Foundations of Mathematical Thinking · Senior Infants

Active learning ideas

Big and Small Shapes

Active learning works for Big and Small Shapes because children need to physically cover and compare spaces to grasp area concepts. Hands-on tasks make abstract ideas visible and allow students to correct their own misunderstandings through trial and error.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Measurement - M.2

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

Activity 01

• Experiential Learning
• 30 min · Small Groups

Hands-On: Triangle Tiling Challenge

Provide cut-out squares, parallelograms, and triangles. Children work to cover larger shapes completely with smaller triangles, counting how many fit. Groups discuss and compare coverings for different base shapes, noting patterns in coverage.

Which shape takes up more space on the table?

Facilitation Tip

During Triangle Tiling Challenge, circulate to ensure children rotate and flip triangles to test full coverage.

What to look for

Provide students with several different shapes cut from cardstock (e.g., a square, a triangle, a parallelogram). Ask them to place the shapes on a large outline of a table and explain which shape covers the most space, using counters to demonstrate their reasoning.

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

Activity 02

• Experiential Learning
• 25 min · Pairs

Pairs: Counter Covering Race

Pairs select two shapes like a triangle and parallelogram. They cover each with counters or buttons, then compare totals. Switch shapes and repeat to check consistency, recording findings on simple charts.

Can you cover this square using triangle pieces?

Facilitation Tip

For Counter Covering Race, remind pairs to agree on a fair unit before starting so comparisons are valid.

What to look for

Present students with two identical triangles. Ask: 'What happens to the amount of space covered if we push these two triangles together to make a parallelogram?' Encourage them to use counters or draw to show their thinking.

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

Activity 03

• Experiential Learning
• 35 min · Whole Class

Whole Class: Shape Rearrange Demo

Display large shapes on the floor. Class watches as you cut and rearrange pieces, covering with fabric scraps before and after. Children predict and vote on changes in covered space, then verify together.

Which shape is bigger , how can we check?

Facilitation Tip

In Shape Rearrange Demo, pause after each arrangement to ask the class to predict which shape now covers more space.

What to look for

Give each student a small square outline and a collection of triangle pieces. Ask them to draw or use the triangle pieces to show how many triangles it takes to cover the square. They should write or draw their answer.

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

Activity 04

• Experiential Learning
• 20 min · Individual

Individual: Personal Shape Match

Each child gets outline shapes to fill with provided scraps. They match pairs of shapes that cover the same amount, labeling big, small, or same. Share one match with the class.

Which shape takes up more space on the table?

Facilitation Tip

For Personal Shape Match, provide varied triangles so students notice that not all triangles cover the same space.

What to look for

Provide students with several different shapes cut from cardstock (e.g., a square, a triangle, a parallelogram). Ask them to place the shapes on a large outline of a table and explain which shape covers the most space, using counters to demonstrate their reasoning.

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

A few notes on teaching this unit

Teachers should let students explore first before giving language, so their actions create meaning. Avoid rushing to formulas; instead, focus on repeated experiences where children count and compare coverings. Research shows that concrete experiences build the foundation for later abstract reasoning about area.

Successful learning looks like students using counters, paper scraps, or tiles to measure space fairly, explaining their comparisons with clear reasoning. They should move from guessing by eye to counting and counting to understand how shapes fill surfaces.

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Watch Out for These Misconceptions

• During Triangle Tiling Challenge, watch for children who assume a long thin triangle covers more space than a short wide one.

  After they tile both shapes, ask them to count the counters on each. Have them rearrange the counters to see that length alone does not determine coverage.

• During Counter Covering Race, watch for children who think shapes with the same outline length cover the same space inside.

  After the race, bring pairs together to compare their counters side by side. Ask them to trace the outline of their shapes and count how many counters fit inside each.

• During Personal Shape Match, watch for children who believe all triangles cover the same space.

  After they try to cover the square with their triangle pieces, ask them to count the number of triangles used. Compare results with peers to show that triangles with different bases and heights need different numbers to fill the same square.

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Methods used in this brief

• Experiential Learning