Fraction Operations Sense

Overview

Students solve addition and subtraction problems involving fractions by using equivalent fractions to make the denominators match. The lesson uses visual models (fraction strips/area diagrams) and a number line to connect the method to meaning.

Learning intentions

Students will:

• solve fraction addition and subtraction problems using equivalent fractions
• choose an efficient strategy to find common denominators when needed
• represent solutions using diagrams or number lines and explain their reasoning
• check that answers are reasonable for the given context

Success criteria

Students can:

• rewrite fractions as equivalent fractions with the same denominator
• add or subtract the numerators correctly once denominators match
• explain using an equivalent-fractions statement (e.g., “( \frac{1}{4} = \frac{2}{8} )”)
• show the answer on a fraction strip or number line model

Curriculum links

• Mathematics Year 6 — Number — AC9M6N05: solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions
• AC9M6N05 includes modelling addition/subtraction with diagrams and number lines using equivalent fractions
• AC9M6N05 includes determining common denominators using understanding of factors and multiples

Lesson structure (35 minutes)

1. 0–5 min · Warm-up (equivalent fraction check). Teacher shows three fraction cards (e.g., ( \frac{1}{2}, \frac{2}{4}, \frac{3}{6} )) and asks which two are equal and why; students discuss in pairs and vote using mini-whiteboards.

2. 5–12 min · Direct teach (meaning + method). Teacher models one problem with fraction strips: ( \frac{1}{4} + \frac{1}{8} ).

• Teacher draws strips and shows ( \frac{1}{4} = \frac{2}{8} ), then combines to ( \frac{3}{8} ). Students follow on their own strip diagrams, completing the same rewriting step before adding.

3. 12–20 min · Guided practice (two-step reasoning). Teacher provides a “Match & Add” worksheet on the board with two items: a) ( \frac{2}{3} + \frac{1}{6} ) b) ( \frac{5}{8} - \frac{1}{4} ) Teacher pauses after each to ask: “What denominator do we need and what equivalent fraction do we make?” Students work in pairs, using strips or area diagrams and writing the equivalent-fraction equality.

4. 20–28 min · Worked example to reinforce subtraction (related denominators). Teacher demonstrates: ( \frac{3}{5} - \frac{1}{10} ).

• Teacher shows ( \frac{3}{5} = \frac{6}{10} ), then subtracts parts to get ( \frac{5}{10} = \frac{1}{2} ). Students practise the same structure with a teacher-led “think aloud” checklist: rewrite, subtract numerators, simplify if needed, label on the strip/number line.

5. 28–34 min · Independent problem solving (apply to new context). Students choose one of two tasks (same skills, different numbers) and solve independently using diagrams: Task A: ( \frac{7}{12} + \frac{1}{6} ) Task B: ( \frac{9}{10} - \frac{3}{20} ) Teacher circulates, prompting students to show the equivalent fractions step and to check with the model.

6. 34–35 min · Exit ticket (quick check). Students answer one short item: ( \frac{1}{3} + \frac{1}{6} ). They must include an equivalent-fractions statement and the final simplified answer.

Resources

• Fraction strips or paper folding strips (denominators 2 to 12)
• Fraction wall/area model cards (optional)
• Mini-whiteboards and markers
• Guided practice worksheet with 2–3 problems
• Independent choice cards (Task A and Task B)
• Number line templates from 0 to 2 with common benchmarks
• Sticky notes for students to label equivalent fractions
• Timer (visible to help pacing)

Assessment

• During warm-up: listen for correct justification of equivalence (not just matching answers).
• During guided practice: check that students rewrite fractions into equivalent forms with a common denominator before adding/subtracting.
• Teacher observation in independent work: look for correct subtraction/minus interpretation and whether students simplify answers.
• Exit ticket: verify inclusion of an equivalent-fractions step and correct final answer.

Differentiation

• Support:
• Provide sentence starters: “To add/subtract, I rewrite ( \frac{a}{b} ) as ( \frac{?}{?} ) because the strips show they are equal.”
• Offer a partially completed example on the worksheet (common denominator already chosen for one step).
• Use colour coding on strips (same denominator parts shaded the same colour).
• Extension:
• Challenge students to create their own fraction addition/subtraction problem using the same method and explain the common denominator choice.
• Add a simplification check: ask “Can you express your answer with a smaller denominator? Why?”
• EAL/SEN considerations:
• Keep language consistent: “equivalent”, “same denominator”, “parts”, “combine”, “take away”.
• Allow diagram-first responses (numerals can be completed after the model makes sense).
• Provide extra wait time for processing and use pair talk before whole-class responses.