Visual Models: Error Analysis & Misconceptions

Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads

About This Worksheet

A worksheet focusing on using visual models to understand equivalent fractions, identifying common misconceptions, and developing procedural mastery through error analysis and problem solving.

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Visual Models: Error Analysis & Misconceptions

Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet

Grade GCSE Foundation
A

Practice Questions

Answer all questions. Show your working clearly in the grid spaces provided.
1.
Using visual models, find the fraction equivalent to 1/2 shown in the diagram below. Explain your reasoning.
[3 marks]
2.
Construct a visual model that shows why 2/4 and 1/2 are equivalent. Use shading to illustrate your answer.
[3 marks]
3.
Look at the two visual models below showing different fractions. Identify which is incorrect and explain the common misconception displayed.
[4 marks]
4.
A student claims that shading half of a circle and shading a quarter of it twice are not equivalent. Use visual models to evaluate this statement and correct any misconception.
[4 marks]
5.
Identify the error in the visual model where a rectangle is divided into 8 equal parts, with 3 shaded, and the student claims this represents 3/8 but says it's not equivalent to 3/8. What mistake might they have made?
[2 marks]
6.
Using visual models, determine if 3/6 and 1/2 are equivalent. Show your reasoning with diagrams.
[3 marks]
7.
A diagram shows a shaded circle divided into 4 equal parts, with 2 shaded. Another diagram shows a rectangle divided into 8 parts, with 4 shaded. Are these visual representations equivalent fractions? Justify your answer.
[4 marks]
8.
Construct a visual model to show why multiplying the numerator and denominator by the same number gives an equivalent fraction. Use shading to illustrate your explanation.
[3 marks]
9.
A student tries to shade 3/4 of a rectangle but accidentally shades 6/8. They claim it's not equivalent. Use visual models to assess and explain the misconception.
[4 marks]
10.
Identify and correct the mistake in this visual model: a square divided into 5 equal parts, with 2 shaded, but the student writes the fraction as 2/5 and says it is not equivalent to 4/10.
[2 marks]
11.
Challenge: Construct a visual model to compare the fractions 5/10 and 1/2. Show that they are equivalent and explain your reasoning.
[4 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet