Fraction Operations Focus

Overview

This lesson is lesson 5 of 20 in “Mastering Maths Concepts”. Students practise adding and subtracting fractions using like and unlike denominators, building accuracy and choosing efficient strategies.

Learning intentions

Students will:

• add and subtract fractions with like denominators by combining numerators and keeping the denominator.
• add and subtract fractions with unlike denominators by finding a common denominator (e.g. using equivalent fractions).
• explain their method using words and models (area/number line/paper strips) and check their answer for reasonableness.

Success criteria

Students can:

• correctly add or subtract fractions with the same denominator.
• correctly convert fractions to equivalent fractions with a common denominator when required.
• give a final answer in simplest form (reduce when possible) and justify why it matches the model.

Curriculum links

• Number — fractions and decimals: performing operations on fractions using appropriate strategies.
• Mathematical reasoning: using models, patterns, and explanations to support answers.
• Numeracy and problem-solving: selecting efficient methods (equivalent fractions and common denominators) and verifying results.

Lesson structure (30 minutes)

1. 0–4 min · Retrieval check. Teacher writes two quick items on the board: 3/8 + 1/8 and 5/12 − 2/12, asks for answers and one step written. Student completes both answers in their workbook, showing one short reason (e.g. “denominator stays the same because…”).

2. 4–10 min · Mini-lesson: like denominators. Teacher demonstrates with paper strips: show 3/8 + 1/8 as eight equal parts with 3 shaded plus 1 more, then model subtraction for 5/12 − 2/12. Student replicates with two strips (or a drawn rectangle) and writes the rule: “same denominator → add/subtract numerators”.

3. 10–18 min · Mini-lesson: unlike denominators. Teacher works through one example: 1/6 + 1/4.

• Finds common denominator (12)
• Converts: 1/6 = 2/12 and 1/4 = 3/12
• Adds: 2/12 + 3/12 = 5/12 Teacher highlights a strategy statement: “Make equivalent fractions, then add/subtract.” Student follows the steps for a second example given by the teacher: 2/3 − 1/6, using equivalent fractions to a common denominator (e.g. 6).

4. 18–25 min · Guided practice task (teacher circulates). Teacher gives a 5-question set, mixed like/unlike denominators, for independent work. Students choose one method: drawings, number line jumps, or fraction bar diagrams. Student answers all five questions, including at least one requiring simplification in the final response.

Example set (write and solve):

• A) 3/10 + 2/10
• B) 7/9 − 2/9
• C) 1/3 + 1/6
• D) 5/8 + 1/4
• E) 3/5 − 2/15

5. 25–28 min · Check and discuss. Teacher selects one question (likely D or E) and asks the class to compare methods and confirm common denominator and simplification. Student explains their method for that chosen question in one or two sentences, then verifies by re-checking with an equivalent form.

6. 28–30 min · Exit ticket. Teacher collects answers to two items:

• F) 4/7 + 1/14
• G) 9/16 − 3/8 Student shows working to a common denominator and reduces the final answer.

Resources

• Fraction strips or paper rectangles (6, 8, 9, 10, 12, 14, 15, 16-part templates)
• Coloured pencils or markers for shading
• Whiteboard/marker or interactive board
• Student workbook and pens/pencils
• Simplifying prompts chart (e.g. “reduce by common factor”)
• Calculator allowed only for checking (teacher discretion)

Assessment

• Formative check during retrieval: whether numerators are added/subtracted correctly for like denominators.
• Observation during unlike-denominator work: students identify and apply a common denominator and produce correct equivalent fractions.
• Exit ticket: ability to add/subtract unlike denominators and simplify; partial credit for correct common denominator even if arithmetic slips.

Differentiation

• Support:
• Sentence starters for explaining: “I found a common denominator of…”, “I changed each fraction to…”, “Then I…”.
• Provide a partially completed example for the first unlike-denominator question (common denominator already chosen, student fills equivalent fractions).
• Use fraction bars to reduce cognitive load (focus on conversion rather than computation).
• Extension:
• Include a question where denominators require careful choice of common denominator (e.g. two-step simplification after conversion).
• Ask students to compare two strategies: drawing versus using common denominator algebraically, and justify which is more efficient.
• SEN/EAL considerations:
• Allow responses using diagrams plus minimal writing.
• Keep language consistent: “common denominator”, “equivalent fraction”, “simplify”.
• Provide a bank of common denominators for frequent pairs (e.g. 3 and 6 → 6; 4 and 8 → 8; 5 and 15 → 15).