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- Patterns

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Get Started Now- Intro Lesson: a2:08
- Intro Lesson: b11:33
- Intro Lesson: c2:58
- Intro Lesson: d2:46
- Lesson: 1a1:06
- Lesson: 1b1:33
- Lesson: 2a1:43
- Lesson: 2b2:07
- Lesson: 3a3:23
- Lesson: 3b5:09
- Lesson: 4a3:28
- Lesson: 4b3:11
- Lesson: 4c5:46
- Lesson: 4d2:56

In this lesson, we will learn:

- T-table are tools for keeping track of patterns and can help you predict the next terms in the pattern
- There are growing patterns and shrinking patterns involving figures and blocks/line segments/shapes or more realistic problems involving time and money

- A T-table is a table with 2 columns (or more) that keeps track of patterns.

- A
**T-table**is a table with 2 columns (or more) that keeps track of patterns. - The second column (right) keeps track of the number of things being counted (ex. blocks, line segments, dollars, etc.)

- The two types of patterns you will see in T-tables are:
**growing patterns**where the numbers in the pattern are*getting bigger*(increasing) in each successive line of the T-table**shrinking patterns**where the numbers in the pattern are*getting smaller*(decreasing) in each successive line of the T-table

Example: a growing pattern with blocks starts with a 4-block figure and adds 2 each time to make the next figure has a T-table filled out like this:

- T-tables allow you to
**predict**and calculate the next**terms**in the pattern - Using the previous block example, you can continue the pattern even if you don’t have pictures of the next figures (4
^{th}and 5^{th}figures):

- The same idea will apply for a shrinking pattern, but the relationship between each row will be subtracting an amount instead of adding.

- IntroductionIntroduction to Showing Patterns in T-tables:a)What is a T-table?b)How do you show a growing pattern in a T-table?c)How do you show a shrinking pattern in a T-table?d)Summary of patterns in T-tables
- 1.
**T-table block patterns: addition**

The T-table shows a growing pattern of blocks. How many blocks are added to make a new figure each time?a)Fill in the circles

b)Fill in the circles

- 2.
**T-table block patterns: extending a growing pattern**

Extend the number pattern in the T-table. How many blocks are in the 5^{th}figure?a)

b)

- 3.
**T-table line segment patterns**

Complete the growing pattern by drawing line segments. Complete the next figures and fill in the rest of the T-table.a)

b)

- 4.
**T-table patterns: word problems**

Complete the T-table for the scenario and answer:a)If Jamie makes $11 every hour that he works at a hot dog stand, how much will he earn for 5 hours of work?

b)Anna is buying trading card packs. She really wants to find a rare card! After buying her first pack, she has $37 left in her wallet. If every card pack is $5, how much money will she have left over after buying the 5th pack?

c)Garrett makes a bracelet design using trapezoids and triangles. At each stage, two triangles and a trapezoid are added. If there are 12 triangles, how many trapezoids were used?

d)Kiera makes an increasing pattern with blocks. The figures in sequence use: 4 blocks, 7 blocks, 10 blocks, and then 13 blocks. After making the fourth figure, she has 15 blocks left. Does Kiera have enough blocks to make the 5^{th}figure?