Mathematics · Year 3

Active learning ideas

Area of Rectangles (Informal Units)

Active learning lets students feel area rather than just hear about it. When children cover rectangles with tiles or counters, they see why gaps or overlaps make measuring impossible and why squares fit perfectly. This hands-on work builds lasting understanding before moving to formal units.

• ACARA Content Descriptions
• AC9M3M02

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Placemat Activity
• 35 min · Small Groups

Hands-On: Rectangle Cover-Up

Cut rectangles from card in various sizes. Students select informal units like buttons or multilink cubes and cover each rectangle completely without gaps or overlaps. They count units and record findings on a class chart, noting patterns between length, width, and total area.

Compare the concepts of perimeter and area, highlighting their differences.

Facilitation Tip

During Rectangle Cover-Up, circulate and ask each pair to explain how their tiles match the rectangle’s length and width without gaps.

What to look for

Provide students with two different-sized rectangles drawn on grid paper. Ask them to count the squares to find the area of each. Then, ask: 'Which rectangle has a larger area? How do you know?'

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Relationship Skills

Activity 02

• Placemat Activity
• 25 min · Pairs

Perimeter vs Area Sort

Provide pre-cut rectangles with measured perimeters and areas. In pairs, students sort them into groups by perimeter or area, then justify choices. Extend by predicting area from perimeter and testing with units.

Design a method to estimate the area of an irregular shape.

Facilitation Tip

Before Perimeter vs Area Sort, model tracing a shape’s boundary with string so students feel the difference between the line and the space inside.

What to look for

Give students a small, irregular shape drawn on grid paper. Ask them to estimate the area by counting the full squares and estimating the partial squares. On the back, have them write one sentence explaining why they chose their estimate.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Relationship Skills

Activity 03

• Placemat Activity
• 40 min · Small Groups

Irregular Shape Estimators

Draw irregular shapes on grid paper. Students partition into rectangles, cover with square cm tiles, and estimate total area. Groups share methods and refine estimates collaboratively.

Explain why square units are used to measure area.

Facilitation Tip

During Irregular Shape Estimators, encourage students to share their counting strategies and agree on a group method before moving on.

What to look for

Pose the question: 'Why do we use squares to measure area, and not circles or triangles?' Facilitate a class discussion where students explain how squares fit together perfectly without gaps.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Relationship Skills

Activity 04

• Placemat Activity
• 30 min · Individual

Unit Tiling Challenge

Give students square and non-square units. They tile rectangles, noting gaps or overlaps with non-squares, then explain why squares work best. Record comparisons in journals.

Compare the concepts of perimeter and area, highlighting their differences.

Facilitation Tip

In Unit Tiling Challenge, watch that students rotate tiles to align edges and avoid overlapping corners.

What to look for

Provide students with two different-sized rectangles drawn on grid paper. Ask them to count the squares to find the area of each. Then, ask: 'Which rectangle has a larger area? How do you know?'

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teachers start with physical units so students experience the need for uniformity and complete coverage. Avoid rushing to formulas before students grasp why squares tile perfectly. Research shows that students who build rectangles with tiles remember area as a measure of space, not just a number. Use questioning to guide discoveries rather than telling answers.

Students will confidently explain that area measures surface space covered by a rectangle and calculate it using informal units. They will distinguish area from perimeter and justify why squares work best. Peer discussions will show clear reasoning about length, width, and coverage.

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Watch Out for These Misconceptions

• During Perimeter vs Area Sort, watch for students who confuse the outline of a shape with the space inside.

  Ask students to trace the perimeter with string in one color and cover the area with tiles in another color, then explain the difference between the two lengths of string and the number of tiles.

• During Unit Tiling Challenge, watch for students who assume any unit shape can measure area accurately.

  Provide circles and triangles alongside squares and have students test coverage on the same rectangle, then discuss which shapes leave gaps or overlaps.

• During Rectangle Cover-Up, watch for students who multiply length and width before trying to tile, skipping the concrete coverage step.

  Ask students to first tile the rectangle completely with counters, then count rows and columns to see how multiplication matches their tiling.

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Methods used in this brief

• Placemat Activity