Session 1 - Similarity, Right Triangles, and Trigonometry

Similarity, Right Triangles, and Trigonometry - Grade Band: High School.

Step 1

Get Prepared (5 minutes):

Gather materials and review the lesson.
Before starting this toolkit, students should be able to complete the background activities:
You will need copies of the following handouts. Make copies or turn on computers.

Step 2

Think: Pre-Lesson Knowledge Check! (15 minutes)

Pre-Lesson Knowledge Check Task: Height of a Building

Please Note

If your students benefit from hands-on activities, building triangles out of popsicle sticks (or any other material that represents a line) may help them understand how these triangles are similar or congruent. Use the popsicle sticks to mimic the visuals shown in the activities below.

Pre-lesson Knowledge Check Task:

Height of a Building

Directions for Giving the Task:

This activity will be revisited later in Step 3 of the toolkit.
The idea is to help students understand why they need different math skills to solve this problem.
If a student gets frustrated in doing this or does not know where to start, have them do their best or skip the Knowledge check and go right to the warm-up. Continued practice in the preskills activities may also help students.
Use your knowledge of similar triangles and proportions to find the height of the building. Directions are in the worksheet as well.

Focus: MP4: Model with mathematics

Decorative question mark:

Why are students doing this/what are they getting out of it?

The purpose of this pre-assessment is as a preview of what is to come in this toolkit. Students might be ready to tackle the problem head-on, but others may need ideas of where to start. If a student is stuck, then feel free to skip this and move on to the first part of the lesson.

Directions for Scoring & Understanding Student Responses

While students are doing the Pre-Lesson Knowledge Check, you will want to watch how they tackle this task. 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.

Sample Thinking Prompts:

Common Problems	Question to Pose to Student
Student doesn’t know how to begin.	Do you notice any shapes in here that are similar?
The student recognizes similar triangles but does not know what to do next.	Do you remember how we scaled things before? Do you remember what a common factor is?
Students incorrectly set up the proportions.	Can you draw the triangles away from the picture? Can you label which ones are the same?

Common Problems

Question to Pose to Student

Student doesn’t know how to begin.

Do you notice any shapes in here that are similar?

The student recognizes similar triangles but does not know what to do next.

Do you remember how we scaled things before?

Do you remember what a common factor is?

Students incorrectly set up the proportions.

Can you draw the triangles away from the picture?

Can you label which ones are the same?

The answer: The answer to this problem is 20 feet.