Prompt:
Misconception:
Does not reverse the order of operations when finding the input of a function machine

Question:
![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The next rectangle has "− 1" written inside it, the next rectangle has "✕ 2" written inside it and the final rectangle on the right has "output" written above it and "8" written inside it.]() What is the input of this function machine?

Options:
A. \( 15 \)
B. \( 5 \)
C. \( 14 \)
D. \( 4.5 \)

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


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

Question:
Factorise this expression, if possible:
\(
p^{2}-5 p
\)

Options:
A. \( p(p-5) \)
B. \( (p+5)(p-5) \)
C. \( (p+\sqrt{5})(p-\sqrt{5}) \)
D. Does not factorise

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


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

Question:
Factorise this expression, if possible:
\(
p^{2}-5 p
\)

Options:
A. \( p(p-5) \)
B. \( (p+5)(p-5) \)
C. \( (p+\sqrt{5})(p-\sqrt{5}) \)
D. Does not factorise

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


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

Question:
Tom and Katie are discussing arithmetic sequences.

Tom says this is an arithmetic sequence: \( 5,8,11,14,17, \ldots \)

Katie says this is an arithmetic sequence: \( 5,15,45,135,405, \ldots \)

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 arithmetic sequences.

Tom says this is an arithmetic sequence: \( 5,8,11,14,17, \ldots \)

Katie says this is an arithmetic sequence: \( 5,15,45,135,405, \ldots \)

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 arithmetic sequences.

Tom says this is an arithmetic sequence: \( 5,8,11,14,17, \ldots \)

Katie says this is an arithmetic sequence: \( 5,15,45,135,405, \ldots \)

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:
When reading a dash on a number line does not take into account the number at the start or the width of each division

Question:
What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]()

Options:
A. \( \frac{3}{4} \)
B. \( \frac{2}{6} \)
C. \( \frac{5}{12} \)
D. There is no such fraction

Solve the problem as a student with the misconception above.
You 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 arrow on a number line points to the middle value

Question:
What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]()

Options:
A. \( \frac{3}{4} \)
B. \( \frac{2}{6} \)
C. \( \frac{5}{12} \)
D. There is no such fraction

Solve the problem as a student with the misconception above.
You 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 you can use equivalent fractions to break fractions up into smaller divisions

Question:
What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/6. On the rightmost dash is the number 3/6. An arrow points to the 4th dash from the left]()

Options:
A. \( \frac{3}{4} \)
B. \( \frac{2}{6} \)
C. \( \frac{5}{12} \)
D. There is no such fraction

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


Prompt:
Misconception:
Gets order of ratio wrong

Question:
A lassi drink is made of yoghurt and water in the ratio \( 3: 1 \). What fraction of the drink is water?

Options:
A. \( \frac{1}{4} \)
B. \( \frac{3}{4} \)
C. \( \frac{1}{3} \)
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 converting ratio to fractions, puts the other side of the ratio as the denominator rather than the total

Question:
A lassi drink is made of yoghurt and water in the ratio \( 3: 1 \). What fraction of the drink is water?

Options:
A. \( \frac{1}{4} \)
B. \( \frac{3}{4} \)
C. \( \frac{1}{3} \)
D. Not enough information

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


Prompt:
Misconception:
Does not understand the relationship between a ratio and fraction

Question:
A lassi drink is made of yoghurt and water in the ratio \( 3: 1 \). What fraction of the drink is water?

Options:
A. \( \frac{1}{4} \)
B. \( \frac{3}{4} \)
C. \( \frac{1}{3} \)
D. Not enough information

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


Prompt:
Misconception:
Thinks a horizontal line on a distance time graph means a distance of 0

Question:
How far away from home was Rachel at 12:15? ![A line graph with title "A graph to show the distance Rachel travels from her home on her daily run."
The x-axis is titled "Time" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.
The y-axis is titled "Distance from home (Km)" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0).
]()

Options:
A. \( 0 \mathrm{~km} \)
B. \( 7.5 \mathrm{~m} \)
C. \( 750 \mathrm{~m} \)
D. \( 7500 \mathrm{~m} \)

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


Prompt:
Misconception:
When reading values from graphs, writes down the wrong units

Question:
How far away from home was Rachel at 12:15? ![A line graph with title "A graph to show the distance Rachel travels from her home on her daily run."
The x-axis is titled "Time" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.
The y-axis is titled "Distance from home (Km)" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0).
]()

Options:
A. \( 0 \mathrm{~km} \)
B. \( 7.5 \mathrm{~m} \)
C. \( 750 \mathrm{~m} \)
D. \( 7500 \mathrm{~m} \)

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


Prompt:
Misconception:
Thinks there are 100m and a km

Question:
How far away from home was Rachel at 12:15? ![A line graph with title "A graph to show the distance Rachel travels from her home on her daily run."
The x-axis is titled "Time" and is labelled with times from 0800 to 1300 in steps of 1 hour, with the axis going half an hour beyond 1300.
The y-axis is titled "Distance from home (Km)" and the scale is from 0 to 8 in steps of 1km. The following points are plotted and joined together: (0800, 0), (0830, 2), (0900, 3.5),(1000, 6), (1030, 7), (1100, 7.5),(1230, 7.5),(1300, 4.5), (1330, 0).
]()

Options:
A. \( 0 \mathrm{~km} \)
B. \( 7.5 \mathrm{~m} \)
C. \( 750 \mathrm{~m} \)
D. \( 7500 \mathrm{~m} \)

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


Prompt:
Misconception:
Believes a number raised to a power will always give a positive answer

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

Options:
A. \( t^{2}-27=0 \)
B. \( t^{2}=-27 \)
C. \( t^{3}=-27 \)
D. \( t-27=-27 \)

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


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

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

Options:
A. \( t^{2}-27=0 \)
B. \( t^{2}=-27 \)
C. \( t^{3}=-27 \)
D. \( t-27=-27 \)

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


Prompt:
Misconception:
Does not reduce the denominator when an item is not replaced in a probability question

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() Kate picks a yellow ball out and does not replace it.

She then has a second pick.
What is the probability the second pick is a red ball?

Options:
A. \( \frac{3}{7} \)
B. \( \frac{3}{6} \)
C. \( \frac{4}{7} \)
D. \( \frac{4}{6} \)

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 the solution to an equation with matching coefficients of variables on both sides will always be 0

Question:
What is the solution for this equation? \( 4(3 x-2)=2(6 x-8) \)

Options:
A. This equation is impossible to solve
B. \( x=0 \)
C. \( x=-\frac{2}{3} \)
D. This equation has an infinite number of 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:
Believes lines can be parallel by having the same y intercept OR gradient

Question:
Tom and Katie are discussing parallel lines
Tom says \( y=2 x+5 \) and \( y=2 x-7 \) are parallel
Katie says \( y=2 x+5 \) and \( y=3 x+5 \) are parallel
Who is correct?

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

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


Prompt:
Misconception:
Does not understand equivalent fractions

Question:
By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out?

Options:
A. ![A rectangle with 1/3 shaded in red]()
B. ![A rectangle with 2/6 shaded in blue]()
C. ![A rectangle with 3/9 shaded in purple]()
D. ![A rectangle with 6/12 shaded in orange]()

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


Prompt:
Misconception:
Does not understand equivalent fractions

Question:
By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out?

Options:
A. ![A rectangle with 1/3 shaded in red]()
B. ![A rectangle with 2/6 shaded in blue]()
C. ![A rectangle with 3/9 shaded in purple]()
D. ![A rectangle with 6/12 shaded in orange]()

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


Prompt:
Misconception:
Does not understand equivalent fractions

Question:
By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out?

Options:
A. ![A rectangle with 1/3 shaded in red]()
B. ![A rectangle with 2/6 shaded in blue]()
C. ![A rectangle with 3/9 shaded in purple]()
D. ![A rectangle with 6/12 shaded in orange]()

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


Prompt:
Misconception:
Does not understand the term quadratic

Question:
Tom and Katie are discussing quadratic sequences.

Tom says this is a quadratic sequence: \( 3,5,10,17,26, \ldots \)

Katie says this is a quadratic sequence: \( 3,6,12,24,48, \ldots \)

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 understand the term quadratic

Question:
Tom and Katie are discussing quadratic sequences.

Tom says this is a quadratic sequence: \( 3,5,10,17,26, \ldots \)

Katie says this is a quadratic sequence: \( 3,6,12,24,48, \ldots \)

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 multiplying two negatives gives a negative answer

Question:
\( -\frac{3}{4} \times \star=-1 \) What should replace the star?

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

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

Question:
\( -\frac{3}{4} \times \star=-1 \) What should replace the star?

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

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:
In ratio question where the difference between the sides is given, uses that as the total for one side instead

Question:
Bill and Mischa share their profit in a ratio of \( 9: 5 \) Bill gets \( £ 72 \) more than Mischa. How much money did they receive altogether?

Options:
A. \( £ 112 \)
B. \( £ 432 \)
C. \( £ 252 \)
D. £162

Solve the problem as a student with the misconception above.
You 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 ratio question where the difference between the sides is given, uses that as one part without dividing

Question:
Bill and Mischa share their profit in a ratio of \( 9: 5 \) Bill gets \( £ 72 \) more than Mischa. How much money did they receive altogether?

Options:
A. \( £ 112 \)
B. \( £ 432 \)
C. \( £ 252 \)
D. £162

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

Question:
\( 3 \times 5 \times 20= \)

Options:
A. \( 150 \)
B. \( 300 \)
C. \( 28 \)
D. \( 30 \)

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:
When multiplying multiples of ten and the answer requires an extra digit, leaves off that extra digit

Question:
\( 3 \times 5 \times 20= \)

Options:
A. \( 150 \)
B. \( 300 \)
C. \( 28 \)
D. \( 30 \)

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:
When subtracting a fraction from a mixed number, assumes they just subtract the numerator from the integer of the mixed number

Question:
\(
1 \frac{2}{3}-\frac{1}{3}
\)
Which of the following is a correct way to write the answer to this calculation?

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

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


Prompt:
Misconception:
When subtracting a fraction from a mixed number, assumes they subtract the numerator from the integer and the numerator of the mixed number

Question:
\(
1 \frac{2}{3}-\frac{1}{3}
\)
Which of the following is a correct way to write the answer to this calculation?

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

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


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

Question:
What is the answer to this subtraction problem? ![\begin{tabular}{r|r|}
\( 503 \) \\
\( -\quad 98 \) \\
\hline
\end{tabular}]()

Options:
A. \( 495 \)
B. \( 415 \)
C. \( 405 \)
D. \( 595 \)

Solve the problem as a student with the misconception above.
You 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:
What is the answer to this subtraction problem? ![\begin{tabular}{r|r|}
\( 503 \) \\
\( -\quad 98 \) \\
\hline
\end{tabular}]()

Options:
A. \( 495 \)
B. \( 415 \)
C. \( 405 \)
D. \( 595 \)

Solve the problem as a student with the misconception above.
You 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:
Summer buys a dress for \( £ 73 \) and two pairs of shoes for \( £ 41 \) each.
She pays using a \( £ 40 \) gift voucher and some cash.

How much cash does she pay?

Options:
A. £115
B. £154
C. £188
D. £195

Solve the problem as a student with the misconception above.
You 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 can be parallel by having the same y intercept OR gradient

Question:
Tom and Katie are discussing parallel lines
Tom says \( y=4-3 x \) and \( y=4-2 x \) are parallel
Katie says \( y=4-3 x \) and \( y=2-3 x \) are parallel
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 the ten thousands and thousands place value columns

Question:
What is the value of the \( 3 \) in the number below?
\(
43075
\)

Options:
A. \( 30000 \)
B. \( 3 \)
C. \( 30 \)
D. \( 3000 \)

Solve the problem as a student with the misconception above.
You 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 the value of a digit, just gives the digit

Question:
What is the value of the \( 3 \) in the number below?
\(
43075
\)

Options:
A. \( 30000 \)
B. \( 3 \)
C. \( 30 \)
D. \( 3000 \)

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


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

Question:
What is the value of the \( 3 \) in the number below?
\(
43075
\)

Options:
A. \( 30000 \)
B. \( 3 \)
C. \( 30 \)
D. \( 3000 \)

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


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

Question:
Factorise the following expression \( x^{2}+6 x+5 \)

Options:
A. \( (x+2)(x+3) \)
B. Cannot be factorised
C. \( (x+1)(x+5) \)
D. \( x(x+6)+5 \)

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 factorising a quadratic means factorising the variable terms into a single bracket, and leaving out the constant

Question:
Factorise the following expression \( x^{2}+6 x+5 \)

Options:
A. \( (x+2)(x+3) \)
B. Cannot be factorised
C. \( (x+1)(x+5) \)
D. \( x(x+6)+5 \)

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


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

Question:
Kieran thinks of a number. He doubles it and adds \( 6 \). He then divides it by \( 2 \). The answer is \( 8 \). What was his original number? ![A cartoon of a man, in this question called Kieran, wearing a shirt, tie, grey trousers and black shoes. He is thinking of a number, we can tell this because he has a thought bubble above his head with a '?' in it.]()

Options:
A. \( 5 \)
B. \( 11 \)
C. \( 20 \)
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 solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation

Question:
Kieran thinks of a number. He doubles it and adds \( 6 \). He then divides it by \( 2 \). The answer is \( 8 \). What was his original number? ![A cartoon of a man, in this question called Kieran, wearing a shirt, tie, grey trousers and black shoes. He is thinking of a number, we can tell this because he has a thought bubble above his head with a '?' in it.]()

Options:
A. \( 5 \)
B. \( 11 \)
C. \( 20 \)
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:
Only reads the percentage symbol as applying to the units digit

Question:
What is \( 72 \% \) written as a fraction?

Options:
A. \( 7 \frac{2}{100} \)
B. \( \frac{1}{72} \)
C. \( \frac{18}{25} \)
D. None of these options

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


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

Question:
What is \( 72 \% \) written as a fraction?

Options:
A. \( 7 \frac{2}{100} \)
B. \( \frac{1}{72} \)
C. \( \frac{18}{25} \)
D. None of these options

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


Prompt:
Misconception:
Does not recognise when simplifying a fraction may be helpful

Question:
What is \( 72 \% \) written as a fraction?

Options:
A. \( 7 \frac{2}{100} \)
B. \( \frac{1}{72} \)
C. \( \frac{18}{25} \)
D. None of these options

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


Prompt:
Misconception:
Adds instead of multiplying when expanding bracket

Question:
Which of the following answers shows a correct expansion of the expression below?
\[
(x+4)(x-1)
\]

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

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:
Rounds incorrectly when the nearest 10 is a multiple of 100

Question:
What is \( 4296 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 4290 \)
B. \( 4310 \)
C. \( 4300 \)
D. \( 4000 \)

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


Prompt:
Misconception:
Rounds incorrectly when the nearest 10 is a multiple of 100

Question:
What is \( 4296 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 4290 \)
B. \( 4310 \)
C. \( 4300 \)
D. \( 4000 \)

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


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

Question:
What is \( 4296 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 4290 \)
B. \( 4310 \)
C. \( 4300 \)
D. \( 4000 \)

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


Prompt:
Misconception:
Thinks 1l = 1 cubic metre

Question:
\[
100 \text { litres = }
\square \, cubic \, metres
\]

Options:
A. \( 100 \)
B. \( 10 \)
C. \( 0.1 \)
D. \( 0.001 \)

Solve the problem as a student with the misconception above.
You 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 10l = 1 cubic metre

Question:
\[
100 \text { litres = }
\square \, cubic \, metres
\]

Options:
A. \( 100 \)
B. \( 10 \)
C. \( 0.1 \)
D. \( 0.001 \)

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


Prompt:
Misconception:
When adding powers of 10 adds onto the wrong column

Question:
What number is \( 100 \) more than \( 72980 ? \)

Options:
A. \( 73,080 \)
B. \( 73,980 \)
C. \( 7,298,000 \)
D. \( 72,080 \)

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


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

Question:
What number is \( 100 \) more than \( 72980 ? \)

Options:
A. \( 73,080 \)
B. \( 73,980 \)
C. \( 7,298,000 \)
D. \( 72,080 \)

Solve the problem as a student with the misconception above.
You 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 number is \( 100 \) more than \( 72980 ? \)

Options:
A. \( 73,080 \)
B. \( 73,980 \)
C. \( 7,298,000 \)
D. \( 72,080 \)

Solve the problem as a student with the misconception above.
You 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 more digits a number has the greater it is, regardless of place value

Question:
Here are the depths below sea level of \( 3 \) creatures:
Starfish: \( -7 m \)
Shark: \( -9 m \)
Dolphin: \( -8.3 \mathrm{~m} \)
Arrange their depths in ascending order, starting with the deepest

Options:
A. \( 1^{\text {st }} \) Dolphin
\( 2^{\text {nd }} \) Shark
\( 3^{\text {rd }} \) Starfish
B. \( 1^{\text {st }} \) Starfish \( 2^{\text {nd }} \) Dolphin \( 3^{\text {rd }} \) Shark
C. \( 1^{\text {st }} \) Shark
\( 2^{\text {nd }} \) Dolphin
\( 3^{\text {rd }} \) Starfish
D. \( 1^{\text {st }} \) Starfish
\( 2^{\text {nd }} \) Shark
\( 3^{\text {rd }} \) Dolphin

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


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

Question:
Here are the depths below sea level of \( 3 \) creatures:
Starfish: \( -7 m \)
Shark: \( -9 m \)
Dolphin: \( -8.3 \mathrm{~m} \)
Arrange their depths in ascending order, starting with the deepest

Options:
A. \( 1^{\text {st }} \) Dolphin
\( 2^{\text {nd }} \) Shark
\( 3^{\text {rd }} \) Starfish
B. \( 1^{\text {st }} \) Starfish \( 2^{\text {nd }} \) Dolphin \( 3^{\text {rd }} \) Shark
C. \( 1^{\text {st }} \) Shark
\( 2^{\text {nd }} \) Dolphin
\( 3^{\text {rd }} \) Starfish
D. \( 1^{\text {st }} \) Starfish
\( 2^{\text {nd }} \) Shark
\( 3^{\text {rd }} \) Dolphin

Solve the problem as a student with the misconception above.
You 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 vertically opposite angles with angles on a straight line

Question:
Which angle is vertically opposite to angle \( p \) ? ![A diagram with 3 lines. 2 of the lines go from the left to the right of the diagram, getting closer to each other on the right hand side (the lines are not parallel). The 3rd line cuts through these 2 lines from top left to bottom right. Where the lines cross near the top left of the diagram, 4 angles are made. The angle which is nearest the top left corner of the diagram is labelled "A". Clockwise from A, the other angles around this point are labelled "C", "B" and "p". Where the lines cross near the bottom right of the diagram, 4 angles are also made, only one of these is labelled (the angle that is nearest to the top left of the diagram): "D". ]()

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

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


Prompt:
Misconception:
Confuses vertically opposite angles with angles on a straight line

Question:
Which angle is vertically opposite to angle \( p \) ? ![A diagram with 3 lines. 2 of the lines go from the left to the right of the diagram, getting closer to each other on the right hand side (the lines are not parallel). The 3rd line cuts through these 2 lines from top left to bottom right. Where the lines cross near the top left of the diagram, 4 angles are made. The angle which is nearest the top left corner of the diagram is labelled "A". Clockwise from A, the other angles around this point are labelled "C", "B" and "p". Where the lines cross near the bottom right of the diagram, 4 angles are also made, only one of these is labelled (the angle that is nearest to the top left of the diagram): "D". ]()

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

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


Prompt:
Misconception:
Adds when calculating area instead of multiplying

Question:
What is the area of this rectangle? ![A rectangle with a base length 5 cm and a perpendicular height of 8 cm.]()

Options:
A. \( 13 \mathrm{~cm}^{2} \)
B. \( 40 \mathrm{~cm}^{2} \)
C. \( 26 \mathrm{~cm}^{2} \)
D. Not enough information in the diagram

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


Prompt:
Misconception:
Calculates perimeter when asked for area

Question:
What is the area of this rectangle? ![A rectangle with a base length 5 cm and a perpendicular height of 8 cm.]()

Options:
A. \( 13 \mathrm{~cm}^{2} \)
B. \( 40 \mathrm{~cm}^{2} \)
C. \( 26 \mathrm{~cm}^{2} \)
D. Not enough information in the diagram

Solve the problem as a student with the misconception above.
You 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 recall rectangle side length property

Question:
What is the area of this rectangle? ![A rectangle with a base length 5 cm and a perpendicular height of 8 cm.]()

Options:
A. \( 13 \mathrm{~cm}^{2} \)
B. \( 40 \mathrm{~cm}^{2} \)
C. \( 26 \mathrm{~cm}^{2} \)
D. Not enough information in the diagram

Solve the problem as a student with the misconception above.
You 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 straight lines count as edges on 3D shapes

Question:
How many edges does this shape have? ![\( \Delta \)]()

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
D. \( 3 \)

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


Prompt:
Misconception:
Confuses the terms faces and edges

Question:
How many edges does this shape have? ![\( \Delta \)]()

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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 parts of a 3D diagram that look straight class as edges

Question:
How many edges does this shape have? ![\( \Delta \)]()

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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:
Halves when asked to find the square root

Question:
What is the value of the missing number? ![\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{\( 13^{2} \)} \\
\hline\( \ldots \ldots \ldots \) & \( 12^{2} \) \\
\hline
\end{tabular}]()

Options:
A. \( 5 \)
B. \( 12.5 \)
C. \( 1 \)
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:
Thinks the sum of 2 numbers, each squared first, is the same as adding the two numbers and then squaring the total

Question:
What is the value of the missing number? ![\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{\( 13^{2} \)} \\
\hline\( \ldots \ldots \ldots \) & \( 12^{2} \) \\
\hline
\end{tabular}]()

Options:
A. \( 5 \)
B. \( 12.5 \)
C. \( 1 \)
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 multiplying decimals, divides by the wrong power of 10 when reinserting the decimal

Question:
\( 0.8 \times 0.15= \)

Options:
A. \( 1.2 \)
B. \( 1.20 \)
C. \( 0.012 \)
D. \( 0.12 \)

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


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

Question:
\( 0.8 \times 0.15= \)

Options:
A. \( 1.2 \)
B. \( 1.20 \)
C. \( 0.012 \)
D. \( 0.12 \)

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


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

Question:
\( 0.8 \times 0.15= \)

Options:
A. \( 1.2 \)
B. \( 1.20 \)
C. \( 0.012 \)
D. \( 0.12 \)

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


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

Question:
The perimeter of this rectangle is \( 1.6 \mathrm{~m} \).

What is the length of the side marked with a star? ![A rectangle with base length 0.35 m and the side length labelled with a gold, star]()

Options:
A. \( 1.25 \mathrm{~m} \)
B. \( 0.45 \mathrm{~m} \)
C. \( 2.7 \mathrm{~m} \)
D. \( 0.55 \mathrm{~m} \)

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


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

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

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

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


Prompt:
Misconception:
Believes adding two negatives gives a positive answer

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

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

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


Prompt:
Misconception:
Confuses square rooting and halving the number

Question:
A square has an area of \( 64 \mathrm{~cm}^{2} \) What is the length of the square?

Options:
A. \( 32 \mathrm{~cm} \)
B. \( 16 \mathrm{~cm} \)
C. \( 8 \mathrm{~cm} \)
D. \( 64 \mathrm{~cm} \)

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:
Confuses perimeter and area

Question:
A square has an area of \( 64 \mathrm{~cm}^{2} \) What is the length of the square?

Options:
A. \( 32 \mathrm{~cm} \)
B. \( 16 \mathrm{~cm} \)
C. \( 8 \mathrm{~cm} \)
D. \( 64 \mathrm{~cm} \)

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:
Multiplies the number of whole units by the numerator when converting from a mixed number to an improper fraction

Question:
Convert \( 3 \frac{1}{5} \) to an improper fraction.

Options:
A. \( \frac{16}{5} \)
B. \( \frac{3}{5} \)
C. \( \frac{15}{5} \)
D. \( \frac{16}{15} \)

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:
Forgets to add the numerator when converting from a mixed number to an improper fraction

Question:
Convert \( 3 \frac{1}{5} \) to an improper fraction.

Options:
A. \( \frac{16}{5} \)
B. \( \frac{3}{5} \)
C. \( \frac{15}{5} \)
D. \( \frac{16}{15} \)

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


Prompt:
Misconception:
Does not know multiplying by a unit fraction is equivalent to: dividing by its denominator value

Question:
\( 7 \times \frac{1}{4}=7 \div ? \)

Options:
A. \( \frac{4}{4} \)
B. \( \frac{1}{4} \)
C. \( 4 \)
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 dividing an integer by a fraction, thinks they can just multiply instead.

Question:
\( 7 \times \frac{1}{4}=7 \div ? \)

Options:
A. \( \frac{4}{4} \)
B. \( \frac{1}{4} \)
C. \( 4 \)
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 know multiplying by a unit fraction is equivalent to: dividing by its denominator value

Question:
\( 7 \times \frac{1}{4}=7 \div ? \)

Options:
A. \( \frac{4}{4} \)
B. \( \frac{1}{4} \)
C. \( 4 \)
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 realise that the sum of the two shorter sides must be greater than the third side for it to be a possible triangle

Question:
Tom and Katie are arguing about constructing triangles.

Tom says you can construct a triangle with lengths \( 11 \mathrm{~cm}, 10 \mathrm{~cm} \) and \( 2 \mathrm{~cm} \).

Katie says you can construct a triangle with lengths \( 8 \mathrm{~cm}, 5 \mathrm{~cm} \) and \( 3 \mathrm{~cm} \).

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 realise that the sum of the two shorter sides must be greater than the third side for it to be a possible triangle

Question:
Tom and Katie are arguing about constructing triangles.

Tom says you can construct a triangle with lengths \( 11 \mathrm{~cm}, 10 \mathrm{~cm} \) and \( 2 \mathrm{~cm} \).

Katie says you can construct a triangle with lengths \( 8 \mathrm{~cm}, 5 \mathrm{~cm} \) and \( 3 \mathrm{~cm} \).

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 if you multiply a fraction by itself you get a whole

Question:
\( \frac{2}{7} \times ?=1 \)

Options:
A. \( \frac{5}{7} \)
B. \( \frac{7}{2} \)
C. \( \frac{2}{7} \)
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:
When interpreting a pictogram, thinks each symbol stands for 1

Question:
![Pictogram showing smiley faces, where each smiley face is worth 10 people. Game 1 has 5 smiley faces. Game 2 has 2 smiley faces. Game 3 has 3 smiley faces. Game 4 has 2 smiley faces.]() The pictogram shows how many people came to watch a netball match.
What is the mean number of people at each game?

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 10 \)
D. \( 120 \)

Solve the problem as a student with the misconception above.
You 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 you can find the mean from a pictogram

Question:
![Pictogram showing smiley faces, where each smiley face is worth 10 people. Game 1 has 5 smiley faces. Game 2 has 2 smiley faces. Game 3 has 3 smiley faces. Game 4 has 2 smiley faces.]() The pictogram shows how many people came to watch a netball match.
What is the mean number of people at each game?

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 10 \)
D. \( 120 \)

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


Prompt:
Misconception:
When calculating the mean from a list of data, adds up the numbers but does not divide

Question:
![Pictogram showing smiley faces, where each smiley face is worth 10 people. Game 1 has 5 smiley faces. Game 2 has 2 smiley faces. Game 3 has 3 smiley faces. Game 4 has 2 smiley faces.]() The pictogram shows how many people came to watch a netball match.
What is the mean number of people at each game?

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 10 \)
D. \( 120 \)

Solve the problem as a student with the misconception above.
You 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 divide by 2 when calculating the area of a triangle

Question:
What is the area of the triangle? ![An image of a triangle. The width is marked /sqrt(64) and the vertical height is marked 4cm. ]()

Options:
A. \( 32 \mathrm{~cm}^{2} \)
B. \( 64 \mathrm{~cm}^{2} \)
C. \( 256 \mathrm{~cm}^{2} \)
D. \( 16 \mathrm{~cm}^{2} \)

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:
Thinks they double rather than halve when finding the area of a triangle

Question:
What is the area of the triangle? ![An image of a triangle. The width is marked /sqrt(64) and the vertical height is marked 4cm. ]()

Options:
A. \( 32 \mathrm{~cm}^{2} \)
B. \( 64 \mathrm{~cm}^{2} \)
C. \( 256 \mathrm{~cm}^{2} \)
D. \( 16 \mathrm{~cm}^{2} \)

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:
Writes the variable before the coefficient in an algebraic term

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
y \times x+b \times 3
\)

Options:
A. \( y x+b 3 \)
B. \( x y+3 b \)
C. \( y+3 b x \)
D. \( 3 b x y \)

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:
Multiplies all terms together when simplifying an expression

Question:
Which answer shows the following calculation using the correct algebraic convention?
\(
y \times x+b \times 3
\)

Options:
A. \( y x+b 3 \)
B. \( x y+3 b \)
C. \( y+3 b x \)
D. \( 3 b x y \)

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:
Cannot identify a line of symmetry in a simple shape

Question:
![A rectangle]() How many lines of symmetry does this shape have?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
D. \( 4 \)

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


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

Question:
![A rectangle]() How many lines of symmetry does this shape have?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
D. \( 4 \)

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


Prompt:
Misconception:
Thinks rectangles have line symmetry in the diagonals

Question:
![A rectangle]() How many lines of symmetry does this shape have?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
D. \( 4 \)

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


Prompt:
Misconception:
Thinks there are 10 minutes in an hour

Question:
\( 2.5 \) hours \( =_____ \) minutes

Options:
A. \( 150 \)
B. \( 125 \)
C. \( 250 \)
D. \( 205 \)

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


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

Question:
\( 2.5 \) hours \( =_____ \) minutes

Options:
A. \( 150 \)
B. \( 125 \)
C. \( 250 \)
D. \( 205 \)

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


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

Question:
\( 2.5 \) hours \( =_____ \) minutes

Options:
A. \( 150 \)
B. \( 125 \)
C. \( 250 \)
D. \( 205 \)

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


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

Question:
The pictogram shows the number of each type of tree in a small wood.

There are \( 50 \) oak trees.
How many tree symbols would you need to draw to represent this? ![A pictogram with a key showing that 1 tree picture = 20 trees. Elm has 5 tree pictures. Ash has 7 and a half tree pictures. Oak has no tree pictures. Beech has 2 tree pictures.]()

Options:
A. \( 50 \)
B. \( 5 \)
C. \( 2.5 \)
D. \( 10 \)

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


Prompt:
Misconception:
Assumes value of symbols in a pictogram without checking the key

Question:
The pictogram shows the number of each type of tree in a small wood.

There are \( 50 \) oak trees.
How many tree symbols would you need to draw to represent this? ![A pictogram with a key showing that 1 tree picture = 20 trees. Elm has 5 tree pictures. Ash has 7 and a half tree pictures. Oak has no tree pictures. Beech has 2 tree pictures.]()

Options:
A. \( 50 \)
B. \( 5 \)
C. \( 2.5 \)
D. \( 10 \)

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


Prompt:
Misconception:
Assumes value of symbols in a pictogram without checking the key

Question:
The pictogram shows the number of each type of tree in a small wood.

There are \( 50 \) oak trees.
How many tree symbols would you need to draw to represent this? ![A pictogram with a key showing that 1 tree picture = 20 trees. Elm has 5 tree pictures. Ash has 7 and a half tree pictures. Oak has no tree pictures. Beech has 2 tree pictures.]()

Options:
A. \( 50 \)
B. \( 5 \)
C. \( 2.5 \)
D. \( 10 \)

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


Prompt:
Misconception:
Goes the wrong direction in the sequence when identifying term-to-term rule

Question:
Which statement correctly describes this sequence?

\[
7,2,-3, \ldots
\]

Options:
A. The first term is \( 7 \) and the term-to-term rule is \( +5 \)
B. The first term is \( 7 \) and the position-to-term rule is \( -5 \)
C. The first term is \( 7 \) and the term-to-term rule is \( -5 \)
D. The first term is \( 12 \) and the position-to-term rule is \( -5 \)

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:
Describes term to term rules using position to term rules

Question:
Which statement correctly describes this sequence?

\[
7,2,-3, \ldots
\]

Options:
A. The first term is \( 7 \) and the term-to-term rule is \( +5 \)
B. The first term is \( 7 \) and the position-to-term rule is \( -5 \)
C. The first term is \( 7 \) and the term-to-term rule is \( -5 \)
D. The first term is \( 12 \) and the position-to-term rule is \( -5 \)

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 the first term in a sequence is the term before the sequence begins (0th term)

Question:
Which statement correctly describes this sequence?

\[
7,2,-3, \ldots
\]

Options:
A. The first term is \( 7 \) and the term-to-term rule is \( +5 \)
B. The first term is \( 7 \) and the position-to-term rule is \( -5 \)
C. The first term is \( 7 \) and the term-to-term rule is \( -5 \)
D. The first term is \( 12 \) and the position-to-term rule is \( -5 \)

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


Prompt:
Misconception:
Does not see fraction diagrams as equivalent if the shading is in a different pattern

Question:
By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out?

Options:
A. ![A rectangle with 3/4 shaded in red]()
B. ![A rectangle with 6/8 shaded in blue]()
C. ![A rectangle with 8/12 shaded in purple]()
D. ![A rectangle with 12/16 shaded in orange]()

Solve the problem as a student with the misconception above.
You 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 see fraction diagrams as equivalent if the shading is in a different pattern

Question:
By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out?

Options:
A. ![A rectangle with 3/4 shaded in red]()
B. ![A rectangle with 6/8 shaded in blue]()
C. ![A rectangle with 8/12 shaded in purple]()
D. ![A rectangle with 12/16 shaded in orange]()

Solve the problem as a student with the misconception above.
You 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 see fraction diagrams as equivalent if the shading is in a different pattern

Question:
By comparing the fraction of the rectangle that is shaded in each diagram, decide which is the odd one out?

Options:
A. ![A rectangle with 3/4 shaded in red]()
B. ![A rectangle with 6/8 shaded in blue]()
C. ![A rectangle with 8/12 shaded in purple]()
D. ![A rectangle with 12/16 shaded in orange]()

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


Prompt:
Misconception:
When factorising into double brackets, believes the sum of the two values in the brackets equals bx rather than b

Question:
Jo says when she is factorising \( x^{2}-4 x \) she tries to think of two numbers that multiply together to give \( -4 \) and add together to give \( 0 \)

Paul says when he is factorising \( x^{2}-\frac{4}{25} \) he tries to think of two numbers that multiply together to give \( -\frac{4}{25} \) and add together to give \( \frac{2}{25} \)
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:
Heads towards zero when subtracting from a negative

Question:
Which step of the balance diagram is incorrect? ![Image of an equation and three lines of working to solve it.
The equation is 4p+5=2p-9
Step A is 4p=2p-4
Step B is 2p= -4
Step C is p= -2]()

Options:
A. A
B. B
C. C
D. They are all correct

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


Prompt:
Misconception:
Forgets to swap the sign of roots when placing into brackets

Question:
Which of the following could be the equation of this curve? ![A quadratic curve with a minimum turning point at (-2, -1). The curve crosses the x axis at the points (-3,0) and (-1,0). It crosses the y axis at (0,3).]()

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

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


Prompt:
Misconception:
Does not understand the link between the sign of the root and the sign in the bracket

Question:
Which of the following could be the equation of this curve? ![A quadratic curve with a minimum turning point at (-2, -1). The curve crosses the x axis at the points (-3,0) and (-1,0). It crosses the y axis at (0,3).]()

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

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


Prompt:
Misconception:
Does not understand the link between the sign of the root and the sign in the bracket

Question:
Which of the following could be the equation of this curve? ![A quadratic curve with a minimum turning point at (-2, -1). The curve crosses the x axis at the points (-3,0) and (-1,0). It crosses the y axis at (0,3).]()

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

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


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

Question:
\( \frac{3}{7} \) of a group of students are boys.
What would be a possible ratio of boys to girls?

Options:
A. \( 3: 7 \)
B. \( 3: 4 \)
C. \( 3: 10 \)
D. \( 4: 3 \)

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


Prompt:
Misconception:
When converting fractions to ratios, puts the other side of the ratio as the total of the numerator and denominator

Question:
\( \frac{3}{7} \) of a group of students are boys.
What would be a possible ratio of boys to girls?

Options:
A. \( 3: 7 \)
B. \( 3: 4 \)
C. \( 3: 10 \)
D. \( 4: 3 \)

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


Prompt:
Misconception:
Gets order of ratio wrong

Question:
\( \frac{3}{7} \) of a group of students are boys.
What would be a possible ratio of boys to girls?

Options:
A. \( 3: 7 \)
B. \( 3: 4 \)
C. \( 3: 10 \)
D. \( 4: 3 \)

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


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

Question:
Solve the equation:

\(
3 p=\frac{1}{12}
\)

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

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


Prompt:
Misconception:
Does not understand that the numerator and denominator of fractions represent groupings and have the same order of priority as brackets

Question:
\( a, b \) and \( c \) are different numbers
\(
\frac{a}{b+c}=a \div(b+c)
\)
Is the above relationship...

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

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


Prompt:
Misconception:
Does not understand that the numerator and denominator of fractions represent groupings and have the same order of priority as brackets

Question:
\( a, b \) and \( c \) are different numbers
\(
\frac{a}{b+c}=a \div(b+c)
\)
Is the above relationship...

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

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


Prompt:
Misconception:
Does not understand that the numerator and denominator of fractions represent groupings and have the same order of priority as brackets

Question:
\( a, b \) and \( c \) are different numbers
\(
\frac{a}{b+c}=a \div(b+c)
\)
Is the above relationship...

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

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


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

Question:
Which multiplication will help factorise \( x^{2}+33 x+32 \) ?

Options:
A. \( 1 \times 32 \)
B. \( 2 \times 16 \)
C. \( 4 \times 8 \)
D. none of these

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


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

Question:
Which multiplication will help factorise \( x^{2}+33 x+32 \) ?

Options:
A. \( 1 \times 32 \)
B. \( 2 \times 16 \)
C. \( 4 \times 8 \)
D. none of these

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


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

Question:
This is the final stage of Beth's solution to a quadratic equation.
What should replace the star?

\[
(h-8)(h+3)=0
\] \( h=\bigstar \) or \( h=-3 \)

Options:
A. \( 8 \)
B. \( -8 \)
C. \( -3 \)
D. \( 0 \)

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 both solutions of a quadratic will have the same absolute value, even when the graph is not symmetrical about the y axis

Question:
This is the final stage of Beth's solution to a quadratic equation.
What should replace the star?

\[
(h-8)(h+3)=0
\] \( h=\bigstar \) or \( h=-3 \)

Options:
A. \( 8 \)
B. \( -8 \)
C. \( -3 \)
D. \( 0 \)

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 all quadratic equations have a solution of 0

Question:
This is the final stage of Beth's solution to a quadratic equation.
What should replace the star?

\[
(h-8)(h+3)=0
\] \( h=\bigstar \) or \( h=-3 \)

Options:
A. \( 8 \)
B. \( -8 \)
C. \( -3 \)
D. \( 0 \)

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:
Uses sin when tan is required

Question:
Which ratio would you use to find the value of \( p \) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]()

Options:
A. \( \operatorname{Sin} \)
B. Cos
C. Tan
D. None of these

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


Prompt:
Misconception:
Uses cos when tan is required

Question:
Which ratio would you use to find the value of \( p \) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]()

Options:
A. \( \operatorname{Sin} \)
B. Cos
C. Tan
D. None of these

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


Prompt:
Misconception:
Does not understand how to apply sohcahtoa

Question:
Which ratio would you use to find the value of \( p \) ? ![A right-angled triangle with the angle labelled 32 degrees, the side adjacent to this is 6cm and the side opposite is p.]()

Options:
A. \( \operatorname{Sin} \)
B. Cos
C. Tan
D. None of these

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


Prompt:
Misconception:
When squaring a variable, believes they also need to square the coefficient

Question:
Express the following as a single fraction, writing your answer as simply as possible: \( \frac{t}{s}+\frac{2 s}{t} \)

Options:
A. \( \frac{t^{2}+4 s^{2}}{s t} \)
B. \( \frac{t+2 s}{s+t} \)
C. \( \frac{2 s t}{s+t} \)
D. \( \frac{t^{2}+2 s^{2}}{s t} \)

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


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

Question:
Express the following as a single fraction, writing your answer as simply as possible: \( \frac{t}{s}+\frac{2 s}{t} \)

Options:
A. \( \frac{t^{2}+4 s^{2}}{s t} \)
B. \( \frac{t+2 s}{s+t} \)
C. \( \frac{2 s t}{s+t} \)
D. \( \frac{t^{2}+2 s^{2}}{s t} \)

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


Prompt:
Misconception:
When adding/subtracting fractions, adds/subtracts the denominators and multiplies the numerators

Question:
Express the following as a single fraction, writing your answer as simply as possible: \( \frac{t}{s}+\frac{2 s}{t} \)

Options:
A. \( \frac{t^{2}+4 s^{2}}{s t} \)
B. \( \frac{t+2 s}{s+t} \)
C. \( \frac{2 s t}{s+t} \)
D. \( \frac{t^{2}+2 s^{2}}{s t} \)

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


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

Question:
Which of the following pairs of function machines are correct?

Options:
A. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "+ 3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "✕ 2" written inside the next rectangle, "+ 3"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
B. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "+ 3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "+ 3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
C. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "✕ 2" written inside the next rectangle, "+ 3"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
D. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside 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:
Does not follow the arrows through a function machine, changes the order of the operations asked.

Question:
Which of the following pairs of function machines are correct?

Options:
A. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "+ 3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "✕ 2" written inside the next rectangle, "+ 3"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
B. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "+ 3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "+ 3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
C. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "✕ 2" written inside the next rectangle, "+ 3"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
D. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside 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:
Does not follow the arrows through a function machine, changes the order of the operations asked.

Question:
Which of the following pairs of function machines are correct?

Options:
A. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "+ 3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "✕ 2" written inside the next rectangle, "+ 3"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
B. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "✕ 2" written inside the next rectangle, "+ 3" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "+ 3" written inside the next rectangle, "✕ 2"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
C. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has  "✕ 2" written inside the next rectangle, "+ 3"  written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside it.]()
D. ![2 function machines both with 4 rectangles in a row and joined by arrows pointing from left to right. The first function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "3 + 2p" written inside it.
 The second function machine has "p" written inside the first rectangle on the left and "input" written above it; it has "+ 3" written inside the next rectangle, "✕ 2" written inside the next rectangle and the final rectangle on the right has "output" written above it and "2(3 + p)" written inside 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 an equation, uses the same operation rather than the inverse.

Question:
Isaac is trying to solve the equation below.

Here are his steps.

Which steps, if any, are correct? ![An equation 15 =  2p - 4 on the first line.
On the second line, Step 1 : 11 = 2p.
On the third line, Step 2: 22 = p]()

Options:
A. Only step \( 1 \)
B. Only step \( 2 \)
C. Both steps are correct
D. Both steps are incorrect

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


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

Question:
Isaac is trying to solve the equation below.

Here are his steps.

Which steps, if any, are correct? ![An equation 15 =  2p - 4 on the first line.
On the second line, Step 1 : 11 = 2p.
On the third line, Step 2: 22 = p]()

Options:
A. Only step \( 1 \)
B. Only step \( 2 \)
C. Both steps are correct
D. Both steps are incorrect

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


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

Question:
Isaac is trying to solve the equation below.

Here are his steps.

Which steps, if any, are correct? ![An equation 15 =  2p - 4 on the first line.
On the second line, Step 1 : 11 = 2p.
On the third line, Step 2: 22 = p]()

Options:
A. Only step \( 1 \)
B. Only step \( 2 \)
C. Both steps are correct
D. Both steps are incorrect

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


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

Question:
Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]()

Options:
A. \( \frac{40 \times 25}{2} \)
B. \( \frac{40 \times 25 \times 15}{2} \)
C. \( \frac{40 \times 15}{2} \)
D. \( \frac{20 \times 15}{2} \)

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


Prompt:
Misconception:
Has multiplied base by slant height and perpendicular height to find area of a triangle

Question:
Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]()

Options:
A. \( \frac{40 \times 25}{2} \)
B. \( \frac{40 \times 25 \times 15}{2} \)
C. \( \frac{40 \times 15}{2} \)
D. \( \frac{20 \times 15}{2} \)

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:
Halves base but still divides product by 2 when finding area of a triangle

Question:
Which of the following calculations would give the area of this triangle? ![A triangle with the base labelled with 40cm, the perpendicular height 15cm and the slant height labelled with 25 cm]()

Options:
A. \( \frac{40 \times 25}{2} \)
B. \( \frac{40 \times 25 \times 15}{2} \)
C. \( \frac{40 \times 15}{2} \)
D. \( \frac{20 \times 15}{2} \)

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:
Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round

Question:
Which vector correctly describes the translation that maps object \( Q \) onto object \(P \)? ![The image shows a set of axes and two congruent trapezia P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (4, 2), (5, 4), (7, 4), (8, 2).]()

Options:
A. \( \left(\begin{array}{c}-5 \\ 3\end{array}\right) \)
B. \( \left(\begin{array}{c}5 \\ -3\end{array}\right) \)
C. \( \left(\begin{array}{c}-3 \\ 5\end{array}\right) \)
D. \( \left(\begin{array}{c}3 \\ -5\end{array}\right) \)

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


Prompt:
Misconception:
When describing a translation, goes from the image to the original

Question:
Which vector correctly describes the translation that maps object \( Q \) onto object \(P \)? ![The image shows a set of axes and two congruent trapezia P and Q. Trapezium P has vertices at (1, 7), (2, 9), (4, 9), (5, 7). Trapezium Q has vertices at (4, 2), (5, 4), (7, 4), (8, 2).]()

Options:
A. \( \left(\begin{array}{c}-5 \\ 3\end{array}\right) \)
B. \( \left(\begin{array}{c}5 \\ -3\end{array}\right) \)
C. \( \left(\begin{array}{c}-3 \\ 5\end{array}\right) \)
D. \( \left(\begin{array}{c}3 \\ -5\end{array}\right) \)

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


Prompt:
Misconception:
Believes  c, in y=mx+c, will be the y value of the coordinate given despite the x coordinate not being 0.

Question:
A line has a gradient of \( 2 \) and passes through the point \( (1,1) \)
The equation of this line could be...

Options:
A. \( y=2 x+1 \)
B. \( y=x+2 \)
C. \( y=2 x-1 \)
D. \( y=2 x \)

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


Prompt:
Misconception:
When adding powers of 10 adds onto the wrong column

Question:
Sunita wants to buy a sandwich and a tea.

How much money will she need? Joe's Café
Sandwich \( £3.25 \)
Pasty \( £ 2.99 \)
Cake \( £ 2.25 \)
Soup \( £ 3.19 \)
Tea \( £ 1.55 \)
Coffee \( £ 1.95 \)
Orange \( 89\)p

Options:
A. £5.70
B. £4.80
C. £5.80
D. £4.70

Solve the problem as a student with the misconception above.
You 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:
Sunita wants to buy a sandwich and a tea.

How much money will she need? Joe's Café
Sandwich \( £3.25 \)
Pasty \( £ 2.99 \)
Cake \( £ 2.25 \)
Soup \( £ 3.19 \)
Tea \( £ 1.55 \)
Coffee \( £ 1.95 \)
Orange \( 89\)p

Options:
A. £5.70
B. £4.80
C. £5.80
D. £4.70

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


Prompt:
Misconception:
Thinks the interior angles of any polygon add up to 180 degrees

Question:
The octagon below is regular. Find angle \( x \). ![A regular octagon (8 sided polygon). Each side is marked with a single dash to show that all sides are equal in length. One of the interior angles of the octagon is labelled with the letter "x".]()

Options:
A. \( 22.5^{\circ} \)
B. \( 120^{\circ} \)
C. \( 135^{\circ} \)
D. \( 45^{\circ} \)

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


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

Question:
The octagon below is regular. Find angle \( x \). ![A regular octagon (8 sided polygon). Each side is marked with a single dash to show that all sides are equal in length. One of the interior angles of the octagon is labelled with the letter "x".]()

Options:
A. \( 22.5^{\circ} \)
B. \( 120^{\circ} \)
C. \( 135^{\circ} \)
D. \( 45^{\circ} \)

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


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

Question:
When this expression is fully factorised, what is left inside the brackets? \( 24 a b c^{2}-16 b^{2} c \equiv 8 b c(\square) \)

Options:
A. \( 8 a b c \)
B. \( 3 a c-2 b \)
C. \( 3 a c \)
D. \( 3 a-2 \)

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 realise multiplying a variable by itself results in a power of that variable

Question:
When this expression is fully factorised, what is left inside the brackets? \( 24 a b c^{2}-16 b^{2} c \equiv 8 b c(\square) \)

Options:
A. \( 8 a b c \)
B. \( 3 a c-2 b \)
C. \( 3 a c \)
D. \( 3 a-2 \)

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 adding decimals with a different number of decimal places, lines up the digits incorrectly

Question:
\( 0.15+0.2= \)

Options:
A. \( 0.35 \)
B. \( 0.17 \)
C. \( 0.37 \)
D. \( 0.152 \)

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


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

Question:
\( 0.15+0.2= \)

Options:
A. \( 0.35 \)
B. \( 0.17 \)
C. \( 0.37 \)
D. \( 0.152 \)

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


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

Question:
![\begin{tabular}{|lll|}
\hline\( \bullet \) & \( 8 \) & \( 8 \) \\
\hline
\end{tabular}]() How many circles will the next term in this sequence have?

Options:
A. \( 8 \)
B. \( 9 \)
C. \( 12 \)
D. \( 10 \)

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


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

Question:
![\begin{tabular}{|lll|}
\hline\( \bullet \) & \( 8 \) & \( 8 \) \\
\hline
\end{tabular}]() How many circles will the next term in this sequence have?

Options:
A. \( 8 \)
B. \( 9 \)
C. \( 12 \)
D. \( 10 \)

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


Prompt:
Misconception:
Only looks at the difference between one pair of terms when discerning the pattern

Question:
![\begin{tabular}{|lll|}
\hline\( \bullet \) & \( 8 \) & \( 8 \) \\
\hline
\end{tabular}]() How many circles will the next term in this sequence have?

Options:
A. \( 8 \)
B. \( 9 \)
C. \( 12 \)
D. \( 10 \)

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


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

Question:
\( 5 \) hours \( +500 \) minutes \( = \)

Options:
A. \( 10 \) hours
B. \( 8 \) hours and \( 20 \) minutes
C. \( 13 \) hours and \( 20 \) minutes
D. \( 13 \) hours and \( 33 \) minutes

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


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

Question:
\( 5 \) hours \( +500 \) minutes \( = \)

Options:
A. \( 10 \) hours
B. \( 8 \) hours and \( 20 \) minutes
C. \( 13 \) hours and \( 20 \) minutes
D. \( 13 \) hours and \( 33 \) minutes

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


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

Question:
Which function matches the equation
\[
y=5(x+1) ?
\]

Options:
A. ![A function machine which has 4 parts joined by arrows pointing from left to right. "y" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "✕ 5" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 1" written inside it, followed by a horizontal arrow pointing to "𝑥"]()
B. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "✕ 5" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 1" written inside it, followed by a horizontal arrow pointing to "y"]()
C. ![A function machine which has 4 parts joined by arrows pointing from left to right. "y" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 1" written inside it, followed by a horizontal arrow pointing to a rectangle that has "✕ 5" written inside it, followed by a horizontal arrow pointing to "𝑥"]()
D. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 1" written inside it, followed by a horizontal arrow pointing to a rectangle that has "✕ 5" written inside it, followed by a horizontal arrow pointing to "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:
When writing a function as a function machine confuses the input and the output.

Question:
Which function matches the equation
\[
y=5(x+1) ?
\]

Options:
A. ![A function machine which has 4 parts joined by arrows pointing from left to right. "y" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "✕ 5" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 1" written inside it, followed by a horizontal arrow pointing to "𝑥"]()
B. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "✕ 5" written inside it, followed by a horizontal arrow pointing to a rectangle that has "+ 1" written inside it, followed by a horizontal arrow pointing to "y"]()
C. ![A function machine which has 4 parts joined by arrows pointing from left to right. "y" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 1" written inside it, followed by a horizontal arrow pointing to a rectangle that has "✕ 5" written inside it, followed by a horizontal arrow pointing to "𝑥"]()
D. ![A function machine which has 4 parts joined by arrows pointing from left to right. "𝑥" is the first part, written on the left, followed by a horizontal arrow pointing to a rectangle that has "+ 1" written inside it, followed by a horizontal arrow pointing to a rectangle that has "✕ 5" written inside it, followed by a horizontal arrow pointing to "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:
Changes the given operation when substituting

Question:
\( x+y=20 \) Which pair of numbers fits the equation?

Options:
A. \( \begin{array}{c}x=10 \\ y=2\end{array} \)
B. \( \begin{array}{l}x=10 \\ y=-2\end{array} \)
C. \( \begin{array}{c}x=8 \\ y=12\end{array} \)
D. \( \begin{array}{l}x=-8 \\ y=12\end{array} \)

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


Prompt:
Misconception:
substitutes incorrectly

Question:
\( x+y=20 \) Which pair of numbers fits the equation?

Options:
A. \( \begin{array}{c}x=10 \\ y=2\end{array} \)
B. \( \begin{array}{l}x=10 \\ y=-2\end{array} \)
C. \( \begin{array}{c}x=8 \\ y=12\end{array} \)
D. \( \begin{array}{l}x=-8 \\ y=12\end{array} \)

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


Prompt:
Misconception:
substitutes incorrectly

Question:
\( x+y=20 \) Which pair of numbers fits the equation?

Options:
A. \( \begin{array}{c}x=10 \\ y=2\end{array} \)
B. \( \begin{array}{l}x=10 \\ y=-2\end{array} \)
C. \( \begin{array}{c}x=8 \\ y=12\end{array} \)
D. \( \begin{array}{l}x=-8 \\ y=12\end{array} \)

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:
Confused mixed numbers with improper fractions

Question:
\( 2 \frac{7}{10}+2 \frac{1}{4}= \) Leave your answer as a mixed number

Options:
A. \( \frac{99}{20} \)
B. \( 4 \frac{19}{20} \)
C. \( \frac{99}{40} \)
D. \( 4 \frac{8}{14} \)

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


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

Question:
\( 2 \frac{7}{10}+2 \frac{1}{4}= \) Leave your answer as a mixed number

Options:
A. \( \frac{99}{20} \)
B. \( 4 \frac{19}{20} \)
C. \( \frac{99}{40} \)
D. \( 4 \frac{8}{14} \)

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


Prompt:
Misconception:
Does not find a common denominator when adding/subtracting fractions

Question:
\( 2 \frac{7}{10}+2 \frac{1}{4}= \) Leave your answer as a mixed number

Options:
A. \( \frac{99}{20} \)
B. \( 4 \frac{19}{20} \)
C. \( \frac{99}{40} \)
D. \( 4 \frac{8}{14} \)

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


Prompt:
Misconception:
When asked to find data points below a certain value, gives the number of data points above this value

Question:
How many months have an average temperature below 25⁰C ? ![A line graph with title "Monthly Average temperatures for Zakynthos, Greece. (⁰C)".
The x-axis is labelled with the first letter of every month of the year and is titled "months".
The y-axis is titled "Average temperature (⁰C)" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]()

Options:
A. \( 3 \)
B. \( 4 \)
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 asked to find data points below a certain value, gives the number of data points above this value

Question:
How many months have an average temperature below 25⁰C ? ![A line graph with title "Monthly Average temperatures for Zakynthos, Greece. (⁰C)".
The x-axis is labelled with the first letter of every month of the year and is titled "months".
The y-axis is titled "Average temperature (⁰C)" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]()

Options:
A. \( 3 \)
B. \( 4 \)
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:
Includes a data point with the value, when asked to find the number of data points below a value

Question:
How many months have an average temperature below 25⁰C ? ![A line graph with title "Monthly Average temperatures for Zakynthos, Greece. (⁰C)".
The x-axis is labelled with the first letter of every month of the year and is titled "months".
The y-axis is titled "Average temperature (⁰C)" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]()

Options:
A. \( 3 \)
B. \( 4 \)
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}.