 # Unit 4: Algebra (Grades 7-8th)

Algebra is the branch of mathematics that engineers and scientists use to solve problems and get answers to things they don't know. It's how we represent the real world and figure things out on paper or with computers using math tools and skills to figure out solutions.

This course is going to be taught live for Grades 7-8th over 4 months. Students may need multiple weeks per session to thoroughly work through each concept covered during each live session. We will have multiple live class opportunities each week to support your child as they work through the content.

## Algebra Session #1

### Pre-Algebra & Intro to Algebra

#### Uses Algebra Workbook Set #1: "Operations on Integers" and also "Variables, Terms & Expressions"

Getting Started with Algebra You need to be very comfortable with  performing all four operations (add, subtract, multiply and divide) for fractions and decimals, and also be fluent in handling ratios, proportion, and percent in order to be ready for algebra.

For example, how much fuel do you need to get your rocket into the upper atmosphere in under 30 seconds? How far will your car go on a tank of gas? Will you have enough money at the end of the month to go skiing if you eat out every day?

You will use arithmetic and apply it to solve for something you want to know, which means you'll be doing addition, subtraction, multiplication and division with positive and negative integers, fractions, decimals and percent. In this section, you'll find a special set of videos for you to make sure you're ready for Algebra.

Skills: Types of numbers; operations with integers (positive & negative); order of operations; algebraic properties including identity, zero, associate commutative, & distributive; factoring & prime factorization; translating phrases into algebraic expressions; inequalities; handling exponents; combining like terms; number line graphs; absolute value; practical applications of algebra using physics topics such as orbital mechanics and Kepler's Laws of Planetary Motion.

## Algebra Session #2

### Multi-step Equations

#### Uses Algebra Workbook Set #2: "Equations" Workbook

This session is one of the most important foundations for the entire Algebra course. We will be discovering how to solve linear equations that require one or two steps to find a solution.

We'll start by exploring how to use our basic operations to solve simple, one-step equations. Then, we'll progress to more complex problems that require two or more steps to solve for unknown variables. We'll play fun games, puzzle through challenges, and create unique solutions that really make sense.

Algebra is the part of mathematics that we use to represent the real world down on paper to help us find solutions to real problems. We assign letters like x to things we don’t know, like how much gas we’ll need on our next road trip, or how many cookies we can buy for \$20. We will be learning different tools to help us solve math equations that really mean something in the real world.

Skills: order of operations; solving one and two step equations, algebraic properties including identity, zero, associate commutative, & distributive; translating phrases into algebraic expressions; handling exponents; combining like terms; practical applications of algebra using physics topics such as orbital mechanics and universal gravitation concepts.

## Algebra Session #3

### Rational Numbers & Inequalities

#### Uses Algebra Workbook Set #2: "Rational Numbers" Workbook

We're going to discover how algebra solves real-world problems by learning how to represent those problems using mathematical equations and expressions.

This session, we'll be covering a couple of really important areas and all of these concepts are covered in the workbook for this session: Rational Numbers. With rational numbers, students will explore how inequalities are used when there's an imbalance in our equations.

Instead of an equal sign: "=" sign, you will see a ">" or "<" to describe the situation Think about the speed limit: you can travel at different speeds up to the limit, but if you go over you will get a ticket. Or we could use an inequality to describe how many text messages can you send before you get charged an additional fee. These are written as mathematical inequalities.

Skills: Simplify algebraic expressions and equations; represent math relationships using algebra; evaluate variable expressions and functions; absolute value in expressions and equations; number line representations and modeling; interpret and solve linear equations and inequalities.

## Algebra Session #4

### Graphing Equations

#### Uses Algebra Workbook Set #2: "Graphing" Workbook

We're going to dive into the world of graphing by learning how to plot data, calculate equations based on that data, and also how to compare different types of equations called functions.

Imagine you were curious about how the shape of a wing affected the flight of a paper airplane. You fold several different designs, test each one, and get a bunch of data on time aloft and distance traveled. How would you make sense of the data so you could tell which one had the best wing design? Graphing helps us do this! It also helps us learn what the relationship between two (or more) variables are.

We can also look at the lines and determine things we didn't measure directly, like velocity and acceleration from a position-time graph. Students will spend time evaluating different types of linear relationships both in graphical and  equation forms.

Skills: Solve systems of linear equations using graphing, elimination and substitution methods; simplify algebraic expressions and equations; represent math relationships using algebra; graph linear functions; model and describe slope as a rate of change; identify the slope from a graph, table or equation; evaluate variable expressions and functions; scatter plots for bivariate data.

## Algebra Session #5

### Systems of Linear Equations

#### Uses Algebra Workbook Set #2: "Systems of Linear Equations" Workbook

Linear relationships are really common in the real world: the further you go, the longer it takes to get there if you are going the speed limit. The more ingredients you put in a cake, the larger the cake is going to be.

The tricky part is when you have two (or more) variables that are connected to each other. Imagine you're on the freeway and you hit the brakes, how long does it take to come to a stop and how far did you travel before stopping? It depends on how fast you were going in the first place! Using physics, we can write two separate equations that describe this situation, and each one will have both distance and time in the equation. Being able to solve for both variables is trickier than when it's just one, so that's what we're going to practice this week.

This session will focus on how to solve systems of linear equations. You'll develop a strong working foundation of linear equations in all forms, including how to write these in math form (including specific notation), how to graph what we're solving for, modeling situations with graphs to figure out solutions that make sense in the real world, and more!

Please make sure you work through all the content in the previous sessions before starting this session.

Skills: Solve systems of linear equations using graphing, elimination and substitution methods; simplify algebraic expressions and equations; represent math relationships using algebra; graph linear functions; model and describe slope as a rate of change; identify the slope from a graph, table or equation; evaluate variable expressions and functions.

## Algebra Session #6

### Polynomials, Factoring & Exponents

#### Uses Algebra Workbook Set #3: "Polynomials" Workbook

It's POLYNOMIAL time! We are going to explore how to solve equations that are more complex than simple linear equations.

These equations appear all over science and engineering: calculating the speed of an accelerating rocket, how much of a solution will make the right stuff come out of a chemical reaction, how long it takes to hit terminal velocity when you jump out of a helicopter, and so much more!

In our activities and projects this week, students will be making a master reference guide for all of the different techniques for solving polynomials (hint: there's a lot). They will also explore how to handle fractions with exponents and solve riddles, navigate mazes, and piece together pyramid puzzles as they practice their new math skills.

Advanced students will get to take an engineering course in Heat Transfer and learn how energy is transferred through three different methods, and what the math looks like behind it.

We'll learn how to factor, deal with exponents, graph solutions to our equations, and practice the distributive property during this session. Please make sure you work through all the content in the previous sessions before starting this session.

Skills: Solve non-linear equations using factoring, greatest common factors, differences in squares and cubes, sum of cubes, completing the square, trinomial solving techniques, four terms, mixed factoring, and third degree polynomial techniques. Students will continue to practice word problems, simplifying algebraic expressions and equations; representing math relationships using graphs and functions; and evaluating variable expressions and functions.

## Algebra Session #7

#### Use Algebra Workbook Set #3: "Quadratics"

Explore how to simplify and evaluate rational equations, deal with square roots and radicals, and  discover the most powerful quadratic equation solver ever! This quadratic formula is the sledgehammer of math techniques for attacking polynomials.  It's quick and easy to learn, so we'll spend part of our time reviewing everything from this unit to make sure you've got it all covered.

We will review working with integers, variables, equations and expressions; methods for solving both linear equations and inequalities; graphing tables and functions of linear and non-linear equations and inequalities; solving systems of linear equations; working with polynomials using a dozen different solution methods, including the quadratic formula.

Please make sure you work through all the content in the previous sessions before starting this session.

Skills: handling variables, terms, expressions; linear and non-linear equations and expressions as they appear in word problems; factoring and related methods of solving polynomials and systems of linear equations; simplifying algebraic expressions and equations; representing math relationships using graphs and functions; and evaluating variable expressions and functions.

## Algebra Sessions #1-4 Review

Since Unit 4 covers quite a lot of content, there are already two review sessions built into the program in Session #4 (about half-way down, called "28 Stations" and also "10 Stations"). Be sure to complete those first before completing the one below.

The review session video below is an additional review after your student has completed all the Beginner and Intermediate work in Sessions #1-4. Print out the packet and watch the video to get started!

## Algebra Sessions #5-7 Review

This is the second review session for our students. This review is done live with our students and is in addition to the unit reviews posted in Session #7 Print out the handout at the link below and let's get started!

## Do you have a calculator that will work for this class?

PARENTS! If your child is ready for algebra, please make sure they have an good scientific calculator.

Here's an inexpensive option if you need a recommendation (\$10-20):
Texas Instruments TI-30Xa Scientific Calculator.

Your calculator should have these features: