Adding and Subtracting Fractions — Year 5 Lesson Plan
National Curriculum: Mathematics — Number: fractions, Year 5
Overview
Pupils learn to add and subtract fractions with the same denominator and with related denominators (where one is a multiple of the other). They extend this to adding and subtracting mixed numbers, converting between improper fractions and mixed numbers as needed.
Learning Objectives
- Add and subtract fractions with the same denominator.
- Find a common denominator to add and subtract fractions with related denominators.
- Convert between improper fractions and mixed numbers.
- Add and subtract mixed numbers, including where regrouping is required.
Key Vocabulary
Suggested Lesson Structure
Recap equivalent fractions: find three fractions equivalent to ½, ⅓, ¾. Establish that changing the denominator without changing the value is key to today's lesson.
Start with same-denominator addition (3/8 + 2/8 = 5/8). Move to related denominators: ½ + ¼ — convert to quarters first. Model improper fractions: 5/4 = 1¼. Demonstrate adding mixed numbers and the need to regroup when subtracting (e.g. 3¼ − 1¾).
Pupils work through a sequence of problems: same denominator → related denominator → mixed numbers. Use fraction strips to support. Share and compare methods.
Differentiated practice: fluency (same/related denominators), then reasoning ('Explain why ¾ + ⅔ cannot be solved by adding the numerators and adding the denominators'), then challenge (mixed number problems).
Which is correct: ½ + ⅓ = 2/5 or 5/6? Pupils explain. Reinforce that only the numerator changes when adding.
Common Misconceptions
- Adding both numerators and denominators: ½ + ⅓ = 2/5 — a very common error; use bar models to show why this is wrong.
- Not converting to a common denominator before adding fractions with different denominators.
Prior Knowledge
Pupils should already be able to:
- Confident knowledge of equivalent fractions.
- Ability to convert between improper fractions and mixed numbers.
- Understanding of fraction as a part of a whole.
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