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By: Deia Sanders 2a: Recognize, describe, and state the rule of generalized numerical and geometric patterns using tables, graphs, words, and symbols. (DOK 2)
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“Have you ever heard of the Fibonacci sequence?” 1, 1, 2, 3, 5, 8, 13, 21, 34, 55….. Can you find the pattern?
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Vocabulary Pattern – usually represents a sequence of numbers that could be continued on by either repeating or following a specific rule Rule – specifies what is happening within a pattern; often represented by an equation Dots at the end of a series of numbers indicate that the pattern continues. Example: 2, 4, 8, 16, …
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Patterns Representing Patterns by Graphs It is helpful to write the values that correspond to the points on the table. Look for a pattern between one value and the next. A number may be added, subtracted, multiplied, or divided to yield the value of the next term. In some cases, the only solution is reasoning. Look at graphs on page 132
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In pairs, complete the pattern and state the rule in complete sentences. 1) 1, 22, 333, 4444, ____, ____, ____ 2) 101, 1001, 10001, 100001, ____, ____, ____ 3) 45678, 84567, 78456, 67845, ____, _____, _____ 4) 1, 4, 9, 16, ____, ____, ____
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Solutions 1) 55555, 666666, 7777777; the next term is the next digit written the same number of times as the digit, i.e. four 4’s, five 5’s, etc. 2) 1000001, 10000001, 100000001; the second term has 2 zeros. The 5th term has 5 zeros. 3) 56784, 45678, 84567; the last digit moves to the front of the following term. 4) 25, 36, 49; the first term is 12. The second term is 22.
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Let’s Work Together! Turn to handout #1 Page 142
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More Patterns Representing Patterns in Words and Symbols In some cases, the term is dependent on the preceding term. In some cases, it may be dependent on one or more of the previous terms. Some patterns may be visual. There is no common difference between the terms, so look for another pattern. Pattern: The 3rd term is the sum of the 1st and 2nd terms. The 4th term is the sum of the 2nd and 3rd terms. 1) 2, 3, 5, 8, 13, … 2) 1, 4, 7, 10, … For this pattern each term is three more than the previous term. Pattern: Add 3 to the previous term
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Additional Examples Each term is twice the previous term. The pattern is, multiply by 2. 2, 4, 8, …. From the 1st term to the 2nd, add 3. From the 2nd term to the 3rd, subtract 2. This pattern continues for the next numbers. The pattern is, “Add 3. Subtract 2.” 1, 4, 2, 5, 3, 6 …
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More Patterns… Representing Patterns in Tables Tables are often used to show the relationship between data. The value of the data in the second column will be found in relation to the value in the first column. Let’s look at tables on page 133!
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Additional Example In the following table choose the function rule that works for all pairs. (DOK 2) a) y = x – 1 b) y = x + 1 c) y = 2x + 1 d) y = 2x – 1 X Y 0 1 1 3 5 2
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