Page 83 - IM_Algebra2_FL Print Sample.pdf

Student Response
Sample responses:
• The next number in the list comes from always multiplying the previous number by the same value.
• If we choose a number in the list and divide it by the previous number, we always get the same value.
Activity Synthesis
Students will describe the “same thing” happening with consecutive terms. Encourage students to use the word term, and to be speci c when they describe what is happening, for example
• “In the rst list, you always multiply a term by 3 to get the next term.”
• “In the last list, if you divide any term by the previous term, you always get ”
Tell students that this “same thing” is called the common ratio. For example, in the second list, the common ratio is 4 because , , , and .
Emphasize that the common ratio is de ned to be the multiplier from one term to the next; said another way, the quotient of a term and the previous term. For example, many students will want to say that the pattern of the third sequence is “divide by 2 each time.” This is true, but the common ratio is , because the common ratio is the number you multiply by to get the next term.
In previous courses, students may have learned that a ratio has two or more parts. In more advanced courses (like this one), ratio is sometimes used as a synonym for quotient.
Note that it is natural to make a shift to using “the term” when we mean “the value of the term.” At this point, it is appropriate and unambiguous to use this slightly abbreviated language. It is unlikely that this will cause confusion, but good to be aware of.
2.2 Paper Slicing
25 minutes
In this activity, students generate two geometric sequences from a mathematical context. The purpose is to create representations of geometric sequences using tables and graphs, and to de ne the term geometric sequence.
Monitor for students sketching reasonably neat and accurate graphs for display during discussion, if possible. (For example if you have a document camera or can snap a photo of their work to show on a projector). If you notice that students are struggling to sketch a graph, pause the class and demonstrate sketching and scaling the axes.
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Teacher Guide Algebra