The Sum of Consecutive Odd Integers

Materials: Handouts

Goals (you need to fill in the blanks):

¨ Follow a pattern.

¨ Collect data from a sequence and make a conjecture for the formula of the nth term of the sequence.

¨ Represent odd and even integers both with formulas and with diagrams.

¨ Prove that the sum of an even and an odd is _____, the sum of an odd and an odd is _____, and the sum of and even and an even is _____ using diagrams and/or formulas.

¨ Make a connection between visual and analytic representations of mathematical concepts.

¨ Prove that the sum of the first n consecutive odd integers is _____.

Step 1:

¨ Complete the following table. What conclusions can you make from your results? How can we write the general sum of first n consecutive odd integers?

n = The number of consecutive odd integers	Adding the first n consecutive odd integers together	The sum of the first n consecutive odd integers
1	1	1
2	1 + 3	4
3	1 + 3 + 5
4	1 + 3 + 5 + 7
5
6
7
8
9

¨ Actively read Investigation 4.2: Patterns in Odd and Even Number on pp. 192-3 of Bassarear.

¨ Actively read "Even and Odd Numbers" from Masingila, etal.

¨ Do problem 8a on p. 203 of Bassarear.

¨ Explain in words the connections between the two diagrams from "Proofs Without Words" and the formula .