Page 172 - IM_Algebra2_FL Print Sample.pdf

This context naturally lends itself to nding the sum of the terms of a sequence.
Launch
Arrange students in groups of 4. It may be helpful to assign one student to be “Tyler” to carry out the actions described in the task.
Student Task Statement
1. Tyler has a piece of paper and is sharing it with Elena, Jada, and Noah. He folds and cuts the paper to create four equal pieces, then hands one piece each to the others. What fraction of the original piece of paper does each person have?
2. Tyler then takes his remaining paper and does it again. He folds and cuts it to create four equal pieces, then hands one piece each to the others. What fraction of the original piece of paper does each person have now?
3. Tyler then takes his remaining paper and does it again. What fraction of the original piece of paper does each person have now? What happens after more steps of the same process?
Student Response
1. Each of them has
2. Tyler now has
of the original paper.
of the original paper. The others each have . of the original paper. The others each have
3. Tyler now has
Tyler will just about run out of paper, and the others will each have about paper.
. Sample response: of the original
Activity Synthesis
Ask students where they see a sequence in this activity. Challenge them to write the amount of paper that one person holds after 3 cuts as the sum of the terms of a sequence. Clarify that a sequence is still a list of numbers, so the sequence in question is whereas the total
amount of paper held by one person could be represented by summing the terms:
Show using technology that this sum is close to , and that if you keep summing additional terms you get closer and closer to . This matches the intuition that each person would end up holding very close to of the original piece of paper after several rounds of cutting and distributing paper.
10.3 A Threefold Design
15 minutes
This activity is an opportunity to contrast a situation where it doesn’t make sense to sum a series (the number of sides) with a situation where it does (the total number of triangles). This task is relatively unsca olded compared to previous lessons, giving students opportunities to make sense
Unit 1 Lesson 10: Adding Up 107