 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  MENU          Session 2, Part B:
Patterns in Situations

In This Part: Toothpick Triangles | More Toothpick Triangles  Problem B5 How does the table in Problem B4 compare to the table from Problem A1? Is there more than one way to extend the triangle and toothpick table? Explain.
Note 6

Table from Problem B4

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

Table from Problem A1

 Input Output  1 6 2 10 3 14 4 18 5 22 6 26 ? ? ? ? Problem B6 Which of the descriptions below from Problem A5 are valid for the toothpick triangles? Why are the others invalid?

 a. As the input increases by 1, the output increases by 4. b. If you add 2 to 1 and double it, you get 6. If you add 3 to 2 and double it, you get 10. If you add 4 to 3 and double it, you get 14. Or, if you add the input to the next input, double that, you get the output. c. The units digits are in the sequence 6, 0, 4, 8, 2, so the next number would be 26, then 30, 34, 38, and 42, and then 46, 50, 54, 58, 62, etc. d. To get the output, multiply the input by 4 and add 2. e. To get the output, triple the input, then add 2 more than the input. f. After 6 as an input, the output numbers repeat over again: 6, 10, 14, 18, 22, 26, etc. g. After 6, the output numbers remain constant: 26, 26, 26, etc. Problem B7 Explain your rule for calculating the number of triangles if you are given the number of toothpicks. Why does it work? Note 7 Problem B8 Will every number of toothpicks correspond to a number of triangles? What does this tell you about your rule?   Session 2: Index | Notes | Solutions | Video

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