Pattern

Student: How can you tell if you're seeing a pattern or not?

Mentor: Well, do you think you can define a pattern?

Student: Something that is the same over and over again; something that repeats.

Mentor: Good.

Student: So a sequence of the same exact object repeated over and over again would be a pattern?

Mentor: It doesn't have to be the exact same object; it could be a part of the object, or one feature of the object, like color, or shape.

Student: Ok. Patterns with color and shape are pretty easy to recognize. You just have to find the similarities between objects that are repeated and find how often they are repeated. But what about patterns with numbers?

Mentor: Good question. Patterns with numbers often have an operation that is repeated rather than a feature of the object. Can you recognize the pattern here: 2, 6, 10, 14, 18, 22?

Student: Starting with 2, 4 is added to every number.

Mentor: Good job. The operation of addition is repeated in this pattern with every number. See if you can find the pattern here: 2, 3, 5, 9, 17, 33, 65...

Student: I don't know, I can't think of an operation that would make this pattern.

Mentor: I'll give you a hint, there are two steps to this pattern- two different operations are used.

Student: Oh! You multiply by 2 and then subtract 1.

Mentor: Good! When we see a pattern like this using math, it is often called a sequence. The pattern or set of operations that are used is often called the rule. We can write the rule of this sequence like this: 2*n - 1.

Student: What does the "n" mean?

Mentor: The "n" stands for any number in the sequence. So this rule tells you that for any number already in the sequence, you multiply it by 2 and then subtract 1 from it to get the next number in the sequence. Then, you do the same thing to that number.

Student: Oh, I see. So if I wrote this rule: n^2 + 4, that would mean you square a number and then add 4 to it to get the next number in the sequence.

Mentor: Good job! I think you understand how to form sequences and how they relate to patterns!