Lesson Note for Primary 6
Lesson Note on Mathematics
Subject: Mathematics
Theme: Area
Topic: Area of a Circle
Sub Topic: Deriving the Formula for area of a circle
Date: dd/mm/yyyy
Class: Basic 6
Duration: 35 Minutes
No of Learners: 30
Learning Objectives:
By the end of the lesson learners should be able to: Say what a circle is
A plane curve everywhere equidistant from a given fixed point, the centre.
Derive the formula for the area of a circle
Rectangle with the sectors of a circle
But, Area of Rectangle = Length x Width
where Length = 1/2 circumference of the circle
= 1/2 x 2πr = πr
Width = radius
Area of the rectangle with the sector of a circle =πr x r
= πrᶺ2
Rationale:
The concept of the area of a circle is useful and applicable in daily real-life activities. The knowledge will assist pupils to understand its application in finding amongst others the base area of wells; pipes; fences; wheels of automobiles and cycles.
Prerequisite skills and knowledge:
- Measurement of lengths of the object including Area of rectangles.
- learners can draw as well as identify parts of a circle particularly the circumference radius, diameter and sectors
- concept of pi (π)
Teaching/ Learning Materials:
Manila cards/Pair of scissors/Glue/starch/Circular Cut-out.
Reference Materials:
Online resources
- Area of a Circle
Lesson Development:
STAGE | TEACHER'S ACTIVITY | LEARNER'S ACTIVITY | LEARNING POINTS |
INTRODUCTION & GROUPING full class session (3mins) | Review learners previous knowledge by asking them to find the area of a rectangle (e.g. length 6cm and width 4cm) | (In groups) solve the problem and present their results | Learner’s entry points. Area of rectangle = length × width |
|
STEP 1 5mins. Development | provide learners with circular cut-out | Students identify parts of the circle. | Recognize circumference, diameter, radius and sectors |
STEP 2 7mins | provide pupils in each group the materials mentioned above | (In groups) cut along the lines of the sectors of the circle to obtain 16 equal sectors | Different strategies of obtaining sectors. |
STEP 3 8mins | guide learners to divide one of the sectors into two equal parts and join this to the widths of both sides of the figure and stick the all cut-outs with the glue on the manila cards as shown | - (In groups) describe the figure they have formed
- state and name the height(width) of the figure as the radius of the circle.
- state and name the length as one-half the circumference of the circle = 1/2 circumference
= 1/2 (2πr) = πr - derive the area of the rectangle formed using the length (πr) and the width (r) as
A = Length x width = πr x r = πrᶺ2
- (In groups) discuss the relationship between the figure formed and the circle
| - Forming a rectangle with the sectors of a circle.
Recognize a semi-circle (e.g. shaded part) as half of the circumference - The figure formed with the sectors of the circle looks like a rectangle Recognize that:
- Height or width = radius (r) of the circle and
- Length as half circumference of circle = πr
Area of circle = πr x r = πrᶺ2
- The figure formed has the same area as that of the circle
|
|
EVALUATION 5mins | The teacher guide learners to solve the following problems. Calculate the area of a circle whose radius is- 20cm
- 1.5m (take π = 22/7)
| Area (A) of a circle = πrᶺ2 - But 1cm = 0.01m
Therefore 20cm = 20 x 0.01 = 0.2m Therefore A = 22/7 x (0.2)ᶺ2 = 0.125mᶺ2 - A = 22/7 x (1.5)ᶺ2
= 7.017mᶺ2 | Asking the learners questions to assess the achievement of the set objectives. |
CONCLUSION 2mins | What is the formula for the area of a circle | A = πrᶺ2 | Improving their level of understanding of the Area of a circle. |
|
ASSIGNMENT | - If the circumference of a circular plate is 600cm, find the maximum area it covers on the surface of a dining table. (Take π = 3.14)
- Deriving the Formula for Area of a Circle
Hint: - Cut out the sectors of the circle along the lines
- Arrange the sectors to form a figure such the coloured parts are up and the uncoloured down
- Divide one of the uncoloured sectors into two equal parts and join it to the widths of both sides of the figure and stick all the cut-outs sectors with the glue on the manila cards.
- Describe the figure formed after arranging the sectors
- What is the:
- Height of the figure?
- Length of the figure?
- Area of the figure formed?
- What is the relationship between the figure formed and the circle?
- If the circumference of a circular plate is 600cm, find the maximum area it covers on the surface of a dining table. (Take π = 3.14)
| Students solve other problems. | Improving their level of understanding of the Area of a circle. |
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