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:

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

Figure from the jhs1 mathematics curriculum, printed page 64

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.

Area of a triangle = 1 (Areaof the rectangle = 1 base × perpendicular 2 2
height

Figure from the jhs1 mathematics curriculum, printed page 65

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