Lesson Plan and Lesson Note

Lesson Note on Mensuration

Subject: Mathematics

Theme: Mensuration

Topic: Areas of Plane Shapes

Sub Topic: Area of Triangles

Date: xx/xx/xxxx

Class: J.S.S.3

Duration: 35 Minutes

No of Learners: 30

Learning Objectives:

By the end of the lesson learners should be able to:

  1. Understand the concept of area.

    2. The area of an object can be taken to be an enclosed region bounded by either straight lines and/or curve or arcs. The area of an object is the space occupied by that object.
    Mathematically, the concept of area is usually conceived as length multiplied by breadth.

    • Concept of Area

  2. Understand the given sides/angle of a Triangle, and derived the concept of the area of a Triangle.

    • Triangle

    • Derived the Formula of the Area of a Triangle

  3. State the formulae of the area of a triangle under a specific condition(s).

    • Area of a triangle when the height is given



    • Area of a triangle when the sides and included angle are given



    • Area of a triangle when only the three sides are given

  4. Solve problems in the area of a triangle.
    1. Calculate the area of a triangle with a base of 8cm and a height of 6cm.

      SOLUTION
      Area of Triangle = lenght x bright
      = 1/2 x 8 x 6
      = 24 cm sq

  5. Find the area of a triangle whose dimensions are 3cm, 4cm, and 5cm.
    SOLUTION
    • Exercise on area of a Triangle 1

  6. Calculate the area of the diagrams below.

    • Exercise on area of a Triangle 2


    • Exercise on area of a Triangle 2



    • Exercise on area of a Triangle 2

Rationale:

There are many authentic and real-life reasons why we would need to calculate the area of various shapes. For instance, suppose you are looking to sod your lawn; you would need to know the area of your lawn to purchase enough sod. Or, you may wish to lay carpet in your living room, halls, and bedrooms. Again, you need to calculate the area to determine how much carpeting to purchase for the various sizes of your rooms. Knowing the formulas to calculate areas will help you determine the areas of the rooms.

Prerequisite/ Previous knowledge:

Measurements, scale drawing, ratios, conversions from one unit to another, sets.

Teaching/ Learning Materials:

Mathematical set, real objects, worksheets, pencils, rulers, 2D dimensional shapes.

Reference Materials:

New General Mathematics for Junior Secondary Schools Books 3 By Pearson, Advance level Mathematics, Ordinary Level Mathematics.





Lesson Development:
STAGE
TEACHER'S ACTIVITY
LEARNER'S ACTIVITY
LEARNING POINTS
INTRODUCTION
full class session (5mins) 		The teacher provides learners with several different objects, figures/shapes and asks learners to:
  1. Observe the objects and find the area of each object, figures/shapes such as; A rectangle, Square, etc.
  2. What do you understand by an area of an object?
 Learners respond to the teacher's questions:
  1. The area of a rectangle is length times the breadth.
    • The area of a square is length times the breadth.
  2. The area of an object is simply length multiplied by breadth.
 Learner’s entry points.
STEP 1
20mins.
Development and Grouping		 How would you describe the area of the rectangular A4 papers?

The teacher explains to learners that the concept of area is usually conceived as length multiplied by the breadth and that the area of an object can be taken to be an enclosed region bounded by either straight lines and/or curves or arcs.
In the case of three-dimensional solids and objects, the total surface area and/or cross-sectional area of the objects is considered, e.g prisms, pyramids, cuboids, cylinders, cones, etc, because the surface of each of the objects is made up of plane shapes like rectangles, squares, or triangles. hence finding the area of a prism, for example, means finding the areas of the triangles and rectangles which were combined to form the prism.
  • Folded A4 Paper
Students respond to the teacher's question.
  1. The area of the A4 papers is the space occupied by the A4 papers, that is; the space bounded by the boundaries of the A4 papers.
 Developing the ideal of the concept area.
STEP 2
10mins.
Area of a triangle.		 The teacher asks learners to study the triangles in the learner's activity and understand how the sides and angles are named.
  • Triangle

Learners observed that each angle is named with upper case letters while the side facing each angle is named with lower case letters of the angles respectively, learners also observed how the height and base of a rectangle are determined.

 Developing and improving the idea of a triangle.
The teacher explains the area of a triangle to learners.

  • Derived the Formula of the Area of a Triangle


The teacher guides the learners to derive the formula of a triangles
  1. when the height of the triangle is given.
  2. when the sides and an included angle are given.
  3. When the three sides are given.
  • Area of a triangle when the height is given


  • Area of a triangle when the sides and included angle are given

  • Area of a triangle when only the three sides are given

 Identify similar objects by comparing corresponding sides and angles.
EVALUATION
5mins		 The teacher asks the students questions.
  1. What do you understand by the concept of the area?
  2. What is the area of a triangle when the length of the triangle is given?
  3. What is the area of a triangle when the sides and an included angle of the triangle are given?
  4. What is the area of a triangle when the three sides of the triangle are given?
  5. Calculate the area of a triangle XYZ such that
    XY = 4cm, YZ = 7cm and angle Y = 30 degree
  6. Calculate the height of a triangle having a base of 24cm and an area of 120cm sq.
  7. Find the area of an equilateral triangle inscribed in a circle of radius 5cm
  8. Calculate the area of a regular pentagon inscribed in a circle of radius 4cm
  9. Find the area of a regular hexagon of side 15cm
  10. Three points A, B and X define a triangular piece of land, A is 8m 035 degrees of X and B is 10m 335 degrees of X. Calculate the area of the triangular piece of land.

Learners respond to teacher's questions

 Ask the learners questions to assess the achievement of the set objectives.
ASSIGNMENT
 Teacher gives learners take a home.
  • Questions on area of a triangle

 Improving their level of understanding of the Area of a Triangle.
CONCLUSION
5mins 		How would you find the area of a triangle, when;
  1. the height is given,
  2. the sides and an included angle are given,
  3. the three sides are given.
 The area of the triangle is;
  • Area of a triangle when the height is given


  • Area of a triangle when the sides and included angle are given

  • Area of a triangle when only the three sides are given

 Improving their level of understanding of the Area of a triangle.




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