Session 2, Part B:
Patterns in Situations (45 mintues)

In This Part: Toothpick Triangles | More Toothpick Triangles

 Problem A5 describes several different ways to extend the pattern given in Problem A1. When a sequence of numbers is not tied to a context, there is no way to determine which extension of a pattern is "correct." Note 5 Describing patterns is most useful when the regularity is embedded in some well-understood situation. For example, examine the toothpick pattern given here: Problem B1 Describe the pattern in as many ways as you can.

Problem B2

Imagine you keep adding triangles. Complete the following table:

 Triangles Toothpicks 1 2 3 4 10

 Triangles Toothpicks 1 6 2 10 3 14 4 18 10 42 hide answers

 Problem B3 If someone tells you the number of triangles, explain how to tell them the number of toothpicks they would need. How do you know your description will always give the right number of toothpicks?

Problem B4

Use your explanation to complete this table:

 Triangles Toothpicks 1 2 3 4 10 100 26 46 102

 Triangles Toothpicks 1 6 2 10 3 14 4 18 10 42 100 402 6 26 11 46 25 102 hide answers

 Video Segment In this segment, participants describe and explain different patterns they found in the toothpick triangles problem, and Professor Cossey discusses the importance of understanding where a pattern comes from. Watch the segment after you have completed the toothpick triangles problems, Problems B1-B4, and consider the different patterns that the onscreen participants identified. Do Sue-Anne and Frederick's rules extend the table in the same way? Is there only one correct way to extend the table in Problem B2? You can find this segment on the session video, approximately 14 minutes and 10 seconds after the Annenberg Media logo.

 Session 2: Index | Notes | Solutions | Video