Mastering Mathematical Thinking: 4th Class · 4th Class · The Science of Measurement · Summer Term

Perimeter and Area of 2D Shapes

Calculating the perimeter and area of various 2D shapes, including composite shapes.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Geometry and Trigonometry - GT.11
• NCCA: Junior Cycle - Geometry and Trigonometry - GT.12

About This Topic

Area and perimeter are often confused by students, making this one of the most important topics in the 4th Class measurement strand. Perimeter is the distance around the edge of a shape (the 'fence'), while area is the amount of surface the shape covers (the 'grass'). The NCCA curriculum emphasizes moving from counting squares to understanding the relationship between the side lengths and the total area.

This topic is highly practical and connects directly to real world tasks like gardening, painting, or flooring. By exploring these concepts through active investigation, students learn that shapes can have the same area but very different perimeters. This topic comes alive when students can physically measure the classroom or use string and tiles to create shapes with specific dimensions.

Key Questions

1. Explain the difference between perimeter and area and their respective units of measurement.
2. Construct a method for finding the area of a composite shape.
3. Justify why different formulas are used for the area of a rectangle versus a triangle.

Learning Objectives

• Calculate the perimeter of rectilinear shapes using addition and multiplication.
• Calculate the area of rectangles and squares using the formula length × width.
• Compare the perimeters and areas of different shapes, identifying shapes with equal areas but different perimeters.
• Construct a method for finding the area of composite rectilinear shapes by decomposing them into smaller rectangles.
• Explain the difference between perimeter and area, and justify the units of measurement for each.

Before You Start

Introduction to Measurement: Length

Why: Students need a foundational understanding of measuring length and using standard units before they can calculate perimeter and area.

Properties of 2D Shapes

Why: Understanding the characteristics of shapes like rectangles and squares, including their sides and angles, is essential for calculating perimeter and area.

Multiplication and Division Facts

Why: Students require fluency with multiplication facts to efficiently calculate the area of rectangles and the perimeter of shapes.

Key Vocabulary

Perimeter	The total distance around the outside edge of a two-dimensional shape. It is measured in linear units, such as centimetres or metres.
Area	The amount of flat surface a two-dimensional shape covers. It is measured in square units, such as square centimetres or square metres.
Rectilinear Shape	A shape whose boundaries are made up of straight lines meeting at right angles. Examples include rectangles, squares, and L-shapes.
Composite Shape	A shape made up of two or more simpler shapes joined together. For this topic, it refers to shapes made from rectangles.
Square Unit	A unit of area measurement, such as a square centimetre or a square metre, representing the area of a square with sides of one unit.

Watch Out for These Misconceptions

Common Misconception

Students think that if the area of a shape increases, the perimeter must also increase.

What to Teach Instead

Use 12 square tiles. Have students arrange them in a 3x4 rectangle and then in a long 1x12 line. They will see the area stays the same while the perimeter changes drastically. Peer comparison of these shapes is very powerful.

Common Misconception

Students confuse the units, using cm for area and cm squared for perimeter.

What to Teach Instead

Relate the units to the action. We use a 'line' (cm) to measure a 'line' (perimeter). We use a 'square' (cm2) to measure a 'surface' (area). Hands-on measuring with actual physical squares helps reinforce this.

Active Learning Ideas

Inquiry Circle: The Perimeter Challenge

Give each group a piece of string exactly 24cm long. They must create as many different rectangles as possible using that string as the perimeter. They then calculate the area of each rectangle to see which shape 'holds' the most space.

40 min·Small Groups

Simulation Game: The Garden Designer

Students are given a 'budget' of 20 square tiles (area). They must arrange them to create a garden. They then calculate the 'cost' of the fencing (perimeter) for their design. They compete to find the design with the lowest fencing cost.

35 min·Small Groups

Gallery Walk: Irregular Area

Place large irregular shapes (like a giant footprint or a pond) on the floor using masking tape. Students use 'square meter' templates to estimate the area and then walk the perimeter to estimate the distance around, comparing their methods.

30 min·Pairs

Real-World Connections

• Builders and architects calculate the perimeter of rooms to determine the amount of skirting board needed and the area to estimate the amount of carpet or flooring required.
• Gardeners measure the perimeter of flower beds to plan for fencing and calculate the area to determine how much soil or mulch to purchase.
• Interior designers use area calculations to determine the quantity of paint needed for walls or the number of tiles for a backsplash.

Assessment Ideas

Exit Ticket

Provide students with a diagram of a composite rectilinear shape. Ask them to: 1. Calculate the perimeter of the shape. 2. Calculate the area of the shape, showing their steps for decomposing it. 3. Write one sentence explaining why the units for perimeter and area are different.

Quick Check

Display two different rectilinear shapes on the board, one with a larger perimeter but smaller area, and one with a smaller perimeter but larger area. Ask students to write down the perimeter and area for each shape. Then, ask: 'Which shape has the larger area? Which has the larger perimeter? How do you know?'

Discussion Prompt

Pose the question: 'Imagine you have 24 square tiles. Can you arrange them to make different rectangles? What are the perimeters of these rectangles?' Facilitate a discussion where students share their arrangements and compare the perimeters, leading them to discover that different rectangles can have the same area but different perimeters.

Frequently Asked Questions

How can active learning help students understand area and perimeter?

Active learning helps students distinguish between 'covering' and 'surrounding.' By physically laying tiles to find area and stretching string to find perimeter, students build a sensory memory of the two concepts. This prevents the common mistake of mixing up the formulas, as they can visualize the 'squares' versus the 'lines' they worked with.

What is the easiest way to explain perimeter?

Think of it as the 'rim' or the 'boundary.' If an ant walked all the way around the edge of your notebook, the distance it traveled would be the perimeter.

How do we find the area of a shape that isn't a rectangle?

In 4th Class, we usually do this by counting the squares inside the shape on a grid. For partial squares, we can combine them to make whole ones.

Why do we use 'square' units for area?

Because area measures a 2D surface. We are literally counting how many little squares it would take to cover that surface completely.