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.

  2. Derive the formula for the area of a circle

    Area of a Circle

    3. 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
  • Properties of a Circle

Students identify parts of the circle.

 Recognize circumference, diameter, radius and sectors
STEP 2
7mins		 provide pupils in each group the materials mentioned above
  • Section Area of a Circle

(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. Sector area of a Circle

  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.




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