Chapter 2 Wrap Up

Problems based on patterns provide excellent experiences for students of all ages to describe patterns, make generalizations, and then make mathematical arguments. Problems like these can stem from a hands-on activity or process that the students can see and lead to an abstract generalization.  The repeating and growing patterns in this chapter provided a foundation for the more abstract patterns we see in sequences. The use of the variable n highlights the importance of algebra in clearly and concisely describing patterns. The next chapter combines algebra and patterns into the concept of a function which relates two quantities. Explicit formulas for sequences are a specific type of function because they relate the position (n) of each term to the term itself. More details to come in chapter 3!

Hint for Example 2.2.6 (b)