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Patterns & Sequences - PowerPoint PPT Presentation

Patterns & Sequences. Lesson 1. Define. Some people say that mathematics is the science of patterns. That's not a bad description. Not only do patterns take many forms over the range of school mathematics, they are also a unifying theme. Continued….

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Patterns & Sequences

Lesson 1

• Some people say that mathematics is the science of patterns.

• That's not a bad description.

• Not only do patterns take many forms over the range of school mathematics, they are also a unifying theme.

• Number patterns—such as 3, 6, 9, 12—arefamiliar to us since they are among the patterns we first learn as young students.

• How can you tell if a number sequence is a pattern?

• Anumber sequence is a pattern if the sequence follows a specific rule.

Is it a pattern? Why or Why Not?

19, 28, 37, 46, 55, …

63, 58, 53, 48, 43, …

-2, -4, -6, -8, -10, …

-7, 45, 89, 15, -36, …

32, 36, 41, 47, 54, …

4, 8, 11, 22, 25, 50, 53, …

Yes, subtract 5

Yes, subtract 2

No

Yes, +4, +5, +6, +7…

Yes, •2, +3, •2, +3, •2, +3, …

Is it a pattern? Why or Why Not?

1.

2.

3.

4.

Yes, subtract 4

Yes, multiply by ½

Yes, multiply by 2

• Iterative Pattern

• Follows a rule

• Can be represented as an input/output model

• For example: 4, 8, 12, 16… is an Iterative pattern because it follows the rule “add 4.”

• Recursive Pattern

• Is defined by the previous term

• For example: 1, 1, 2, 3, 5, 8, 13… is a recursive pattern because to get the next term you have to add the two previous terms together.

Determine if the pattern is Iterative or Recursive. Explain.

• 19, 28, 37, 46, 55, …

• 63, 58, 53, 48, 43, …

• -2, -4, -6, -8, -10, …

• -7, 45, 89, 15, -36, …

• 32, 36, 41, 47, 54, …

• 4, 8, 11, 22, 25, 50, 53, …

Iterative. You subtract 5.

Iterative. You subtract 2.

Not a pattern.

Recursive. You add 4, then add 5 to the previous term then add 6 to the previous term.

Recursive. You multiply the previous term by 2 then the next term you add 3.

Determine if the pattern is Iterative or Recursive. Explain.

1.

2.

3.

4.

Recursive. You double the previous number and subtract 5.