Mathematics · Year 2

Active learning ideas

Fair Sharing and Grouping

Active learning makes fair sharing and grouping concrete for students. When children physically distribute items, they see equality in action, which builds a strong foundation for division concepts. Hands-on tasks turn abstract rules into visible results, helping students trust the process of equal distribution.

• ACARA Content Descriptions
• AC9M2N04

• 15–35 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 30 min · Small Groups

Simulation Game: The Fair Feast

Students are given a 'feast' of items (counters or beads) and must share them equally among a varying number of 'guests' (paper plates). They must negotiate what to do with the 'leftovers' and record their results as 'X shared between Y is Z'.

What does it mean for a share to be fair in mathematics?

Facilitation Tip

During The Fair Feast, sit with students and model the language of fair sharing by saying, 'I give one to you, one to me, one to you' as you place items on plates.

What to look for

Provide students with 10 counters and ask them to show two ways to share them equally. On the back, ask them to draw how many groups of 3 counters they can make from 10 counters and what is leftover.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Role Play
• 35 min · Small Groups

Role Play: The Packing Factory

Students act as factory workers who must put items into 'packs' of a specific size (e.g., packs of 5). They are given a large bucket of items and must determine how many full packs they can make and how many items are 'waste' (remainders).

How can we predict if a number can be shared equally between two people?

Facilitation Tip

In The Packing Factory, assign roles so students must communicate quantities clearly, such as 'I need 3 more boxes for 15 items.'

What to look for

Present a scenario: 'There are 15 stickers to share equally among 4 friends. Draw a picture to show how many stickers each friend gets and how many are left over.' Observe student drawings and explanations.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Is it Fair?

The teacher shows an image of a 'unfair' share (e.g., one person has 4, another has 2). Students discuss with a partner why this isn't a mathematical 'share' and how they would fix it to make it equal.

What happens when we have items left over after sharing?

Facilitation Tip

For Is it Fair?, pause after the think phase to prompt pairs to explain their reasoning before sharing with the class.

What to look for

Pose the question: 'Imagine you have 7 apples and want to make bags with 2 apples in each. Can you share them all perfectly? What happens?' Encourage students to use the terms 'grouping' and 'leftover' in their answers.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach fair sharing by starting with small numbers and using materials students can move. Avoid abstract symbols until they are secure in the process. Research shows that students who physically deal items develop stronger mental models for division than those who only see pictures or numbers. Always connect the activity to real-life contexts they understand, like sharing snacks or organizing classroom items.

Students will demonstrate understanding by distributing items equally without prompting and explaining why each group must have the same amount. They should use terms like 'groups' and 'leftover' correctly and identify whether a problem is sharing or grouping. Confidence in explaining their actions shows deep understanding.

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Watch Out for These Misconceptions

• During The Fair Feast, watch for students giving equal turns but not equal amounts, such as giving one large piece to a friend and a small piece to themselves.

  Have students recount aloud as they place each item, saying, 'One for you, one for me,' to reinforce equal distribution and remind them that fairness means equal size and number.

• During The Packing Factory, watch for students labeling trays with the number of groups instead of the number of items in each group.

  Ask students to point to a tray and say, 'This tray holds 4 items. How many trays will we need for 20 items?' This refocuses their attention on the quantity inside each group.

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Methods used in this brief

• Simulation Game
• Role Play
• Think-Pair-Share