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Lesson 9: Situations and Sequence Types
• Determine whether a sequence based on a situation is geometric, arithmetic, or neither. • Practice representing situations with recursive and closed-form functions.
Lesson Narrative
The purpose of this lesson is to practice recognizing whether sequences are arithmetic, geometric, or neither, and representing them with recursive and closed-form functions. The problems in this lesson are relatively unsca olded compared to the work up until this point, giving students ample opportunities to persevere in problem solving (MP1) and use appropriate tools strategically (MP5).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Student Learning Goals
• Let’s decide what type of sequence we are looking at and how to represent it. 9.1 How Does It Grow?
Warm Up: 10 minutes
In previous courses, students worked with percent change and representing percent change with an exponential function. They learned about the relationship between a growth rate and growth factor The purpose of this warm-up is to prepare students to recognize 20% growth and use a growth factor of 1.2 when it appears later in this lesson.
Student Task Statement
1. Here is a geometric sequence. What is the common ratio? 16, 24, 36, 54, 81
2. One way to describe its growth is to say it’s growing by 50% each time. Why does that make sense?
3. For each sequence, nd the common ratio and the percentage change from term to term.
a. 64, 80, 100, 125 b. 64, 112, 196, 343 c. 64, 128, 256, 512
d. 125, 100, 80, 64
Unit 1
Lesson 9: Situations and Sequence Types 93