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

Question:
Which statement correctly describes the following algebraic expression?
\(
3+a b
\)

Options:
A. "Add \( 3 \) to a multiplied by b."
B. "Add \( \mathrm{a} \) and \( \mathrm{b} \) then add three."
C. "Add three to a and then multiply by b."
D. "Add three to \( \mathrm{b} \) and then multiply by a."

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


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

Question:
Which statement correctly describes the following algebraic expression?
\(
3+a b
\)

Options:
A. "Add \( 3 \) to a multiplied by b."
B. "Add \( \mathrm{a} \) and \( \mathrm{b} \) then add three."
C. "Add three to a and then multiply by b."
D. "Add three to \( \mathrm{b} \) and then multiply by a."

Solve the problem as a student with the misconception above.
You 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 base and perpendicular height when calculating the area of a trapezium

Question:
The area of this trapezium is \( 45 \mathrm{~cm}^{2} \). What would the perpendicular height, \( h \), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]()

Options:
A. \( h=4.5 \mathrm{~cm} \)
B. \( h=3 \mathrm{~cm} \)
C. \( h=9 \mathrm{~cm} \)
D. \( h=6 \mathrm{~cm} \)

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


Prompt:
Misconception:
Does not divide by 2 when calculating the area of a trapezium

Question:
The area of this trapezium is \( 45 \mathrm{~cm}^{2} \). What would the perpendicular height, \( h \), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]()

Options:
A. \( h=4.5 \mathrm{~cm} \)
B. \( h=3 \mathrm{~cm} \)
C. \( h=9 \mathrm{~cm} \)
D. \( h=6 \mathrm{~cm} \)

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


Prompt:
Misconception:
Uses only the base and perpendicular height when calculating the area of a trapezium

Question:
The area of this trapezium is \( 45 \mathrm{~cm}^{2} \). What would the perpendicular height, \( h \), of the trapezium be? ![A trapezium with the parallel sides a and b labelled as 10cm and 5cm and the perpendicular height labelled with h]()

Options:
A. \( h=4.5 \mathrm{~cm} \)
B. \( h=3 \mathrm{~cm} \)
C. \( h=9 \mathrm{~cm} \)
D. \( h=6 \mathrm{~cm} \)

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


Prompt:
Misconception:
Adds the index to the number

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

Options:
A. \( 6 \)
B. \( 9 \)
C. \( 27 \)
D. \( 33 \)

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


Prompt:
Misconception:
Multiplies by the index

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

Options:
A. \( 6 \)
B. \( 9 \)
C. \( 27 \)
D. \( 33 \)

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


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

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

Options:
A. \( 6 \)
B. \( 9 \)
C. \( 27 \)
D. \( 33 \)

Solve the problem as a student with the misconception above.
You 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 every dash on a scale represents an increase of 1

Question:
What is the equation of this line? ![A graph showing a vertical line going through a number on the x axis. The number is one box to the right of -10, where there are 5 boxes between 0 and -10.]()

Options:
A. \( y=10 \)
B. \( x=-9 \)
C. \( x=-8 \)
D. \( y=-8 \)

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 the equations of vertical and horizontal lines

Question:
What is the equation of this line? ![A graph showing a vertical line going through a number on the x axis. The number is one box to the right of -10, where there are 5 boxes between 0 and -10.]()

Options:
A. \( y=10 \)
B. \( x=-9 \)
C. \( x=-8 \)
D. \( y=-8 \)

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 multiplying a positive by a negative gives a positive answer

Question:
Molly is expanding these two brackets.

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

Options:
A. \( +6 p \)
B. \( +8 p \)
C. \( -2 p \)
D. \( -8 p \)

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


Prompt:
Misconception:
When dividing, ignores any remainders

Question:
\( 0.4 \div 0.6= \)

Options:
A. \( 0.6 \)
B. \( 4.6 \)
C. \( 0.666 \ldots \)
D. \( 1.5 \)

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


Prompt:
Misconception:
Believes division is commutative

Question:
\( 0.4 \div 0.6= \)

Options:
A. \( 0.6 \)
B. \( 4.6 \)
C. \( 0.666 \ldots \)
D. \( 1.5 \)

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


Prompt:
Misconception:
When writing ratio from diagram, writes total as one side

Question:
![A group of six squares and three circles]() What is the ratio of squares to circles?

Options:
A. \( 2: 3 \)
B. \( 6: 9 \)
C. \( 6: 3 \)
D. \( 3: 6 \)

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


Prompt:
Misconception:
When writing ratio from diagram, writes total as one side

Question:
![A group of six squares and three circles]() What is the ratio of squares to circles?

Options:
A. \( 2: 3 \)
B. \( 6: 9 \)
C. \( 6: 3 \)
D. \( 3: 6 \)

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:
Mixes up sides of a ratio

Question:
![A group of six squares and three circles]() What is the ratio of squares to circles?

Options:
A. \( 2: 3 \)
B. \( 6: 9 \)
C. \( 6: 3 \)
D. \( 3: 6 \)

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


Prompt:
Misconception:
Does not understand that in a ratio 1:n that one part of the ratio would be n times bigger than the one part

Question:
Kate and Isaac share some biscuits in the ratio \( 1: 4 \). Isaac has  \( _____ \) times as many biscuits as Kate.
What number completes the sentence?

Options:
A. \( 4 \)
B. \( 5 \)
C. \( 1 \)
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:
Does not understand that in a ratio 1:n that one part of the ratio would be n times bigger than the one part

Question:
Kate and Isaac share some biscuits in the ratio \( 1: 4 \). Isaac has  \( _____ \) times as many biscuits as Kate.
What number completes the sentence?

Options:
A. \( 4 \)
B. \( 5 \)
C. \( 1 \)
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:
Finds the mean instead of the median

Question:
The median of these four numbers is \( 5 \).
\(
\begin{array}{cccc}
3&12&1&?
\end{array}
\)
Find the value of the missing number.

Options:
A. \( 7 \)
B. \( 4 \)
C. \( 16 \)
D. \( 6.5 \)

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

Question:
What is the \( 6 \) th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is one orange square. The second pattern is 3 orange squares arranged in an incomplete 2 by 2 square shape with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle with base 3 and height 2, with the top left orange square missing.]()

Options:
A. ![6 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left and top right orange squares missing.]()
B. ![7 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left orange square missing.]()
C. ![11 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left orange square missing.]()
D. ![10 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left and top right orange squares missing.]()

Solve the problem as a student with the misconception above.
You 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:
What is the \( 6 \) th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is one orange square. The second pattern is 3 orange squares arranged in an incomplete 2 by 2 square shape with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle with base 3 and height 2, with the top left orange square missing.]()

Options:
A. ![6 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left and top right orange squares missing.]()
B. ![7 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left orange square missing.]()
C. ![11 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left orange square missing.]()
D. ![10 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left and top right orange squares missing.]()

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


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

Question:
Convert \( \frac{97}{250} \) into a decimal

Options:
A. \( 0.291 \)
B. \( 0.97 \)
C. \( 97.25 \)
D. \( 0.388 \)

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


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

Question:
Convert \( \frac{97}{250} \) into a decimal

Options:
A. \( 0.291 \)
B. \( 0.97 \)
C. \( 97.25 \)
D. \( 0.388 \)

Solve the problem as a student with the misconception above.
You 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 the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an "L" shape.  The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The top rectangle is shaded red.]()

Options:
A. \( 14 \mathrm{~cm}^{2} \)
B. \( 78 \mathrm{~cm}^{2} \)
C. \( 48 \mathrm{~cm}^{2} \)
D. \( 28 \mathrm{~cm}^{2} \)

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:
When calculating the area of a rectilinear compound shape, calculates the are of the surrounding rectangle

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an "L" shape.  The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The top rectangle is shaded red.]()

Options:
A. \( 14 \mathrm{~cm}^{2} \)
B. \( 78 \mathrm{~cm}^{2} \)
C. \( 48 \mathrm{~cm}^{2} \)
D. \( 28 \mathrm{~cm}^{2} \)

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:
Calculates perimeter when asked for area

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an "L" shape.  The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The top rectangle is shaded red.]()

Options:
A. \( 14 \mathrm{~cm}^{2} \)
B. \( 78 \mathrm{~cm}^{2} \)
C. \( 48 \mathrm{~cm}^{2} \)
D. \( 28 \mathrm{~cm}^{2} \)

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 that only the angles need to be the same for a polygon to be regular

Question:
Tom and Katie are discussing regular polygons.
Tom says if all the angles are Katie says if all the sides are equal equal then the polygon must be length then the polygon must be regular regular
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 that only the sides need to be equal for a polygon to be regular

Question:
Tom and Katie are discussing regular polygons.
Tom says if all the angles are Katie says if all the sides are equal equal then the polygon must be length then the polygon must be regular regular
Who is correct?

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

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


Prompt:
Misconception:
Does not understand that all angles and sides must be equal for regular shapes

Question:
Tom and Katie are discussing regular polygons.
Tom says if all the angles are Katie says if all the sides are equal equal then the polygon must be length then the polygon must be regular regular
Who is correct?

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

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


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

Question:
What is \( \frac{17}{40} \) written as a percentage?

Options:
A. \( 34 \% \)
B. \( 68 \% \)
C. \( 42.5 \% \)
D. 17%

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


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

Question:
What is \( \frac{17}{40} \) written as a percentage?

Options:
A. \( 34 \% \)
B. \( 68 \% \)
C. \( 42.5 \% \)
D. 17%

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


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

Question:
What is \( \frac{17}{40} \) written as a percentage?

Options:
A. \( 34 \% \)
B. \( 68 \% \)
C. \( 42.5 \% \)
D. 17%

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


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

Question:
This pictogram shows the different types of music Bob has in his music collection.
Bob has \( 2 \) rave CDs.

How would he display this on the pictogram? ![A pictogram showing the number of CDs Bob has in his musical collection. Pop has 3 and a half symbols, rock has 2 symbols, blues has 2 and a quarter symbols, jazz has 3 and a quarter symbols and classical has 1 and three-quarter symbols. Each symbol represents 4 CDs.]()

Options:
A. ![(1)]()
B. ![\( 00 \)]()
C. ![\( 0 \)]()
D. ![\( \Delta \)]()

Solve the problem as a student with the misconception above.
You 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 steeper downwards line on a graph means a slower decrease

Question:
Sunita accelerates quickly, then travels at a constant speed, then slowly comes to rest. Which of the following velocity \( (v) \) time \( (t) \) graphs is most likely to illustrate Sunita's journey?

Options:
A. ![A graph with time on the horizontal axis and velocity on the vertical axis. The graph at a point above the origin, travels horizontally right, travels down and right in a straight line, then travels horizontally right again.]()
B. ![A graph with time on the horizontal axis and velocity on the vertical axis. The graph starts at the origin, travels right and up in a steep straight line, travels horizontally right, then travels right and down in a less steep straight line than the start, until it reaches the horizontal axis.]()
C. ![A graph with time on the horizontal axis and velocity on the vertical axis. The graph starts at the origin, travels right and up in a straight line, travels horizontally right, then travels right and up in a more steep straight line than the start.]()
D. ![A graph with time on the horizontal axis and distance on the vertical axis. The graph starts at the origin, travels right and up in a straight line, travels horizontally right, then travels right and down in a more steep straight line than the start, until it reaches the horizontal axis.]()

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


Prompt:
Misconception:
When converting from an improper fraction to a mixed number, just writes the tens digit as the number of wholes

Question:
What mixed number fraction is represented below? ![Four bars, each split into six equal parts. In three of the shapes, all six parts are shaded. In the fourth shape, five out of six parts are shaded.]()

Options:
A. \( 2 \frac{3}{6} \)
B. \( 3 \frac{5}{6} \)
C. \( \frac{23}{6} \)
D. \( 4 \frac{5}{6} \)

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:
Confused mixed numbers with improper fractions

Question:
What mixed number fraction is represented below? ![Four bars, each split into six equal parts. In three of the shapes, all six parts are shaded. In the fourth shape, five out of six parts are shaded.]()

Options:
A. \( 2 \frac{3}{6} \)
B. \( 3 \frac{5}{6} \)
C. \( \frac{23}{6} \)
D. \( 4 \frac{5}{6} \)

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


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

Question:
What is the 7th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is 1 orange square. The second pattern is 3 orange squares arranged as an incomplete rectangle of base 2 and height 2, with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle of base 3 and height 2, with the top left orange square missing.]()

Options:
A. ![7 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left orange square missing.]()
B. ![9 orange squares arranged as an incomplete rectangle of base 5 and height 2, with the top left orange square missing.]()
C. ![11 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left orange square missing.]()
D. ![13 orange squares arranged as an incomplete rectangle of base 7 and height 2, with the top left orange square missing.]()

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


Prompt:
Misconception:
When asked for a specific term in a sequence gives a different term, which is not the next

Question:
What is the 7th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is 1 orange square. The second pattern is 3 orange squares arranged as an incomplete rectangle of base 2 and height 2, with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle of base 3 and height 2, with the top left orange square missing.]()

Options:
A. ![7 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left orange square missing.]()
B. ![9 orange squares arranged as an incomplete rectangle of base 5 and height 2, with the top left orange square missing.]()
C. ![11 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left orange square missing.]()
D. ![13 orange squares arranged as an incomplete rectangle of base 7 and height 2, with the top left orange square missing.]()

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


Prompt:
Misconception:
When asked for a specific term in a sequence gives a different term, which is not the next

Question:
What is the 7th pattern in this sequence? ![Three consecutive patterns in a sequence. The first pattern is 1 orange square. The second pattern is 3 orange squares arranged as an incomplete rectangle of base 2 and height 2, with the top left orange square missing. The third pattern is 5 orange squares arranged as an incomplete rectangle of base 3 and height 2, with the top left orange square missing.]()

Options:
A. ![7 orange squares arranged as an incomplete rectangle of base 4 and height 2, with the top left orange square missing.]()
B. ![9 orange squares arranged as an incomplete rectangle of base 5 and height 2, with the top left orange square missing.]()
C. ![11 orange squares arranged as an incomplete rectangle of base 6 and height 2, with the top left orange square missing.]()
D. ![13 orange squares arranged as an incomplete rectangle of base 7 and height 2, with the top left orange square missing.]()

Solve the problem as a student with the misconception above.
You 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 \( 10,000 \) more than \( 298,603 \) ?

Options:
A. \( 398,603 \)
B. \( 2,986,030,000 \)
C. \( 208,603 \)
D. \( 308,603 \)

Solve the problem as a student with the misconception above.
You 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 \( 10,000 \) more than \( 298,603 \) ?

Options:
A. \( 398,603 \)
B. \( 2,986,030,000 \)
C. \( 208,603 \)
D. \( 308,603 \)

Solve the problem as a student with the misconception above.
You 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 \( 10,000 \) more than \( 298,603 \) ?

Options:
A. \( 398,603 \)
B. \( 2,986,030,000 \)
C. \( 208,603 \)
D. \( 308,603 \)

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


Prompt:
Misconception:
Thinks angles which look the same on diagram will be equal

Question:
What is the size of angle \( p \) ? ![A triangle with angles labelled 49 degrees, 51 degrees and p [not to scale]]()

Options:
A. \( 51^{\circ} \)
B. \( 70^{\circ} \)
C. \( 80^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Does not know that angles in a triangle sum to 180 degrees

Question:
What is the size of angle \( p \) ? ![A triangle with angles labelled 49 degrees, 51 degrees and p [not to scale]]()

Options:
A. \( 51^{\circ} \)
B. \( 70^{\circ} \)
C. \( 80^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Multiplies by the index

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{8}^{\boldsymbol{x}} \) \begin{tabular}{|l|c|}
\hline\( x \) & \( \frac{1}{3} \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( \frac{8}{3} \)
B. \( \sqrt{8} \)
C. \( 2 \)
D. \( 24 \)

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


Prompt:
Misconception:
Mixes up square rooting and cube rooting

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{8}^{\boldsymbol{x}} \) \begin{tabular}{|l|c|}
\hline\( x \) & \( \frac{1}{3} \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( \frac{8}{3} \)
B. \( \sqrt{8} \)
C. \( 2 \)
D. \( 24 \)

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


Prompt:
Misconception:
Divides by the index

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{8}^{\boldsymbol{x}} \) \begin{tabular}{|l|c|}
\hline\( x \) & \( \frac{1}{3} \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( \frac{8}{3} \)
B. \( \sqrt{8} \)
C. \( 2 \)
D. \( 24 \)

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


Prompt:
Misconception:
Does not think we can have negative powers in standard form

Question:
Write the following number in standard form:
\[
0.0003001
\]

Options:
A. \( 3.001 \times 10^{4} \)
B. \( 3.1 \times 10^{-4} \)
C. \( 3.001 \times 10^{-4} \)
D. \( 3.1 \times 10^{-7} \)

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


Prompt:
Misconception:
When changing a number to standard form omits zero's of significance

Question:
Write the following number in standard form:
\[
0.0003001
\]

Options:
A. \( 3.001 \times 10^{4} \)
B. \( 3.1 \times 10^{-4} \)
C. \( 3.001 \times 10^{-4} \)
D. \( 3.1 \times 10^{-7} \)

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


Prompt:
Misconception:
Subtracts instead of adds when answering worded problems

Question:
Write the following number in standard form:
\[
0.0003001
\]

Options:
A. \( 3.001 \times 10^{4} \)
B. \( 3.1 \times 10^{-4} \)
C. \( 3.001 \times 10^{-4} \)
D. \( 3.1 \times 10^{-7} \)

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


Prompt:
Misconception:
Thinks the number of wholes in a mixed number represents the tens from the numerator of an improper fraction

Question:
Convert this into an improper fraction:
\(
4 \frac{2}{3}
\)

Options:
A. \( \frac{42}{3} \)
B. \( \frac{14}{3} \)
C. \( \frac{11}{3} \)
D. \( \frac{12}{3} \)

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


Prompt:
Misconception:
Thinks you multiply by the numerator and add the denominator when converting a mixed number to an improper fraction

Question:
Convert this into an improper fraction:
\(
4 \frac{2}{3}
\)

Options:
A. \( \frac{42}{3} \)
B. \( \frac{14}{3} \)
C. \( \frac{11}{3} \)
D. \( \frac{12}{3} \)

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

Question:
Convert this into an improper fraction:
\(
4 \frac{2}{3}
\)

Options:
A. \( \frac{42}{3} \)
B. \( \frac{14}{3} \)
C. \( \frac{11}{3} \)
D. \( \frac{12}{3} \)

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


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

Question:
![A set of axes with a vertical line going through 3 on the x axis]() What is the equation of this line?

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

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:
Confuses lines of the form y = a and y= ax

Question:
![A set of axes with a vertical line going through 3 on the x axis]() What is the equation of this line?

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

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:
Does not recognise metres as a unit of length

Question:
George has answered a question on perimeter and worked out an answer of \( 310 \).

Behind the star he has written the units that he used.

Which of the following units is definitely wrong? \( 310 \color{yellow} \bigstar\)

Options:
A. \( m \)
B. \(mm \)
C. \( f t \)
D. \( m l \)

Solve the problem as a student with the misconception above.
You 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 millimetres as a unit of length

Question:
George has answered a question on perimeter and worked out an answer of \( 310 \).

Behind the star he has written the units that he used.

Which of the following units is definitely wrong? \( 310 \color{yellow} \bigstar\)

Options:
A. \( m \)
B. \(mm \)
C. \( f t \)
D. \( m l \)

Solve the problem as a student with the misconception above.
You 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 feet (ft) as a unit of length

Question:
George has answered a question on perimeter and worked out an answer of \( 310 \).

Behind the star he has written the units that he used.

Which of the following units is definitely wrong? \( 310 \color{yellow} \bigstar\)

Options:
A. \( m \)
B. \(mm \)
C. \( f t \)
D. \( m l \)

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


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

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

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

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


Prompt:
Misconception:
Thinks the inverse of addition is multiplication

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

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

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


Prompt:
Misconception:
Thinks the inverse of addition is division

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

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

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


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

Question:
Which of the following could be the equation of this curve? ![A graph of a quadratic curve that crosses the x axis at (1,0) and (3,0) and 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 graph of a quadratic curve that crosses the x axis at (1,0) and (3,0) and 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 graph of a quadratic curve that crosses the x axis at (1,0) and (3,0) and 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:
In ratio where total is given, treats that as one part without dividing

Question:
Tom and Katie share \( £ 30 \) in the ratio \( 3\;: 2 \).
Which of the following diagrams best represents this situation?

Options:
A. ![A bar split into 3 pink blocks and 2 blue blocks. All the blocks are the same size and each block is labelled £30.]()
B. ![A pink bar split into 3 blocks, and below it a shorter blue bar split into 2 blocks. All the blocks are the same size. The difference in length between the pink bar and the blue bar is labelled £30.]()
C. ![A bar split into 3 pink blocks and 2 blue blocks. All the blocks are the same size and the length of the whole bar is labelled £30.]()
D. ![A pink bar split into 3 blocks, and below it a shorter blue bar split into 2 blocks. All the blocks are the same size. The length of the pink bar is labelled £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 drawing bar diagram for ratio, shows the total as the difference between parts

Question:
Tom and Katie share \( £ 30 \) in the ratio \( 3\;: 2 \).
Which of the following diagrams best represents this situation?

Options:
A. ![A bar split into 3 pink blocks and 2 blue blocks. All the blocks are the same size and each block is labelled £30.]()
B. ![A pink bar split into 3 blocks, and below it a shorter blue bar split into 2 blocks. All the blocks are the same size. The difference in length between the pink bar and the blue bar is labelled £30.]()
C. ![A bar split into 3 pink blocks and 2 blue blocks. All the blocks are the same size and the length of the whole bar is labelled £30.]()
D. ![A pink bar split into 3 blocks, and below it a shorter blue bar split into 2 blocks. All the blocks are the same size. The length of the pink bar is labelled £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 drawing bar diagram for ratio, shows the total amount as the total of one side

Question:
Tom and Katie share \( £ 30 \) in the ratio \( 3\;: 2 \).
Which of the following diagrams best represents this situation?

Options:
A. ![A bar split into 3 pink blocks and 2 blue blocks. All the blocks are the same size and each block is labelled £30.]()
B. ![A pink bar split into 3 blocks, and below it a shorter blue bar split into 2 blocks. All the blocks are the same size. The difference in length between the pink bar and the blue bar is labelled £30.]()
C. ![A bar split into 3 pink blocks and 2 blue blocks. All the blocks are the same size and the length of the whole bar is labelled £30.]()
D. ![A pink bar split into 3 blocks, and below it a shorter blue bar split into 2 blocks. All the blocks are the same size. The length of the pink bar is labelled £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:
Multiplies the numerators when adding fractions with a common denominator

Question:
Calculate:
\(
\frac{2}{7}+\frac{1}{7}
\)

Options:
A. \( \frac{2}{7} \)
B. \( \frac{2}{49} \)
C. \( \frac{3}{7} \)
D. \( \frac{3}{14} \)

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 add fractions, multiplies instead

Question:
Calculate:
\(
\frac{2}{7}+\frac{1}{7}
\)

Options:
A. \( \frac{2}{7} \)
B. \( \frac{2}{49} \)
C. \( \frac{3}{7} \)
D. \( \frac{3}{14} \)

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:
Calculate:
\(
\frac{2}{7}+\frac{1}{7}
\)

Options:
A. \( \frac{2}{7} \)
B. \( \frac{2}{49} \)
C. \( \frac{3}{7} \)
D. \( \frac{3}{14} \)

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:
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|}{\( 15^{2} \)} \\
\hline\( \square^{2} \) & \( 2 \) \\
\hline
\end{tabular}]()

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 9 \)
D. \( 40.5 \)

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:
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|}{\( 15^{2} \)} \\
\hline\( \square^{2} \) & \( 2 \) \\
\hline
\end{tabular}]()

Options:
A. \( 3 \)
B. \( 6 \)
C. \( 9 \)
D. \( 40.5 \)

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


Prompt:
Misconception:
Subtracts instead of adds

Question:
A \( 4 \) digit number belongs in this box to make the calculation true
\(
\square -7806=1253
\)
What is the \( 4^{\text {th }} \) digit of the number that belongs in the box?

Options:
A. \( 9 \)
B. \( 3 \)
C. \( 8 \)
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 the meaning of the word digit

Question:
A \( 4 \) digit number belongs in this box to make the calculation true
\(
\square -7806=1253
\)
What is the \( 4^{\text {th }} \) digit of the number that belongs in the box?

Options:
A. \( 9 \)
B. \( 3 \)
C. \( 8 \)
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 recognise that addition is the inverse operation of subtraction

Question:
A \( 4 \) digit number belongs in this box to make the calculation true
\(
\square -7806=1253
\)
What is the \( 4^{\text {th }} \) digit of the number that belongs in the box?

Options:
A. \( 9 \)
B. \( 3 \)
C. \( 8 \)
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:
Believes that adding a negative will increase the value of the original number

Question:
\( (-9)+(-4)= \)

Options:
A. \( -5 \)
B. \( 5 \)
C. \( 13 \)
D. \( -13 \)

Solve the problem as a student with the misconception above.
You 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:
\( (-9)+(-4)= \)

Options:
A. \( -5 \)
B. \( 5 \)
C. \( 13 \)
D. \( -13 \)

Solve the problem as a student with the misconception above.
You 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 sequences Tom says \( (2 n+1)^{2} \) would produce a linear sequence Katie says \( 1-\frac{n}{2} \) would produce a linear sequence 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 sequences Tom says \( (2 n+1)^{2} \) would produce a linear sequence Katie says \( 1-\frac{n}{2} \) would produce a linear sequence 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 linear sequences cannot include fractions

Question:
Tom and Katie are discussing sequences Tom says \( (2 n+1)^{2} \) would produce a linear sequence Katie says \( 1-\frac{n}{2} \) would produce a linear sequence 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 two digits sum to 10 or more during an addition problem, does not add one to the preceding digit

Question:
\( 3.52+2.75= \)

Options:
A. \( 5.27 \)
B. \( 7.17 \)
C. \( 6.27 \)
D. \( 5.127 \)

Solve the problem as a student with the misconception above.
You 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, just adds the digits and ignores place value

Question:
\( 3.52+2.75= \)

Options:
A. \( 5.27 \)
B. \( 7.17 \)
C. \( 6.27 \)
D. \( 5.127 \)

Solve the problem as a student with the misconception above.
You 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, just adds the digits and ignores place value

Question:
\( 3.52+2.75= \)

Options:
A. \( 5.27 \)
B. \( 7.17 \)
C. \( 6.27 \)
D. \( 5.127 \)

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


Prompt:
Misconception:
Thinks x = 1 at the x axis

Question:
What is the equation of the \( x \) axis?

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

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:
Confuses the equations of vertical and horizontal lines

Question:
What is the equation of the \( x \) axis?

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

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


Prompt:
Misconception:
Thinks x = y is an axis

Question:
What is the equation of the \( x \) axis?

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

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:
Identifies the biggest value for the range

Question:
What is the range of this set of data?
\[
4 \mathrm{~cm}, \quad 22 \mathrm{~cm}, \quad 5 \mathrm{~cm}, \quad 7 \mathrm{~cm}
\]

Options:
A. \( 18 \mathrm{~cm} \)
B. \( 22 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 26 \mathrm{~cm} \)

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


Prompt:
Misconception:
Thinks the range is just the first value subtracted from the last value, without ordering

Question:
What is the range of this set of data?
\[
4 \mathrm{~cm}, \quad 22 \mathrm{~cm}, \quad 5 \mathrm{~cm}, \quad 7 \mathrm{~cm}
\]

Options:
A. \( 18 \mathrm{~cm} \)
B. \( 22 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 26 \mathrm{~cm} \)

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

Question:
What is the range of this set of data?
\[
4 \mathrm{~cm}, \quad 22 \mathrm{~cm}, \quad 5 \mathrm{~cm}, \quad 7 \mathrm{~cm}
\]

Options:
A. \( 18 \mathrm{~cm} \)
B. \( 22 \mathrm{~cm} \)
C. \( 3 \mathrm{~cm} \)
D. \( 26 \mathrm{~cm} \)

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


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

Question:
Which of the following is the most accurate way to describe this sequence?

\[
4,10,16,22,28, \ldots
\]

Options:
A. The first term is \( 6 \) and the common difference is positive \( 4 \)
B. The first term is \( 6 \) and the common difference is negative \( 4 \)
C. The first term is \( 4 \) and the common difference is positive \( 6 \)
D. The first term is \( 4 \) and the common difference is negative \( 6 \)

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


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

Question:
Which of the following is the most accurate way to describe this sequence?

\[
4,10,16,22,28, \ldots
\]

Options:
A. The first term is \( 6 \) and the common difference is positive \( 4 \)
B. The first term is \( 6 \) and the common difference is negative \( 4 \)
C. The first term is \( 4 \) and the common difference is positive \( 6 \)
D. The first term is \( 4 \) and the common difference is negative \( 6 \)

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:
Lines up the digits incorrectly when doing an addition involving two numbers with a different amount of digits

Question:
\( 23+108= \)

Options:
A. \( 1238 \)
B. \( 338 \)
C. \( 121 \)
D. \( 131 \)

Solve the problem as a student with the misconception above.
You 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:
\( 23+108= \)

Options:
A. \( 1238 \)
B. \( 338 \)
C. \( 121 \)
D. \( 131 \)

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


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

Question:
\( 0.2=\frac{1}{5}=? \% \)

Options:
A. \( 15 \% \)
B. \( 20 \% \)
C. \( 50 \% \)
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:
Multiplies by 10 instead of 100 when converting decimal to percentage

Question:
\( 0.2=\frac{1}{5}=? \% \)

Options:
A. \( 15 \% \)
B. \( 20 \% \)
C. \( 50 \% \)
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 factorising, finds a factor that goes into only the first term of the expression

Question:
What should replace the star and triangle when this expression is fully factorised? \( 8 m - 10 \equiv {\bigstar}(\triangle m-\bigcirc) \)

Options:
A. \( \begin{array}{l}{\bigstar}=8 \\ \Delta=1\end{array} \)
B. \( \begin{array}{l}{\bigstar}=2 \\ \Delta=4\end{array} \)
C. \( \begin{array}{l}{\bigstar}=5 \\ \Delta=3\end{array} \)
D. \( \begin{array}{l}{\bigstar}=4 \\ \Delta=2\end{array} \)

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


Prompt:
Misconception:
Believes factors add to give a number

Question:
What should replace the star and triangle when this expression is fully factorised? \( 8 m - 10 \equiv {\bigstar}(\triangle m-\bigcirc) \)

Options:
A. \( \begin{array}{l}{\bigstar}=8 \\ \Delta=1\end{array} \)
B. \( \begin{array}{l}{\bigstar}=2 \\ \Delta=4\end{array} \)
C. \( \begin{array}{l}{\bigstar}=5 \\ \Delta=3\end{array} \)
D. \( \begin{array}{l}{\bigstar}=4 \\ \Delta=2\end{array} \)

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


Prompt:
Misconception:
Believes that when a shape touches the mirror line, all of its vertices will stay the same when reflected

Question:
The triangle is reflected in the \( x \)-axis
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 8, y-axis from -5 to 6. Three points are plotted and joined to make a triangle: (2, 0), (4, 0), (2, 3). Point (2, 3) is labelled with the letter "P". ]()

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

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


Prompt:
Misconception:
Believes that reflection always switches the x and y coordinates

Question:
The triangle is reflected in the \( x \)-axis
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 8, y-axis from -5 to 6. Three points are plotted and joined to make a triangle: (2, 0), (4, 0), (2, 3). Point (2, 3) is labelled with the letter "P". ]()

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

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


Prompt:
Misconception:
Believes the equation of a horizontal line is in the form x = ay, where a is the y intercept

Question:
What is the equation of this line? ![A graph showing a horizontal line going through 4 on the y axis.]()

Options:
A. \( y=4 \)
B. \( x=4 y \)
C. \( y=4 x \)
D. \( x=4 \)

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

Question:
What is the equation of this line? ![A graph showing a horizontal line going through 4 on the y axis.]()

Options:
A. \( y=4 \)
B. \( x=4 y \)
C. \( y=4 x \)
D. \( x=4 \)

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:
Confuses the equations of vertical and horizontal lines

Question:
What is the equation of this line? ![A graph showing a horizontal line going through 4 on the y axis.]()

Options:
A. \( y=4 \)
B. \( x=4 y \)
C. \( y=4 x \)
D. \( x=4 \)

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:
Chooses the correct scale when measuring angles on a protractor but starts from the wrong number when the angle is in between two labelled dashes

Question:
Which diagram shows an angle of \( 135^{\circ} \) ?

Options:
A. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise, to the red line that is half way between 130 and 140 (inner scale) and halfway between 50 and 40 (outer scale).]()
B. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise, to the red line that is half way between 120 and 130 (inner scale) and halfway between 60 and 50 (outer scale).]()
C. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise , to the red line that is half way between 40 and 50 (inner scale) and halfway between 140 and 130 (outer scale).]()
D. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, to the red line that is half way between 50 and 60 (inner scale) and halfway between 130 and 120 (outer scale).]()

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


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

Question:
Which diagram shows an angle of \( 135^{\circ} \) ?

Options:
A. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise, to the red line that is half way between 130 and 140 (inner scale) and halfway between 50 and 40 (outer scale).]()
B. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise, to the red line that is half way between 120 and 130 (inner scale) and halfway between 60 and 50 (outer scale).]()
C. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise , to the red line that is half way between 40 and 50 (inner scale) and halfway between 140 and 130 (outer scale).]()
D. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the protractor, to the red line that is half way between 50 and 60 (inner scale) and halfway between 130 and 120 (outer scale).]()

Solve the problem as a student with the misconception above.
You 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 highest from the lowest when calculating the range

Question:
The data is in ascending order.
\(
\begin{array}{llllll}
x & 5 & 8 & y & 19 & 25
\end{array}
\)
Write an expression for the range.

Options:
A. \( x-25 \)
B. \( y-8 \)
C. \( 25-x \)
D. \( \frac{57+y+x}{6} \)

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:
Finds the mean instead of the range

Question:
The data is in ascending order.
\(
\begin{array}{llllll}
x & 5 & 8 & y & 19 & 25
\end{array}
\)
Write an expression for the range.

Options:
A. \( x-25 \)
B. \( y-8 \)
C. \( 25-x \)
D. \( \frac{57+y+x}{6} \)

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


Prompt:
Misconception:
When given a linear sequence, cannot match it to a visual pattern

Question:
Which sequence matches this graph? ![Position]()

Options:
A. ![The sequence 5, 7, 9 represented pictorially using black line segments shaped into triangles which share a side.]()
B. ![The sequence 3, 5, 7 represented pictorially using squares. For the first term 3 squares are placed with two squares as the base and one square stacked on top of the square on the left hand side. For each additional term, 2 squares, stacked on top of each other are added to the left hand side of the previous term's image.]()
C. ![The sequence 4, 7, 10  represented pictorially using red line segments shaped to form squares.]()
D. ![The first three triangular numbers represented using purple dots.]()

Solve the problem as a student with the misconception above.
You 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 given a linear sequence, cannot match it to a visual pattern

Question:
Which sequence matches this graph? ![Position]()

Options:
A. ![The sequence 5, 7, 9 represented pictorially using black line segments shaped into triangles which share a side.]()
B. ![The sequence 3, 5, 7 represented pictorially using squares. For the first term 3 squares are placed with two squares as the base and one square stacked on top of the square on the left hand side. For each additional term, 2 squares, stacked on top of each other are added to the left hand side of the previous term's image.]()
C. ![The sequence 4, 7, 10  represented pictorially using red line segments shaped to form squares.]()
D. ![The first three triangular numbers represented using purple dots.]()

Solve the problem as a student with the misconception above.
You 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 given a linear sequence, cannot match it to a visual pattern

Question:
Which sequence matches this graph? ![Position]()

Options:
A. ![The sequence 5, 7, 9 represented pictorially using black line segments shaped into triangles which share a side.]()
B. ![The sequence 3, 5, 7 represented pictorially using squares. For the first term 3 squares are placed with two squares as the base and one square stacked on top of the square on the left hand side. For each additional term, 2 squares, stacked on top of each other are added to the left hand side of the previous term's image.]()
C. ![The sequence 4, 7, 10  represented pictorially using red line segments shaped to form squares.]()
D. ![The first three triangular numbers represented using purple dots.]()

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


Prompt:
Misconception:
Subtracts instead of adds when using inverse operations to solve an equation

Question:
Solve the following equation for \( a \) :
\[
2=3 a-4
\]

Options:
A. \( a=2 \)
B. \( a=-\frac{2}{3} \)
C. \( a=-6 \)
D. \( a=-2 \)

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 that gradient represents rate of change

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

The gradient of the positive sloping section would tell us... ![A graph with time (secs) on the horizontal axis and mass (g) on the vertical axis. The graph starts at the origin, travels in a straight line up and right, travels horizontally, then travels in a straight line down and right back to the x-axis, more steeply than the start. ]()

Options:
A. The temperature of the sand is rising
B. The rate the mass of sand in the bucket is decreasing
C. The mass of sand in the bucket
D. The rate the mass of sand in the bucket is increasing

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


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

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

Options:
A. \( 27 \)
B. \( -27 \)
C. \( -11 \)
D. \( -19 \)

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


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
![A solid yellow equilateral triangle (3 sided polygon with all 3 sides of equal length).]() What is the order of rotational symmetry of this equilateral triangle?

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:
Gives one fewer order of rotational symmetry than there is

Question:
![A solid yellow equilateral triangle (3 sided polygon with all 3 sides of equal length).]() What is the order of rotational symmetry of this equilateral triangle?

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

Question:
Tom and Katie are discussing linear sequences Tom says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares so the bottom line is two squares long. The second shape is also an L but with a bottom line of three squares. The fourth shape is the same but the bottom line is four squares long.  ]() Katie says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares. The second shape is an L made of 5 squares, two on the top row and three on the bottom row. The third shape is an L made of 7 squares, 3 on the top row and four on the bottom. ]() Who is correct?

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

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


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

Question:
Tom and Katie are discussing linear sequences Tom says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares so the bottom line is two squares long. The second shape is also an L but with a bottom line of three squares. The fourth shape is the same but the bottom line is four squares long.  ]() Katie says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares. The second shape is an L made of 5 squares, two on the top row and three on the bottom row. The third shape is an L made of 7 squares, 3 on the top row and four on the bottom. ]() Who is correct?

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

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


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

Question:
Tom and Katie are discussing linear sequences Tom says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares so the bottom line is two squares long. The second shape is also an L but with a bottom line of three squares. The fourth shape is the same but the bottom line is four squares long.  ]() Katie says this is a linear sequence: ![Three shapes made of squares. The first is an L-shape made of 3 squares. The second shape is an L made of 5 squares, two on the top row and three on the bottom row. The third shape is an L made of 7 squares, 3 on the top row and four on the bottom. ]() Who is correct?

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

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


Prompt:
Misconception:
Believes that a number divided by itself equals 0

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\frac{\mathbf{1}}{\boldsymbol{x}} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( 0 \) \\
\hline\( y \) & \(\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 3 \)
B. \( 1 \)
C. \( 0 \)
D. The equation is undefined at this value

Solve the problem as a student with the misconception above.
You 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 a reciprocal equation is defined when the denominator is 0

Question:
This is a part of the table of values for the equation \( \boldsymbol{y}=\frac{\mathbf{1}}{\boldsymbol{x}} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( 0 \) \\
\hline\( y \) & \(\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 3 \)
B. \( 1 \)
C. \( 0 \)
D. The equation is undefined at this value

Solve the problem as a student with the misconception above.
You 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 midpoint calculation is just half of the difference

Question:
What is the midpoint of these two coordinates? ![A set of axes with two points (-4,5) and (6,2) plotted.]()

Options:
A. \( (1,3.5) \)
B. \( (5,3.5) \)
C. \( (2,7) \)
D. \( (2,3) \)

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


Prompt:
Misconception:
Does not divide by 2 when finding midpoint

Question:
What is the midpoint of these two coordinates? ![A set of axes with two points (-4,5) and (6,2) plotted.]()

Options:
A. \( (1,3.5) \)
B. \( (5,3.5) \)
C. \( (2,7) \)
D. \( (2,3) \)

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


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

Question:
If three cups of tea and two cups of coffee cost \( £ 2.40 \), and two cups of tea and five cups of coffee cost £3.80, what is the cost of a cup of tea and a cup of coffee?

Options:
A. \( \begin{array}{l}\text { Tea }=60 p \\ \text { coffee }=40 p\end{array} \)
B. \( \begin{array}{l}\text { Tea }=40 p \\ \text { coffee }=60 p\end{array} \)
C. \( \begin{array}{l}\text { Tea }=80 p, \\ \text { coffee }=44 p\end{array} \)
D. \( \begin{array}{l}\text { Tea }=£ 2.40 \\ \text { coffee }=£ 1.40\end{array} \)

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

Question:
I think of a number. I add on five and then multiply the result by four. The answer I get is \( 17 \).
Which of the following equations represents this?

Options:
A. \( n+5 \times 4=17 \)
B. \( 4 n+5=17 \)
C. \( n^{4}+5=17 \)
D. \( 4(n+5)=17 \)

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


Prompt:
Misconception:
Does not include brackets when attempting to multiply an expression

Question:
I think of a number. I add on five and then multiply the result by four. The answer I get is \( 17 \).
Which of the following equations represents this?

Options:
A. \( n+5 \times 4=17 \)
B. \( 4 n+5=17 \)
C. \( n^{4}+5=17 \)
D. \( 4(n+5)=17 \)

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


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

Question:
![An image of a function machine. The input is 20 and the function is squared.]() What is the output of this function machine?

Options:
A. \( 400 \)
B. \( 40 \)
C. \( 22 \)
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:
Mixes up squaring and addition

Question:
![An image of a function machine. The input is 20 and the function is squared.]() What is the output of this function machine?

Options:
A. \( 400 \)
B. \( 40 \)
C. \( 22 \)
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:
Mixes up squaring and halving

Question:
![An image of a function machine. The input is 20 and the function is squared.]() What is the output of this function machine?

Options:
A. \( 400 \)
B. \( 40 \)
C. \( 22 \)
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 correctly apply the distributive property of multiplication

Question:
Tom and Katie are discussing ways to calculate \( 21 \times 12 \) mentally Tom does \( 12 \times 7 \) and then multiplies his answer by \( 3 \) Katie does \( 21 \times 6 \) and then doubles her answer Who would get the correct answer?

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

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


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

Question:
Tom and Katie are discussing ways to calculate \( 21 \times 12 \) mentally Tom does \( 12 \times 7 \) and then multiplies his answer by \( 3 \) Katie does \( 21 \times 6 \) and then doubles her answer Who would get the correct answer?

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

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


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

Question:
Tom and Katie are discussing ways to calculate \( 21 \times 12 \) mentally Tom does \( 12 \times 7 \) and then multiplies his answer by \( 3 \) Katie does \( 21 \times 6 \) and then doubles her answer Who would get the correct answer?

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

Question:
Tom and Katie are arguing about simplifying fractions. Tom says \( \frac{3 p-1}{p} \equiv 2 \) Katie says \( \frac{3 p-1}{p} \equiv 3-\frac{1}{p} \) 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:
Gives a rounded whole number instead of a decimal

Question:
Work out:
\[
0.6 \times 11
\]

Options:
A. \( 6.6 \)
B. \( 6.06 \)
C. \( 7 \)
D. \( 66 \)

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


Prompt:
Misconception:
When multiplying a decimal by an integer, ignores decimal point and just multiplies the digits

Question:
Work out:
\[
0.6 \times 11
\]

Options:
A. \( 6.6 \)
B. \( 6.06 \)
C. \( 7 \)
D. \( 66 \)

Solve the problem as a student with the misconception above.
You 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 cl and ml

Question:
\[
650 \text { centilitres }=\bigstar \text { litres }
\]
What should replace the star?

Options:
A. \( 6.5 \)
B. \( 0.65 \)
C. \( 65000 \)
D. \( 65 \)

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


Prompt:
Misconception:
Multiplies when converting to a larger unit

Question:
\[
650 \text { centilitres }=\bigstar \text { litres }
\]
What should replace the star?

Options:
A. \( 6.5 \)
B. \( 0.65 \)
C. \( 65000 \)
D. \( 65 \)

Solve the problem as a student with the misconception above.
You 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 10cl in a litre

Question:
\[
650 \text { centilitres }=\bigstar \text { litres }
\]
What should replace the star?

Options:
A. \( 6.5 \)
B. \( 0.65 \)
C. \( 65000 \)
D. \( 65 \)

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


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

Question:
One of these pairs of numbers does not fit
the inequality \( d \geq h \)

Can you find which pair?

Options:
A. \( \begin{array}{l}d=-5 \\ h=-1\end{array} \)
B. \( \begin{array}{c}d=1 \\ h=-4\end{array} \)
C. \( \begin{array}{l}d=2 \\ h=2\end{array} \)
D. \( \begin{array}{l}d=5 \\ h=4\end{array} \)

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


Prompt:
Misconception:
Does not understand inequality notation

Question:
One of these pairs of numbers does not fit
the inequality \( d \geq h \)

Can you find which pair?

Options:
A. \( \begin{array}{l}d=-5 \\ h=-1\end{array} \)
B. \( \begin{array}{c}d=1 \\ h=-4\end{array} \)
C. \( \begin{array}{l}d=2 \\ h=2\end{array} \)
D. \( \begin{array}{l}d=5 \\ h=4\end{array} \)

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


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

Question:
One of these pairs of numbers does not fit
the inequality \( d \geq h \)

Can you find which pair?

Options:
A. \( \begin{array}{l}d=-5 \\ h=-1\end{array} \)
B. \( \begin{array}{c}d=1 \\ h=-4\end{array} \)
C. \( \begin{array}{l}d=2 \\ h=2\end{array} \)
D. \( \begin{array}{l}d=5 \\ h=4\end{array} \)

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


Prompt:
Misconception:
Divides by the order of the root

Question:
\( \sqrt[3]{8}= \)

Options:
A. \( 2 . \dot{6} \)
B. \( 4 \)
C. \( 64 \)
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:
Halves when asked to find the cube root

Question:
\( \sqrt[3]{8}= \)

Options:
A. \( 2 . \dot{6} \)
B. \( 4 \)
C. \( 64 \)
D. \( 2 \)

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


Prompt:
Misconception:
Confuses cube rooting with squaring a number

Question:
\( \sqrt[3]{8}= \)

Options:
A. \( 2 . \dot{6} \)
B. \( 4 \)
C. \( 64 \)
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:
Mixes up squaring and multiplying by 2 or doubling

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

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

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

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


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

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

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

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

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


Prompt:
Misconception:
Believes a downward slope on a distance-time graph means travelling away

Question:
Jadon decides to go for a run starting from home.
The graph on the right shows Jadon's distance in metres \( (d) \) over time in seconds
\( (t) \).

The gradient of the negative sloping section of the graph is \( 0.5 \).

Which of the following does that \( 0.5 \) best represent? ![A sketch of a graph with d on the y axis and t on the x axis. A straight line slopes upwards from the origin 2/3 of the way up the graph, 1/5 across the graph. It then becomes horizontal for the next 1/5 of the graph, before sloping downwards in a straight line for the remainder of the graph. ]()

Options:
A. Jadon is travelling away from home at a speed of \( 0.5 \mathrm{~m} / \mathrm{s} \)
B. Jadon is decelerating at a rate of \( 0.5 \mathrm{~m} / \mathrm{s}^{2} \)
C. Jadon is accelerating at a rate of \( 0.5 \mathrm{~m} / \mathrm{s}^{2} \)
D. Jadon is travelling back home at a speed of \( 0.5 \mathrm{~m} / \mathrm{s} \)

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


Prompt:
Misconception:
Believes the gradient of a distance-time graph is the acceleration

Question:
Jadon decides to go for a run starting from home.
The graph on the right shows Jadon's distance in metres \( (d) \) over time in seconds
\( (t) \).

The gradient of the negative sloping section of the graph is \( 0.5 \).

Which of the following does that \( 0.5 \) best represent? ![A sketch of a graph with d on the y axis and t on the x axis. A straight line slopes upwards from the origin 2/3 of the way up the graph, 1/5 across the graph. It then becomes horizontal for the next 1/5 of the graph, before sloping downwards in a straight line for the remainder of the graph. ]()

Options:
A. Jadon is travelling away from home at a speed of \( 0.5 \mathrm{~m} / \mathrm{s} \)
B. Jadon is decelerating at a rate of \( 0.5 \mathrm{~m} / \mathrm{s}^{2} \)
C. Jadon is accelerating at a rate of \( 0.5 \mathrm{~m} / \mathrm{s}^{2} \)
D. Jadon is travelling back home at a speed of \( 0.5 \mathrm{~m} / \mathrm{s} \)

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


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

Question:
What does the following equal?
\[
3-5+4 \times 2
\]

Options:
A. \( 6 \)
B. \( 4 \)
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:
Performs addition ahead of subtraction

Question:
What does the following equal?
\[
3-5+4 \times 2
\]

Options:
A. \( 6 \)
B. \( 4 \)
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:
Subtracts instead of adds

Question:
What does the following equal?
\[
3-5+4 \times 2
\]

Options:
A. \( 6 \)
B. \( 4 \)
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 recall the steps required to draw an angle

Question:
When drawing an angle, which step will you complete last?

Options:
A. Draw a line to join up the end of the line segment and the marker.
B. Make sure the centre of the protractor is at the end of the line segment.
C. Draw a marker to show where the angle needs to be drawn.
D. Draw a line segment

Solve the problem as a student with the misconception above.
You 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 the steps required to draw an angle

Question:
When drawing an angle, which step will you complete last?

Options:
A. Draw a line to join up the end of the line segment and the marker.
B. Make sure the centre of the protractor is at the end of the line segment.
C. Draw a marker to show where the angle needs to be drawn.
D. Draw a line segment

Solve the problem as a student with the misconception above.
You 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 the steps required to draw an angle

Question:
When drawing an angle, which step will you complete last?

Options:
A. Draw a line to join up the end of the line segment and the marker.
B. Make sure the centre of the protractor is at the end of the line segment.
C. Draw a marker to show where the angle needs to be drawn.
D. Draw a line segment

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


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

Question:
Which diagram shows an angle of \( 55^{\circ} \) ?

Options:
A. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 130 and 140 (inner scale) and halfway between 50 and 40 (outer scale).]()
B. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 120 and 130 (inner scale) and halfway between 60 and 50 (outer scale).]()
C. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 40 and 50 (inner scale) and halfway between 140 and 130 (outer scale).]()
D. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 50 and 60 (inner scale) and halfway between 130 and 120 (outer scale).]()

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


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

Question:
Which diagram shows an angle of \( 55^{\circ} \) ?

Options:
A. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 130 and 140 (inner scale) and halfway between 50 and 40 (outer scale).]()
B. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 120 and 130 (inner scale) and halfway between 60 and 50 (outer scale).]()
C. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 40 and 50 (inner scale) and halfway between 140 and 130 (outer scale).]()
D. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 50 and 60 (inner scale) and halfway between 130 and 120 (outer scale).]()

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


Prompt:
Misconception:
Chooses the correct scale when measuring angles on a protractor but starts from the wrong number when the angle is in between two labelled dashes

Question:
Which diagram shows an angle of \( 55^{\circ} \) ?

Options:
A. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 130 and 140 (inner scale) and halfway between 50 and 40 (outer scale).]()
B. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 120 and 130 (inner scale) and halfway between 60 and 50 (outer scale).]()
C. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 40 and 50 (inner scale) and halfway between 140 and 130 (outer scale).]()
D. ![A 180 degree protractor (straight edge at the bottom) with 2 red lines and a blue sector marking out an angle being measured by the protractor. The angle is between the red line that is at 0 (inner scale) and 180 (outer scale) on the right of the protractor, anti-clockwise to the red line that is half way between 50 and 60 (inner scale) and halfway between 130 and 120 (outer scale).]()

Solve the problem as a student with the misconception above.
You 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? \( (x+5)(x-2) \)

Options:
A. \( x^{2}-2 x+5 x-10 \)
B. \( x^{2}+2 x+5 x-3 \)
C. \( x^{2}-2 x-5 x+10 \)
D. \( x^{2}-2 x+5 x+3 \)

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 divide by 2 when finding midpoint

Question:
Points \( P, Q \) and \( R \) are equally spaced along the line segment, as shown in the sketch.

The coordinates of \( \mathrm{P} \) and \( \mathrm{R} \) are marked on the diagram.

What are the coordinates of \( Q \) ? ![A graph with 4 quadrants showing a line joining points R(2, 7), Q (unknown coordinate in 3rd quadrant) and P (-4, -10)]()

Options:
A. \( (-1,-1) \)
B. \( (-2,-3) \)
C. \( (-1,-2) \)
D. \( (-1,-1.5) \)

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


Prompt:
Misconception:
Believes the mode is the most common frequency rather than the highest frequency

Question:
The frequency table shows the grade achieved by some students in a maths exam.
What was the modal grade? ![\begin{tabular}{|c|c|}
\hline Grade & Frequency \\
\hline \( 1 \) & \( 3 \) \\
\hline \( 2 \) & \( 7 \) \\
\hline \( 3 \) & \( 3 \) \\
\hline \( 4 \) & \( 9 \) \\
\hline \( 5 \) & \( 1 \) \\
\hline
\end{tabular}]()

Options:
A. \( 3 \)
B. \( 2 \)
C. \( 9 \)
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 the mode is the frequency rather than the value/group

Question:
The frequency table shows the grade achieved by some students in a maths exam.
What was the modal grade? ![\begin{tabular}{|c|c|}
\hline Grade & Frequency \\
\hline \( 1 \) & \( 3 \) \\
\hline \( 2 \) & \( 7 \) \\
\hline \( 3 \) & \( 3 \) \\
\hline \( 4 \) & \( 9 \) \\
\hline \( 5 \) & \( 1 \) \\
\hline
\end{tabular}]()

Options:
A. \( 3 \)
B. \( 2 \)
C. \( 9 \)
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:
Finds one part of a ratio but doesn't multiply that by the number of parts needed

Question:
\( \square \square \square \triangle \square \square \square \triangle \square \square \square \triangle \) For every \( 3 \) triangles there are \(___\) squares

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