Fractions Mastery

Overview

In this lesson (Lesson 6 of 20) students extend earlier fraction and multiplication ideas by using visual representations to multiply and divide fractions. Students focus on choosing efficient strategies and interpreting answers in context.

Learning intentions

Students will:

• recognise how multiplying fractions changes “how much” using area/length models
• model division of fractions using sharing and “how many groups” representations
• use the 4 operations with rational numbers to solve fraction problems accurately
• explain their thinking using diagrams, words, and fraction notation

Success criteria

Students can:

• multiply two fractions and show the method with a visual model
• divide a fraction by a whole number and by another fraction using an appropriate model
• check whether an answer is reasonable by referring to the model and the size of the result
• communicate the strategy they used clearly (diagram + explanation)

Curriculum links

• Mathematics — Number: use the 4 operations with rational numbers, choosing and using efficient strategies and digital tools where appropriate
• Mathematics — Number: model and interpret solutions involving rational numbers in practical situations

Lesson structure (30 minutes)

1. 0–4 min · Retrieval starter. Teacher writes two quick prompts on the board: “Half of 3/4” and “1/3 of 6/5” (without computing yet). Students do a fast think-pair-share: what visual would help and what operation is happening (multiply vs divide).
2. 4–10 min · Mini-lesson: multiplying fractions (visual first). Teacher shows an area model: a rectangle split into equal columns and rows (e.g., 3/4 of a strip, then 2/5 of that part), then labels each region to show why the result is the product of numerators/denominators. Students complete one guided example together:

• Example: (2/3) × (3/5) using the diagram idea (rows for 2/3, columns for 3/5). Teacher prompts: “What does each fraction represent on the picture? How do the regions combine?”

3. 10–16 min · Worked example: dividing fractions as groups. Teacher demonstrates division of fractions with a “how many groups” visual. Use a length/area strip where dividing by a fraction means each group is smaller, so more groups are needed. Example:

• Example: (1/2) ÷ (1/4). Show the same whole partitioned into halves, then subdivide to match the divisor’s size. Students record the key statement: “Dividing by 1/4 asks: how many 1/4 parts fit into 1/2?”

4. 16–24 min · Practice set (you choose a model). Teacher gives 4 tasks (two for multiplication, two for division). Students choose a diagram type and must include a short written explanation.

• Task A: 3/5 × 2/7
• Task B: 5/6 × 4 (use the idea of “4 wholes” or an area model repeated)
• Task C: 3/4 ÷ 1/2
• Task D: 2/3 ÷ 3/8 Teacher circulates, checking for correct modelling, fraction simplification, and whether answers make sense (e.g., division by a smaller fraction should increase).

5. 24–27 min · Whole-class check and reasoning. Teacher selects one student method for each operation type (multiplication and division). Students compare diagrams: “Do both visuals show the same result? What is different about the strategy?”
6. 27–30 min · Exit ticket (quick and precise). Students answer 2 questions independently:

• (1) 2/9 × 3/4
• (2) 3/5 ÷ 1/5 They must show a visual for at least one of the two, and write one sentence explaining why the answer should be larger or smaller.

Resources

• Centimetre-square paper or blank grids for area models
• Coloured pencils or markers (at least two colours)
• Fraction cards or fraction strips (optional)
• Student whiteboards (or scrap paper) for quick checks
• Digital tool access (calculator optional for checking only, not replacing diagrams)
• Teacher slide/board examples showing partitioned rectangles and strips

Assessment

• Teacher formative checks during Step 2–4: correct diagram partitioning (equal parts), correct interpretation of numerator/denominator in the model
• Teacher checks in Step 4: student explanations reference the visual (not just rule memorisation)
• Exit ticket in Step 6: accuracy and the reasonableness of results, plus whether students can justify with a diagram

Differentiation

• Support: provide a pre-drawn grid/strip template for each question, plus sentence starters such as “I split the model into __ equal parts because…” and “Dividing by a smaller fraction means…”
• Support: allow students to work with unit fractions first (e.g., division by 1/2) before attempting harder division by a fraction (Task D)
• Extension: for any student who finishes early, ask them to create a “compare the answers” statement (e.g., “My division answer should be greater than the original because…”), and swap the divisor to predict how the size changes before calculating
• EAL/SEN considerations: keep language consistent (“share into equal groups”, “how many groups”, “of that amount”), use labelled diagrams, and reduce copying by letting students colour only relevant regions