Mathematics · Year 3 · Parts of a Whole: Fractions · Term 3

Area of Rectangles (Informal Units)

Introducing the concept of area as the amount of surface covered, using informal units and square centimeters.

• ACARA Content Descriptions
• AC9M3M02

About This Topic

In Year 3 Mathematics under the Australian Curriculum, students investigate area as the measure of surface space covered by a rectangle. They cover shapes using informal units like counters, tiles, or squares on grid paper, then formalise with square centimetres. This process highlights that area requires complete coverage without gaps or overlaps, and it multiplies length by width for efficiency.

Students compare area to perimeter, noting perimeter traces the outline while area fills the interior. They design estimation methods for irregular shapes by breaking them into rectangles or using consistent units, and explain why squares tile neatly. These explorations align with AC9M3M02 and connect to fractions through partitioning.

Active learning benefits this topic greatly. Hands-on covering lets students physically manipulate units, test arrangements, and observe patterns firsthand. Group discussions of strategies reveal efficiencies, such as counting by rows, while peer comparisons correct errors and build justification skills essential for measurement reasoning.

Key Questions

1. Compare the concepts of perimeter and area, highlighting their differences.
2. Design a method to estimate the area of an irregular shape.
3. Explain why square units are used to measure area.

Learning Objectives

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

Before You Start

Introduction to Length and Measurement

Why: Students need to understand the concept of measuring length before they can grasp the concept of measuring the space a shape covers.

Identifying 2D Shapes

Why: Students must be able to identify rectangles and understand their properties to measure their area.

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.

Watch Out for These Misconceptions

Common Misconception

Area and perimeter measure the same thing.

What to Teach Instead

Hands-on activities where students trace perimeters with string then cover areas with tiles show clear differences. Peer discussions help students articulate that perimeter is boundary length while area is interior space, reinforcing the distinction through tangible comparisons.

Common Misconception

Rectangles with the same perimeter have the same area.

What to Teach Instead

Provide sets of rectangles with equal perimeters but different areas. Students cover each with units to measure and compare, discovering long thin shapes cover less space. Group sharing of results builds understanding of length-width trade-offs.

Common Misconception

Any shaped unit can measure area accurately.

What to Teach Instead

Students test circles or triangles as units on rectangles, observing gaps and overlaps. Switching to squares demonstrates perfect coverage. Collaborative trials highlight why uniform squares provide consistent, reliable measures.

Active Learning Ideas

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.

35 min·Small Groups

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.

25 min·Pairs

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.

40 min·Small Groups

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.

30 min·Individual

Real-World Connections

• Tilers use area measurements to calculate how many tiles are needed to cover a bathroom floor or a kitchen backsplash, ensuring they purchase the correct amount.
• Interior designers calculate the area of rooms to determine how much carpet or flooring is required, and to arrange furniture effectively within the space.
• Gardeners measure the area of garden beds to know how much soil to buy or how many plants can fit in a specific space.

Assessment Ideas

Quick Check

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?'

Exit Ticket

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.

Discussion Prompt

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.

Frequently Asked Questions

How do you introduce area to Year 3 students?

Start with familiar rectangles like desks or books. Have students cover them with everyday informal units such as coins or erasers, emphasising complete coverage without gaps. Transition to grid paper and square cm tiles, guiding them to count by rows for efficiency. This builds intuition before formulas, aligning with AC9M3M02.

What is the difference between perimeter and area in Year 3?

Perimeter measures the distance around a shape's boundary, like fencing a yard, while area measures the space inside, like carpet needed. Students trace perimeters with yarn then fill areas with tiles to feel the contrast. Activities comparing both on identical rectangles clarify that equal perimeters yield different areas.

How can active learning help teach area measurement?

Active approaches like tiling rectangles with physical units make abstract concepts concrete, as students manipulate and arrange tiles to see coverage patterns. Collaborative estimation of irregular shapes encourages strategy sharing and peer feedback, reducing misconceptions. Whole-class charts of results visualise connections between dimensions and total area, boosting engagement and retention.

How to estimate area of irregular shapes in Year 3?

Teach partitioning into rectangles or familiar shapes, then cover each part with informal units or square cm grids. Students overlay string to approximate outlines or use overlays for quick counts. Group practice refines methods, with discussions justifying choices and improving accuracy over time.