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Lesson 3: Di erent Types of Sequences
• Compare geometric and arithmetic sequences.
• Use tables, graphs, and equations to understand arithmetic sequences.
Lesson Narrative
The purpose of this lesson is to introduce arithmetic sequences, and for students to understand that arithmetic sequences are characterized by common di erences (or said another way, by adding a constant value to get from each term to the next.)
In the rst activity, students examine three sequences. They notice that one is geometric and characterize another as having the same value added from each term to the next term. (The third sequence is neither.) Similarities and di erences between them are articulated, bringing the need for language like “arithmetic” and “geometric.” In the second activity, students inspect a graph representing an arithmetic sequence, describe it, and create another representation.
Student Learning Goals
• Let’s look at other types of sequences.
3.1 Math Talk: Remembering Function Notation
Warm Up: 10 minutes
The purpose of this Math Talk is to informally assess strategies and understandings students have for interpreting function notation, which they should have learned about in a previous course. These understandings help students develop uency and will be helpful in the following lesson when students will need to express a recursive de nition of a sequence using function notation.
Instructional Routines
• Math talk
What: In these warm-ups, one problem is displayed at a time. Students are given a few minutes to quietly think and give a signal when they have an answer and a strategy. The teacher selects students to share di erent strategies for each problem, “Who thought about it a di erent way?” Their explanations are recorded for all to see. Students might be pressed to provide more details about why they decided to approach a problem a certain way. It may not be possible to share every possible strategy for the given limited time; the teacher may only gather two or three distinctive strategies per problem. Problems are purposefully chosen to elicit di erent approaches, often in a way that builds from one problem to the next.
Why: Math talks build uency by encouraging students to think about the numbers, shapes, or algebraic expressions and rely on what they know about structure, patterns, and properties of
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Teacher Guide Algebra