Proper: Error Analysis & Misconceptions
Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads
About This Worksheet
This worksheet focuses on multiplying proper fractions, addressing common misconceptions and errors students make when working with proper fractions. It aims to develop procedural mastery and understanding through varied question types.
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Proper: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Fluency & Practice
Calculate the following products of proper fractions. Show your working clearly.
1.
Calculate 3/4 × 2/5.
[2 marks]2.
Calculate 7/8 × 3/4.
[2 marks]3.
Calculate 5/6 × 4/9.
[2 marks]B
Problem Solving & Reasoning
Solve the multi-step problems below. Explain your reasoning clearly.
1.
A recipe requires 3/4 cup of sugar. If you want to make half the recipe, how much sugar do you need? Show your calculation.
[4 marks]2.
A painter mixes 2/3 of a litre of blue paint with 3/4 of a litre of yellow paint. What is the total amount of paint mixed? Explain your steps.
[4 marks]C
Real-world Applications
Apply your understanding of multiplying proper fractions to these real-world scenarios.
1.
A garden bed is 3/4 meters long. If a gardener plants flowers along half the length, how many meters of flowers does she plant? Show your work.
[3 marks]2.
A manufacturer produces 5/8 of a batch of widgets each day. If they aim to produce 3/4 of a batch in a day, how much more do they need to produce? Explain your reasoning.
[3 marks]D
Challenge & Extension
Tackle these more challenging problems involving proper fractions.
1.
Calculate (2/3 × 3/4) × (4/5 × 5/6). Show all steps.
[4 marks]2.
Construct a rectangle such that one side is 3/4 units long and the other is 2/3 units long. Calculate the area, then verify your answer by multiplying the two proper fractions.
[4 marks]E
Mixed Review & Error Analysis
Identify the mistakes in the following incorrect solutions and correct them.
1.
Student's work: 2/3 × 3/4 = 6/12 = 1/2. Is this correct? If not, explain the mistake and find the correct answer.
[3 marks]2.
Student's work: 5/6 × 4/9 = 20/36 = 5/9. Is this correct? If not, identify and correct the mistake.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet