Videos to help Grade 6 students construct the altitude for three different cases and de-construct triangles to justify that the area of a triangle is exactly one half the area of a parallelogram.

New York State Common Core Math Module 5, Grade 6, Lesson 4

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Common Core For Grade 6

Lesson 4 Student Outcomes

• Students construct the altitude for three different cases: an altitude that is a side of a right angle, an altitude that lies over the base, and an altitude that is outside the triangle.

• Students deconstruct triangles to justify that the area of a triangle is exactly one half the area of a parallelogram.

Opening Exercise

Draw and label the height of each triangle below.Exploratory Challenge

1. Use rectangle x and the triangle with the altitude inside (triangle x) to show the area formula for the triangle is A = 1/2 x base x height.

a. Step One: Find the area of rectangle x.

b. Step Two: What is half the area of rectangle x?

c. Step Three: Prove, by decomposing triangle x, that it is the same as half of rectangle x. Please glue your decomposed triangle onto a separate sheet of paper. Glue it next to rectangle x.

2. Use rectangle y and the triangle with a side that is the altitude (triangle y) to show the area formula for the triangle is A = 1/2 x base x height.

a. Step One: Find the area of rectangle y.

b. Step Two: What is half the area of rectangle y?

c. Step Three: Prove, by decomposing triangle y, that it is the same as half of rectangle y. Please glue your decomposed triangle onto a separate sheet of paper. Glue it next to rectangle y.

3. Use rectangle z and the triangle with a side that is the altitude (triangle z) to show the area formula for the triangle is A = 1/2 x base x height.

a. Step One: Find the area of rectangle z.

b. Step Two: What is half the area of rectangle z?

c. Step Three: Prove, by decomposing triangle z, that it is the same as half of rectangle z. Please glue your decomposed triangle onto a separate sheet of paper. Glue it next to rectangle z.

4. When finding the area of a triangle, does it matter where the altitude is located?

5. How can you determine which part of the triangle is the base and the height?

6 - 7. Calculate the area of each triangle. Figures are not drawn to scale.

8. Draw three triangles (acute, right, and obtuse) that have the same area. Explain how you know they have the same area.

Lessons 2 - 4

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