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Instructional Routines
• Notice and wonder
What: This routine can appear as a warm-up or in the launch of a classroom activity. Students are shown some media or a mathematical representation. The prompt to students is “What do you notice? What do you wonder?” Students are given a few minutes to write down things they notice and things they wonder. After students have had a chance to write down their responses, the teacher asks several students to share things they noticed and things they wondered; these are recorded by the teacher for all to see. Usually, the teacher steers the conversation to wondering about something mathematical that the class is about to focus on.
Why: The purpose is to lower the bar for entry into a mathematical task for all students with these two low-stakes questions; by thinking about them and responding, students gain entry into the context and might get their curiosity piqued. Taking steps to become familiar with a context and the mathematics that might be involved is making sense of problems (MP1).
Launch
Display these two sequences for all to see, and ask students what they notice and wonder:
Students might notice and wonder many things, but highlight the fact that • The rst sequence ( ) starts with term 0, and has a total of four terms.
• The second sequence ( ) starts with term 1, and has a total of three terms.
Tell students that sometimes it’s convenient to start with term 0 and sometimes it’s convenient to
start with term 1. It’s important to be clear about how many terms you are dealing with.
If students have access to a spreadsheet, suggest that it might be a helpful tool in this activity.
Student Task Statement
Given the information about each sequence, choose which expression represents the 10th term. Be prepared to explain your reasoning.
1. An arithmetic sequence has rst term 2 and second term 6. a.
b.
2. A geometric sequence has rst term 2 and second term 6. a.
b.
3. An arithmetic sequence has zeroth term 100 and rst term 90.
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Teacher Guide
Algebra