Prompt:
Misconception:
When describing a translation, identifies the correct number of jumps but mixes up the directions .

Question:
How would you describe the movement to get from the star to the triangle? ![Positive coordinate grid from 0 to 5 in the x and y directions with a gold star at (1,4) and a purple triangle at (4,3)]()

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

Solve the problem as a student with the misconception above.
You 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 factorising into double brackets, believes the sum of the two values in the brackets equals bx rather than b

Question:
When factorising \( x^{2}+6 x+8 \) we need two numbers that:

Options:
A. Add to give \( 6 \) and multiply to give \( 8 \)
B. Add to give \( 6 x \) and multiply to give \( 8 \)
C. Add to give \( 8 \) and multiply to give \( 6 \)
D. Add to give \( 8 x \) and multiply to give \( 6 \)

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


Prompt:
Misconception:
Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term

Question:
When factorising \( x^{2}+6 x+8 \) we need two numbers that:

Options:
A. Add to give \( 6 \) and multiply to give \( 8 \)
B. Add to give \( 6 x \) and multiply to give \( 8 \)
C. Add to give \( 8 \) and multiply to give \( 6 \)
D. Add to give \( 8 x \) and multiply to give \( 6 \)

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


Prompt:
Misconception:
Believes a sample space should show repeated outcomes, not just unique possible outcomes.

Question:
Tom and Katie are discussing the probability spinner

Tom says the sample space can be written as: \( S=\{1,2\} \)

Katie says the sample space can be written as: \( S=\{1,1,2,2,2\} \)
Who do you agree with? ![Circle divided into 5 equal sections. 2 sections labelled with a blue number 1. 3 sections labelled with a red number 2.]()

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

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


Prompt:
Misconception:
Confuses a formula with an equation

Question:
Which of the following is the most appropriate word to describe: \( A=\frac{b h}{2} \) ![A triangle with base labelled b and height labelled h.]()

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

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


Prompt:
Misconception:
Confuses a variable with a formula

Question:
Which of the following is the most appropriate word to describe: \( A=\frac{b h}{2} \) ![A triangle with base labelled b and height labelled h.]()

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

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


Prompt:
Misconception:
Confuses a formula with an expression

Question:
Which of the following is the most appropriate word to describe: \( A=\frac{b h}{2} \) ![A triangle with base labelled b and height labelled h.]()

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

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


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

Question:
What is \( 637 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 640 \)
B. \( 650 \)
C. \( 600 \)
D. \( 630 \)

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


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

Question:
What is \( 637 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 640 \)
B. \( 650 \)
C. \( 600 \)
D. \( 630 \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( 637 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 640 \)
B. \( 650 \)
C. \( 600 \)
D. \( 630 \)

Solve the problem as a student with the misconception above.
You 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 subtracting a positive number from a negative number makes the answer less negative

Question:
Tom and Katie are arguing about points on the line
\[
y=2 x-3
\]

Tom says \( (5,7) \) lies on the line \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{3} \)

Katie says \( (-5,-7) \) lies on the line \( \boldsymbol{y}=\mathbf{2 x}-\mathbf{3} \)

Who is correct?

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

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


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

Question:
\begin{tabular}{|l|l|l|l|l|l|}
\hline\( x \) & \( 0 \) & \( 1 \) & \( 2 \) & \( 3 \) & \( 4 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) &
\end{tabular} This is a table of values for \( 4 x+2 y=10 \)
What should replace the star?

Options:
A. \( 20 \)
B. \( 3 \)
C. \( 5 \)
D. \( 2.5 \)

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


Prompt:
Misconception:
Believes 0 multiplied by a number gives the number

Question:
\begin{tabular}{|l|l|l|l|l|l|}
\hline\( x \) & \( 0 \) & \( 1 \) & \( 2 \) & \( 3 \) & \( 4 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) &
\end{tabular} This is a table of values for \( 4 x+2 y=10 \)
What should replace the star?

Options:
A. \( 20 \)
B. \( 3 \)
C. \( 5 \)
D. \( 2.5 \)

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


Prompt:
Misconception:
Mixes up the value of two terms when substituting

Question:
\begin{tabular}{|l|l|l|l|l|l|}
\hline\( x \) & \( 0 \) & \( 1 \) & \( 2 \) & \( 3 \) & \( 4 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) &
\end{tabular} This is a table of values for \( 4 x+2 y=10 \)
What should replace the star?

Options:
A. \( 20 \)
B. \( 3 \)
C. \( 5 \)
D. \( 2.5 \)

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


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

Question:
Isaac is halfway through solving a pair of simultaneous equations, one of which is below.

\(
2 j-k=-10
\)

Isaac found that \( k=8 \)
What does \( j \) equal?

Options:
A. \( j=1 \)
B. \( j=9 \)
C. \( j=-9 \)
D. \( j=-1 \)

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:
Ignores the negative signs when adding positive and negative numbers

Question:
Isaac is halfway through solving a pair of simultaneous equations, one of which is below.

\(
2 j-k=-10
\)

Isaac found that \( k=8 \)
What does \( j \) equal?

Options:
A. \( j=1 \)
B. \( j=9 \)
C. \( j=-9 \)
D. \( j=-1 \)

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


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

Question:
Isaac is halfway through solving a pair of simultaneous equations, one of which is below.

\(
2 j-k=-10
\)

Isaac found that \( k=8 \)
What does \( j \) equal?

Options:
A. \( j=1 \)
B. \( j=9 \)
C. \( j=-9 \)
D. \( j=-1 \)

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:
Believes multiplying two negatives gives a negative answer

Question:
Tom and Katie are arguing about factorising. Tom says \( x^{2}+5 x+6 \equiv(x+3)(x+2) \)
Katie says \( x^{2}-5 x-6 \equiv(x-3)(x-2) \)
Who is correct?

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

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


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( \mathbf{9 0 . 6 8 2} \) rounded to the nearest integer?

Options:
A. \( 90 \)
B. \( 90.7 \)
C. \( 91 \)
D. \( 92 \)

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


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

Question:
What is \( \mathbf{9 0 . 6 8 2} \) rounded to the nearest integer?

Options:
A. \( 90 \)
B. \( 90.7 \)
C. \( 91 \)
D. \( 92 \)

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


Prompt:
Misconception:
Rounds incorrectly by changing multiple place values

Question:
What is \( \mathbf{9 0 . 6 8 2} \) rounded to the nearest integer?

Options:
A. \( 90 \)
B. \( 90.7 \)
C. \( 91 \)
D. \( 92 \)

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


Prompt:
Misconception:
Counts on in the wrong direction on a number line

Question:
Peter is counting up in threes. He starts at \( -16 \)
What is the \( 5^{\text {th }} \) number he says?

Options:
A. \( -28 \)
B. \( -4 \)
C. \( -1 \)
D. \( -31 \)

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


Prompt:
Misconception:
Counts on in the wrong direction on a number line

Question:
Peter is counting up in threes. He starts at \( -16 \)
What is the \( 5^{\text {th }} \) number he says?

Options:
A. \( -28 \)
B. \( -4 \)
C. \( -1 \)
D. \( -31 \)

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


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

Question:
Tom and Katie are discussing this sequence. ![The first 3 patterns in a sequence are shown. The first pattern is a blue rectangle with 6 yellow circles attached to its perimeter: 2 circles on each of the longer sides and 1 circle on each of the shorter sides.
Pattern 2 is made up of 2 blue rectangles, attached together in a row by their short edges. There are also 10 yellow circles in this pattern, attached to the perimeter of the rectangles: 2 circles on every longer side of each rectangle and 1 circle on each of the two free shorter sides (i.e. that are not attached to the other rectangle).
Pattern 3 is made up of 3 blue rectangles, attached together in a row by their short edges. There are also 14 yellow circles in this pattern, attached to the perimeter of the rectangles: 2 circles on every longer side of each rectangle and 1 circle on each of the two free shorter sides (i.e. that are not attached to another rectangle).]() Tom says the number of circles in the \( 10^{\text {th }} \) term will be
double the number of circles in the \( 5^{\text {th }} \) term.

Katie says the number of rectangles in the \( 10^{\text {th }} \) term will be
double the number of rectangles in the \( 5^{\text {th }} \) term.

Who do you agree with?

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

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


Prompt:
Misconception:
Does not understand that in the ratio 1:n the total number of parts would be 1+n

Question:
Tom and Katie are arguing about the information on the right.

Tom says there are \( 9 \) times as many students as teachers.

Katie says one in ten people are teachers.
Who is correct? On a school trip, the ratio of teachers to students is:
teachers : students
\(
1: 9
\)

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 in a ratio 1:n that one part of the ratio would be n times bigger than the one part

Question:
Tom and Katie are arguing about the information on the right.

Tom says there are \( 9 \) times as many students as teachers.

Katie says one in ten people are teachers.
Who is correct? On a school trip, the ratio of teachers to students is:
teachers : students
\(
1: 9
\)

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 in the ratio 1:n the total number of parts would be 1+n

Question:
Tom and Katie are arguing about the information on the right.

Tom says there are \( 9 \) times as many students as teachers.

Katie says one in ten people are teachers.
Who is correct? On a school trip, the ratio of teachers to students is:
teachers : students
\(
1: 9
\)

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 asked for a specific term in a sequence gives the term after

Question:
\(
x_{n+1}=10-\frac{1}{x_{n}}
\)

Using a starting value of \( x_{1}=4 \), what is the value of \( x_{2} \) ?

Options:
A. \( 9.75 \)
B. \( 9.8974 \ldots \)
C. \( 2.25 \)
D. Another answer

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


Prompt:
Misconception:
Believes you can square root a negative number

Question:
What is the equation of this curve? ![A set of axes with a quadratic graph drawn on. The graph is y=x^2 translated 2 squares to the left and 5 squares down.]()

Options:
A. \( y=(x+2)^{2}-5 \)
B. \( y=(x+2)^{2}+5 \)
C. \( y=(x-2)^{2}+5 \)
D. \( y=(x-2)^{2}-5 \)

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


Prompt:
Misconception:
Believes you can square root a negative number

Question:
What is the equation of this curve? ![A set of axes with a quadratic graph drawn on. The graph is y=x^2 translated 2 squares to the left and 5 squares down.]()

Options:
A. \( y=(x+2)^{2}-5 \)
B. \( y=(x+2)^{2}+5 \)
C. \( y=(x-2)^{2}+5 \)
D. \( y=(x-2)^{2}-5 \)

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


Prompt:
Misconception:
Believes that in completed square form, the x co-ordinate of the turning point has the same sign as the constant in the brackets.

Question:
What is the equation of this curve? ![A set of axes with a quadratic graph drawn on. The graph is y=x^2 translated 2 squares to the left and 5 squares down.]()

Options:
A. \( y=(x+2)^{2}-5 \)
B. \( y=(x+2)^{2}+5 \)
C. \( y=(x-2)^{2}+5 \)
D. \( y=(x-2)^{2}-5 \)

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


Prompt:
Misconception:
Confuses the meaning of parallel and perpendicular

Question:
Which of the following lines is perpendicular to
\[
y=2 x+1 \text { ? }
\]

Options:
A. \( y=7-\frac{1}{2} x \)
B. \( y=2 x-1 \)
C. \( x=2 y+1 \)
D. \( y=\frac{1}{2} x-3 \)

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


Prompt:
Misconception:
Believes switching the x and y variables in a linear equation gives a perpendicular line

Question:
Which of the following lines is perpendicular to
\[
y=2 x+1 \text { ? }
\]

Options:
A. \( y=7-\frac{1}{2} x \)
B. \( y=2 x-1 \)
C. \( x=2 y+1 \)
D. \( y=\frac{1}{2} x-3 \)

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


Prompt:
Misconception:
Believes the gradients of perpendicular lines are reciprocals of the same sign

Question:
Which of the following lines is perpendicular to
\[
y=2 x+1 \text { ? }
\]

Options:
A. \( y=7-\frac{1}{2} x \)
B. \( y=2 x-1 \)
C. \( x=2 y+1 \)
D. \( y=\frac{1}{2} x-3 \)

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


Prompt:
Misconception:
Confuses a formula with an equation

Question:
Which of the following words is the correct description for:
\(x+3=5 ?\)

Options:
A. Equation
B. Formula
C. Identity
D. Expression

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


Prompt:
Misconception:
Confuses an equation with an identity

Question:
Which of the following words is the correct description for:
\(x+3=5 ?\)

Options:
A. Equation
B. Formula
C. Identity
D. Expression

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


Prompt:
Misconception:
Confuses an equation with an expression

Question:
Which of the following words is the correct description for:
\(x+3=5 ?\)

Options:
A. Equation
B. Formula
C. Identity
D. Expression

Solve the problem as a student with the misconception above.
You 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 rounding numbers down would give an overestimate

Question:
Tom and Katie are discussing using estimation when multiplying
Tom says \( 82 \times 4<320 \)
Katie says \( 41 \times 8>320 \)
Without calculating the exact answers, 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 remember that a rhombus has equal sides

Question:
Tom and Katie are discussing this shape
Tom says it is a parallelogram
Katie says it is a rhombus
Who do you agree with? ![Pink parallelogram with parallel sides labelled]()

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 remember that a rhombus has equal sides

Question:
Tom and Katie are discussing this shape
Tom says it is a parallelogram
Katie says it is a rhombus
Who do you agree with? ![Pink parallelogram with parallel sides labelled]()

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

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


Prompt:
Misconception:
Does not recognise a parallelogram

Question:
Tom and Katie are discussing this shape
Tom says it is a parallelogram
Katie says it is a rhombus
Who do you agree with? ![Pink parallelogram with parallel sides labelled]()

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:
Chooses an example when asked for a counter-example

Question:
Tom and Katie are discussing the conjecture:

All numbers have an even number of factors because factors come in pairs

Tom says a counter-example is \( 24 \)

Katie says a counter-example is \( 16 \)

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:
Divides rather than subtracts when given the command 'less than'

Question:
What number is \( 100 \) less than \( 325,076 \) ?

Options:
A. \( 324,976 \)
B. \( 3250.76 \)
C. \( 325,176 \)
D. \( 324,076 \)

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


Prompt:
Misconception:
Adds rather than subtracts when answering worded problems

Question:
What number is \( 100 \) less than \( 325,076 \) ?

Options:
A. \( 324,976 \)
B. \( 3250.76 \)
C. \( 325,176 \)
D. \( 324,076 \)

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


Prompt:
Misconception:
When subtracting a power of 10, subtracts from the wrong column

Question:
What number is \( 100 \) less than \( 325,076 \) ?

Options:
A. \( 324,976 \)
B. \( 3250.76 \)
C. \( 325,176 \)
D. \( 324,076 \)

Solve the problem as a student with the misconception above.
You 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 ratios are written as 1:total

Question:
What is the ratio of
\[
A B: B C \text { ? }
\] ![A line AC which is 10 units long. B is on it so that AB:BC is 1:2]()

Options:
A. \( 1: 6 \)
B. \( 1: 4 \)
C. \( 1: 3 \)
D. \( 1: 2 \)

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


Prompt:
Misconception:
Does not recognise that a surd will simplify to a whole number and not longer be a surd if the number under the surd is a square number

Question:
Which of the following is not a surd?

Options:
A. \( \sqrt{45} \)
B. \( \sqrt{47} \)
C. \( \sqrt{49} \)
D. \( \sqrt{51} \)

Solve the problem as a student with the misconception above.
You 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 surd will simplify to a whole number and not longer be a surd if the number under the surd is a square number

Question:
Which of the following is not a surd?

Options:
A. \( \sqrt{45} \)
B. \( \sqrt{47} \)
C. \( \sqrt{49} \)
D. \( \sqrt{51} \)

Solve the problem as a student with the misconception above.
You 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 surd will simplify to a whole number and not longer be a surd if the number under the surd is a square number

Question:
Which of the following is not a surd?

Options:
A. \( \sqrt{45} \)
B. \( \sqrt{47} \)
C. \( \sqrt{49} \)
D. \( \sqrt{51} \)

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


Prompt:
Misconception:
Performs addition ahead of multiplication

Question:
What does the following equal?

\(
3 \times 5+4-2
\)

Options:
A. \( 17 \)
B. \( 25 \)
C. \( 21 \)
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:
Performs addition ahead of multiplication

Question:
What does the following equal?

\(
3 \times 5+4-2
\)

Options:
A. \( 17 \)
B. \( 25 \)
C. \( 21 \)
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 order of operations does not affect the answer to a calculation

Question:
What does the following equal?

\(
3 \times 5+4-2
\)

Options:
A. \( 17 \)
B. \( 25 \)
C. \( 21 \)
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:
Does not know how to find order of rotational symmetry

Question:
![This shape is a line drawing of 2 ellipses whose centres, marked with a black dot, are lined up, but one ellipse is at right angles to the other.]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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:
Does not know how to find order of rotational symmetry

Question:
![This shape is a line drawing of 2 ellipses whose centres, marked with a black dot, are lined up, but one ellipse is at right angles to the other.]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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:
Does not know how to find order of rotational symmetry

Question:
![This shape is a line drawing of 2 ellipses whose centres, marked with a black dot, are lined up, but one ellipse is at right angles to the other.]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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 asked for a specific term in a sequence gives the next term

Question:
\begin{tabular}{lclclclc|c|} \hline \(\bigstar\) & \( \;\) & 712 & \( \;\) &  \( \;\)\end{tabular} A descending linear sequence has a constant difference of \( 22 \) and the \( 3^{\text {rd }} \) term is \( 712 \).
What should replace the star?

Options:
A. \( 734 \)
B. \( 756 \)
C. \( 690 \)
D. \( 668 \)

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


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

Question:
\begin{tabular}{lclclclc|c|} \hline \(\bigstar\) & \( \;\) & 712 & \( \;\) &  \( \;\)\end{tabular} A descending linear sequence has a constant difference of \( 22 \) and the \( 3^{\text {rd }} \) term is \( 712 \).
What should replace the star?

Options:
A. \( 734 \)
B. \( 756 \)
C. \( 690 \)
D. \( 668 \)

Solve the problem as a student with the misconception above.
You 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 subtract rather than add when finding the previous term in a descending linear sequence

Question:
\begin{tabular}{lclclclc|c|} \hline \(\bigstar\) & \( \;\) & 712 & \( \;\) &  \( \;\)\end{tabular} A descending linear sequence has a constant difference of \( 22 \) and the \( 3^{\text {rd }} \) term is \( 712 \).
What should replace the star?

Options:
A. \( 734 \)
B. \( 756 \)
C. \( 690 \)
D. \( 668 \)

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


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

Question:
\( 4514-328= \)

Options:
A. \( 4196 \)
B. \( 1234 \)
C. \( 4214 \)
D. \( 4186 \)

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


Prompt:
Misconception:
Lines up the digits incorrectly when doing a subtraction involving two numbers with a different amount of digits

Question:
\( 4514-328= \)

Options:
A. \( 4196 \)
B. \( 1234 \)
C. \( 4214 \)
D. \( 4186 \)

Solve the problem as a student with the misconception above.
You 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 the smallest digit from the largest digit

Question:
\( 4514-328= \)

Options:
A. \( 4196 \)
B. \( 1234 \)
C. \( 4214 \)
D. \( 4186 \)

Solve the problem as a student with the misconception above.
You 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:
This graph shows how much a block of ice melted over time. ![A line graph with the x-axis titled "Time (minutes)". The x-axis scale is labelled from 0 to 5 in steps of 1 minute.
The y-axis is titled "Water depth (cm)" and the scale is labelled from 0 to 12 in steps of 2. The following points are plotted and joined together: (0, 0),(1,1),(2, 3),(3, 6),(4, 9),(5, 10).
]() What was the difference between the first minute and third minute?

Options:
A. \( 5 \)
B. \( 6 \mathrm{~cm} \)
C. \( 5 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \)

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 understand the command word 'difference'

Question:
This graph shows how much a block of ice melted over time. ![A line graph with the x-axis titled "Time (minutes)". The x-axis scale is labelled from 0 to 5 in steps of 1 minute.
The y-axis is titled "Water depth (cm)" and the scale is labelled from 0 to 12 in steps of 2. The following points are plotted and joined together: (0, 0),(1,1),(2, 3),(3, 6),(4, 9),(5, 10).
]() What was the difference between the first minute and third minute?

Options:
A. \( 5 \)
B. \( 6 \mathrm{~cm} \)
C. \( 5 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \)

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

Question:
This graph shows how much a block of ice melted over time. ![A line graph with the x-axis titled "Time (minutes)". The x-axis scale is labelled from 0 to 5 in steps of 1 minute.
The y-axis is titled "Water depth (cm)" and the scale is labelled from 0 to 12 in steps of 2. The following points are plotted and joined together: (0, 0),(1,1),(2, 3),(3, 6),(4, 9),(5, 10).
]() What was the difference between the first minute and third minute?

Options:
A. \( 5 \)
B. \( 6 \mathrm{~cm} \)
C. \( 5 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \)

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:
Thinks there are 100 mg in a gram

Question:
\( 30 \) grams = \(\bigstar \) milligrams What should replace the star?

Options:
A. \( 3000 \)
B. \( 300 \)
C. \( 0.03 \)
D. \( 30000 \)

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


Prompt:
Misconception:
Thinks there are 10 mg in a gram

Question:
\( 30 \) grams = \(\bigstar \) milligrams What should replace the star?

Options:
A. \( 3000 \)
B. \( 300 \)
C. \( 0.03 \)
D. \( 30000 \)

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


Prompt:
Misconception:
Divides when converting to a smaller unit

Question:
\( 30 \) grams = \(\bigstar \) milligrams What should replace the star?

Options:
A. \( 3000 \)
B. \( 300 \)
C. \( 0.03 \)
D. \( 30000 \)

Solve the problem as a student with the misconception above.
You 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 common denominator can only be the lowest common multiple

Question:
Tom and Katie are discussing how to work out the answer to \( \frac{5}{6}-\frac{1}{3} \)
Tom says you could change both denominators to \( 6 \)
Katie says you could change both denominators to \( 18 \)
Who is correct?

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

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


Prompt:
Misconception:
Believes a common denominator must always be the two denominators multiplied together

Question:
Tom and Katie are discussing how to work out the answer to \( \frac{5}{6}-\frac{1}{3} \)
Tom says you could change both denominators to \( 6 \)
Katie says you could change both denominators to \( 18 \)
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 equivalent fractions

Question:
Tom and Katie are discussing how to work out the answer to \( \frac{5}{6}-\frac{1}{3} \)
Tom says you could change both denominators to \( 6 \)
Katie says you could change both denominators to \( 18 \)
Who is correct?

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

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


Prompt:
Misconception:
Believes you multiply matching bases when carrying out a multiplication

Question:
Jo and Paul are arguing about powers.
Jo says \( 9^{4}=3^{8} \)
Paul says \( 9^{4}=3^{2} \times 3^{2} \)
Who is correct?

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

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


Prompt:
Misconception:
Thinks powers with different bases cannot be equal

Question:
Jo and Paul are arguing about powers.
Jo says \( 9^{4}=3^{8} \)
Paul says \( 9^{4}=3^{2} \times 3^{2} \)
Who is correct?

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

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


Prompt:
Misconception:
Confuses rest and movement on a distance time graph

Question:
This graph shows how far Jodie is from home whilst she is out on a walk.
What might the horizontal represent? ![The image is a distance-time graph. The graph is in three sections. The first section starts at (0,0) and is a sloped line with positive gradient. The second section is a horizontal line. The third section is a sloped line with negative gradient that ends when it touches the Time axis.]()

Options:
A. Jodie is accelerating
B. Jodie is walking away from home
C. Jodie is walking towards home
D. Jodie has stopped walking

Solve the problem as a student with the misconception above.
You 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 rest and movement on a distance time graph

Question:
This graph shows how far Jodie is from home whilst she is out on a walk.
What might the horizontal represent? ![The image is a distance-time graph. The graph is in three sections. The first section starts at (0,0) and is a sloped line with positive gradient. The second section is a horizontal line. The third section is a sloped line with negative gradient that ends when it touches the Time axis.]()

Options:
A. Jodie is accelerating
B. Jodie is walking away from home
C. Jodie is walking towards home
D. Jodie has stopped walking

Solve the problem as a student with the misconception above.
You 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 rest and movement on a distance time graph

Question:
This graph shows how far Jodie is from home whilst she is out on a walk.
What might the horizontal represent? ![The image is a distance-time graph. The graph is in three sections. The first section starts at (0,0) and is a sloped line with positive gradient. The second section is a horizontal line. The third section is a sloped line with negative gradient that ends when it touches the Time axis.]()

Options:
A. Jodie is accelerating
B. Jodie is walking away from home
C. Jodie is walking towards home
D. Jodie has stopped walking

Solve the problem as a student with the misconception above.
You 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:
Expand \( 4(3 c+2) \)

Options:
A. \( 7 c+6 \)
B. \( 12 c+8 \)
C. \( 12 c+6 \)
D. \( 12 c+2 \)

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

Question:
Expand \( 4(3 c+2) \)

Options:
A. \( 7 c+6 \)
B. \( 12 c+8 \)
C. \( 12 c+6 \)
D. \( 12 c+2 \)

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:
Answers as if there are 100 minutes in an hour when changing from hours to minutes

Question:
A school trip lasted \( 5 \) hours and \( 25 \) minutes. How long is this in minutes?

Options:
A. \( 525 \) minutes
B. \( 325 \) minutes
C. \( 300 \) minutes
D. \( 5.25 \) minutes

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


Prompt:
Misconception:
Answers as if there are 100 minutes in an hour when writing minutes as decimals

Question:
A school trip lasted \( 5 \) hours and \( 25 \) minutes. How long is this in minutes?

Options:
A. \( 525 \) minutes
B. \( 325 \) minutes
C. \( 300 \) minutes
D. \( 5.25 \) minutes

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


Prompt:
Misconception:
Finds unit amount but doesn't multiply up

Question:
The pie chart shows colours of motorbikes in a shop.

There are \( \mathbf{3 0} \) more blue bikes than white. How many bikes are there altogether? ![Pie chart with 8 equal sections. One section is black, one white, three green and three blue.]()

Options:
A. \( 120 \)
B. \( 15 \)
C. \( 240 \)
D. \( 80 \)

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


Prompt:
Misconception:
Multiplies up without finding unit amount

Question:
The pie chart shows colours of motorbikes in a shop.

There are \( \mathbf{3 0} \) more blue bikes than white. How many bikes are there altogether? ![Pie chart with 8 equal sections. One section is black, one white, three green and three blue.]()

Options:
A. \( 120 \)
B. \( 15 \)
C. \( 240 \)
D. \( 80 \)

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


Prompt:
Misconception:
When two digits multiply to 10 or more during a multiplication problem, does not add carried value to the preceding digit

Question:
Which working out is correct for $72 \times 36$?

Options:
A. ![ Long multiplication for 72 multiplied by 36 with incorrect working and incorrect final answer. First row of working is incorrect: 4 2 2. Second row of working is incorrect: 2 7. Final answer is incorrect: 4 4 9.]()
B. ![ Long multiplication for 72 multiplied by 36 with incorrect working and incorrect final answer. First row of working is correct: 4 3 2. Second row of working is incorrect: 2 1 6. Final answer is incorrect: 6 4 8.]()
C. ![ Long multiplication for 72 multiplied by 36 with correct working and incorrect final answer. First row of working is correct: 4 3 2. Second row of working is correct: 2 1 6 0. Final answer is incorrect: 2 7 0 0.]()
D. ![ Long multiplication for 72 multiplied by 36 with correct working and correct final answer. First row of working is correct: 4 3 2. Second row of working is correct: 2 1 6 0. Final answer is correct: 2 5 9 2.]()

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


Prompt:
Misconception:
Does not write the place holder zero when doing column multiplication

Question:
Which working out is correct for $72 \times 36$?

Options:
A. ![ Long multiplication for 72 multiplied by 36 with incorrect working and incorrect final answer. First row of working is incorrect: 4 2 2. Second row of working is incorrect: 2 7. Final answer is incorrect: 4 4 9.]()
B. ![ Long multiplication for 72 multiplied by 36 with incorrect working and incorrect final answer. First row of working is correct: 4 3 2. Second row of working is incorrect: 2 1 6. Final answer is incorrect: 6 4 8.]()
C. ![ Long multiplication for 72 multiplied by 36 with correct working and incorrect final answer. First row of working is correct: 4 3 2. Second row of working is correct: 2 1 6 0. Final answer is incorrect: 2 7 0 0.]()
D. ![ Long multiplication for 72 multiplied by 36 with correct working and correct final answer. First row of working is correct: 4 3 2. Second row of working is correct: 2 1 6 0. Final answer is correct: 2 5 9 2.]()

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


Prompt:
Misconception:
When reading graph, chooses nearest marked value on axis instead of reading accurately

Question:
The bar chart shows the number of cups of tea and coffee sold in a café over \( 4 \) days.

How many cups of coffee were sold on Wednesday? ![A dual bar chart showing number of cups of tea and coffee sold Monday to Thursday. On Monday 25 teas and 38 coffees sold, Tuesday 10 teas and 45 coffees, Wednesday 25 teas and 30 coffees, Thursday 43 teas and 40 coffees.]()

Options:
A. \( 30 \)
B. \( 31 \)
C. \( 26 \)
D. \( 38 \)

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


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

Question:
Tom and Katie are discussing mental addition and subtraction strategies.

Tom says a good way to add \( 9 \) is to add \( 10 \) and then subtract \( 1 \).

Katie says a good way to subtract \( 9 \) is to subtract \( 10 \) and then subtract \( 1 \).

Who is correct?

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

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


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

Question:
Tom and Katie are discussing mental addition and subtraction strategies.

Tom says a good way to add \( 9 \) is to add \( 10 \) and then subtract \( 1 \).

Katie says a good way to subtract \( 9 \) is to subtract \( 10 \) and then subtract \( 1 \).

Who is correct?

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

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


Prompt:
Misconception:
Misremembers the quadratic formula

Question:
Vera wants to solve this equation using the quadratic formula.
\(
3 h^{2}-10 h+4=0
\)

What should replace the square? \( \frac{?\pm \sqrt{?-\square}}{?} \)

Options:
A. \( 48 \)
B. \( 12 \)
C. \( 11 \)
D. \( -48 \)

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


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

Question:
Vera wants to solve this equation using the quadratic formula.
\(
3 h^{2}-10 h+4=0
\)

What should replace the square? \( \frac{?\pm \sqrt{?-\square}}{?} \)

Options:
A. \( 48 \)
B. \( 12 \)
C. \( 11 \)
D. \( -48 \)

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


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

Question:
\(
x_{n+1}=\sqrt{\frac{1}{x_{n}+11}}
\)

Using a starting value of \( x_{1}=0.6 \), what is the value of \( x_{2} \) ?

Options:
A. \( 0.2975 \ldots \)
B. \( 0.0862 \ldots \)
C. \( 0.2936 \ldots \)
D. Another answer

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


Prompt:
Misconception:
When solving an equation, thinks the divisor and dividend are the opposite way around

Question:
This is a part of the table of values for the equation
\[
y=10-6 x
\] \begin{tabular}{|l|l|}
\hline\( x \) & \( \bigstar \) \\
\hline\( y \) & \( 0 \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( \frac{10}{6} \)
B. \( \frac{6}{10} \)
C. \( 10 \)
D. \( -\frac{6}{10} \)

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 the value of two terms when substituting

Question:
This is a part of the table of values for the equation
\[
y=10-6 x
\] \begin{tabular}{|l|l|}
\hline\( x \) & \( \bigstar \) \\
\hline\( y \) & \( 0 \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( \frac{10}{6} \)
B. \( \frac{6}{10} \)
C. \( 10 \)
D. \( -\frac{6}{10} \)

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 know that 7 and -7 are different

Question:
Which statement about the temperatures \( -7^{\circ} \mathrm{C} \) and \( 5^{\circ} \mathrm{C} \) is true?

Options:
A. \( 5^{\circ} \mathrm{C} \) is \( 2^{\circ} \mathrm{C} \)
colder than
\( -7^{\circ} \mathrm{C} \)
B. \( 5^{\circ} \mathrm{C} \) is \( 12^{\circ} \mathrm{C} \)
colder than
\( -7^{\circ} \mathrm{C} \)
C. \( 5^{\circ} \mathrm{C} \) is \( 2^{\circ} \mathrm{C} \)
hotter than
\( -7^{\circ} \mathrm{C} \)
D. \( 5^{\circ} \mathrm{C} \) is \( 12^{\circ} \mathrm{C} \)
hotter than
\( -7^{\circ} \mathrm{C} \)

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


Prompt:
Misconception:
Mixes up colder and hotter when comparing temperatures

Question:
Which statement about the temperatures \( -7^{\circ} \mathrm{C} \) and \( 5^{\circ} \mathrm{C} \) is true?

Options:
A. \( 5^{\circ} \mathrm{C} \) is \( 2^{\circ} \mathrm{C} \)
colder than
\( -7^{\circ} \mathrm{C} \)
B. \( 5^{\circ} \mathrm{C} \) is \( 12^{\circ} \mathrm{C} \)
colder than
\( -7^{\circ} \mathrm{C} \)
C. \( 5^{\circ} \mathrm{C} \) is \( 2^{\circ} \mathrm{C} \)
hotter than
\( -7^{\circ} \mathrm{C} \)
D. \( 5^{\circ} \mathrm{C} \) is \( 12^{\circ} \mathrm{C} \)
hotter than
\( -7^{\circ} \mathrm{C} \)

Solve the problem as a student with the misconception above.
You 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:
Which statement about the temperatures \( -7^{\circ} \mathrm{C} \) and \( 5^{\circ} \mathrm{C} \) is true?

Options:
A. \( 5^{\circ} \mathrm{C} \) is \( 2^{\circ} \mathrm{C} \)
colder than
\( -7^{\circ} \mathrm{C} \)
B. \( 5^{\circ} \mathrm{C} \) is \( 12^{\circ} \mathrm{C} \)
colder than
\( -7^{\circ} \mathrm{C} \)
C. \( 5^{\circ} \mathrm{C} \) is \( 2^{\circ} \mathrm{C} \)
hotter than
\( -7^{\circ} \mathrm{C} \)
D. \( 5^{\circ} \mathrm{C} \) is \( 12^{\circ} \mathrm{C} \)
hotter than
\( -7^{\circ} \mathrm{C} \)

Solve the problem as a student with the misconception above.
You 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, believes that when they get to ax = b, b is the solution

Question:
Solve the following pair of simultaneous equations: \( \begin{array}{l}3 x+2 y=14 \\ 2 x+2 y=10\end{array} \)

Options:
A. \( \begin{array}{l}x=5 \\ y=-0.5\end{array} \)
B. \( \begin{array}{l}x=4 \\ y=2\end{array} \)
C. \( \begin{array}{l}x=4 \\ y=1\end{array} \)
D. \( \begin{array}{l}x=1 \\ y=4\end{array} \)

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


Prompt:
Misconception:
Adds rather than subtracts when answering worded problems

Question:
For which of these questions would you calculate \( 50+25 \) ?

Options:
A. Decrease \( 50 \) by \( 25 \).
B. Increase \( 50 \) by \( 25 \).
C. Find the product of \( 50 \) and \( 25 \).
D. How many \( 25 \) s are there in \( 50 ? \)

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


Prompt:
Misconception:
Adds rather than multiplies when asked for a product

Question:
For which of these questions would you calculate \( 50+25 \) ?

Options:
A. Decrease \( 50 \) by \( 25 \).
B. Increase \( 50 \) by \( 25 \).
C. Find the product of \( 50 \) and \( 25 \).
D. How many \( 25 \) s are there in \( 50 ? \)

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


Prompt:
Misconception:
Adds rather than divides when answering worded problems

Question:
For which of these questions would you calculate \( 50+25 \) ?

Options:
A. Decrease \( 50 \) by \( 25 \).
B. Increase \( 50 \) by \( 25 \).
C. Find the product of \( 50 \) and \( 25 \).
D. How many \( 25 \) s are there in \( 50 ? \)

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


Prompt:
Misconception:
Believes the inverse of square rooting is doubling

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "square root" written inside it and the final rectangle has "output" written above it and "16" written inside it.]() What is the input of this function machine?

Options:
A. \( 32 \)
B. \( 8 \)
C. \( 4 \)
D. \( 256 \)

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


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

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "square root" written inside it and the final rectangle has "output" written above it and "16" written inside it.]() What is the input of this function machine?

Options:
A. \( 32 \)
B. \( 8 \)
C. \( 4 \)
D. \( 256 \)

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


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

Question:
![A function machine with 3 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The middle rectangle has "square root" written inside it and the final rectangle has "output" written above it and "16" written inside it.]() What is the input of this function machine?

Options:
A. \( 32 \)
B. \( 8 \)
C. \( 4 \)
D. \( 256 \)

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


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

Question:
How do you write \( 2.5 \% \) as a decimal?

Options:
A. \( 0.025 \)
B. \( 0.25 \)
C. \( 2.5 \)
D. \( 2.50 \)

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


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

Question:
How do you write \( 2.5 \% \) as a decimal?

Options:
A. \( 0.025 \)
B. \( 0.25 \)
C. \( 2.5 \)
D. \( 2.50 \)

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


Prompt:
Misconception:
Cannot reflect shape when line of symmetry is diagonal

Question:
Which image completes a symmetric figure on the Geo board? ![A figure drawn in one half of a box, with a red dotted line running diagonally across the box. ]()

Options:
A. ![An incorrect reflection of the given figure. ]()
B. ![An incorrect reflection of the given figure. ]()
C. ![A correct reflection of the given figure. ]()
D. ![An incorrect reflection of the given figure. ]()

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


Prompt:
Misconception:
Cannot reflect shape when line of symmetry is diagonal

Question:
Which image completes a symmetric figure on the Geo board? ![A figure drawn in one half of a box, with a red dotted line running diagonally across the box. ]()

Options:
A. ![An incorrect reflection of the given figure. ]()
B. ![An incorrect reflection of the given figure. ]()
C. ![A correct reflection of the given figure. ]()
D. ![An incorrect reflection of the given figure. ]()

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


Prompt:
Misconception:
Cannot reflect shape when line of symmetry is diagonal

Question:
Which image completes a symmetric figure on the Geo board? ![A figure drawn in one half of a box, with a red dotted line running diagonally across the box. ]()

Options:
A. ![An incorrect reflection of the given figure. ]()
B. ![An incorrect reflection of the given figure. ]()
C. ![A correct reflection of the given figure. ]()
D. ![An incorrect reflection of the given figure. ]()

Solve the problem as a student with the misconception above.
You 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 numerators to convert fractions to ratio despite different denominators

Question:
\( \frac{1}{5} \) of the counters in a bag are blue.
\( \frac{3}{10} \) of the counters are red.
\( \frac{1}{2} \) of the counters are purple.
Which of these show the ratio of blue : red : purple? ![An image of a bag]()

Options:
A. \( 2: 3: 5 \)
B. \( 1: 3: 1 \)
C. \( 5: 10: 2 \)
D. \( 1: 4: 5 \)

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


Prompt:
Misconception:
Uses the denominator when converting from fractions to ratio, rather than numerator.

Question:
\( \frac{1}{5} \) of the counters in a bag are blue.
\( \frac{3}{10} \) of the counters are red.
\( \frac{1}{2} \) of the counters are purple.
Which of these show the ratio of blue : red : purple? ![An image of a bag]()

Options:
A. \( 2: 3: 5 \)
B. \( 1: 3: 1 \)
C. \( 5: 10: 2 \)
D. \( 1: 4: 5 \)

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


Prompt:
Misconception:
Divides instead of multiplies when calculating total frequency

Question:
Dave has recorded the number of pets his classmates have in the frequency table on the right. \begin{tabular}{|c|c|}
\hline Number of pets & Frequency \\
\hline \( 0 \) & \( 4 \) \\
\hline \( 1 \) & \( 6 \) \\
\hline \( 2 \) & \( 3 \) \\
\hline \( 3 \) & \( 2 \) \\
\hline \( 4 \) & \( 5 \) \\
\hline
\end{tabular} If Dave wanted to work out the total number of pets own by his classmates, what would be a useful column to include?

Options:
A. Number of pets \( x \) Frequency
B. Number of pets \( \div \) Frequency
C. Number of pets + Frequency
D. Number of pets -
Frequency

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


Prompt:
Misconception:
Adds instead of multiplies when calculating total frequency

Question:
Dave has recorded the number of pets his classmates have in the frequency table on the right. \begin{tabular}{|c|c|}
\hline Number of pets & Frequency \\
\hline \( 0 \) & \( 4 \) \\
\hline \( 1 \) & \( 6 \) \\
\hline \( 2 \) & \( 3 \) \\
\hline \( 3 \) & \( 2 \) \\
\hline \( 4 \) & \( 5 \) \\
\hline
\end{tabular} If Dave wanted to work out the total number of pets own by his classmates, what would be a useful column to include?

Options:
A. Number of pets \( x \) Frequency
B. Number of pets \( \div \) Frequency
C. Number of pets + Frequency
D. Number of pets -
Frequency

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


Prompt:
Misconception:
Subtracts rather than multiplies when calculating total frequency

Question:
Dave has recorded the number of pets his classmates have in the frequency table on the right. \begin{tabular}{|c|c|}
\hline Number of pets & Frequency \\
\hline \( 0 \) & \( 4 \) \\
\hline \( 1 \) & \( 6 \) \\
\hline \( 2 \) & \( 3 \) \\
\hline \( 3 \) & \( 2 \) \\
\hline \( 4 \) & \( 5 \) \\
\hline
\end{tabular} If Dave wanted to work out the total number of pets own by his classmates, what would be a useful column to include?

Options:
A. Number of pets \( x \) Frequency
B. Number of pets \( \div \) Frequency
C. Number of pets + Frequency
D. Number of pets -
Frequency

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


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

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

Options:
A. \( 15.983 \)
B. \( 0.0199 \)
C. \( 0.038 \)
D. \( 0.472 \)

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


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

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

Options:
A. \( 15.983 \)
B. \( 0.0199 \)
C. \( 0.038 \)
D. \( 0.472 \)

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


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

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

Options:
A. \( 15.983 \)
B. \( 0.0199 \)
C. \( 0.038 \)
D. \( 0.472 \)

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


Prompt:
Misconception:
Mixes up cubing with multiplying by 10

Question:
\( 100^{3}= \)

Options:
A. \( 100000 \)
B. \( 1003 \)
C. \( 1000000 \)
D. \( 300 \)

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


Prompt:
Misconception:
Writes the index as a digit on the end of a number

Question:
\( 100^{3}= \)

Options:
A. \( 100000 \)
B. \( 1003 \)
C. \( 1000000 \)
D. \( 300 \)

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


Prompt:
Misconception:
Multiplies by the index

Question:
\( 100^{3}= \)

Options:
A. \( 100000 \)
B. \( 1003 \)
C. \( 1000000 \)
D. \( 300 \)

Solve the problem as a student with the misconception above.
You 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:
Julie wants to estimate the answer to this calculation by rounding each number to \( 1 \) significant figure.

\[
0.5841 \times 36.3
\]

What number should replace \( \mathbf{0 . 5 8 4 1} \) in her estimation?

Options:
A. \( 1 \)
B. \( 0.5000 \)
C. \( 0.6 \)
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:
Rounds down instead of up

Question:
Julie wants to estimate the answer to this calculation by rounding each number to \( 1 \) significant figure.

\[
0.5841 \times 36.3
\]

What number should replace \( \mathbf{0 . 5 8 4 1} \) in her estimation?

Options:
A. \( 1 \)
B. \( 0.5000 \)
C. \( 0.6 \)
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:
Rounds down instead of up

Question:
Julie wants to estimate the answer to this calculation by rounding each number to \( 1 \) significant figure.

\[
0.5841 \times 36.3
\]

What number should replace \( \mathbf{0 . 5 8 4 1} \) in her estimation?

Options:
A. \( 1 \)
B. \( 0.5000 \)
C. \( 0.6 \)
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:
Uses sin when tan is required

Question:
Which ratio would you use to find the value of \( \theta \) ? ![A right angled triangle with the two shorter side lengths given as 7cm and 10cm. The length of the longest side of the triangle is not given. The interior angle of the triangle that is opposite the 10cm side is labelled θ.]()

Options:
A. Sin
B. Cos
C. Tan
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:
Uses cos when tan is required

Question:
Which ratio would you use to find the value of \( \theta \) ? ![A right angled triangle with the two shorter side lengths given as 7cm and 10cm. The length of the longest side of the triangle is not given. The interior angle of the triangle that is opposite the 10cm side is labelled θ.]()

Options:
A. Sin
B. Cos
C. Tan
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 how to apply sohcahtoa

Question:
Which ratio would you use to find the value of \( \theta \) ? ![A right angled triangle with the two shorter side lengths given as 7cm and 10cm. The length of the longest side of the triangle is not given. The interior angle of the triangle that is opposite the 10cm side is labelled θ.]()

Options:
A. Sin
B. Cos
C. Tan
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:
When converting a percentage to a decimal, just writes all the digits after a decimal point.

Question:
How do you write \( 803 \% \) as a decimal?

Options:
A. \( 8.03 \)
B. \( 0.803 \)
C. \( 8.3 \)
D. \( 0.83 \)

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


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

Question:
How do you write \( 803 \% \) as a decimal?

Options:
A. \( 8.03 \)
B. \( 0.803 \)
C. \( 8.3 \)
D. \( 0.83 \)

Solve the problem as a student with the misconception above.
You 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 the denominator when converting from fractions to ratio, rather than numerator.

Question:
James and Cameron are watching a film. They pause it with one seventh left to watch.

What is the ratio of how much they have watched to how much the have yet to see? ![An image of a television]()

Options:
A. \( 1: 7 \)
B. 7:1
C. \( 6: 1 \)
D. 1:6

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


Prompt:
Misconception:
Gets order of ratio wrong

Question:
James and Cameron are watching a film. They pause it with one seventh left to watch.

What is the ratio of how much they have watched to how much the have yet to see? ![An image of a television]()

Options:
A. \( 1: 7 \)
B. 7:1
C. \( 6: 1 \)
D. 1:6

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


Prompt:
Misconception:
When adding, just writes the digit to the right of the number without considering place value

Question:
If \( h=3 \) what is the value of \( 2+h \) ?

Options:
A. \( 5 \)
B. \( 23 \)
C. \( -1 \)
D. We cannot tell because \( h \) is a variable.

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


Prompt:
Misconception:
Subtracts instead of adds

Question:
If \( h=3 \) what is the value of \( 2+h \) ?

Options:
A. \( 5 \)
B. \( 23 \)
C. \( -1 \)
D. We cannot tell because \( h \) is a variable.

Solve the problem as a student with the misconception above.
You 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 variable must remain unknown and cannot be substituted with a value

Question:
If \( h=3 \) what is the value of \( 2+h \) ?

Options:
A. \( 5 \)
B. \( 23 \)
C. \( -1 \)
D. We cannot tell because \( h \) is a variable.

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Factorise this expression, if possible:
\(
p^{2}-4
\)

Options:
A. \( (p-2)(p+2) \)
B. \( p(p-2) \)
C. \( (p-2)(p-2) \)
D. Does not
factorise

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


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

Question:
Factorise this expression, if possible:
\(
p^{2}-4
\)

Options:
A. \( (p-2)(p+2) \)
B. \( p(p-2) \)
C. \( (p-2)(p-2) \)
D. Does not
factorise

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
Factorise this expression, if possible:
\(
p^{2}-4
\)

Options:
A. \( (p-2)(p+2) \)
B. \( p(p-2) \)
C. \( (p-2)(p-2) \)
D. Does not
factorise

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


Prompt:
Misconception:
Subtracts instead of adds

Question:
\(\square\quad -\quad 1.534=2.7 \)

Options:
A. \( 1.166 \)
B. \( 1.234 \)
C. \( 3.541 \)
D. \( 4.234 \)

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


Prompt:
Misconception:
Subtracts instead of adds

Question:
\(\square\quad -\quad 1.534=2.7 \)

Options:
A. \( 1.166 \)
B. \( 1.234 \)
C. \( 3.541 \)
D. \( 4.234 \)

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


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

Question:
\(\square\quad -\quad 1.534=2.7 \)

Options:
A. \( 1.166 \)
B. \( 1.234 \)
C. \( 3.541 \)
D. \( 4.234 \)

Solve the problem as a student with the misconception above.
You 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:
Tom and Katie are discussing how to solve:
\(
\frac{x-6}{2}=10
\)

Tom says a correct next line of working could be: \( \frac{x}{2}=16 \)
Katie says a correct next line of working could be: \( x-6=5 \)
Who is correct?

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

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


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

Question:
Tom and Katie are discussing how to solve:
\(
\frac{x-6}{2}=10
\)

Tom says a correct next line of working could be: \( \frac{x}{2}=16 \)
Katie says a correct next line of working could be: \( x-6=5 \)
Who is correct?

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

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


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

Question:
What number replaces the circle to make these two fractions equivalent? \( \frac{2}{7}=\frac{6}{?} \)

Options:
A. \( 14 \)
B. \( 21 \)
C. \( 11 \)
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:
Does not understand equivalent fractions

Question:
What number replaces the circle to make these two fractions equivalent? \( \frac{2}{7}=\frac{6}{?} \)

Options:
A. \( 14 \)
B. \( 21 \)
C. \( 11 \)
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:
Estimates shares of a ratio instead of calculating

Question:
Share \( £360 \) in the ratio \( 2: 7 \)

Options:
A. \( £ 60: £ 300 \)
B. \( £ 180: £ 51 \)
C. \( £ 100: £ 160 \)
D. \( £ 80: £ 280 \)

Solve the problem as a student with the misconception above.
You 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 total amount by each side of the ratio instead of dividing by the sum of the parts

Question:
Share \( £360 \) in the ratio \( 2: 7 \)

Options:
A. \( £ 60: £ 300 \)
B. \( £ 180: £ 51 \)
C. \( £ 100: £ 160 \)
D. \( £ 80: £ 280 \)

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


Prompt:
Misconception:
Estimates shares of a ratio instead of calculating

Question:
Share \( £360 \) in the ratio \( 2: 7 \)

Options:
A. \( £ 60: £ 300 \)
B. \( £ 180: £ 51 \)
C. \( £ 100: £ 160 \)
D. \( £ 80: £ 280 \)

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


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

Question:
What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form a step structure.  The base of the shape is horizontal and is 23m long. The vertical height of the whole shape is 22m. The horizontal width of the top part of the shape is 6m. The horizontal width of the first step is 7m. The vertical height of the bottom rectangle is 5m.  The vertical height of the top rectangle is 8m.]()

Options:
A. \( 86 \mathrm{~m} \)
B. \( 88 \mathrm{~m} \)
C. \( 90 \mathrm{~m} \)
D. \( 71 \mathrm{~m} \)

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


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

Question:
What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form a step structure.  The base of the shape is horizontal and is 23m long. The vertical height of the whole shape is 22m. The horizontal width of the top part of the shape is 6m. The horizontal width of the first step is 7m. The vertical height of the bottom rectangle is 5m.  The vertical height of the top rectangle is 8m.]()

Options:
A. \( 86 \mathrm{~m} \)
B. \( 88 \mathrm{~m} \)
C. \( 90 \mathrm{~m} \)
D. \( 71 \mathrm{~m} \)

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


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

Question:
What is the perimeter of this composite shape made from rectangles? ![A composite shape made from three rectangles that form a step structure.  The base of the shape is horizontal and is 23m long. The vertical height of the whole shape is 22m. The horizontal width of the top part of the shape is 6m. The horizontal width of the first step is 7m. The vertical height of the bottom rectangle is 5m.  The vertical height of the top rectangle is 8m.]()

Options:
A. \( 86 \mathrm{~m} \)
B. \( 88 \mathrm{~m} \)
C. \( 90 \mathrm{~m} \)
D. \( 71 \mathrm{~m} \)

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


Prompt:
Misconception:
Uses the numerator of an improper fraction as the denominator of the equivalent mixed number

Question:
Convert \( \frac{11}{5} \) to a mixed number.

Options:
A. \( 2 \frac{1}{11} \)
B. \( \frac{33}{15} \)
C. \( 2 \) remainder \( 1 \)
D. \( 2 \frac{1}{5} \)

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


Prompt:
Misconception:
Finds an equivalent improper fraction when asked for a mixed number

Question:
Convert \( \frac{11}{5} \) to a mixed number.

Options:
A. \( 2 \frac{1}{11} \)
B. \( \frac{33}{15} \)
C. \( 2 \) remainder \( 1 \)
D. \( 2 \frac{1}{5} \)

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


Prompt:
Misconception:
Does not understand that a remainder can be written as a fraction

Question:
Convert \( \frac{11}{5} \) to a mixed number.

Options:
A. \( 2 \frac{1}{11} \)
B. \( \frac{33}{15} \)
C. \( 2 \) remainder \( 1 \)
D. \( 2 \frac{1}{5} \)

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


Prompt:
Misconception:
When finding the area of a parallelogram finds base x perpendicular height but divides the answer by 2

Question:
What is the area of this parallelogram?
 ![Parallelogram with base length 5cm, perpendicular height 4cm, and slant length 6cm.]()

Options:
A. \( 10 \mathrm{~cm}^{2} \)
B. \( 120 \mathrm{~cm}^{2} \)
C. \( 20 \mathrm{~cm}^{2} \)
D. \( 30 \mathrm{~cm}^{2} \)

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


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

Question:
What is the area of this parallelogram?
 ![Parallelogram with base length 5cm, perpendicular height 4cm, and slant length 6cm.]()

Options:
A. \( 10 \mathrm{~cm}^{2} \)
B. \( 120 \mathrm{~cm}^{2} \)
C. \( 20 \mathrm{~cm}^{2} \)
D. \( 30 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Has used slant height and base to find area rather than perpendicular height and base

Question:
What is the area of this parallelogram?
 ![Parallelogram with base length 5cm, perpendicular height 4cm, and slant length 6cm.]()

Options:
A. \( 10 \mathrm{~cm}^{2} \)
B. \( 120 \mathrm{~cm}^{2} \)
C. \( 20 \mathrm{~cm}^{2} \)
D. \( 30 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Divided by 10 rather than 100

Question:
How do you write \( 2 \% \) as a decimal?

Options:
A. \( 0.2 \)
B. \( 2.0 \)
C. \( 0.02 \)
D. \( 200 \)

Solve the problem as a student with the misconception above.
You 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 \( 2 \% \) as a decimal?

Options:
A. \( 0.2 \)
B. \( 2.0 \)
C. \( 0.02 \)
D. \( 200 \)

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


Prompt:
Misconception:
Multiplied by 100 rather than divided by 100

Question:
How do you write \( 2 \% \) as a decimal?

Options:
A. \( 0.2 \)
B. \( 2.0 \)
C. \( 0.02 \)
D. \( 200 \)

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


Prompt:
Misconception:
When reading decimals on a number line, assumes each dash is 0.1

Question:
![A number line between 0 and 1 split into 5 parts with a red arrow pointing to the marker representing the value 0.6]() What number is the arrow pointing to?

Options:
A. \( 0.6 \)
B. \( 0.3 \)
C. \( 3 \)
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:
Gives a rounded whole number instead of a decimal

Question:
A number, \( n \), has been rounded to \( 2 \) decimal places to give \( \mathbf{4 . 0 0} \)
What is the smallest \( n \) can be?

Options:
A. \( 3.9 \)
B. \( 3.995 \)
C. \( 3.99 \)
D. \( 3.9995 \)

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


Prompt:
Misconception:
Gives a rounded whole number instead of a decimal

Question:
A number, \( n \), has been rounded to \( 2 \) decimal places to give \( \mathbf{4 . 0 0} \)
What is the smallest \( n \) can be?

Options:
A. \( 3.9 \)
B. \( 3.995 \)
C. \( 3.99 \)
D. \( 3.9995 \)

Solve the problem as a student with the misconception above.
You 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 which place value is the one that determines if a number rounds up or down

Question:
A number, \( n \), has been rounded to \( 2 \) decimal places to give \( \mathbf{4 . 0 0} \)
What is the smallest \( n \) can be?

Options:
A. \( 3.9 \)
B. \( 3.995 \)
C. \( 3.99 \)
D. \( 3.9995 \)

Solve the problem as a student with the misconception above.
You 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 interior angle of a regular polygon is 10n

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

Options:
A. \( 60^{\degree} \)
B. \( 135^{\degree} \)
C. \( 120^{\degree} \)
D. \( 160^{\degree} \)

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 you add 2 instead of subtracting 2 to the numbers of sides when finding total interior angles

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

Options:
A. \( 60^{\degree} \)
B. \( 135^{\degree} \)
C. \( 120^{\degree} \)
D. \( 160^{\degree} \)

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:
Assumes that opposite angles in a quadrilateral sum to 180 degrees

Question:
What is the size of angle \( q \) ? ![A parallelogram with an angle of 120 degrees in the top left corner find the angle q which is opposite in the bottom right corner of the shape.]()

Options:
A. \( 60^{\circ} \)
B. \( 80^{\circ} \)
C. \( 120^{\circ} \)
D. Not enough information

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


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

Question:
What is the size of angle \( q \) ? ![A parallelogram with an angle of 120 degrees in the top left corner find the angle q which is opposite in the bottom right corner of the shape.]()

Options:
A. \( 60^{\circ} \)
B. \( 80^{\circ} \)
C. \( 120^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Assumes a fact without considering enough examples

Question:
Tom and Katie are arguing about statements that can be made about the equation on the right. \( x=y-4 \) Tom says this is always true: \( 2 x>y-4 \)
Katie says this is always true: \( x>y-5 \)
Who is correct?

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

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


Prompt:
Misconception:
Confuses collecting like terms with multiplication

Question:
Simplify, if possible:
\[
c+a
\]

Options:
A. \( c a \)
B. \( a c \)
C. \( c^{a} \)
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 realise that two letters together, or a number and letter together, are multiplying

Question:
Simplify, if possible:
\[
c+a
\]

Options:
A. \( c a \)
B. \( a c \)
C. \( c^{a} \)
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:
Believes addition of terms and powers of terms are equivalent e.g. a + c = a^c

Question:
Simplify, if possible:
\[
c+a
\]

Options:
A. \( c a \)
B. \( a c \)
C. \( c^{a} \)
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:
Believes a horizontal line can show a constant rate of change

Question:
The graph on the right shows the mass of sand in a bucket over time

What might the horizontal section represent? ![A graph with time (secs) on the horizontal axis and mass (g) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis, more steeply than the start. ]()

Options:
A. The temperature of the sand is falling
B. Sand is being added to the bucket
C. Sand is being tipped out
D. The bucket is full

Solve the problem as a student with the misconception above.
You 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 horizontal line can show a constant rate of change

Question:
The graph on the right shows the mass of sand in a bucket over time

What might the horizontal section represent? ![A graph with time (secs) on the horizontal axis and mass (g) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis, more steeply than the start. ]()

Options:
A. The temperature of the sand is falling
B. Sand is being added to the bucket
C. Sand is being tipped out
D. The bucket is full

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


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

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

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

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


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

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

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

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


Prompt:
Misconception:
Does not recognise when one part of a fraction is the negative of the other

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

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

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


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( \mathbf{3 . 5 1 6 3} \) rounded to \( 2 \) decimal places?

Options:
A. \( 3.51 \)
B. \( 3.52 \)
C. \( 4.51 \)
D. \( 4.52 \)

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


Prompt:
Misconception:
Rounds incorrectly by changing multiple place values

Question:
What is \( \mathbf{3 . 5 1 6 3} \) rounded to \( 2 \) decimal places?

Options:
A. \( 3.51 \)
B. \( 3.52 \)
C. \( 4.51 \)
D. \( 4.52 \)

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


Prompt:
Misconception:
Rounds incorrectly by changing multiple place values

Question:
What is \( \mathbf{3 . 5 1 6 3} \) rounded to \( 2 \) decimal places?

Options:
A. \( 3.51 \)
B. \( 3.52 \)
C. \( 4.51 \)
D. \( 4.52 \)

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


Prompt:
Misconception:
Converts a fraction to a decimal by using only the numerator after the decimal point

Question:
Convert \( \frac{3}{20} \) into a decimal

Options:
A. \( 0.15 \)
B. \( 0.3 \)
C. \( 3.20 \)
D. \( 0.12 \)

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


Prompt:
Misconception:
Converts a fraction to a decimal by placing a decimal point between the numerator and denominator

Question:
Convert \( \frac{3}{20} \) into a decimal

Options:
A. \( 0.15 \)
B. \( 0.3 \)
C. \( 3.20 \)
D. \( 0.12 \)

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


Prompt:
Misconception:
When counting partial symbols on pictogram, uses the fraction rather than the amount it represents

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

How many Blues CDs does Bob have? ![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. \( 8.25 \)
B. \( 9 \)
C. \( 2 \)
D. \( 2.25 \)

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


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

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

How many Blues CDs does Bob have? ![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. \( 8.25 \)
B. \( 9 \)
C. \( 2 \)
D. \( 2.25 \)

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


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

Question:
How many rectangles would you need to shade so that \( 22 \% \) of this shape is shaded? \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline
\end{tabular}

Options:
A. \( 22 \)
B. \( 44 \)
C. \( 11 \)
D. Not possible

Solve the problem as a student with the misconception above.
You 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:
How many rectangles would you need to shade so that \( 22 \% \) of this shape is shaded? \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline
\end{tabular}

Options:
A. \( 22 \)
B. \( 44 \)
C. \( 11 \)
D. Not possible

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


Prompt:
Misconception:
Does not understand a percentage can be applied to something not out of 100

Question:
How many rectangles would you need to shade so that \( 22 \% \) of this shape is shaded? \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline & \(\space\) & \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) &  \(\space\) & \\
\hline
\end{tabular}

Options:
A. \( 22 \)
B. \( 44 \)
C. \( 11 \)
D. Not possible

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


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

Question:
What is \( \frac{3}{5} \) as a decimal?

Options:
A. \( 0.5 \)
B. \( 0.3 \)
C. \( 0.35 \)
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}.