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Recursion: Smaller Sibling Pyramids

Lesson Focus 
Recursion, 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
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.
Lesson Activities 

Recursion, 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.

Alignment to Curriculum Frameworks

Curriculum alignment sheet is included in PDF.

Categories 

Alignment to Curriculum Frameworks
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