## 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.

## Recommended Reading

“The Cat in the Hat Comes Back”, Dr. Seuss, Random House Children’s Books, 1958. Although clearly below anticipated grade level, this is an outstanding book for young students to begin thinking about recursion and its ramifications.

Your school math textbook series will typically include examples of patterns and functions. Please choose grade-appropriate materials from your math text or from lower grade level texts.

## 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.