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:
  1. Say what a circle is

  2. A plane curve everywhere equidistant from a given fixed point, the centre.

  3. Derive the formula for the area of a circle


  4. 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

  1. 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
  1. (In groups) describe the figure they have formed

  2. state and name the height(width) of the figure as the radius of the circle.
  3. state and name the length as one-half the circumference of the circle = 1/2 circumference
    = 1/2 (2πr)
    = πr
  4. derive the area of the rectangle formed using the length (πr) and the width (r) as
    A = Length x width
    = πr x r
    = πrᶺ2


  5. (In groups) discuss the relationship between the figure formed and the circle
  1. Forming a rectangle with the sectors of a circle.
    Recognize a semi-circle (e.g. shaded part) as half of the circumference
  2. The figure formed with the sectors of the circle looks like a rectangle Recognize that:
  3. Height or width = radius (r) of the circle and
  4. Length as half circumference of circle = πr
    Area of circle = πr x r
    = πrᶺ2


  5. 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
  1. 20cm
  2. 1.5m (take π = 22/7)
Area (A) of a circle = πrᶺ2
  1. But 1cm = 0.01m
    Therefore 20cm = 20 x 0.01
    = 0.2m
    Therefore A = 22/7 x (0.2)ᶺ2
    = 0.125mᶺ2
  2. 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
  1. 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)
  2. 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.
  3. Describe the figure formed after arranging the sectors
  4. 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.