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Lesson 6: Representing Sequences
• Identify arithmetic and geometric sequences represented in di erent ways. • Understand the limitations of recursive form.
Lesson Narrative
The purpose of this lesson is to practice interpreting and writing recursive-form de nitions of sequences. In the rst activity, students write a recursive de nition for a sequence that represents a mathematical context. They see an example of a closed-form de nition of this same sequence and notice that this version of the de nition makes it easier to nd any term. (In the following lesson, they learn how to write closed-form de nitions.) In the second activity, they participate in an Information Gap activity and create di erent representations of sequences.
Required Materials
Pre-printed slips, cut from copies of the blackline master
Required Preparation
Prepare 1 copy of the blackline master for every 2 students, and cut them up ahead of time. Students are likely to write on the slips of paper, so copies should not be reused for multiple class periods.
Student Learning Goals
• Let’s look at di erent ways to represent a sequence.
6.1 Which One Doesn’t Belong: Recursive
De nitions
Warm Up: 10 minutes
This warm-up prompts students to compare four recursive de nitions of sequences. 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. To allow all students to access the activity, each item has one obvious reason it does not belong. Encourage students to move past the obvious reasons and nd reasons based on mathematical properties.
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 are prompted to explain their rationale for deciding that one option doesn’t belong and given opportunities to make their rationale more precise.
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Teacher Guide Algebra