# Patterns: Describing patterns using tables and solving variables

0/6

##### Intros

###### Lessons

- Introduction to Describing Patterns using Tables and Solving Variables:
- What is a function machine and what is a function table?
- What are two-step rules?
- How do we write number pattern rules as formulas with variables?
- Solving the formula for one-step rules
- Solving the formula for two-step rules with consecutive inputs
- Solving for formula for two-step rules with random inputs

0/16

##### Examples

###### Lessons

**Solve for the Function Table's Missing Variables**

Use the rule to complete the function table:**Solving for Function Table Rules**

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

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

Use the two-step rule to complete the function table.**Solving for Two-Step Rules in Function Tables**

Write the two-step rule for the function table.

0%

##### Practice

###### Free to Join!

StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

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

__Notes:__- 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 $\large\frac{\Delta y}{\Delta x}$

2

videos

remaining today

remaining today

5

practice questions

remaining today

remaining today