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Systems of Linear Equations
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!
Download your Algebra Workbook Set #2
To help you with your daily practice, I've put together a set of four workbooks. This session, we are working through the last workbook in the second series. Beginner and Intermediate students will work through Algebra Set #2: Systems of Linear Equations. Plan to complete 3-4 pages per day. After you complete the pages, you may check the answer key.
Algebra Workbook: Systems of Linear Equations
This is the fourth of four workbooks in Set #2. I've put together a set of videos that will walk you through selected problems in this workbook, Systems of Linear Equations. Plan to complete 3-4 pages per day. After you complete the pages, you may check the answer key.
Measurement Practice: Liquid Measures
If you love to cook or bake, then you've probably run into the problem of needing to know how many teaspoons in a tablespoon or cups in a gallon. This is a fun lab where you'll first make your own reference sheet and then use to to answer questions on the following pages in the packet.
Math Activity: Linear Relationship Packet #2
Please make sure you have completed Linear Relationships Packet #1 (from last session) before you begin this packet. We're going to explore deeper how equations can be graphed and their results interpreted to figure out solutions. This is an in-depth packet that includes two quizzes, a review and test and a study guide in addition to homework sets and class notes.
Math Activity: Math Mazes
Do you like solving mazes? Let's practice our skills with linear systems of equations using this fun math maze!
Math Activity: Math Clocks
This is a fun 12-step puzzle where you get to solve 12 different linear equation sets and figure out which one goes where on the clock face!
Math Activity: Puzzle Train
After working through the workbook, it's time to practice those skills in a fun and challenging way! This is a fun way to practice using both substitution and elimination to solve systems of linear equations.
Math Activity: Matching Card Sort
This fun activity will have you practicing different aspects of solving systems of linear equations and doing a hands-on activity at the same time. This one helps you practice both graphing and substitution techniques for solving your equations.
Math Activity: Scavenger Hunt
Do you enjoy scavenger hunts? This one has you solving systems of linear equations to figure out where our friends will meet up. There's a treasure map that you get to use as you work your way through the different questions.
Advanced Level Math Class
If you are already good at all three methods of solving systems of linear equations, the video below will walk you through how to handle inequalities and also do practical applications with chemistry and physics.
Then below the first video is the first activity for advanced students. It's a review for the content on this page (Solving Systems of Linear Equations). Be sure to work through this as a quick and fun way to review the three different methods of solving sets of equations.
Math Review (All Three Methods)
This is a fun review that gives you the chance to try out all three different methods of solving systems of linear equations. Take your time and work through as many as you can to get a really good review of the different methods. We want to get good at all of them so you can have your choice as to which one you'll use to get the answer the quickest!
Astronomy & Orbital Mechanics Labs
This week, we'll do several labs that cover different areas of Algebra and even start to introduce ideas from Geometry. If you've worked through all of the Beginner and Intermediate level content from all of Algebra, then you are ready for the labs here in this section.
I am going to provide you with the equations you'll need from physics and your job is to learn how and where we use algebra to solve for something we want to know.
Math Challenge
Each session, I have a special Math Challenge for you to work on after you work through some of the content in this area of math. The goal for these special math challenges is for you to be able to communicate your great ideas with your family and friends, without them being in a math class or having any knowledge of a specific area of math. You should be able to convey your great ideas to most people that are interested in hearing what you have to share. Many families find this part of the math program exciting for them to participate in with their student!
Solution to Algebra Session #4 Math Challenge
Can you find your way through without making any LEFT turns? You may want to print this out place a small car on the pathways so you can remember which way is left, no matter which way you are oriented.
