1.2_Finding_a_Pattern_Revised_08_23_10 - 34 38 and 42 and...

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Finding and Describing Patterns 1. Describe several different patterns that you see in this table. 2. If you wanted to extend this table, which of your descriptions would be most effective? 3. What is the 100 th entry in the table? Explain. 4. Would 102 ever be in the output column of this table? Explain. Would 1004 ever be in the output column? Explain. 5. Below are descriptions of the table in problem 1. Do all of these descriptions produce the same list of outputs? Are all of these descriptions valid for the table? 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,
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Unformatted text preview: 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. 6. Describe the pattern below in as many ways as possible. 7. Imagine you keep adding triangles. Make a table that shows the number of triangles and the number of toothpicks used. 8. If someone tells you the number of triangles, explain how to tell them the number of toothpicks they would need. How does this problem relate to the pattern in problem 1? How do the descriptions in problem 5 relate? 9. Extend the sequence 1, 2, 3, … in as many different ways as you can and explain. Input Output 1 6 2 10 3 14 4 18 5 22 6 26...
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