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Polynomials, Factoring & Exponents

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.

Beginner Level Math Class

We're going to explore different algebra skills in our workbooks. We'll continue to practice with concept and word problems and have fun learning!

Download your Algebra Workbook Set #3

To help you with your daily practice, I've put together the a new workbook for you. Beginner and Intermediate students will work through Algebra Set #3: Polynomials. Plan to complete 3-4 pages per day. After you complete the pages, you may check the answer key. 

Algebra Workbook:  Polynomials

This is the first workbook in Set #3. I've put together a set of videos that will walk you through selected problems in this workbook, Polynomials. Plan to complete 3-4 pages per day. After you complete the pages, you may check the answer key.

Measurement Practice: Converting between Standard & Metric

It's important to have a good idea of how many centimeters per inch and how many kilometers per mile, but it's impossible to know how to convert every measurement without using a table. We're going to learn how to use the tables usually found on on the inside covers of science and engineering textbooks so you'll be able to convert quickly using a plain old (non-fancy) calculator.

Intermediate Level Math Class

Are you ready to really practice your new math skills? Let's get really good at solving polynomials by doing several different activities and games as we are figuring out solutions!

Math Activity: Factoring Polynomials Flip Book Reference Guide

Please make sure you have completed the Polynomials workbook before starting the video series below. These videos cover 70 problems using 7 different methods of factoring which stem from the work you did in the workbook. The videos below are intended to create a quick and easy reference for you to keep handy when factoring polynomials.

Please be sure to print pages 2-9 and follow the directions carefully in the first video below for assembly!

Bonus Videos in Factoring

Here are bonus videos for you to add to your notes in your math journal! These are not in the reference guide, but I thought it would come in handy to have in case you run into these in the future!

Math Activity: Math Mazes

Do you like solving mazes? Let's practice our skills with multiplying polynomials using this fun set of three math mazes!

Math Activity: Pyramid Puzzle

This is a fun math puzzle where you get to build a triangular shape as you factor and multiply polynomials! 

Advanced Level Math Class

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. 

Bonus Math Lesson: Exponents

This week, our advanced students will review how to handle fractions with exponents and how to handle negative signs with this bonus lesson (originally in Unit 1: Fractions, Week #4, Advanced section)

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 #5 Math Challenge

Let x = Red City’s present age in seconds

Let y = Blue’s age in seconds

A billion seconds ago the city would have been x – 1 billion seconds old and a billion seconds from now Blue’s age would be y + 1.

2x=y

x-1 = (2/5)(y+1)

The Red city is 7 billion seconds old, and Blue is 14 billion seconds old.