Parts 1-4 Drawing from a set of descriptions by Lee (1996), the following sequence of chal-lenges to students, played out over time, can help them do some generalizing byextension. The extensions, which touch on both Building Rules to RepresentFunctions and Abstracting from Computation, first correspond to "What if thenumber changes?" then to "What if the operation changes?" The early challengesare accessible to middle and high school students; the later ones may be appropri-ate for high school students only. Several of the challenges are addressed later inthis chapter:Challenge 1: Show that the sum of any two consecutive whole numbers is anodd number.Challenge 2: What can you say about the sum of three consecutive numbers?Challenge 3: What can you say about the sum of four consecutive numbers?Challenge 4: What can you say about the sum of n consecutive numbers?

Definition: Consecutive whole numbers are numbers that follow each other in order without any gaps.…

Challenge 1: Show that the sum of any two consecutive whole numbers is an odd number. Challenge 2: What can you say about the sum of three consecutive numbers? Challenge 3: What can you say about the sum of four consecutive numbers? Challenge 4: What can you say about the sum of n consecutive numbers?

Challenge 1: Show that the sum of any two consecutive whole numbers is an odd number. Challenge 2: What can you say about the sum of three consecutive numbers? Challenge 3: What can you say about the sum of four consecutive numbers? Challenge 4: What can you say about the sum of n consecutive numbers?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

See similar textbooks