Page 136 - IM_Algebra2_FL Print Sample.pdf

Lesson 7: Closed Form De nitions
• Represent sequences using a closed-form de nition. Lesson Narrative
In this lesson, students write closed form de nitions for arithmetic and geometric sequences. In the rst activity, this work is sca olded because the sequence represents a mathematical context (paper cutting). Also, students compute the value of speci c terms several times before generalizing, so they are expressing regularity in repeated reasoning (MP8). In the second activity, students encounter sequences that start at either the zeroth or rst term. They realize that a closed-form expression to calculate a speci c term needs to account for this, which is a part of attending to precision (MP6) when writing closed-form de nitions of sequences.
Required Materials Copies of blackline master
Scissors
Required Preparation
Use of the blackline master and scissors is optional. Students can either consider the paper cutting in the rst activity as a thought experiment, or they can actually cut paper. If using, prepare 1 pair of scissors and 2 copies of the blackline master for every 2 students.
Student Learning Goals
• Let’s nd terms of sequences directly.
7.1 Which One Doesn’t Belong: Repeated
Operations
Warm Up: 10 minutes
This warm-up prompts students to compare four expressions. It gives students a reason to use language precisely (MP6) and gives you the opportunity to hear how they use terminology and talk about characteristics of the items in comparison to one another.
The purpose of this activity is to remind students that repeated addition can be represented with multiplication, and repeated multiplication can be represented with an exponent.
Instructional Routines
• Which One Doesn’t Belong?
What: Students are presented with four gures, diagrams, graphs, or expressions with the prompt “Which one doesn’t belong?” Typically, each of the four options “doesn’t belong” for a di erent reason, and the similarities and di erences are mathematically signi cant. Students
Unit 1 Lesson 7: Closed Form De nitions 71