CCS: 6.OA.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.

Objectives:• To Continue a Number Pattern• To Write a Rule for a Number

Pattern

Lesson 2.1

Patterns and Sequences

Want a feather in your cap?Number patterns are a snap!To solve them's easy; that's a fact...Just learn to count, add, or subtract!

Patterns and Sequences

We often need to spot a pattern

in order to predict what will

happen next.

In math, the correct name for a pattern of numbers is called a SEQUENCE.

The first number in a SEQUENCE is sometimes called the FIRST TERM; the second is the SECOND TERM and so on.

Patterns and SequencesFor any pattern it is important to try to spot what is happening before you can predict the next number.

The first 2 or 3 numbers is rarely enough to show the full pattern - 4 or 5 numbers are best.

Patterns and SequencesFor any pattern it is important to try to spot what is happening before you can predict the next number.

1, 2, …… What’s the next number?

Patterns and sequencesFor any pattern it is important to try to spot what is happening before you can predict the next number.

1, 2, 4,… Who thought that the next

number was 3?

What comes next?

Patterns and sequencesFor any pattern it is important to try to spot what is happening before you can predict the next number.

1, 2, 4, 8, 16, …

What comes next?32

Patterns and sequencesLook at what is happening from 1 TERM to the next. See if that is what is happening for every TERM.

5, 8, 12, 17, 23, …, …

+ 3

Patterns and sequences

Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM.

5, 8, 12, 17, 23, …, …

+ 3 + 3

X

Patterns and sequencesLook at what is happening from 1 TERM to the next. See if that is what is happening for every TERM.

5, 8, 12, 17, 23, …, …

+ 3 + 4

Patterns and sequencesLook at what is happening from 1 TERM to the next. See if that is what is happening for every TERM.

5, 8, 12, 17, 23, …, …

+ 3 + 4

+ 5

Patterns and sequencesLook at what is happening from 1 TERM to the next. See if that is what is happening for every TERM.

5, 8, 12, 17, 23, …, …

+ 3 + 4

+ 5

+ 6

Patterns and sequencesLook at what is happening from 1 TERM to the next. See if that is what is happening for every TERM.

5, 8, 12, 17, 23, 30, …

+ 3 + 4

+ 5

+ 6

+ 7

Patterns and sequencesNow try these patterns:

3, 7, 11, 15, 19, …, …

128, 64, 32, 16, 8, …, …

1000, 100, 10, 1, …, …

5, 15, 45, 135, …, …

Writing Number Patterns From Rules

• To describe a number pattern, give the first term and the RULE.

• REMEMBER: A rule is the explanation of how you got from one term to the next.

• EXAMPLE: 5, 9, 13, 17• RULE: Start with 5 and add 4 repeatedly.• NOTE: All rules are written in this form:

****Start with the first term and state the rule repeatedly

Writing Number Patterns From Rules

• Write the first six terms in each number pattern.

• Start with 90 and subtract 15 repeatedly:• 90• 75• 60• 45• 30• 15• In math, we write this pattern: 90,75,60,45,30,15…

Writing Number Patterns From Rules

• Start with 1 and multiply by 3 repeatedly:• 1,3,9,27,81,243…• Start with 6 and add 10 repeatedly:• 6,16,26,36,46,56…• Start with 80 and subtract 5 repeatedly:• 80,75,70,65,60,55…

Writing a Rule

• Write the next three terms in each pattern and then write a rule for the pattern.

• 53,49,45,41• 37• 33• 29• What’s the RULE?• Start with 53 and subtract 4 repeatedly

Writing Rules

• 1.5, 4.5,13.5, 40.5• To get from one term to the next, we

multiply by 3.• 121.5• 364.5• 1093.5• What’s the RULE?• Start with 1.5 and multiply by 3 repeatedly.

Classwork

• Go to this site to create your own patterns and rules:

• Crack the Code• Try this game for pattern recognition

Number Patterns from BBC. Then take the online quiz.

Homework• pg. 65, 1-42 Even