Page 149 - IM_Algebra2_FL Print Sample.pdf

Student Response
1. See image.
2. 1,1,2,3,5
3. 8, 13
4. Sample response: Each side length is the sum of the previous two side lengths.
5. for
6. The integers where or equivalent
Activity Synthesis
Display the sequence 1, 1, 2, 3, 5, 8, 13 and the recursive de nition
for all to see. Either give students a minute to think
about writing a closed-form de nition, or just tell them that the closed form is di cult and complicated to derive. A recursive de nition is still useful when we can’t easily nd a closed form de nition.
For the last question, highlight both the details of the domain and how to express it. It is up to the person writing the function whether they want to start at the 0th term or the 1st term, and this choice a ects the domain. For simplicity’s sake, the problem speci ed to start with the rst term. If students are unfamiliar with the term integer this is a good place to de ne it. Possible questions:
• “What does the domain of a function mean?” (It is the set of possible inputs to the function.)
• “How could we express the domain of this function using words?” (The positive integers.)
• “What does the word integer mean?” (The integers are all the counting numbers and their opposites, including zero. One way to write the integers is . . . ,-3, -2, -1, 0, 1, 2, 3, . . .
• “How could we express the domain of this function using symbols?” ( is an integer and or we could say )
84
Teacher Guide
Algebra