Perimeter, Rectangle Perimeters and Comparing Equal Areas for Primary 6

Class: Primary 6
Term: 2nd Term
Week: 9
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Measurement
Previous Lesson: Time, Minutes, Seconds, Journeys and Timetables.
Topic: PERIMETER
Subject Matter: Meaning of perimeter as distance round a shape, perimeter of a rectangle using side lengths, drawing rectangles with given dimensions, comparing rectangles with equal area but different perimeters.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define perimeter as the distance around a shape.
• Calculate the perimeter of given rectangles using appropriate formulas.
• Compare rectangles with equal area but different perimeters.

Affective Domain:

• Appreciate the importance of perimeter in real-life situations.
• Develop a systematic approach to solving problems involving perimeter.

Psychomotor Domain:

• Draw rectangles accurately given their dimensions.
• Measure the sides of various shapes to determine their perimeters.

Social Domain:

• Collaborate with peers to discuss and compare findings related to perimeter.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum
• State Unified Scheme of Work
• New General Mathematics for Primary Schools 6

Instructional Materials

The teacher will teach this lesson with the aid of:

• Textbook
• Workbook
• Formula book
• Charts showing different shapes
• Ruler
• Pencil
• Paper

Rationale for the Lesson

This lesson helps pupils understand how to measure the boundary of different shapes. Knowing perimeter is important for practical tasks like fencing a compound, framing a picture, or decorating the edges of a table.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of basic plane shapes like rectangles and squares, and how to measure lengths using a ruler.

Lesson Content/Board Summary

PERIMETER

Meaning of Perimeter

Perimeter is the total distance around the outside edge of a two-dimensional shape. It is found by adding the lengths of all the sides of the shape.

Perimeter of a Rectangle

A rectangle is a four-sided shape with four right angles, where opposite sides are equal in length.

To find the perimeter of a rectangle, use the formula:

Perimeter (P) = Length (L) + Width (W) + Length (L) + Width (W)

Or, more simply:

P = 2(L + W)

Examples:

1. Find the perimeter of a rectangle with a length of 10 cm and a width of 5 cm.

Solution:
Step 1: Write down the formula: P = 2(L + W)
Step 2: Substitute the given values: P = 2(10 cm + 5 cm)
Step 3: Add the values inside the bracket: P = 2(15 cm)
Step 4: Multiply by 2: P = 30 cm
The perimeter of the rectangle is 30 cm.

2. A rectangular garden has a length of 8 meters and a width of 4 meters. Calculate its perimeter.

Solution:
Step 1: Write down the formula: P = 2(L + W)
Step 2: Substitute the given values: P = 2(8 m + 4 m)
Step 3: Add the values inside the bracket: P = 2(12 m)
Step 4: Multiply by 2: P = 24 m
The perimeter of the garden is 24 meters.

How to solve for Length (L) or Width (W) if Perimeter (P) is given:

If P = 2(L + W), then L + W = P/2

• To find Length (L): L = (P/2) – W
• To find Width (W): W = (P/2) – L

Example: The perimeter of a rectangle is 36 cm and its width is 7 cm. Find its length.

Solution:
Step 1: Use the formula: L = (P/2) – W
Step 2: Substitute values: L = (36 cm / 2) – 7 cm
Step 3: Divide P by 2: L = 18 cm – 7 cm
Step 4: Subtract: L = 11 cm
The length of the rectangle is 11 cm.

NOTE: Always ensure units are consistent. If different units are given, convert them to a common unit before calculating.

Drawing Rectangles with Given Dimensions

To draw a rectangle with given dimensions:

• Draw a line segment representing the length.
• From each end of the length, draw perpendicular lines representing the width.
• Connect the ends of the width lines to complete the rectangle.
• Ensure accurate measurements using a ruler.

Comparing Rectangles with Equal Area but Different Perimeters

It is possible for two different rectangles to have the same area but different perimeters.

Consider the following two rectangles:

• Rectangle A: Length = 8 cm, Width = 3 cm
• Rectangle B: Length = 6 cm, Width = 4 cm

Calculations:

• For Rectangle A:
  • Area = L × W = 8 cm × 3 cm = 24 cm²
  • Perimeter = 2(L + W) = 2(8 cm + 3 cm) = 2(11 cm) = 22 cm
• For Rectangle B:
  • Area = L × W = 6 cm × 4 cm = 24 cm²
  • Perimeter = 2(L + W) = 2(6 cm + 4 cm) = 2(10 cm) = 20 cm

Conclusion: Both Rectangle A and Rectangle B have an area of 24 cm², but Rectangle A has a perimeter of 22 cm while Rectangle B has a perimeter of 20 cm. This shows that shapes can have the same area but different perimeters.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Set Induction

Teacher’s Activity: The teacher greets the pupils and asks them if they know what “distance around” something means. The teacher draws a rectangle on the board and asks pupils what they would do if they wanted to put a fence around it or a frame around a picture. This leads to the concept of perimeter.

Pupils’ Activity: Pupils respond to the teacher’s questions and share their ideas about measuring the distance around objects.

Learning Point: Pupils are introduced to the concept of measuring the boundary of a shape.

Step 2: Meaning of Perimeter

Time: 7 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher guides pupils to define perimeter using the examples discussed. The teacher writes the definition on the board and explains that perimeter is found by adding all the side lengths of a shape.

Pupils’ Activity: Pupils state the meaning of perimeter and copy the definition from the board.

Learning Point: Pupils understand and can state the definition of perimeter.

Step 3: Perimeter of a Rectangle

Time: 10 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher introduces the formula for the perimeter of a rectangle (P = 2(L + W)). The teacher works through two examples on the board, showing step-by-step calculations and how to find a missing side if the perimeter is known.

Pupils’ Activity: Pupils observe, ask questions, and solve the examples along with the teacher.

Learning Point: Pupils learn how to apply the formula to calculate the perimeter of a rectangle and find missing sides.

Step 4: Drawing Rectangles with Given Dimensions

Time: 7 minutes

Teaching Skill: Practical Demonstration

Teacher’s Activity: The teacher demonstrates how to draw a rectangle accurately on the board using a ruler, given specific length and width. The teacher ensures pupils understand the importance of precise measurements.

Pupils’ Activity: Pupils practice drawing rectangles in their notebooks using given dimensions (e.g., L=7cm, W=4cm).

Learning Point: Pupils develop the skill of drawing rectangles accurately.

Step 5: Comparing Rectangles with Equal Area but Different Perimeters

Time: 5 minutes

Teaching Skill: Comparison/Analysis

Teacher’s Activity: The teacher presents the example of two rectangles with the same area but different perimeters (e.g., Rectangle A: 8×3, Rectangle B: 6×4). The teacher guides pupils through calculating both area and perimeter for each, highlighting the difference in perimeters despite having the same area.

Pupils’ Activity: Pupils calculate and compare the areas and perimeters of the given rectangles and discuss their observations.

Learning Point: Pupils understand that shapes can have the same area but different perimeters.

Step 6: Class Activity/Practice

Time: 5 minutes

Teaching Skill: Independent Practice

Teacher’s Activity: The teacher provides a few practice questions for pupils to solve individually or in pairs. For example: “Find the perimeter of a rectangle with L=12cm, W=6cm.” and “Draw a rectangle with L=9cm, W=2cm.”

Pupils’ Activity: Pupils work on the practice questions in their notebooks.

Learning Point: Pupils apply their understanding to solve problems independently.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is perimeter?
2. State the formula for finding the perimeter of a rectangle.
3. Calculate the perimeter of a rectangle with length 15 cm and width 8 cm.
4. Can two rectangles have the same area but different perimeters? Give an example.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 1 minute

Teaching Skill: Summarization

Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the definition of perimeter and how to calculate it for rectangles. The teacher assigns homework for pupils to practice finding perimeters of various rectangular objects at home.

Pupils’ Activity: Pupils listen attentively and copy down the homework.

Learning Point: Pupils consolidate their learning and are prepared for further practice.

Home Task: Solve three new exercises on PERIMETER. Show each step and check each answer.

Lesson Keywords

• Perimeter – The total distance around the outside edge of a two-dimensional shape.
• Rectangle – A four-sided plane figure with four right angles and opposite sides equal in length.
• Length – The longer dimension of a rectangle.
• Width – The shorter dimension of a rectangle.
• Area – The amount of surface covered by a two-dimensional shape.

Differentiation

For pupils who grasp concepts quickly, challenge them with problems involving finding the perimeter of composite shapes or working backwards to find dimensions given the perimeter. For pupils who need more support, provide additional guided examples, visual aids, and simplified problems.

Note for teachers using this lesson plan

Encourage pupils to use rulers accurately when drawing and measuring. Emphasize the units of measurement for perimeter (e.g., cm, m). Provide real-life examples of perimeter to make the lesson more relatable. Ensure pupils understand the difference between area and perimeter, especially when comparing rectangles with equal area but different perimeters.