Equivalent Fractions

Overview

This is lesson 4 of 5 in the unit Fractions: Equal Parts. Students build on their understanding of halves and quarters by investigating why one-half is equivalent to two-quarters when the wholes are the same size, using folding, diagrams, matching and mathematical explanation.

Learning intentions

• WALT recognise that one-half and two-quarters can represent the same amount.
• WALT partition the same whole into halves and quarters.
• WALT explain why the whole must be the same size when comparing fractions.
• WALT use the word equivalent to describe equal amounts.

Success criteria

• I can partition the same whole into halves and quarters.
• I can show that (1/2) and (2/4) cover the same amount.
• I can use the word equivalent correctly.
• I can explain why the wholes must be the same size.

Curriculum links

• Mathematics and Statistics — recognising, representing and comparing fractions as equal parts of a whole.
• Mathematics and Statistics — using visual representations and mathematical language to explain relationships.
• Mathematics and Statistics — communicating mathematical thinking, justifying ideas and responding to others.
• Mathsteasers — higher-order thinking and challenge through reasoning, discussion and problem solving.

Lesson structure (60 minutes)

1. 0–5 min · Connect and predict. Teacher displays the WALT and asks, “Which is more: one-half or two-quarters?” Record predictions without confirming the answer. Open with the fraction prediction hook. Students turn and talk, then explain how they might prove their prediction.

2. 5–15 min · Teacher demonstration. Teacher uses two identical paper rectangles. Fold the first into two equal parts and shade one-half. On the second, fold or mark four equal parts and shade two-quarters. Place the rectangles together so the shaded areas can be compared. Use the slides to show the equation (1/2 = 2/4), and introduce: “Equivalent means the same amount or value.” Students observe, describe what is the same, and help complete: “Two quarters are equivalent to one half because…”

3. 15–28 min · Pair investigation. Teacher gives each pair scrap paper and asks them to create matching wholes, partition one into halves and the other into quarters, and shade the compared amounts. Distribute the equivalent halves and quarters investigation sheet for students to record drawings and complete the sentence frame. Students may draw, fold or shade, then compare their representations. Teacher conferences with each pair, checking that students compare area of the same-sized whole rather than counting pieces only. Ask: “Are the wholes the same size? How do you know?” and “What part of the quartered whole is shaded?”

4. 28–42 min · Matching and justification. Teacher forms two groups of four and provides matching cards showing diagrams, (1/2), (2/4), and the word equivalent. Display the sorting instructions in the matching-card challenge. Students match the cards, discuss disagreements and select one match to justify to the class. Require each group to use a drawing or overlay and the sentence frame: “___ quarters cover the same amount as one half because…”

5. 42–52 min · Same whole, different whole. Teacher shows two rectangles of different sizes: one large rectangle with one-half shaded and one smaller rectangle with two-quarters shaded. Ask, “Do these always show equivalent amounts?” Guide discussion towards the idea that the fractions may describe the same proportion, but the actual areas are not the same if the wholes differ. Students explain why comparing equal-sized wholes matters and identify whether examples on the board are valid comparisons.

6. 52–60 min · Individual check and reflection. Teacher asks each student to complete (1/2 = __/4) and explain the answer orally or in writing. Students complete the final question on the equivalent halves and quarters investigation sheet by drawing a quick example of (1/2) and (2/4) using the same whole. Invite two students to share explanations and revisit the WALT and success criteria using the plenary and self-check.

Resources

• the equivalent fractions teaching and discussion deck
• the equivalent halves and quarters investigation sheet
• Two identical paper rectangles for demonstration
• Scrap paper for folding and drawing
• Pencils and colouring pencils
• Matching cards showing diagrams, (1/2), (2/4) and equivalent
• Board or whiteboard
• Transparent overlay sheets, if available

Assessment

• Listen during pair investigations for accurate partitioning and whether students compare the same-sized whole.
• During group justification, assess use of equivalent and whether explanations refer to shaded area rather than piece count alone.
• Check each student’s response to (1/2 = __/4) and their exit drawing. Ask individuals to explain orally if writing is a barrier.

Differentiation

• Support learners with pre-drawn rectangles, folding lines, coloured shading, transparent overlays and repeated teacher modelling. Provide the sentence frame: “___ quarters cover the same amount as one half because…”
• Use concrete materials before moving to symbols. Pair students strategically and allow oral, drawn or written explanations.
• For learners needing language support, explicitly teach and display whole, half, quarter, same amount and equivalent, with gestures and diagrams. Rephrase questions and check understanding privately.
• Advanced learners investigate whether (2/4) and (1/2) remain equivalent in differently shaped but equal-sized wholes, such as a circle and rectangle, then write or present a short explanation. They may also create a false example using different-sized wholes and explain why it is misleading.

Extension

• Give advanced learners equal-sized wholes with different shapes and ask them to demonstrate (1/2 = 2/4) in two ways.
• Ask them to create a matching card that could challenge another group, including a diagram, fraction notation and a justification.