Compare and Represent Fractions

Overview

This is lesson 3 of 5 in the unit Fair Sharing: Hautau. Students use identical pizza and toast wholes to model, draw, name and compare halves and quarters, focusing on fairness through equal-sized parts.

Learning intentions

• WALT represent halves and quarters using models, drawings, words and symbols.
• WALT compare fractions when the wholes are the same size.
• WALT explain why one fraction is more, less or equal to another.
• WALT use mathematical language to communicate our thinking.

Success criteria

• I can show (1/2), (1/4), (2/4) and (4/4) with a model or drawing.
• I can explain that (1/2) is the same amount as (2/4).
• I can say which fraction is more, less or the same when the wholes match.
• I can use words such as haurua, hauwhā, nui ake, iti iho and ōrite.

Curriculum links

• Represent simple fractions that arise through equal sharing.
• Recognise and use halves and quarters in familiar contexts.
• Compare and order numbers and quantities using mathematical language.
• Communicate mathematical ideas, justify answers and solve problems collaboratively.

Lesson structure (50 minutes)

1. 0–7 minutes – Same kai, different sharing kōrero

Open with the opening kai-sharing slides. Show two identical pizza or toast wholes and ask: “If two people share one fairly, what must we check first?” Discuss that fairness depends on equal-sized parts of the same whole, while respecting different food preferences and whānau practices. Introduce whakataurite (compare), nui ake (more), iti iho (less), ōrite (equal), haurua (half) and hauwhā (quarter).

2. 7–15 minutes – Model halves and quarters

Use identical pizza and toast models. Fold or mark one whole into two equal parts and then four equal parts. Ask: “Are the wholes the same size?” and “What makes these parts fair?” Connect the models to (1/2) and (1/4), explaining that the bottom number tells how many equal parts the whole has. Keep the focus on meaning rather than memorising terminology.

3. 15–24 minutes – Build a fraction strip

In pairs, students fold paper strips into halves and quarters, label the parts, and place the strips together. Guide them to see that one half covers two quarters: (1/2 = 2/4), and the whole is (4/4). Ask: “How can the strips prove your answer?” and “Can two different fraction names describe the same amount?” Display the completed strip in the fraction-strip teaching slide.

4. 24–34 minutes – Partner compare and sort

Give each pair identical pizza/toast models, fraction strips and fraction cards. Students compare (1/4), (1/2), (2/4) and (4/4), then place cards into hoops labelled “less than (1/2)”, “equal to (1/2)” and “more than (1/2)”. They must explain each placement to a partner using a model, drawing or words. Circulate and listen for justification.

5. 34–43 minutes – Differentiated recording task

Distribute the compare-and-represent worksheet. Year 2 students draw or shade matching pizza and toast models, identify (1/2) and (1/4), and answer with “more”, “less” or “same”. Year 3 students order (1/4), (1/2), (2/4) and (4/4), explain (1/2 = 2/4), and solve questions such as “Which is more pizza: (2/4) or (1/4)? Explain.”

6. 43–48 minutes – Share and address misconceptions

Invite pairs to share one comparison. Revisit errors using matched models, especially “the denominator is bigger, so the fraction is bigger”, comparing unequal wholes, or claiming (2/4) is greater than (1/2). Ask: “Are the wholes the same size?” and “How can the strips prove your answer?”

7. 48–50 minutes – Exit response

Students complete the final draw-and-explain task on the compare-and-represent worksheet: draw or use words to show why (1/2) and (2/4) are equal. Collect responses as students leave.

Resources

• the opening and teaching slide deck
• the compare-and-represent worksheet
• Identical pizza and toast cards or paper models
• Paper strips for folding into halves and quarters
• Fraction cards showing (1/2), (1/4), (2/4) and (4/4)
• Hoops or floor circles labelled less than, equal to and more than (1/2)
• Comparison symbol cards: (<), (=), (>)
• Mini-whiteboards and pens
• Pencils, crayons and scissors

Assessment

• Observe pair work: can students make equal parts and compare only when the wholes are the same size?
• Listen for explanations using nui ake, iti iho, ōrite, haurua and hauwhā, and note whether students justify answers with models or strips.
• Review the worksheet and exit response for correct representations of (1/2), (1/4), (2/4), (4/4), and the equivalence (1/2 = 2/4).

Differentiation

• Support Year 2 learners with pre-folded strips, large picture models, partner talk and the sentence frame: “___ is more/less/the same because ___.”
• Provide fewer cards and concrete models first; use “more”, “less” and “same” before expecting formal symbols.
• Extend Year 3 learners by asking them to order all four fractions and justify each position using the strip, then investigate thirds or a tenths bar while stressing equal parts.
• Support EAL and learners requiring additional scaffolding through gestures, repeated bilingual vocabulary, visual word cards, adult scribing and opportunities to explain orally or by pointing and drawing.