Page 160 - IM_Algebra2_FL Print Sample.pdf

• Graphing the number of white squares for each image number to see that it is not arithmetic.
• Making a table of total squares, black squares, and white squares for each image number and looking at the di erence between successive terms to determine whether the pattern is arithmetic.
• Using a recursive de nition of recursive de nition of
• Visualizing ways that the black squares grow as black squares is a rectangle where one side is long.
• Visualizing ways that the black squares grow as rectangle is composed of a square with sides
Pattern B:
for compared to a for .
. For example, each group of squares long and the other is squares
. For example, each black and a row that is a 1 by rectangle.
• Using the table to determine whether the sequence is arithmetic or geometric.
• Graphing the data to determine whether the sequence is arithmetic or geometric. • Using a spreadsheet to determine whether the sequence is arithmetic or geometric.
Identify students who use these strategies so they could present their work later. If a strategy is not used, you do not have to introduce it.
Instructional Routines
• Anticipate, monitor, select, sequence, connect
What: Fans of 5 Practices for Orchestrating Productive Mathematical Discussions (Smith and Stein, 2011) will recognize these as the 5 Practices. In this curriculum, much of the work of anticipating, sequencing, and connecting is handled by the materials in the activity narrative, launch, and synthesis sections. But teachers will need to take this ball and run with it by developing the capacity to prepare for and conduct whole-class discussions. The book itself would make excellent fodder for a teacher PLC or study group.
Why: In a problem-based curriculum, many activities can be described as “do math and talk about it,” but the 5 Practices lend more structure to these activities so that they more reliably result in students making connections and learning new mathematics.
Launch
Arrange students in groups of 2–4.
If students have access to a spreadsheet, suggest that it might be a helpful tool in this activity.
Unit 1 Lesson 9: Situations and Sequence Types 95