Mathematics · Grade 3

Active learning ideas

Understanding Area

Active learning works well for understanding area because students need to physically manipulate units to grasp the concept of covering space. Hands-on tiling and building activities make abstract ideas concrete, helping students see why area is measured in square units rather than linear units.

• Ontario Curriculum Expectations
• 3.MD.C.5.A
• 3.MD.C.5.B

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 35 min · Small Groups

Tiling Stations: Regular Shapes

Set up stations with square tiles and outlines of rectangles, triangles, and squares. Students cover each shape, count units, and record areas on charts. Rotate groups every 10 minutes to try different shapes.

Explain what 'area' means in your own words.

Facilitation Tip

During Tiling Stations, remind students to align tiles precisely along the edges of shapes to avoid gaps or overlaps.

What to look for

Provide students with a simple rectangle drawn on grid paper. Ask them to write the area of the rectangle in square units and explain in one sentence how they found it.

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

Activity 02

• Experiential Learning
• 30 min · Pairs

Irregular Shape Builders

Provide grid paper and counters. Pairs draw irregular shapes, cover with unit squares, and estimate partial squares. They swap drawings to verify each other's area calculations.

Compare how measuring area is different from measuring perimeter.

Facilitation Tip

For Irregular Shape Builders, encourage students to count partial squares carefully and discuss strategies as a group.

What to look for

Present students with two shapes: one rectangle and one irregular shape, both covered with the same number of square units. Ask: 'Are the areas of these two shapes the same? How do you know?' Encourage them to explain their reasoning.

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

Activity 03

• Experiential Learning
• 40 min · Individual

Area vs Perimeter Compare

Give students string for perimeters and tiles for areas of classroom objects like mats. Individually measure both, then share data whole class to spot patterns.

Design a method to find the area of an irregular shape using square units.

Facilitation Tip

In Area vs Perimeter Compare, have students trace both the boundary and the interior of shapes with different colored markers to visually separate the concepts.

What to look for

Give students a set of square tiles and a drawing of a shape with a curved edge. Ask them to cover the shape with tiles and count how many tiles they used. Then, ask them to draw a rectangle on grid paper that has the same area.

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

Activity 04

• Experiential Learning
• 45 min · Small Groups

Design Your Floor Plan

Students sketch room floor plans on grid paper, calculate areas for different flooring options. Small groups present plans, explaining unit counts and choices.

Explain what 'area' means in your own words.

What to look for

Provide students with a simple rectangle drawn on grid paper. Ask them to write the area of the rectangle in square units and explain in one sentence how they found it.

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

A few notes on teaching this unit

Teach area by starting with simple rectangles and moving to irregular shapes, ensuring students master tiling before estimating partial squares. Avoid rushing to formulas; let students discover that area is about counting units, not measuring edges. Use real-world contexts like carpeting or tiling to make the concept meaningful and memorable.

Successful learning looks like students accurately covering shapes with square units without gaps or overlaps, counting units correctly, and explaining their process clearly. They should also confidently compare area and perimeter and apply these skills to real-world tasks like designing floor plans.

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Watch Out for These Misconceptions

• During Tiling Stations, watch for students measuring only the edges of shapes and calling it area.

  Have students recount the interior square units they covered and ask them to point out why the edge length alone does not give the area.

• During Irregular Shape Builders, watch for students assuming irregular shapes cannot be measured accurately.

  Ask students to place tiles along the edges first, then fill the interior, demonstrating that partial units can still be counted for an estimate.

• During Area vs Perimeter Compare, watch for students believing shapes with the same perimeter must have the same area.

  Challenge groups to tile rectangles with the same perimeter but different areas, then discuss why the number of interior squares varies.

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Methods used in this brief

• Experiential Learning