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Recognizing number patterns is also an important problem-solving skill. If you see a pattern when you look systematically at specific examples, you can use that pattern to generalize what you see into a broader solution to a problem.
Here are two activities that show the variety and fun of number patterns. (Don't forget to read the activity background for more ideas on classroom use and connections to standards.)
The youngest children begin simply by counting. They count by 1s, then by 2s, 5s, and 10s. These patterns give students a natural strategy to understand addition and multiplication. When considering a number pattern such as 2, 4, 6..., a young student will ask herself, By what number can I count (add) to get to the next number in the pattern and the next and the next?
As the student gets older, her knowledge of patterns advances from sums to products. When asked for the 50th number in the pattern, she will know to multiply 2 times 50.
High school students can start to understand functions, such as f(x) = 2x + 2, where x is the numerical sequence 0, 1, 2, 3,?. They begin with simple in-out machines and gradually adapt their understanding to the abstractions of algebra.
NCTM Standard 2 (1998) sets the purpose of patterns, functions, and algebra in mathematics education at all grade levels.
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Mathematics is especially useful when it helps you predict, and number patterns are all about prediction. What will the 50th number of this pattern be? How many cupcakes would we need if we gave a party for the town instead of just our class? Working with number patterns leads directly to the concept of functions in mathematics: a formal description of the relationships among different quantities.
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