The purpose of this Warm-up is to informally assess strategies and understandings students currently have for interpreting function notation, which they learned about in an earlier course. Students will use function notation when they define sequences with equations in later lessons, so this Warm-up is an opportunity for practice.

Some students may believe that function notation "distributes," that is, that expressions like are equivalent to . If students do this, consider asking:

• “Can you explain how you evaluated the function?”
• “What is the same and different about and ?”

Ask students to share their strategies for each problem. Record and display their responses for all to see.

Math Community
After the Warm-up, display the class Math Community Chart for all to see and explain that the listed “Doing Math” actions come from the sticky notes students wrote in the first exercise. Give students 1 minute to review the chart. Then invite students to identify something on the chart they agree with and hope for the class or something they feel is missing from the chart and would like to add. Record any additions on the chart. Tell students that the chart will continue to grow and that they can suggest other additions that they think of throughout today’s lesson during the Cool-down.

The purpose of this activity is for students to contrast three different types of sequences and to introduce the term "arithmetic sequence."

Monitor for students using precise language (MP6), either orally or in writing, during work time to invite to share during the whole-class discussion.

This is the first time Math Language Routine 2: Collect and Display is suggested in this course. In this routine, the teacher circulates and listens to student talk while jotting down words, phrases, drawings, or writing that students use. The language collected is displayed visually for the whole class to use throughout the lesson and unit. The purpose of this routine is to capture a variety of students’ words and phrases—including, especially, everyday or social language and non-English—in a display that students can refer to, build on, or make connections with during future discussions, and to increase students’ awareness of language used in mathematics conversations.

The purpose of this activity is for students to create another representation of a given sequence and to give them an opportunity to use the vocabulary they have learned for geometric and arithmetic sequences.

Monitor for students who create Mai's graph in order to understand her reasoning and for students who reason about whether the sequence is defined by a rate of change or a growth factor to invite to share during the discussion.