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Get Started Now- Intro Lesson: a6:40
- Intro Lesson: b3:52
- Intro Lesson: c7:32
- Intro Lesson: d7:21
- Intro Lesson: e4:13
- Intro Lesson: f10:03
- Lesson: 1a3:26
- Lesson: 1b3:27
- Lesson: 1c4:47
- Lesson: 1d4:36
- Lesson: 2a3:08
- Lesson: 2b4:22
- Lesson: 2c4:03
- Lesson: 2d3:48
- Lesson: 3a3:35
- Lesson: 3b2:48
- Lesson: 3c6:11
- Lesson: 3d5:52
- Lesson: 4a9:38
- Lesson: 4b13:02
- Lesson: 4c10:34
- Lesson: 4d15:30

In this lesson, we will learn:

- How to describe number patterns using a function table (input output table)
- How to write formulas with variables for function tables and solve for variables
- The steps for solving the rule (one-step and two-step) or formula for a function table

- We can think of the relationship between
**numbers in a pattern**as a*machine* - The machine takes the number you give it (the “
”), applies a__input__(the “__function__” or math operations), and gives you a resulting number (the “__rule__”)__output__

- The
(or__input output table__) keeps track of these inputs and outputs__function table__ - Unlike the
**number sequence**, order is__not__necessary for a**function table** - Ex. for the number sequence/pattern “start at 1 and add 3 each time” it would be:

- Ex. but for the function table with a rule of “add 3” it could be:

- It is also possible to have
for__two-step rules__**function tables** - The first step is to either multiply or divide (× or ÷)
- The second step is to either add or subtract (+ or –)
- Instead of writing “input” and “output” in the function table,
can be written instead__variables__ **Variables**are symbols (letters) that represent values that can change (“varying”)- Variables can be used to write a
for the function table using the format:__formula__ - $(output variable) = (multiplier/divisor) x (input variable) \pm (addend/subtrahend)$
- Or more commonly written as $y = m x + b$
- To
**solve**for the variables in function tables: - If solving for an
**output**: plug the input value into the formula - If solving for an
**input**: plug the output value in and solve backwards ()*algebra* - If you are given a complete function table and asked to
:__solve for the formula__ - Check horizontally across input/output for one-step rules
- If it is
__not__a one-step rule: - If the inputs are
, the multiplier m (in formula $y = m x + b$) is the__consecutive__**difference between outputs** - If the inputs are random, the formula can be either found by:
- (#1) trial and error
- OR (#2) using two pairs of input/output and m is the ratio of $\large\frac{\Delta y}{\Delta x}$

- IntroductionIntroduction to Describing Patterns using Tables and Solving Variables:a)What is a function machine and what is a function table?b)What are two-step rules?c)How do we write number pattern rules as formulas with variables?d)Solving the formula for one-step rulese)Solving the formula for two-step rules with consecutive inputsf)Solving for formula for two-step rules with random inputs
- 1.
**Solve for the Function Table's Missing Variables**

Use the rule to complete the function table:a)

b)

c)

d)

- 2.
**Solving for Function Table Rules**

Write the rule for the function table- Write the one-step rule as a formula with a variable

a)

b)

c)

d)

- 3.
**Using Two-Step Rules to Complete Function Tables**

Use the two-step rule to complete the function table.a)

b)

c)

d)

- 4.
**Solving for Two-Step Rules in Function Tables**

Write the two-step rule for the function table.a)$output = (m) input \pm b$

b)$output = (m) input \pm b$

c)$output = (m) input \pm b$

d)$output = (m) input \pm b$