Area of Triangles

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Objective

SWBAT develop and use a derived formula for finding the area of triangles

Big Idea

What does a triangle have to do with a parallelogram?

Launch

5 minutes
  • POD

As students enter the room, they will have a seat, take out their Problem of the Day (POD) sheet and begin to work on the question on the SMARTboard. The POD allows students to use MP 3 continually based on the discussions we have about the problem each day.

How are triangles related to parallelograms?

I want students to start class thinking about any relationship between triangles and parallelograms. Do they already know that a triangle is half a parallelogram? Does the number of sides or angles get introduced into the discussion? What does that relationship represent to students?

Explore

30 minutes

Since we are working to derive the formula for finding the area of triangles, what the students think about triangles and parallelograms will be important. We will start the Explore section of the lesson by reviewing the different classifications of triangles and parallelograms. Next, students will receive a copy of the “Developing the Area Formula for Triangles” sheet. Students will draw a congruent triangle, rotated 180o and connected to the original triangle so that they form a parallelogram. I want to discuss with students how to find the area of the parallelogram they just created. Once we identify how to find the area of the parallelogram, I want them to determine how to find the area of the original triangle (A = ½ bh). Once we have determined the formula for area of a triangle, students can practice by creating additional triangles on grid paper and working in partners or small groups to prove that the formula works.

Landing

5 minutes

To end class, the exit ticket will ask students to use one of the two ways that we discussed in class to find the area of a triangle that has the following dimensions: base = 3 in and height = 5 in. I am interested to see which of the two strategies students use. Who prefers to draw the parallelogram and who is comfortable using the formula we have derived?