Equivalent Fractions

Overview

In this lesson, students build an understanding of equivalent fractions by using hands-on shape work (cutting and comparing parts) to see that different fraction names can represent the same amount.

Learning intentions

Students will be able to:

• recognise that fractions show “equal parts of a whole”
• generate equivalent fractions using visual and physical representations
• explain why two fractions can be equivalent by comparing the same-sized parts
• use fraction vocabulary accurately (numerator, denominator) in simple explanations

Success criteria

• I can match fractions that represent the same part of a whole using models.
• I can show equivalence by building or cutting shapes into equal parts and comparing.
• I can use words like “same amount”, “same size parts”, and “equal shares” to justify my thinking.
• I can record equivalent fractions using fraction notation with support.

Curriculum links

• Understanding fractions as equal parts of a whole and representing them in different ways.
• Reasoning with fractions by comparing and explaining equivalence using models.
• Communicating mathematical thinking using clear spoken and written explanations.

Lesson structure (45 minutes)

1. 0–5 min: Launch and recap

• Quick recap: What does the denominator tell us? What does the numerator tell us?
• Teacher shows one paper strip already partitioned (e.g., halves) and asks: “How many equal parts are there? What fraction is one part?”

2. 5–10 min: Introduce equivalent fractions through a prompt

• Display two area models: one partitioned into 2 equal parts with 1 shaded, and another partitioned into 4 equal parts with 2 shaded.
• Ask: “Are these the same amount? How can we check?” Students turn-and-talk using the sentence starter: “They are equivalent because…”

3. 10–22 min: Hands-on cutting—make and compare

• Students receive square or circle cards (same size) and cutting tools (or pre-scored templates), plus task cards.
• Task sequence (small groups, teacher circulates):
• Make halves: partition into 2 equal parts, shade 1 part.
• Make quarters: partition into 4 equal parts, shade 2 parts.
• Compare the shaded regions by placing them side-by-side: “Do they cover the same amount?”
• Students record: half and quarter pairings they observe (e.g., “1 out of 2 equals 2 out of 4”).

4. 22–30 min: Fraction language and recording

• Whole-class debrief. Teacher charts student language:
• “Same amount” = same area shaded
• “Equal shares” = same-sized parts
• Students complete a short recording sheet:
• Draw/trace their cut shapes and write two equivalent fraction statements they found.
• Teacher reminds: fractions must have equal-sized parts to compare fairly.

5. 30–40 min: Matching game—equivalent fraction cards

• Students play a teacher-led game in pairs:
• Set A cards show a fraction name (e.g., 1/2, 1/4, 3/4).
• Set B cards show an area model already shaded.
• Students match fraction names to models that represent the same shaded amount.
• For each match, they must say one justification: “These are equivalent because the shaded parts are the same size / same area.”

6. 40–45 min: Exit check and closure

• Individual exit question (quick, not time-consuming): show two models; students circle the equivalent fraction pair and write one sentence justification.
• Closure: “Equivalent fractions name the same amount even when the parts look different.”

Resources

• Pre-scored paper circles/squares (same overall size) for 2 parts and 4 parts; spare templates
• Student cutting tools or scissors (with safety reminders) and glue sticks/tape for assembling models
• Coloured pencils or markers for shading equal parts
• Fraction recording sheet (simple grids for drawing and writing equivalent pairs)
• Equivalent fraction card sets (fraction names and matching area models)
• Sentence starters for justification on display
• Visual fraction models (teacher-made examples for halves and quarters)
• Timer and teacher chart paper for capturing vocabulary

Assessment

• Teacher observation during cutting and matching: Can students recognise equivalent amounts and use correct reasoning language?
• Exit ticket: Identify an equivalent fraction pair and provide a basic justification in words.
• Review of recording sheets: Accuracy in written fraction statements and correct linking to the shaded model.

Differentiation

• Support:
• Provide extra pre-cut templates and limit tasks to halves and quarters only for some students.
• Offer partially completed sentence starters and a model example of how to record equivalence.
• Use small-group teacher instruction during the cutting stage.
• Extension:
• Challenge students to find more than one equivalent name for the same shaded amount (e.g., using halves/quarters with different representations).
• Ask them to explain how they know parts are equal-sized, not just “looks similar”.
• EAL:
• Use visual gestures for “same amount” and “equal parts”.
• Allow oral responses or recording with drawing first, then add fraction notation with teacher support.
• SEN:
• Provide reduced cutting load (pre-scored lines with limited steps).
• Use colour-coding: same colour indicates the “shaded amount” across representations.