# 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 - 13Objectives

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

### Alignment to Curriculum Frameworks

Curriculum alignment sheet is included in PDF.

Categories

Alignment to Curriculum Frameworks