Page 162 - IM_Algebra2_FL Print Sample.pdf

cannot be made from repeatedly multiplying by the same number, nor by repeatedly adding the same number.
Pattern B:
1. Recursive: for Closed:
2. Recursive: for Closed:
3. Population 1 is arithmetic and Population 2 is geometric.
4. Sample response: Yes, Population 2 surpassed Population 1 between 2011 and 2012 (years 21 and 22). This happens because exponential growth eventually exceeds linear growth.
Activity Synthesis
Invite selected students to share their responses for Pattern A in the sequence shown in the Activity Narrative. The sequence reveals di erent representations (graph, table, recursive de nition, closed form de nition) and gives students an opportunity to make connections between the representations.
For Pattern B, invite selected students to share their responses for Population 1 in the sequence shown in the Activity Narrative, along with the recursive and closed form de nitions. Then invite selected students to share their responses for Population 2 in the sequence shown in the Activity Narrative, along with the recursive and closed form de nitions. Ask students how each representation shows di erent features of the sequence, for example, the common ratio or common di erence.
Lesson Synthesis
Highlight di erent representations of Patterns A and B and connections between them. Ask students "Is one representation easier to use than another?" Students might note that depends on how the information is given and what question is being asked. For example, graphing the closed form de nition might be easier for determining whether and when Population 2 ever overtakes Population 1. But the table might be easier for determining whether the sequences are arithmetic, geometric, or neither. Using a spreadsheet might be most e cient for determining whether and when Population 2 ever overtakes Population 1 and whether the sequences are arithmetic, geometric, or neither.
9.3 Counting Circles
Cool Down: 0 minutes
This task asks for the number of circles in stage , but doesn’t specify which form to use.
Unit 1 Lesson 9: Situations and Sequence Types
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