Sharing Fairly

Overview

This is lesson 1 of 5 in Division Explorers. Students build the meaning of division by sharing collections equally among 2–5 people, using counters and drawings before connecting their actions to division symbols and number sentences.

Learning intentions

• WALT share a collection equally between 2–5 people.
• WALT explain what division means using objects, drawings and words.
• WALT connect equal sharing with the symbols ÷ and =.
• WALT listen to and explain a partner’s mathematical thinking.

Success criteria

• I can share a collection so each group has the same number.
• I can show my sharing with counters, a drawing or a sharing mat.
• I can write a division number sentence to match my model.
• I can explain how I know my sharing is fair.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen mathematical understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge tasks connect with relevant mathematical content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: opportunities to reason, justify and explore patterns.
• Te Mātaiaho mathematical competencies: communicating thinking, using representations, and making connections between concrete actions and symbols.

Lesson structure (30 minutes)

1. 0–5 min · Story and notice. Teacher tells a brief story: “Four explorers find 12 shells and want to share them fairly. How could they do this?” Display the opening question in the story and notice slides and model placing one counter at a time into four labelled groups. Students quietly notice, then turn and talk: “What would make the sharing fair?” Invite two or three explanations and introduce the words equal, share, groups and division.

2. 5–12 min · Teacher modelling. Teacher uses colour-coded counters and a large sharing mat to model 10 objects shared between 2 people, then records 10 ÷ 2 = 5. Refer to the equal-sharing modelling slides and demonstrate that ÷ can be read as “shared equally between”. Think aloud: “I dealt one counter to each group until all counters were used. Both groups have 5, so the sharing is fair.” Students help check each group and rehearse the sentence: “Ten shared between two equals five.”

3. 12–20 min · Hands-on group exploration. Organise students into five groups of four, with pre-grouped materials matched to need. Give each group counters, number cards and the Division Sharing Mats. Display the task instructions in the hands-on exploration slides. Students solve several teacher-called problems, such as 8 shared between 2, 12 between 3, 15 between 5 and 16 between 4. They build each problem, draw or mark the groups on the mat, and record the matching number sentence. Pause twice to ask: “How do you know it is equal?” and “What does each number in your sentence mean?”

4. 20–27 min · Partner practice. Pair students within groups and distribute the equal-sharing practice sheet. Partners take turns being the sharer and the checker. The sharer models each problem with counters or a drawing; the checker confirms that the groups are equal and asks, “How do you know?” Students complete a small set of problems involving divisors 2–5, then explain one answer to their partner using the frame: “___ shared between ___ equals ___ because ___.” Use the partner practice and discussion slides for reminders and prompts.

5. 27–30 min · Exit check. Hand out the Division Facts Exit Ticket Slips. Students complete one suitable question, for example 12 ÷ 3, and show their thinking with a quick drawing, counters or words. Ask two students to share different representations. Collect slips to identify who can model equal sharing and who needs further concrete practice in lesson 2.

Resources

• Sharing Fairly teaching deck
• Equal-sharing practice sheet
• Division Sharing Mats
• Division Facts Exit Ticket Slips
• Colour-coded counters, 10–20 per group
• Small bowls, hoops or paper circles for groups
• Number cards from 2–5 and selected collections
• Board and markers
• Pencils, crayons and erasers
• Large-print instructions in a clear sans-serif font

Assessment

• During modelling, check whether students distribute one object at a time and recognise equal group sizes.
• During group and partner work, listen for correct use of share, equal, groups and division; ask students to explain rather than only state an answer.
• Use exit slips to sort students for the next lesson: secure with equal sharing, developing with prompts, or requiring further modelling with smaller collections.

Differentiation

• Support learners with smaller numbers, such as 4, 6, 8 or 10, pre-grouped counters, clearly labelled sharing mats and teacher modelling of one short step at a time.
• Provide visual group circles, colour-coded counters and sentence frames. Accept spoken explanations, drawings, pointing or oral recording instead of extended writing.
• For dyslexia-friendly access, read every instruction aloud, use a clear sans-serif font and large spacing, avoid dense text, and present only one instruction at a time.
• Challenge advanced learners to investigate all the different ways to share 24 objects equally. They record which divisors from 2–5 work, identify any other divisors they know, and explain the pattern using drawings, equations or multiplication checks.