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

Question:
Which of the following is the correct solution to the inequality?
\(
x^{2}<64
\)

Options:
A. \( \{-32<x<32\} \)
B. \( \{x<8\} \)
C. \( \{-8<x<8\} \)
D. \( \{x<-8\} \cup\{x>8\} \)

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


Prompt:
Misconception:
When dividing decimals with the same number of decimal places as each other, assumes the answer also has the same number of decimal places

Question:
\( 0.9 \div 0.3= \)

Options:
A. \( 0.3 \)
B. \( 9.3 \)
C. \( 0.333 \ldots \)
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 division is commutative

Question:
\( 0.9 \div 0.3= \)

Options:
A. \( 0.3 \)
B. \( 9.3 \)
C. \( 0.333 \ldots \)
D. \( 3 \)

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


Prompt:
Misconception:
Confuses chord and radius

Question:
What is the correct name for the line marked on the circle? ![\( \theta \)]()

Options:
A. Radius
B. Chord
C. Tangent
D. Diameter

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


Prompt:
Misconception:
Confuses tangent and chord

Question:
What is the correct name for the line marked on the circle? ![\( \theta \)]()

Options:
A. Radius
B. Chord
C. Tangent
D. Diameter

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


Prompt:
Misconception:
Confuses diameter and chord

Question:
What is the correct name for the line marked on the circle? ![\( \theta \)]()

Options:
A. Radius
B. Chord
C. Tangent
D. Diameter

Solve the problem as a student with the misconception above.
You 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:
This is a part of the table of values for the equation
\[
10 x-6 y=30
\] \begin{tabular}{|l|l|}
\hline\( x \) & \( \bigstar \) \\
\hline\( y \) & \( 0.5 \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 4.25 \)
B. \( -4.25 \)
C. \( 3.3 \)
D. \( 2.7 \)

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


Prompt:
Misconception:
Assumes a fact without considering enough examples

Question:
\(
n-2 \geq \frac{n}{2}
\)

If \( n \) can represent any number, is the statement above...

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:
Assumes a fact without considering enough examples

Question:
\(
n-2 \geq \frac{n}{2}
\)

If \( n \) can represent any number, is the statement above...

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

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


Prompt:
Misconception:
Thinks a dashed line marking a region means the line is included

Question:
Which inequality is represented by the shaded region? ![A graph of a quadratic equation. There are dashed vertical lines through the roots of the quadratic. The shaded region is between these vertical lines. ]()

Options:
A. \( x^{2}+x-5 \leq 0 \)
B. \( x^{2}+x-5 \geq 0 \)
C. \( x^{2}+x-5<0 \)
D. \( x^{2}+x-5>0 \)

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


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

Question:
Which inequality is represented by the shaded region? ![A graph of a quadratic equation. There are dashed vertical lines through the roots of the quadratic. The shaded region is between these vertical lines. ]()

Options:
A. \( x^{2}+x-5 \leq 0 \)
B. \( x^{2}+x-5 \geq 0 \)
C. \( x^{2}+x-5<0 \)
D. \( x^{2}+x-5>0 \)

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


Prompt:
Misconception:
Divides length of original by length of image rather finding length of image divided by length of original to find an enlargement scale factor.

Question:
Shape A has been enlarged to get shape B. What is the scale factor of the enlargement? ![Triangle A is two squares across one square up. Triangle B is six squares across and three squares up.]()

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

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:
Divides length of original by length of image rather finding length of image divided by length of original to find an enlargement scale factor.

Question:
Shape A has been enlarged to get shape B. What is the scale factor of the enlargement? ![Triangle A is two squares across one square up. Triangle B is six squares across and three squares up.]()

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

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


Prompt:
Misconception:
Believes squaring a negative number just changes the sign

Question:
Which of the following points lies on the circle with equation:
\(
x^{2}+y^{2}=10
\)

Options:
A. \( (-9,1) \)
B. \( (0,5) \)
C. \( (3,-1) \)
D. \( (6,4) \)

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


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

Question:
Which of the following points lies on the circle with equation:
\(
x^{2}+y^{2}=10
\)

Options:
A. \( (-9,1) \)
B. \( (0,5) \)
C. \( (3,-1) \)
D. \( (6,4) \)

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


Prompt:
Misconception:
Thinks measures of area must end in squared

Question:
Which of the following formulae gives the area of this rectangle? ![Rectangle with base 3 and height 2x.]()

Options:
A. \( A=6 x \)
B. \( A=36 x^{2} \)
C. \( A=3+2 x \)
D. \( A=6+4 x \)

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


Prompt:
Misconception:
Adds when calculating area instead of multiplying

Question:
Which of the following formulae gives the area of this rectangle? ![Rectangle with base 3 and height 2x.]()

Options:
A. \( A=6 x \)
B. \( A=36 x^{2} \)
C. \( A=3+2 x \)
D. \( A=6+4 x \)

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


Prompt:
Misconception:
Calculates perimeter when asked for area

Question:
Which of the following formulae gives the area of this rectangle? ![Rectangle with base 3 and height 2x.]()

Options:
A. \( A=6 x \)
B. \( A=36 x^{2} \)
C. \( A=3+2 x \)
D. \( A=6+4 x \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
Which option is the best estimate for
\[
17,984-2,407 ?
\]

Options:
A. \( 17,000-2,000 \)
B. \( 18,000-3,000 \)
C. \( 18,000-2,000 \)
D. \( 17,000-3,000 \)

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


Prompt:
Misconception:
Rounds up instead of down

Question:
Which option is the best estimate for
\[
17,984-2,407 ?
\]

Options:
A. \( 17,000-2,000 \)
B. \( 18,000-3,000 \)
C. \( 18,000-2,000 \)
D. \( 17,000-3,000 \)

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


Prompt:
Misconception:
When interpreting a pictogram, thinks each symbol stands for 1

Question:
This pictogram shows the different types of music Bob has in his music collection.

Which of the following numbers of CDs could Bob represent with whole symbols? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]()

Options:
A. \( 2 \)
B. \( 22 \)
C. \( 32 \)
D. \( 42 \)

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


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

Question:
What is the next term in this sequence?

\[
105, \quad 97, \quad 89, \quad \ldots
\]

Options:
A. \( 81 \)
B. \( 71 \)
C. \( 8 \)
D. Not enough information

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


Prompt:
Misconception:
Does not know how to find the next term in a sequence

Question:
What is the next term in this sequence?

\[
105, \quad 97, \quad 89, \quad \ldots
\]

Options:
A. \( 81 \)
B. \( 71 \)
C. \( 8 \)
D. Not enough information

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


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

Question:
Solve this equation, giving all solutions:
\[
k^{2}=4 k
\]

Options:
A. \( k=-4 \)
B. \( k=4 \)
C. \[
k=0
\]
or
\[
k=4
\]
D. \[
k=2
\]
or
\[
k=-2
\]

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 do not need to give the direction when describing a rotation

Question:
Tom and Katie are arguing about how to fully describe the rotation from shape \( P \) to shape \( Q \)

Tom says: "a rotation of \( 90^{\degree} \) about point \( (1,1) \) "

Katie says: "a rotation of \( 90^{\degree} \) clockwise"

Who is correct? ![A coordinate grid with two pentagons drawn on it labelled P and Q. Pentagon P has the coordinates: (-3,-1) (-3,0) (-2,3) (-1,0) and (-1,-1). Pentagon A has the coordinates: (-1,5) (0,5) (3,4) (0,3) and -1,3).]()

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:
Forgets to give the centre of rotation

Question:
Tom and Katie are arguing about how to fully describe the rotation from shape \( P \) to shape \( Q \)

Tom says: "a rotation of \( 90^{\degree} \) about point \( (1,1) \) "

Katie says: "a rotation of \( 90^{\degree} \) clockwise"

Who is correct? ![A coordinate grid with two pentagons drawn on it labelled P and Q. Pentagon P has the coordinates: (-3,-1) (-3,0) (-2,3) (-1,0) and (-1,-1). Pentagon A has the coordinates: (-1,5) (0,5) (3,4) (0,3) and -1,3).]()

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 you do not need to give the direction when describing a rotation

Question:
Tom and Katie are arguing about how to fully describe the rotation from shape \( P \) to shape \( Q \)

Tom says: "a rotation of \( 90^{\degree} \) about point \( (1,1) \) "

Katie says: "a rotation of \( 90^{\degree} \) clockwise"

Who is correct? ![A coordinate grid with two pentagons drawn on it labelled P and Q. Pentagon P has the coordinates: (-3,-1) (-3,0) (-2,3) (-1,0) and (-1,-1). Pentagon A has the coordinates: (-1,5) (0,5) (3,4) (0,3) and -1,3).]()

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

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


Prompt:
Misconception:
When multiplying a multiple of 10, just multiplies the non-zero digits

Question:
If you use the grid method to calculate \( 35 \times 26 \) what should replace the star? \begin{tabular}{|c|c|c|}
\hline\( \times \) & \( 30 \) & \( 5 \) \\
\hline \( 20 \) &   & \(\bigstar\) \\
\hline \( 6 \) &  \\
\hline
\end{tabular}

Options:
A. \( 10 \)
B. \( 1000 \)
C. \( 25 \)
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:
When multiplying by a multiple of 10, gives an answer 10 times bigger than it should be

Question:
If you use the grid method to calculate \( 35 \times 26 \) what should replace the star? \begin{tabular}{|c|c|c|}
\hline\( \times \) & \( 30 \) & \( 5 \) \\
\hline \( 20 \) &   & \(\bigstar\) \\
\hline \( 6 \) &  \\
\hline
\end{tabular}

Options:
A. \( 10 \)
B. \( 1000 \)
C. \( 25 \)
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:
Adds instead of multiplies when using grid method

Question:
If you use the grid method to calculate \( 35 \times 26 \) what should replace the star? \begin{tabular}{|c|c|c|}
\hline\( \times \) & \( 30 \) & \( 5 \) \\
\hline \( 20 \) &   & \(\bigstar\) \\
\hline \( 6 \) &  \\
\hline
\end{tabular}

Options:
A. \( 10 \)
B. \( 1000 \)
C. \( 25 \)
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:
When dividing a fraction by an integer, divides the denominator by the integer

Question:
Calculate:
\(
\frac{6}{9} \div 3
\)

Options:
A. \( \frac{6}{3} \)
B. \( \frac{2}{18} \)
C. \( \frac{2}{9} \)
D. \( \frac{2}{3} \)

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


Prompt:
Misconception:
when dividing a fraction by an integer, both multiplies the denominator and divides the denominator

Question:
Calculate:
\(
\frac{6}{9} \div 3
\)

Options:
A. \( \frac{6}{3} \)
B. \( \frac{2}{18} \)
C. \( \frac{2}{9} \)
D. \( \frac{2}{3} \)

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


Prompt:
Misconception:
When dividing a fraction by an integer, divides both the numerator and denominator by the integer

Question:
Calculate:
\(
\frac{6}{9} \div 3
\)

Options:
A. \( \frac{6}{3} \)
B. \( \frac{2}{18} \)
C. \( \frac{2}{9} \)
D. \( \frac{2}{3} \)

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


Prompt:
Misconception:
Believes the reciprocal button writes a fraction

Question:
Which of the following would allow you to type \( \frac{3}{7} \) on your calculator? ![A scientific calculator]()

Options:
A. ![The number 3, then a calculator button labelled \(\frac{\square}{\square}\), then the number 7]()
B. ![The number 3, then a calculator button labelled \( x^{-1} \), then the number 7]()
C. ![The number 3, then a calculator button labelled \(\cdot\), then the number 7]()
D. ![The number 3, then a calculator button labelled \(-\), then the number 7]()

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


Prompt:
Misconception:
Believes the decimal point button writes a fraction

Question:
Which of the following would allow you to type \( \frac{3}{7} \) on your calculator? ![A scientific calculator]()

Options:
A. ![The number 3, then a calculator button labelled \(\frac{\square}{\square}\), then the number 7]()
B. ![The number 3, then a calculator button labelled \( x^{-1} \), then the number 7]()
C. ![The number 3, then a calculator button labelled \(\cdot\), then the number 7]()
D. ![The number 3, then a calculator button labelled \(-\), then the number 7]()

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


Prompt:
Misconception:
Believes the subtraction button writes a fraction

Question:
Which of the following would allow you to type \( \frac{3}{7} \) on your calculator? ![A scientific calculator]()

Options:
A. ![The number 3, then a calculator button labelled \(\frac{\square}{\square}\), then the number 7]()
B. ![The number 3, then a calculator button labelled \( x^{-1} \), then the number 7]()
C. ![The number 3, then a calculator button labelled \(\cdot\), then the number 7]()
D. ![The number 3, then a calculator button labelled \(-\), then the number 7]()

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


Prompt:
Misconception:
Believes they can ignore the coefficient when expanding double brackets

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
(3 m+2)(m-2) \equiv \bigstar \ m^{2} \triangle \  m \bigcirc
\)

Options:
A. \(
\triangle=+0
\)
(no \( \mathrm{m} \) term)
B. \( \triangle=-4 \)
C. \( \triangle=+8 \)
D. \( \triangle=+4 \)

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


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

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
(3 m+2)(m-2) \equiv \bigstar \ m^{2} \triangle \  m \bigcirc
\)

Options:
A. \(
\triangle=+0
\)
(no \( \mathrm{m} \) term)
B. \( \triangle=-4 \)
C. \( \triangle=+8 \)
D. \( \triangle=+4 \)

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


Prompt:
Misconception:
Thinks signs are interchangeable when adding or subtracting positive and negative numbers

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
(3 m+2)(m-2) \equiv \bigstar \ m^{2} \triangle \  m \bigcirc
\)

Options:
A. \(
\triangle=+0
\)
(no \( \mathrm{m} \) term)
B. \( \triangle=-4 \)
C. \( \triangle=+8 \)
D. \( \triangle=+4 \)

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


Prompt:
Misconception:
Adds or subtracts from numerator first when solving an equation with a fraction

Question:
Which of the following is a correct first step to solve this equation:
\(\frac{5 r+6}{6 r}=7\)

Options:
A. \( \frac{5 r}{6 r}=1 \)
B. \( 5 r+1=7 r \)
C. \( 5 r+6=42 r \)
D. \( \frac{5}{6}+r=7 \)

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:
Does not understand how to maintain equivalence in fractions

Question:
Which of the following is a correct first step to solve this equation:
\(\frac{5 r+6}{6 r}=7\)

Options:
A. \( \frac{5 r}{6 r}=1 \)
B. \( 5 r+1=7 r \)
C. \( 5 r+6=42 r \)
D. \( \frac{5}{6}+r=7 \)

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:
Does not understand equivalent fractions

Question:
Which of the following is a correct first step to solve this equation:
\(\frac{5 r+6}{6 r}=7\)

Options:
A. \( \frac{5 r}{6 r}=1 \)
B. \( 5 r+1=7 r \)
C. \( 5 r+6=42 r \)
D. \( \frac{5}{6}+r=7 \)

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


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

Question:
Which of the following answers shows a correct expansion and simplification of the expression below?

\(
(x-3)^{2}
\)

Options:
A. \( x^{2}-6 x-9 \)
B. \( x^{2}-9 \)
C. \( x^{2}+9 \)
D. \( x^{2}-6 x+9 \)

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


Prompt:
Misconception:
Believes they only need to multiply the first and last pairs of terms when expanding double brackets

Question:
Which of the following answers shows a correct expansion and simplification of the expression below?

\(
(x-3)^{2}
\)

Options:
A. \( x^{2}-6 x-9 \)
B. \( x^{2}-9 \)
C. \( x^{2}+9 \)
D. \( x^{2}-6 x+9 \)

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


Prompt:
Misconception:
Does not think a number can be a factor of itself

Question:
Which of these is not a factor of \( 12 \) ?

Options:
A. Four
B. Six
C. Twelve
D. Twenty-four

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


Prompt:
Misconception:
Confuses factors and multiples

Question:
What is the lowest common multiple of \( 6 \) and \( 7 \) ?

Options:
A. \( 1 \)
B. \( 13 \)
C. \( 42 \)
D. They do not have a lowest common multiple

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


Prompt:
Misconception:
Believes adding two numbers finds their lowest common multiple

Question:
What is the lowest common multiple of \( 6 \) and \( 7 \) ?

Options:
A. \( 1 \)
B. \( 13 \)
C. \( 42 \)
D. They do not have a lowest common multiple

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


Prompt:
Misconception:
Ignores the negative sign

Question:
What is the range of the following numbers?
\[
2,2,4,17,-10
\]

Options:
A. \( 15 \)
B. \( 12 \)
C. \( 7 \)
D. \( 27 \)

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


Prompt:
Misconception:
When calculating the range does not reorder the data to find the largest number minus the smallest number

Question:
What is the range of the following numbers?
\[
2,2,4,17,-10
\]

Options:
A. \( 15 \)
B. \( 12 \)
C. \( 7 \)
D. \( 27 \)

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


Prompt:
Misconception:
To find the range adds the biggest and smallest number rather than subtract

Question:
What is the range of the following numbers?
\[
2,2,4,17,-10
\]

Options:
A. \( 15 \)
B. \( 12 \)
C. \( 7 \)
D. \( 27 \)

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


Prompt:
Misconception:
Thinks there are 100mm in a centimetre

Question:
A \( 2 \) metre long rope has \( 0.5 \) centimetres chopped off the end.
What is the length of the rope that remains?
Give your answer in millimetres

Options:
A. \( 1999.5 \mathrm{~mm} \)
B. \( 1995 \mathrm{~mm} \)
C. \( 1950 \mathrm{~mm} \)
D. \( 199.5 \mathrm{~mm} \)

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


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

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
m(m+2)(m-2) \equiv m^{3} \bigstar \ m^{2} \triangle \ m
\)

Options:
A. \(
\triangle=+0
\)
(no \( m \) term)
B. \( \triangle=+4 \)
C. \( \triangle=+2 \)
D. \( \triangle=-4 \)

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


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

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
m(m+2)(m-2) \equiv m^{3} \bigstar \ m^{2} \triangle \ m
\)

Options:
A. \(
\triangle=+0
\)
(no \( m \) term)
B. \( \triangle=+4 \)
C. \( \triangle=+2 \)
D. \( \triangle=-4 \)

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


Prompt:
Misconception:
When multiplying out 2 or more brackets, does not multiply all the combinations of terms

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
m(m+2)(m-2) \equiv m^{3} \bigstar \ m^{2} \triangle \ m
\)

Options:
A. \(
\triangle=+0
\)
(no \( m \) term)
B. \( \triangle=+4 \)
C. \( \triangle=+2 \)
D. \( \triangle=-4 \)

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


Prompt:
Misconception:
Does not equate the value of a number with the place value column it is in

Question:
What is the value of the \( 4 \) in this number?
\( 31405 \)

Options:
A. \( 4 \)
B. \( 40 \)
C. \( 400 \)
D. \( 4000 \)

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


Prompt:
Misconception:
Confuses the hundreds and tens place value columns

Question:
What is the value of the \( 4 \) in this number?
\( 31405 \)

Options:
A. \( 4 \)
B. \( 40 \)
C. \( 400 \)
D. \( 4000 \)

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


Prompt:
Misconception:
Confuses the hundreds and thousands place value columns

Question:
What is the value of the \( 4 \) in this number?
\( 31405 \)

Options:
A. \( 4 \)
B. \( 40 \)
C. \( 400 \)
D. \( 4000 \)

Solve the problem as a student with the misconception above.
You 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 include units in answer.

Question:
If five cups of tea and two cups of coffee cost \( £ 3.70 \), and two cups of tea and five cups of coffee cost \( £ 4.00 \), what is the cost of a cup of tea and a cup of coffee?

Options:
A. \( \begin{array}{l}\text { Tea }=0.5 \\ \text { coffee }=0.6\end{array} \)
B. \( \begin{array}{l}\text { Tea }=30 p, \\ \text { coffee }=£ 1.10\end{array} \)
C. \( \begin{array}{l}\text { Tea }=60 p \\ \text { coffee }=50 p\end{array} \)
D. Tea \( =50 \mathrm{p} \) coffee \( =60 p \)

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 asked to solve simultaneous equations, believes they can just find values that work in one equation

Question:
If five cups of tea and two cups of coffee cost \( £ 3.70 \), and two cups of tea and five cups of coffee cost \( £ 4.00 \), what is the cost of a cup of tea and a cup of coffee?

Options:
A. \( \begin{array}{l}\text { Tea }=0.5 \\ \text { coffee }=0.6\end{array} \)
B. \( \begin{array}{l}\text { Tea }=30 p, \\ \text { coffee }=£ 1.10\end{array} \)
C. \( \begin{array}{l}\text { Tea }=60 p \\ \text { coffee }=50 p\end{array} \)
D. Tea \( =50 \mathrm{p} \) coffee \( =60 p \)

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

Question:
What length replaces the \( \color{green}\bigstar \)? ![A diagram showing a compound shape. It is an L shape rotated 90 degrees clockwise. The top full width is 3x+4, the partial width to the right is 2x. The left full height is 5, the partial height on the right is 2. There is a green star on the left partial width at the bottom of the diagram.]()

Options:
A. \( 5 x+11 \)
B. \( x-3 \)
C. \( x+4 \)
D. Not enough information

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


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

Question:
What length replaces the \( \color{green}\bigstar \)? ![A diagram showing a compound shape. It is an L shape rotated 90 degrees clockwise. The top full width is 3x+4, the partial width to the right is 2x. The left full height is 5, the partial height on the right is 2. There is a green star on the left partial width at the bottom of the diagram.]()

Options:
A. \( 5 x+11 \)
B. \( x-3 \)
C. \( x+4 \)
D. Not enough information

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


Prompt:
Misconception:
Adds instead of multiplying when expanding bracket

Question:
Expand:
\[
3(1-2 p)
\]

Options:
A. \( 4-6 p \)
B. \( 3-6 p \)
C. \( 1-6 p \)
D. \( 6 p-3 \)

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


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

Question:
Expand:
\[
3(1-2 p)
\]

Options:
A. \( 4-6 p \)
B. \( 3-6 p \)
C. \( 1-6 p \)
D. \( 6 p-3 \)

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 subtraction is commutative

Question:
Expand:
\[
3(1-2 p)
\]

Options:
A. \( 4-6 p \)
B. \( 3-6 p \)
C. \( 1-6 p \)
D. \( 6 p-3 \)

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 find a common denominator when adding/subtracting fractions

Question:
\( \frac{3}{4}-\frac{1}{4} \times \frac{1}{5}= \)

Options:
A. \( \frac{2}{16} \)
B. \( \frac{1}{10} \)
C. \( \frac{7}{10} \)
D. \( \frac{5}{10} \)

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

Question:
\( \frac{3}{4}-\frac{1}{4} \times \frac{1}{5}= \)

Options:
A. \( \frac{2}{16} \)
B. \( \frac{1}{10} \)
C. \( \frac{7}{10} \)
D. \( \frac{5}{10} \)

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:
Divides rather than adds when answering worded problems

Question:
Which of the following calculations would solve this problem?
Harvey is monitoring the growth of his plant. The plant was \( 35 \mathrm{~cm} \) tall. It grew \( 7 \mathrm{~cm} \) more.
How tall is the plant now?

Options:
A. \( 35 \div 7 \)
B. \( 35-7 \)
C. \( 35+7 \)
D. \( 35 \times 7 \)

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:
Subtracts instead of adds when answering worded problems

Question:
Which of the following calculations would solve this problem?
Harvey is monitoring the growth of his plant. The plant was \( 35 \mathrm{~cm} \) tall. It grew \( 7 \mathrm{~cm} \) more.
How tall is the plant now?

Options:
A. \( 35 \div 7 \)
B. \( 35-7 \)
C. \( 35+7 \)
D. \( 35 \times 7 \)

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

Question:
Which of the following calculations would solve this problem?
Harvey is monitoring the growth of his plant. The plant was \( 35 \mathrm{~cm} \) tall. It grew \( 7 \mathrm{~cm} \) more.
How tall is the plant now?

Options:
A. \( 35 \div 7 \)
B. \( 35-7 \)
C. \( 35+7 \)
D. \( 35 \times 7 \)

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


Prompt:
Misconception:
Confuses pyramid with prism

Question:
This is the net of a.. ![An image of a square with shapes attached to each of its sides. To the left hand side are three identical squares all connected, in a row. On the top side is a hexagon. On the right hand side are two squares identical to the central square and the squares on the left. So there is a row of 5 squares along the middle of the image. On the bottom side is an identical hexagon to the top.]()

Options:
A. Hexagonalbased pyramid
B. Hexagonal prism
C. Hexagon
D. This net would not create a 3D shape

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


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

Question:
This is the net of a.. ![An image of a square with shapes attached to each of its sides. To the left hand side are three identical squares all connected, in a row. On the top side is a hexagon. On the right hand side are two squares identical to the central square and the squares on the left. So there is a row of 5 squares along the middle of the image. On the bottom side is an identical hexagon to the top.]()

Options:
A. Hexagonalbased pyramid
B. Hexagonal prism
C. Hexagon
D. This net would not create a 3D shape

Solve the problem as a student with the misconception above.
You 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:
\(
 \frac{3 x}{2} + 1 =5
\)

Tom says a correct next line of working could be: \( \frac{3 x}{2}=4 \)

Katie says a correct next line of working could be: \( 3 x+1=10 \)

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:
\(
 \frac{3 x}{2} + 1 =5
\)

Tom says a correct next line of working could be: \( \frac{3 x}{2}=4 \)

Katie says a correct next line of working could be: \( 3 x+1=10 \)

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:
Difficulty with translating a mathematical answer into a real world context

Question:
\( 321 \) children are going on a school trip. One adult is needed for every seven children.

How many adults are needed?

Options:
A. \( 45 \) r6
B. \( 46 \)
C. \( 45 \frac{6}{7} \)
D. \( 45 \)

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


Prompt:
Misconception:
Difficulty with translating a mathematical answer into a real world context

Question:
\( 321 \) children are going on a school trip. One adult is needed for every seven children.

How many adults are needed?

Options:
A. \( 45 \) r6
B. \( 46 \)
C. \( 45 \frac{6}{7} \)
D. \( 45 \)

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


Prompt:
Misconception:
Difficulty with translating a mathematical answer into a real world context

Question:
\( 321 \) children are going on a school trip. One adult is needed for every seven children.

How many adults are needed?

Options:
A. \( 45 \) r6
B. \( 46 \)
C. \( 45 \frac{6}{7} \)
D. \( 45 \)

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


Prompt:
Misconception:
Confuses the number of regions in a Venn diagram as the total number of entries in the diagram

Question:
All the students in a class were asked if they have a brother, sister, both or none.

The Venn Diagram shows the results. ![A Venn diagram with two sets, one labelled Brother and one labelled Sister. The number 11 is written in Brother without the intersection , number 7 is in Sister without the intersection, the number 4 is in the intersection of Brother and Sister. The number 6 is outside the circles.]() How many students are in the class?

Options:
A. \( 4 \)
B. \( 24 \)
C. \( 28 \)
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:
Forgets to include values outside of the Venn diagram when finding the total

Question:
All the students in a class were asked if they have a brother, sister, both or none.

The Venn Diagram shows the results. ![A Venn diagram with two sets, one labelled Brother and one labelled Sister. The number 11 is written in Brother without the intersection , number 7 is in Sister without the intersection, the number 4 is in the intersection of Brother and Sister. The number 6 is outside the circles.]() How many students are in the class?

Options:
A. \( 4 \)
B. \( 24 \)
C. \( 28 \)
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:
Does not interpret the correct order of operations from a worded problem

Question:
This is how Dora calculates the answer to \( 12.3+4.5 \) mentally Dora uses the same method to calculate \( 2.7+35.9 \). Which of the following shows how she would do this? ![A diagram showing 3 thought bubbles from Dora's head. The first bubble says "I added the whole part first 12 + 4 = 16". The second bubble says "I then added the decimal part 0.3 + 0.5 = 0.8". The third bubble says "I then added 16 and 0.8 to get 16.8. So 12.3 + 4.5 = 16.8".]()

Options:
A. \( \begin{array}{c}2+35=37 \\ 0.7+0.9=1.6 \\ 37+1.6=38.6\end{array} \)
B. \( \begin{array}{c}2.7+35=37.7 \\ 37.7+0.9=38.6\end{array} \)
C. \( \begin{array}{c}2+35=37 \\ 0.7+0.9=1.6 \\ 37+1.6=37.16\end{array} \)
D. \( \begin{array}{c}2+35=37 \\ 0.7+0.9=0.16 \\ 35+0.16=35.16\end{array} \)

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:
Ignores place value when adding a whole number and a decimal

Question:
This is how Dora calculates the answer to \( 12.3+4.5 \) mentally Dora uses the same method to calculate \( 2.7+35.9 \). Which of the following shows how she would do this? ![A diagram showing 3 thought bubbles from Dora's head. The first bubble says "I added the whole part first 12 + 4 = 16". The second bubble says "I then added the decimal part 0.3 + 0.5 = 0.8". The third bubble says "I then added 16 and 0.8 to get 16.8. So 12.3 + 4.5 = 16.8".]()

Options:
A. \( \begin{array}{c}2+35=37 \\ 0.7+0.9=1.6 \\ 37+1.6=38.6\end{array} \)
B. \( \begin{array}{c}2.7+35=37.7 \\ 37.7+0.9=38.6\end{array} \)
C. \( \begin{array}{c}2+35=37 \\ 0.7+0.9=1.6 \\ 37+1.6=37.16\end{array} \)
D. \( \begin{array}{c}2+35=37 \\ 0.7+0.9=0.16 \\ 35+0.16=35.16\end{array} \)

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


Prompt:
Misconception:
Believes the sides of an inequality can be switched without changing the direction of the sign

Question:
Solve
\[
42 \geq 6(2 n+1)
\]

Options:
A. \( n \geq 3 \)
B. \( \frac{43}{12} \geq n \)
C. \( \frac{35}{12} \geq n \)
D. \( 3 \geq n \)

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

Question:
Solve
\[
42 \geq 6(2 n+1)
\]

Options:
A. \( n \geq 3 \)
B. \( \frac{43}{12} \geq n \)
C. \( \frac{35}{12} \geq n \)
D. \( 3 \geq n \)

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

Question:
\[
-1,4,11,20,31, \ldots
\]

When calculating the nth-term rule of this sequence, what should replace the square? nth-term rule:
\(
n^{2}+2 n \) \(\square\)

Options:
A. \[
+0
\]
(no number term)
B. \( -6 \)
C. \( -4 \)
D. \( +4 \)

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


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

Question:
\[
-1,4,11,20,31, \ldots
\]

When calculating the nth-term rule of this sequence, what should replace the square? nth-term rule:
\(
n^{2}+2 n \) \(\square\)

Options:
A. \[
+0
\]
(no number term)
B. \( -6 \)
C. \( -4 \)
D. \( +4 \)

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


Prompt:
Misconception:
Believes subtraction is commutative

Question:
\[
-1,4,11,20,31, \ldots
\]

When calculating the nth-term rule of this sequence, what should replace the square? nth-term rule:
\(
n^{2}+2 n \) \(\square\)

Options:
A. \[
+0
\]
(no number term)
B. \( -6 \)
C. \( -4 \)
D. \( +4 \)

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


Prompt:
Misconception:
When calculating perimeter, multiplies instead of adds

Question:
What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length a and side length b]()

Options:
A. \( 2 a+2 b \)
B. \( a b \)
C. \( a+b \)
D. Not enough information

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


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

Question:
What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length a and side length b]()

Options:
A. \( 2 a+2 b \)
B. \( a b \)
C. \( a+b \)
D. Not enough information

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


Prompt:
Misconception:
Fails to use the properties of simple shapes to work out missing lengths

Question:
What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length a and side length b]()

Options:
A. \( 2 a+2 b \)
B. \( a b \)
C. \( a+b \)
D. Not enough information

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


Prompt:
Misconception:
Does not understand that an obtuse angle is between 90 and 180 degrees

Question:
An angle measures \( 212^{\degree} \). This means it is...

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

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


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

Question:
An angle measures \( 212^{\degree} \). This means it is...

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

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


Prompt:
Misconception:
Does not know that a right angle is 90 degrees

Question:
An angle measures \( 212^{\degree} \). This means it is...

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

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


Prompt:
Misconception:
Confuses corresponding and alternate angles

Question:
What type of angles are highlighted in this diagram? ![The diagram is of a pair of parallel lines with a line crossing them. The two highlighted angles each have a parallel line above it and the transverse line to the left of it.]()

Options:
A. alternate angles
B. corresponding angles
C. co-interior angles
D. opposite angles

Solve the problem as a student with the misconception above.
You 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:
What type of angles are highlighted in this diagram? ![The diagram is of a pair of parallel lines with a line crossing them. The two highlighted angles each have a parallel line above it and the transverse line to the left of it.]()

Options:
A. alternate angles
B. corresponding angles
C. co-interior angles
D. opposite angles

Solve the problem as a student with the misconception above.
You 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:
What type of angles are highlighted in this diagram? ![The diagram is of a pair of parallel lines with a line crossing them. The two highlighted angles each have a parallel line above it and the transverse line to the left of it.]()

Options:
A. alternate angles
B. corresponding angles
C. co-interior angles
D. opposite angles

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


Prompt:
Misconception:
Confuses the y-intercept with the turning point of a curve

Question:
This is the graph of
\(y=(x+1)(x-3)\) ![A set of axes with the graph y=(x+1)(x-3) drawn on.]() What is the equation of the line of symmetry?

Options:
A. \( y=-3 \)
B. \( x=-3 \)
C. \( x=1 \)
D. \( y=1 \)

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


Prompt:
Misconception:
Confuses the y-intercept with the turning point of a curve

Question:
This is the graph of
\(y=(x+1)(x-3)\) ![A set of axes with the graph y=(x+1)(x-3) drawn on.]() What is the equation of the line of symmetry?

Options:
A. \( y=-3 \)
B. \( x=-3 \)
C. \( x=1 \)
D. \( y=1 \)

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


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

Question:
This is the graph of
\(y=(x+1)(x-3)\) ![A set of axes with the graph y=(x+1)(x-3) drawn on.]() What is the equation of the line of symmetry?

Options:
A. \( y=-3 \)
B. \( x=-3 \)
C. \( x=1 \)
D. \( y=1 \)

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


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

Question:
Which of the following is the best way to describe this sequence: ![First three patterns in a sequence. They are all rectangles made up of small squares. Pattern 1 is three small squares on top of one another, so the dimensions of the rectangle are 1 across and 3 up. Pattern 2 is a rectangle of dimensions 2 squares across and 6 up. Pattern 3 is a rectangle of dimensions 3 squares across and 9 squares up.]()

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

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


Prompt:
Misconception:
Does not understand the term quadratic

Question:
Which of the following is the best way to describe this sequence: ![First three patterns in a sequence. They are all rectangles made up of small squares. Pattern 1 is three small squares on top of one another, so the dimensions of the rectangle are 1 across and 3 up. Pattern 2 is a rectangle of dimensions 2 squares across and 6 up. Pattern 3 is a rectangle of dimensions 3 squares across and 9 squares up.]()

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

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


Prompt:
Misconception:
Does not know what a Fibonacci sequence is

Question:
Which of the following is the best way to describe this sequence: ![First three patterns in a sequence. They are all rectangles made up of small squares. Pattern 1 is three small squares on top of one another, so the dimensions of the rectangle are 1 across and 3 up. Pattern 2 is a rectangle of dimensions 2 squares across and 6 up. Pattern 3 is a rectangle of dimensions 3 squares across and 9 squares up.]()

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

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


Prompt:
Misconception:
When collecting like terms, assigns positivity or negativity incorrectly.

Question:
Simplify the following expression by collecting
like terms
\(6 x-2 y-z+3 y\)

Options:
A. \( 6 x-y-z \)
B. \( 6 x+y-z \)
C. \( 6 x-5 y-z \)
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 collecting like terms, assigns positivity or negativity incorrectly.

Question:
Simplify the following expression by collecting
like terms
\(6 x-2 y-z+3 y\)

Options:
A. \( 6 x-y-z \)
B. \( 6 x+y-z \)
C. \( 6 x-5 y-z \)
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 when like terms can be collected

Question:
Simplify the following expression by collecting
like terms
\(6 x-2 y-z+3 y\)

Options:
A. \( 6 x-y-z \)
B. \( 6 x+y-z \)
C. \( 6 x-5 y-z \)
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:
Has taken the percentage from the original

Question:
I increase \( £ 150 \) by \( 60 \% \).
Then, I increase the new amount by \( 10 \% \).
What percentage of the original amount do I have now?

Options:
A. \( 170 \% \)
B. \( 176 \% \)
C. \( 166 \% \)
D. \( 264 \% \)

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


Prompt:
Misconception:
Has taken the percentage from the original

Question:
I increase \( £ 150 \) by \( 60 \% \).
Then, I increase the new amount by \( 10 \% \).
What percentage of the original amount do I have now?

Options:
A. \( 170 \% \)
B. \( 176 \% \)
C. \( 166 \% \)
D. \( 264 \% \)

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


Prompt:
Misconception:
Thinks they had to give the new amount rather than the total percentage that the original has been increased by.

Question:
I increase \( £ 150 \) by \( 60 \% \).
Then, I increase the new amount by \( 10 \% \).
What percentage of the original amount do I have now?

Options:
A. \( 170 \% \)
B. \( 176 \% \)
C. \( 166 \% \)
D. \( 264 \% \)

Solve the problem as a student with the misconception above.
You 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 squaring a variable, believes they also need to square the coefficient

Question:
Find the first \( 2 \) numbers in the sequence using the \( n \)th term \( 4 n^{2}+2 n-5 \)

Options:
A. \( 1,7 \)
B. \( 5,19 \)
C. \( 13,63 \)
D. \( 1,15 \)

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


Prompt:
Misconception:
Does not know the meaning of equilateral

Question:
Triangle \( A B C \) is an equilateral triangle. Find length \(AC\). ![A triangle with vertices labelled A, B, C. Side BC is 8cm, side AC is labelled with a question mark.]()

Options:
A. \( 7 \mathrm{~cm} \)
B. \( 90 \mathrm{~cm} \)
C. \( 8 \mathrm{~cm} \)
D. \( 60 \mathrm{~cm} \)

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


Prompt:
Misconception:
Does not know the meaning of equilateral

Question:
Triangle \( A B C \) is an equilateral triangle. Find length \(AC\). ![A triangle with vertices labelled A, B, C. Side BC is 8cm, side AC is labelled with a question mark.]()

Options:
A. \( 7 \mathrm{~cm} \)
B. \( 90 \mathrm{~cm} \)
C. \( 8 \mathrm{~cm} \)
D. \( 60 \mathrm{~cm} \)

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


Prompt:
Misconception:
Does not know the meaning of equilateral

Question:
Triangle \( A B C \) is an equilateral triangle. Find length \(AC\). ![A triangle with vertices labelled A, B, C. Side BC is 8cm, side AC is labelled with a question mark.]()

Options:
A. \( 7 \mathrm{~cm} \)
B. \( 90 \mathrm{~cm} \)
C. \( 8 \mathrm{~cm} \)
D. \( 60 \mathrm{~cm} \)

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


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

Question:
\(
y=x^{2}-10 x+25
\)

Where does this curve intercept the \( x \) axis?

Options:
A. \( (-5,0) \)
B. \[
(-5,0)
\] and \[
(5,0)
\]
C. \( (5,0) \)
D. It doesn't intercept the \( x \) axis

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


Prompt:
Misconception:
Mixes up clockwise and anticlockwise

Question:
Ada turns clockwise from facing \( \mathrm{NW} \) to facing \( \mathrm{S} \)

How many degrees has Ada turned? ![A image of a compass.]()

Options:
A. \( 225^{\degree} \)
B. \( 315^{\degree} \)
C. \( 135^{\degree} \)
D. \( 180^{\degree} \)

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


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

Question:
Which line gives the reflection of shape \( P \) onto shape Q? ![A coordinate grid with two right angled triangles drawn, labelled P and Q. P has the coordinates: (2,5) (2,8) and (4,5). Q has the coordinates: (5,2) (8,2) and (5,4).]()

Options:
A. \( y=x \)
B. \( y=4.5 \)
C. \( y=-x \)
D. This is not a reflection

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


Prompt:
Misconception:
Confuses the lines y=x and y=-x

Question:
Which line gives the reflection of shape \( P \) onto shape Q? ![A coordinate grid with two right angled triangles drawn, labelled P and Q. P has the coordinates: (2,5) (2,8) and (4,5). Q has the coordinates: (5,2) (8,2) and (5,4).]()

Options:
A. \( y=x \)
B. \( y=4.5 \)
C. \( y=-x \)
D. This is not a reflection

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


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

Question:
Which line gives the reflection of shape \( P \) onto shape Q? ![A coordinate grid with two right angled triangles drawn, labelled P and Q. P has the coordinates: (2,5) (2,8) and (4,5). Q has the coordinates: (5,2) (8,2) and (5,4).]()

Options:
A. \( y=x \)
B. \( y=4.5 \)
C. \( y=-x \)
D. This is not a reflection

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


Prompt:
Misconception:
Thinks you need to just add a % sign to a decimal to convert to a percentage

Question:
What is \( 0.07 \) written as a percentage?

Options:
A. \( 0.07 \% \)
B. \( 70 \% \)
C. \( 7 \% \)
D. \( 0.7 \% \)

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


Prompt:
Misconception:
Believes a decimal with one significant figure is a multiple of 10 when converted to a percentage, regardless of place value

Question:
What is \( 0.07 \) written as a percentage?

Options:
A. \( 0.07 \% \)
B. \( 70 \% \)
C. \( 7 \% \)
D. \( 0.7 \% \)

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


Prompt:
Misconception:
Multiplies by 10 instead of 100 when converting decimal to percentage

Question:
What is \( 0.07 \) written as a percentage?

Options:
A. \( 0.07 \% \)
B. \( 70 \% \)
C. \( 7 \% \)
D. \( 0.7 \% \)

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


Prompt:
Misconception:
Believes squaring a fraction requires you to double both parts

Question:
\( \frac{1}{4} \times\left(\frac{2}{3}\right)^{2}= \)

Options:
A. \( \frac{1}{36} \)
B. \( \frac{1}{6} \)
C. \( \frac{1}{9} \)
D. \( \frac{1}{4} \)

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


Prompt:
Misconception:
Rounds every number up when estimating

Question:
Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct
\[
397 \div 209
\]

Options:
A. \( 1.332 \ldots \)
B. \( 2.243 \ldots \)
C. \( 1.533 \ldots \)
D. \( 1.899 \ldots \)

Solve the problem as a student with the misconception above.
You 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:
Without working out the exact answer, use estimation to decide which of the following answer is the most likely to be correct
\[
397 \div 209
\]

Options:
A. \( 1.332 \ldots \)
B. \( 2.243 \ldots \)
C. \( 1.533 \ldots \)
D. \( 1.899 \ldots \)

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

Question:
Which of the following lines is perpendicular to x = -10 ?

Options:
A. \( y=7 \)
B. \(x=-10\)
C. \( x=-\frac{1}{10} \)
D. \( x=\frac{1}{10} \)

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:
Thinks that in the equation x=a, a is the gradient

Question:
Which of the following lines is perpendicular to x = -10 ?

Options:
A. \( y=7 \)
B. \(x=-10\)
C. \( x=-\frac{1}{10} \)
D. \( x=\frac{1}{10} \)

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:
Subtracts instead of divides

Question:
\( 0.4 \div 0.8= \)

Options:
A. \( 0.4 \)
B. \( 2 \)
C. \( 0.32 \)
D. \( 0.5 \)

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


Prompt:
Misconception:
Believes division is commutative

Question:
\( 0.4 \div 0.8= \)

Options:
A. \( 0.4 \)
B. \( 2 \)
C. \( 0.32 \)
D. \( 0.5 \)

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


Prompt:
Misconception:
Multiplies rather than divides

Question:
\( 0.4 \div 0.8= \)

Options:
A. \( 0.4 \)
B. \( 2 \)
C. \( 0.32 \)
D. \( 0.5 \)

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


Prompt:
Misconception:
Believes that when finding area under graph you can use the upper y value rather than average of upper and lower

Question:
Here is a speed-time graph for a car.

Which of the following gives the best estimate for the distance travelled between \( 8 \) and \( 10 \) seconds? ![A graph showing time in seconds on the x axis and speed in metres per second on the y axis. The curve passes through the points (8,15) and (10,24)]()

Options:
A. \( 19.5 m \)
B. \( 48 m \)
C. \( 120 m \)
D. \( 39 m \)

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


Prompt:
Misconception:
Does not understand that area under a speed time graph gives distance because distance = speed x time

Question:
Here is a speed-time graph for a car.

Which of the following gives the best estimate for the distance travelled between \( 8 \) and \( 10 \) seconds? ![A graph showing time in seconds on the x axis and speed in metres per second on the y axis. The curve passes through the points (8,15) and (10,24)]()

Options:
A. \( 19.5 m \)
B. \( 48 m \)
C. \( 120 m \)
D. \( 39 m \)

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


Prompt:
Misconception:
Believes expanding a squared expression means writing it as a set of double brackets

Question:
Expand and simplify:
\(
(2 y-3)^{2}
\)

Options:
A. \( (2 y-3)(2 y-3) \)
B. \( 4 y^{2}-9 \)
C. \( 4 y^{2}+9 \)
D. \( 4 y^{2}-12 y+9 \)

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


Prompt:
Misconception:
Believes they only need to multiply the first and last pairs of terms when expanding double brackets

Question:
Expand and simplify:
\(
(2 y-3)^{2}
\)

Options:
A. \( (2 y-3)(2 y-3) \)
B. \( 4 y^{2}-9 \)
C. \( 4 y^{2}+9 \)
D. \( 4 y^{2}-12 y+9 \)

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


Prompt:
Misconception:
Believes they only need to multiply the first and last pairs of terms when expanding double brackets

Question:
Expand and simplify:
\(
(2 y-3)^{2}
\)

Options:
A. \( (2 y-3)(2 y-3) \)
B. \( 4 y^{2}-9 \)
C. \( 4 y^{2}+9 \)
D. \( 4 y^{2}-12 y+9 \)

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:
Divided by 10 rather than 100

Question:
How do you write \( 23 \% \) as a decimal?

Options:
A. \( 2.3 \)
B. \( 0.23 \)
C. \( 23 \)
D. \( 23.00 \)

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


Prompt:
Misconception:
Thinks you need to just remove the percentage sign to convert from a percentage to a decimal

Question:
How do you write \( 23 \% \) as a decimal?

Options:
A. \( 2.3 \)
B. \( 0.23 \)
C. \( 23 \)
D. \( 23.00 \)

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


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

Question:
How do you write \( 23 \% \) as a decimal?

Options:
A. \( 2.3 \)
B. \( 0.23 \)
C. \( 23 \)
D. \( 23.00 \)

Solve the problem as a student with the misconception above.
You 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 term to term rule is applied to position number, not previous term

Question:
![Square then subtract \( 2 \)]() The first three terms of which sequence below is produced by this term-to-term rule?

Options:
A. \( -1,-1,-1 \)
B. \( -1,2,7 \)
C. \( -1,-3,-11 \)
D. \( -1,-4,-10 \)

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


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

Question:
![Square then subtract \( 2 \)]() The first three terms of which sequence below is produced by this term-to-term rule?

Options:
A. \( -1,-1,-1 \)
B. \( -1,2,7 \)
C. \( -1,-3,-11 \)
D. \( -1,-4,-10 \)

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:
Mixes up squaring and multiplying by 2 or doubling

Question:
![Square then subtract \( 2 \)]() The first three terms of which sequence below is produced by this term-to-term rule?

Options:
A. \( -1,-1,-1 \)
B. \( -1,2,7 \)
C. \( -1,-3,-11 \)
D. \( -1,-4,-10 \)

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

Question:
Which function machine matches the equation \( y=x^{2}+4 ? \)

Options:
A. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to "y".]()
B. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "✕ 2" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to "y".]()
C. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to "y".]()
D. ![A function machine which has 4 parts joined by arrows pointing from left to right. "y" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to "𝑥"]()

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


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

Question:
Which function machine matches the equation \( y=x^{2}+4 ? \)

Options:
A. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to "y".]()
B. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "✕ 2" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to "y".]()
C. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to "y".]()
D. ![A function machine which has 4 parts joined by arrows pointing from left to right. "y" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to "𝑥"]()

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


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

Question:
Which function machine matches the equation \( y=x^{2}+4 ? \)

Options:
A. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to "y".]()
B. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "✕ 2" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to "y".]()
C. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to "y".]()
D. ![A function machine which has 4 parts joined by arrows pointing from left to right. "y" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 4" written inside it, followed by a horizontal arrow pointing to a rectangle that has "square" written inside it, followed by a horizontal arrow pointing to "𝑥"]()

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


Prompt:
Misconception:
Believes percentages cannot be converted into fractions

Question:
This pie chart shows how an average American household uses water.

Which of the following can not be found from this pie chart? ![A pie chart showing multiple sections: Toilet 26.7%, Leaks 13.7%, Other 5.3%, Clothes Washer 21.7%, Faucet 15.7%, Shower 16.8% ]()

Options:
A. The fraction of the different uses of water
B. The mean amount of water used
C. The angle of each of the sectors
D. The modal use of water

Solve the problem as a student with the misconception above.
You 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 cannot find the angle size in a pie chart when given its percentage value

Question:
This pie chart shows how an average American household uses water.

Which of the following can not be found from this pie chart? ![A pie chart showing multiple sections: Toilet 26.7%, Leaks 13.7%, Other 5.3%, Clothes Washer 21.7%, Faucet 15.7%, Shower 16.8% ]()

Options:
A. The fraction of the different uses of water
B. The mean amount of water used
C. The angle of each of the sectors
D. The modal use of water

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


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

Question:
This pie chart shows how an average American household uses water.

Which of the following can not be found from this pie chart? ![A pie chart showing multiple sections: Toilet 26.7%, Leaks 13.7%, Other 5.3%, Clothes Washer 21.7%, Faucet 15.7%, Shower 16.8% ]()

Options:
A. The fraction of the different uses of water
B. The mean amount of water used
C. The angle of each of the sectors
D. The modal use of water

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


Prompt:
Misconception:
When simplifying surds, leaves the square root of the biggest square number under the root and puts the other number on the outside

Question:
\( \sqrt{12}+\sqrt{27} \) Simplify, if possible.

Options:
A. \( 3 \sqrt{5} \)
B. \( \sqrt{39} \)
C. \( 5 \sqrt{3} \)
D. Cannot be simplified

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


Prompt:
Misconception:
When adding or subtracting surds, just adds or subtracts the numbers under the surd rather than first trying to simplifying to find like surds

Question:
\( \sqrt{12}+\sqrt{27} \) Simplify, if possible.

Options:
A. \( 3 \sqrt{5} \)
B. \( \sqrt{39} \)
C. \( 5 \sqrt{3} \)
D. Cannot be simplified

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


Prompt:
Misconception:
Does not recognise when a surd can be simplified

Question:
\( \sqrt{12}+\sqrt{27} \) Simplify, if possible.

Options:
A. \( 3 \sqrt{5} \)
B. \( \sqrt{39} \)
C. \( 5 \sqrt{3} \)
D. Cannot be simplified

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


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

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The outer scale goes from 0 to 360 clockwise. The angle is between one red line that is at 0 (outer scale) and 180 (inner scale), clockwise  to the other red line that is half way between 210 and 220 (outer scale) and halfway between 330 and 320 (inner scale).
]()

Options:
A. \( 335^{\circ} \)
B. \( 215^{\circ} \)
C. \( 345^{\circ} \)
D. \( 210^{\circ} \)

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


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

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The outer scale goes from 0 to 360 clockwise. The angle is between one red line that is at 0 (outer scale) and 180 (inner scale), clockwise  to the other red line that is half way between 210 and 220 (outer scale) and halfway between 330 and 320 (inner scale).
]()

Options:
A. \( 335^{\circ} \)
B. \( 215^{\circ} \)
C. \( 345^{\circ} \)
D. \( 210^{\circ} \)

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


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

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The outer scale goes from 0 to 360 clockwise. The angle is between one red line that is at 0 (outer scale) and 180 (inner scale), clockwise  to the other red line that is half way between 210 and 220 (outer scale) and halfway between 330 and 320 (inner scale).
]()

Options:
A. \( 335^{\circ} \)
B. \( 215^{\circ} \)
C. \( 345^{\circ} \)
D. \( 210^{\circ} \)

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 describing a translation, goes from the image to the original

Question:
How would you describe the movement to get from the star to the triangle? ![A set of axes: x-axis from 0 to 5, y-axis from 0 to 5. A purple triangle symbol is at point (2,1) and a yellow star symbol is at point (1, 4).]()

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

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


Prompt:
Misconception:
Confuses left and right

Question:
How would you describe the movement to get from the star to the triangle? ![A set of axes: x-axis from 0 to 5, y-axis from 0 to 5. A purple triangle symbol is at point (2,1) and a yellow star symbol is at point (1, 4).]()

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

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


Prompt:
Misconception:
When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.

Question:
How would you describe the movement to get from the star to the triangle? ![A set of axes: x-axis from 0 to 5, y-axis from 0 to 5. A purple triangle symbol is at point (2,1) and a yellow star symbol is at point (1, 4).]()

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

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


Prompt:
Misconception:
Has used the wrong data point on the graph

Question:
![A line graph with title "Goals scored in the UK".
The x-axis scale is labelled: Aug, Sept, Oct, Nov, Dec, Jan, Feb, Mar, Apr, May.
The y-axis is titled "Number of goals" and the scale is labelled from 0 to 3000 in steps of 500. The following points are plotted and joined together: (Aug, 500), (Sept, 850 approx.), (Oct, 950 approx.),(Nov, 1000), (Dec, 1175 approx.), (Jan, 1200 approx.), (Feb, 500), (Mar, 1000), (Apr, 1500), (May, 2000).
]() What was the total number of goals scored in the winter season (Dec, Jan, Feb)?

Options:
A. \( 3375 \)
B. \( 2875 \)
C. \( 3875 \)
D. \( 2000 \)

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


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

Question:
Tom and Katie are discussing this function machine ![A function machine with an input of a+4, the function is not labelled and then an output of 4a+4]() Tom says the function could be \( +3 a \)
Katie says the function could be \( \times 4 \)
Who do you agree with?

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

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


Prompt:
Misconception:
Thinks a positive x value in a column vector means to move left rather than right

Question:
Sam has translated the red flag \( \left(\begin{array}{l}2 \\ 3\end{array}\right) \) ![Image showing two identical shapes on a coordinate grid. The red shape has the point (2,1) and the corresponding point on the blue shape is (4,3).]() What error has Sam made?

Options:
A. Sam has gone left when he should have gone right
B. Sam has not moved right the correct number of places
C. Sam has started counting from his initial position when counting right
D. Sam has not moved up the correct number of places

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


Prompt:
Misconception:
When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.

Question:
Sam has translated the red flag \( \left(\begin{array}{l}2 \\ 3\end{array}\right) \) ![Image showing two identical shapes on a coordinate grid. The red shape has the point (2,1) and the corresponding point on the blue shape is (4,3).]() What error has Sam made?

Options:
A. Sam has gone left when he should have gone right
B. Sam has not moved right the correct number of places
C. Sam has started counting from his initial position when counting right
D. Sam has not moved up the correct number of places

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


Prompt:
Misconception:
When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.

Question:
Sam has translated the red flag \( \left(\begin{array}{l}2 \\ 3\end{array}\right) \) ![Image showing two identical shapes on a coordinate grid. The red shape has the point (2,1) and the corresponding point on the blue shape is (4,3).]() What error has Sam made?

Options:
A. Sam has gone left when he should have gone right
B. Sam has not moved right the correct number of places
C. Sam has started counting from his initial position when counting right
D. Sam has not moved up the correct number of places

Solve the problem as a student with the misconception above.
You 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 sides of an inequality can be switched without changing the direction of the sign

Question:
Solve
\[
36 \leq 4(5 n-1)
\]

Options:
A. \( 2 \leq n \)
B. \( \frac{33}{5} \leq n \)
C. \( n \leq 2 \)
D. \( \frac{37}{20} \leq n \)

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

Question:
Solve
\[
36 \leq 4(5 n-1)
\]

Options:
A. \( 2 \leq n \)
B. \( \frac{33}{5} \leq n \)
C. \( n \leq 2 \)
D. \( \frac{37}{20} \leq n \)

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:
Thinks the inverse of subtraction is multiplication

Question:
Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.
What operation should replace the star? ![The image shows two lines of working and an arrow from the top line to the bottom line with a star next to it where the operation would be labelled. The top line of working is x - 7 = ..., and the bottom line is x = ...]()

Options:
A. \( +7 \)
B. \( \times 7 \)
C. \( \div 7 \)
D. \( -7 \)

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


Prompt:
Misconception:
Thinks the inverse of subtraction is division

Question:
Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.
What operation should replace the star? ![The image shows two lines of working and an arrow from the top line to the bottom line with a star next to it where the operation would be labelled. The top line of working is x - 7 = ..., and the bottom line is x = ...]()

Options:
A. \( +7 \)
B. \( \times 7 \)
C. \( \div 7 \)
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:
When solving an equation, uses the same operation rather than the inverse.

Question:
Isaac is solving an equation. This is the left-hand side of two lines of working from Isaac's book. Isaac always records what operation he has done to both sides of the equation.
What operation should replace the star? ![The image shows two lines of working and an arrow from the top line to the bottom line with a star next to it where the operation would be labelled. The top line of working is x - 7 = ..., and the bottom line is x = ...]()

Options:
A. \( +7 \)
B. \( \times 7 \)
C. \( \div 7 \)
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:
Subtracts instead of divides

Question:
\[
15 \times 12=15 \times(4 \times \text { 年 })
\]
What should replace the star to make this calculation correct?

Options:
A. \( 8 \)
B. \( 12 \)
C. \( 3 \)
D. \( 24 \)

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


Prompt:
Misconception:
Confuses isosceles and equilateral triangles

Question:
What is the size of angle \( w \) ? ![An isosceles triangle with a base angle labelled with w and the angle vertically opposite the vertex angle labelled with 33 degrees]()

Options:
A. \( 49^{\degree} \)
B. \( 34^{\degree} \)
C. \( 54^{\degree} \)
D. \( 73.5^{\degree} \)

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


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

Question:
What is the size of angle \( w \) ? ![An isosceles triangle with a base angle labelled with w and the angle vertically opposite the vertex angle labelled with 33 degrees]()

Options:
A. \( 49^{\degree} \)
B. \( 34^{\degree} \)
C. \( 54^{\degree} \)
D. \( 73.5^{\degree} \)

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


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

Question:
What is the size of angle \( w \) ? ![An isosceles triangle with a base angle labelled with w and the angle vertically opposite the vertex angle labelled with 33 degrees]()

Options:
A. \( 49^{\degree} \)
B. \( 34^{\degree} \)
C. \( 54^{\degree} \)
D. \( 73.5^{\degree} \)

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


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

Question:
There are \( 7 \) shelves of plates. Three of the shelves hold \( 17 \) plates each. Two of the shelves hold \( 21 \) plates each. The other shelves hold \( 19 \) plates each.
How many plates are there in total?

Options:
A. \( 112 \)
B. \( 69 \)
C. \( 131 \)
D. \( 57 \)

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


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

Question:
Which symbol makes the following statement correct?
\(
\frac{3}{4}\space \square\space \frac{5}{8}
\)

Options:
A. \( = \)
B. \( > \)
C. \( < \)
D. None of these

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


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

Question:
Which symbol makes the following statement correct?
\(
\frac{3}{4}\space \square\space \frac{5}{8}
\)

Options:
A. \( = \)
B. \( > \)
C. \( < \)
D. None of these

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


Prompt:
Misconception:
Does not understand inequality notation

Question:
Which symbol makes the following statement correct?
\(
\frac{3}{4}\space \square\space \frac{5}{8}
\)

Options:
A. \( = \)
B. \( > \)
C. \( < \)
D. None of these

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


Prompt:
Misconception:
Does not know how to calculate the sum of interior angles

Question:
What is the size of each interior angle in a regular octagon?

Options:
A. \( 80^{\degree} \)
B. \( 135^{\degree} \)
C. \( 120^{\degree} \)
D. \( 180^{\degree} \)

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


Prompt:
Misconception:
Does not know how to calculate the sum of interior angles

Question:
What is the size of each interior angle in a regular octagon?

Options:
A. \( 80^{\degree} \)
B. \( 135^{\degree} \)
C. \( 120^{\degree} \)
D. \( 180^{\degree} \)

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


Prompt:
Misconception:
Does not understand to find each interior angle of a regular polygon you divide the sum by the number of sides

Question:
What is the size of each interior angle in a regular octagon?

Options:
A. \( 80^{\degree} \)
B. \( 135^{\degree} \)
C. \( 120^{\degree} \)
D. \( 180^{\degree} \)

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


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

Question:
\( 0.3 \times 0.9= \)

Options:
A. \( 2.7 \)
B. \( 1.2 \)
C. \( 0.27 \)
D. \( 0.027 \)

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


Prompt:
Misconception:
Adds instead of multiplies

Question:
\( 0.3 \times 0.9= \)

Options:
A. \( 2.7 \)
B. \( 1.2 \)
C. \( 0.27 \)
D. \( 0.027 \)

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


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

Question:
\( 0.3 \times 0.9= \)

Options:
A. \( 2.7 \)
B. \( 1.2 \)
C. \( 0.27 \)
D. \( 0.027 \)

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


Prompt:
Misconception:
Added rather than multiplied by a scale factor

Question:
\( 3 \) miles \( \approx 5 \mathrm{~km} \) \( 300 \mathrm{~km} \approx \square \) miles

Options:
A. \( 298 \)
B. \( 500 \)
C. \( 180 \)
D. \( 1500 \)

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


Prompt:
Misconception:
Ignores the negative signs when adding positive and negative numbers

Question:
Jo and Paul are arguing about a first step to solve this equation:
\(5-2 v=3-6 v\)

Jo says you can write: \( 2 v=8-6 v \)

Paul says you can write: \( 5+8 v=3 \)

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}.