Page 125 - IM_Algebra2_FL Print Sample.pdf

Activity Synthesis
Ask each group to share one reason why a particular item does not belong. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which one does not belong, attend to students’ explanations and ensure the reasons given are correct.
6.2 Squares of Squares
15 minutes
The purpose of this task is to write a recursive de nition for a sequence that represents a mathematical context, see an example of a closed-form de nition, and understand why in some cases a closed-form de nition is more useful.
Making a spreadsheet available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Keep students in the same groups. Encourage them to check in with their partner frequently as they work through the task.
If students have access to a spreadsheet, suggest that it might be a helpful tool in this activity.
Student Task Statement
Here is a pattern where the number of small squares increases with each new stage.
1.
2. 3. 4. 5.
Describe how the total number of small squares in Stage 4 relates to the total number of small squares in Stage 3.
Write a recursive de nition for , the total number of small squares in Stage .
Create a table, that gives the total number of small squares for stages 0–7.
Is this sequence geometric, arithmetic, or neither?
The number of small squares is also given by the formula . Find . Which version of the de nition of is easier to use?
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Teacher Guide
Algebra