## DevelopingTriangleAreaFormula.docx - Section 2: Explore

# Area of Triangles

Lesson 12 of 12

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

*40 minutes*

#### Launch

*5 min*

**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?

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#### Explore

*30 min*

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.

#### Resources

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#### Landing

*5 min*

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?

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- UNIT 1: Welcome to 7th Grade!
- UNIT 2: Number System
- UNIT 3: Geometric Measurement
- UNIT 4: Integers
- UNIT 5: Simplifying Expressions
- UNIT 6: Proportional Relationships
- UNIT 7: Percent Relationships
- UNIT 8: Equations and Inequalities
- UNIT 9: 2-D Measurements
- UNIT 10: 3-D Measurements
- UNIT 11: Angles
- UNIT 12: Probability

- LESSON 1: Circles Pre Assesment
- LESSON 2: Circles Vocabulary
- LESSON 3: Introduction to Circles
- LESSON 4: Circumference and Area
- LESSON 5: Eight Circles
- LESSON 6: More Eight Circles
- LESSON 7: Exploring Circumference
- LESSON 8: Write It Wednesday-Circles
- LESSON 9: Circles and Parallelograms
- LESSON 10: Circles Review
- LESSON 11: Circles Post Assessment
- LESSON 12: Area of Triangles