Session 3 - Similarity, Right Triangles, and Trigonometry

Collaborative Activity #1: (15 - 20 minutes)

Activity:  Height of a Building

Focus: MP3: Construct viable arguments and critique the reasoning of others and MP4: Model with mathematics

Note: This activity is from our Pre-Lesson Knowledge Check in Step 2. The activity is used in this step so that the concepts can now be formally taught and/or reviewed. Some students may have little or some developing knowledge of this concept, so the review will help solidify the content.

Directions:

1. To solve this problem you need to set up the ratio of the sides according to their similarity and solve for the unknown. Since the building height and its shadow are similar to the triangle of the pole and its shadow, we set the proportion of the building height: shadow and pole height: shadow
2. The ratio will be set up as  equivalent fractions: h12=53
3. Students will solve for h. If they use equivalent fractions they will see that h=20.
4. Bailey would like to know the height of a building.
5. He gets Balin to hold up a 5-foot pole near the building and measure the length of its shadow. 
6. The shadow of the pole is 3 feet long, and the shadow of the building is 12 feet long.
7. Use your knowledge of similar triangles and proportions to find the height of the building.

Progress Monitoring

Directions:

1. While students are working, you will want to be watching how they approach this task. 
2. When they feel ready to share, look at their answers/responses. Use the suggestions below to help decide if they “got it” or are still struggling with this skill.  
3. Students should create equivalent triangles and use equivalent fractions or cross multiplication to arrive at the answer. 
4. The answer: The answer to this problem is 20 feet.