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

Question:
What should replace the star? \( 0.03 \times \bigstar=0.00009 \)

Options:
A. \( 0.003 \)
B. \( 0.03 \)
C. \( 0.3 \)
D. \( 0.0003 \)

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


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

Question:
What should replace the star? \( 0.03 \times \bigstar=0.00009 \)

Options:
A. \( 0.003 \)
B. \( 0.03 \)
C. \( 0.3 \)
D. \( 0.0003 \)

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


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

Question:
What should replace the star? \( 0.03 \times \bigstar=0.00009 \)

Options:
A. \( 0.003 \)
B. \( 0.03 \)
C. \( 0.3 \)
D. \( 0.0003 \)

Solve the problem as a student with the misconception above.
You 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 a problem that requires an inverse operation (e.g. missing number problems), does the original operation

Question:
What should replace the star?
\[
\bigstar-26=28
\]

Options:
A. \( 54 \)
B. \( 2 \)
C. \( -2 \)
D. \( 44 \)

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


Prompt:
Misconception:
When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation

Question:
What should replace the star?
\[
\bigstar-26=28
\]

Options:
A. \( 54 \)
B. \( 2 \)
C. \( -2 \)
D. \( 44 \)

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


Prompt:
Misconception:
When two digits sum to 10 or more during an addition problem, does not add one to the preceding digit

Question:
What should replace the star?
\[
\bigstar-26=28
\]

Options:
A. \( 54 \)
B. \( 2 \)
C. \( -2 \)
D. \( 44 \)

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


Prompt:
Misconception:
When asked to multiply fractions, uses the method for adding instead

Question:
Express the following as a single fraction, writing your answer as simply as possible:

\(
\frac{1}{s} \times \frac{2}{t}
\)

Options:
A. \( \frac{2}{s t} \)
B. \( \frac{t+2 s}{s t} \)
C. \( \frac{3}{s+t} \)
D. \( \frac{3}{s t} \)

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


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

Question:
Express the following as a single fraction, writing your answer as simply as possible:

\(
\frac{1}{s} \times \frac{2}{t}
\)

Options:
A. \( \frac{2}{s t} \)
B. \( \frac{t+2 s}{s t} \)
C. \( \frac{3}{s+t} \)
D. \( \frac{3}{s t} \)

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


Prompt:
Misconception:
When multiplying fractions, adds the numerators and multiplies the denominators

Question:
Express the following as a single fraction, writing your answer as simply as possible:

\(
\frac{1}{s} \times \frac{2}{t}
\)

Options:
A. \( \frac{2}{s t} \)
B. \( \frac{t+2 s}{s t} \)
C. \( \frac{3}{s+t} \)
D. \( \frac{3}{s t} \)

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


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

Question:
\( 18 \div 2+2 \times 2= \)

Options:
A. \( 3 \)
B. \( 13 \)
C. \( 22 \)
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:
Carries out operations from left to right regardless of priority order

Question:
\( 18 \div 2+2 \times 2= \)

Options:
A. \( 3 \)
B. \( 13 \)
C. \( 22 \)
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:
Cannot identify a fraction on a number line

Question:
What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]()

Options:
A. \( \frac{2}{3} \)
B. \( 1 \frac{2}{3} \)
C. \( \frac{5}{3} \)
D. \( \frac{4}{2} \)

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


Prompt:
Misconception:
Confused mixed numbers with improper fractions

Question:
What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]()

Options:
A. \( \frac{2}{3} \)
B. \( 1 \frac{2}{3} \)
C. \( \frac{5}{3} \)
D. \( \frac{4}{2} \)

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


Prompt:
Misconception:
Cannot identify a fraction on a number line

Question:
What improper fraction is shown on the number line? ![Line with 5 dashes spaced equally. No dashes at the start and end of the line. First dash marked with a 1 fourth dash marked with a 2. Blue arrow pointing upwards towards the third dash.]()

Options:
A. \( \frac{2}{3} \)
B. \( 1 \frac{2}{3} \)
C. \( \frac{5}{3} \)
D. \( \frac{4}{2} \)

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


Prompt:
Misconception:
When 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?

\[
2,2,3,3,2
\]

Options:
A. \( 2 \)
B. A little more than \( 2 \)
C. \( 3 \)
D. A little less than \( 2 \)

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


Prompt:
Misconception:
Believes the mean is the middle number

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

\[
2,2,3,3,2
\]

Options:
A. \( 2 \)
B. A little more than \( 2 \)
C. \( 3 \)
D. A little less than \( 2 \)

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


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

Question:
![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners
What is the probability of getting a \( 1 \) on both spinners?

Options:
A. \( \frac{1}{9} \)
B. \( \frac{1}{20} \)
C. \( \frac{2}{9} \)
D. \( \frac{2}{20} \)

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


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

Question:
![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners
What is the probability of getting a \( 1 \) on both spinners?

Options:
A. \( \frac{1}{9} \)
B. \( \frac{1}{20} \)
C. \( \frac{2}{9} \)
D. \( \frac{2}{20} \)

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


Prompt:
Misconception:
When multiplying fractions, adds the numerators and multiplies the denominators

Question:
![Two spinners shown. The first spinner has the numbers 1-4 and the second spinner has the number 1-5.]() You spin the above fair spinners
What is the probability of getting a \( 1 \) on both spinners?

Options:
A. \( \frac{1}{9} \)
B. \( \frac{1}{20} \)
C. \( \frac{2}{9} \)
D. \( \frac{2}{20} \)

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


Prompt:
Misconception:
Believes if you changed all values by the same proportion the range would not change

Question:
Tom and Katie are discussing the \( 5 \) plants with these heights:
\[
23 \mathrm{~cm}, \quad 17 \mathrm{~cm}, \quad 40 \mathrm{~cm}, \quad 25 \mathrm{~cm}, \quad 31 \mathrm{~cm}
\]

Tom says if all the plants doubled in height, the range wouldn't change.

Katie says if all the plants grew by \( 12 \mathrm{~cm} \) each, the range wouldn't change.
Who do you agree with?

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

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


Prompt:
Misconception:
Believes if you changed all values by the same proportion the range would not change

Question:
Tom and Katie are discussing the \( 5 \) plants with these heights:
\[
23 \mathrm{~cm}, \quad 17 \mathrm{~cm}, \quad 40 \mathrm{~cm}, \quad 25 \mathrm{~cm}, \quad 31 \mathrm{~cm}
\]

Tom says if all the plants doubled in height, the range wouldn't change.

Katie says if all the plants grew by \( 12 \mathrm{~cm} \) each, the range wouldn't change.
Who do you agree with?

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

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


Prompt:
Misconception:
Believes if you add the same value to all numbers in the dataset the range will change

Question:
Tom and Katie are discussing the \( 5 \) plants with these heights:
\[
23 \mathrm{~cm}, \quad 17 \mathrm{~cm}, \quad 40 \mathrm{~cm}, \quad 25 \mathrm{~cm}, \quad 31 \mathrm{~cm}
\]

Tom says if all the plants doubled in height, the range wouldn't change.

Katie says if all the plants grew by \( 12 \mathrm{~cm} \) each, the range wouldn't change.
Who do you agree with?

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

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


Prompt:
Misconception:
Thinks you can divide terms by different factors when simplifying an algebraic fraction

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

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

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


Prompt:
Misconception:
Does not recognise difference of two squares

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

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

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


Prompt:
Misconception:
Only looks at the difference between one pair of terms when discerning the pattern

Question:
If the original sequence looks like this: ![Two patterns made of squares. Pattern 1 consists of a central column of three squares, with an extra square either side, making a cross. Pattern two consists of two central columns of three squares with one extra square either side. ]() There are \( 302 \) squares in Pattern \( 100 \). But if the shape changes to this: ![These patterns are the same as those in the first picture except that in each, the second block from each column of three has been removed. ]() How many squares would there be in Pattern \( 100 \) now?

Options:
A. \( 301 \)
B. \( 300 \)
C. \( 299 \)
D. \( 202 \)

Solve the problem as a student with the misconception above.
You 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 looks at the difference between one pair of terms when discerning the pattern

Question:
If the original sequence looks like this: ![Two patterns made of squares. Pattern 1 consists of a central column of three squares, with an extra square either side, making a cross. Pattern two consists of two central columns of three squares with one extra square either side. ]() There are \( 302 \) squares in Pattern \( 100 \). But if the shape changes to this: ![These patterns are the same as those in the first picture except that in each, the second block from each column of three has been removed. ]() How many squares would there be in Pattern \( 100 \) now?

Options:
A. \( 301 \)
B. \( 300 \)
C. \( 299 \)
D. \( 202 \)

Solve the problem as a student with the misconception above.
You 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:
\[
0.059623
\]
What is this number rounded to the nearest integer?

Options:
A. \( 0.06 \)
B. \( 0.05 \)
C. \( 1 \)
D. \( 0 \)

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


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

Question:
\[
0.059623
\]
What is this number rounded to the nearest integer?

Options:
A. \( 0.06 \)
B. \( 0.05 \)
C. \( 1 \)
D. \( 0 \)

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


Prompt:
Misconception:
Rounds up instead of down

Question:
\[
0.059623
\]
What is this number rounded to the nearest integer?

Options:
A. \( 0.06 \)
B. \( 0.05 \)
C. \( 1 \)
D. \( 0 \)

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


Prompt:
Misconception:
Thinks co-interior angles are equal

Question:
What is the size of angle \( p \) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]()

Options:
A. \( 65^{\circ} \)
B. \( 125^{\circ} \)
C. \( 115^{\circ} \)
D. Not enough information to work it out

Solve the problem as a student with the misconception above.
You 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:
What is the size of angle \( p \) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]()

Options:
A. \( 65^{\circ} \)
B. \( 125^{\circ} \)
C. \( 115^{\circ} \)
D. Not enough information to work it out

Solve the problem as a student with the misconception above.
You 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 parallel lines angle rules applied inside a shape

Question:
What is the size of angle \( p \) in this quadrilateral? ![Parallelogram showing 65 degrees in bottom left angles, and missing angle p, in top left]()

Options:
A. \( 65^{\circ} \)
B. \( 125^{\circ} \)
C. \( 115^{\circ} \)
D. Not enough information to work it out

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


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

Question:
A shape is made up of a square and a rectangle. ![\begin{tabular}{|l|l|}
\hline & \\
\hline & \\
\hline
\end{tabular}]() The perimeter of the shape is \( 30 \mathrm{~cm} \). The area of the square is \( 16 \mathrm{~cm}^{2} \).
What is the area of the shape?

Options:
A. \( 4 \mathrm{~cm}^{2} \)
B. \( 60 \mathrm{~cm}^{2} \)
C. \( 44 \mathrm{~cm}^{2} \)
D. \( 104 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Rounds up instead of down

Question:
A number rounds to \( 20,000 \) when rounded to the nearest ten thousand, thousand and hundred.
Which number could this be?

Options:
A. \( 19199 \)
B. \( 20074 \)
C. \( 20043 \)
D. \( 19949 \)

Solve the problem as a student with the misconception above.
You 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:
A number rounds to \( 20,000 \) when rounded to the nearest ten thousand, thousand and hundred.
Which number could this be?

Options:
A. \( 19199 \)
B. \( 20074 \)
C. \( 20043 \)
D. \( 19949 \)

Solve the problem as a student with the misconception above.
You 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:
A number rounds to \( 20,000 \) when rounded to the nearest ten thousand, thousand and hundred.
Which number could this be?

Options:
A. \( 19199 \)
B. \( 20074 \)
C. \( 20043 \)
D. \( 19949 \)

Solve the problem as a student with the misconception above.
You 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 corresponding and alternate angles

Question:
These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]()

Options:
A. Alternate
B. Corresponding
C. Co-Interior
D. Parallel

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


Prompt:
Misconception:
Confuses co-interior and alternate angles

Question:
These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]()

Options:
A. Alternate
B. Corresponding
C. Co-Interior
D. Parallel

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


Prompt:
Misconception:
Describes lines when asked to describe angles

Question:
These marked angles are: ![A pair of parallel lines drawn pointing up to the right. A straight line is drawn that crosses both parallel lines. The angles formed above the straight line and to the right of each of the parallel lines is marked.]()

Options:
A. Alternate
B. Corresponding
C. Co-Interior
D. Parallel

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


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

Question:
![A linear graph showing that 10 miles = £8. ]() The graph can be used to work out how much Kay's company pays her for travel.

Kay's company paid her \( £ 80 \)

How many miles did she travel?

Options:
A. \( 96 \)
B. \( 100 \)
C. \( 64 \)
D. \( 80 \)

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


Prompt:
Misconception:
Believes direct proportion means a 1:1 ratio

Question:
![A linear graph showing that 10 miles = £8. ]() The graph can be used to work out how much Kay's company pays her for travel.

Kay's company paid her \( £ 80 \)

How many miles did she travel?

Options:
A. \( 96 \)
B. \( 100 \)
C. \( 64 \)
D. \( 80 \)

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


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

Question:
\( 0.4=\frac{2}{5}=? \% \)

Options:
A. \( 25 \% \)
B. \( 40 \% \)
C. \( 50 \% \)
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:
Multiplies by 10 instead of 100 when converting decimal to percentage

Question:
\( 0.4=\frac{2}{5}=? \% \)

Options:
A. \( 25 \% \)
B. \( 40 \% \)
C. \( 50 \% \)
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:
Counts squares instead of the correct scale when plotting coordinates

Question:
What is the equation of this line? ![A coordinate grid with a red line drawn on passing through the points: (-2,-10) (-2,-2) (-2, 0) (-2,4) (-2,10)]()

Options:
A. \( y=10 \)
B. \( x=-1 \)
C. \( y=-2 \)
D. \( x=-2 \)

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


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

Question:
What is the equation of this line? ![A coordinate grid with a red line drawn on passing through the points: (-2,-10) (-2,-2) (-2, 0) (-2,4) (-2,10)]()

Options:
A. \( y=10 \)
B. \( x=-1 \)
C. \( y=-2 \)
D. \( x=-2 \)

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


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

Question:
![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape?

Options:
A. Square
B. Rhombus
C. Kite
D. Rectangle

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


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

Question:
![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape?

Options:
A. Square
B. Rhombus
C. Kite
D. Rectangle

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


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

Question:
![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape?

Options:
A. Square
B. Rhombus
C. Kite
D. Rectangle

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


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

Question:
\( 53, \quad 46, \quad 39, \quad \ldots \) What is the \( 8^{\text {th }} \) term in this linear sequence?

Options:
A. \( 32 \)
B. \( 5 \)
C. \( 4 \)
D. \( -3 \)

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


Prompt:
Misconception:
When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "+¼" written inside it and the final rectangle has "output" written above it and "8" written inside it.]() What is the input of this function machine?

Options:
A. \( 8 \frac{1}{4} \)
B. \( 7 \frac{3}{4} \)
C. \( 2 \)
D. \( 32 \)

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


Prompt:
Misconception:
Thinks the inverse of addition is multiplication

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "+¼" written inside it and the final rectangle has "output" written above it and "8" written inside it.]() What is the input of this function machine?

Options:
A. \( 8 \frac{1}{4} \)
B. \( 7 \frac{3}{4} \)
C. \( 2 \)
D. \( 32 \)

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


Prompt:
Misconception:
Thinks the inverse of addition is division

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "+¼" written inside it and the final rectangle has "output" written above it and "8" written inside it.]() What is the input of this function machine?

Options:
A. \( 8 \frac{1}{4} \)
B. \( 7 \frac{3}{4} \)
C. \( 2 \)
D. \( 32 \)

Solve the problem as a student with the misconception above.
You 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 proportion of a whole is whole/part not part/whole

Question:
The pie chart shows the meal choices of guests at a wedding.

If there were \( 540 \) people at the wedding, which of the following would calculate how many people chose pork? ![A pie chart split into four parts, labelled with meal choices. The part for Beef is 150 degrees, Pork is 40 degrees and Other is 80 degrees. The angle for Vegetarian is labelled with a square right angle symbol.]()

Options:
A. \( \frac{360}{40} \times 540 \)
B. \( \frac{40}{360} \times 540 \)
C. \( \frac{40}{540} \times 360 \)
D. You 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:
Believes it is not possible to calculate the frequency for a pie chart sector despite being given enough information to do so

Question:
The pie chart shows the meal choices of guests at a wedding.

If there were \( 540 \) people at the wedding, which of the following would calculate how many people chose pork? ![A pie chart split into four parts, labelled with meal choices. The part for Beef is 150 degrees, Pork is 40 degrees and Other is 80 degrees. The angle for Vegetarian is labelled with a square right angle symbol.]()

Options:
A. \( \frac{360}{40} \times 540 \)
B. \( \frac{40}{360} \times 540 \)
C. \( \frac{40}{540} \times 360 \)
D. You 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:
Performs subtraction in wrong order

Question:
\( 609-1000= \)

Options:
A. \( -401 \)
B. \( 391 \)
C. \( -391 \)
D. This problem cannot be solved

Solve the problem as a student with the misconception above.
You 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 not take away a larger number from a smaller one

Question:
\( 609-1000= \)

Options:
A. \( -401 \)
B. \( 391 \)
C. \( -391 \)
D. This problem cannot be solved

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


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

Question:
Tom and Katie are arguing about a first step to solve this equation:
\(
\frac{m}{4}-1=20
\)
Tom says you can write: \( \frac{m}{4}=21 \)
Katie says you can write: \( m-1=80 \)
Who is correct?

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

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


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

Question:
Tom and Katie are arguing about a first step to solve this equation:
\(
\frac{m}{4}-1=20
\)
Tom says you can write: \( \frac{m}{4}=21 \)
Katie says you can write: \( m-1=80 \)
Who is correct?

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

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


Prompt:
Misconception:
Does not know how to solve linear equations involving fractions

Question:
Tom and Katie are arguing about a first step to solve this equation:
\(
\frac{m}{4}-1=20
\)
Tom says you can write: \( \frac{m}{4}=21 \)
Katie says you can write: \( m-1=80 \)
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 direction of North East, North West, South East and South West cardinal points

Question:
On what bearing is North-West? ![Shows a compass.]()

Options:
A. \( 270^{\circ} \)
B. \( 225^{\circ} \)
C. \( 045^{\circ} \)
D. \( 315^{\circ} \)

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


Prompt:
Misconception:
Does not measure bearing clockwise from the north line

Question:
On what bearing is North-West? ![Shows a compass.]()

Options:
A. \( 270^{\circ} \)
B. \( 225^{\circ} \)
C. \( 045^{\circ} \)
D. \( 315^{\circ} \)

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Factorise this expression, if possible: \( p^{2}-100 \)

Options:
A. \( p(p-10) \)
B. \( (p-10)(p-10) \)
C. \( (p-10)(p+10) \)
D. Does not factorise

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


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

Question:
Factorise this expression, if possible: \( p^{2}-100 \)

Options:
A. \( p(p-10) \)
B. \( (p-10)(p-10) \)
C. \( (p-10)(p+10) \)
D. Does not factorise

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Factorise this expression, if possible: \( p^{2}-100 \)

Options:
A. \( p(p-10) \)
B. \( (p-10)(p-10) \)
C. \( (p-10)(p+10) \)
D. Does not factorise

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


Prompt:
Misconception:
Does not understand the term factor

Question:
Tom and Katie are discussing factors of \( \mathbf{1 2 y} \)
Tom says \( y \) is a factor of \( 12 y \)
Katie says \( 3 \) is a factor of \( 12 y \)
Who do you agree with?

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

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


Prompt:
Misconception:
Believes factors of algebraic terms/expressions will only be numbers

Question:
Tom and Katie are discussing factors of \( \mathbf{1 2 y} \)
Tom says \( y \) is a factor of \( 12 y \)
Katie says \( 3 \) is a factor of \( 12 y \)
Who do you agree with?

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

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


Prompt:
Misconception:
Does not understand the term factor

Question:
Tom and Katie are discussing factors of \( \mathbf{1 2 y} \)
Tom says \( y \) is a factor of \( 12 y \)
Katie says \( 3 \) is a factor of \( 12 y \)
Who do you agree with?

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

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


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

Question:
What is \( \mathbf{3 2 0} 050 \) rounded to the nearest hundred?

Options:
A. \( 321000 \)
B. \( 320050 \)
C. \( 320100 \)
D. \( 320000 \)

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


Prompt:
Misconception:
Believes adding b to any integer gives a multiple of b

Question:
Which of the following expressions is always a multiple of \( 5 \) if \( n \) is a positive integer.

Options:
A. \( n+5 \)
B. \( 2 n+3 \)
C. \( 10 n \)
D. \( 5 n+2 \)

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


Prompt:
Misconception:
Believes they can find the nth term based on the first term only

Question:
Which of the following expressions is always a multiple of \( 5 \) if \( n \) is a positive integer.

Options:
A. \( n+5 \)
B. \( 2 n+3 \)
C. \( 10 n \)
D. \( 5 n+2 \)

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


Prompt:
Misconception:
Believes that an + b is still a multiple of a

Question:
Which of the following expressions is always a multiple of \( 5 \) if \( n \) is a positive integer.

Options:
A. \( n+5 \)
B. \( 2 n+3 \)
C. \( 10 n \)
D. \( 5 n+2 \)

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:
What is \( \mathbf{4 5 . 6 2 8} \) rounded to one significant figure?

Options:
A. \( 45.6 \)
B. \( 50 \)
C. \( 40 \)
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:
Rounds down instead of up

Question:
What is \( \mathbf{4 5 . 6 2 8} \) rounded to one significant figure?

Options:
A. \( 45.6 \)
B. \( 50 \)
C. \( 40 \)
D. \( 4 \)

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


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

Question:
Tom and Katie are discussing how to solve:
\(\frac{5 x}{3}-1=-2\)

Tom says a correct next line of working could be: \( 5 x-3=-6 \)

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

Who is correct?

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

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


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

Question:
Tom and Katie are discussing how to solve:
\(\frac{5 x}{3}-1=-2\)

Tom says a correct next line of working could be: \( 5 x-3=-6 \)

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

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:
Finds the y intercept when asked to read the solution to a quadratic equation from a graph

Question:
According to the graph, what is the approximate solution to
\(x^{2}-x-9=-6\) ![A set of axes with the quadratic graph y=x^2-x-9 drawn on.]()

Options:
A. \( x=-9 \)
B. \( x=3.5, \quad x=-2.5 \)
C. \( x=2.2, \quad x=-1.2 \)
D. No real solutions

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


Prompt:
Misconception:
Solves for y=0 instead of given y-value when reading from a quadratic graph

Question:
According to the graph, what is the approximate solution to
\(x^{2}-x-9=-6\) ![A set of axes with the quadratic graph y=x^2-x-9 drawn on.]()

Options:
A. \( x=-9 \)
B. \( x=3.5, \quad x=-2.5 \)
C. \( x=2.2, \quad x=-1.2 \)
D. No real solutions

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


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 5, y-axis from -3 to 4. Three points are plotted and joined to make a triangle: (2, 2), (4, 2), (3, 3). Point (3, 3) is labelled with the letter "P". The line y=1 is shown with a purple dashed line.
]()

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

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:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 5, y-axis from -3 to 4. Three points are plotted and joined to make a triangle: (2, 2), (4, 2), (3, 3). Point (3, 3) is labelled with the letter "P". The line y=1 is shown with a purple dashed line.
]()

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

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:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 5, y-axis from -3 to 4. Three points are plotted and joined to make a triangle: (2, 2), (4, 2), (3, 3). Point (3, 3) is labelled with the letter "P". The line y=1 is shown with a purple dashed line.
]()

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

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:
Thinks the inverse of subtraction is multiplication

Question:
![Image of a function machine. The function is subtract 3 and the output is 7]() What is the input of this function machine?

Options:
A. \( 21 \)
B. \( -4 \)
C. \( 4 \)
D. \( 10 \)

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


Prompt:
Misconception:
Believes subtraction is commutative

Question:
![Image of a function machine. The function is subtract 3 and the output is 7]() What is the input of this function machine?

Options:
A. \( 21 \)
B. \( -4 \)
C. \( 4 \)
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 finding an input of a function machine thinks you apply the operations given rather than the inverse operation.

Question:
![Image of a function machine. The function is subtract 3 and the output is 7]() What is the input of this function machine?

Options:
A. \( 21 \)
B. \( -4 \)
C. \( 4 \)
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:
Makes an assumption about line segments being equal within a shape

Question:
What is the area of this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled 15 cm, 12 cm, 7 cm and 7 cm. Two sides are unlabelled]()

Options:
A. \( 124 \mathrm{~cm}^{2} \)
B. \( 154 \mathrm{~cm}^{2} \)
C. \( 180 \mathrm{~cm}^{2} \)
D. \( 189 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
When calculating the area of a rectilinear compound shape, calculates the are of the surrounding rectangle

Question:
What is the area of this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled 15 cm, 12 cm, 7 cm and 7 cm. Two sides are unlabelled]()

Options:
A. \( 124 \mathrm{~cm}^{2} \)
B. \( 154 \mathrm{~cm}^{2} \)
C. \( 180 \mathrm{~cm}^{2} \)
D. \( 189 \mathrm{~cm}^{2} \)

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


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

Question:
If I put the numbers \( 4 \) and \( 9 \) into this function machine, what comes out? ![Flow chart starting with instruction "In" inside a blue rimmed circle, then "+ 5" inside a red rimmed square, then "double" inside a red rimmed square and lastly,  "Out" inside a blue rimmed circle.]()

Options:
A. \( 9 \) and \( 14 \)
B. \( 18 \) and \( 28 \)
C. \( 81 \) and \( 196 \)
D. \( -3 \) and \( -0.5 \)

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


Prompt:
Misconception:
When using a function machine, confuses the input and the output.

Question:
If I put the numbers \( 4 \) and \( 9 \) into this function machine, what comes out? ![Flow chart starting with instruction "In" inside a blue rimmed circle, then "+ 5" inside a red rimmed square, then "double" inside a red rimmed square and lastly,  "Out" inside a blue rimmed circle.]()

Options:
A. \( 9 \) and \( 14 \)
B. \( 18 \) and \( 28 \)
C. \( 81 \) and \( 196 \)
D. \( -3 \) and \( -0.5 \)

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


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

Question:
Add brackets to this calculation to make the answer \( 7 \). \( 16-6+4 \div 2 \)

Options:
A. \( 16-(6+4) \div 2 \)
B. \( (16-6)+4 \div 2 \)
C. \( 16-6+(4 \div 2) \)
D. \( (16-6+4) \div 2 \)

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

Question:
Add brackets to this calculation to make the answer \( 7 \). \( 16-6+4 \div 2 \)

Options:
A. \( 16-(6+4) \div 2 \)
B. \( (16-6)+4 \div 2 \)
C. \( 16-6+(4 \div 2) \)
D. \( (16-6+4) \div 2 \)

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

Question:
Add brackets to this calculation to make the answer \( 7 \). \( 16-6+4 \div 2 \)

Options:
A. \( 16-(6+4) \div 2 \)
B. \( (16-6)+4 \div 2 \)
C. \( 16-6+(4 \div 2) \)
D. \( (16-6+4) \div 2 \)

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


Prompt:
Misconception:
Thinks you can find missing values in a given table by treating the row as linear and adding on the difference between the first two values given.

Question:
This is a table of values for \( y=2 x+c \) What should replace the star? ![\begin{tabular}{l|l|l|c}
\( x \) & & \( 0 \) & \( 3 \) \\
\hline\( y \) & \( -5 \) & \( -3 \) & ఔ
\end{tabular}]()

Options:
A. \( -1 \)
B. \( 3 \)
C. \( 6 \)
D. \( -3 \)

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


Prompt:
Misconception:
Does not realise that a pair of coordinates can be used to find missing parts of an equation

Question:
This is a table of values for \( y=2 x+c \) What should replace the star? ![\begin{tabular}{l|l|l|c}
\( x \) & & \( 0 \) & \( 3 \) \\
\hline\( y \) & \( -5 \) & \( -3 \) & ఔ
\end{tabular}]()

Options:
A. \( -1 \)
B. \( 3 \)
C. \( 6 \)
D. \( -3 \)

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


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

Question:
How many rectangles would you need to shade so that \( 60 \% \) of this shape is shaded? ![A rectangle split into 20 equal parts]()

Options:
A. \( 6 \)
B. \( 3 \)
C. \( 16 \)
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:
Divides rather than multiplies when scaling up in direct proportion problems

Question:
How many rectangles would you need to shade so that \( 60 \% \) of this shape is shaded? ![A rectangle split into 20 equal parts]()

Options:
A. \( 6 \)
B. \( 3 \)
C. \( 16 \)
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:
Mixes up cubing and multiplying by 3

Question:
Which of the following numbers is a cube number?

Options:
A. \( 1 \)
B. \( 3 \)
C. \( 9 \)
D. None of these numbers are cube 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:
Mixes up square numbers and cube numbers

Question:
Which of the following numbers is a cube number?

Options:
A. \( 1 \)
B. \( 3 \)
C. \( 9 \)
D. None of these numbers are cube 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:
Does not know what a cube number is

Question:
Which of the following numbers is a cube number?

Options:
A. \( 1 \)
B. \( 3 \)
C. \( 9 \)
D. None of these numbers are cube 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:
Confuses inequality symbols with equality

Question:
The diagram on the right shows the lines \( 2=x+y \) and \( x=y \)

Which of the following coordinates satisfies the following inequalities?
\[
2<x+y \text { and } x<y
\] ![A graph showing all 4 quadrants. x axis from -2 to 5 and y axis from -3 to 5. A red line from top left sloping downwards to bottom right, going through 2 on the x axis and 2 on the y axis. A black line going from bottom left sloping upwards to top right. Going through 0 on the x axis and 0 on the y axis (only one intercept) ]()

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

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


Prompt:
Misconception:
When dividing, ignores any remainders

Question:
\[
3 \times \square=384
\]

Find the missing number.

Options:
A. \( 121 \)
B. \( 1152 \)
C. \( 128 \)
D. \( 161 \)

Solve the problem as a student with the misconception above.
You 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 a problem that requires an inverse operation (e.g. missing number problems), does the original operation

Question:
\[
3 \times \square=384
\]

Find the missing number.

Options:
A. \( 121 \)
B. \( 1152 \)
C. \( 128 \)
D. \( 161 \)

Solve the problem as a student with the misconception above.
You 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 a problem using written division (bus-stop method), does the calculation from right to left

Question:
\[
3 \times \square=384
\]

Find the missing number.

Options:
A. \( 121 \)
B. \( 1152 \)
C. \( 128 \)
D. \( 161 \)

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


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

Question:
Which shape has rotational symmetry order \( 2 \) ?

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

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


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

Question:
Which shape has rotational symmetry order \( 2 \) ?

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

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


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

Question:
Which shape has rotational symmetry order \( 2 \) ?

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

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


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

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that looks like a staircase going up from left to right, consisting of 3 steps. The full width of the diagram is 23m, the width of the first lower step is 7m, the width of the third top step is 6m. The full height of the diagram is 22m, the height os the first lower step is 5m, the height of the third top step is 8m. The shaded section is a rectangle which starts in the top left of the second (middle) step and finishes in the bottom right of the diagram.]()

Options:
A. \( 120 \mathrm{~m}^{2} \)
B. \( 224 \mathrm{~m}^{2} \)
C. \( 130 \mathrm{~m}^{2} \)
D. \( 108 \mathrm{~m}^{2} \)

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


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

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that looks like a staircase going up from left to right, consisting of 3 steps. The full width of the diagram is 23m, the width of the first lower step is 7m, the width of the third top step is 6m. The full height of the diagram is 22m, the height os the first lower step is 5m, the height of the third top step is 8m. The shaded section is a rectangle which starts in the top left of the second (middle) step and finishes in the bottom right of the diagram.]()

Options:
A. \( 120 \mathrm{~m}^{2} \)
B. \( 224 \mathrm{~m}^{2} \)
C. \( 130 \mathrm{~m}^{2} \)
D. \( 108 \mathrm{~m}^{2} \)

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


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

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that looks like a staircase going up from left to right, consisting of 3 steps. The full width of the diagram is 23m, the width of the first lower step is 7m, the width of the third top step is 6m. The full height of the diagram is 22m, the height os the first lower step is 5m, the height of the third top step is 8m. The shaded section is a rectangle which starts in the top left of the second (middle) step and finishes in the bottom right of the diagram.]()

Options:
A. \( 120 \mathrm{~m}^{2} \)
B. \( 224 \mathrm{~m}^{2} \)
C. \( 130 \mathrm{~m}^{2} \)
D. \( 108 \mathrm{~m}^{2} \)

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


Prompt:
Misconception:
Believes the number of sides gives the order of rotational symmetry

Question:
In which region would an isosceles triangle belong? ![Venn diagram with two circles labelled with 'exactly one line of symmetry' and 'rotational symmetry of order 3'. A is in the only exactly one line of symmetry region, B is in the intersection, C is in the only rotational symmetry of order 3 region and D is outside the two circles.]()

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:
When simplifying surds, does not square root the largest square number that goes into the number under the surd before putting it in front of the surd

Question:
\(
\sqrt{75}=n \sqrt{3}
\)

What is the value of \( n \) ?

Options:
A. \( 5 \)
B. \( 25 \)
C. \( 9 \)
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:
When simplifying surds, adds the number on the outside of the surd to the number under the surd

Question:
\(
\sqrt{75}=n \sqrt{3}
\)

What is the value of \( n \) ?

Options:
A. \( 5 \)
B. \( 25 \)
C. \( 9 \)
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:
Mixes up clockwise and anticlockwise

Question:
The blue shape is rotated \( 90^{\circ} \) anticlockwise about \( (-2,2) \). Which shape gives the correct answer? ![A coordinate grid with 5 congruent shapes, one blue and 4 red, which are labelled A, B, C and D. The blue shape has vertices at (-3,5) (-3,4) (-2,4) (-2,3) and (-3,3). Shape A has vertices at (-1,2) (0,2) (1,2) (0,1) (-1,1). Shape B has vertices at (0,-2) (1,-2) (1,-3) (0,-3) (-1,-3). Shape C has vertices at (-4,-2) (-3,-2) (-3,-3) (-4,-3) (-5,-3). Shape D has vertices at (-4,2) (-3,2) (-3,1) (-4,1) (-5,1).]()

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

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


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

Question:
The blue shape is rotated \( 90^{\circ} \) anticlockwise about \( (-2,2) \). Which shape gives the correct answer? ![A coordinate grid with 5 congruent shapes, one blue and 4 red, which are labelled A, B, C and D. The blue shape has vertices at (-3,5) (-3,4) (-2,4) (-2,3) and (-3,3). Shape A has vertices at (-1,2) (0,2) (1,2) (0,1) (-1,1). Shape B has vertices at (0,-2) (1,-2) (1,-3) (0,-3) (-1,-3). Shape C has vertices at (-4,-2) (-3,-2) (-3,-3) (-4,-3) (-5,-3). Shape D has vertices at (-4,2) (-3,2) (-3,1) (-4,1) (-5,1).]()

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:
Believes the centre of rotation is always the origin

Question:
The blue shape is rotated \( 90^{\circ} \) anticlockwise about \( (-2,2) \). Which shape gives the correct answer? ![A coordinate grid with 5 congruent shapes, one blue and 4 red, which are labelled A, B, C and D. The blue shape has vertices at (-3,5) (-3,4) (-2,4) (-2,3) and (-3,3). Shape A has vertices at (-1,2) (0,2) (1,2) (0,1) (-1,1). Shape B has vertices at (0,-2) (1,-2) (1,-3) (0,-3) (-1,-3). Shape C has vertices at (-4,-2) (-3,-2) (-3,-3) (-4,-3) (-5,-3). Shape D has vertices at (-4,2) (-3,2) (-3,1) (-4,1) (-5,1).]()

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 realize we can simplify a term that involves powers

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
l \times 3 \times l \times l \times g \times g
\)

Options:
A. \(l3llgg\)
B. \( l 3 l^{2} g^{2} \)
C. \( 3 g^{2} l^{3} \)
D. \( 3 g g l^{3} \)

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 correctly apply the commutative property of multiplication

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
l \times 3 \times l \times l \times g \times g
\)

Options:
A. \(l3llgg\)
B. \( l 3 l^{2} g^{2} \)
C. \( 3 g^{2} l^{3} \)
D. \( 3 g g l^{3} \)

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


Prompt:
Misconception:
Does not realize we can simplify a term that involves powers

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
l \times 3 \times l \times l \times g \times g
\)

Options:
A. \(l3llgg\)
B. \( l 3 l^{2} g^{2} \)
C. \( 3 g^{2} l^{3} \)
D. \( 3 g g l^{3} \)

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:
Counts leading zero as a significant figure

Question:
What is \( \mathbf{0 . 0 3 7 3} \) rounded to two significant figures?

Options:
A. \( 0 \)
B. \( 0.0 \)
C. \( 0.04 \)
D. \( 0.037 \)

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


Prompt:
Misconception:
Counts leading zero as a significant figure

Question:
What is \( \mathbf{0 . 0 3 7 3} \) rounded to two significant figures?

Options:
A. \( 0 \)
B. \( 0.0 \)
C. \( 0.04 \)
D. \( 0.037 \)

Solve the problem as a student with the misconception above.
You 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:
What is \( \mathbf{0 . 0 3 7 3} \) rounded to two significant figures?

Options:
A. \( 0 \)
B. \( 0.0 \)
C. \( 0.04 \)
D. \( 0.037 \)

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


Prompt:
Misconception:
Confuses a variable with an equation

Question:
Which of the following is the most appropriate word to describe: \( 6-3 g=3 \)

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

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


Prompt:
Misconception:
Confuses an equation with an expression

Question:
Which of the following is the most appropriate word to describe: \( 6-3 g=3 \)

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

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


Prompt:
Misconception:
Confuses a term with an equation

Question:
Which of the following is the most appropriate word to describe: \( 6-3 g=3 \)

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

Solve the problem as a student with the misconception above.
You 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 nth term of a descending sequence will have a positive coefficient of n

Question:
Here are the first three terms of a sequence \( \begin{array}{llll}94 & 86 & 78 & \ldots\end{array} \) Find an expression for the \( n \)th term of this sequence.

Options:
A. \( 8 n+86 \)
B. \( -8 n+106 \)
C. \( -8 n \)
D. \( -8 n+102 \)

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


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

Question:
Here are the first three terms of a sequence \( \begin{array}{llll}94 & 86 & 78 & \ldots\end{array} \) Find an expression for the \( n \)th term of this sequence.

Options:
A. \( 8 n+86 \)
B. \( -8 n+106 \)
C. \( -8 n \)
D. \( -8 n+102 \)

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


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

Question:
Tom and Katie are discussing the output of this \( 2 \)-step function machine input \(x\rightarrow+ 10\rightarrow\) multiplied by 3\(\rightarrow\) output Tom says the output is \( \mathbf{3 x}+\mathbf{3 0} \)
Katie says the output is \( \mathbf{1 0}+\mathbf{3} \boldsymbol{x} \)
Who is correct?

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

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


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

Question:
This notation means that these two lines are: ![Pair of parallel lines]()

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

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


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

Question:
This notation means that these two lines are: ![Pair of parallel lines]()

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

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


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

Question:
This notation means that these two lines are: ![Pair of parallel lines]()

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

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


Prompt:
Misconception:
When using a function machine, confuses the input and the output.

Question:
![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "8" written inside it. The next rectangle has "✕2" written inside it, the next rectangle has "−1" written inside it and the final rectangle on the right is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 15 \)
B. \( 5 \)
C. \( 14 \)
D. \( 4.5 \)

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 follow the arrows through a function machine, changes the order of the operations asked.

Question:
![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left has "input" written above it and "8" written inside it. The next rectangle has "✕2" written inside it, the next rectangle has "−1" written inside it and the final rectangle on the right is empty and has "output" written above it.]() What is the output of this function machine?

Options:
A. \( 15 \)
B. \( 5 \)
C. \( 14 \)
D. \( 4.5 \)

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


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

Question:
\( 4+12 \div(2+2)= \)

Options:
A. \( 10 \)
B. \( 7 \)
C. \( 12 \)
D. \( 4 \)

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


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

Question:
\( 4+12 \div(2+2)= \)

Options:
A. \( 10 \)
B. \( 7 \)
C. \( 12 \)
D. \( 4 \)

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


Prompt:
Misconception:
Performs addition ahead of division

Question:
\( 4+12 \div(2+2)= \)

Options:
A. \( 10 \)
B. \( 7 \)
C. \( 12 \)
D. \( 4 \)

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


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

Question:
In which region would \( y=(x+4)(x-2) \) belong? ![A Venn diagram with two overlapping sets. The set on the left is 'Line of symmetry at x = 3' and the set on the right is 'y intercept is negative'. A is in only  'Line of symmetry at x = 3', B is in the intersection, C is in only 'y intercept is negative' and D is outside both sets.]()

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 know the definition of a prism

Question:
Which of the following shapes is a hexagonal prism?

Options:
A. ![A hexagon.]()
B. ![A 3D-shape with 2 identical hexagonal faces connected by 6 rectangular faces.]()
C. ![A 3D-shape with a hexagonal base and 6 triangular faces that meet at a single vertex above the hexagonal base.]()
D. ![A 3D-shape with 2 identical octagonal faces connected by 8 rectangular faces.]()

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


Prompt:
Misconception:
Confuses pyramid with prism

Question:
Which of the following shapes is a hexagonal prism?

Options:
A. ![A hexagon.]()
B. ![A 3D-shape with 2 identical hexagonal faces connected by 6 rectangular faces.]()
C. ![A 3D-shape with a hexagonal base and 6 triangular faces that meet at a single vertex above the hexagonal base.]()
D. ![A 3D-shape with 2 identical octagonal faces connected by 8 rectangular faces.]()

Solve the problem as a student with the misconception above.
You 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 hexagon has 8 sides.

Question:
Which of the following shapes is a hexagonal prism?

Options:
A. ![A hexagon.]()
B. ![A 3D-shape with 2 identical hexagonal faces connected by 6 rectangular faces.]()
C. ![A 3D-shape with a hexagonal base and 6 triangular faces that meet at a single vertex above the hexagonal base.]()
D. ![A 3D-shape with 2 identical octagonal faces connected by 8 rectangular faces.]()

Solve the problem as a student with the misconception above.
You 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 \( \mathbf{9 8 9 . 9 8 9} \) rounded to the nearest ten?

Options:
A. \( 990 \)
B. \( 1000 \)
C. \( 989 \)
D. \( 980 \)

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


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

Question:
What is \( \mathbf{9 8 9 . 9 8 9} \) rounded to the nearest ten?

Options:
A. \( 990 \)
B. \( 1000 \)
C. \( 989 \)
D. \( 980 \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( \mathbf{9 8 9 . 9 8 9} \) rounded to the nearest ten?

Options:
A. \( 990 \)
B. \( 1000 \)
C. \( 989 \)
D. \( 980 \)

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


Prompt:
Misconception:
Thinks that when you cancel identical terms from the numerator and denominator, they just disappear

Question:
Simplify the following, if possible:
\(
\frac{3 m+15}{m^{2}-2 m+15}
\)

Options:
A. \( \frac{3}{m-2} \)
B. \( \frac{3 m}{m^{2}-2 m} \)
C. \( \frac{3}{m-3} \)
D. Does not simplify

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


Prompt:
Misconception:
Does not know how to read information off a pie chart

Question:
A darts player hits his target \( 40 \% \) of the time. Which pie chart represents his hits and misses?

Options:
A. ![Pie chart showing hits highlighted with 320 degrees of the chart and misses with 40 degrees.]()
B. ![Pie chart showing hits with 2/3 of the chart and misses, highlighted in red, with 1/3]()
C. ![Pie chart showing hits, in white, with 320 degrees of the chart and misses, highlighted in red, with 40 degrees.]()
D. ![Pie chart showing hits with just over 1/3 of the chart, highlighted in red and misses, in white, with just under 2/3]()

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 realise that a pictogram needs a title or question

Question:
![A pictogram is shown. One smiley face = 12 people. Salt and vinegar 2 faces. Ready salted 1 face. Prawn cocktail 3.5 faces. Other 2 faces]() What is missing from this pictogram?

Options:
A. What question was asked
B. Nothing
C. A key
D. Other needs to
say what
flavour it is

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


Prompt:
Misconception:
Does not think 'other' is an acceptable category for data

Question:
![A pictogram is shown. One smiley face = 12 people. Salt and vinegar 2 faces. Ready salted 1 face. Prawn cocktail 3.5 faces. Other 2 faces]() What is missing from this pictogram?

Options:
A. What question was asked
B. Nothing
C. A key
D. Other needs to
say what
flavour it is

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


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

Question:
What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the points (1,2) and (0,6).]()

Options:
A. \( -1 \)
B. \( -\frac{1}{4} \)
C. \( -1.5 \)
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 gradient of a line is given by the x intercept

Question:
What is the gradient of this line? ![A set of axes with a graph drawn on. The graph passes through the points (1,2) and (0,6).]()

Options:
A. \( -1 \)
B. \( -\frac{1}{4} \)
C. \( -1.5 \)
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 in completed square form, the x co-ordinate of the turning point has the same sign as the constant in the brackets.

Question:
Sally wants to write the equation of the curve in the form \( y=(\boldsymbol{x}+\boldsymbol{p})^{2}+\boldsymbol{q} \).
What is the value of \( \boldsymbol{p} \) ? ![A set of axes with the quadratic graph y=x^2-2x-3 drawn on.]()

Options:
A. \( 1 \)
B. \( -1 \)
C. \( 4 \)
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:
In completed square form, confuses the x and y coordinates of the turning point

Question:
Sally wants to write the equation of the curve in the form \( y=(\boldsymbol{x}+\boldsymbol{p})^{2}+\boldsymbol{q} \).
What is the value of \( \boldsymbol{p} \) ? ![A set of axes with the quadratic graph y=x^2-2x-3 drawn on.]()

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

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


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

Question:
\( 70.04-0.1= \)

Options:
A. \( 69.93 \)
B. \( 70.94 \)
C. \( 70.03 \)
D. \( 69.94 \)

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


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

Question:
\( 70.04-0.1= \)

Options:
A. \( 69.93 \)
B. \( 70.94 \)
C. \( 70.03 \)
D. \( 69.94 \)

Solve the problem as a student with the misconception above.
You 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 when converting to a larger unit

Question:
\( 10 \) litres \( =\square \) cubic metres

Options:
A. \( 10000 \)
B. \( 100 \)
C. \( 10 \)
D. \( 0.01 \)

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


Prompt:
Misconception:
Thinks 1l = 1 cubic metre

Question:
\( 10 \) litres \( =\square \) cubic metres

Options:
A. \( 10000 \)
B. \( 100 \)
C. \( 10 \)
D. \( 0.01 \)

Solve the problem as a student with the misconception above.
You 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 inverse of square rooting is doubling

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "Square root" written inside it and the final rectangle has "output" written above it and "12" written inside it.]() What is the input of this function machine?

Options:
A. \( 24 \)
B. \( 6 \)
C. \( \sqrt{12} \)
D. \( 144 \)

Solve the problem as a student with the misconception above.
You 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 inverse of square rooting is halving

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "Square root" written inside it and the final rectangle has "output" written above it and "12" written inside it.]() What is the input of this function machine?

Options:
A. \( 24 \)
B. \( 6 \)
C. \( \sqrt{12} \)
D. \( 144 \)

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


Prompt:
Misconception:
When finding an input of a function machine thinks you apply the operations given rather than the inverse operation.

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "Square root" written inside it and the final rectangle has "output" written above it and "12" written inside it.]() What is the input of this function machine?

Options:
A. \( 24 \)
B. \( 6 \)
C. \( \sqrt{12} \)
D. \( 144 \)

Solve the problem as a student with the misconception above.
You 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 corresponding angles sum to 90 degrees

Question:
Calculate \( t \). ![Two parallel horizontal lines with a transversal. The lower interior angle to the right of the transversal is marked 't'. The angle to the right of the transversal and lying above the upper parallel line is marked '78'. ]()

Options:
A. \( t=12^{\circ} \)
B. \( t=78^{\circ} \)
C. \( t=102^{\circ} \)
D. \( t=282^{\circ} \)

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 corresponding angles sum to 180 degrees

Question:
Calculate \( t \). ![Two parallel horizontal lines with a transversal. The lower interior angle to the right of the transversal is marked 't'. The angle to the right of the transversal and lying above the upper parallel line is marked '78'. ]()

Options:
A. \( t=12^{\circ} \)
B. \( t=78^{\circ} \)
C. \( t=102^{\circ} \)
D. \( t=282^{\circ} \)

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 corresponding angles sum to 360 degrees

Question:
Calculate \( t \). ![Two parallel horizontal lines with a transversal. The lower interior angle to the right of the transversal is marked 't'. The angle to the right of the transversal and lying above the upper parallel line is marked '78'. ]()

Options:
A. \( t=12^{\circ} \)
B. \( t=78^{\circ} \)
C. \( t=102^{\circ} \)
D. \( t=282^{\circ} \)

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:
Adds instead of subtracts when using an area model for multiplication

Question:
![A rectangle with one part shaded, labelled with dimensions 20, 8 and 6]() Which of the following calculations would correctly work out the area of the section shaded with a solid colour?

Options:
A. \( 8 \times 20-8 \times 6 \)
B. \( 8 \times 20+8 \times 6 \)
C. \( 8 \times 14-8 \times 6 \)
D. \( 8 \times 14+8 \times 6 \)

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


Prompt:
Misconception:
When finding part of the area of a shape, subtracts from the side length before multiplying but still subtracts the unshaded area too.

Question:
![A rectangle with one part shaded, labelled with dimensions 20, 8 and 6]() Which of the following calculations would correctly work out the area of the section shaded with a solid colour?

Options:
A. \( 8 \times 20-8 \times 6 \)
B. \( 8 \times 20+8 \times 6 \)
C. \( 8 \times 14-8 \times 6 \)
D. \( 8 \times 14+8 \times 6 \)

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


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

Question:
Tom and Katie are discussing this bar model ![\begin{tabular}{|l|l|l|l|l|}
\hline \multicolumn{5}{|c|}{\( 205 \)} \\
\hline \( 41 \) & \( 41 \) & \( 41 \) & \( 41 \) & \( 41 \) \\
\hline
\end{tabular}]() Tom uses the bar model to write:
\[
205 \div 5=41
\] Katie uses the bar model to write:
\[
205 \div 41=5
\]

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

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


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

Question:
Tom and Katie are discussing this bar model ![\begin{tabular}{|l|l|l|l|l|}
\hline \multicolumn{5}{|c|}{\( 205 \)} \\
\hline \( 41 \) & \( 41 \) & \( 41 \) & \( 41 \) & \( 41 \) \\
\hline
\end{tabular}]() Tom uses the bar model to write:
\[
205 \div 5=41
\] Katie uses the bar model to write:
\[
205 \div 41=5
\]

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

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


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

Question:
Tom and Katie are discussing this bar model ![\begin{tabular}{|l|l|l|l|l|}
\hline \multicolumn{5}{|c|}{\( 205 \)} \\
\hline \( 41 \) & \( 41 \) & \( 41 \) & \( 41 \) & \( 41 \) \\
\hline
\end{tabular}]() Tom uses the bar model to write:
\[
205 \div 5=41
\] Katie uses the bar model to write:
\[
205 \div 41=5
\]

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 rather than multiplies when using the product rule for counting

Question:
These are fair spinners

How many possible outcomes are there if they are spun together and both scores are recorded? ![Two spinners. One is a four-sided spinner with 4 equal sections labelled 1, 2, 3 and 4. One is a five-sided spinner with 5 equal sections labelled 1, 2, 3, 4 and 5.]()

Options:
A. \( 20 \)
B. \( 9 \)
C. \( 5 \)
D. \( 2 \)

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


Prompt:
Misconception:
Confuses all possible outcomes with options available

Question:
These are fair spinners

How many possible outcomes are there if they are spun together and both scores are recorded? ![Two spinners. One is a four-sided spinner with 4 equal sections labelled 1, 2, 3 and 4. One is a five-sided spinner with 5 equal sections labelled 1, 2, 3, 4 and 5.]()

Options:
A. \( 20 \)
B. \( 9 \)
C. \( 5 \)
D. \( 2 \)

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


Prompt:
Misconception:
Confused mixed numbers with improper fractions

Question:
\( 5 \frac{3}{5}-2 \frac{1}{2}= \) Leave your answer as a mixed number

Options:
A. \( \frac{23}{3} \)
B. \( 3 \frac{1}{10} \)
C. \( \frac{31}{10} \)
D. \( 3 \frac{2}{3} \)

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:
\( 5 \frac{3}{5}-2 \frac{1}{2}= \) Leave your answer as a mixed number

Options:
A. \( \frac{23}{3} \)
B. \( 3 \frac{1}{10} \)
C. \( \frac{31}{10} \)
D. \( 3 \frac{2}{3} \)

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:
Forgets to swap the sign of roots when placing into brackets

Question:
What is the equation of this curve? ![A quadratic curve that passes through (-2,0) and (1,0) on the x-axis.]()

Options:
A. \( y=(x-2)(x+1) \)
B. \( y=(x-1)(x+2) \)
C. \( y=x^{2}-2 \)
D. \( y=x^{2}-2 x \)

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


Prompt:
Misconception:
Believes both solutions of a quadratic will have the same absolute value, even when the graph is not symmetrical about the y axis

Question:
What is the equation of this curve? ![A quadratic curve that passes through (-2,0) and (1,0) on the x-axis.]()

Options:
A. \( y=(x-2)(x+1) \)
B. \( y=(x-1)(x+2) \)
C. \( y=x^{2}-2 \)
D. \( y=x^{2}-2 x \)

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


Prompt:
Misconception:
Does not use the associative property of multiplication to find other factors of a number

Question:
"Common multiples of \( 2 \) and \( 5 \) are also multiples of \( 25 " \)
Is this statement...

Options:
A. always true
B. sometimes true
C. never true
D. Impossible to say

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


Prompt:
Misconception:
Does not use the associative property of multiplication to find other factors of a number

Question:
"Common multiples of \( 2 \) and \( 5 \) are also multiples of \( 25 " \)
Is this statement...

Options:
A. always true
B. sometimes true
C. never true
D. Impossible to say

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


Prompt:
Misconception:
Confuses triangular prism with pyramid

Question:
Which of the following shapes is a triangular prism?

Options:
A. ![The correct answer]()
B. ![An incorrect answer]()
C. ![An incorrect answer]()
D. ![An incorrect answer]()

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


Prompt:
Misconception:
Does not realise a triangular prism is a 3D shape

Question:
Which of the following shapes is a triangular prism?

Options:
A. ![The correct answer]()
B. ![An incorrect answer]()
C. ![An incorrect answer]()
D. ![An incorrect answer]()

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


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

Question:
Which of the following shapes is a triangular prism?

Options:
A. ![The correct answer]()
B. ![An incorrect answer]()
C. ![An incorrect answer]()
D. ![An incorrect answer]()

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


Prompt:
Misconception:
Mistakes the number of rows for the total frequency in a frequency table

Question:
Dave has recorded the number of pets his classmates have in the frequency table on the right. \begin{tabular}{|c|c|}
\hline Number of pets & Frequency \\
\hline \( 0 \) & \( 4 \) \\
\hline \( 1 \) & \( 6 \) \\
\hline \( 2 \) & \( 3 \) \\
\hline \( 3 \) & \( 2 \) \\
\hline \( 4 \) & \( 5 \) \\
\hline
\end{tabular} How many people did Dave record the results of?

Options:
A. \( 4 \)
B. \( 5 \)
C. \( 10 \)
D. \( 20 \)

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


Prompt:
Misconception:
Adds up the variable column when asked for total frequency

Question:
Dave has recorded the number of pets his classmates have in the frequency table on the right. \begin{tabular}{|c|c|}
\hline Number of pets & Frequency \\
\hline \( 0 \) & \( 4 \) \\
\hline \( 1 \) & \( 6 \) \\
\hline \( 2 \) & \( 3 \) \\
\hline \( 3 \) & \( 2 \) \\
\hline \( 4 \) & \( 5 \) \\
\hline
\end{tabular} How many people did Dave record the results of?

Options:
A. \( 4 \)
B. \( 5 \)
C. \( 10 \)
D. \( 20 \)

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


Prompt:
Misconception:
Does not realise that all circles are similar

Question:
Which of these statements is false?

Options:
A. "All circles are similar"
B. "All equilateral triangles are similar"
C. "All rhombuses are similar"
D. "All regular decagons are similar"

Solve the problem as a student with the misconception above.
You 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 all regular shapes of a certain type will be similar

Question:
Which of these statements is false?

Options:
A. "All circles are similar"
B. "All equilateral triangles are similar"
C. "All rhombuses are similar"
D. "All regular decagons are similar"

Solve the problem as a student with the misconception above.
You 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 all regular shapes of a certain type will be similar

Question:
Which of these statements is false?

Options:
A. "All circles are similar"
B. "All equilateral triangles are similar"
C. "All rhombuses are similar"
D. "All regular decagons are similar"

Solve the problem as a student with the misconception above.
You 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 two digits sum to 10 or more during an addition problem, does not add one to the preceding digit

Question:
What number is \( 10,000 \) more than \( 899,051 \) ?

Options:
A. \( 909,051 \)
B. \( 809,051 \)
C. \( 999,051 \)
D. \( 8,990,510,000 \)

Solve the problem as a student with the misconception above.
You 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 powers of 10 adds onto the wrong column

Question:
What number is \( 10,000 \) more than \( 899,051 \) ?

Options:
A. \( 909,051 \)
B. \( 809,051 \)
C. \( 999,051 \)
D. \( 8,990,510,000 \)

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


Prompt:
Misconception:
Multiplies rather than adds when given the command word 'more'

Question:
What number is \( 10,000 \) more than \( 899,051 \) ?

Options:
A. \( 909,051 \)
B. \( 809,051 \)
C. \( 999,051 \)
D. \( 8,990,510,000 \)

Solve the problem as a student with the misconception above.
You 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 when converting to a smaller unit

Question:
\( 3 \) kilograms \( =\bigstar \) grams What should replace the star?

Options:
A. \( 0.3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000 \)

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


Prompt:
Misconception:
Thinks there are 10g in a kilogram

Question:
\( 3 \) kilograms \( =\bigstar \) grams What should replace the star?

Options:
A. \( 0.3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000 \)

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


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

Question:
\( 3 \) kilograms \( =\bigstar \) grams What should replace the star?

Options:
A. \( 0.3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000 \)

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


Prompt:
Misconception:
When multiplying a fraction by an integer, multiplies both numerator and denominator by the integer

Question:
Tom and Katie are arguing about the answer to \( \frac{1}{5} \times 9 \)
Tom says \( \frac{1}{5} \times 9=1 \frac{4}{5} \)
Katie says \( \frac{1}{5} \times 9=\frac{9}{45} \)
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 graphs of inverse proportion meet the axes

Question:
Which of the following graphs is most likely to illustrate the time taken to complete a job \( (t) \) changes depending on the number of people working on it \( (p) \)

Options:
A. ![A straight line from bottom left to top right, starting from above the origin ]()
B. ![A straight line from top left to bottom right, starting from above the origin]()
C. ![A curved line from top left rapidly descending as it moves right before slowing down and levelling out ]()
D. ![A straight line from bottom left to top right, starting from the origin]()

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