Prompt:
Misconception:
When calculating surface area, only includes visible faces

Question:
Which of the following calculations would give you the total surface area of this cuboid in \( \mathrm{cm}^{2} \) ? ![A cuboid. The height is 4cm, the depth is 3cm and the width is 6cm.]()

Options:
A. \( (6 \times 4)+(6 \times 3)+(4 \times 3) \)
B. \( 6 \times 4 \times 3 \)
C. \( (6 \times 4) \times(6 \times 3) \times(4 \times 3) \)
D. \( [(6 \times 4)+(6 \times 3)+(4 \times 3)] \times 2 \)

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


Prompt:
Misconception:
Finds volume when asked for surface area

Question:
Which of the following calculations would give you the total surface area of this cuboid in \( \mathrm{cm}^{2} \) ? ![A cuboid. The height is 4cm, the depth is 3cm and the width is 6cm.]()

Options:
A. \( (6 \times 4)+(6 \times 3)+(4 \times 3) \)
B. \( 6 \times 4 \times 3 \)
C. \( (6 \times 4) \times(6 \times 3) \times(4 \times 3) \)
D. \( [(6 \times 4)+(6 \times 3)+(4 \times 3)] \times 2 \)

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


Prompt:
Misconception:
When calculating surface area, only includes visible faces

Question:
Which of the following calculations would give you the total surface area of this cuboid in \( \mathrm{cm}^{2} \) ? ![A cuboid. The height is 4cm, the depth is 3cm and the width is 6cm.]()

Options:
A. \( (6 \times 4)+(6 \times 3)+(4 \times 3) \)
B. \( 6 \times 4 \times 3 \)
C. \( (6 \times 4) \times(6 \times 3) \times(4 \times 3) \)
D. \( [(6 \times 4)+(6 \times 3)+(4 \times 3)] \times 2 \)

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


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

Question:
\[
1+2 \times(3-4)=
\]

Which calculation should you do first?

Options:
A. \( 1+2 \)
B. \( 2 \times 3 \)
C. \( 3-4 \)
D. It doesn't matter: you get the same answer

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


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

Question:
\[
1+2 \times(3-4)=
\]

Which calculation should you do first?

Options:
A. \( 1+2 \)
B. \( 2 \times 3 \)
C. \( 3-4 \)
D. It doesn't matter: you get the same answer

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


Prompt:
Misconception:
Believes order of operations does not affect the answer to a calculation

Question:
\[
1+2 \times(3-4)=
\]

Which calculation should you do first?

Options:
A. \( 1+2 \)
B. \( 2 \times 3 \)
C. \( 3-4 \)
D. It doesn't matter: you get the same answer

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


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

Question:
Solve the equation:
\(
5 p=\frac{1}{10}
\)

Options:
A. \( p=\frac{1}{2} \)
B. \( p=\frac{1}{5} \)
C. \( p=2 \)
D. \( p=\frac{1}{50} \)

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


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

Question:
Problem P: \( 4-5+6= \)
Problem Q: \( 4+5 \times 6= \)

Which calculation should you do first in each problem?

Options:
A. Problem P: \( 4-5 \)
Problem Q: \( 4+5 \)
B. Problem P: \( 4-5 \)
Problem Q: \( 5 \times 6 \)
C. Problem P: \( 5+6 \)
Problem Q: \( 4+5 \)
D. Problem P: \( 5+6 \)
Problem Q: \( 5 \times 6 \)

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


Prompt:
Misconception:
Performs addition ahead of any other operation

Question:
Problem P: \( 4-5+6= \)
Problem Q: \( 4+5 \times 6= \)

Which calculation should you do first in each problem?

Options:
A. Problem P: \( 4-5 \)
Problem Q: \( 4+5 \)
B. Problem P: \( 4-5 \)
Problem Q: \( 5 \times 6 \)
C. Problem P: \( 5+6 \)
Problem Q: \( 4+5 \)
D. Problem P: \( 5+6 \)
Problem Q: \( 5 \times 6 \)

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


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

Question:
Problem P: \( 4-5+6= \)
Problem Q: \( 4+5 \times 6= \)

Which calculation should you do first in each problem?

Options:
A. Problem P: \( 4-5 \)
Problem Q: \( 4+5 \)
B. Problem P: \( 4-5 \)
Problem Q: \( 5 \times 6 \)
C. Problem P: \( 5+6 \)
Problem Q: \( 4+5 \)
D. Problem P: \( 5+6 \)
Problem Q: \( 5 \times 6 \)

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


Prompt:
Misconception:
Mixes up term in a sequence and position of a term

Question:
Eliza is trying to work out if \( 82 \) is a term in the sequence \( 3 n+1 \)

Below is her working out. What conclusion should Eliza draw?

 \( \begin{aligned} 3 n+1 & =82 \\ 3 n & =81 \\ n & =27\end{aligned} \)

Options:
A. \( 82 \) is in the sequence and is the \( 27^{\text {th }} \) term
B. \( 27 \) is in the sequence and is the \( 82^{\text {nd }} \) term
C. \( 82 \) is not in the sequence because \( 27 \) is an integer
D. Eliza's method does not answer this question

Solve the problem as a student with the misconception above.
You 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 position of a sequence cannot be an integer

Question:
Eliza is trying to work out if \( 82 \) is a term in the sequence \( 3 n+1 \)

Below is her working out. What conclusion should Eliza draw?

 \( \begin{aligned} 3 n+1 & =82 \\ 3 n & =81 \\ n & =27\end{aligned} \)

Options:
A. \( 82 \) is in the sequence and is the \( 27^{\text {th }} \) term
B. \( 27 \) is in the sequence and is the \( 82^{\text {nd }} \) term
C. \( 82 \) is not in the sequence because \( 27 \) is an integer
D. Eliza's method does not answer this question

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


Prompt:
Misconception:
Does not know how to calculate the position of a term in a sequence

Question:
Eliza is trying to work out if \( 82 \) is a term in the sequence \( 3 n+1 \)

Below is her working out. What conclusion should Eliza draw?

 \( \begin{aligned} 3 n+1 & =82 \\ 3 n & =81 \\ n & =27\end{aligned} \)

Options:
A. \( 82 \) is in the sequence and is the \( 27^{\text {th }} \) term
B. \( 27 \) is in the sequence and is the \( 82^{\text {nd }} \) term
C. \( 82 \) is not in the sequence because \( 27 \) is an integer
D. Eliza's method does not answer this question

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


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

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

Options:
A. \( t+2 \)
B. \( t+1 \)
C. \( t^{2}+t \)
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:
Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator

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

Options:
A. \( t+2 \)
B. \( t+1 \)
C. \( t^{2}+t \)
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 factorising a quadratic

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

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

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


Prompt:
Misconception:
Does not understand parts must be equal in a fraction diagram

Question:
Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 2 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]()

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

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


Prompt:
Misconception:
Divides rather than multiplies

Question:
Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 2 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]()

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

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


Prompt:
Misconception:
Does not understand parts must be equal in a fraction diagram

Question:
Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 2 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]()

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

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


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

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

Options:
A. EFA
B. GEA
C. AEF
D. E

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


Prompt:
Misconception:
Gives the vertex instead of the 3-letter angle notation

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

Options:
A. EFA
B. GEA
C. AEF
D. E

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


Prompt:
Misconception:
Believes nth term rules for patterns must be given in standard an + b form

Question:
Jo and Paul are arguing about the best way to count the number of squares in Pattern \( 15 \).
Jo does: \( 15 \times 3+4 \)
Paul does: \( (15+2) \times 3-4 \)
Who is correct? ![The 3rd and 4th terms in a sequence of patterns. Each pattern is made from red squares. Pattern 3 is 11 squares: they are arranged as a rectangle, 3 squares high and 3 squares wide and then 2 more squares, 1 each side of the middle squares (vertically). Pattern 4 is 14 squares arranged as a rectangle, 3 squares high and 4 squares wide and then 2 more squares, 1 each side of the middle squares.]()

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

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


Prompt:
Misconception:
Believes nth term rules for patterns must be given in standard an + b form

Question:
Jo and Paul are arguing about the best way to count the number of squares in Pattern \( 15 \).
Jo does: \( 15 \times 3+4 \)
Paul does: \( (15+2) \times 3-4 \)
Who is correct? ![The 3rd and 4th terms in a sequence of patterns. Each pattern is made from red squares. Pattern 3 is 11 squares: they are arranged as a rectangle, 3 squares high and 3 squares wide and then 2 more squares, 1 each side of the middle squares (vertically). Pattern 4 is 14 squares arranged as a rectangle, 3 squares high and 4 squares wide and then 2 more squares, 1 each side of the middle squares.]()

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

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


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

Question:
Simplify, if possible:
\(
a^{2} \times a
\)

Options:
A. \( 2 a^{2} \)
B. \( 3 a \)
C. \( a^{3} \)
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:
Multiplies by the index

Question:
Simplify, if possible:
\(
a^{2} \times a
\)

Options:
A. \( 2 a^{2} \)
B. \( 3 a \)
C. \( a^{3} \)
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 understand how to multiply algebraic terms

Question:
Simplify, if possible:
\(
a^{2} \times a
\)

Options:
A. \( 2 a^{2} \)
B. \( 3 a \)
C. \( a^{3} \)
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:
When multiplying with negative numbers, assumes any negative sign can be ignored

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

Options:
A. \( 15 \)
B. \( -15 \)
C. \( 8 \)
D. \( -8 \)

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


Prompt:
Misconception:
Writes the remainder as the digit after the decimal point

Question:
John has been asked to work out the answer to:
\[
232 \div 5
\]
He gets the answer \( 46 \) remainder \( 2 \)
What is the exact value of that remainder?

Options:
A. \( 0.2 \)
B. \( 0.4 \)
C. \( 2 \)
D. \( 0.25 \)

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


Prompt:
Misconception:
Does not understand remainders in division

Question:
John has been asked to work out the answer to:
\[
232 \div 5
\]
He gets the answer \( 46 \) remainder \( 2 \)
What is the exact value of that remainder?

Options:
A. \( 0.2 \)
B. \( 0.4 \)
C. \( 2 \)
D. \( 0.25 \)

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


Prompt:
Misconception:
Does not understand remainders in division

Question:
John has been asked to work out the answer to:
\[
232 \div 5
\]
He gets the answer \( 46 \) remainder \( 2 \)
What is the exact value of that remainder?

Options:
A. \( 0.2 \)
B. \( 0.4 \)
C. \( 2 \)
D. \( 0.25 \)

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


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

Question:
STEP \( 1 \)
Which of the options is a correct first step to express the following as a single fraction?
\(
\frac{3}{x-2}-\frac{5}{x}
\)

Options:
A. \( \frac{3-5}{x-2-x} \)
B. \( \frac{3(x-2)}{x(x-2)}-\frac{5 x}{x(x-2)} \)
C. \( \frac{3 x}{x(x-2)}-\frac{5(x-2)}{x(x-2)} \)
D. \( 9 x-5(x-2) \)

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


Prompt:
Misconception:
Does not understand how to maintain equivalence in fractions

Question:
STEP \( 1 \)
Which of the options is a correct first step to express the following as a single fraction?
\(
\frac{3}{x-2}-\frac{5}{x}
\)

Options:
A. \( \frac{3-5}{x-2-x} \)
B. \( \frac{3(x-2)}{x(x-2)}-\frac{5 x}{x(x-2)} \)
C. \( \frac{3 x}{x(x-2)}-\frac{5(x-2)}{x(x-2)} \)
D. \( 9 x-5(x-2) \)

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


Prompt:
Misconception:
Removes the common denominator when making equivalent algebraic fractions

Question:
STEP \( 1 \)
Which of the options is a correct first step to express the following as a single fraction?
\(
\frac{3}{x-2}-\frac{5}{x}
\)

Options:
A. \( \frac{3-5}{x-2-x} \)
B. \( \frac{3(x-2)}{x(x-2)}-\frac{5 x}{x(x-2)} \)
C. \( \frac{3 x}{x(x-2)}-\frac{5(x-2)}{x(x-2)} \)
D. \( 9 x-5(x-2) \)

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


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

Question:
Which of the numbers is the same when rounded to \( 2 \) decimal places or to \( 2 \) significant figures?

Options:
A. \( 23.725 \)
B. \( 0.391 \)
C. \( 0.038 \)
D. \( 0.0599 \)

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


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

Question:
Which of the numbers is the same when rounded to \( 2 \) decimal places or to \( 2 \) significant figures?

Options:
A. \( 23.725 \)
B. \( 0.391 \)
C. \( 0.038 \)
D. \( 0.0599 \)

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


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

Question:
Which of the numbers is the same when rounded to \( 2 \) decimal places or to \( 2 \) significant figures?

Options:
A. \( 23.725 \)
B. \( 0.391 \)
C. \( 0.038 \)
D. \( 0.0599 \)

Solve the problem as a student with the misconception above.
You 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 decimals, just adds the digits and ignores place value

Question:
\( 1.39+2.53= \)

Options:
A. \( 4.01 \)
B. \( 3.812 \)
C. \( 3.82 \)
D. \( 3.92 \)

Solve the problem as a student with the misconception above.
You 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:
\( 1.39+2.53= \)

Options:
A. \( 4.01 \)
B. \( 3.812 \)
C. \( 3.82 \)
D. \( 3.92 \)

Solve the problem as a student with the misconception above.
You 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:
\( 1.39+2.53= \)

Options:
A. \( 4.01 \)
B. \( 3.812 \)
C. \( 3.82 \)
D. \( 3.92 \)

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


Prompt:
Misconception:
Misremembers the quadratic formula

Question:
Which option gives a correct substitution into the quadratic formula to solve the quadratic equation?

\(
3 x^{2}+2 x-5=0
\)

Options:
A. \( -2 \pm \frac{\sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
B. \( 2 \pm \frac{\sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
C. \( \frac{-2 \pm \sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
D. \( \frac{2 \pm \sqrt{2^{2}-4(3)(-5)}}{2(3)} \)

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:
Misremembers the quadratic formula

Question:
Which option gives a correct substitution into the quadratic formula to solve the quadratic equation?

\(
3 x^{2}+2 x-5=0
\)

Options:
A. \( -2 \pm \frac{\sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
B. \( 2 \pm \frac{\sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
C. \( \frac{-2 \pm \sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
D. \( \frac{2 \pm \sqrt{2^{2}-4(3)(-5)}}{2(3)} \)

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:
Misremembers the quadratic formula

Question:
Which option gives a correct substitution into the quadratic formula to solve the quadratic equation?

\(
3 x^{2}+2 x-5=0
\)

Options:
A. \( -2 \pm \frac{\sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
B. \( 2 \pm \frac{\sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
C. \( \frac{-2 \pm \sqrt{2^{2}-4(3)(-5)}}{2(3)} \)
D. \( \frac{2 \pm \sqrt{2^{2}-4(3)(-5)}}{2(3)} \)

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 solving an equation, multiplies instead of dividing

Question:
What should replace the star?
\(
0.3 \div \bigstar=1.2
\)

Options:
A. \( 0.25 \)
B. \( 0.4 \)
C. \( 4 \)
D. \( 0.9 \)

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


Prompt:
Misconception:
When solving an equation, adds instead of dividing

Question:
What should replace the star?
\(
0.3 \div \bigstar=1.2
\)

Options:
A. \( 0.25 \)
B. \( 0.4 \)
C. \( 4 \)
D. \( 0.9 \)

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


Prompt:
Misconception:
Multiplies all given dimensions when calculating an area

Question:
What is the area of this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled 10 cm, 7 cm, 3 cm and 4 cm. Two sides are unlabelled]()

Options:
A. \( 840 \mathrm{~cm}^{2} \)
B. \( 52 \mathrm{~cm}^{2} \)
C. \( 42 \mathrm{~cm}^{2} \)
D. \( 51 \mathrm{~cm}^{2} \)

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:
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 10 cm, 7 cm, 3 cm and 4 cm. Two sides are unlabelled]()

Options:
A. \( 840 \mathrm{~cm}^{2} \)
B. \( 52 \mathrm{~cm}^{2} \)
C. \( 42 \mathrm{~cm}^{2} \)
D. \( 51 \mathrm{~cm}^{2} \)

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:
Uses an incorrect side length when splitting a composite shape into parts

Question:
What is the area of this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled 10 cm, 7 cm, 3 cm and 4 cm. Two sides are unlabelled]()

Options:
A. \( 840 \mathrm{~cm}^{2} \)
B. \( 52 \mathrm{~cm}^{2} \)
C. \( 42 \mathrm{~cm}^{2} \)
D. \( 51 \mathrm{~cm}^{2} \)

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

Question:
Alison is expanding these two brackets.

What should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the 5p in the first bracket and the -3 in the second bracket.]()

Options:
A. \( -15 p \)
B. \( +15 p \)
C. \( +2 p \)
D. \( +8 p \)

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


Prompt:
Misconception:
Adds instead of multiplying when expanding bracket

Question:
Alison is expanding these two brackets.

What should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the 5p in the first bracket and the -3 in the second bracket.]()

Options:
A. \( -15 p \)
B. \( +15 p \)
C. \( +2 p \)
D. \( +8 p \)

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


Prompt:
Misconception:
When multiplying decimals, ignores place value and just multiplies the digits

Question:
Work out:
\[
0.3 \times 12
\]

Options:
A. \( 36 \)
B. \( 3.6 \)
C. \( 0.36 \)
D. \( 0.036 \)

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


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

Question:
Work out:
\[
0.3 \times 12
\]

Options:
A. \( 36 \)
B. \( 3.6 \)
C. \( 0.36 \)
D. \( 0.036 \)

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


Prompt:
Misconception:
When multiplying a decimal less than 1 by an integer, gives an answer 100 times smaller than it should be

Question:
Work out:
\[
0.3 \times 12
\]

Options:
A. \( 36 \)
B. \( 3.6 \)
C. \( 0.36 \)
D. \( 0.036 \)

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Factorise \( x^{2}+15 x+36 \) Factorise \( x^{2}+15 x+36 \)

Options:
A. \( (x+4)(x+9) \) \( (x+4)(x+9) \)
B. \( (x+3)(x+12) \) \( (x+3)(x+12) \)
C. \( (x+1)(x+36) \) \( (x+1)(x+36) \)
D. \( (x+7)(x+18) \) \( (x+7)(x+18) \)

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Factorise \( x^{2}+15 x+36 \) Factorise \( x^{2}+15 x+36 \)

Options:
A. \( (x+4)(x+9) \) \( (x+4)(x+9) \)
B. \( (x+3)(x+12) \) \( (x+3)(x+12) \)
C. \( (x+1)(x+36) \) \( (x+1)(x+36) \)
D. \( (x+7)(x+18) \) \( (x+7)(x+18) \)

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


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x

Question:
Factorise \( x^{2}+15 x+36 \) Factorise \( x^{2}+15 x+36 \)

Options:
A. \( (x+4)(x+9) \) \( (x+4)(x+9) \)
B. \( (x+3)(x+12) \) \( (x+3)(x+12) \)
C. \( (x+1)(x+36) \) \( (x+1)(x+36) \)
D. \( (x+7)(x+18) \) \( (x+7)(x+18) \)

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


Prompt:
Misconception:
Does not recognise the properties of a kite

Question:
Which of the following quadrilaterals could not be classified as a kite?

Options:
A. Square
B. Rhombus
C. Trapezium
D. None of them are kites

Solve the problem as a student with the misconception above.
You 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 properties of a kite

Question:
Which of the following quadrilaterals could not be classified as a kite?

Options:
A. Square
B. Rhombus
C. Trapezium
D. None of them are kites

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


Prompt:
Misconception:
Does not believe a shape can have two correct names e.g. rectangle and parallelogram

Question:
Which of the following quadrilaterals could not be classified as a kite?

Options:
A. Square
B. Rhombus
C. Trapezium
D. None of them are kites

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


Prompt:
Misconception:
Assumes a 1/4 of a whole is 25

Question:
How many degrees are there in \( 1 \frac{1}{4} \) full turns?

Options:
A. \( 450^{\circ} \)
B. \( 385^{\circ} \)
C. \( 125^{\circ} \)
D. \( 90^{\circ} \)

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


Prompt:
Misconception:
Believes there are 100 degrees in a full turn

Question:
How many degrees are there in \( 1 \frac{1}{4} \) full turns?

Options:
A. \( 450^{\circ} \)
B. \( 385^{\circ} \)
C. \( 125^{\circ} \)
D. \( 90^{\circ} \)

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


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

Question:
\( \frac{2}{5} \times \star=-1 \) What should replace the star?

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

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


Prompt:
Misconception:
Rounds down instead of up

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

Options:
A. \( 990 \)
B. \( 100 \)
C. \( 900 \)
D. \( 1000 \)

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


Prompt:
Misconception:
When rounding up from a 9, does not add one on to the digit to the left

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

Options:
A. \( 990 \)
B. \( 100 \)
C. \( 900 \)
D. \( 1000 \)

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

Options:
A. \( 990 \)
B. \( 100 \)
C. \( 900 \)
D. \( 1000 \)

Solve the problem as a student with the misconception above.
You 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:
Calculate:
\(
\frac{2}{9}+\frac{1}{3}
\)

Options:
A. \( \frac{5}{9} \)
B. \( \frac{3}{12} \)
C. \( \frac{3}{9} \)
D. \( \frac{1}{6} \)

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


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

Question:
Calculate:
\(
\frac{2}{9}+\frac{1}{3}
\)

Options:
A. \( \frac{5}{9} \)
B. \( \frac{3}{12} \)
C. \( \frac{3}{9} \)
D. \( \frac{1}{6} \)

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


Prompt:
Misconception:
Subtracts instead of adds

Question:
Calculate:
\(
\frac{2}{9}+\frac{1}{3}
\)

Options:
A. \( \frac{5}{9} \)
B. \( \frac{3}{12} \)
C. \( \frac{3}{9} \)
D. \( \frac{1}{6} \)

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


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

Question:
Tom and Katie are discussing the order of operations
Tom says: \( 0.1-0.2 \div 0.3 \equiv 0.1-(0.2 \div 0.3) \)
Katie says: \( 0.1-0.2 \div 0.3 \equiv 0.2 \div 0.3-0.1 \)
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:
Performs subtraction right to left if priority order means doing a calculation to the right first

Question:
Tom and Katie are discussing the order of operations
Tom says: \( 0.1-0.2 \div 0.3 \equiv 0.1-(0.2 \div 0.3) \)
Katie says: \( 0.1-0.2 \div 0.3 \equiv 0.2 \div 0.3-0.1 \)
Who is correct?

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

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


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

Question:
Tom and Katie are discussing the order of operations
Tom says: \( 0.1-0.2 \div 0.3 \equiv 0.1-(0.2 \div 0.3) \)
Katie says: \( 0.1-0.2 \div 0.3 \equiv 0.2 \div 0.3-0.1 \)
Who is correct?

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

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


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

Question:
\(
2 \frac{2}{5}-\frac{1}{15}=2 \frac{1}{\bigstar}
\)
What should replace the star?

Options:
A. \( 10 \)
B. \( 15 \)
C. \( 5 \)
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:
Forgot to simplify the fraction

Question:
\(
2 \frac{2}{5}-\frac{1}{15}=2 \frac{1}{\bigstar}
\)
What should replace the star?

Options:
A. \( 10 \)
B. \( 15 \)
C. \( 5 \)
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:
Believes when simplifying a fraction you can divide the numerator and denominator by different values

Question:
\(
2 \frac{2}{5}-\frac{1}{15}=2 \frac{1}{\bigstar}
\)
What should replace the star?

Options:
A. \( 10 \)
B. \( 15 \)
C. \( 5 \)
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:
Forgotten that anything to the power of 0 equals 1

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{9}^{x} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( 0 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 9 \)
B. \( 0 \)
C. \( 1 \)
D. The equation is undefined at this value

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


Prompt:
Misconception:
Forgotten that anything to the power of 0 equals 1

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{9}^{x} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( 0 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 9 \)
B. \( 0 \)
C. \( 1 \)
D. The equation is undefined at this value

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


Prompt:
Misconception:
Forgotten that anything to the power of 0 equals 1

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{9}^{x} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( 0 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 9 \)
B. \( 0 \)
C. \( 1 \)
D. The equation is undefined at this value

Solve the problem as a student with the misconception above.
You 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:
\(
\frac{x}{3}-5=12
\)

Tom says a correct next line of working could be: \( \frac{x}{3}=17 \)

Katie says a correct next line of working could be: \( x-5=36 \)
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:
\(
\frac{x}{3}-5=12
\)

Tom says a correct next line of working could be: \( \frac{x}{3}=17 \)

Katie says a correct next line of working could be: \( x-5=36 \)
Who is correct?

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

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


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

Question:
Tom and Katie are discussing how to solve:
\(
\frac{x}{3}-5=12
\)

Tom says a correct next line of working could be: \( \frac{x}{3}=17 \)

Katie says a correct next line of working could be: \( x-5=36 \)
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 subtraction is commutative

Question:
\( 0.26-0.6= \)

Options:
A. \( -0.34 \)
B. \( 0.34 \)
C. \( -0.44 \)
D. \( 0.2 \)

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 you subtract the smaller digit from the larger digit in column subtraction, regardless of position

Question:
\( 0.26-0.6= \)

Options:
A. \( -0.34 \)
B. \( 0.34 \)
C. \( -0.44 \)
D. \( 0.2 \)

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


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

Question:
\( 0.26-0.6= \)

Options:
A. \( -0.34 \)
B. \( 0.34 \)
C. \( -0.44 \)
D. \( 0.2 \)

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:
Converts a fraction to a decimal by using the denominator after the decimal point

Question:
The probability of picking a green ball is \( \frac{1}{5} \) Where is this value on the probability scale? ![B
c
D]()

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

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


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

Question:
Jo and Paul are discussing mental addition and subtraction strategies.

Jo says a good way to add \( 19 \) is to add \( 10 \), then another \( 10 \) and then subtract \( 1 \).

Paul says a good way to subtract \( 19 \) is to subtract \( 10 \), then another \( 10 \) and then add \( 1 \).

Who is correct?

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

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


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

Question:
Jo and Paul are discussing mental addition and subtraction strategies.

Jo says a good way to add \( 19 \) is to add \( 10 \), then another \( 10 \) and then subtract \( 1 \).

Paul says a good way to subtract \( 19 \) is to subtract \( 10 \), then another \( 10 \) and then add \( 1 \).

Who is correct?

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

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


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

Question:
Jo and Paul are discussing mental addition and subtraction strategies.

Jo says a good way to add \( 19 \) is to add \( 10 \), then another \( 10 \) and then subtract \( 1 \).

Paul says a good way to subtract \( 19 \) is to subtract \( 10 \), then another \( 10 \) and then add \( 1 \).

Who is correct?

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

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


Prompt:
Misconception:
Counts partial symbols as if they were whole on pictograms

Question:
![A pictogram where one smiley face =8 people. Game 1 has 4 faces. Game 2 has 3 faces. Game 3 has 2 faces. Game 4 has 2.75 faces.]() The pictogram shows the number of people who went to watch a netball match.
How many people went to game 4?

Options:
A. \( 24 \)
B. \( 16 \)
C. \( 2.75 \)
D. \( 22 \)

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


Prompt:
Misconception:
Ignores partial symbols on pictograms

Question:
![A pictogram where one smiley face =8 people. Game 1 has 4 faces. Game 2 has 3 faces. Game 3 has 2 faces. Game 4 has 2.75 faces.]() The pictogram shows the number of people who went to watch a netball match.
How many people went to game 4?

Options:
A. \( 24 \)
B. \( 16 \)
C. \( 2.75 \)
D. \( 22 \)

Solve the problem as a student with the misconception above.
You 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 interpreting a pictogram, thinks each symbol stands for 1

Question:
![A pictogram where one smiley face =8 people. Game 1 has 4 faces. Game 2 has 3 faces. Game 3 has 2 faces. Game 4 has 2.75 faces.]() The pictogram shows the number of people who went to watch a netball match.
How many people went to game 4?

Options:
A. \( 24 \)
B. \( 16 \)
C. \( 2.75 \)
D. \( 22 \)

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


Prompt:
Misconception:
Divides by 1000 instead of 100 when converting a percentage to a decimal

Question:
Jo and Paul are arguing about percentages.
Jo says \( 52 \%=0.052 \)
Paul says \( 52 \%<\frac{20}{41} \)
Who is correct?

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

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


Prompt:
Misconception:
Can identify the multiplier used to form an equivalent fraction but does not apply to the numerator

Question:
Complete the statement \( \frac{4}{6}=\frac{}{12} \)

Options:
A. \( \frac{4}{6}=\frac{2}{12} \)
B. \( \frac{4}{6}=\frac{4}{12} \)
C. \( \frac{4}{6}=\frac{10}{12} \)
D. \( \frac{4}{6}=\frac{8}{12} \)

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


Prompt:
Misconception:
Does not understand equivalent fractions

Question:
Complete the statement \( \frac{4}{6}=\frac{}{12} \)

Options:
A. \( \frac{4}{6}=\frac{2}{12} \)
B. \( \frac{4}{6}=\frac{4}{12} \)
C. \( \frac{4}{6}=\frac{10}{12} \)
D. \( \frac{4}{6}=\frac{8}{12} \)

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:
Believes equivalent fractions are formed with addition not multiplication

Question:
Complete the statement \( \frac{4}{6}=\frac{}{12} \)

Options:
A. \( \frac{4}{6}=\frac{2}{12} \)
B. \( \frac{4}{6}=\frac{4}{12} \)
C. \( \frac{4}{6}=\frac{10}{12} \)
D. \( \frac{4}{6}=\frac{8}{12} \)

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:
Confuses a term with a variable

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

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 expression with a term

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

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 \( 3 g \) in this: \( 6-3 g \)

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:
Fails to reflect across mirror line

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

Options:
A. \( (-3,-1) \)
B. \( (0,-1) \)
C. \( (-2,-1) \)
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:
Fails to reflect across mirror line

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

Options:
A. \( (-3,-1) \)
B. \( (0,-1) \)
C. \( (-2,-1) \)
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:
Fails to reflect across mirror line

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

Options:
A. \( (-3,-1) \)
B. \( (0,-1) \)
C. \( (-2,-1) \)
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:
Does not understand that a point on the line of reflection will stay the same when reflected

Question:
![A grid of 7 squares across and 7 squares up. A red vertical line goes from the bottom to the top of the grid, it is 4 squares left from the edge of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn to the left of the red line, with its right-hand side on the red line.  The bottom side of the rectangle is 3 squares up from the bottom of the grid. The top right corner of the rectangle is marked with the letter P, which is 5 squares up from the bottom of the grid on the red line. The bottom right corner of the rectangle is marked with the letter Q, which is 3 squares up from the bottom of the grid on the red line. ]() Tom and Katie are discussing reflections

Tom says if you reflect the rectangle in the vertical line, Point \( P \) stays in the same position

Katie says if you reflect the rectangle in the vertical line, Point \( Q \) stays in the same position
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 an obtuse angle is between 90 and 180 degrees

Question:
Which of the following is an obtuse angle?

Options:
A. \( 85^{\circ} \)
B. \( 270^{\circ} \)
C. \( 110^{\circ} \)
D. \( 180^{\circ} \)

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 understand that an obtuse angle is between 90 and 180 degrees

Question:
Which of the following is an obtuse angle?

Options:
A. \( 85^{\circ} \)
B. \( 270^{\circ} \)
C. \( 110^{\circ} \)
D. \( 180^{\circ} \)

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


Prompt:
Misconception:
Believes 180 degrees is an obtuse angle

Question:
Which of the following is an obtuse angle?

Options:
A. \( 85^{\circ} \)
B. \( 270^{\circ} \)
C. \( 110^{\circ} \)
D. \( 180^{\circ} \)

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 remember that a rhombus has equal sides

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

Options:
A. Parallelogram
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 recognise the properties of a kite

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

Options:
A. Parallelogram
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:
What shape do you get if you join up the midpoints of the sides of this shape? ![An irregular quadrilateral drawn on a grid]()

Options:
A. Parallelogram
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 cube the conversion factor when converting cubed units

Question:
\(
0.7 m^3 =\bigstar \,cm^3
\)

What should replace the star?

Options:
A. \( 70 \)
B. \( 7000 \)
C. \( 700000 \)
D. \( 700 \)

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


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

Question:
What is \( \mathbf{1 2 6 . 0 5} \) rounded to the nearest ten?

Options:
A. \( 100 \)
B. \( 120 \)
C. \( 130 \)
D. \( 126 \)

Solve the problem as a student with the misconception above.
You 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 \( \mathbf{1 2 6 . 0 5} \) rounded to the nearest ten?

Options:
A. \( 100 \)
B. \( 120 \)
C. \( 130 \)
D. \( 126 \)

Solve the problem as a student with the misconception above.
You 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 \( \mathbf{1 2 6 . 0 5} \) rounded to the nearest ten?

Options:
A. \( 100 \)
B. \( 120 \)
C. \( 130 \)
D. \( 126 \)

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


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

Question:
Kate and Isaac share some yoghurt in the ratio \( 2: 5 \).
Kate has \(_____\) of the total yoghurt
What fraction completes the sentence?

Options:
A. \( \frac{3}{2} \)
B. \( \frac{3}{5} \)
C. \( \frac{2}{5} \)
D. \( \frac{2}{7} \)

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


Prompt:
Misconception:
Thinks two variables next to each other represent addition

Question:
Calculate the displacement \( (s) \), of a particle when initial velocity \( (u)=2.9 \mathrm{~ms}^{-1} \), final velocity \( (v)=3.5 \mathrm{~ms}^{-1} \), and the time \( (t) \) taken is \( 5.2 \) seconds. \( s=\frac{1}{2}(u+v) t \)

Options:
A. \( \begin{array}{c}s=\frac{1}{2}(2.9+3.5)+5.2 \\ s=8.4\end{array} \)
B. \( \begin{array}{c}s=\frac{1}{2}(2.9+3.5+5.2) \\ s=5.8\end{array} \)
C. \( \begin{array}{c}s=2.9+3.5+\left(\frac{1}{2} \times 5.2\right) \\ s=9\end{array} \)
D. \( \begin{array}{c}s=\frac{1}{2}(2.9+3.5) \times 5.2 \\ s=16.64\end{array} \)

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


Prompt:
Misconception:
Thinks two variables next to each other represent addition

Question:
Calculate the displacement \( (s) \), of a particle when initial velocity \( (u)=2.9 \mathrm{~ms}^{-1} \), final velocity \( (v)=3.5 \mathrm{~ms}^{-1} \), and the time \( (t) \) taken is \( 5.2 \) seconds. \( s=\frac{1}{2}(u+v) t \)

Options:
A. \( \begin{array}{c}s=\frac{1}{2}(2.9+3.5)+5.2 \\ s=8.4\end{array} \)
B. \( \begin{array}{c}s=\frac{1}{2}(2.9+3.5+5.2) \\ s=5.8\end{array} \)
C. \( \begin{array}{c}s=2.9+3.5+\left(\frac{1}{2} \times 5.2\right) \\ s=9\end{array} \)
D. \( \begin{array}{c}s=\frac{1}{2}(2.9+3.5) \times 5.2 \\ s=16.64\end{array} \)

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


Prompt:
Misconception:
Thinks there are 50 weeks in a year

Question:
How many days in a non-leap year?

Options:
A. \( 350 \)
B. \( 366 \)
C. \( 365 \)
D. \( 100 \)

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


Prompt:
Misconception:
Does not know how many days are in a leap year

Question:
How many days in a non-leap year?

Options:
A. \( 350 \)
B. \( 366 \)
C. \( 365 \)
D. \( 100 \)

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


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

Question:
Which calculation is incorrect?

Options:
A. \( (-7) \times 2=-14 \)
B. \( (-7) \times(-2)=-14 \)
C. \( 7 \times 2=14 \)
D. \( 7 \times(-2)=-14 \)

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


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

Question:
Which calculation is incorrect?

Options:
A. \( (-7) \times 2=-14 \)
B. \( (-7) \times(-2)=-14 \)
C. \( 7 \times 2=14 \)
D. \( 7 \times(-2)=-14 \)

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


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

Question:
Which calculation is incorrect?

Options:
A. \( (-7) \times 2=-14 \)
B. \( (-7) \times(-2)=-14 \)
C. \( 7 \times 2=14 \)
D. \( 7 \times(-2)=-14 \)

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


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

Question:
The probability of an event occurring is \( \frac{2}{7} \).

What is the probability of the event not occurring?

Options:
A. \( \frac{2}{7} \)
B. \( \frac{5}{7} \)
C. \( 5 \)
D. \( \frac{2}{5} \)

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


Prompt:
Misconception:
Gives probability as an integer instead of a fraction

Question:
The probability of an event occurring is \( \frac{2}{7} \).

What is the probability of the event not occurring?

Options:
A. \( \frac{2}{7} \)
B. \( \frac{5}{7} \)
C. \( 5 \)
D. \( \frac{2}{5} \)

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


Prompt:
Misconception:
Mixes up squaring with dividing by 2

Question:
\( (16)^{2}=? \)

Options:
A. \( 8 \)
B. \( 32 \)
C. \( 64 \)
D. \( 256 \)

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


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

Question:
\( (16)^{2}=? \)

Options:
A. \( 8 \)
B. \( 32 \)
C. \( 64 \)
D. \( 256 \)

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


Prompt:
Misconception:
Believes addition comes before indices, in orders of operation

Question:
This is a part of the table of values for the equation
\(y=x^{2}+4\) \begin{tabular}{|l|l|}
\hline\( x \) & \( -6 \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 40 \)
B. \( 4 \)
C. \( -24 \)
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 the square of a negative will also be negative

Question:
This is a part of the table of values for the equation
\(y=x^{2}+4\) \begin{tabular}{|l|l|}
\hline\( x \) & \( -6 \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 40 \)
B. \( 4 \)
C. \( -24 \)
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:
Counts half-squares as full squares when calculating area on a square grid

Question:
What is the area of this shape? ![Parallelogram drawn on square grid with area of 6 squares]()

Options:
A. \( 6 \)
B. \( 8 \)
C. \( 4 \)
D. \( 7 \)

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


Prompt:
Misconception:
Underestimates the area of shapes when counting squares when some squares are neither wholes nor halves

Question:
What is the area of this shape? ![Parallelogram drawn on square grid with area of 6 squares]()

Options:
A. \( 6 \)
B. \( 8 \)
C. \( 4 \)
D. \( 7 \)

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


Prompt:
Misconception:
Counts half-squares as full squares when calculating area on a square grid

Question:
What is the area of this shape? ![Parallelogram drawn on square grid with area of 6 squares]()

Options:
A. \( 6 \)
B. \( 8 \)
C. \( 4 \)
D. \( 7 \)

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


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

Question:
\( -(16)^{2}=? \)

Options:
A. \( -256 \)
B. \( -32 \)
C. \( 32 \)
D. \( 256 \)

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


Prompt:
Misconception:
Does not understand that the negative outside the bracket means answer will be negative

Question:
\( -(16)^{2}=? \)

Options:
A. \( -256 \)
B. \( -32 \)
C. \( 32 \)
D. \( 256 \)

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


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

Question:
Which quadrilateral has the highest order of rotational symmetry?

Options:
A. ![Trapezium]()
B. ![Irregular quadrilateral]()
C. ![Parallelogram]()
D. They each have the same order of rotational symmetry

Solve the problem as a student with the misconception above.
You 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 quadrilateral has the highest order of rotational symmetry?

Options:
A. ![Trapezium]()
B. ![Irregular quadrilateral]()
C. ![Parallelogram]()
D. They each have the same order of rotational symmetry

Solve the problem as a student with the misconception above.
You 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:
Which quadrilateral has the highest order of rotational symmetry?

Options:
A. ![Trapezium]()
B. ![Irregular quadrilateral]()
C. ![Parallelogram]()
D. They each have the same order of rotational symmetry

Solve the problem as a student with the misconception above.
You 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 integers on a number line, assumes each dash is 2

Question:
What number is the arrow pointing to? ![A number line from 100 to 200 with an arrow pointing to the value 160]()

Options:
A. \( 154 \)
B. \( 170 \)
C. \( 152 \)
D. \( 160 \)

Solve the problem as a student with the misconception above.
You 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 integers on a number line, assumes each dash is 10

Question:
What number is the arrow pointing to? ![A number line from 100 to 200 with an arrow pointing to the value 160]()

Options:
A. \( 154 \)
B. \( 170 \)
C. \( 152 \)
D. \( 160 \)

Solve the problem as a student with the misconception above.
You 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 integers on a number line, assumes each dash is 1

Question:
What number is the arrow pointing to? ![A number line from 100 to 200 with an arrow pointing to the value 160]()

Options:
A. \( 154 \)
B. \( 170 \)
C. \( 152 \)
D. \( 160 \)

Solve the problem as a student with the misconception above.
You 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 account for grammar when writing algebra e.g. ,then making a group

Question:
Which of the following is the correct way of writing:

\( m \) multiplied by \( n \), then add \( 5 \)

using algebraic convention?

Options:
A. \( m(n+5) \)
B. \( m \times n+5 \)
C. \( m n+5 \)
D. \( 5 m n \)

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


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

Question:
Which of the following is the correct way of writing:

\( m \) multiplied by \( n \), then add \( 5 \)

using algebraic convention?

Options:
A. \( m(n+5) \)
B. \( m \times n+5 \)
C. \( m n+5 \)
D. \( 5 m n \)

Solve the problem as a student with the misconception above.
You 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 any lines that cross are perpendicular

Question:
Line \( X Y \) is... ![A pair of parallel lines are drawn with the arrows pointing up to the left.
A straight red line, XY, is drawn so that it diagonally crosses the pair of parallel lines. The red line rises from X on the left up to Y.]()

Options:
A. Parallel
B. Perpendicular
C. Skew
D. A transversal

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

Question:
Line \( X Y \) is... ![A pair of parallel lines are drawn with the arrows pointing up to the left.
A straight red line, XY, is drawn so that it diagonally crosses the pair of parallel lines. The red line rises from X on the left up to Y.]()

Options:
A. Parallel
B. Perpendicular
C. Skew
D. A transversal

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


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

Question:
If we want to write
"\( m \) multiplied by \( m \) multiplied by \( m \)"
using algebra, this would be:

Options:
A. \( m \times m \times m \)
B. \( m^{3} \)
C. \( 3 m \)
D. \( \mathrm{mmm} \)

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


Prompt:
Misconception:
Multiplies by the index

Question:
If we want to write
"\( m \) multiplied by \( m \) multiplied by \( m \)"
using algebra, this would be:

Options:
A. \( m \times m \times m \)
B. \( m^{3} \)
C. \( 3 m \)
D. \( \mathrm{mmm} \)

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


Prompt:
Misconception:
Writes repeated letters instead of using index form of a variable

Question:
If we want to write
"\( m \) multiplied by \( m \) multiplied by \( m \)"
using algebra, this would be:

Options:
A. \( m \times m \times m \)
B. \( m^{3} \)
C. \( 3 m \)
D. \( \mathrm{mmm} \)

Solve the problem as a student with the misconception above.
You 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 don't need to numerically order the data before calculating the median

Question:
What is the median of the following numbers?
\[
2,2,4,7,10,-15
\]

Options:
A. \( 7 \)
B. \( 4 \)
C. \( 3 \)
D. \( 5.5 \)

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

Question:
What is the median of the following numbers?
\[
2,2,4,7,10,-15
\]

Options:
A. \( 7 \)
B. \( 4 \)
C. \( 3 \)
D. \( 5.5 \)

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


Prompt:
Misconception:
Believes you don't need to numerically order the data before calculating the median

Question:
What is the median of the following numbers?
\[
2,2,4,7,10,-15
\]

Options:
A. \( 7 \)
B. \( 4 \)
C. \( 3 \)
D. \( 5.5 \)

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:
![Think of a number, then subtract \( 5 \), next divide by \( 8 \), next add 4, and finally multiply by \( 7 \).]() Jo says you can write this as:
\[
7\left(\frac{(n-5)}{8}+4\right)
\]
Paul says you can write this as:
\[
7((n-5) \div 8)+4
\]
Who is correct?

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

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


Prompt:
Misconception:
When solving an equation forgets to eliminate the coefficient in front of the variable in the last step

Question:
A line has equation \( 4 x+3 y=5 \)
What is it's gradient?

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

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


Prompt:
Misconception:
Believes that for a line written in the form ax + by = c, a is the gradient

Question:
A line has equation \( 4 x+3 y=5 \)
What is it's gradient?

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

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


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

Question:
A line has equation \( 4 x+3 y=5 \)
What is it's gradient?

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

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
Which model does not correctly represent the following expression?
\(2(n+3)\)

Options:
A. ![\begin{tabular}{|c|c|}
\hline\( n \) & \( 3 \) \\
\hline\( n \) & \( 3 \) \\
\hline
\end{tabular}]()
B. ![\begin{tabular}{|l|l|l|l|}
\hline \( \mathrm{n} \) & \( 3 \) & \( \mathrm{n} \) & \( 3 \) \\
\hline
\end{tabular}]()
C. ![\begin{tabular}{|l|l|l|l|}
\hline \( \mathrm{n} \) & \( \mathrm{n} \) & \( 3 \) & \( 3 \) \\
\hline
\end{tabular}]()
D. ![\begin{tabular}{|c|c|}
\hline\( n \) & \( 2 \) \\
\hline\( n \) & \( 2 \) \\
\hline\( n \) & \( 2 \) \\
\hline
\end{tabular}]()

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
Which model does not correctly represent the following expression?
\(2(n+3)\)

Options:
A. ![\begin{tabular}{|c|c|}
\hline\( n \) & \( 3 \) \\
\hline\( n \) & \( 3 \) \\
\hline
\end{tabular}]()
B. ![\begin{tabular}{|l|l|l|l|}
\hline \( \mathrm{n} \) & \( 3 \) & \( \mathrm{n} \) & \( 3 \) \\
\hline
\end{tabular}]()
C. ![\begin{tabular}{|l|l|l|l|}
\hline \( \mathrm{n} \) & \( \mathrm{n} \) & \( 3 \) & \( 3 \) \\
\hline
\end{tabular}]()
D. ![\begin{tabular}{|c|c|}
\hline\( n \) & \( 2 \) \\
\hline\( n \) & \( 2 \) \\
\hline\( n \) & \( 2 \) \\
\hline
\end{tabular}]()

Solve the problem as a student with the misconception above.
You 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 distributive property

Question:
Which model does not correctly represent the following expression?
\(2(n+3)\)

Options:
A. ![\begin{tabular}{|c|c|}
\hline\( n \) & \( 3 \) \\
\hline\( n \) & \( 3 \) \\
\hline
\end{tabular}]()
B. ![\begin{tabular}{|l|l|l|l|}
\hline \( \mathrm{n} \) & \( 3 \) & \( \mathrm{n} \) & \( 3 \) \\
\hline
\end{tabular}]()
C. ![\begin{tabular}{|l|l|l|l|}
\hline \( \mathrm{n} \) & \( \mathrm{n} \) & \( 3 \) & \( 3 \) \\
\hline
\end{tabular}]()
D. ![\begin{tabular}{|c|c|}
\hline\( n \) & \( 2 \) \\
\hline\( n \) & \( 2 \) \\
\hline\( n \) & \( 2 \) \\
\hline
\end{tabular}]()

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
\[
3 k+2<m+2
\]
Using the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()

Options:
A. always true
B. sometimes true
C. never true
D. Need more information

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
\[
3 k+2<m+2
\]
Using the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()

Options:
A. always true
B. sometimes true
C. never true
D. Need more information

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


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
\[
3 k+2<m+2
\]
Using the diagram on the right, is the expression above... ![A bar model where the same length is represented by either 3 lengths of 'k' or 1 length of 'm']()

Options:
A. always true
B. sometimes true
C. never true
D. Need more information

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


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

Question:
Tom and Katie are discussing regular polygons. Tom says this is a regular polygon ![A triangle with 3 equal sides and 3 equal angles]() Katie says this is a regular polygon ![A parallelogram with 2 pairs of parallel sides marked]() Who is correct?

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

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


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

Question:
Tom and Katie are discussing regular polygons. Tom says this is a regular polygon ![A triangle with 3 equal sides and 3 equal angles]() Katie says this is a regular polygon ![A parallelogram with 2 pairs of parallel sides marked]() Who is correct?

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

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


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

Question:
Tom and Katie are discussing regular polygons. Tom says this is a regular polygon ![A triangle with 3 equal sides and 3 equal angles]() Katie says this is a regular polygon ![A parallelogram with 2 pairs of parallel sides marked]() 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:
Uses slant height instead of perpendicular height to find area of a trapezium

Question:
When calculating the area of this trapezium, what is the value of \( h \) in the formula? Area \( =\left(\frac{a+b}{2}\right) h \) ![Trapezium with the slanted sides labelled 8cm and 7.5cm. The parallel sides labelled 3cm and 8cm. The perpendicular height labelled 7cm.]()

Options:
A. \( 8 \)
B. \( 7.5 \)
C. \( 7 \)
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:
Uses slant height instead of perpendicular height to find area of a trapezium

Question:
When calculating the area of this trapezium, what is the value of \( h \) in the formula? Area \( =\left(\frac{a+b}{2}\right) h \) ![Trapezium with the slanted sides labelled 8cm and 7.5cm. The parallel sides labelled 3cm and 8cm. The perpendicular height labelled 7cm.]()

Options:
A. \( 8 \)
B. \( 7.5 \)
C. \( 7 \)
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:
Uses base instead of height as h in area of a trapezium formula

Question:
When calculating the area of this trapezium, what is the value of \( h \) in the formula? Area \( =\left(\frac{a+b}{2}\right) h \) ![Trapezium with the slanted sides labelled 8cm and 7.5cm. The parallel sides labelled 3cm and 8cm. The perpendicular height labelled 7cm.]()

Options:
A. \( 8 \)
B. \( 7.5 \)
C. \( 7 \)
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:
Fails to reflect across mirror line

Question:
![A grid of 7 squares across and 7 squares up. A red vertical line goes from the bottom to the top of the grid, it is 4 squares left from the edge of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn to the left of the red line, with its right-hand side on the red line.  The bottom side of the rectangle is 3 squares up from the bottom of the grid. The bottom left corner of the rectangle is marked with the letter P, which is 3 squares up from the bottom of the grid and 3 squares to the left of the red line. The bottom right corner of the rectangle is marked with the letter Q, which is 3 squares up from the bottom of the grid on the red line. ]() Tom and Katie are discussing reflections

Tom says if you reflect the rectangle in the vertical line, Point \( P \) stays in the same position

Katie says if you reflect the rectangle in the vertical line, Point \( Q \) stays in the same position
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:
Fails to reflect across mirror line

Question:
![A grid of 7 squares across and 7 squares up. A red vertical line goes from the bottom to the top of the grid, it is 4 squares left from the edge of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn to the left of the red line, with its right-hand side on the red line.  The bottom side of the rectangle is 3 squares up from the bottom of the grid. The bottom left corner of the rectangle is marked with the letter P, which is 3 squares up from the bottom of the grid and 3 squares to the left of the red line. The bottom right corner of the rectangle is marked with the letter Q, which is 3 squares up from the bottom of the grid on the red line. ]() Tom and Katie are discussing reflections

Tom says if you reflect the rectangle in the vertical line, Point \( P \) stays in the same position

Katie says if you reflect the rectangle in the vertical line, Point \( Q \) stays in the same position
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:
Fails to reflect across mirror line

Question:
![A grid of 7 squares across and 7 squares up. A red vertical line goes from the bottom to the top of the grid, it is 4 squares left from the edge of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn to the left of the red line, with its right-hand side on the red line.  The bottom side of the rectangle is 3 squares up from the bottom of the grid. The bottom left corner of the rectangle is marked with the letter P, which is 3 squares up from the bottom of the grid and 3 squares to the left of the red line. The bottom right corner of the rectangle is marked with the letter Q, which is 3 squares up from the bottom of the grid on the red line. ]() Tom and Katie are discussing reflections

Tom says if you reflect the rectangle in the vertical line, Point \( P \) stays in the same position

Katie says if you reflect the rectangle in the vertical line, Point \( Q \) stays in the same position
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:
Confuses square rooting and halving the number

Question:
Without using a calculator, which two integers must \( \sqrt{89} \) lie between?

Options:
A. \( 44 \) and \( 45 \)
B. \( 8 \) and \( 9 \)
C. \( 81 \) and \( 100 \)
D. \( 9 \) and \( 10 \)

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 solving an equation with a fraction, thinks you don't need to multiply every term on both sides when multiplying by the denominator

Question:
Jo and Paul are arguing about a first step to solve this equation:
\(
\frac{m}{6}-4=24
\)
Jo says you can write: \( \frac{m}{6}=28 \)
Paul says you can write: \( m-4=144 \)
Who is correct?

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

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


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

Question:
Jo and Paul are arguing about a first step to solve this equation:
\(
\frac{m}{6}-4=24
\)
Jo says you can write: \( \frac{m}{6}=28 \)
Paul says you can write: \( m-4=144 \)
Who is correct?

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

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


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

Question:
\begin{tabular}{l|l|l|l}
\( x \) & \( \) & \( 0 \) & \( 3 \) \\
\hline\( y \) & \( -7 \) & \( -5 \) &  \( \color{gold}\bigstar\ \) \\
\end{tabular}
 This is a table of values for \( y=2 x+c \)
What should replace the star?

Options:
A. \( 6 \)
B. \( -3 \)
C. \( 1 \)
D. \( -5 \)

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


Prompt:
Misconception:
Does not recognise that a shape translated would not change orientation

Question:
John rotates rectangle \( A B C D 90^{\circ} \) clockwise from the centre \( (3,2) \). What error has he made? ![A positive, coordinate grid with two rectangles drawn on it. The rectangle labelled ABCD has the coordinates: A(1,3) B(1,5) C(2,5) and D(2,3). The other rectangle has the coordinates: (4,3) (6,3) (6,2) and (4,2).]()

Options:
A. He hasn't, this is correct
B. He has translated by the vector \( \left(\begin{array}{l}3 \\ 2\end{array}\right) \)
C. He has rotated \( 90^{\circ} \) anticlockwise
D. He has used the wrong centre

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


Prompt:
Misconception:
Mixes up clockwise and anticlockwise

Question:
John rotates rectangle \( A B C D 90^{\circ} \) clockwise from the centre \( (3,2) \). What error has he made? ![A positive, coordinate grid with two rectangles drawn on it. The rectangle labelled ABCD has the coordinates: A(1,3) B(1,5) C(2,5) and D(2,3). The other rectangle has the coordinates: (4,3) (6,3) (6,2) and (4,2).]()

Options:
A. He hasn't, this is correct
B. He has translated by the vector \( \left(\begin{array}{l}3 \\ 2\end{array}\right) \)
C. He has rotated \( 90^{\circ} \) anticlockwise
D. He has used the wrong centre

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


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

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 (2, 2) is labelled with the letter "P". The line y=2 is shown with a purple dashed line.]()

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

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


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

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 (2, 2) is labelled with the letter "P". The line y=2 is shown with a purple dashed line.]()

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

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


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

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 (2, 2) is labelled with the letter "P". The line y=2 is shown with a purple dashed line.]()

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

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


Prompt:
Misconception:
Confuses corresponding and vertically opposite angles

Question:
Which angle is corresponding to angle \( p \) ? ![Image showing two parallel lines cut by a transversal creating two distinct angles around a point. On the left hand side the pink angle is labelled with A, vertically opposite this is the angle labelled p. On the right hand side, angle B is co-interior to p. Then lying on the same straight line as B is the angle labelled C. Vertically opposite angle C is the angle labelled D.]()

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

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


Prompt:
Misconception:
Confuses co-interior and corresponding angles

Question:
Which angle is corresponding to angle \( p \) ? ![Image showing two parallel lines cut by a transversal creating two distinct angles around a point. On the left hand side the pink angle is labelled with A, vertically opposite this is the angle labelled p. On the right hand side, angle B is co-interior to p. Then lying on the same straight line as B is the angle labelled C. Vertically opposite angle C is the angle labelled D.]()

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

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


Prompt:
Misconception:
Confuses corresponding and alternate angles

Question:
Which angle is corresponding to angle \( p \) ? ![Image showing two parallel lines cut by a transversal creating two distinct angles around a point. On the left hand side the pink angle is labelled with A, vertically opposite this is the angle labelled p. On the right hand side, angle B is co-interior to p. Then lying on the same straight line as B is the angle labelled C. Vertically opposite angle C is the angle labelled D.]()

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

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


Prompt:
Misconception:
Mistakes rotations for translations

Question:
John rotates hexagon \( \mathrm{ABCDEF}  90^{\degree} \) clockwise from the centre \( (5,4) \). What error has he made? ![A positive, coordinate grid with two L-shaped hexagons drawn on it. The hexagon labelled ABCDEF has the coordinates: A(2,4) B(2,1) C(4,1) D(4,2) E(3,2) and F (3,4). The other hexagon has the coordinates: (6,7) (3,7) (3,5) (4,5) (4,6) and (6,6)]()

Options:
A. He has translated by the vector \( \left(\begin{array}{l}5 \\ 4\end{array}\right) \)
B. He has rotated \( 90^{\circ} \) anticlockwise
C. He has used the wrong centre
D. He hasn't, this is correct

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


Prompt:
Misconception:
Mixes up clockwise and anticlockwise

Question:
John rotates hexagon \( \mathrm{ABCDEF}  90^{\degree} \) clockwise from the centre \( (5,4) \). What error has he made? ![A positive, coordinate grid with two L-shaped hexagons drawn on it. The hexagon labelled ABCDEF has the coordinates: A(2,4) B(2,1) C(4,1) D(4,2) E(3,2) and F (3,4). The other hexagon has the coordinates: (6,7) (3,7) (3,5) (4,5) (4,6) and (6,6)]()

Options:
A. He has translated by the vector \( \left(\begin{array}{l}5 \\ 4\end{array}\right) \)
B. He has rotated \( 90^{\circ} \) anticlockwise
C. He has used the wrong centre
D. He hasn't, this is correct

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


Prompt:
Misconception:
Assumes a ratio is part to part instead of part to whole

Question:
Given that \( A C=3 A B \), what are the coordinates of \( C \) ? ![A straight line labelled y=2x-1 is drawn on a set of axes. Points A, B and C are all on the line. Point A is (2,3) and B is (5,9).]()

Options:
A. \( (14,27) \)
B. \( (21,36) \)
C. \( (11,21) \)
D. \( (9,18) \)

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


Prompt:
Misconception:
Does not know how to find the length of a line segment from coordinates

Question:
Given that \( A C=3 A B \), what are the coordinates of \( C \) ? ![A straight line labelled y=2x-1 is drawn on a set of axes. Points A, B and C are all on the line. Point A is (2,3) and B is (5,9).]()

Options:
A. \( (14,27) \)
B. \( (21,36) \)
C. \( (11,21) \)
D. \( (9,18) \)

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


Prompt:
Misconception:
Adds instead of multiplying when expanding bracket

Question:
Expand:
\[
6(2-3 p)
\]

Options:
A. \( 8-18 p \)
B. \( 2-18 p \)
C. \( 12-18 p \)
D. \( 18 p-6 \)

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


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

Question:
Expand:
\[
6(2-3 p)
\]

Options:
A. \( 8-18 p \)
B. \( 2-18 p \)
C. \( 12-18 p \)
D. \( 18 p-6 \)

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


Prompt:
Misconception:
Believes subtraction is commutative

Question:
Expand:
\[
6(2-3 p)
\]

Options:
A. \( 8-18 p \)
B. \( 2-18 p \)
C. \( 12-18 p \)
D. \( 18 p-6 \)

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}.