Remembering Fair Shares

Overview

In this first lesson of the eight-lesson unit, students revisit familiar experiences of sharing kai fairly. They use concrete materials, folding and drawings to recognise and make equal parts, with a focus on halves and quarters. The lesson builds from prior learning in Term 1 and establishes the language and ideas needed for later fraction work.

Learning intentions

• WALT identify and make equal parts.
• WALT share one whole fairly between people.
• WALT name halves and quarters.
• WALT explain how we know parts are fair.

Success criteria

• I can share one whole fairly.
• I can make and name halves and quarters.
• I can show my thinking with objects, a fold or a drawing.
• I can explain why unequal parts are not fair.

Curriculum links

• Mathematics and Statistics — Mathsteasers: challenging thinking and deepening understanding through mathematical problems.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge tasks with familiar mathematical content.
• Mathematics and Statistics — Additional resources for advanced learners: providing opportunities to reason, explain and justify mathematical ideas.
• Mathematical competencies: communicating mathematical thinking, using representations, and reasoning about fairness and equality.

Lesson structure (45 minutes)

1. 0–5 min · Kai sharing hook. Teacher displays a picture of one pizza, sandwich or piece of fruit and asks, “Four children are hungry. How could we share this fairly?” Open with the kai-sharing hook slide. Students turn and talk, then share ideas; teacher listens for “same amount”, “equal” and “fair”.

2. 5–12 min · Reconnect to prior learning. Teacher uses a paper circle or square to model one whole, folds it into two equal parts and introduces or revisits half and halves. Open with the whole, half and quarter teaching slides. Students copy the folding with a paper shape, compare the two parts and explain why they are equal. Repeat by folding into four equal parts and name each part a quarter.

3. 12–18 min · Fair or unfair? Teacher shows examples of shapes divided into equal and unequal parts, including a deliberately misleading shape with lines that do not create equal areas. Students signal “fair” or “not fair”, then justify their choice using a partner sentence: “It is fair because…” or “It is not fair because…”. Teacher records key language: whole, equal parts, half, halves, quarter, quarters.

4. 18–32 min · Small-group fair sharing. Teacher places students in three flexible groups and explains that each group will show, draw and talk about sharing. Students work with paper shapes and counters, recording on the fair-sharing worksheet.

• Supporting: Share one paper “kai” between two people. Fold or partition it into two equal parts and circle or draw the two halves. Teacher prompts: “Are both parts the same? How do you know?”
• Within: Make and identify halves and quarters using paper shapes. Students draw one whole, two equal parts and four equal parts, then label the parts.
• Extending: Examine equal and unequal partitions and explain why an unequal share is not fair. Students create one fair and one unfair example and explain their reasoning orally or in a drawing. Teacher rotates between groups, asking students to demonstrate rather than simply name an answer.

5. 32–40 min · Share strategies. Teacher brings the class together and selects examples from each group. Open with the group-share and discussion slides. Students explain how they checked that parts were equal. Teacher highlights folding, matching, comparing size and counting equal parts, while reinforcing that parts must make the whole and be equal in size.

6. 40–45 min · Plenary and exit check. Teacher displays two final shapes: one split into two equal parts and one split into two unequal parts. Open with the final check slide. Students independently complete the final boxes on the fair-sharing worksheet by drawing a half, drawing four quarters and finishing the sentence, “This share is fair because…”. Invite two or three students to explain their thinking before collecting the sheets.

Resources

• the Remembering Fair Shares slide deck
• the fair-sharing worksheet
• Paper circles, squares and rectangles
• Child-safe scissors, if needed
• Counters or small classroom objects
• Pencils, crayons and whiteboards
• Prepared examples of equal and unequal partitions
• A familiar kai image or clean, shareable food item

Assessment

• Observe whether students make equal parts rather than simply draw dividing lines. Note who can identify a whole, half and quarter.
• During group work, ask: “How do you know the parts are equal?” Record evidence of concrete, pictorial and emerging fraction language.
• Use the final worksheet check to identify students who are ready to work with quarters, need further experience with halves, or require support recognising equal size.

Differentiation

• Support: Work alongside students using one whole and two large paper parts first. Use matching, folding and the sentence frame “The parts are equal because…”. Accept pointing, demonstrating or drawing before expecting complete verbal explanations.
• Within: Provide repeated opportunities to fold, build, draw and label halves and quarters. Pair students so they can compare their models.
• Extension: Ask students to find more than one way to divide a shape into two equal parts, or defend why a tempting unequal share is unfair.
• EAL and additional learning needs: Use gestures, real objects, photographs and repeated vocabulary. Keep models visible, reduce the amount of writing and allow oral explanation, drawing or demonstration. The progression from concrete materials to pictures and then words supports the planned PAC approach. The lesson moves learners from SOLO prestructural responses towards unistructural identification and naming.