Recursion: Smaller Sibling Pyramids

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Lesson synopsis

humanRecursion, Iteration (Looping), and Concurrency. In the first of two sessions (at most an hour each), students are asked to calculate a simple summation by themselves, based on a procedure they are given. Then, through a guided role-playing procedure, students are asked to do the same problem by pushing a sub-problem off onto a ‘little sibling’. In the second session, they use a divide-and-conquer approach to understand a simple formula for summation. During this session they also talk about the big ideas behind these three problem solving methods.

Age Levels

8 - 13 years

Objectives

Introduce students to:
how arithmetic sequences solve real world problems
tail-end recursive algorithms for arithmetic series
a divide and conquer approach that leads to a simple formula
informal ideas about time complexity.

Anticipated learner outcomes

Students will be able to describe how to solve an arithmetic sequence summation problem:
by doing it again and again (non-concurrent iteration)
with a smaller sibling (tail-end recursively)
articulate that both methods take the same number of steps, but recursion is less work for the individual
divide and conquer has a surprising outcome – namely a formula that can be calculated in only a few steps.

Optional Writing Activity

This activity introduced the idea of how to efficiently calculate an arithmetic series, such as 1+2+3+4. This could be used to calculate the simple human pyramid where one person is added as support for each layer. Invent your own problem that produces a different arithmetic pattern such as 1,5,9,13,17. Ask someone in your class to solve it by simple addition, by recursion, and to see if they can come up with a formula based on divide and conquer.

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Ray Tomlinson

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