Reflection: Diverse Entry Points Decreasing Geometric Sequences - Section 3: Discussion


I find Questions 6 though 8 to be very rich tasks for students. I don't want to rush their understanding here about exponential decay and they'll have the opportunity to revisit this idea in the Functions Unit. For that reason, I might allow students to continue to multiply by 60% and subtract for some time before showing them they can just multiply repeatedly by 40%.  Once they have generated a table, the long way, that shows the amount of candy remaining based on the number of days passed, I might ask them to think of another way they could find the common ratio by.  Based on their previous work, they might remember they can look at the ratios in the out column and find a common ratio that way.  If they do find it, I might ask them if there is any significance to this 40% number.  Can they think of how it might relate to the problem?  In my opinion, this is not the time to rush student thinking. I might leave these questions open for a while to help them develop their own understanding about percents and exponential decay.

  Finding another way to .4
  Diverse Entry Points: Finding another way to .4
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Decreasing Geometric Sequences

Unit 6: Arithmetic & Geometric Sequences
Lesson 6 of 10

Objective: SWBAT compare and contrast an arithmetic and geometric sequence. SWBAT represent a geometric sequence with a constant ratio between 0 and 1 using multiple representations.

Big Idea: What happens when you give away 60% of your candy stash? Students explore what happens when a geometric sequence has a constant ratio between 0 and 1.

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Math, Algebra, exponential growth, arithmetic sequences, Algebra 1, geometric sequence, constant ratio, exponential decay, sequences
  60 minutes
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