Foundations of Mathematical Thinking · 1st Class

Active learning ideas

Sharing Objects Equally

Active learning with physical objects helps first graders grasp division by making abstract ideas concrete. Sharing counters or real snacks lets students see fairness in action, building their understanding of equal groups before moving to symbols.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.1
• NCCA: Junior Cycle - Strand 3: Number - N.1.2

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 25 min · Small Groups

Circle Share: Counter Division

Place 12-18 counters in the center of small groups. Students take turns sharing into two or three piles, counting each to check equality. Record the number per group on mini-whiteboards and discuss any remainders.

What does it mean to share a group of objects equally between two or three people?

Facilitation Tip

During Circle Share, model how to redistribute counters until each pile looks the same size, emphasizing that fairness means matching counts, not taking turns.

What to look for

Give each student 12 counters. Ask them to share the counters equally between two imaginary friends. Observe if they can distribute them one by one to each friend until none are left. Ask: 'How many counters does each friend get?'

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

Activity 02

• Experiential Learning
• 20 min · Pairs

Snack Split: Real Food Sharing

Provide shared snacks like 10 raisins or biscuits per pair. Partners divide equally between two bowls, count each, and trade to verify. Extend by trying three-way shares with a third student.

How do you know if you have shared objects fairly?

Facilitation Tip

For Snack Split, pre-cut food into small pieces so students focus on sharing portions fairly rather than cutting skills.

What to look for

Provide students with a worksheet showing 3 groups and 15 stars. Ask them to draw lines to share the stars equally among the groups. Then, ask them to write the number of stars in each group.

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

Activity 03

• Experiential Learning
• 30 min · Individual

Draw and Divide: Picture Partitioning

Give sheets with 15 dots or shapes. Individually, students circle into two or three equal groups and label counts. Pairs then compare and explain their divisions.

Can you share 12 counters equally between 3 groups and say how many are in each group?

Facilitation Tip

In Draw and Divide, provide grid paper to help students align equal groups neatly when sketching their partitions.

What to look for

Present a scenario: 'I have 10 stickers to share between 3 children. Can I share them equally? How do you know?' Facilitate a class discussion where students explain their reasoning, using counters if needed to demonstrate.

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

Activity 04

• Experiential Learning
• 35 min · Whole Class

Fair Trade Game: Whole Class Exchange

Teacher distributes uneven object sets to students. In a circle, they negotiate trades to make two or three equal groups across the class, counting aloud to confirm.

What does it mean to share a group of objects equally between two or three people?

Facilitation Tip

Play Fair Trade Game with three student teams rotating roles to ensure everyone practices both sharing and receiving objects.

What to look for

Give each student 12 counters. Ask them to share the counters equally between two imaginary friends. Observe if they can distribute them one by one to each friend until none are left. Ask: 'How many counters does each friend get?'

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

A few notes on teaching this unit

Start with hands-on tools before symbols, letting students explore fairness through trial and error with counters or blocks. Avoid rushing to written division sentences; instead, have them describe their process aloud first. Research shows that verbalizing actions strengthens early division concepts more than abstract notation.

Students will demonstrate that equal sharing means same-sized groups by redistributing objects without leftovers when possible. They will explain their methods using both actions and words, showing growing confidence in partitioning sets of up to 20 items.

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Watch Out for These Misconceptions

• During Circle Share, watch for students giving one counter to each friend in turns until none are left, ignoring whether piles are equal.

  Prompt them to recount each pile after distributing all counters and adjust any uneven group by moving one counter at a time until matches appear.

• During Snack Split, watch for students assuming sharing failed if food pieces are unequal in size instead of counting total portions.

  Have them recount the total pieces first, then check each plate to confirm counts match, normalizing that size differences don’t affect fairness of count.

• During Draw and Divide, watch for students thinking more groups always means fewer items per group without checking the total objects.

  Ask them to write the total objects first, then divide the total by the number of groups before drawing, reinforcing that totals dictate fairness.

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Methods used in this brief

• Experiential Learning