Fair Shares Together

Overview

In this first lesson of the 12-lesson unit, students revisit the idea of a whole and explore what makes sharing fair. Using familiar objects and sets, they model and describe equal shares, halves and quarters before explaining why some groups have not been divided fairly.

Learning intentions

• WALT identify a whole and its equal parts.
• WALT share objects fairly between people or groups.
• WALT recognise and name halves and quarters.
• WALT explain why a share is fair or unfair.

Success criteria

• I can show one whole and split it into equal shares.
• I can identify a half and a quarter.
• I can use the words whole, equal, half and quarter.
• I can explain how I know whether sharing is fair.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen mathematical understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge is connected to familiar mathematical content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: opportunities to reason, explain and justify mathematical ideas.

Lesson structure (30 minutes)

1. 0–4 min · Hook and connect. Teacher displays the opening slides from the Revisiting Equal Shares slide deck and shows four children sharing eight counters, first equally and then with one child receiving more. Students silently decide which sharing is fair, then turn to a partner and explain why.

2. 4–9 min · Model a whole and equal shares. Teacher uses one paper plate or piece of paper to represent one whole, then folds or marks it into two equal parts and names each part a half; repeat with four equal parts and name each part a quarter, using the whole, halves and quarters slides. Students make the gestures “whole”, “half” and “quarter”, and notice that the parts must be the same size.

3. 9–16 min · Hands-on fair sharing. Teacher places students in pairs and gives each pair counters, cubes or small classroom objects, referring to the fair-sharing activity instructions. Call out simple situations such as “Share 6 counters between 2 people”, “Share 8 counters between 4 people” and “Share 5 counters between 2 people”. Students share, draw or arrange the objects, and decide whether each situation is fair; they may record their thinking on the equal shares investigation sheet.

4. 16–22 min · Sort and justify. Teacher displays pictures of shapes and groups that show equal halves, equal quarters, unequal parts and unequal groups on the fair or unfair sorting slides. Students show thumbs up for fair/equal and thumbs down for unfair/unequal, then justify one decision using the sentence frame, “It is fair/unfair because…”. Invite several students to challenge or agree with an explanation.

5. 22–27 min · Independent check. Teacher distributes the equal shares investigation sheet and models how to complete one example without giving answers. Students circle or draw the fair shares, shade one half and one quarter, and complete the sentence “Equal shares are…” with words or a labelled drawing. Teacher conferences with students and checks whether they are comparing the size or number of shares, rather than simply counting parts.

6. 27–30 min · Plenary and exit response. Teacher returns to the final prompt in the plenary and exit question slides: “Sam says these two pieces are halves because there are two pieces. Is Sam correct?” Students think, pair-share and respond with a drawing or oral explanation before handing in their worksheet.

Resources

• the Revisiting Equal Shares slide deck
• the equal shares investigation sheet
• Paper plates, paper circles or sheets of paper
• Counters, linking cubes or small classroom objects
• Pencils, crayons and erasers
• Whiteboard and markers
• Pre-prepared examples of fair and unfair sharing

Assessment

• During modelling, ask: “How do you know these are equal?” and listen for students referring to equal size, not just the number of pieces.
• During partner sharing, observe whether students distribute objects one at a time and check that each person receives the same number.
• Use the worksheet and final response to identify students who can recognise halves and quarters and explain fairness. Note students needing further support with the meaning of “equal”.

Differentiation

• Support students by using smaller quantities, sharing between two people first, and providing sentence starters: “It is fair because…” and “This is a half/quarter because…”.
• Give students physical objects and allow them to draw or explain orally instead of relying on written responses. Pair students thoughtfully and model each instruction before releasing them to work.
• For students needing an additional visual scaffold, outline the whole before dividing it and use colour to show the equal parts.
• Challenge confident students to find more than one way to share 12 objects fairly, compare sharing between two and four people, and explain what changes when the number of sharers changes.