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# Introduction to solving patterns in T-tables and equations

- Intro Lesson: a10:22
- Intro Lesson: b5:07
- Intro Lesson: c7:21
- Intro Lesson: d6:17
- Lesson: 1a3:19
- Lesson: 1b4:03
- Lesson: 1c4:18
- Lesson: 1d4:10
- Lesson: 2a6:16
- Lesson: 2b7:01
- Lesson: 2c6:24
- Lesson: 2d7:34
- Lesson: 3a1:56
- Lesson: 3b3:59
- Lesson: 3c2:02
- Lesson: 3d4:00
- Lesson: 4a2:18
- Lesson: 4b6:36
- Lesson: 4c4:20
- Lesson: 4d5:03

### Introduction to solving patterns in T-tables and equations

#### Lessons

In this lesson, we will learn:

- How to determine and write one-step and two-step relationships in T-tables as equations with variables
- How to solve equations: isolating variables in two-step relationships (opposite operation to both sides)

__Notes:__- Recall that
**T-tables**keep track of**patterns**and allow calculation of subsequent terms

- What is a fast way to find the 100
^{th}term? Adding by 2 each time is not efficient.

- T-table
**columns**have a**relationship**between them. By writing this relationship as an**equation**, you can put in any number and find information about that term quickly. - Ask: how do you go from the left column to the right column?
- Find
through__one-step relationships__*trial and error*(if numbers are getting bigger it is + or ×; if numbers are getting smaller it is - or ÷) - Assign
**variables**to each column and use these variables in your equation

- For more complicated patterns (
) the equation will have two operations: the first step will be [× or ÷] and then the second step will be [+ or -]__two-step relationships__ - Similar to one-step relationships, they can be found through
*trial and error* - Isolating variables in two-step equations by “doing the opposite to both sides” in the
__backwards__**order of operations**(solve by doing + or - first and then × or ÷ after)

- IntroductionIntroduction to Solving Patterns in T-tables and Equations:a)Finding one-step relationships between columns in a T-tableb)Writing equations for T-table relationships (one-step)c)Writing equations for T-table relationships (two-step)d)How to isolate variables in two-step equations (solving algebra equations)
- 1.
**T-tables and one-step equations**

Write the equation for the relationship between the two variables. Follow the pattern to complete the T-table.a)variables $a$ and $b$*a**b*1

14

2

15

3

16

4

20

b)variables $f$ and $g$*f**g*50

28

49

27

48

26

47

25

c)variables $q$ and $r$*q**r*8

32

9

36

10

40

11

1

d)variables $v$ and $w$*v**w*27

9

24

8

21

7

18

3

- 2.
**T-tables and two-step equations**

Write the equation for the relationship between the two variables. Follow the pattern to complete the T-table.a)variables $i$ and $j$*i**j*1

3

2

5

3

7

4

10

b)variables $d$ and $e$*d**e*5

13

6

16

7

19

8

1

c)variables $x$ and $y$*x**y*20

13

18

12

16

11

14

100

d)variables $x$ and $y$*x**y*24

4

21

3

18

2

15

300

- 3.
**T-tables and equations: word problem - 1**

It costs $8 to rent a bicycle for the first hour. It costs $2 every hour after that.a)Fill out a T-table for the cost of the first five hours.*hour**cost*

b)Write an equation with variables for the relationship between hours ($h$) and the cost ($C$).c)How much would it cost to rent a bicycle for 24 hours?d)If someone paid a total of $26, how many hours did they rent a bicycle for? - 4.
**T-tables and equations: word problem - 2**

After the first month, seed A grew into a 2cm plant and continued to grow 5cm each month after that. Seed B grew to 6cm and continued to grow 3 cm each month after that.a)Fill out a T-table for the cost of the first three months for both seeds.*month**height*_{A}

*month**height*_{B}

b)Write an equation for each seed's growth, relating the number of months ($m$_{A}, $m$_{B}) and the height ($H$_{A}, $H$_{B}).c)After 1 year, what is the height difference between the two plants?d)When will each plant reach 42cm in height?