Equivalent Fractions Connected

Overview

Lesson 2 of 15 in Number Connections: Fractions, Decimals, Percentages. Students use visual models, multiplication and division to generate, justify and simplify equivalent fractions, building connections between representations and mathematical operations.

Learning intentions

• WALT find and explain equivalent fractions.
• WALT use multiplication and division to scale numerators and denominators.
• WALT connect fraction symbols with visual models.
• WALT simplify familiar fractions.

Success criteria

• I can generate equivalent fractions by multiplying or dividing the numerator and denominator by the same number.
• I can use a model to prove that two fractions are equivalent.
• I can simplify familiar fractions, such as 4/8 = 1/2.
• I can explain why the whole fraction value stays the same.

Curriculum links

• Number: recognise, represent, compare and connect fractions in familiar contexts.
• Number: use multiplication and division strategies to find equivalent fractions and simplify fractions.
• Mathematical practices: reason, represent, communicate and justify mathematical thinking.
• Progress through the refreshed curriculum: use structured representations, make connections between ideas, and explain efficient strategies.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and retrieval

Open with the fraction comparison hook. Display 1/2 and 2/4 and ask: “Which person gets more pizza, or do they get the same amount? How do you know?” Students think-pair-share, then recall the meaning of numerator, denominator and equal parts. Record students’ explanations without confirming all answers immediately.

2. 5–12 minutes – Build the concept

Use the visual model examples to show one whole divided into 2 equal parts and the same whole divided into 4 equal parts. Shade 1/2 and 2/4, then connect the model to the statement 1/2 = 2/4. Explicitly teach: multiplying both numerator and denominator by the same non-zero number creates an equivalent fraction because the size of each part and the number of parts change together.

3. 12–20 minutes – MNP worked examples

Model a multiplication example: 2/5 × 2/2 = 4/10. Then model division to simplify: 6/8 ÷ 2/2 = 3/4. Keep the fraction value unchanged by scaling both parts equally. Pause for mini-whiteboard checks: “Complete 3/4 =?/8” and “Simplify 10/20.” Invite students to explain the operation, not just state the answer.

4. 20–32 minutes – Supported partner practice

Place students in mixed-readiness pairs and distribute the equivalent fractions practice worksheet. Students complete visual-model questions first, then generate equivalent fractions and simplify familiar fractions. Provide learners needing support with the fraction wall and strip cards and encourage them to match 1/2, 2/4, 5/10 and related representations before recording answers. Circulate and ask: “What stayed the same?” and “What did you multiply or divide by?”

5. 32–40 minutes – Explain and challenge

Students use the partner challenge instructions to complete selected worksheet questions and explain one answer to another pair. Early finishers use the equivalent fractions dominoes to match visual and numerical representations, then create an equivalence puzzle such as “I am equivalent to 3/5. My denominator is greater than 20. What could I be?” They must justify the answer using a generalisation: multiplying or dividing both parts by the same number preserves the value.

6. 40–45 minutes – Plenary and formative check

Return to the exit reflection prompt. Students respond verbally or on the bottom of the worksheet: “How can you prove that 4/6 and 2/3 are equivalent?” Select two students to share different representations. Revisit the learning intentions and identify which success criterion each explanation demonstrates.

Resources

• the equivalent fractions lesson deck
• the equivalent fractions practice worksheet
• the fraction wall and strip cards
• the equivalent fractions dominoes
• Mini-whiteboards, pens and erasers
• Pencils and rulers
• One fraction wall or enlarged visual model for teacher demonstration
• Board space for recording student strategies

Assessment

• Listen for whether students explain that both numerator and denominator must be multiplied or divided by the same number.
• Check worksheet models and calculations, particularly 3/4 = 6/8, 2/5 = 4/10 and 6/8 = 3/4.
• Use the plenary explanation to identify students who can justify equivalence, rather than relying on procedural answers alone.

Differentiation

• Support: work with denominators of 2, 4, 5 and 10; use the fraction wall, shaded models, paired talk and sentence frames such as “___ is equivalent to ___ because both parts were multiplied by ___.”
• Support for EAL and learners with additional needs: pre-teach numerator, denominator, equivalent and simplify with gestures and visuals; read worksheet instructions aloud and provide one worked example at a time.
• Core: require students to represent each answer symbolically and visually, then explain the scaling operation.
• Extension: investigate equivalence puzzles with larger denominators and explain why multiplying or dividing both numerator and denominator by the same number preserves the fraction’s value.