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.

• Senior Infants
• Foundations of Mathematical Thinking
• 4 activities
• 20 min–35 min

Learning Objectives

1. Compare the area covered by different two-dimensional shapes using non-standard units.
2. Classify shapes based on their ability to tessellate and cover a given surface.
3. Demonstrate that rearranging pieces of a shape does not change its total area.
4. Identify pairs of congruent triangles that can form a parallelogram.

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Triangle Tiling Challenge, provide cardstock shapes and a table outline. Ask students to place shapes on the outline and explain which covers the most space using counters to justify their answer.

Discussion Prompt

During Shape Rearrange Demo, present two identical triangles and ask: 'What happens to the space covered if we push these together to make a parallelogram?' Observe if students use counters or drawings to show that the space covered increases when combined.

Exit Ticket

After Personal Shape Match, give each student a small square outline and triangle pieces. Ask them to cover the square and write or draw how many triangles they used, showing their understanding that area is about total coverage.

Extensions & Scaffolding

• Challenge pairs who finish early to find two different shapes that cover the same amount of space using only eight counters.
• Scaffolding for students who struggle: Provide outlines of squares pre-divided into triangles so they start with a clear structure.
• Deeper exploration: Ask students to create their own shape pairings and write or dictate a sentence explaining which covers more space and why.

Key Vocabulary

Area	The amount of flat space a shape covers. We can measure it by seeing how many small objects fit inside.
Tessellate	To fit together without any gaps or overlaps, like tiles on a floor. Some shapes can tessellate to cover a surface.
Congruent	Exactly the same size and shape. Two congruent triangles can be put together to make a larger shape.
Parallelogram	A four-sided shape where opposite sides are parallel and equal in length. It looks like a slanted rectangle.