Prompt:
Misconception:
Converts a fraction to a decimal by using only the numerator 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}.


Prompt:
Misconception:
Converts a fraction to a decimal by placing all values of the fraction 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}.


Prompt:
Misconception:
Uses formula for area of a parallelogram when finding the area of a trapezium

Question:
The area of this trapezium is
\(
30 \mathrm{~cm}^{2}
\)
What measurement should replace the star? ![A trapezium with 8cm and a star on the parallel sides, and the perpendicular height is 5cm.]()

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 3.75 \mathrm{~cm} \)
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:
Thinks you multiply parallel sides to find the area of a trapezium

Question:
The area of this trapezium is
\(
30 \mathrm{~cm}^{2}
\)
What measurement should replace the star? ![A trapezium with 8cm and a star on the parallel sides, and the perpendicular height is 5cm.]()

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 3.75 \mathrm{~cm} \)
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 formula for area of a trapezium

Question:
The area of this trapezium is
\(
30 \mathrm{~cm}^{2}
\)
What measurement should replace the star? ![A trapezium with 8cm and a star on the parallel sides, and the perpendicular height is 5cm.]()

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 3.75 \mathrm{~cm} \)
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:
Mixes up sides of a ratio

Question:
The ratio of adults to children at a party is \( 1\;: 4 \)
There are \( 20 \) adults.
How many children are there?

Options:
A. \( 4 \)
B. \( 5 \)
C. \( 80 \)
D. \( 20 \)

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


Prompt:
Misconception:
Shares equally instead of in given ratio

Question:
The ratio of adults to children at a party is \( 1\;: 4 \)
There are \( 20 \) adults.
How many children are there?

Options:
A. \( 4 \)
B. \( 5 \)
C. \( 80 \)
D. \( 20 \)

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


Prompt:
Misconception:
When solving an equation with x in the denominator, thinks the inverse operation is to make it the numerator on the other side

Question:
Tom and Katie are discussing how to solve:
\(
\frac{24}{x}=6
\)

Tom says a correct next line of working could be: \( 24=6 x \)

Katie says a correct next line of working could be: \( 24=\frac{x}{6} \)

Who is correct?

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

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


Prompt:
Misconception:
When solving an equation with x in the denominator, thinks the inverse operation is to make it the numerator on the other side

Question:
Tom and Katie are discussing how to solve:
\(
\frac{24}{x}=6
\)

Tom says a correct next line of working could be: \( 24=6 x \)

Katie says a correct next line of working could be: \( 24=\frac{x}{6} \)

Who is correct?

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

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


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

Question:
Tom and Katie are discussing how to solve:
\(
\frac{24}{x}=6
\)

Tom says a correct next line of working could be: \( 24=6 x \)

Katie says a correct next line of working could be: \( 24=\frac{x}{6} \)

Who is correct?

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

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


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

Question:
Tom and Katie are discussing how to solve:
\(\frac{3 x}{2}+1=1.6\)

Tom says a correct next line of working could be: \( \frac{3 x}{2}=0.6 \)

Katie says a correct next line of working could be: \( 3 x+2=2.12 \)

Who is correct?

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

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


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

Question:
Tom and Katie are discussing how to solve:
\(\frac{3 x}{2}+1=1.6\)

Tom says a correct next line of working could be: \( \frac{3 x}{2}=0.6 \)

Katie says a correct next line of working could be: \( 3 x+2=2.12 \)

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 division is commutative

Question:
Tom and Katie are discussing written division strategies.

Tom says \( 918 \div 34=934 \div 18 \)

Katie says \( 918 \div 34=34 \div 918 \)

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:
Reflects in an axis, instead of the given mirror line

Question:
Which is the correct point for E when reflected in the line \( x=-1 \) ? ![A set of axes: x-axis from -5 to 5, y-axis from -5 to 3. Four points are plotted and joined to make a rectangle: (1,1), (3, 1), (3, 3) and (1,3). Point (3, 3) is labelled with the letter "E". ]()

Options:
A. (-3, 3)
B. (-5, 3)
C. (3, -3)
D. (3, -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:
Reflects in an axis, instead of the given mirror line

Question:
Which is the correct point for E when reflected in the line \( x=-1 \) ? ![A set of axes: x-axis from -5 to 5, y-axis from -5 to 3. Four points are plotted and joined to make a rectangle: (1,1), (3, 1), (3, 3) and (1,3). Point (3, 3) is labelled with the letter "E". ]()

Options:
A. (-3, 3)
B. (-5, 3)
C. (3, -3)
D. (3, -5)

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


Prompt:
Misconception:
Thinks x = ? is a horizontal line through ?

Question:
Which is the correct point for E when reflected in the line \( x=-1 \) ? ![A set of axes: x-axis from -5 to 5, y-axis from -5 to 3. Four points are plotted and joined to make a rectangle: (1,1), (3, 1), (3, 3) and (1,3). Point (3, 3) is labelled with the letter "E". ]()

Options:
A. (-3, 3)
B. (-5, 3)
C. (3, -3)
D. (3, -5)

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


Prompt:
Misconception:
Thinks that when raising a variable with a coefficient to a power, only the coefficient is affected by the power

Question:
Which of the following expressions is equivalent to:
\(
\left(2 p^{2}\right)^{3}
\)

Options:
A. \( 2 p^{8} \)
B. \( 8 p^{2} \)
C. \( 2 p^{5} \)
D. \( 8 p^{6} \)

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


Prompt:
Misconception:
Does not know the meaning of perpendicular

Question:
Tom and Katie are discussing this pair of lines
Tom says they are equal length
Katie says they are perpendicular
Who do you agree with? ![Two blue lines, each with a little red line marked across them. The blue lines don't touch each other, but they are closer together at one end.]()

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

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


Prompt:
Misconception:
Does not know what dashes on the sides of shapes mean

Question:
Tom and Katie are discussing this pair of lines
Tom says they are equal length
Katie says they are perpendicular
Who do you agree with? ![Two blue lines, each with a little red line marked across them. The blue lines don't touch each other, but they are closer together at one end.]()

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

Question:
![Image of a function machine. The function is add one third, and the output is 7]() What is the input of this function machine?

Options:
A. \( 7 \frac{1}{3} \)
B. \( \frac{7}{3} \)
C. \( 6 \frac{2}{3} \)
D. \( 21 \)

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


Prompt:
Misconception:
Thinks the inverse of addition is multiplication

Question:
![Image of a function machine. The function is add one third, and the output is 7]() What is the input of this function machine?

Options:
A. \( 7 \frac{1}{3} \)
B. \( \frac{7}{3} \)
C. \( 6 \frac{2}{3} \)
D. \( 21 \)

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


Prompt:
Misconception:
Thinks the inverse of addition is division

Question:
![Image of a function machine. The function is add one third, and the output is 7]() What is the input of this function machine?

Options:
A. \( 7 \frac{1}{3} \)
B. \( \frac{7}{3} \)
C. \( 6 \frac{2}{3} \)
D. \( 21 \)

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


Prompt:
Misconception:
Assumes a fact without considering enough examples

Question:
\( n \times 5 \geq \frac{n}{5} \) If \( n \) can represent any number, is the statement above...

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

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


Prompt:
Misconception:
Assumes a fact without considering enough examples

Question:
\( n \times 5 \geq \frac{n}{5} \) If \( n \) can represent any number, is the statement above...

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

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


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

Question:
Which of the following statements is true when \( n=1.5 \) ?

Options:
A. \( 5 n>n+5 \)
B. \( 5 n<n+5 \)
C. \( 5 n=n+5 \)
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:
Thinks subtracting a negative makes your answer smaller

Question:
Solve the inequality:
\(-3>p-1\)

Options:
A. \( p<-4 \)
B. \( p>-4 \)
C. \( p>-2 \)
D. \( p<-2 \)

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


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

Question:
Solve the inequality:
\(-3>p-1\)

Options:
A. \( p<-4 \)
B. \( p>-4 \)
C. \( p>-2 \)
D. \( p<-2 \)

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:
Adds instead of multiplies

Question:
\( 0.6 \times 0.4= \)

Options:
A. \( 0.24 \)
B. \( 1 \)
C. \( 2.4 \)
D. \( 0.024 \)

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


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

Question:
\( 0.6 \times 0.4= \)

Options:
A. \( 0.24 \)
B. \( 1 \)
C. \( 2.4 \)
D. \( 0.024 \)

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


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

Question:
\( 0.6 \times 0.4= \)

Options:
A. \( 0.24 \)
B. \( 1 \)
C. \( 2.4 \)
D. \( 0.024 \)

Solve the problem as a student with the misconception above.
You 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:
Write the following as simply as possible: \( \frac{x^{2}-1}{x+1} \)

Options:
A. \( x+1 \)
B. \( x \)
C. \( x-1 \)
D. None of the options

Solve the problem as a student with the misconception above.
You 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:
Write the following as simply as possible: \( \frac{x^{2}-1}{x+1} \)

Options:
A. \( x+1 \)
B. \( x \)
C. \( x-1 \)
D. None of the options

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


Prompt:
Misconception:
Subtracted rather than divided by a scale factor

Question:
Rectangle \( \mathrm{P} \) has been enlarged by a scale factor of \( 1.5 \) to give rectangle \( \mathrm{Q} \).

What length should replace the star? ![Two rectangles, the smaller labelled P and the larger labelled Q. Q has width 9cm and length 12cm. The length of P is marked with a star.]()

Options:
A. \( 8 \mathrm{~cm} \)
B. \( 10.5 \mathrm{~cm} \)
C. \( 9 \mathrm{~cm} \)
D. \( 6 \mathrm{~cm} \)

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 recognise the corresponding sides in similar shapes or enlargements

Question:
Rectangle \( \mathrm{P} \) has been enlarged by a scale factor of \( 1.5 \) to give rectangle \( \mathrm{Q} \).

What length should replace the star? ![Two rectangles, the smaller labelled P and the larger labelled Q. Q has width 9cm and length 12cm. The length of P is marked with a star.]()

Options:
A. \( 8 \mathrm{~cm} \)
B. \( 10.5 \mathrm{~cm} \)
C. \( 9 \mathrm{~cm} \)
D. \( 6 \mathrm{~cm} \)

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

Question:
Jo and Paul are arguing about how to solve this equation:
\(
x^{2}-9 x=0
\)

Jo says one solution is \( x=0 \)

Paul says one solution is \( x=3 \)
Who is correct?

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

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


Prompt:
Misconception:
Forgets to include the intersection value when asked for total value of a set in a Venn diagram

Question:
\( 60 \) people completed an online survey about the car they own.
The results are shown in the Venn Diagram.

How many people own a \( 4 \times 4 \) ? ![A Venn diagram with two circles labelled Owns a 4x4 and Owns a Black Car. The number 27 is in the Owns a 4x4 only region, 15 is in the intersection, and 8 is in the Owns a Black Car only region]()

Options:
A. \( 27 \)
B. \( 15 \)
C. \( 8 \)
D. \( 42 \)

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


Prompt:
Misconception:
Believes the intersection on a Venn diagram represents the total of one set

Question:
\( 60 \) people completed an online survey about the car they own.
The results are shown in the Venn Diagram.

How many people own a \( 4 \times 4 \) ? ![A Venn diagram with two circles labelled Owns a 4x4 and Owns a Black Car. The number 27 is in the Owns a 4x4 only region, 15 is in the intersection, and 8 is in the Owns a Black Car only region]()

Options:
A. \( 27 \)
B. \( 15 \)
C. \( 8 \)
D. \( 42 \)

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


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

Question:
Here is a function machine ![Input \( \rightarrow-2 \rightarrow\times 5 \rightarrow \) Output]() The input is \( 7 \).
Which calculation gives the correct output?

Options:
A. \( 7-2 \times 5 \)
B. \( 7(5-2) \)
C. \( 7 \times 5-2 \)
D. \( 5(7-2) \)

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:
In a function machine, confuses an operation with the input

Question:
Here is a function machine ![Input \( \rightarrow-2 \rightarrow\times 5 \rightarrow \) Output]() The input is \( 7 \).
Which calculation gives the correct output?

Options:
A. \( 7-2 \times 5 \)
B. \( 7(5-2) \)
C. \( 7 \times 5-2 \)
D. \( 5(7-2) \)

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

Question:
Here is a function machine ![Input \( \rightarrow-2 \rightarrow\times 5 \rightarrow \) Output]() The input is \( 7 \).
Which calculation gives the correct output?

Options:
A. \( 7-2 \times 5 \)
B. \( 7(5-2) \)
C. \( 7 \times 5-2 \)
D. \( 5(7-2) \)

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:
Adds rather than multiplies when using the product rule for counting

Question:
Jumbo Restaurant has \( 34 \) choices of starters, \( 92 \) choices of main course, and \( 27 \) choices of dessert.
Sally wants a starter, main course and dessert.

Which of the following calculations would correctly work out the total possible combinations of available to Sally?

Options:
A. \( 34 \times 92 \times 27 \)
B. \( 3 \times 34 \times 92 \times 27 \)
C. \( 34+92+27 \)
D. \( 3 \times(34+92+27) \)

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


Prompt:
Misconception:
When solving simultaneous equations graphically, they think the solutions are the y-intercepts

Question:
According to the graph, what are the solutions to the simultaneous equations? ![The image is of a set of axes with two straight lines drawn on. The red line goes through the points (0,6) and (3,0). The blue line goes through the points (0,3) and (6,0)and the two lines cross at (2,2).]()

Options:
A. \( x=3, \quad y=6 \)
B. \( x=6, \quad y=3 \)
C. \( x=2, \quad y=2 \)
D. \( x=2, \quad y=1 \)

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


Prompt:
Misconception:
When solving simultaneous equations graphically, they think the solutions are the x-intercepts

Question:
According to the graph, what are the solutions to the simultaneous equations? ![The image is of a set of axes with two straight lines drawn on. The red line goes through the points (0,6) and (3,0). The blue line goes through the points (0,3) and (6,0)and the two lines cross at (2,2).]()

Options:
A. \( x=3, \quad y=6 \)
B. \( x=6, \quad y=3 \)
C. \( x=2, \quad y=2 \)
D. \( x=2, \quad y=1 \)

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


Prompt:
Misconception:
Assumes an addition pyramid works in a different way to how it actually does

Question:
Jo and Paul are talking about which term could replace the star in this addition pyramid.
Jo says it could be: \( f \)
Paul says it could be: \( g \)
Who is correct? ![A diagram showing 3 rows of boxes. the bottom row has 3 boxes, containing a star, and empty box and 2g from left to right. The next row up contains two boxes, overlapping the joins of the boxes below. The left one contains 4f+6g, the right one is empty. The top row is one box, centered over the join of the two below, it is empty.]()

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:
Assumes an addition pyramid works in a different way to how it actually does

Question:
Jo and Paul are talking about which term could replace the star in this addition pyramid.
Jo says it could be: \( f \)
Paul says it could be: \( g \)
Who is correct? ![A diagram showing 3 rows of boxes. the bottom row has 3 boxes, containing a star, and empty box and 2g from left to right. The next row up contains two boxes, overlapping the joins of the boxes below. The left one contains 4f+6g, the right one is empty. The top row is one box, centered over the join of the two below, it is empty.]()

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

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


Prompt:
Misconception:
Does not know the definition of term or term-to-term rule

Question:
![2 arrows pointing to the right. + 7 in the first arrow. divide by 2 in the second arrow]() The rule above is used to generate a term-to-term sequence.
If the third term is \( 9 \), what is the first term?

Options:
A. \( 15 \)
B. \( 4 \)
C. \( 11 \)
D. \( 8 \)

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


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

Question:
![2 arrows pointing to the right. + 7 in the first arrow. divide by 2 in the second arrow]() The rule above is used to generate a term-to-term sequence.
If the third term is \( 9 \), what is the first term?

Options:
A. \( 15 \)
B. \( 4 \)
C. \( 11 \)
D. \( 8 \)

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


Prompt:
Misconception:
Does not know the definition of term or term-to-term rule

Question:
![2 arrows pointing to the right. + 7 in the first arrow. divide by 2 in the second arrow]() The rule above is used to generate a term-to-term sequence.
If the third term is \( 9 \), what is the first term?

Options:
A. \( 15 \)
B. \( 4 \)
C. \( 11 \)
D. \( 8 \)

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


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

Question:
What is the height of the rectangle as indicated by the arrow? ![A pair of axes with no labels. 4 points are marked and joined with straight lines to make a rectangle. The top left corner of the rectangle is labelled with co-ordinate (-4,7).  The bottom right corner of the rectangle is labelled with co-ordinate (2,-12). A double-ended vertical arrow spans the height of the rectangle, starting level with (2,-12) and ending level with the corner of the rectangle directly above (2,-12).]()

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 2 \)
D. \( 19 \)

Solve the problem as a student with the misconception above.
You 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 width and height of a rectangle

Question:
What is the height of the rectangle as indicated by the arrow? ![A pair of axes with no labels. 4 points are marked and joined with straight lines to make a rectangle. The top left corner of the rectangle is labelled with co-ordinate (-4,7).  The bottom right corner of the rectangle is labelled with co-ordinate (2,-12). A double-ended vertical arrow spans the height of the rectangle, starting level with (2,-12) and ending level with the corner of the rectangle directly above (2,-12).]()

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 2 \)
D. \( 19 \)

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


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

Question:
What is the height of the rectangle as indicated by the arrow? ![A pair of axes with no labels. 4 points are marked and joined with straight lines to make a rectangle. The top left corner of the rectangle is labelled with co-ordinate (-4,7).  The bottom right corner of the rectangle is labelled with co-ordinate (2,-12). A double-ended vertical arrow spans the height of the rectangle, starting level with (2,-12) and ending level with the corner of the rectangle directly above (2,-12).]()

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 2 \)
D. \( 19 \)

Solve the problem as a student with the misconception above.
You 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 first term in a sequence is the term before the sequence begins (0th term)

Question:
How many terms are greater than zero in this sequence:
\[
22-5 n
\]

Options:
A. \( 22 \)
B. \( 17 \)
C. \( 5 \)
D. \( 4 \)

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


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

Question:
Tom and Katie are discussing fractions, decimals and percentages. Tom says \( \frac{11}{50}=0.11 \) Katie says \( \frac{11}{50}=22 \% \) 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:
Converts a fraction to a decimal by using only the numerator after the decimal point

Question:
Tom and Katie are discussing fractions, decimals and percentages. Tom says \( \frac{11}{50}=0.11 \) Katie says \( \frac{11}{50}=22 \% \) 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 fractions, decimals and percentages. Tom says \( \frac{11}{50}=0.11 \) Katie says \( \frac{11}{50}=22 \% \) 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:
Starts at the wrong end of the dividend when dividing

Question:
When using long-division to solve this problem, what digit should replace the rectangle to give the correct answer (quotient)? ![Division sum written out in Bus Stop format with dividend = 735, divisor = 3, the digits of the quotient are represented by a yellow star, a purple triangle and a blue rectangle.]()

Options:
A. \( 0 \)
B. \( 2 \)
C. \( 1 \)
D. \( 5 \)

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


Prompt:
Misconception:
Subtracts instead of divides

Question:
When using long-division to solve this problem, what digit should replace the rectangle to give the correct answer (quotient)? ![Division sum written out in Bus Stop format with dividend = 735, divisor = 3, the digits of the quotient are represented by a yellow star, a purple triangle and a blue rectangle.]()

Options:
A. \( 0 \)
B. \( 2 \)
C. \( 1 \)
D. \( 5 \)

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


Prompt:
Misconception:
Starts at the wrong end of the dividend when dividing

Question:
When using long-division to solve this problem, what digit should replace the rectangle to give the correct answer (quotient)? ![Division sum written out in Bus Stop format with dividend = 735, divisor = 3, the digits of the quotient are represented by a yellow star, a purple triangle and a blue rectangle.]()

Options:
A. \( 0 \)
B. \( 2 \)
C. \( 1 \)
D. \( 5 \)

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


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

Question:
\( 5+4 \times 3= \)

Options:
A. \( 27 \)
B. \( 17 \)
C. \( 60 \)
D. \( 12 \)

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


Prompt:
Misconception:
Multiplies rather than adds

Question:
\( 5+4 \times 3= \)

Options:
A. \( 27 \)
B. \( 17 \)
C. \( 60 \)
D. \( 12 \)

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


Prompt:
Misconception:
When solving simultaneous equations, thinks they can ignore one of the variables

Question:
Chris orders \( 3 \) cups of tea and a cake, and his bill comes to £3.10

Amy orders \( 5 \) cups of tea and a cake, and her bill comes to \( £ 4.50 \).
How much does one cup of tea cost?

Options:
A. \( 70 p \)
B. \( 90 p \)
C. E1
D. \( £ 1.40 \)

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


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

Question:
Chris orders \( 3 \) cups of tea and a cake, and his bill comes to £3.10

Amy orders \( 5 \) cups of tea and a cake, and her bill comes to \( £ 4.50 \).
How much does one cup of tea cost?

Options:
A. \( 70 p \)
B. \( 90 p \)
C. E1
D. \( £ 1.40 \)

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


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

Question:
Chris orders \( 3 \) cups of tea and a cake, and his bill comes to £3.10

Amy orders \( 5 \) cups of tea and a cake, and her bill comes to \( £ 4.50 \).
How much does one cup of tea cost?

Options:
A. \( 70 p \)
B. \( 90 p \)
C. E1
D. \( £ 1.40 \)

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


Prompt:
Misconception:
Reads 10,000 as 1000

Question:
Which number line shows a good estimate for the position of the number shown?

Options:
A. ![A number line from 0 to 10000 with the value 857 incorrectly labelled, with an arrow, between the midpoint and 10000]()
B. ![A number line from 0 to 1000 with the value 499 incorrectly labelled, with an arrow, just after the midpoint]()
C. ![A number line from 1000 to 2000 with the value 1250 correctly labelled, with an arrow, between 1000 and the midpoint]()
D. ![A number line from 0 to 10000 with the value 8967 incorrectly labelled, with an arrow, after the midpoint]()

Solve the problem as a student with the misconception above.
You 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 negative sign when expanding bracket

Question:
Expand:
\(
-(2-3 p)
\)

Options:
A. \( 2-3 p \)
B. \( -2-3 p \)
C. \( 2+3 p \)
D. \( -2+3 p \)

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


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

Question:
Expand:
\(
-(2-3 p)
\)

Options:
A. \( 2-3 p \)
B. \( -2-3 p \)
C. \( 2+3 p \)
D. \( -2+3 p \)

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


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

Question:
Expand:
\(
-(2-3 p)
\)

Options:
A. \( 2-3 p \)
B. \( -2-3 p \)
C. \( 2+3 p \)
D. \( -2+3 p \)

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


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

Question:
Which of the three marked lengths is not needed when calculating the volume of this shape? ![A triangular prism with length 6cm. The triangular face is a right-angled triangle with base 4cm, height 3cm and longest edge 5cm. ]()

Options:
A. \( 3 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 5 \mathrm{~cm} \)
D. \( 6 \mathrm{~cm} \)

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:
Has used slant height and base to find area of a triangle rather than perpendicular height and base

Question:
Which of the three marked lengths is not needed when calculating the volume of this shape? ![A triangular prism with length 6cm. The triangular face is a right-angled triangle with base 4cm, height 3cm and longest edge 5cm. ]()

Options:
A. \( 3 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 5 \mathrm{~cm} \)
D. \( 6 \mathrm{~cm} \)

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:
Finds area of one face when asked for volume

Question:
Which of the three marked lengths is not needed when calculating the volume of this shape? ![A triangular prism with length 6cm. The triangular face is a right-angled triangle with base 4cm, height 3cm and longest edge 5cm. ]()

Options:
A. \( 3 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 5 \mathrm{~cm} \)
D. \( 6 \mathrm{~cm} \)

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 a percentage can be applied to something not out of 100

Question:
What is \( 4 \% \) of \( 200 ? \)

Options:
A. \( 4 \)
B. \( 204 \)
C. \( 80 \)
D. \( 8 \)

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


Prompt:
Misconception:
Added the values together instead of finding the percentage

Question:
What is \( 4 \% \) of \( 200 ? \)

Options:
A. \( 4 \)
B. \( 204 \)
C. \( 80 \)
D. \( 8 \)

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


Prompt:
Misconception:
Believes that dividing by 10 gives 1%

Question:
What is \( 4 \% \) of \( 200 ? \)

Options:
A. \( 4 \)
B. \( 204 \)
C. \( 80 \)
D. \( 8 \)

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


Prompt:
Misconception:
Thinks there are 5 days in a week

Question:
Which one of the following calculations would work out the number of hours in \( 10 \) weeks?

Options:
A. \( 10 \times 5 \times 24 \)
B. \( 10 \times 7 \times 24 \)
C. \( 10 \times 24 \)
D. \( 10 \times 7 \times 12 \)

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:
Forgets to multiply up for the correct time frame in a worded question

Question:
Which one of the following calculations would work out the number of hours in \( 10 \) weeks?

Options:
A. \( 10 \times 5 \times 24 \)
B. \( 10 \times 7 \times 24 \)
C. \( 10 \times 24 \)
D. \( 10 \times 7 \times 12 \)

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:
Thinks there are 12 hours in 1 day

Question:
Which one of the following calculations would work out the number of hours in \( 10 \) weeks?

Options:
A. \( 10 \times 5 \times 24 \)
B. \( 10 \times 7 \times 24 \)
C. \( 10 \times 24 \)
D. \( 10 \times 7 \times 12 \)

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


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

Question:
Here are \( 3 \) vertices of a rectangle:
\((-6,-2),(-3,2),(0,0) \text {, }\)

What are the coordinates of the \( 4^{\text {th }} \) vertex?

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

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


Prompt:
Misconception:
Believes the sides of a rectangle must be horizontal and vertical, not diagonal

Question:
Here are \( 3 \) vertices of a rectangle:
\((-6,-2),(-3,2),(0,0) \text {, }\)

What are the coordinates of the \( 4^{\text {th }} \) vertex?

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

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


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

Question:
Here are \( 3 \) vertices of a rectangle:
\((-6,-2),(-3,2),(0,0) \text {, }\)

What are the coordinates of the \( 4^{\text {th }} \) vertex?

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

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


Prompt:
Misconception:
Only applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction

Question:
Simplify the following if possible: \( \frac{6+9 m}{3} \)

Options:
A. \( 2+3 m \)
B. \( 6+3 m \)
C. \( 2+9 m \)
D. None of the options

Solve the problem as a student with the misconception above.
You 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 applies a division to one of multiple terms in a numerator when simplifying an algebraic fraction

Question:
Simplify the following if possible: \( \frac{6+9 m}{3} \)

Options:
A. \( 2+3 m \)
B. \( 6+3 m \)
C. \( 2+9 m \)
D. None of the options

Solve the problem as a student with the misconception above.
You 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 simplify algebraic fractions

Question:
Simplify the following if possible: \( \frac{6+9 m}{3} \)

Options:
A. \( 2+3 m \)
B. \( 6+3 m \)
C. \( 2+9 m \)
D. None of the options

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


Prompt:
Misconception:
Converted seconds to minutes instead of seconds to hours

Question:
How many hours is \( 3600 \) seconds?

Options:
A. \( 60 \)
B. \( 36 \)
C. \( 3.6 \)
D. \( 1 \)

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


Prompt:
Misconception:
Thinks there are 100 seconds in an hour

Question:
How many hours is \( 3600 \) seconds?

Options:
A. \( 60 \)
B. \( 36 \)
C. \( 3.6 \)
D. \( 1 \)

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


Prompt:
Misconception:
Thinks there are 1000 seconds in an hour

Question:
How many hours is \( 3600 \) seconds?

Options:
A. \( 60 \)
B. \( 36 \)
C. \( 3.6 \)
D. \( 1 \)

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


Prompt:
Misconception:
Thinks the sign of solutions in a quadratic equation is always the same as the constant term

Question:
Tom and Katie are discussing how to solve this quadratic equation:
\(
(5 x+2)(2 x-5)=0
\)

Tom says one solution is: \( x=\frac{2}{5} \)

Katie says one solution is: \( x=-\frac{5}{2} \)

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:
Believes that the solution to ax + b = 0 is x = -a/b

Question:
Tom and Katie are discussing how to solve this quadratic equation:
\(
(5 x+2)(2 x-5)=0
\)

Tom says one solution is: \( x=\frac{2}{5} \)

Katie says one solution is: \( x=-\frac{5}{2} \)

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:
Believes that fractions with larger denominators are greater in size

Question:
Which signs belong in the boxes to make the statement correct?
\(
\frac{1}{5} \;\square\; \frac{1}{6}\; \square \;\frac{1}{3}
\)

Options:
A. \( >< \)
B. \( << \)
C. \( >> \)
D. \( <> \)

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


Prompt:
Misconception:
Thinks the interior angles of any polygon add up to 360

Question:
What do all the interior angles of this shape add up to? ![Irregular hexagon]()

Options:
A. \( 360^{\degree} \)
B. \( 540^{\degree} \)
C. \( 720^{\degree} \)
D. Not enough information to work it out

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


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

Question:
What do all the interior angles of this shape add up to? ![Irregular hexagon]()

Options:
A. \( 360^{\degree} \)
B. \( 540^{\degree} \)
C. \( 720^{\degree} \)
D. Not enough information to work it out

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


Prompt:
Misconception:
Believes that you are unable to calculate the sum of the interior angles of an irregular polygon given the number of sides

Question:
What do all the interior angles of this shape add up to? ![Irregular hexagon]()

Options:
A. \( 360^{\degree} \)
B. \( 540^{\degree} \)
C. \( 720^{\degree} \)
D. Not enough information to work it out

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


Prompt:
Misconception:
Uses sin when cos is required

Question:
Which ratio would you use to find the value of \( \theta \) ? ![A right angled triangle with the longest side labelled 10cm. The base of the triangle is 6cm. The angle made between the 6cm and 10cm sides is labelled as 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 tan when cos is required

Question:
Which ratio would you use to find the value of \( \theta \) ? ![A right angled triangle with the longest side labelled 10cm. The base of the triangle is 6cm. The angle made between the 6cm and 10cm sides is labelled as 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 longest side labelled 10cm. The base of the triangle is 6cm. The angle made between the 6cm and 10cm sides is labelled as 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:
Identifies the first term rather than the next term in a sequence

Question:
\(
x_{n+1}=5-\frac{1}{x_{n}}
\)

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

Options:
A. \( 2 \)
B. \( 4.5 \)
C. \( 4.7777 \ldots \)
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 asked for a specific term in a sequence gives the term after

Question:
\(
x_{n+1}=5-\frac{1}{x_{n}}
\)

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

Options:
A. \( 2 \)
B. \( 4.5 \)
C. \( 4.7777 \ldots \)
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:
Believes the gradient of a line is given by an intercept

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

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

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


Prompt:
Misconception:
Thinks the gradient of a line includes the variable x

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

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

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

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

Options:
A. \( -1+2 p \)
B. \( -1-2 p \)
C. \( 1+2 p \)
D. \( 1-2 p \)

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


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

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

Options:
A. \( -1+2 p \)
B. \( -1-2 p \)
C. \( 1+2 p \)
D. \( 1-2 p \)

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


Prompt:
Misconception:
Ignores negative sign when expanding bracket

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

Options:
A. \( -1+2 p \)
B. \( -1-2 p \)
C. \( 1+2 p \)
D. \( 1-2 p \)

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


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

Question:
When Aneesa expands these brackets, how many terms should she get after she simplifies? \( (p+3)(p+4)(p+5) \)

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

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


Prompt:
Misconception:
Believes that they can fully factorise an expression by taking out any common factor, not just the HCF

Question:
Factorise fully \( 18 a-12 \)

Options:
A. \( 2(9 a-6) \)
B. \( 18(a-6) \)
C. \( 6(3 a-2) \)
D. \( 9(2 a-1) \)

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 factorising into single brackets, factorises the first term correctly but subtracts the number outside the bracket with the second term in the expression to find the second term in the bracket

Question:
Factorise fully \( 18 a-12 \)

Options:
A. \( 2(9 a-6) \)
B. \( 18(a-6) \)
C. \( 6(3 a-2) \)
D. \( 9(2 a-1) \)

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:
Counts leading zero as a significant figure

Question:
When estimating the answer to a complicated problem involving \( 0.0584 \), you should instead use...

Options:
A. \( 0 \)
B. \( 0.05 \)
C. \( 0.058 \)
D. \( 0.06 \)

Solve the problem as a student with the misconception above.
You 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:
When estimating the answer to a complicated problem involving \( 0.0584 \), you should instead use...

Options:
A. \( 0 \)
B. \( 0.05 \)
C. \( 0.058 \)
D. \( 0.06 \)

Solve the problem as a student with the misconception above.
You 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 too little when estimating

Question:
When estimating the answer to a complicated problem involving \( 0.0584 \), you should instead use...

Options:
A. \( 0 \)
B. \( 0.05 \)
C. \( 0.058 \)
D. \( 0.06 \)

Solve the problem as a student with the misconception above.
You 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 to find the next traingle number you add the previous two numbers together i.e. Fibonacci

Question:
Here are two consecutive triangle numbers: \( 120,136, \ldots \) What is the next triangle number in the sequence?

Options:
A. \( 153 \)
B. \( 256 \)
C. \( 151 \)
D. \( 152 \)

Solve the problem as a student with the misconception above.
You 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 difference between triangle numbers decreases by 1 each time

Question:
Here are two consecutive triangle numbers: \( 120,136, \ldots \) What is the next triangle number in the sequence?

Options:
A. \( 153 \)
B. \( 256 \)
C. \( 151 \)
D. \( 152 \)

Solve the problem as a student with the misconception above.
You 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 difference between triangle numbers remains the same

Question:
Here are two consecutive triangle numbers: \( 120,136, \ldots \) What is the next triangle number in the sequence?

Options:
A. \( 153 \)
B. \( 256 \)
C. \( 151 \)
D. \( 152 \)

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


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

Question:
Which answer shows the correct factorisation of:
\(
x^{2}-x-6
\)

Options:
A. \( (x-3)(x+2) \)
B. \( (x-3)(x-2) \)
C. \( (x+3)(x+2) \)
D. \( (x+3)(x-2) \)

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


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

Question:
Which answer shows the correct factorisation of:
\(
x^{2}-x-6
\)

Options:
A. \( (x-3)(x+2) \)
B. \( (x-3)(x-2) \)
C. \( (x+3)(x+2) \)
D. \( (x+3)(x-2) \)

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


Prompt:
Misconception:
Converts fraction to percentage by multiplying the denominator by 10

Question:
This four-sided spinner is fair.
What is the probability of spinning a \( 2 \) ?
Give your answer as a percentage ![A four sided spinner labelled with 1, 2, 3 and 4]()

Options:
A. \( 25 \% \)
B. \( 40 \% \)
C. \( 20 \% \)
D. \( 33.333 \ldots \% \)

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


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

Question:
The fractions in the two circles below add to give the fraction in the circle above.

What should replace the question mark? ![Fractions 3/5 and 1/4 in two separate circles, both linked to a third circle above.]()

Options:
A. \( \frac{4}{9} \)
B. \( \frac{4}{20} \)
C. \( \frac{7}{20} \)
D. \( \frac{17}{20} \)

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


Prompt:
Misconception:
When adding fractions, changes to common denominator but leaves numerators the same

Question:
The fractions in the two circles below add to give the fraction in the circle above.

What should replace the question mark? ![Fractions 3/5 and 1/4 in two separate circles, both linked to a third circle above.]()

Options:
A. \( \frac{4}{9} \)
B. \( \frac{4}{20} \)
C. \( \frac{7}{20} \)
D. \( \frac{17}{20} \)

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


Prompt:
Misconception:
Believes you multiply the constant difference by the term number to get the term value

Question:
Here are the first \( 4 \) terms of a sequence \( \begin{array}{lllll}11 & 15 & 19 & 23 & \ldots\end{array} \) What position in the sequence is the number \( 67 \) ?

Options:
A. \( 16.75 \)
B. \( 275 \)
C. \( 4 n+7 \)
D. \( 15 \)

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


Prompt:
Misconception:
When factorising a quadratic without a non variable term, tries to double bracket factorise

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

Options:
A. \( p(p+100) \)
B. \( (p-10)(p+10) \)
C. \( (p+10)(p+10) \)
D. Does not factorise

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


Prompt:
Misconception:
When factorising a quadratic without a non variable term, tries to double bracket factorise

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

Options:
A. \( p(p+100) \)
B. \( (p-10)(p+10) \)
C. \( (p+10)(p+10) \)
D. Does not factorise

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


Prompt:
Misconception:
Thinks a quadratic without a non variable term, can not be factorised

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

Options:
A. \( p(p+100) \)
B. \( (p-10)(p+10) \)
C. \( (p+10)(p+10) \)
D. Does not factorise

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


Prompt:
Misconception:
Believes reflection in y = -x changes sign of x coordinate only

Question:
A point, \( Q \), has coordinates \( (-3,3) \)
The point is reflected in the line \( y=-x \)
What are the new coordinates of point \( Q \) ?

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

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


Prompt:
Misconception:
Believes reflection in y = -x changes sign of y coordinate only

Question:
A point, \( Q \), has coordinates \( (-3,3) \)
The point is reflected in the line \( y=-x \)
What are the new coordinates of point \( Q \) ?

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

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


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

Question:
A point, \( Q \), has coordinates \( (-3,3) \)
The point is reflected in the line \( y=-x \)
What are the new coordinates of point \( Q \) ?

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

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


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

Question:
\(
20.4593
\)

What is the first significant figure in the number above?

Options:
A. \( 2 \)
B. \( 0 \)
C. \( 4 \)
D. \( 5 \)

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


Prompt:
Misconception:
Identifies first decimal place value when asked for first significant figure

Question:
\(
20.4593
\)

What is the first significant figure in the number above?

Options:
A. \( 2 \)
B. \( 0 \)
C. \( 4 \)
D. \( 5 \)

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


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

Question:
\(
20.4593
\)

What is the first significant figure in the number above?

Options:
A. \( 2 \)
B. \( 0 \)
C. \( 4 \)
D. \( 5 \)

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


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

Question:
The dashes on the sides tell us that this is a \(__________\) polygon

What word completes the sentence? ![A shape with five equal sides. Each side has a small dash through the middle.]()

Options:
A. Parallel
B. Pentagon
C. Irregular
D. Regular

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


Prompt:
Misconception:
Does not know what dashes on the sides of shapes mean

Question:
The dashes on the sides tell us that this is a \(__________\) polygon

What word completes the sentence? ![A shape with five equal sides. Each side has a small dash through the middle.]()

Options:
A. Parallel
B. Pentagon
C. Irregular
D. Regular

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


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

Question:
The dashes on the sides tell us that this is a \(__________\) polygon

What word completes the sentence? ![A shape with five equal sides. Each side has a small dash through the middle.]()

Options:
A. Parallel
B. Pentagon
C. Irregular
D. Regular

Solve the problem as a student with the misconception above.
You 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 differences between terms in a sequence, believes they can do so from right to left

Question:
\(10,21,34,49,66, \ldots\)

When calculating the nth-term rule of this sequence,
what should replace the triangle?

nth-term rule: \( n^{2} \)\( \color{red}\triangle \)  \(n\) \( \color{purple}\square \)

Options:
A. \( 5.5 \)
B. \( -8 \)
C. \[
+1
\]
(or just a + sign)
D. \( +8 \)

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


Prompt:
Misconception:
When finding the nth term rule for a quadratic sequence, believes that the coefficient of n is half the second difference

Question:
\(10,21,34,49,66, \ldots\)

When calculating the nth-term rule of this sequence,
what should replace the triangle?

nth-term rule: \( n^{2} \)\( \color{red}\triangle \)  \(n\) \( \color{purple}\square \)

Options:
A. \( 5.5 \)
B. \( -8 \)
C. \[
+1
\]
(or just a + sign)
D. \( +8 \)

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


Prompt:
Misconception:
Estimated when not appropriate

Question:
Find the value of \( P \). ![Horizontal green bar divided into 5 equal sections. Each section is labelled with a "P". Curly bracket shows that 3 of the sections sum to 615.]()

Options:
A. \( 200 \)
B. \( 123 \)
C. \( 205 \)
D. \( 1845 \)

Solve the problem as a student with the misconception above.
You 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 amount given is for the whole rather than a part

Question:
Find the value of \( P \). ![Horizontal green bar divided into 5 equal sections. Each section is labelled with a "P". Curly bracket shows that 3 of the sections sum to 615.]()

Options:
A. \( 200 \)
B. \( 123 \)
C. \( 205 \)
D. \( 1845 \)

Solve the problem as a student with the misconception above.
You 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 instead of divides to find one part given the total

Question:
Find the value of \( P \). ![Horizontal green bar divided into 5 equal sections. Each section is labelled with a "P". Curly bracket shows that 3 of the sections sum to 615.]()

Options:
A. \( 200 \)
B. \( 123 \)
C. \( 205 \)
D. \( 1845 \)

Solve the problem as a student with the misconception above.
You 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 positive by a negative gives a positive answer

Question:
Here is the graph of
\(
y=\frac{4}{x}
\)

What is the value of \( y \) when \( x=-1 \) ? ![A graph with two curves. Y axis from -5 to 5 and x axis from -5 to 5 marked in increments of 1.  One curve is in the positive x, positive y quadrant. It starts at the top close to the line x = 1, as we move right it drops very quickly towards the x axis then levels off to travel almost parallel to the line y =1. It goes through (1, 4) (2,2) and (4,1).  One curve is in the negative x negative y quadrant. It starts at the top left of the quadrant almost parallel to y = -1, then we move right and it curves downwards towards the y axis then levels off to travel almost parallel to the x = -1 line. It goes through (-4, -1) (-2, -2) and (-1,-4)]()

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

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:
Cannot estimate the relative volume order, for different objects

Question:
Each of these measurements matches one of these objects. ![An image of 4 objects and 4 measurements. The objects are an egg cup, a cereal box, a chest of drawers and a piggy bank. And, the measurements are 87 cm^3, 1013 cm^3, 4172 cm^3 and 197,177 cm^3.]() Which measurement most likely matches the egg cup?

Options:
A. \( 87 \mathrm{~cm}^{3} \)
B. \( 1013 \mathrm{~cm}^{3} \)
C. \( 4172 \mathrm{~cm}^{3} \)
D. \( 197177 \mathrm{~cm}^{3} \)

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:
Cannot estimate the relative volume order, for different objects

Question:
Each of these measurements matches one of these objects. ![An image of 4 objects and 4 measurements. The objects are an egg cup, a cereal box, a chest of drawers and a piggy bank. And, the measurements are 87 cm^3, 1013 cm^3, 4172 cm^3 and 197,177 cm^3.]() Which measurement most likely matches the egg cup?

Options:
A. \( 87 \mathrm{~cm}^{3} \)
B. \( 1013 \mathrm{~cm}^{3} \)
C. \( 4172 \mathrm{~cm}^{3} \)
D. \( 197177 \mathrm{~cm}^{3} \)

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:
Cannot estimate the relative volume order, for different objects

Question:
Each of these measurements matches one of these objects. ![An image of 4 objects and 4 measurements. The objects are an egg cup, a cereal box, a chest of drawers and a piggy bank. And, the measurements are 87 cm^3, 1013 cm^3, 4172 cm^3 and 197,177 cm^3.]() Which measurement most likely matches the egg cup?

Options:
A. \( 87 \mathrm{~cm}^{3} \)
B. \( 1013 \mathrm{~cm}^{3} \)
C. \( 4172 \mathrm{~cm}^{3} \)
D. \( 197177 \mathrm{~cm}^{3} \)

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 the equations of vertical and horizontal lines

Question:
What is the equation of this line? ![The diagram shows a pair of axes, x and y ranging from -6 to 5 horizontally and -3 to 4 vertically. There is a horizontal line that passes through the y axis at -2. ]()

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

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:
Includes the x variable when giving the equation of a horizontal line

Question:
What is the equation of this line? ![The diagram shows a pair of axes, x and y ranging from -6 to 5 horizontally and -3 to 4 vertically. There is a horizontal line that passes through the y axis at -2. ]()

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

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


Prompt:
Misconception:
Believes the equation for a horizontal line is in the form xy = a, where a is the y intercept

Question:
What is the equation of this line? ![The diagram shows a pair of axes, x and y ranging from -6 to 5 horizontally and -3 to 4 vertically. There is a horizontal line that passes through the y axis at -2. ]()

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

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


Prompt:
Misconception:
Confuses an equation with an identity

Question:
Which of the following is the most appropriate name for this:
\(p-3 \equiv-(3-p)\)

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

Solve the problem as a student with the misconception above.
You 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 incorrect belief about the meaning of "expression"

Question:
Which of the following is the most appropriate name for this:
\(p-3 \equiv-(3-p)\)

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

Solve the problem as a student with the misconception above.
You 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 incorrect belief about the meaning of "formula"

Question:
Which of the following is the most appropriate name for this:
\(p-3 \equiv-(3-p)\)

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

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


Prompt:
Misconception:
Confuses all possible outcomes with options available

Question:
This is a fair spinner.

How many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]()

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

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:
Fails to consider all possible outcomes

Question:
This is a fair spinner.

How many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]()

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

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:
Lists outcomes rather than counts how many outcomes

Question:
This is a fair spinner.

How many possible outcomes are there if it is spun once? ![A hexagonal shaped spinner with 6 equal sections labelled 1, 3, 3, 5, 5 and 5.]()

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

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

Question:
Which of the following answers shows a correct expansion of the expression below? \( (x-2)^{3} \)

Options:
A. \( x^{3}-8 \)
B. \( x^{3}-6 x^{2}-6 x-8 \)
C. \( x^{3}-6 x^{2}+12 x-8 \)
D. \( x^{3}-12 x^{2}+6 x-8 \)

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


Prompt:
Misconception:
Has not noticed the difference between 'subtract' and 'subtract from'

Question:
Tom and Katie are discussing the output of this 2-step function machine ![A two step function machine with x as the input. The first functions is x5 and the second function says 'subtracted from 8'. The output is blank.]() Tom says the output is \( \mathbf{5} \boldsymbol{x}-\mathbf{8} \)

Katie says the output is \( \mathbf{8}-\mathbf{5} \boldsymbol{x} \)

Who is correct?

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

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


Prompt:
Misconception:
Has not noticed the difference between 'subtract' and 'subtract from'

Question:
Tom and Katie are discussing the output of this 2-step function machine ![A two step function machine with x as the input. The first functions is x5 and the second function says 'subtracted from 8'. The output is blank.]() Tom says the output is \( \mathbf{5} \boldsymbol{x}-\mathbf{8} \)

Katie says the output is \( \mathbf{8}-\mathbf{5} \boldsymbol{x} \)

Who is correct?

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

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


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

Question:
Jamie is counting up in threes. He starts at \( -14 \).

What is the \( 5^{\text {th }} \) number he says?

Options:
A. \( -26 \)
B. \( 1 \)
C. \( -2 \)
D. \( -29 \)

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


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

Question:
Jamie is counting up in threes. He starts at \( -14 \).

What is the \( 5^{\text {th }} \) number he says?

Options:
A. \( -26 \)
B. \( 1 \)
C. \( -2 \)
D. \( -29 \)

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


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

Question:
What is \( \mathbf{1 6 5 1 . 4 3} \) rounded to the nearest hundred?

Options:
A. \( 1700 \)
B. \( 2000 \)
C. \( 1600 \)
D. \( 1650 \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( \mathbf{1 6 5 1 . 4 3} \) rounded to the nearest hundred?

Options:
A. \( 1700 \)
B. \( 2000 \)
C. \( 1600 \)
D. \( 1650 \)

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


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

Question:
What is \( \mathbf{1 6 5 1 . 4 3} \) rounded to the nearest hundred?

Options:
A. \( 1700 \)
B. \( 2000 \)
C. \( 1600 \)
D. \( 1650 \)

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


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

Question:
What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]()

Options:
A. \( 15^{\circ} \)
B. \( 165^{\circ} \)
C. \( 0^{\circ} \)
D. This is not an angle

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


Prompt:
Misconception:
Reads 0 on protractor as size of angle when angle is not in usual orientation

Question:
What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]()

Options:
A. \( 15^{\circ} \)
B. \( 165^{\circ} \)
C. \( 0^{\circ} \)
D. This is not an angle

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


Prompt:
Misconception:
Thinks angles can only be measured when one line is horizontal

Question:
What is the size of this angle? ![An image of a protractor. There is a red line going from the middle to 0/180 and another line from the middle to in between 160/20 and 170/10. ]()

Options:
A. \( 15^{\circ} \)
B. \( 165^{\circ} \)
C. \( 0^{\circ} \)
D. This is not an angle

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


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

Question:
Convert this fraction to a percentage
\( \frac{4}{5} \)

Options:
A. \( 80 \% \)
B. \( 40 \% \)
C. \( 45 \% \)
D. \( 75 \% \)

Solve the problem as a student with the misconception above.
You 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 factors of an algebraic expression, thinks any part of a term will be a factor

Question:
Which of the following is a factor of: \( 6 n^{2}-9 \)

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

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


Prompt:
Misconception:
When asked for factors of an algebraic expression, thinks a term will be a factor

Question:
Which of the following is a factor of: \( 6 n^{2}-9 \)

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

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


Prompt:
Misconception:
When asked for factors of an algebraic expression, thinks any part of a term will be a factor

Question:
Which of the following is a factor of: \( 6 n^{2}-9 \)

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

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


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

Question:
Which region describes where \( \boldsymbol{x}>\mathbf{0} \) and \( \boldsymbol{y}<\mathbf{0} \) ? ![A set of axis showing all four quadrants. y axis from -3 to 3 and x axis from -3 to 3]()

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

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


Prompt:
Misconception:
Believes 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: \( S=\{5,6\} \)

Katie says the sample space can be written as: \( S=\{5,5,6,6,6\} \)
Who do you agree with? ![A circle divided into 5 equal sections. 3 of the sections are labelled with a purple number 6. 2 of the sections are labelled with a blue number 5.]()

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

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


Prompt:
Misconception:
Believes greater than/less than symbols include end values

Question:
In which region would \( x=-5.3 \) belong? ![A Venn diagram made up of two overlapping circles. One circle is labelled x+5.3 is less than or equal to 0 and the other circle is labelled -(5.3+x)/2 is greater than 0.
A is in the x+5.3 is less than or equal to 0 circle only.
B is in the overlap of the two circles.
C is in the -(5.3+x)/2 is great than 0 circle only.
D is outside both circles.]()

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

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


Prompt:
Misconception:
Thinks there are 100kg in a tonne

Question:
\( 3000 \mathrm{~kg} \) is the same as \( ___ \) tonnes

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000000 \)

Solve the problem as a student with the misconception above.
You 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 10kg in a tonne

Question:
\( 3000 \mathrm{~kg} \) is the same as \( ___ \) tonnes

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000000 \)

Solve the problem as a student with the misconception above.
You 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:
\( 3000 \mathrm{~kg} \) is the same as \( ___ \) tonnes

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000000 \)

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


Prompt:
Misconception:
Halves when asked to find the square root

Question:
What is the square root of sixteen?

Options:
A. \( 8 \)
B. \( 32 \)
C. \( 256 \)
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:
Mixes up square rooting and multiplying by 2 or doubling

Question:
What is the square root of sixteen?

Options:
A. \( 8 \)
B. \( 32 \)
C. \( 256 \)
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:
Squares when asked to find the square root

Question:
What is the square root of sixteen?

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

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


Prompt:
Misconception:
Rounds up instead of down

Question:
Round this number to \( 1 \) significant figure:
\[
73975
\]

Options:
A. \( 70000 \)
B. \( 80000 \)
C. \( 7 \)
D. \( 74000 \)

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


Prompt:
Misconception:
Forgotten placeholders when rounding to significant figures

Question:
Round this number to \( 1 \) significant figure:
\[
73975
\]

Options:
A. \( 70000 \)
B. \( 80000 \)
C. \( 7 \)
D. \( 74000 \)

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


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

Question:
Round this number to \( 1 \) significant figure:
\[
73975
\]

Options:
A. \( 70000 \)
B. \( 80000 \)
C. \( 7 \)
D. \( 74000 \)

Solve the problem as a student with the misconception above.
You 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:
A taxi company has a \( £ 1.50 \) fixed charge and then charges \( 60 p \) per mile. Sam correctly sketches a graph to show the cost of different length journeys with the company. Which of the following graphs would best match Sam's sketch?

Options:
A. ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at a point on the positive horizontal axis and travels horizontally right and upwards in a steep straight line.]()
B. ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at a point on the positive vertical axis and travels horizontally right.]()
C. ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at the origin and travels in a straight line right and upwards.]()
D. ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at a point on the positive vertical axis and travels horizontally right and upwards in a straight line.]()

Solve the problem as a student with the misconception above.
You 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 a graph always starts at the origin

Question:
A taxi company has a \( £ 1.50 \) fixed charge and then charges \( 60 p \) per mile. Sam correctly sketches a graph to show the cost of different length journeys with the company. Which of the following graphs would best match Sam's sketch?

Options:
A. ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at a point on the positive horizontal axis and travels horizontally right and upwards in a steep straight line.]()
B. ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at a point on the positive vertical axis and travels horizontally right.]()
C. ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at the origin and travels in a straight line right and upwards.]()
D. ![A graph with distance on the horizontal axis and cost on the vertical axis. The graph starts at a point on the positive vertical axis and travels horizontally right and upwards in a straight line.]()

Solve the problem as a student with the misconception above.
You 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 multiplying two or more negative numbers together always gives a positive answer, regardless of how many negative numbers there are in the sum

Question:
Tom and Katie are discussing the table of values for \( \boldsymbol{y}=\boldsymbol{x}^{\mathbf{3}} \) \begin{tabular}{|l|l|}
\hline\( x \) & \(\color{gold}\bigstar\) \\
\hline\( y \) & \( 27 \) \\
\hline
\end{tabular} Tom says the star could be \( 3 \).

Katie says the star could be \( -3 \).

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:
Adds instead of multiplying when expanding bracket

Question:
What should replace the circle when these two brackets are expanded and simplified?
\(
(p+5)(p-4) \equiv p^{2} \triangle p \bigcirc
\)

Options:
A. \( \bigcirc=+1 \)
B. \( \bigcirc=+20 \)
C. \( \bigcirc=-9 \)
D. \( \bigcirc=-20 \)

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


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

Question:
What should replace the circle when these two brackets are expanded and simplified?
\(
(p+5)(p-4) \equiv p^{2} \triangle p \bigcirc
\)

Options:
A. \( \bigcirc=+1 \)
B. \( \bigcirc=+20 \)
C. \( \bigcirc=-9 \)
D. \( \bigcirc=-20 \)

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


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

Question:
What number is \( 100 \) less than \( 876,099 ? \)

Options:
A. \( 876.099 \)
B. \( 876,199 \)
C. \( 875,999 \)
D. \( 875,099 \)

Solve the problem as a student with the misconception above.
You 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 \( 876,099 ? \)

Options:
A. \( 876.099 \)
B. \( 876,199 \)
C. \( 875,999 \)
D. \( 875,099 \)

Solve the problem as a student with the misconception above.
You 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:
\( 50.09 \div 0.1= \)

Options:
A. \( 50.009 \)
B. \( 500.9 \)
C. \( 500.09 \)
D. \( 5.009 \)

Solve the problem as a student with the misconception above.
You 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:
\( 50.09 \div 0.1= \)

Options:
A. \( 50.009 \)
B. \( 500.9 \)
C. \( 500.09 \)
D. \( 5.009 \)

Solve the problem as a student with the misconception above.
You 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 by 0.1 is the same as dividing by 10

Question:
\( 50.09 \div 0.1= \)

Options:
A. \( 50.009 \)
B. \( 500.9 \)
C. \( 500.09 \)
D. \( 5.009 \)

Solve the problem as a student with the misconception above.
You 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 minutes in an hour

Question:
\( 0.6 \) hours \( = _____\) minutes

Options:
A. \( 6 \)
B. \( 120 \)
C. \( 36 \)
D. \( 60 \)

Solve the problem as a student with the misconception above.
You 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:
\( 0.6 \) hours \( = _____\) minutes

Options:
A. \( 6 \)
B. \( 120 \)
C. \( 36 \)
D. \( 60 \)

Solve the problem as a student with the misconception above.
You 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 identifies angles as vertically opposite

Question:
What is the size of angle \( x \) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]()

Options:
A. \( 290^{\circ} \)
B. \( 70^{\circ} \)
C. \( 50^{\circ} \)
D. \( 45^{\circ} \)

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


Prompt:
Misconception:
Does not know that angles around a point sum to 360

Question:
What is the size of angle \( x \) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]()

Options:
A. \( 290^{\circ} \)
B. \( 70^{\circ} \)
C. \( 50^{\circ} \)
D. \( 45^{\circ} \)

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


Prompt:
Misconception:
Does not know that angles around a point sum to 360

Question:
What is the size of angle \( x \) ? ![Angles around a point split into two parts, one is labelled 290 degrees and the other x]()

Options:
A. \( 290^{\circ} \)
B. \( 70^{\circ} \)
C. \( 50^{\circ} \)
D. \( 45^{\circ} \)

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


Prompt:
Misconception:
Changes the given operation when substituting

Question:
\[
x+y=8
\]
Which pair of numbers fits the equation?

Options:
A. \( \begin{array}{l}x=10 \\ y=2\end{array} \)
B. \( \begin{array}{c}x=10 \\ y=-2\end{array} \)
C. \( \begin{array}{l}x=8 \\ y=1\end{array} \)
D. \( \begin{array}{c}x=-8 \\ y=1\end{array} \)

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:
Changes the given operation when substituting

Question:
\[
x+y=8
\]
Which pair of numbers fits the equation?

Options:
A. \( \begin{array}{l}x=10 \\ y=2\end{array} \)
B. \( \begin{array}{c}x=10 \\ y=-2\end{array} \)
C. \( \begin{array}{l}x=8 \\ y=1\end{array} \)
D. \( \begin{array}{c}x=-8 \\ y=1\end{array} \)

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:
substitutes incorrectly

Question:
\[
x+y=8
\]
Which pair of numbers fits the equation?

Options:
A. \( \begin{array}{l}x=10 \\ y=2\end{array} \)
B. \( \begin{array}{c}x=10 \\ y=-2\end{array} \)
C. \( \begin{array}{l}x=8 \\ y=1\end{array} \)
D. \( \begin{array}{c}x=-8 \\ y=1\end{array} \)

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

Question:
What number is \( 10,000 \) less than \( 509,570 \) ?

Options:
A. \( 499,570 \)
B. \( 519,570 \)
C. \( 50.957 \)
D. \( 409,570 \)

Solve the problem as a student with the misconception above.
You 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 \( 10,000 \) less than \( 509,570 \) ?

Options:
A. \( 499,570 \)
B. \( 519,570 \)
C. \( 50.957 \)
D. \( 409,570 \)

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