Adding and Subtracting Fractions

Overview

Year Group: 7
Duration: 45 minutes
Class Size: 1
Unit: Mastering Fractions & Percentages (Lesson 2 of 5)
Curriculum Reference:
This lesson aligns with the National Curriculum for England, Key Stage 3, Mathematics, Number and Algebra domain, specifically:

Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
Add and subtract fractions with different denominators and mixed numbers, using equivalent fractions
(Reference: Key Stage 3 Programme of Study, Number - Fractions, decimals and percentages)

Learning Objectives

By the end of this lesson, the student will be able to:

Identify and find common denominators for two or more fractions.
Convert fractions to equivalent fractions with a common denominator.
Accurately add and subtract proper and improper fractions using the common denominator method.
Simplify the resulting fractions to their lowest terms or convert to mixed numbers where appropriate.
Explain their reasoning clearly when performing addition and subtraction of fractions.

Success Criteria

Writes fractions with common denominators correctly.
Adds and subtracts fractions accurately using the common denominator.
Simplifies fractions correctly and converts improper fractions to mixed numbers.
Demonstrates understanding verbally or in writing of each step in the calculation.
Applies these skills confidently in a problem-solving context.

Key Vocabulary

Numerator
Denominator
Common denominator
Equivalent fractions
Simplifying fractions
Improper fraction
Mixed number

Resources Needed

Paper and pencil
Fraction strips or fraction circles (physical or digital)
Whiteboard or notebook for working through examples
Worksheets with practice questions tailored for single-student interaction
Self-assessment checklist

Lesson Breakdown

1. Starter (5 minutes)

Objective: Recap prior knowledge and introduce the concept of common denominators.

Brief discussion with the student about what they remember from the previous lesson on fractions and percentages.
Quick activity: Show two fractions with different denominators (e.g., 1/4 and 1/3). Ask the student if they can add or subtract them as they are.
Introduce or review the key idea that fractions need a common denominator to be added or subtracted.
Use fraction strips/circles to visually demonstrate why common denominators are necessary for addition/subtraction.

2. Teaching Input (10 minutes)

Objective: Model the process of finding common denominators, adding, subtracting, and simplifying fractions.

Work through a step-by-step example on the whiteboard/notebook:
Example 1: 2/5 + 1/3
- Find the least common denominator (LCD) — explore multiples of 5 and 3.
- Rewrite both fractions as equivalent fractions with the common denominator.
- Add the numerators.
- Simplify the final fraction if possible.
Example 2: Subtraction with improper fraction result: 7/6 - 2/3
- Find LCD, rewrite, subtract numerators.
- Convert improper fraction to mixed number.
Emphasise clear written method and thinking aloud to model correct reasoning.
Highlight simplification and mixed number conversion rules.

3. Guided Practice (10 minutes)

Objective: Support the student as they practise adding and subtracting fractions.

Present a set of 3-4 problems scaffolded for gradual challenge:
- Adding two proper fractions with different denominators.
- Subtracting fractions including improper fractions.
- Including one problem requiring simplification and mixed number conversion.
Student works through problems aloud, explaining each step to reinforce understanding.
Teacher provides immediate feedback, clarifies misunderstandings, and prompts deeper thinking where appropriate.

4. Independent Task (10 minutes)

Objective: Provide opportunity for the student to demonstrate mastery independently.

Set 3 additional mixed problems, increasing in complexity (e.g., different denominators, larger numbers, requiring simplification).
Ask student to write full solutions with explanations.
Encourage neat and logical presentation.

5. Review and Reflect (7 minutes)

Objective: Consolidate learning and self-assess understanding.

Discuss the completed independent task with the student.
Use a self-assessment checklist:
- Can I find a common denominator?
- Can I write equivalent fractions?
- Can I add/subtract fractions correctly?
- Can I simplify my answers?
- Can I explain my working?
Ask student to identify what they found easy and what was challenging.
Summarise key learning points.

6. Plenary (3 minutes)

Objective: End on a confident and positive note with a quick problem-solving challenge.

Pose a “real-life” problem involving adding or subtracting fractions, for example:
"You baked 3/4 of a cake yesterday and 2/5 of a cake today. How much cake did you bake in total?"
Student solves mentally or with written work, explaining method.

Assessment

Formative assessment through questioning and observation during guided and independent practice.
Review of independent task for accuracy, clarity, and method.
Self-assessment checklist completion and reflection discussion to evaluate conceptual understanding.

Differentiation

For advanced understanding: Introduce addition/subtraction of mixed numbers with unlike denominators.
For additional support: Use more visual aids and start with fractions sharing denominators, progressing slowly. Use manipulatives throughout.

Extension Ideas

Challenge the student to create their own fraction addition or subtraction problems involving common denominators and explain the reasoning behind their method.
Link to percentages: Convert answers into percentages to consolidate connections between fractions and percentages.

Notes for Teacher

Constantly check for understanding by asking the student to explain each step in their own words.
Use manipulatives flexibly to suit the student’s learning style — visual or kinaesthetic.
Encourage neat, stepwise notation to build mathematical communication skills.
Maintain a positive, encouraging tone to build confidence with potentially challenging fraction operations.

This detailed and curriculum-aligned plan ensures the student not only performs addition and subtraction of fractions but understands the underlying procedures conceptually and can clearly articulate the process, meeting all National Curriculum expectations for Year 7.