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- Patterns

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Get Started Now- Intro Lesson: a18:11
- Lesson: 1a2:22
- Lesson: 1b2:57
- Lesson: 1c2:59
- Lesson: 1d4:19
- Lesson: 2a2:43
- Lesson: 2b3:17
- Lesson: 2c5:23
- Lesson: 2d4:48
- Lesson: 3a8:59
- Lesson: 3b4:45
- Lesson: 4a4:12
- Lesson: 4b1:31

In this lesson, we will learn:

- How to find the rule for a number sequence and write an expression for it
- How to predict the next term in a number sequence

can also be called__Number patterns____number sequences__- A number sequence is a list of numbers (or terms) in order
- The order of number is decided by a mathematical
__rule__ - The same
**operation**(+, –, ×, ÷) is used between each term. - An
can be written for any number pattern/sequence__expression__ - The expression states what the
**first number**in the list is, and what the**rule**is - “
*start at _[#]_ and _[operation]_by_[#]_ each time*.” - For example,

- The
**rule**is to add 3 and the**expression**is to “start at 1 and add by 3 each time”

- If a
**rule**for a number pattern/sequence is known, you canthe next terms__predict__ - Using the previous example,

- The next two terms in the sequence are 13 and 16

- Always find the
**rule**by using**two**(right next to each other) in the sequence__consecutive__numbers - For example,

- The
**rule**is to add 4, therefore the entire sequence should be completed as: 6,, 14, 18,__10__, 26__22__

- IntroductionIntroduction to Number Patterns:a)How to describe and predict the pattern in a number sequence
- 1.
**Next Number in the Pattern**

Write the next two numbers in the pattern. Then, describe the pattern with an expression.a)1, 4, 7, 10, ___, ___b)3, 6, 12, 24, ___, ___c)30, 25, 20, 15, ___, ___d)128, 64, 32, 16, ___, ___ - 2.
**Fill in the Blanks for the Number Pattern**

Fill in the blanks for the pattern. Then, describe the pattern with an expression.a)60, 50, ___, 30, 20, ___b)___, 11, 17, 23, ___, 35c)1, $\frac{1}{3}$, ___,$\frac{1}{27}$ , ___d)2, 10, ___, 250, 1250, _____ - 3.
**Special Number Patterns**

Write the next 4 numbers in the special pattern below. Look at how much each term is increased by to find the rule.a)0, 1, 1, 2, 3, 5, 8, 13, 21, __, __, __, __b)1, 1, 2, 4, 7, __, __, __, __ - 4.
**Number Patterns - Word Problem**

Natalie is doing swimming training so that she can hold her breath underwater longer. On the first day, she is only able to hold her breath for 30 seconds. On the second day, she can do it for 45 seconds. On the third day, she can do it for 60 seconds.a)If this pattern in her progress continues, how many seconds will she be able to hold her breath for by the 7^{th}day?b)Describe the pattern with a sentence expression