Sharing Equally

Overview

In this fourth lesson of the nine-lesson unit Rational Numbers in Action, students use pretend picnic items to find halves and quarters by sharing equally. They build on counting and equal groups, then record each sharing result with pictures and words.

Learning intentions

• WALT find one half and one quarter of a small set by sharing equally.
• WALT represent sharing situations with counters, pictures and words.
• WALT explain how we know a share is fair.
• WALT predict and check the result of sharing 4, 8, 12 or 16 objects.

Success criteria

• I can share a set equally between two or four people.
• I can find a half or quarter of a small number.
• I can check that everyone has the same amount.
• I can show my thinking with counters, a drawing and words.

Curriculum links

• Mathematics and Statistics — equal sharing, fractions as parts of a whole, and communicating mathematical thinking.
• Mathematics and Statistics — using concrete materials, pictures and words to represent number relationships.
• Mathsteasers — developing higher-order thinking through challenging, accessible mathematical problems.
• Mathsteasers / Alignment — providing relevant challenge for advanced learners and deepening understanding.

Lesson structure (45 minutes)

1. 0–5 min · Picnic hook. Teacher displays a plate of 8 pretend food items and asks, “Four children are hungry. How can we share these fairly?” Open with the picnic hook slide and allow quiet think time before partner talk. Students predict how many each child might receive and explain what “fair” means.

2. 5–12 min · Model halves and quarters. Teacher models sharing 8 counters between two children, placing one counter at a time in each person’s hoop, then repeats with four children using 12 items. Use the words half, quarter, equal, share and same amount, and show the recording format on the modelling and vocabulary slides. Students help count each share, identify the half or quarter, and rehearse the sentence: “The whole set is __. Each person gets __.”

3. 12–27 min · Practical picnic sharing. Organise 25 students into five mixed groups of five. Give each group counters or play-food items, four character mats or hoops, and the Twenty-frame Mats to support building and counting sets. Teacher provides a set of 4, 8, 12 or 16 items and asks students to share it between two or four children, changing the number and number of children after each successful attempt. Students take turns as sharer, receivers, counter and recorder; they share one item at a time, check that all groups are equal, and state whether they found a half or quarter. Display the instructions on the practical activity instruction slide.

4. 27–36 min · Record and explain. Teacher distributes the equal-sharing recording worksheet and models one example without completing students’ work for them. Students draw the whole set and equal groups, write the amount each person receives, and complete a sentence such as “One quarter of 12 is 3.” Partners compare drawings and use the check: “Does everyone have the same amount?” Teacher conferences with groups, asking, “How do you know it is fair?” and “What did you do first?”

5. 36–41 min · Predict, then check. Teacher shows a new number on the prediction and discussion slides: “Before touching the counters, predict one half of 16 and one quarter of 16.” Students record or share a prediction, then use counters to check it. Invite students to notice that 16 can be shared equally into halves and quarters, while some other numbers may not share equally into four groups.

6. 41–45 min · Plenary and exit check. Teacher revisits the WALT and asks students to explain the difference between finding a half and finding a quarter. Students complete the final worksheet prompt: draw or describe one fair share, name the whole number and state how many each person receives. Invite two students to share different representations, then collect worksheets for assessment.

Resources

• the Sharing Equally slide deck
• the equal-sharing recording worksheet
• Counters, plates, hoops or small character mats
• Pretend picnic or party food items
• Two- and four-person group labels
• Pencils, crayons and whiteboards
• the Twenty-frame Mats

Assessment

• Observe whether students distribute one item at a time and create equal groups; note who can independently find halves and quarters.
• Ask individuals to explain a result using “whole”, “equal groups” and “each person gets”; listen for accurate reasoning rather than only an answer.
• Use the worksheet and final prompt to identify whether students can represent, name and check an equal share.

Differentiation

• Support learners with sets of 4 or 8, two-person sharing first, clearly marked hoops, repeated modelling and an adult-guided group. Encourage touching and counting each item as it is shared.
• Provide sentence starters: “I shared __ between __ people”; “Each person got __”; “It is fair because __.” Pair students strategically and accept oral explanations alongside drawings.
• For EAL learners and students needing additional support, use gestures, real objects, picture labels and repeated vocabulary. Reduce the recording demand while maintaining the practical mathematical goal.
• Extend advanced learners by asking them to predict before sharing, find all even numbers up to 16 that can be shared into halves and quarters, and explain why an odd number cannot be shared equally into two groups.

Extension

• Challenge students to invent a fair picnic-sharing problem using 4, 8, 12 or 16 items, draw it and swap with a partner to solve.
• Ask: “Can a number be shared equally between two children but not four? Find an example and prove it with counters.”