Prompt:
Misconception:
Thinks it can't be called a sequence with a repeated number at the start

Question:
Tom and Katie are discussing Fibonacci sequences.

Tom says this is a Fibonacci sequence: \( 1,1,2,3,5,8, \ldots \)

Katie says this is a Fibonacci sequence: \( 1,2,3,5,8,13, \ldots \)

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 what a Fibonacci sequence is

Question:
Tom and Katie are discussing Fibonacci sequences.

Tom says this is a Fibonacci sequence: \( 1,1,2,3,5,8, \ldots \)

Katie says this is a Fibonacci sequence: \( 1,2,3,5,8,13, \ldots \)

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:
Thinks there are 7 hours in 1 day

Question:
To work out how many hours in a year you could do...

Options:
A. \( 365 \times 7 \)
B. \( 365 \times 60 \)
C. \( 365 \times 12 \)
D. \( 365 \times 24 \)

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


Prompt:
Misconception:
Answers as if there are 60 hours in a day

Question:
To work out how many hours in a year you could do...

Options:
A. \( 365 \times 7 \)
B. \( 365 \times 60 \)
C. \( 365 \times 12 \)
D. \( 365 \times 24 \)

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


Prompt:
Misconception:
Thinks there are 12 hours in 1 day

Question:
To work out how many hours in a year you could do...

Options:
A. \( 365 \times 7 \)
B. \( 365 \times 60 \)
C. \( 365 \times 12 \)
D. \( 365 \times 24 \)

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


Prompt:
Misconception:
Believes we can only take the square root of a perfect square

Question:
One of these equations has no real solutions
Which is it?

Options:
A. \( (w+5)^{2}+25=0 \)
B. \( (w+5)^{2}-25=0 \)
C. \( (w+5)^{2}-5=0 \)
D. \( (w+5)^{2}=0 \)

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


Prompt:
Misconception:
Believes 0 is not a real solution to an equation

Question:
One of these equations has no real solutions
Which is it?

Options:
A. \( (w+5)^{2}+25=0 \)
B. \( (w+5)^{2}-25=0 \)
C. \( (w+5)^{2}-5=0 \)
D. \( (w+5)^{2}=0 \)

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


Prompt:
Misconception:
When multiplying a fraction by an integer, multiplies the denominator instead of the numerator

Question:
\( \frac{2}{7} \times 3=3 \div K \times L \)

Options:
A. \( \begin{array}{l}K=7 \\ L=2\end{array} \)
B. \( \begin{array}{l}K=2 \\ L=7\end{array} \)
C. \( \begin{array}{l}K=7 \\ L=7\end{array} \)
D. Not possible

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


Prompt:
Misconception:
Does not realize we can write a division as a fraction

Question:
\( \frac{2}{7} \times 3=3 \div K \times L \)

Options:
A. \( \begin{array}{l}K=7 \\ L=2\end{array} \)
B. \( \begin{array}{l}K=2 \\ L=7\end{array} \)
C. \( \begin{array}{l}K=7 \\ L=7\end{array} \)
D. Not possible

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


Prompt:
Misconception:
When solving an equation thinks they divide when in fact they need to multiply

Question:
What should replace the star? \( \bigstar \div 0.3=1.5 \)

Options:
A. \( 0.5 \)
B. \( 0.45 \)
C. \( 1.8 \)
D. \( 0.2 \)

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


Prompt:
Misconception:
When solving an equation thinks they add when in fact they need to multiply

Question:
What should replace the star? \( \bigstar \div 0.3=1.5 \)

Options:
A. \( 0.5 \)
B. \( 0.45 \)
C. \( 1.8 \)
D. \( 0.2 \)

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


Prompt:
Misconception:
When solving an equation thinks they divide when in fact they need to multiply

Question:
What should replace the star? \( \bigstar \div 0.3=1.5 \)

Options:
A. \( 0.5 \)
B. \( 0.45 \)
C. \( 1.8 \)
D. \( 0.2 \)

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


Prompt:
Misconception:
Mixes up sides of a ratio

Question:
For every \( 2 \) marbles Karen has, Marty has \( 3 \).
Write the number of marbles Karen and Marty have as a ratio, with Karen's part first.

Options:
A. \( 3\; : 2 \)
B. \( 2\; : 3\; : 5 \)
C. \( 2\; : 5 \)
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:
Thinks you need to include the total as well as the individual parts when asked to write a ratio

Question:
For every \( 2 \) marbles Karen has, Marty has \( 3 \).
Write the number of marbles Karen and Marty have as a ratio, with Karen's part first.

Options:
A. \( 3\; : 2 \)
B. \( 2\; : 3\; : 5 \)
C. \( 2\; : 5 \)
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:
When writing ratio, writes total as one side

Question:
For every \( 2 \) marbles Karen has, Marty has \( 3 \).
Write the number of marbles Karen and Marty have as a ratio, with Karen's part first.

Options:
A. \( 3\; : 2 \)
B. \( 2\; : 3\; : 5 \)
C. \( 2\; : 5 \)
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:
Selects y>a solutions instead of y<a solutions for a quadratic inequality

Question:
Use the graph to approximate the solution to \( x^{2}<5 \) ![A set of axes with the quadratic graph y=x^2 drawn on.]()

Options:
A. \( x<25 \)
B. \( -2.2<x<2.2 \)
C. \( x<-2.2, x>2.2 \)
D. \( x \geq 0 \)

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


Prompt:
Misconception:
Thinks the number in the ratio is the total

Question:
The ratio of cars to vans in a car park is \( 5: 3 \)

If there are \( 80 \) cars, how many vehicles (cars and vans) are there in total?

Options:
A. \( 83 \)
B. \( 48 \)
C. \( 128 \)
D. \( 110 \)

Solve the problem as a student with the misconception above.
You 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 notice all changes in a sequence of visual patterns

Question:
Without drawing any more terms, how many circles do you predict will be in the \( 5 \) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()

Options:
A. \( 30 \)
B. \( 18 \)
C. \( 24 \)
D. \( 22 \)

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


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

Question:
Without drawing any more terms, how many circles do you predict will be in the \( 5 \) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()

Options:
A. \( 30 \)
B. \( 18 \)
C. \( 24 \)
D. \( 22 \)

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


Prompt:
Misconception:
Does not notice all changes in a sequence of visual patterns

Question:
Without drawing any more terms, how many circles do you predict will be in the \( 5 \) th term of this sequence? ![A diagram showing the first 3 patterns in a sequence. Pattern 1 is a rectangle with a total of 6 circles surrounding it. Pattern 2 is 2 rectangles with a total of 10 circles surrounding it. Pattern 3 is 3 rectangles with a total of 14 circles surrounding it.]()

Options:
A. \( 30 \)
B. \( 18 \)
C. \( 24 \)
D. \( 22 \)

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


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

Question:
What should replace the question mark? ![A bar split into 8 equal parts. 3 of the parts are shaded, and the total length of these 3 parts is labelled 3/4. The total length of 6 parts is labelled with a question mark.]()

Options:
A. \( \frac{6}{8} \)
B. \( 6 \)
C. \( \frac{6}{3} \)
D. \( \frac{6}{4} \)

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


Prompt:
Misconception:
Believes that 1 part of a bar model will always have a value of 1

Question:
What should replace the question mark? ![A bar split into 8 equal parts. 3 of the parts are shaded, and the total length of these 3 parts is labelled 3/4. The total length of 6 parts is labelled with a question mark.]()

Options:
A. \( \frac{6}{8} \)
B. \( 6 \)
C. \( \frac{6}{3} \)
D. \( \frac{6}{4} \)

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


Prompt:
Misconception:
Thinks you just add a % sign to the numerator to make a fraction into a percentage

Question:
What is \( \frac{13}{40} \) written as a percentage?

Options:
A. \( 32.5 \% \)
B. \( 13 \% \)
C. \( 26 \% \)
D. \( 52 \% \)

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


Prompt:
Misconception:
Believes a fraction out of a number other than 100 represents a percentage

Question:
What is \( \frac{13}{40} \) written as a percentage?

Options:
A. \( 32.5 \% \)
B. \( 13 \% \)
C. \( 26 \% \)
D. \( 52 \% \)

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


Prompt:
Misconception:
Believes a fraction out of a number other than 100 represents a percentage

Question:
What is \( \frac{13}{40} \) written as a percentage?

Options:
A. \( 32.5 \% \)
B. \( 13 \% \)
C. \( 26 \% \)
D. \( 52 \% \)

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


Prompt:
Misconception:
Does not understand that factors are divisors which split the number into equal groups

Question:
A Zumba teacher wants to split her group of \( 60 \) clients into equal sized classes.
To do this she needs to know the _________ of \( 60 \)
Which word best fills in the gap?

Options:
A. Remainders
B. Fractions
C. Multiples
D. Factors

Solve the problem as a student with the misconception above.
You 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 factors are divisors which split the number into equal groups

Question:
A Zumba teacher wants to split her group of \( 60 \) clients into equal sized classes.
To do this she needs to know the _________ of \( 60 \)
Which word best fills in the gap?

Options:
A. Remainders
B. Fractions
C. Multiples
D. Factors

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


Prompt:
Misconception:
Confuses factors and multiples

Question:
A Zumba teacher wants to split her group of \( 60 \) clients into equal sized classes.
To do this she needs to know the _________ of \( 60 \)
Which word best fills in the gap?

Options:
A. Remainders
B. Fractions
C. Multiples
D. Factors

Solve the problem as a student with the misconception above.
You 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:
This triangle is reflected in the line \( x= \) 4. What will the coordinate of the point marked \( \mathrm{C} \) on the reflected shape be? ![A positive quadrant graph showing a triangle ABC plotted]()

Options:
A. \( (3,5) \)
B. \( (6,3) \)
C. \( (4,5) \)
D. \( (2,5) \)

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


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

Question:
A coach takes \( 3 \) hours \( 50 \) minutes to complete a journey from Manchester to London.

If the coach leaves Manchester at 09:25, what time does it arrive in London?

Options:
A. \( 13: 25 \)
B. \( 12: 75 \)
C. 01:15
D. \( 13: 15 \)

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:
Writes times in the afternoon as if they are morning on a 24 hour clock

Question:
A coach takes \( 3 \) hours \( 50 \) minutes to complete a journey from Manchester to London.

If the coach leaves Manchester at 09:25, what time does it arrive in London?

Options:
A. \( 13: 25 \)
B. \( 12: 75 \)
C. 01:15
D. \( 13: 15 \)

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


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

Question:
Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 3 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]()

Options:
A. \( \frac{3}{6} \times \frac{1}{3} \)
B. \( \frac{1}{4} \div \frac{1}{3} \)
C. \( \frac{3}{6} \div 3 \)
D. \( \frac{1}{4} \times \frac{1}{3} \)

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


Prompt:
Misconception:
Believes that dividing by a decimal is the same as dividing by its reciprocal

Question:
Which calculation gives the fraction that replaces the question mark? ![A horizontal bar divided into 4 equal sections with vertical lines. The left hand section of these is coloured green and is further divided into 3 equal sections with vertical dotted lines. A curly bracket shows that the width of one of these green sections is denoted by a question mark.]()

Options:
A. \( \frac{3}{6} \times \frac{1}{3} \)
B. \( \frac{1}{4} \div \frac{1}{3} \)
C. \( \frac{3}{6} \div 3 \)
D. \( \frac{1}{4} \times \frac{1}{3} \)

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 where to place inputs/ operations/ outputs when drawing a function machine

Question:
Cally wants to use the function machine below to solve this problem:

I think of a number, subtract 2, triple it, and the answer is \( 12 \).

Which of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]()

Options:
A. \( x \)
B. \( -2 \)
C. \( \times 3 \)
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:
Does not follow the arrows through a function machine, changes the order of the operations asked.

Question:
Cally wants to use the function machine below to solve this problem:

I think of a number, subtract 2, triple it, and the answer is \( 12 \).

Which of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]()

Options:
A. \( x \)
B. \( -2 \)
C. \( \times 3 \)
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:
Does not understand where to place inputs/ operations/ outputs when drawing a function machine

Question:
Cally wants to use the function machine below to solve this problem:

I think of a number, subtract 2, triple it, and the answer is \( 12 \).

Which of the following should replace the star? ![A function machine with the input box blank. The first function box blank. The second function box has a purple star in and the output box is blank.]()

Options:
A. \( x \)
B. \( -2 \)
C. \( \times 3 \)
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:
Subtracts the smallest digit from the largest digit

Question:
A \( 3 \) digit number belongs in this box to make the calculation true
\(
467+\square=1253
\)
What is the \( 3^{\text {rd }} \) digit of the number that belongs in the box?

Options:
A. \( 4 \)
B. \( 6 \)
C. \( 0 \)
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:
Adds instead of subtracts

Question:
A \( 3 \) digit number belongs in this box to make the calculation true
\(
467+\square=1253
\)
What is the \( 3^{\text {rd }} \) digit of the number that belongs in the box?

Options:
A. \( 4 \)
B. \( 6 \)
C. \( 0 \)
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:
Divided by 10 rather than 100

Question:
\( 4 \% \) as a fraction is....

Options:
A. \( \frac{2}{5} \)
B. \( \frac{4}{10} \)
C. \( \frac{1}{25} \)
D. \( \frac{1}{4} \)

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


Prompt:
Misconception:
Divided by 10 rather than 100

Question:
\( 4 \% \) as a fraction is....

Options:
A. \( \frac{2}{5} \)
B. \( \frac{4}{10} \)
C. \( \frac{1}{25} \)
D. \( \frac{1}{4} \)

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


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

Question:
\( 4 \% \) as a fraction is....

Options:
A. \( \frac{2}{5} \)
B. \( \frac{4}{10} \)
C. \( \frac{1}{25} \)
D. \( \frac{1}{4} \)

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


Prompt:
Misconception:
Believes lines inside the shape are included when finding perimeter

Question:
A shape is made up a square and regular pentagon.
The area of the square is \( 144 \mathrm{~cm}^{2} \).

What is the perimeter of the compound shape? ![Pentagon and square joined along one edge]()

Options:
A. \( 108 \mathrm{~cm} \)
B. \( 84 \mathrm{~cm} \)
C. \( 252 \mathrm{~cm} \)
D. \( 12 \mathrm{~cm} \)

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:
Adds when calculating area instead of multiplying

Question:
A shape is made up a square and regular pentagon.
The area of the square is \( 144 \mathrm{~cm}^{2} \).

What is the perimeter of the compound shape? ![Pentagon and square joined along one edge]()

Options:
A. \( 108 \mathrm{~cm} \)
B. \( 84 \mathrm{~cm} \)
C. \( 252 \mathrm{~cm} \)
D. \( 12 \mathrm{~cm} \)

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


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

Question:
What is the value of
\( a b \)
when \( a=9 \) and \( b=-0.5 \) ?

Options:
A. \( -45 \)
B. \( -9.05 \)
C. \( -4.5 \)
D. \( 8.5 \)

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 two variables next to each other represent addition

Question:
What is the value of
\( a b \)
when \( a=9 \) and \( b=-0.5 \) ?

Options:
A. \( -45 \)
B. \( -9.05 \)
C. \( -4.5 \)
D. \( 8.5 \)

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


Prompt:
Misconception:
Confuses the part and the whole in fraction of an amount problems

Question:
Here is a number card

 \( \frac{1}{3} \) of \( \mathrm{A} \) is \( 12 \)

 What is \( \frac{1}{2} \) of \( A \) ?
 ![\( A \)]()

Options:
A. \( 2 \)
B. \( 8 \)
C. \( 36 \)
D. \( 18 \)

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


Prompt:
Misconception:
Confuses the part and the whole in fraction of an amount problems

Question:
Here is a number card

 \( \frac{1}{3} \) of \( \mathrm{A} \) is \( 12 \)

 What is \( \frac{1}{2} \) of \( A \) ?
 ![\( A \)]()

Options:
A. \( 2 \)
B. \( 8 \)
C. \( 36 \)
D. \( 18 \)

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


Prompt:
Misconception:
In a worded problem, does not complete all calculations

Question:
Here is a number card

 \( \frac{1}{3} \) of \( \mathrm{A} \) is \( 12 \)

 What is \( \frac{1}{2} \) of \( A \) ?
 ![\( A \)]()

Options:
A. \( 2 \)
B. \( 8 \)
C. \( 36 \)
D. \( 18 \)

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


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

Question:
Tom and Katie are arguing about percentages.
Tom says \( 45 \%>0.059 \)
Katie says \( 45 \%>\frac{16}{31} \)
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:
Thinks they double rather than halve when finding the area of a triangle

Question:
What is the area of the triangle? ![Triangle with base the square root of 144 cm and height 6cm.]()

Options:
A. \( 144 \mathrm{~cm}^{2} \)
B. \( 72 \mathrm{~cm}^{2} \)
C. \( 36 \mathrm{~cm}^{2} \)
D. \( 5184 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Does not have when calculating the area of a triangle

Question:
What is the area of the triangle? ![Triangle with base the square root of 144 cm and height 6cm.]()

Options:
A. \( 144 \mathrm{~cm}^{2} \)
B. \( 72 \mathrm{~cm}^{2} \)
C. \( 36 \mathrm{~cm}^{2} \)
D. \( 5184 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Assumes a fact without considering enough examples

Question:
Jo and Paul are arguing about powers.

Jo says there is no value of \( m \) that means \( 3^{m} \) is even.

Paul says there is no value of \( n \) that means \( 4^{n} \) ends in \( 0 \).
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:
Assumes a fact without considering enough examples

Question:
Jo and Paul are arguing about powers.

Jo says there is no value of \( m \) that means \( 3^{m} \) is even.

Paul says there is no value of \( n \) that means \( 4^{n} \) ends in \( 0 \).
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:
Assumes a fact without considering enough examples

Question:
Jo and Paul are arguing about powers.

Jo says there is no value of \( m \) that means \( 3^{m} \) is even.

Paul says there is no value of \( n \) that means \( 4^{n} \) ends in \( 0 \).
Who is correct?

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

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


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

Question:
Lethna pays at one rate for the first \( 100 \) units of electricity she uses. She pays at a different rate for all the other units of electricity she uses.

How much must she pay for using a total of \( 800 \) units of electricity? ![A graph showing how the cost changes for different numbers of units. The first 100 units cost £0.25 per unit. Then the rate changes to £0.10 per unit.]()

Options:
A. \( £ 110 \)
B. \( £ 95 \)
C. \( £ 200 \)
D. \( £ 140 \)

Solve the problem as a student with the misconception above.
You 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 considers the positive solution when calculating a square root

Question:
A student wishes to solve the equation below.

Which of the following is a correct next step?
\(
(d+3)^{2}-25=0
\)

Step \( 1 \)
\(
(d+3)^{2}=25
\)

Options:
A. \( d+3=5 \)
B. \( d+3=12.5 \)
C. \( d^{2}=22 \)
D. \( d+3= \pm 5 \)

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 the inverse of square rooting is halving

Question:
A student wishes to solve the equation below.

Which of the following is a correct next step?
\(
(d+3)^{2}-25=0
\)

Step \( 1 \)
\(
(d+3)^{2}=25
\)

Options:
A. \( d+3=5 \)
B. \( d+3=12.5 \)
C. \( d^{2}=22 \)
D. \( d+3= \pm 5 \)

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


Prompt:
Misconception:
Believes you can subtract from inside brackets without expanding when solving an equation

Question:
A student wishes to solve the equation below.

Which of the following is a correct next step?
\(
(d+3)^{2}-25=0
\)

Step \( 1 \)
\(
(d+3)^{2}=25
\)

Options:
A. \( d+3=5 \)
B. \( d+3=12.5 \)
C. \( d^{2}=22 \)
D. \( d+3= \pm 5 \)

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:
Misremembers the quadratic formula

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

What should replace the star? \(  \bigstar  \pm \sqrt{ ? - ?  } \)

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

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


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

Question:
An exam question asks students to estimate the size of the bearing on the right
Tom writes his answer as: \( 110\degree\)
Katie writes her answer as: \( 190\degree\)

Who would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]()

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

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


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

Question:
An exam question asks students to estimate the size of the bearing on the right
Tom writes his answer as: \( 110\degree\)
Katie writes her answer as: \( 190\degree\)

Who would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]()

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

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


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

Question:
An exam question asks students to estimate the size of the bearing on the right
Tom writes his answer as: \( 110\degree\)
Katie writes her answer as: \( 190\degree\)

Who would get all the marks for this question in the exam? ![An obtuse angle drawn in a clockwise direction from a vertical north line.]()

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

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


Prompt:
Misconception:
Rounds down instead of up when next digit is 5

Question:
Tom and Katie are arguing about rounding.

Tom says \( \mathbf{6 0 5 . 7 6} \) rounded to \( 1 \) significant figure is \( \mathbf{6 0 0} \)

Katie says \( \mathbf{6 0 5 . 7 6} \) rounded to \( 2 \) significant figures is \( \mathbf{6 0 0} \)

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 place value within a number

Question:
\( 0.15 \times 0.2= \)

Options:
A. \( 3 \)
B. \( 0.03 \)
C. \( 0.3 \)
D. \( 0.003 \)

Solve the problem as a student with the misconception above.
You 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 place value within a number

Question:
\( 0.15 \times 0.2= \)

Options:
A. \( 3 \)
B. \( 0.03 \)
C. \( 0.3 \)
D. \( 0.003 \)

Solve the problem as a student with the misconception above.
You 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 place value within a number

Question:
\( 0.15 \times 0.2= \)

Options:
A. \( 3 \)
B. \( 0.03 \)
C. \( 0.3 \)
D. \( 0.003 \)

Solve the problem as a student with the misconception above.
You 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 diagrams represents \( x \leq 1 \) ?

Options:
A. ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is an empty circle above 1, with an arrow pointing to the right coming off it.]()
B. ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is a filled in circle above 1, with an arrow pointing to the right coming off it.]()
C. ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is an empty circle above 1, with an arrow pointing to the left coming off it.]()
D. ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is a filled in circle above 1, with an arrow pointing to the right coming off it.]()

Solve the problem as a student with the misconception above.
You 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 representing an inequality on a numberline, assumes the filled and unfilled circles have the opposite meaning.

Question:
Which of the following diagrams represents \( x \leq 1 \) ?

Options:
A. ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is an empty circle above 1, with an arrow pointing to the right coming off it.]()
B. ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is a filled in circle above 1, with an arrow pointing to the right coming off it.]()
C. ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is an empty circle above 1, with an arrow pointing to the left coming off it.]()
D. ![A number line with integers from -5 to 5 marked on, with x as the axis label. There is a filled in circle above 1, with an arrow pointing to the right coming off it.]()

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


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

Question:
What number belongs in the box to make the calculation correct? \( 263+\square=900 \)

Options:
A. \( 1163 \)
B. \( 747 \)
C. \( 637 \)
D. \( 647 \)

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


Prompt:
Misconception:
Treats zero as a ten when subtracting

Question:
What number belongs in the box to make the calculation correct? \( 263+\square=900 \)

Options:
A. \( 1163 \)
B. \( 747 \)
C. \( 637 \)
D. \( 647 \)

Solve the problem as a student with the misconception above.
You 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 all triangles have a right angle

Question:
What is the size of angle \( k \) ? ![A triangle with one angle of 40 degrees. One angle of 32 degrees and the third angle is labelled k. ]()

Options:
A. \( 72\degree\)
B. \( 90\degree\)
C. \( 108\degree\)
D. \( 118\degree\)

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


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

Question:
What is the size of angle \( k \) ? ![A triangle with one angle of 40 degrees. One angle of 32 degrees and the third angle is labelled k. ]()

Options:
A. \( 72\degree\)
B. \( 90\degree\)
C. \( 108\degree\)
D. \( 118\degree\)

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


Prompt:
Misconception:
Does not know how to identify common factors from algebraic terms

Question:
Tom and Katie are discussing factors

Tom says \( 4 \) is a common factor of \( 6 x \) and \( 9 y^{2} \)

Katie says \( y \) is a common factor of \( 6 x \) and \( 9 y^{2} \)

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:
Does not know how to identify common factors from algebraic terms

Question:
Tom and Katie are discussing factors

Tom says \( 4 \) is a common factor of \( 6 x \) and \( 9 y^{2} \)

Katie says \( y \) is a common factor of \( 6 x \) and \( 9 y^{2} \)

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:
Does not know how to identify common factors from algebraic terms

Question:
Tom and Katie are discussing factors

Tom says \( 4 \) is a common factor of \( 6 x \) and \( 9 y^{2} \)

Katie says \( y \) is a common factor of \( 6 x \) and \( 9 y^{2} \)

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 only the first term needs to be divided when factorising an expression

Question:
When factorised, \( 9 x^{2}-16 \) will become...

Options:
A. \( (3 x+4)(3 x-4) \)
B. \( 9 x(x-16) \)
C. \( 3 x(3 x-16-) \)
D. \( (3 x+4)(3 x+4) \)

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


Prompt:
Misconception:
Believes only the first term needs to be divided when factorising an expression

Question:
When factorised, \( 9 x^{2}-16 \) will become...

Options:
A. \( (3 x+4)(3 x-4) \)
B. \( 9 x(x-16) \)
C. \( 3 x(3 x-16-) \)
D. \( (3 x+4)(3 x+4) \)

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

Question:
When factorised, \( 9 x^{2}-16 \) will become...

Options:
A. \( (3 x+4)(3 x-4) \)
B. \( 9 x(x-16) \)
C. \( 3 x(3 x-16-) \)
D. \( (3 x+4)(3 x+4) \)

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


Prompt:
Misconception:
When dividing a decimal by a whole number, ignores decimal point and just divides the digits

Question:
\( \frac{(-3) \times(-2)}{(-0.2)}= \)

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

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


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

Question:
\( \frac{(-3) \times(-2)}{(-0.2)}= \)

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

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


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

Question:
Molly is expanding these two brackets.

What should she get when she multiplies the two terms indicated by the arrows? ![The brackets shown are (2p-1)(3p-4). The arrows are pointing at the -1 in the first bracket and the -4 in the second bracket.]()

Options:
A. \( +4 \)
B. \( -4 \)
C. \( +5 \)
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:
Adds instead of multiplying when expanding bracket

Question:
Molly is expanding these two brackets.

What should she get when she multiplies the two terms indicated by the arrows? ![The brackets shown are (2p-1)(3p-4). The arrows are pointing at the -1 in the first bracket and the -4 in the second bracket.]()

Options:
A. \( +4 \)
B. \( -4 \)
C. \( +5 \)
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:
Incorrectly identifies angles as vertically opposite

Question:
What is the size of angle \( w \) ? ![An isosceles triangle with one of the base angles labelled with a w and the angle vertically opposite the vertex angle labelled with 27 degrees]()

Options:
A. \( 27^{\degree} \)
B. \( 51^{\degree} \)
C. \( 54^{\degree} \)
D. \( 76.5^{\degree} \)

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


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

Question:
What is the size of angle \( w \) ? ![An isosceles triangle with one of the base angles labelled with a w and the angle vertically opposite the vertex angle labelled with 27 degrees]()

Options:
A. \( 27^{\degree} \)
B. \( 51^{\degree} \)
C. \( 54^{\degree} \)
D. \( 76.5^{\degree} \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( \mathbf{1 8 7 . 2 5 9} \) rounded to two significant figures?

Options:
A. \( 190 \)
B. \( 180 \)
C. \( 187.26 \)
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:
Rounds to wrong degree of accuracy (decimal places rather than significant figures)

Question:
What is \( \mathbf{1 8 7 . 2 5 9} \) rounded to two significant figures?

Options:
A. \( 190 \)
B. \( 180 \)
C. \( 187.26 \)
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 multiplying a surd by an integer, adds the integer to the number under the surd

Question:
\(9 \times \sqrt{3}\)

Simplify, if possible.

Options:
A. \( \sqrt{12} \)
B. \( \sqrt{27} \)
C. \( 9 \sqrt{3} \)
D. Cannot be simplified

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


Prompt:
Misconception:
When multiplying a surd by an integer, multiplies the integer with the number under the surd

Question:
\(9 \times \sqrt{3}\)

Simplify, if possible.

Options:
A. \( \sqrt{12} \)
B. \( \sqrt{27} \)
C. \( 9 \sqrt{3} \)
D. Cannot be simplified

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


Prompt:
Misconception:
Does not recognise that an integer multiplied by a surd can be simplified

Question:
\(9 \times \sqrt{3}\)

Simplify, if possible.

Options:
A. \( \sqrt{12} \)
B. \( \sqrt{27} \)
C. \( 9 \sqrt{3} \)
D. Cannot be simplified

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


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

Question:
Expand and simplify:
\(
(3 y-4)^{2}
\)

Options:
A. \( 9 y^{2}-16 \)
B. \( 9 y^{2}+16 \)
C. \( 9 y^{2}-24 y+16 \)
D. \( (3 y-4)(3 y-4) \)

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


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

Question:
Expand and simplify:
\(
(3 y-4)^{2}
\)

Options:
A. \( 9 y^{2}-16 \)
B. \( 9 y^{2}+16 \)
C. \( 9 y^{2}-24 y+16 \)
D. \( (3 y-4)(3 y-4) \)

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


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

Question:
Expand and simplify:
\(
(3 y-4)^{2}
\)

Options:
A. \( 9 y^{2}-16 \)
B. \( 9 y^{2}+16 \)
C. \( 9 y^{2}-24 y+16 \)
D. \( (3 y-4)(3 y-4) \)

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


Prompt:
Misconception:
Does not correctly apply the commutative property of multiplication

Question:
Tom and Katie are discussing multiplying decimals.

Tom says \( 5 \times 3.9=3 \times 5.9 \)

Katie says \( 5 \times 3.9=3.9 \times 5 \)

Who is correct?

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

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


Prompt:
Misconception:
Does not correctly apply the commutative property of multiplication

Question:
Tom and Katie are discussing multiplying decimals.

Tom says \( 5 \times 3.9=3 \times 5.9 \)

Katie says \( 5 \times 3.9=3.9 \times 5 \)

Who is correct?

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

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


Prompt:
Misconception:
Believes multiplication is not commutative

Question:
Tom and Katie are discussing multiplying decimals.

Tom says \( 5 \times 3.9=3 \times 5.9 \)

Katie says \( 5 \times 3.9=3.9 \times 5 \)

Who is correct?

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

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


Prompt:
Misconception:
Confuses isosceles and right angle triangles

Question:
Which description describes an isosceles triangle?

Options:
A. A triangle with one right angle.
B. A triangle with two sides of equal length and two equal angles.
C. A triangle with three sides of equal length and three equal angles.
D. A triangle with no sides of equal length and no equal angles.

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


Prompt:
Misconception:
Confuses isosceles and equilateral triangles

Question:
Which description describes an isosceles triangle?

Options:
A. A triangle with one right angle.
B. A triangle with two sides of equal length and two equal angles.
C. A triangle with three sides of equal length and three equal angles.
D. A triangle with no sides of equal length and no equal angles.

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


Prompt:
Misconception:
Confuses isosceles and scalene triangles

Question:
Which description describes an isosceles triangle?

Options:
A. A triangle with one right angle.
B. A triangle with two sides of equal length and two equal angles.
C. A triangle with three sides of equal length and three equal angles.
D. A triangle with no sides of equal length and no equal angles.

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


Prompt:
Misconception:
Does not think a factorised expression is equivalent to its multiplied out form

Question:
Tom and Katie are arguing about the result of this Function Machine:
Tom says the output is: \( 3 n-12 \)
Katie says the output is: \( 3(n-4) \)
Who is correct? ![A function machine with input n and operations subtract 4, multiply by 3]()

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

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


Prompt:
Misconception:
Does not think a factorised expression is equivalent to its multiplied out form

Question:
Tom and Katie are arguing about the result of this Function Machine:
Tom says the output is: \( 3 n-12 \)
Katie says the output is: \( 3(n-4) \)
Who is correct? ![A function machine with input n and operations subtract 4, multiply by 3]()

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

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


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

Question:
Which of the following term-to-term rule describes this sequence?
\[
4, \quad 10, \quad 28, \quad 82, \quad \ldots
\]

Options:
A. To get the next term you add \( 6 \) to the previous term
B. To get the next term you add the previous two terms together
C. To get the next term you double the previous term and add \( 2 \)
D. To get the next term you multiply the previous term by \( 3 \) and subtract \( 2 \)

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


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

Question:
Which of the following term-to-term rule describes this sequence?
\[
4, \quad 10, \quad 28, \quad 82, \quad \ldots
\]

Options:
A. To get the next term you add \( 6 \) to the previous term
B. To get the next term you add the previous two terms together
C. To get the next term you double the previous term and add \( 2 \)
D. To get the next term you multiply the previous term by \( 3 \) and subtract \( 2 \)

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


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

Question:
Round this number to \( 1 \) significant figure:
\( 0.00809 \)

Options:
A. \( 0.01 \)
B. \( 0 \)
C. \( 0.008 \)
D. \( 0.009 \)

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:
Counts leading zero as a significant figure

Question:
Round this number to \( 1 \) significant figure:
\( 0.00809 \)

Options:
A. \( 0.01 \)
B. \( 0 \)
C. \( 0.008 \)
D. \( 0.009 \)

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:
Rounds up instead of down

Question:
Round this number to \( 1 \) significant figure:
\( 0.00809 \)

Options:
A. \( 0.01 \)
B. \( 0 \)
C. \( 0.008 \)
D. \( 0.009 \)

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 recognise factorising a quadratic

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

Options:
A. \( m+1 \)
B. \( m-2 \)
C. \( m-1 \)
D. Does not simplify

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


Prompt:
Misconception:
Uses dividing fractions method for multiplying fractions

Question:
What should replace the star?

\(
(-6) \times \color{gold}\bigstar \color{black} =-8
\)

Options:
A. \( \frac{6}{8} \)
B. \( -\frac{6}{8} \)
C. \( -\frac{8}{6} \)
D. \( \frac{8}{6} \)

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


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

Question:
What should replace the star?

\(
(-6) \times \color{gold}\bigstar \color{black} =-8
\)

Options:
A. \( \frac{6}{8} \)
B. \( -\frac{6}{8} \)
C. \( -\frac{8}{6} \)
D. \( \frac{8}{6} \)

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:
Has confused cube numbers with prime numbers

Question:
What is the first cube number greater than \( 40 \) ?

Options:
A. \( 43 \)
B. \( 49 \)
C. \( 64 \)
D. \( 125 \)

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


Prompt:
Misconception:
Mixes up square numbers and cube numbers

Question:
What is the first cube number greater than \( 40 \) ?

Options:
A. \( 43 \)
B. \( 49 \)
C. \( 64 \)
D. \( 125 \)

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


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

Question:
Tom and Katie are discussing how to order integers

Tom says \( 5000 \) is greater than \( 4987 \)

Katie says \( 3050 \) is greater than \( 3500 \)

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 equate the value of a number with the place value column it is in

Question:
Tom and Katie are discussing how to order integers

Tom says \( 5000 \) is greater than \( 4987 \)

Katie says \( 3050 \) is greater than \( 3500 \)

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 ordering integers, orders from the digits at the end of the number instead of the digits at the start

Question:
Tom and Katie are discussing how to order integers

Tom says \( 5000 \) is greater than \( 4987 \)

Katie says \( 3050 \) is greater than \( 3500 \)

Who is correct?

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

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


Prompt:
Misconception:
Does not know the properties of a linear graph

Question:
Use a graphing program (e.g. Desmos) to plot the following pairs of functions.
\[
y=x^{2} - 4 \quad \text { and } \quad y=x-4
\]

Tom says both functions are linear

Katie says both functions cross the \( y \)-axis at the same point

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 the constant only gives the y-intercept for linear graphs

Question:
Use a graphing program (e.g. Desmos) to plot the following pairs of functions.
\[
y=x^{2} - 4 \quad \text { and } \quad y=x-4
\]

Tom says both functions are linear

Katie says both functions cross the \( y \)-axis at the same point

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 an interior angle in a regular polygon can be found using 180(n+2)/n

Question:
Tom and Katie are discussing how to calculate the size of each interior angle in a regular \( 18 \) sided shape Tom says you can do \( \frac{20 \times 180}{18} \) Katie says you can do \( 360-\frac{180}{18} \) Who is correct?

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

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


Prompt:
Misconception:
Believes an interior angle in a regular polygon can be found using 360 subtract (180 over number of sides)

Question:
Tom and Katie are discussing how to calculate the size of each interior angle in a regular \( 18 \) sided shape Tom says you can do \( \frac{20 \times 180}{18} \) Katie says you can do \( 360-\frac{180}{18} \) Who is correct?

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

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


Prompt:
Misconception:
When finding the gradient from the equation of a line in the form ax + by = c, believes b/a is the gradient

Question:
A line has equation \( 5 x+3 y=7 \)
What is its gradient?

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

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


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

Question:
A line has equation \( 5 x+3 y=7 \)
What is its gradient?

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

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


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

Question:
A line has equation \( 5 x+3 y=7 \)
What is its gradient?

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

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


Prompt:
Misconception:
Does not realise that the area of a triangle is half the area of the contatining rectangle

Question:
What is the area of this shape? ![Purple, right angled triangle on square grid with area of 5 square units. Base length 5 and perpendicular height 2]()

Options:
A. \( 4.5 \)
B. \( 5 \)
C. \( 6 \)
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 realise that the area of a triangle is half the area of the contatining rectangle

Question:
What is the area of this shape? ![Purple, right angled triangle on square grid with area of 5 square units. Base length 5 and perpendicular height 2]()

Options:
A. \( 4.5 \)
B. \( 5 \)
C. \( 6 \)
D. Not enough information

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


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

Question:
The perimeter of this rectangle is \( 5.6 \mathrm{~cm} \).

What is the length of the side marked with a star? ![Rectangle with base length labelled 1.02 cm and side length labelled with a gold star]()

Options:
A. \( 4.58 \mathrm{~cm} \)
B. \( 1.6 \mathrm{~cm} \)
C. \( 1.78 \mathrm{~cm} \)
D. \( 4.4 \mathrm{~cm} \)

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


Prompt:
Misconception:
When doing operations with decimals, ignores significant zeros after the decimal point

Question:
The perimeter of this rectangle is \( 5.6 \mathrm{~cm} \).

What is the length of the side marked with a star? ![Rectangle with base length labelled 1.02 cm and side length labelled with a gold star]()

Options:
A. \( 4.58 \mathrm{~cm} \)
B. \( 1.6 \mathrm{~cm} \)
C. \( 1.78 \mathrm{~cm} \)
D. \( 4.4 \mathrm{~cm} \)

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 copy a given method accurately

Question:
This is how Teddy calculates the answer to \( 600 \div 25 \) mentally "There are \( 4 \) lots of \( 25 \) in 100. I then multiplied \( 4 \) by \( 6 \) to get \( 24 \). So \( 600 \) divided by \( 25 \) is \( 24 \)" Teddy uses the same method to calculate \( 800 \div 25 \). Which of the following shows how he would do this?

Options:
A. There are \( 4 \) lots of \( 25 \) in \( 100 \)
Then I multiplied \( 4 \) by \( 8 \)
So the answer is \( 32 \)
B. There are \( 4 \) lots of \( 25 \) in \( 100 \)
Then I multiplied \( 8 \) by \( 6 \)
So the answer is \( 48 \)
C. There are \( 6 \) lots of \( 25 \) in \( 100 \)
Then I multiplied \( 6 \) by \( 4 \)
So the answer is \( 24 \)
D. There are \( 8 \) lots of \( 25 \) in \( 100 \)
Then I multiplied \( 8 \) by \( 6 \)
So the answer is \( 48 \)

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


Prompt:
Misconception:
Rounds up instead of down

Question:
Two different numbers are equal to \( 4.37 \) to two decimal places.
The numbers could be....

Options:
A. \( 4.3708 \)
and
\( 4.3651 \)
B. \[
4.3728
\]
and
\[
4.3628
\]
C. \( 4.373 \)
and
\( 3.371 \)
D. \[
4.3751
\]
and
\[
4.3659
\]

Solve the problem as a student with the misconception above.
You 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:
Two different numbers are equal to \( 4.37 \) to two decimal places.
The numbers could be....

Options:
A. \( 4.3708 \)
and
\( 4.3651 \)
B. \[
4.3728
\]
and
\[
4.3628
\]
C. \( 4.373 \)
and
\( 3.371 \)
D. \[
4.3751
\]
and
\[
4.3659
\]

Solve the problem as a student with the misconception above.
You 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 shapes are congruent if they have the same size and shape

Question:
Tom and Katie are discussing congruent shapes.
Tom says you can reflect a shape and it will still be congruent to the original.

Katie says you can rotate a shape and it will still be congruent to the original.
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 shapes are congruent if they have the same size and shape

Question:
Tom and Katie are discussing congruent shapes.
Tom says you can reflect a shape and it will still be congruent to the original.

Katie says you can rotate a shape and it will still be congruent to the original.
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 shapes are congruent if they have the same size and shape

Question:
Tom and Katie are discussing congruent shapes.
Tom says you can reflect a shape and it will still be congruent to the original.

Katie says you can rotate a shape and it will still be congruent to the original.
Who is correct?

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

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


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

Question:
\[
34590.8549
\]
What is this number rounded to the nearest \( 100 \) ?

Options:
A. \( 34590 \)
B. \( 34600 \)
C. \( 34500 \)
D. \( 35000 \)

Solve the problem as a student with the misconception above.
You 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:
\[
34590.8549
\]
What is this number rounded to the nearest \( 100 \) ?

Options:
A. \( 34590 \)
B. \( 34600 \)
C. \( 34500 \)
D. \( 35000 \)

Solve the problem as a student with the misconception above.
You 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:
\[
34590.8549
\]
What is this number rounded to the nearest \( 100 \) ?

Options:
A. \( 34590 \)
B. \( 34600 \)
C. \( 34500 \)
D. \( 35000 \)

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


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

Question:
How do you write \( 4.6 \) as a percentage?

Options:
A. \( 46 \% \)
B. \( 0.046 \% \)
C. \( 4.6 \% \)
D. \( 460 \% \)

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


Prompt:
Misconception:
Divides instead of multiplies when converting a decimal to a percentage

Question:
How do you write \( 4.6 \) as a percentage?

Options:
A. \( 46 \% \)
B. \( 0.046 \% \)
C. \( 4.6 \% \)
D. \( 460 \% \)

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


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

Question:
How do you write \( 4.6 \) as a percentage?

Options:
A. \( 46 \% \)
B. \( 0.046 \% \)
C. \( 4.6 \% \)
D. \( 460 \% \)

Solve the problem as a student with the misconception above.
You 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 every number is the mode when you have data with no mode

Question:
What is the mode of the following numbers?
\[
0,0,2,2
\]

Options:
A. \( 0 \) and \( 2 \)
B. \( 2 \)
C. \( 1 \)
D. There is no mode

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


Prompt:
Misconception:
Believes you can only have one mode

Question:
What is the mode of the following numbers?
\[
0,0,2,2
\]

Options:
A. \( 0 \) and \( 2 \)
B. \( 2 \)
C. \( 1 \)
D. There is no mode

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


Prompt:
Misconception:
Finds the median instead of the mode

Question:
What is the mode of the following numbers?
\[
0,0,2,2
\]

Options:
A. \( 0 \) and \( 2 \)
B. \( 2 \)
C. \( 1 \)
D. There is no mode

Solve the problem as a student with the misconception above.
You 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 interior angles are outside a shape

Question:
The diagram shows a regular hexagon and a square.
What is the size of angle \( a \) ? ![A regular hexagon and square, joined on one side, with the angle between them labelled a. Not to scale]()

Options:
A. \( 210^{\circ} \)
B. \( 120^{\circ} \)
C. \( 150^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
In a worded problem, does not complete all calculations

Question:
A magazine costs \( £ 2.70 \).

Isaac pays for it with a \( £ 5 \) note.

How much change should he receive?

Options:
A. \( £ 2.70 \)
B. \( £ 3.30 \)
C. \( £ 7.70 \)
D. \( £ 2.30 \)

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


Prompt:
Misconception:
Ends up £1 out when dealing with change in money

Question:
A magazine costs \( £ 2.70 \).

Isaac pays for it with a \( £ 5 \) note.

How much change should he receive?

Options:
A. \( £ 2.70 \)
B. \( £ 3.30 \)
C. \( £ 7.70 \)
D. \( £ 2.30 \)

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


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

Question:
A magazine costs \( £ 2.70 \).

Isaac pays for it with a \( £ 5 \) note.

How much change should he receive?

Options:
A. \( £ 2.70 \)
B. \( £ 3.30 \)
C. \( £ 7.70 \)
D. \( £ 2.30 \)

Solve the problem as a student with the misconception above.
You 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 isosceles triangles cannot have right angles

Question:
A triangle has the following angles: \( 90^{\degree}, 45^{\degree}, 45^{\degree} \) Statement 1. It must be a right angled triangle
Statement 2. It must be an isosceles triangle
Which is true?

Options:
A. Statement \( 1 \)
B. Statement \( 2 \)
C. Both statements
D. Neither statement

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


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

Question:
A triangle has the following angles: \( 90^{\degree}, 45^{\degree}, 45^{\degree} \) Statement 1. It must be a right angled triangle
Statement 2. It must be an isosceles triangle
Which is true?

Options:
A. Statement \( 1 \)
B. Statement \( 2 \)
C. Both statements
D. Neither statement

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


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

Question:
How many degrees are there in three-quarters of a turn?

Options:
A. \( 75\degree \)
B. \( 90\degree \)
C. \( 180\degree\)
D. \( 270\degree \)

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


Prompt:
Misconception:
Finds the unit fraction when asked to find a non-unit fraction of an amount

Question:
How many degrees are there in three-quarters of a turn?

Options:
A. \( 75\degree \)
B. \( 90\degree \)
C. \( 180\degree\)
D. \( 270\degree \)

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


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( \mathrm{P} \) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]()

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

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


Prompt:
Misconception:
Counts the squares rather than the diagonals when reflecting in y=x or y=-x

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( \mathrm{P} \) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]()

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

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


Prompt:
Misconception:
Counts the squares rather than the diagonals when reflecting in y=x or y=-x

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( \mathrm{P} \) ? ![A coordinate grid with the reflection line y=x drawn and a triangle with the coordinates (2,1) (4,1) and (3,2). P is the point (3,2)]()

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

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 sides of a ratio

Question:
For every \( 3 \) green squares there is \( 1 \) red square.
How many squares should be coloured green in the grid on the right? \begin{tabular}{|c|c|c|}
\hline \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) \\
\hline \(\;\) & \(\;\) & \(\;\) \\
\hline
\end{tabular}

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 8 \)
D. \( 9 \)

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


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

Question:
![A number line from 0 to 1 split into 5 parts with a red arrow pointing to the marker for the value 0.4]() What number is the arrow pointing to?

Options:
A. \( 0.2 \)
B. \( 0.5 \)
C. \( 0.4 \)
D. \( 2 \)

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


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 1

Question:
![A number line from 0 to 1 split into 5 parts with a red arrow pointing to the marker for the value 0.4]() What number is the arrow pointing to?

Options:
A. \( 0.2 \)
B. \( 0.5 \)
C. \( 0.4 \)
D. \( 2 \)

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


Prompt:
Misconception:
Confuses adding 3 with cubing, in algebra

Question:
Simplify, if possible:
\[
e+e+e
\]

Options:
A. \( e^{3} \)
B. e3
C. \( 3 e \)
D. Does not simplify

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


Prompt:
Misconception:
Writes the variable before the coefficient in an algebraic term

Question:
Simplify, if possible:
\[
e+e+e
\]

Options:
A. \( e^{3} \)
B. e3
C. \( 3 e \)
D. Does not simplify

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


Prompt:
Misconception:
Does not understand when like terms can be collected

Question:
Simplify, if possible:
\[
e+e+e
\]

Options:
A. \( e^{3} \)
B. e3
C. \( 3 e \)
D. Does not simplify

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


Prompt:
Misconception:
Thinks only labelled dimensions need to be included when calculating the perimeter

Question:
What is the perimeter of this rectangle? ![A rectangle. The length of a short side is labelled x, and the length of a long side is labelled y.]()

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

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


Prompt:
Misconception:
Calculates area when asked for perimeter

Question:
What is the perimeter of this rectangle? ![A rectangle. The length of a short side is labelled x, and the length of a long side is labelled y.]()

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

Solve the problem as a student with the misconception above.
You 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 positive or negative sign affects the term before it

Question:
What is the value of:

\[
485+78-9
\]

Options:
A. \( 398 \)
B. \( 554 \)
C. \( 572 \)
D. \( 444 \)

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


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

Question:
What is the value of:

\[
485+78-9
\]

Options:
A. \( 398 \)
B. \( 554 \)
C. \( 572 \)
D. \( 444 \)

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


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

Question:
John has been asked to work out the answer to:
\[
231 \div 4
\]
He gets the answer \( 57 \) remainder \( 3 \)
What is the exact value of that remainder?

Options:
A. \( 3 \)
B. \( 0.34 \)
C. \( 0.3 \)
D. \( 0.75 \)

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:
Does not understand remainders in division

Question:
John has been asked to work out the answer to:
\[
231 \div 4
\]
He gets the answer \( 57 \) remainder \( 3 \)
What is the exact value of that remainder?

Options:
A. \( 3 \)
B. \( 0.34 \)
C. \( 0.3 \)
D. \( 0.75 \)

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:
Writes the remainder as the digit after the decimal point

Question:
John has been asked to work out the answer to:
\[
231 \div 4
\]
He gets the answer \( 57 \) remainder \( 3 \)
What is the exact value of that remainder?

Options:
A. \( 3 \)
B. \( 0.34 \)
C. \( 0.3 \)
D. \( 0.75 \)

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 factorising a quadratic without a non variable term, tries to double bracket factorise

Question:
Jo and Paul are arguing about factorising.

Jo says \( p^{2}+16 p \equiv(p+4)(p+4) \)

Paul says \( p^{2}+16 p \equiv p(p+4) \)

Who is correct?

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

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


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

Question:
Tom and Katie are arguing about the solution to this inequality:
\[
15 \geq 4 m
\]

Tom says \( m \) could be \( 4 \)

Katie says \( m \) could be \( 3.75 \)

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 using inequality notation, thinks "greater than/less than or equal to" symbols are instead the "greater than/less than" symbols and vice versa

Question:
Tom and Katie are arguing about the solution to this inequality:
\[
15 \geq 4 m
\]

Tom says \( m \) could be \( 4 \)

Katie says \( m \) could be \( 3.75 \)

Who is correct?

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

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


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

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making a T shape where there is a rectangle across the top and a rectangle attached below this, slightly to the left of the centre. The full width across the top is 32m, the partial width on the left is 10m, the partial width on the right is 11m. The full height on the right is 25m, the partial height on the lower block is 14m. The shaded section is the top rectangle across the full width.]()

Options:
A. \( 352 \mathrm{~m}^{2} \)
B. \( 320 \mathrm{~m}^{2} \)
C. \( 288 \mathrm{~m}^{2} \)
D. \( 332 \mathrm{~m}^{2} \)

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


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

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making a T shape where there is a rectangle across the top and a rectangle attached below this, slightly to the left of the centre. The full width across the top is 32m, the partial width on the left is 10m, the partial width on the right is 11m. The full height on the right is 25m, the partial height on the lower block is 14m. The shaded section is the top rectangle across the full width.]()

Options:
A. \( 352 \mathrm{~m}^{2} \)
B. \( 320 \mathrm{~m}^{2} \)
C. \( 288 \mathrm{~m}^{2} \)
D. \( 332 \mathrm{~m}^{2} \)

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


Prompt:
Misconception:
Does not know what a cube number is

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

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 9 \)
D. None of these numbers are cube numbers

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


Prompt:
Misconception:
Does not know what a cube number is

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

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 9 \)
D. None of these numbers are cube numbers

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


Prompt:
Misconception:
Mixes up square numbers and cube numbers

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

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 9 \)
D. None of these numbers are cube numbers

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


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

Question:
How should you line up the digits to calculate \( 3152-809 \) ?

Options:
A. \( \begin{array}{r}\quad\space3152 \\ -809\end{array} \)
B. \( \begin{array}{r}\quad\quad3152 \\ -89\end{array} \)
C. \( \begin{array}{r}\space3152 \\ -\space809\end{array} \)
D. \( \begin{array}{r}3152 \\ -\space 89\end{array} \)

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:
Does not understand the value of zeros as placeholders

Question:
How should you line up the digits to calculate \( 3152-809 \) ?

Options:
A. \( \begin{array}{r}\quad\space3152 \\ -809\end{array} \)
B. \( \begin{array}{r}\quad\quad3152 \\ -89\end{array} \)
C. \( \begin{array}{r}\space3152 \\ -\space809\end{array} \)
D. \( \begin{array}{r}3152 \\ -\space 89\end{array} \)

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:
Does not understand the value of zeros as placeholders

Question:
How should you line up the digits to calculate \( 3152-809 \) ?

Options:
A. \( \begin{array}{r}\quad\space3152 \\ -809\end{array} \)
B. \( \begin{array}{r}\quad\quad3152 \\ -89\end{array} \)
C. \( \begin{array}{r}\space3152 \\ -\space809\end{array} \)
D. \( \begin{array}{r}3152 \\ -\space 89\end{array} \)

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:
Does not know the 9 timestable

Question:
A common factor of \( 6 \) and \( 9 \) is...

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 9 \)
D. \( 18 \)

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


Prompt:
Misconception:
Does not know the 6 timestable

Question:
A common factor of \( 6 \) and \( 9 \) is...

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 9 \)
D. \( 18 \)

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


Prompt:
Misconception:
Confuses factors and multiples

Question:
A common factor of \( 6 \) and \( 9 \) is...

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 9 \)
D. \( 18 \)

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


Prompt:
Misconception:
Thinks tables of values are symmetrical about (0,0)

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

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

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 realise that subtracting a negative is the same as adding it's additive inverse

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

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

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:
Thinks 1 squared is 2

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

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

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

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

Options:
A. \( 8699 \)
B. \( 8700 \)
C. \( 8690 \)
D. \( 9000 \)

Solve the problem as a student with the misconception above.
You 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 \( \mathbf{8 6 9 8 . 9} \) rounded to the nearest ten?

Options:
A. \( 8699 \)
B. \( 8700 \)
C. \( 8690 \)
D. \( 9000 \)

Solve the problem as a student with the misconception above.
You 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 \( \mathbf{8 6 9 8 . 9} \) rounded to the nearest ten?

Options:
A. \( 8699 \)
B. \( 8700 \)
C. \( 8690 \)
D. \( 9000 \)

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


Prompt:
Misconception:
Student thinks that any two angles along a straight line are equal

Question:
What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]()

Options:
A. They are equal
B. They are parallel
C. They add together to make
\[
180^{\circ}
\]
D. They add together to make
\[
360^{\circ}
\]

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 the meaning of the word parallel

Question:
What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]()

Options:
A. They are equal
B. They are parallel
C. They add together to make
\[
180^{\circ}
\]
D. They add together to make
\[
360^{\circ}
\]

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


Prompt:
Misconception:
Believes angles on a straight line add to 360 degrees

Question:
What is the relationship between these two angles? ![Angles around a point made up of two angles: a green one and a pink one]()

Options:
A. They are equal
B. They are parallel
C. They add together to make
\[
180^{\circ}
\]
D. They add together to make
\[
360^{\circ}
\]

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


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

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

Options:
A. \( p=0.5 \)
B. \( p=50 \)
C. \( p=2 \)
D. There are no solutions

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


Prompt:
Misconception:
Assumes the denominator is divided by the numerator

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

Options:
A. \( p=0.5 \)
B. \( p=50 \)
C. \( p=2 \)
D. There are no solutions

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


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

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

Options:
A. \( p=0.5 \)
B. \( p=50 \)
C. \( p=2 \)
D. There are no solutions

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


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

Question:
Tom and Katie are discussing linear sequences.

Tom says this is a linear sequence: \( 1,2,4,7,11, \ldots \)

Katie says this is a linear sequence: \( 1.2,1.4,1.6,1.8,2, \ldots \)

Who is correct?

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

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


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

Question:
Tom and Katie are discussing linear sequences.

Tom says this is a linear sequence: \( 1,2,4,7,11, \ldots \)

Katie says this is a linear sequence: \( 1.2,1.4,1.6,1.8,2, \ldots \)

Who is correct?

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

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


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

Question:
Tom and Katie are discussing linear sequences.

Tom says this is a linear sequence: \( 1,2,4,7,11, \ldots \)

Katie says this is a linear sequence: \( 1.2,1.4,1.6,1.8,2, \ldots \)

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 they can round when converting units

Question:
\( 27 \mathrm{~cm}=\square \mathrm{m} \)

Options:
A. \( 0.3 \)
B. \( 2700 \)
C. \( 0.27 \)
D. \( 2.7 \)

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


Prompt:
Misconception:
Multiplies when converting to a larger unit

Question:
\( 27 \mathrm{~cm}=\square \mathrm{m} \)

Options:
A. \( 0.3 \)
B. \( 2700 \)
C. \( 0.27 \)
D. \( 2.7 \)

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


Prompt:
Misconception:
Thinks there are 10cm in a metre

Question:
\( 27 \mathrm{~cm}=\square \mathrm{m} \)

Options:
A. \( 0.3 \)
B. \( 2700 \)
C. \( 0.27 \)
D. \( 2.7 \)

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