Lesson 6

Using The Area of a Parallelogram to calculate the Area of a Triangle

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Content

Expectations: E 2.5

Key Concepts

When students understand the properties of a parallelogram and how to calculate the area, they can apply this to calculate the area of a triangle

Every triangle, no matter what type of triangle it is, can be shown to be half of a parallelogram with the same base and height.

Learning Goal

We want students to understand...

When you know the properties of parallelograms you can figure out the area of a triangle

Success Critera

I can calculate the area of a parallelogram.
I can use what I know about the properties of parallelograms, to know how to calculate the area of a triangle.

Pedagogy

Minds On

Geoboard App or Geoboards (F2F)

Have students create a parallelogram and a triangle so that the parallelogram area is half the triangle area.

Teacher Note:

By realizing that the area of a triangle is half of the area of a parallelogram with the same base and height, some students will realize that they can simply ensure the triangle has the same base as the parallelogram and four times the height or the same height and four times the base or double the base and double the height.

Source: Small, M. (2017) Good questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom, 3rd ed. Teachers College press.(P. 203).

Action!

Have students construct triangles using the geoboard app with the same base but different heights. Have them calculate the area of three triangles and compare the measurements.

Teacher Note: The idea that two triangles with the same base and height must have the same area, even if they look different, is very difficult for some students to understand. This can be modelled on a geoboard, where base and heights can be determined by counting horizontal and vertical units. For example, all three triangles below have the same base and the same height so they must have the same area.

Source: Small, M. (2017) Good questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom, 3rd ed. Teachers College press.(P. 203)

consolidation ideas

Discuss the triangle formulas they have come up with. Some will count the squares that the triangles cover (that is okay). But we want them to hopefully land on a formula based on the minds on activity and the cutting of the parallelogram in half.

The formula for the area of a triangle can be written many different ways:

Area= base x height /2

Area = ½ x base x height

Area= base x height

Source: Small, M. (2013) Making Math Meaningful to Canadian Students, K-8. Nelson Education (pp. 444-445)