Thinking Inductively about Adding Odd Positive Integers

Prepared by Shari Davis and Katherine Smith as part of a series of supplemental critical thinking explorations to promote discovery and deeper comprehension.
This project was supported by a 2017 Faculty Innovator Grant through Old Dominion University’s Center for Learning and Teaching.

Part 1

Getting Ready

Students should have familiarity with adding consecutive positive integers. One way to prepare students is to have them complete CReaTE 1.

Video

Students should watch the following video: Critical Thinking Exploration 2 Part 1 Video

Follow-up

After watching the video, students should be given time to think about how the last number in the sum of odd, positive integers is related to the number being squared. This could take place in class, after class or using an online discussion board.

A sample discussion board prompt would be: How is the last number in the sum related to the number we are squaring in the video? Does your method work for every line shown? Does your method still work if you add another line to the example?

Part 2

Getting Ready

Students should have viewed Part 1 of this exploration and had time to complete the follow-up activity.

Video

During this activity, students will be led to discover the formula for adding the first N positive integers.

Students should watch the following video: Critical Thinking Exploration 2 Part 2 Video

Follow-up

This video concludes CReaTE 2. After watching the video, students can discuss how to find an expression for summing the multiples of 3 and other problems they might be able to solve now. This could take place in class, after class or using an online discussion board.

A sample discussion board prompt would be: Can you come up with an expression for summing the multiples of 3? How about multiples of 4 or 5?