Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 2, Part A:
What Do You See? (40 minutes)

In This Part: Finding a Pattern | Descriptions of a Pattern

Patterns are everywhere around us. We use patterns to organize what we see and hear and to make sense of data whether we are driving in a car, listening to music, or solving mathematical problems.
Note 2

Finding, describing, explaining, and using patterns to make predictions are among the most important skills in mathematics. These skills allow users of mathematics to impose order, meaning, and understanding on situations that at first seem like collections of random facts.

Finding patterns is a subjective activity. Different people notice different things, so what one person sees is often different from what another perceives. That's why it's so important to describe patterns in language that everyone understands -- so others can see what you see. Algebra is a tool for describing patterns, and there are many others.

It's important to keep in mind, however, that algebra is much more than a language. As you discovered in Session 1, algebra is also a way to reason about things. In fact, "making sense" is what doing mathematics is all about.

Problem A1

Describe several different patterns that you see in this table:
Note 3

 Input Output 1 6 2 10 3 14 4 18 5 22 6 26

 A description can be an equation, a sentence, or a rule for continuing the pattern.    Close Tip A description can be an equation, a sentence, or a rule for continuing the pattern.

 Video Segment In this segment, participants describe and compare different patterns they found in the table for Problem A1. Watch the segment after you have completed Problem A1 and compare the patterns you identified with those of the onscreen participants. If you get stuck finding patterns in the table, you can watch the video segment to help you. If you wanted to extend the table of Problem A1, which of these descriptions would be most effective? Would they all produce the same table? You can find this segment on the session video, approximately 4 minutes and 46 seconds after the Annenberg Media logo.

 Problem A2 What is the 100th entry in the table? How do you know?

 Try to answer this question by prediction rather than by making a long table of values.   Close Tip Try to answer this question by prediction rather than by making a long table of values.

 Problem A3 Would 102 ever be in the "output" column of this table? What about 1004? Why or why not?

 Try to answer this question by prediction rather than by making a long table of values.   Close Tip Try to answer this question by prediction rather than by making a long table of values.

 Session 2: Index | Notes | Solutions | Video