LessonnotesGH

JHS1 Mathematics · Term 3, Week 3

Measurement

Lesson notes

Learning Objectives

Indicator: B7.3.2.2.1 - Use the relationships between a triangle and a rectangle (or parallelogram) to deduce the formula for determining the area of a triangle.

By the end of the lesson, learners can:

  1. Describe the relationship between a triangle and the rectangle (or parallelogram) that encloses it, identifying the base and perpendicular height.
  2. Determine the number of unit squares inside a triangle by counting and by comparing it with the enclosing rectangle or parallelogram.
  3. Deduce the formula for the area of a triangle, Area = 1/2 × base × height, from the area of a rectangle or parallelogram.
  4. Apply the formula to calculate the area of triangles drawn on square grids with given bases and heights.
  5. Explain, using their own words, why the area of a triangle is half the area of its enclosing rectangle or parallelogram.

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Curriculum details

Strand
Geometry and Measurement (Strand 3)
Sub-strand
Measurement (3.2)
Content standard
B7.3.2.2 - Derive the formula for determining the area of a triangle and use it to solve problems.
Indicator
B7.3.2.2.1 - Use the relationships between a triangle and a rectangle (or parallelogram) to deduce the formula for determining the area of a triangle.
Suggested placement
Term 3, Week 3 (Week 27 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Curriculum reference
Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 64

Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum) 

E.g.1: Determine the number of unit squares enclosed by the triangles below.
i. What is the perpendicular height of each triangle?
ii. What is the area of each of the triangles?
iii. How does the perpendicular heights of each triangle help you in
Wide black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical...
A wide black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions. The wide black-and-white table is arranged with horizontal divisions, vertical divisions. 
calculating its area?
E.g.2: Spot the RECTANGLE enclosing the triangles to find the unit squares in each triangle. Notice the base and height of the triangle.
Three grid-based triangle diagrams labelled A, B, and C show different bases and heights inside rectangular...
Three grid-based triangle diagrams labelled A, B, and C show different bases and heights inside rectangular outlines. Orange edges and dashed construction lines distinguish the enclosing rectangles from the black triangles. 
Area of a triangle = 1 (Areaof the rectangle = 1 base × perpendicular 2 2
height
Wide black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical...
A wide black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions. Visible labels, values, and notation include: E.g.3: Spot the Parallelogram from which the triangle was formed.; Area of the triangle = }(Area of the parallelogram) =} (base of; parallelogram) × height ==b ×h. 
E.g.3: Spot the Parallelogram from which the triangle was formed. Area of the triangle = 1 (Area of the parallelogram)= 1 (base of 2 2
parallelogram) × height = 1 b × h 2
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