Workshop Wednesday: Patterns, Part 2 — Number Patterns

Are you ready for some more patterns? How about making them a little trickier? Our previous article on Patterns focused on learning to recognize patterns of colors or shapes and reproduce them accurately. This article steps that up a few notches with patterns of numbers.

We all learn a very simple number pattern when we first learn to count to 10: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 — a series that increases by one with each step. Skip-counting is increasing each step by an amount larger than one, whether counting by 2’s, 3’s, 5’s, 10’s, or 87’s.

We could even select our starting point and then add by a set increment for another variation of skip-counting:

What if we varied the increments with a consistent pattern? Suppose we started at 0 and added 1, then added 2, then 3, then 4, and so on. Our number pattern would look like this: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, and on and on. If our increment added only by even numbers, the pattern would look like this: 2, 6, 12, 20, 30, 42, 56, 72, 90, 110.

My kids loved to watch an old PBS television show called Square One TV that had a segment called Mathnet, where math “detectives” solved mysteries dealing with numbers. One episode of Mathnet (The Case of the Unnatural) involved a couple of friends who regularly challenged each other with a game they called “Guess My Rule,” where a player had to figure out what rule had been used to create a series of numbers and respond with the next four numbers in the series. The strings of numbers they gave were more complicated than simple skip-counting. For example, the series of 1, 3, 7, 15 is achieved by doubling a number and adding 1: starting at zero, double it (still zero), then add 1, gives 1 as the first number in the series; double it to 2 and add 1, equals 3; and so on. This rule is “double plus 1,” and the next number after 15 would be 31. To play it yourselves, have one player create a series of at least four numbers, and the second player has to determine the “rule” and give the next four number in the series. What number rules can you create to make interesting number patterns? Remember that the rule must be consistent throughout your series.

Another fascinating number pattern is called the Fibonacci series, in which the next number is created by adding the previous two numbers together, for as long as you’d like to keep adding.

Fibonacci numbers are found throughout nature in very intriguing places. You may already know that if you slice a banana and then break that slice apart, the banana will naturally separate into 3 segments. But notice the banana skin: there are 5 segments or sides to an unpeeled banana — 3 and 5 are adjacent Fibonacci numbers. Some very interesting Fibonacci numbers have been observed in nature — petals on some flowers, leaves and branches on some plants, scales on pineapples, bracts on pine cones, and seeds in sunflowers all occur in arrangements that use Fibonacci numbers. Just like the banana segments and the sides of an unpeeled banana, the numbers often show up as adjacent Fibonacci numbers. The Creator of the universe is not just an artist, He’s a mathematician, too!

Check out these websites for more fascinating info on number patterns:

Square One TV/Mathnet, The Case of the Unnatural

Fibonacci in Nature

Fibonacci Numbers, the Golden Section and Plants  — detailed site including do-it-yourself activity ideas

Who Was Fibonacci?  Leonardo of Pisa

See also:

Patterns