
What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]()

Options:
A. \( 5: 4: 9 \)
B. \( 4: 5 \)
C. \( 5: 4 \)
D. \( 5: 9 \)

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 writing ratio from diagram, writes total as one side

Question:
What is the ratio of rectangles to circles? ![A diagram showing 5 blue rectangles and 4 red circles]()

Options:
A. \( 5: 4: 9 \)
B. \( 4: 5 \)
C. \( 5: 4 \)
D. \( 5: 9 \)

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:
Confuses inequality symbols with equality

Question:
Which of these statements show that \( \mathrm{j} \) is smaller than \( 5 \) ?

Options:
A. \( \mathrm{j}<5 \)
B. \( j=5 \)
C. \( \mathrm{j} \geq 5 \)
D. \( \mathrm{j}>5 \)

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 greater than and less than symbols

Question:
Which of these statements show that \( \mathrm{j} \) is smaller than \( 5 \) ?

Options:
A. \( \mathrm{j}<5 \)
B. \( j=5 \)
C. \( \mathrm{j} \geq 5 \)
D. \( \mathrm{j}>5 \)

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


Prompt:
Misconception:
Thinks a variable next to a number means addition rather than multiplication

Question:
Calculate the time taken \( (t) \) for a a particle to travel with acceleration \( (a)=4.1 \mathrm{~ms}^{-2} \), initial velocity \( (u)=2.8 \mathrm{~ms}^{-1} \) and final velocity \( (v)=8.7 \mathrm{~ms}^{-1} \) \( t=\frac{1}{a}(v-u) \)

Options:
A. \( \begin{array}{c}t=\frac{1}{4.1}+(8.7-2.8) \\ t=6.14\end{array} \)
B. \( \begin{array}{c}t=4.1 \times(8.7-2.8) \\ t=24.19\end{array} \)
C. \( \begin{array}{c}t=4.1+(8.7-2.8) \\ t=10\end{array} \)
D. \( \begin{array}{c}t=(8.7-2.8) \div 4.1 \\ t=1.44\end{array} \)

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


Prompt:
Misconception:
When multiplying fractions, multiplies the denominator

Question:
Calculate the time taken \( (t) \) for a a particle to travel with acceleration \( (a)=4.1 \mathrm{~ms}^{-2} \), initial velocity \( (u)=2.8 \mathrm{~ms}^{-1} \) and final velocity \( (v)=8.7 \mathrm{~ms}^{-1} \) \( t=\frac{1}{a}(v-u) \)

Options:
A. \( \begin{array}{c}t=\frac{1}{4.1}+(8.7-2.8) \\ t=6.14\end{array} \)
B. \( \begin{array}{c}t=4.1 \times(8.7-2.8) \\ t=24.19\end{array} \)
C. \( \begin{array}{c}t=4.1+(8.7-2.8) \\ t=10\end{array} \)
D. \( \begin{array}{c}t=(8.7-2.8) \div 4.1 \\ t=1.44\end{array} \)

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


Prompt:
Misconception:
Confuses the meaning of perpendicular and vertical

Question:
![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a diagonal line, with a positive gradient of 1.5. EF is a vertical line measuring 3 units. GH is a diagonal line with a negative gradient of -4/6. IJ is a diagonal line with a negative gradient of -3. KL is a diagonal line with a positive gradient of 1/3. MN is a vertical line measuring 6 units. OP is a diagonal line with a positive gradient of 6/4.]() Which line segment is perpendicular to IJ?

Options:
A. \( \mathrm{KL} \)
B. EF
C. \( \mathrm{MN} \)
D. \( C D \)

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:
Confuses the meaning of perpendicular and vertical

Question:
![An image of 8 line segments on a square grid. AB is a vertical line measuring 4 units. CD is a diagonal line, with a positive gradient of 1.5. EF is a vertical line measuring 3 units. GH is a diagonal line with a negative gradient of -4/6. IJ is a diagonal line with a negative gradient of -3. KL is a diagonal line with a positive gradient of 1/3. MN is a vertical line measuring 6 units. OP is a diagonal line with a positive gradient of 6/4.]() Which line segment is perpendicular to IJ?

Options:
A. \( \mathrm{KL} \)
B. EF
C. \( \mathrm{MN} \)
D. \( C D \)

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

Question:
\( s=u t+\frac{1}{2} a t^{2} \) What is the value of \( S \) when
\[\begin{array}{l} a=4 \\ u=3 \\ t=5\end{array}\]

Options:
A. \( 25 \)
B. \( 115 \)
C. \( 625 \)
D. \( 65 \)

Solve the problem as a student with the misconception above.
You 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:
Work out: \( \frac{5}{7}-\frac{1}{4} \) Give your answer in the simplest form.

Options:
A. \( \frac{27}{28} \)
B. \( \frac{4}{3} \)
C. \( \frac{13}{28} \)
D. \( \frac{1}{7} \)

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


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

Question:
Work out: \( \frac{5}{7}-\frac{1}{4} \) Give your answer in the simplest form.

Options:
A. \( \frac{27}{28} \)
B. \( \frac{4}{3} \)
C. \( \frac{13}{28} \)
D. \( \frac{1}{7} \)

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


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

Question:
Work out: \( \frac{5}{7}-\frac{1}{4} \) Give your answer in the simplest form.

Options:
A. \( \frac{27}{28} \)
B. \( \frac{4}{3} \)
C. \( \frac{13}{28} \)
D. \( \frac{1}{7} \)

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


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

Question:
\(
T=k^{4}
\)

What is the value of \( T \) when \( k=-3 \) ?

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

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


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

Question:
\(
T=k^{4}
\)

What is the value of \( T \) when \( k=-3 \) ?

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

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Which of the following answers shows a correct factorisation of the expression below? \( x^{2}-9 \)

Options:
A. \( (x-3)(x+3) \)
B. \( x(x-9) \)
C. \( (x-3)^{2} \)
D. Cannot be factorised

Solve the problem as a student with the misconception above.
You 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 factorised form of repeated roots and the difference of 2 squares

Question:
Which of the following answers shows a correct factorisation of the expression below? \( x^{2}-9 \)

Options:
A. \( (x-3)(x+3) \)
B. \( x(x-9) \)
C. \( (x-3)^{2} \)
D. Cannot be factorised

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Which of the following answers shows a correct factorisation of the expression below? \( x^{2}-9 \)

Options:
A. \( (x-3)(x+3) \)
B. \( x(x-9) \)
C. \( (x-3)^{2} \)
D. Cannot be factorised

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


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

Question:
\( \frac{1}{3}+\frac{1}{4}+\frac{2}{3}+\frac{3}{4}= \)

Options:
A. \( \frac{7}{12} \)
B. \( \frac{7}{14} \)
C. \( 2 \)
D. \( \frac{28}{12} \)

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


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

Question:
\( \frac{1}{3}+\frac{1}{4}+\frac{2}{3}+\frac{3}{4}= \)

Options:
A. \( \frac{7}{12} \)
B. \( \frac{7}{14} \)
C. \( 2 \)
D. \( \frac{28}{12} \)

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


Prompt:
Misconception:
Does not fully simplify fraction

Question:
Write this as a single fraction as simply as possible
\(
\frac{2}{x}+\frac{3}{x}
\)

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

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


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

Question:
Write this as a single fraction as simply as possible
\(
\frac{2}{x}+\frac{3}{x}
\)

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

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


Prompt:
Misconception:
When asked to add fractions uses the method for multiplying fractions instead.

Question:
Write this as a single fraction as simply as possible
\(
\frac{2}{x}+\frac{3}{x}
\)

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

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


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

Question:
What is the reciprocal of \( 7 \) ?

Options:
A. \( -\frac{1}{7} \)
B. \( \frac{1}{7} \)
C. \( -7 \)
D. \( 0.7 \)

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


Prompt:
Misconception:
Makes the number negative when asked to find the reciprocal

Question:
What is the reciprocal of \( 7 \) ?

Options:
A. \( -\frac{1}{7} \)
B. \( \frac{1}{7} \)
C. \( -7 \)
D. \( 0.7 \)

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


Prompt:
Misconception:
Confuses the equations of vertical and horizontal lines

Question:
This is the graph of \( y=(x+4)(x-2) \) ![\( W \)]() What is the equation of the line of symmetry?

Options:
A. \( y=-8 \)
B. \( x=--4 \)
C. \( y=-1 \)
D. \( x=-1 \)

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


Prompt:
Misconception:
Thinks you can divide the variables and the numerical values by different numbers when simplifying an algebraic fraction

Question:
Write the following as simply as possible: \( \frac{6 p-9}{6 p-3} \)

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

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

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

Options:
A. \( \frac{1}{2} \)
B. \( \frac{5}{18} \)
C. \( \frac{2}{9} \)
D. \( \frac{1}{15} \)

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


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

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

Options:
A. \( \frac{1}{2} \)
B. \( \frac{5}{18} \)
C. \( \frac{2}{9} \)
D. \( \frac{1}{15} \)

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:
Thinks x^2 - a^2x is a valid form of difference of two squares

Question:
Solve this equation, giving all solutions:
\(
k^{2}-8 k=0
\)

Options:
A. \( \begin{array}{c}k=-8 \\ \text { or } \\ k=8\end{array} \)
B. \( k=\sqrt{8} \)
C. \( k=8 \)
D. \(
k=0
\)
or
\(
k=8
\)

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


Prompt:
Misconception:
Believes they can divide by a variable without checking whether it could equal zero

Question:
Solve this equation, giving all solutions:
\(
k^{2}-8 k=0
\)

Options:
A. \( \begin{array}{c}k=-8 \\ \text { or } \\ k=8\end{array} \)
B. \( k=\sqrt{8} \)
C. \( k=8 \)
D. \(
k=0
\)
or
\(
k=8
\)

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


Prompt:
Misconception:
Believes the angle in a pie chart sector is equal to the frequency

Question:
The pie chart shows the favourite subjects of children at a school.

If \( 18 \) students chose Science, how many chose French? ![A pie chart split into four parts, labelled with school subjects. The part for Mathematics is 144 degrees, Science is 36 degrees, English is 72 degrees and French is 108 degrees.]()

Options:
A. \( 36 \)
B. \( 54 \)
C. \( 108 \)
D. \( 50 \)

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


Prompt:
Misconception:
Believes the angle in a pie chart sector is equal to the frequency

Question:
The pie chart shows the favourite subjects of children at a school.

If \( 18 \) students chose Science, how many chose French? ![A pie chart split into four parts, labelled with school subjects. The part for Mathematics is 144 degrees, Science is 36 degrees, English is 72 degrees and French is 108 degrees.]()

Options:
A. \( 36 \)
B. \( 54 \)
C. \( 108 \)
D. \( 50 \)

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


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

Question:
\( \left(3 \times 10^{4}\right)-\left(2 \times 10^{5}\right)= \)

Options:
A. \( 1.7 \times 10^{-5} \)
B. \( 1 \times 10^{-1} \)
C. \( -1.7 \times 10^{5} \)
D. \( -1.7 \times 10^{4} \)

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


Prompt:
Misconception:
When calculating with numbers in standard form, just applies the operation to the number and the power separately

Question:
\( \left(3 \times 10^{4}\right)-\left(2 \times 10^{5}\right)= \)

Options:
A. \( 1.7 \times 10^{-5} \)
B. \( 1 \times 10^{-1} \)
C. \( -1.7 \times 10^{5} \)
D. \( -1.7 \times 10^{4} \)

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:
Names one of the faces of a 3D shape rather than the 3D shape name

Question:
This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]()

Options:
A. Rectangle
B. Cuboid
C. Cube
D. Rectanglebased pyramid

Solve the problem as a student with the misconception above.
You 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 cubes and cuboids

Question:
This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]()

Options:
A. Rectangle
B. Cuboid
C. Cube
D. Rectanglebased pyramid

Solve the problem as a student with the misconception above.
You 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:
This is the net of a... ![An image of six connected rectangles. The six rectangles are 3 lots of identical rectangle pairs. There is a central rectangle with identical rectangles attached to the left and right of it. It then has identical rectangles attached to its top and bottom sides. Below the rectangle attached to the bottom side is another attached rectangle which is identical to the central rectangle.]()

Options:
A. Rectangle
B. Cuboid
C. Cube
D. Rectanglebased pyramid

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


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

Question:
Tom and Katie are arguing about parallel lines.
Tom says \( \boldsymbol{y}=\mathbf{5} \boldsymbol{x}+\mathbf{7} \) and \( \boldsymbol{y}=\mathbf{3 x + 7} \) are parallel.
Katie says \( \boldsymbol{y}=\mathbf{5} \boldsymbol{x}+\mathbf{7} \) and \( \boldsymbol{y}=\mathbf{5} \boldsymbol{x}-\mathbf{2 2} \) are parallel.
Who is correct?

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

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


Prompt:
Misconception:
Believes lines can be parallel by having the same y intercept OR gradient

Question:
Tom and Katie are arguing about parallel lines.
Tom says \( \boldsymbol{y}=\mathbf{5} \boldsymbol{x}+\mathbf{7} \) and \( \boldsymbol{y}=\mathbf{3 x + 7} \) are parallel.
Katie says \( \boldsymbol{y}=\mathbf{5} \boldsymbol{x}+\mathbf{7} \) and \( \boldsymbol{y}=\mathbf{5} \boldsymbol{x}-\mathbf{2 2} \) are parallel.
Who is correct?

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

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


Prompt:
Misconception:
Does not understand inequality notation

Question:
Complete the missing blank as a percentage:
\(
0.4=\frac{2}{5}< \_\_\_\_
\)

Options:
A. \( 40 \% \)
B. \( 20 \% \)
C. \( 60 \% \)
D. \( 2.5 \% \)

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 greater than and less than symbols

Question:
Complete the missing blank as a percentage:
\(
0.4=\frac{2}{5}< \_\_\_\_
\)

Options:
A. \( 40 \% \)
B. \( 20 \% \)
C. \( 60 \% \)
D. \( 2.5 \% \)

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:
Adds instead of multiplies

Question:
\( 0.4 \times 5= \)

Options:
A. \( 2 \)
B. \( 0.9 \)
C. \( 0.20 \)
D. \( 0.45 \)

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


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

Question:
\( 0.4 \times 5= \)

Options:
A. \( 2 \)
B. \( 0.9 \)
C. \( 0.20 \)
D. \( 0.45 \)

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


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

Question:
\( 0.4 \times 5= \)

Options:
A. \( 2 \)
B. \( 0.9 \)
C. \( 0.20 \)
D. \( 0.45 \)

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


Prompt:
Misconception:
Confuses reciprocal and exponential graphs

Question:
Which of the following is most likely to be the graph of a reciprocal function?

Options:
A. ![A curved graph that starts just above the x-axis on the left and travels right and very gradually up. Just before it reaches the y-axis it travels more steeply up and right, going through a point on the y-axis above the origin and continually steeply rising up and right. ]()
B. ![A graph with two curves, in the top right and bottom left quadrants. The top right curves starts up and right of the origin and travels steeply down and right, it then levels off to travel alongside the x-axis without touching it. The bottom left curve starts down and left of the origin, travels steeply up and left, it then levels off just below the x-axis without touching it.]()
C. ![A curved graph that starts in the top left, travels steeply down and right, turns to travel steeply up and right, to the origin, where it turns around to travel down and right again.]()
D. ![A curved graph, an upside down symmetrical U shape. It starts in the bottom left, travels steeply up and right, turns at a point on the y-axis above the origin and travels steeply right and down.]()

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


Prompt:
Misconception:
confuses cubic and reciprocal graphs

Question:
Which of the following is most likely to be the graph of a reciprocal function?

Options:
A. ![A curved graph that starts just above the x-axis on the left and travels right and very gradually up. Just before it reaches the y-axis it travels more steeply up and right, going through a point on the y-axis above the origin and continually steeply rising up and right. ]()
B. ![A graph with two curves, in the top right and bottom left quadrants. The top right curves starts up and right of the origin and travels steeply down and right, it then levels off to travel alongside the x-axis without touching it. The bottom left curve starts down and left of the origin, travels steeply up and left, it then levels off just below the x-axis without touching it.]()
C. ![A curved graph that starts in the top left, travels steeply down and right, turns to travel steeply up and right, to the origin, where it turns around to travel down and right again.]()
D. ![A curved graph, an upside down symmetrical U shape. It starts in the bottom left, travels steeply up and right, turns at a point on the y-axis above the origin and travels steeply right and down.]()

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


Prompt:
Misconception:
Confuses reciprocal and quadratic graphs

Question:
Which of the following is most likely to be the graph of a reciprocal function?

Options:
A. ![A curved graph that starts just above the x-axis on the left and travels right and very gradually up. Just before it reaches the y-axis it travels more steeply up and right, going through a point on the y-axis above the origin and continually steeply rising up and right. ]()
B. ![A graph with two curves, in the top right and bottom left quadrants. The top right curves starts up and right of the origin and travels steeply down and right, it then levels off to travel alongside the x-axis without touching it. The bottom left curve starts down and left of the origin, travels steeply up and left, it then levels off just below the x-axis without touching it.]()
C. ![A curved graph that starts in the top left, travels steeply down and right, turns to travel steeply up and right, to the origin, where it turns around to travel down and right again.]()
D. ![A curved graph, an upside down symmetrical U shape. It starts in the bottom left, travels steeply up and right, turns at a point on the y-axis above the origin and travels steeply right and down.]()

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


Prompt:
Misconception:
Confuses vertically opposite angles and angles around a point

Question:
What is the relationship between these two angles? ![\( \theta \)]()

Options:
A. They are equal
B. They are parallel
C. They add together to make \[180\degree\]
D. They add together to make \[360\degree\]

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


Prompt:
Misconception:
Does not know the meaning of the word parallel

Question:
What is the relationship between these two angles? ![\( \theta \)]()

Options:
A. They are equal
B. They are parallel
C. They add together to make \[180\degree\]
D. They add together to make \[360\degree\]

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


Prompt:
Misconception:
Believes angles around a point sum to 180

Question:
What is the relationship between these two angles? ![\( \theta \)]()

Options:
A. They are equal
B. They are parallel
C. They add together to make \[180\degree\]
D. They add together to make \[360\degree\]

Solve the problem as a student with the misconception above.
You 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 unit fractions with a difference of 1 in the denominator have no other fractions between them

Question:
Which of the following fractions would lie between \( \frac{1}{5} \) and \( \frac{1}{4} \) on a number line?

Options:
A. \( \frac{2}{5} \)
B. \( \frac{4}{20} \)
C. \( \frac{9}{40} \)
D. There are no fractions between these two

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


Prompt:
Misconception:
Does not realize we can write a division as a fraction

Question:
\( a, b \) and \( c \) are different numbers
\(
\frac{a+b}{c}=(a+b) \div c
\)
Is the above relationship...

Options:
A. always true
B. sometimes true
C. never true
D. Need more 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 realize we can write a division as a fraction

Question:
\( a, b \) and \( c \) are different numbers
\(
\frac{a+b}{c}=(a+b) \div c
\)
Is the above relationship...

Options:
A. always true
B. sometimes true
C. never true
D. Need more 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 two variables next to each other represent addition

Question:
Which statement correctly describes the following algebraic expression?
\(
3+a b
\)

Options:
A. "Add \( 3 \) to a multiplied by b."
B. "Add \( \mathrm{a} \) and \( \mathrm{b} \) then add three."
C. "Add three to a and then multiply by b."
D. "Add three to \( \mathrm{b} \) and then multiply by a."

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