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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.

slug 
recursion-smaller-sibling-pyramids

Alignment to Curriculum Frameworks

Curriculum alignment sheet is included in PDF.

Categories 

Alignment to Curriculum Frameworks

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