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.

• Year 3
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

1. Compare the area of two rectangles by covering them with informal units.
2. Calculate the area of a rectangle by multiplying its length and width in informal units.
3. Explain why square units are the standard for measuring area.
4. Design a method to estimate the area of an irregular shape using square units.

Collaborative Problem-Solving

⏱ 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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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

Assessment Ideas

Quick Check

After Rectangle Cover-Up, provide two rectangles on grid paper and ask students to count the squares to find each area. Then ask: ‘Which rectangle has a larger area? How do you know?’

Exit Ticket

After Irregular Shape Estimators, give students an irregular shape on grid paper and ask them to estimate the area by counting full squares and partial squares. On the back, have them write one sentence explaining their estimate.

Discussion Prompt

During Unit Tiling Challenge, 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.

Extensions & Scaffolding

• Challenge: Provide a rectangle and ask students to find all possible tiling arrangements using exactly 12 tiles.
• Scaffolding: Give students a partially tiled rectangle and ask them to complete it, noting the number of tiles needed.
• Deeper exploration: Have students create two rectangles with the same area but different perimeters, then compare how each shape covers space.

Key Vocabulary

Area	The amount of flat surface a shape covers. It is measured in square units.
Square Unit	A unit of measurement shaped like a square, used to measure area. Examples include square centimeters or square inches.
Cover	To place units side by side so that they fill the entire surface of a shape without gaps or overlaps.
Estimate	To find an approximate value or size, often by making an educated guess based on available information.