Mathematics · Grade 3

Active learning ideas

Area of Rectangles by Tiling

Active learning through tiling gives students a tangible way to grasp area as a countable concept. When students physically place unit squares on rectangles, they build spatial reasoning that connects to multiplication, moving beyond abstract formulas to concrete understanding.

• Ontario Curriculum Expectations
• 3.MD.C.6
• 3.MD.C.7.A

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Tiling Challenges

Prepare four stations with grid paper rectangles of varying sizes and square tiles. Students tile each rectangle, record the area, and calculate length x width to check. Groups rotate every 10 minutes, then share one insight as a class.

Explain how tiling a rectangle with unit squares helps us understand its area.

Facilitation Tip

During Station Rotation: Tiling Challenges, provide a mix of rectangle sizes and unit square sets to push flexible thinking about area.

What to look for

Provide students with grid paper and ask them to draw a rectangle with an area of 12 square units. Then, ask them to write the dimensions (length and width) of their rectangle and explain how they know the area is 12.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Outdoor Investigation Session
• 30 min · Pairs

Pairs Build: Target Area Rectangles

Give pairs a target area number and square tiles. They build as many different rectangles as possible that tile to that area, measure side lengths, and list multiplication sentences. Pairs swap builds to verify areas.

Analyze the relationship between the side lengths of a rectangle and its area.

Facilitation Tip

For Pairs Build: Target Area Rectangles, model how to agree on dimensions before building, reinforcing measurement and collaboration.

What to look for

Present students with two different rectangles, each with an area of 16 square units but different dimensions (e.g., 4x4 and 2x8). Ask: 'How can two rectangles have the same area but look different? Use your unit squares to show your thinking.'

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 03

• Outdoor Investigation Session
• 35 min · Whole Class

Whole Class: Rectangle Design Contest

Students design a rectangle on grid paper for a playground or garden with a given area. They tile to confirm, label dimensions and multiplication fact, then vote on the most creative design that matches.

Construct a formula for finding the area of any rectangle.

Facilitation Tip

In Whole Class: Rectangle Design Contest, invite students to explain their designs to peers, using math vocabulary like ‘rows’ and ‘columns’ intentionally.

What to look for

Give each student a card showing a rectangle tiled with unit squares. Ask them to: 1. Count the unit squares to find the area. 2. Write the multiplication sentence that represents the area (length x width = area). 3. Write one sentence explaining why this multiplication works.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Outdoor Investigation Session
• 25 min · Individual

Individual: Virtual Tiling Exploration

Using online grid tools or apps, students create rectangles, tile digitally, and record areas with side lengths. They experiment with changing one side and predict area changes before tiling.

Explain how tiling a rectangle with unit squares helps us understand its area.

Facilitation Tip

With Individual: Virtual Tiling Exploration, circulate to ask guiding questions such as ‘How do you know your rectangle has the right area?’ to assess reasoning.

What to look for

Provide students with grid paper and ask them to draw a rectangle with an area of 12 square units. Then, ask them to write the dimensions (length and width) of their rectangle and explain how they know the area is 12.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

A few notes on teaching this unit

Teach this topic by having students alternate between hands-on tiling and abstract recording. Avoid rushing to formulas; instead, let students discover the length x width pattern through repeated tiling. Research shows that students who physically tile and count are more likely to retain the concept and apply it correctly in new contexts.

Successful students will tile rectangles accurately without gaps or overlaps, count tiles to find area, and write matching multiplication sentences. They will explain how the number of rows times columns matches the total tiles, showing confidence in both visual and numerical representations.

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Watch Out for These Misconceptions

• During Station Rotation: Tiling Challenges, watch for students who trace the perimeter of tiles instead of counting the interior squares.

  Ask students to trace the outside edge of the rectangle with one finger while counting interior tiles, then compare the two counts to clarify the difference.

• During Station Rotation: Tiling Challenges, watch for students who leave gaps or overlap tiles when tiling.

  Set a rule that tiles must fit edge-to-edge and provide a peer checker to verify coverage before counting area.

• During Pairs Build: Target Area Rectangles, watch for students who assume area depends on shape rather than dimensions.

  Have pairs build multiple rectangles with the same area but different dimensions, then discuss how the count of tiles remains constant despite different looks.

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Methods used in this brief

• Stations Rotation
• Outdoor Investigation Session