TabletClass Math Pre-Algebra Course Guidebook

Transcription

1 TabletClass Math Pre-Algebra Course Guidebook Includes Final Exam/Key, Course Grade Calculation Worksheet and Course Certificate Student Name Parent Name School Name Date Started Course Date Completed Course Final Grade Copyright 2013 TabletClass.com, LLC 1

2 Table of Contents Introduction and Special Message From Teacher Chapter Tests Summary Worksheet Course Guidebook Final Exam Directions Final Exam Final Exam Key Course Grade Calculation Worksheet Course Pacing Guidelines Course Certificate Copyright 2013 TabletClass.com, LLC 2

3 Introduction Special Message from the Teacher: Welcome to the TabletClass Math Pre-Algebra course. First I want to say that I m very excited to have you as a student. My goal is to give you an enjoyable and high quality learning experience. Moreover I want you to know that you can master this material if you work hard and never give up. This guidebook and final exam is an important part of the course so I strongly recommend that you use the included material. The secret to being successful in mathematics is your approach to studying the topic- i.e. your study habits. From years of teaching math I can say that those students with the best study habits almost always earn the top grades. As such, parents and teachers must focus on holding students accountable for the quality of their work. Below are critical guidelines for students as they take the course: 1. Never give up- especially when a topic is not understood easily or immediately. 2. Strive to be as neat and organized as possible. 3. Excellent note taking is a must to succeed in math. 4. Show all steps when working problems. 5. Double check your work as you write your solution steps. 6. Always go back and review incorrect problems and discover where the error was made. 7. Master the fundamentals and don t move forward unless you understand previous material. Suggested use of the follow along guidebook and final exam: 1. Maintain the guidebook as a written record of the online TabletClass Math student s account. 2. The guidebook and final are designed to be a part of the student s overall course portfolio. 3. Carefully read the final exam directions before giving the final to student. 4. Use the course grade worksheet as input for the final grade assigned. Remember the course material builds on itself so you want to ensure that you don t skip chapters and sections. Furthermore you want to correct your weak areas before moving onto the next topic. The guidebook and online self-assessment / my pulse software features will help you manage your progress. Lastly, I want to stress that you can be great in math if you work hard. Even if you have struggled in math before I want you to look at this course as a fresh start in your mathematics journey- I know in my heart you can ace this course! Best of luck! John Zimmerman TabletClass Math Teacher Copyright 2013 TabletClass.com, LLC 3

4 Pre-Algebra Chapter Tests Summary Chapter 1: Introduction to Algebra Terms and Concepts Chapter Test Score Date Taken Chapter 2: Real Numbers and Simplifying Variable Expressions Chapter Test Score Date Taken Chapter 3: Fractions and Decimals Chapter Test Score Date Taken Chapter 4: Solving Equations Chapter Test Score Date Taken Chapter 5: Inequalities Chapter Test Score Date Taken Chapter 6: Graphing Linear Equations Chapter Test Score Date Taken Chapter 7: Writing the Equations of Lines Chapter Test Score Date Taken Chapter 8: Introduction to Systems Chapter Test Score Date Taken Chapter 9: Absolute Value Chapter Test Score Date Taken Copyright 2013 TabletClass.com, LLC 4

5 Chapter 10: Powers and Exponents Chapter Test Score Date Taken Chapter 11: Polynomials Chapter Test Score Date Taken Chapter 12: Rational Expressions Chapter Test Score Date Taken Chapter 13: Introduction to Functions and Relations Chapter Test Score Date Taken Chapter 14: Area and Volume Chapter Test Score Date Taken Chapter 15: Right Triangle Theorems and Formulas Chapter Test Score Date Taken Copyright 2013 TabletClass.com, LLC 5

6 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 1 Chapter 1: Introduction to Algebra Terms and Concepts This chapter introduces students to basic terms and concepts used in algebra. Time is taken to ensure the student understands basic number operations, variables and their applications. Additionally, the student gains a fundamental sense of equations, inequalities and their solutions. Section Summary (circle / complete after chapter is finished): 1. Number Operations 2. Variables 3. Order of Operations 4. Translating Verbal and Algebraic Phrases 5. Equations/Inequalities/Solutions Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 6

7 Ch. 1 Section 1 Number Operations This section will be on number operations. You need to understand number operations as it s a fundamental concept in algebra. The lesson will cover operators and associated vocabulary like sum, difference, product and quotient. I must caution that many students find this material so easy that they rush through it without really mastering the concepts. Hence take the time to learn everything covered in the lesson and note taking is absolutely necessary. Example Set D Ch. 1 Section 2 Variables This section will be on variables. Of course algebra is different than basic math because we often work with variables. Knowing how to work with variables is absolutely critical to master algebra. In the lesson you will learn the parts of a variable term and how to evaluate a variable expression. Please pay special attention to evaluating a variable expression with negative values as many students make errors with this task. Example Set D Copyright 2013 TabletClass.com, LLC 7

8 Ch. 1 Section 3 Order Of Operations This section is on the order of operations. Everything you learn in math is important but I would say mastering the order of operations is extra important to math students at this level. As a math teacher I have seen so many student errors due to a lack of really understanding the order of operations. Hence you should pay extra attention to the lesson and follow the procedure called PEMDAS. Don t be fooled into thinking this is easy because you can do a few basic problems you really need to practice more difficult problems to have absolute confidence in this area. Example Set D Ch. 1 Section 4 Translating Verbal and Algebraic Phrases In this section you will be learning how to translate a verbal (word phrase) into a variable expression like an equation or inequality. For many students this skill of translating can be a little confusing but with practice and good note taking you can master the concepts. The reason you need to learn how to translate a verbal phrase into a variable phrase is it helps you solve algebra word problems. Like all lessons watch the video as much as you need to in order to totally understand the objectives. Copyright 2013 TabletClass.com, LLC 8

9 Ch. 1 Section 5 Equations/Inequalities/Solutions In this section you will learn the fundamentals of equations, inequalities and there respective solutions. Of course equations and inequalities are everywhere in algebra so you want to grasp the big picture concepts of what equations and inequalities represent mathematically. Also there are significant differences in the solutions between an equation and inequality. Lastly you will be introduced to verifying if a number is a solution to an equation or inequality- you will be asked to verify solutions a lot in algebra so pay close attention. Copyright 2013 TabletClass.com, LLC 9

10 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 2 Chapter 2: Real Numbers and Simplifying Variable Expressions This chapter focuses on getting the student to master working with the Real Numbers. Students learn the rules of integers and practice through many examples. Also, students will learn to apply the Distributive property and simplify variable expressions by combining like terms. Section Summary (circle / complete after chapter is finished): 1. Real Number System 2. Adding Real Numbers 3. Subtracting Real Numbers 4. Multiplying and Dividing Real Numbers 5. Distributive Property 6. Simplifying by Combining Like Terms Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 10

11 Ch. 2 Section 1 Real Number System This section will cover the concept of Real Numbers. Most students think of Real Numbers as the positive and negative numbers. However, students should understand that the positive and negative numbers include various types of numbers that make up the Real Number system. The main objective of this lesson is to stress the importance of real numbers in describing or modeling real life situations. Of course math is all about solving real life problems so understanding the Real Number system is essential in being able to solve algebra problems. Ch. 2 Section 2 Adding Real Numbers This section will go over the steps to add real numbers (positive and negative numbers). From my experience as a math teacher many students seem to have difficulty when first learning how to add and subtract positive and negative numbers. As such you really want to take your time and understand the exact procedure to add real numbers- it s not hard however it s easy to make a mistake. Copyright 2013 TabletClass.com, LLC 11

12 Ch. 2 Section 3 Subtracting Real Numbers This section covers how to subtract real numbers (positive and negative numbers). Before a student watches this lesson video they want to master the lesson on adding real numbers. The reason is we change all subtraction problems (with real numbers) into adding problems- so the rule to add real numbers will apply. Students will also want to pay special attention to the phrase plus negative as it s the method we change subtraction problems into addition problems. Ch. 2 Section 4 Multiplying and Dividing Real Numbers In this section you will learn how to multiply and divide real numbers (positive and negative numbers). The good news is the rules are very easy and are the same for both multiplication and division. I want to caution you that all the rules for adding, subtracting, multiplying and dividing real numbers are not hard- however they are very easy to confuse. As a matter of fact I would say well over 50% of algebra errors made by students involve confusing the positive and negative number rules. My point: study hard, take good notes and practice, practice, practice until you have mastered the rules. Copyright 2013 TabletClass.com, LLC 12

13 Ch. 2 Section 5 Distributive Property This section will cover the Distributive Property. Algebra has many properties and rules but one of the most used is the Distributive Property. Students must master this property to move forward in their understanding of algebra. The Distributive Property is almost always applied when solving equations, inequalities and other various tasks in algebra. The good news is the Distributive Property is not difficultit s really just another way to multiply. However just because the rule is easy it s also easy to make a mistake. So make sure you understand the lesson and practice the property as much as you can. Ch. 2 Section 6 Simplifying by Combining Like Terms This section is on simplifying like terms. Your main objective in this lesson is to learn when and how we add (combine) variable terms. In algebra a term is the most basic part of what we work with. An example of a variable term would be 3x or -8y. What you will learn in the lesson is how to simplify a variable expression by adding terms. Of course not all variable terms can be added and the lesson will go into detail on how to determine when you can combine variable terms. One special note: make sure you have mastered the rules of Real Numbers (positive and negative numbers) before starting this lesson. Copyright 2013 TabletClass.com, LLC 13

14 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 3 Chapter 3: Fractions and Decimals This chapter reviews how to work with fractions. Although it is assumed students have these skills, time is taken to ensure the student has mastered the procedures to perform operations involving fractions. Section Summary (circle / complete after chapter is finished): 1. Introduction to Fractions and Decimals 2. Least Common Multiple/Denominator 3. Multiplying and Dividing Fractions 4. Adding and Subtracting Fractions Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 14

15 Ch. 3 Section 1 Introduction to Fractions and Decimals This section is an introduction to fractions and decimals. Please do not skip this lesson because many students struggle with fractions they don t know fractions nearly as well as they think they do. Hence use this basic lesson to build a foundation of knowledge in this topic. I will be covering proper and improper fractions and how to convert one type into another type. Also I will show you how to convert a fraction into a decimal. Take good notes and practice as much as you can- fractions are everywhere in math.you need to master them! Example Set D Ch. 3 Section 2 Least Common Multiple/Denominator This section is on the Least Common Multiple (LCM) and the Least Common Denominator (LCD). Knowing how to find the LCM/LCD is absolutely critical to your success with fractions. Many students can find the LCM/LCD when the numbers involved are easy. However when the numbers in fractions are more difficult (larger) it s easy for students to find themselves getting lost- make sure this is not you! Finding the LCM/LCD is part of adding and subtracting fractions so take your time and really master this very important skill. Example Set D Copyright 2013 TabletClass.com, LLC 15

16 Ch. 3 Section 3 Multiplying and Dividing Fractions This section is on multiplying and dividing fractions. The good news is multiplying and dividing fractions is pretty easy. However students often forget to reduce or simplify their answers so make sure you reduce all of your solutions. In the lesson I will explain how to multiply/divide a variety of different fractions to include proper and improper fractions and whole numbers. One last comment before you start the lesson: many of the skills we learn about fractions are easy however they are also easy to confuse- please take good notes and study/practice as much as you can. Example Set D Example Set E Ch. 3 Section 4 Adding and Subtracting Fractions This section is on adding and subtracting fractions. Out of all the topics in fractions, adding and subtracting fractions seems to give students the most problems. From experience a student must master all previous fraction skills before taking on adding/subtracting fractions. Hence a student should know how to reduce a fraction, multiply and divide fractions and find the LCM/LCD before starting this lesson. Once a student can confidently do the tasks I just mentioned they should have no problem learning how to add and subtract fractions. I can t stress how important fraction skills are in math so make sure you watch the lesson videos as much as needed to master the skills. Example Set D Example Set E Copyright 2013 TabletClass.com, LLC 16

17 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 4 Chapter 4: Solving Equations The chapter breaks down the steps to solve multi-step linear equations. Students will build up their skills as they progress from one and two-step equations to more advance equations. Core concepts involved will be reviewed to include the distributive property and combining like terms. Section Summary (circle / complete after chapter is finished): 1. One Step Equations 2. Solving Two Step Equations 3. Solving Multi-Step Equations 4. Formulas and Literal Equations Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 17

18 Ch. 4 Section 1 One Step Equations This section covers one-step equations. Your understanding on how to solve all equations in algebra starts with this lesson- it s very important that you master the concepts. There are 4 basic one-step equation types you will learn how to solve. Pay close attention to the term inverse operation and how we use inverse operations to solve an equation. Also you really need to have mastered the rules of positive and negative numbers and fractions as you will need these skills to learn how to solve equationsstop and review if you need to. Example Set D Ch. 4 Section 2 Solving Two Step Equations In this section you will learn how to solve two step equations. Basically a two step equation is like two 1 step equation problems. Hence, before you watch this lesson you really need to have mastered one step equations. Furthermore, in the next lesson, on multi-step equations, you will need to know how to solve two step equations. Of course it should not come as any surprise that math builds on itself so each lesson and skill is important. Lastly pay careful attention to how I work the problems- try to be as neat and structured as I am in the problem solving process. Example Set D Copyright 2013 TabletClass.com, LLC 18

19 Ch. 4 Section 3 Solving Multi-Step Equations The following section is on multi-step linear equations. Just in case you did not know, you want to have mastered one and two step equations before watching this lesson. Multi-step equations are the foundation of algebra and more advance math- there importance cannot be overstated. As such do everything you can do to master the equation solving process. One of the best things you can do is learn how to write neatly and structured. Before you start the lesson make sure to review any skill that you know you are weak at -common weak areas for students at this point in the course would include: order of operations, positive/negative numbers, fractions and the distributive property. Example Set D Example Set E Ch. 4 Section 4 Formulas and Literal Equations In this section you will learn about formulas and literal equations. When first studying this topic it can be hard however with practice and determination I know you can master the concepts. A literal equation is a type of an equation that has multiple variables. What I will be teaching you is how to solve for a specific variable in a literal equation. Formulas are the most common literal equations we experience, an example would be Area = Base x Height or A=BH. If I asked you to rewrite this equation in terms of B I would be asking you to solve the literal equation (formula) for the variable B. Remember to take notes and review all previous lessons on equations before you take on this lesson. Example Set D Copyright 2013 TabletClass.com, LLC 19

20 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 5 Chapter 5: Inequalities In this chapter students will apply their equation solving skills to solve linear inequalities. Basic concepts and terms are introduced first, along with how to graph inequalities. Section Summary (circle / complete after chapter is finished): 1. Linear Inequalities 2. Compound Inequalities Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 20

21 Ch. 5 Section 1 Linear Inequalities In this section you will be introduced to linear inequalities. Before I teach you this topic please ensure that you have mastered the chapter on equations as linear inequalities are very similar. Inequalities are extremely important in mathematics and you will see inequalities in future topics such as quadratic inequalities, systems of inequalities, absolute value inequalities, and the list goes on and on. What I will teach you in this lesson is the foundation to all inequality related topics so make sure you take good notes and practice as much as you can. Example Set D Ch. 5 Section 2 Compound Inequalities In this section we will study compound inequalities. Please make sure you watch my videos on linear inequalities before starting this lesson. A compound inequality is basically two linear inequality problems all wrapped up into one expression. The steps we take to solve a compound inequality are very similar to those of solving equations- hence make sure you have strong equation solving skills as well. Lastly we like to express the solution to an inequality in terms of a graph so make sure you finish all problems by sketching a graph. Copyright 2013 TabletClass.com, LLC 21

22 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 6 Chapter 6: Graphing Linear Equations This very important chapter walks the student step-by-step to master how to graph linear equations. Concepts involving the coordinate plane, slope and methods to graph lines are thoroughly reviewed and introduced. Upon completion of the chapter students will gain the necessary knowledge and skills needed to learn more advance topics involving linear equations. Section Summary (circle / complete after chapter is finished): 1. Graphing Lines with One Variable 2. Graphing Lines with Two Variables 3. The Slope of a Line 4. Slope Intercept Method 5. XY Intercept Method Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 22

23 Ch. 6 Section 1 Graphing Lines with One Variable In this section you will learn how to graph a basic line- a linear equation with one variable. You most likely will find this lesson very easy but it s important to learn/review all the other things I go over in the lesson to include the parts of the x-y plane. A little warning, many students confuse the equations to graphing a vertical and horizontal line not because it s hard but because the steps are easy. Please remember that when a task is easy, often times it s easy to make a mistake- it s just human nature. So take your time, enjoy the lesson and double check that you re following the correct procedure to graph one variable lines. Ch. 6 Section 2 Graphing Lines with Two Variables In this section I will teach you the fundamentals of graphing lines with two variables. The proper name for a line equation is linear equation. Hence this lesson is about graphing two variable linear equations. However this lesson is only the start to an in-depth study of the topic of graphing lines. You will be learning how to graph a two variable line using a table of values in this lesson but the chapter will cover many more graphing techniques as well. Copyright 2013 TabletClass.com, LLC 23

24 Ch. 6 Section 3 The Slope of a Line In this section I will teach you about the slope of a line. We will be using the slope of a line all though this chapter so you really need to master the procedure I m going to teach you in the lesson. Basically, the slope of a line is a fraction that expresses the angle or steepness of a line. The slope is represented with the variable m and we define the slope as the rise over the run of a line. Example Set D Example Set E Ch. 6 Section 4 Slope Intercept Method In this section I will be teaching you the slope intercept method of graphing a line. By far this is the most common way to graph a two variable line, you may know the slope intercept method as the y = mx + b method. The good news about graphing a line with the slope intercept method is its very direct and straight forward. Moreover it s a method you must master as you will be graphing many, many lines in algebra. Lastly this lesson is one of many ways you will learn to graph a line so take good notes and practice, practice, practice. Copyright 2013 TabletClass.com, LLC 24

25 Ch. 6 Section 5 XY Intercept Method In this section I will teach you how to graph lines using the x and y intercepts. Please make sure have watched all other lessons in this chapter before starting this topic. As stated in previous lessons there are many ways to graph a line (linear equation). All the methods have there pros and cons- this method is great when a line is written in standard form. So please keep in mind that just because you can graph a line using another method that s all you need to learn. Every method we study is important so you want to take good notes and practice as much as you can. Example Set D Copyright 2013 TabletClass.com, LLC 25

26 Chapter 7: Writing the Equations of Lines TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 7 The chapter builds on the student s prior knowledge and skill of linear equations. Various methods to find and write the equation of a line are introduced and practiced. The chapter focuses on the proper way to set-up and use formulas to write linear equations. Additional related topics are explored to include linear models, linear regression and word problems. Section Summary (circle / complete after chapter is finished): 1. Using Slope-Intercept Form 2. Using Point-Slope intercept 3. Given the Slope and a Point 4. Given Two Points 5. Standard Form of Linear Equations 6. Best Fitting Line 7. Linear Models/Word Problems Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 26

27 Ch. 7 Section 1 Using Slope-Intercept Form In this section I will show you how to find the equation of a line using the slope-intercept method. Recall the slope-intercept method is when we graph a line using the form y=mx + b where m is the slope and b is the y-intercept. Just to be clear when we are looking for the equation of a line (as we will be doing in this lesson) we need the slope of the line and at least one (x, y) point that is on the line. So given the slope and a point we can find the equation of any line. Also we want to write our final solutions in y=mx + b form unless otherwise told. This chapter will explore many ways to find the equation of a line and each is important to understand. Ch. 7 Section 2 Using Point-Slope intercept In this section I will teach you the point-slope formula. This is a great formula to find the equation of a line. You will need to have the slope and at least one point that is on the line to use the formula. I think all students should use the point-slope formula as their primary way to find the equation of a linehowever you still need to master the other methods as well. As in all formulas be very careful of the values you plug into the formula. Also try not to memorize the formula when you practice- once you re comfortable on how to use the formula correctly then work on memorizing it. Copyright 2013 TabletClass.com, LLC 27

28 Ch. 7 Section 3 Given the Slope and a Point In this section we will learn how to find the equation of a line when you are given its slope and one point that lies on the line. An example problem would be find the equation of the line in y=mx + b form that has a slope of 3 and goes through the point (1, 9). Now if you watched the other lessons in the chapter you will have a few methods to find the equation. I prefer the point-slope formula so I would suggest using that method as your primary approach. However you want to be able to find the equation using all methods we learn. Good luck and make sure you take good notes- this stuff is extremely important in algebra! Ch. 7 Section 4 Given Two Points In this section I will teach you how to find the equation of a line given two points that lie on the line. The first thing you have to do is find the slope given the two points so make sure to review the slope lesson if you need to. Once you have the slope and the two given points on the line it s easy to find the equation by just using the point-slope formula. If you watched the other lessons in the chapter you know I m a big fan of the point-slope formula because it s direct, straight forward and works for all situations. Please practice as much as you can as finding the equation of a line is a critical algebra skill. Copyright 2013 TabletClass.com, LLC 28

29 Ch. 7 Section 5 Standard Form of Linear Equations In this section I will teach you about the standard form of a linear equation. If you recall y=mx + b is the general format of a line when it s in slope-intercept form. When a line is in standard form its general format will be Ax + By = C. The main benefit of having a line in standard form is you can easily graph it using the x-y intercepts. In the lesson I will also discuss how to convert a line from y=mx + b form into Ax + By = C standard form. As you learn more about lines and there various equations it s easy to get confused so make sure you take good notes and review/practice as much as you can. Ch. 7 Section 6 Best Fitting Line In this section I will teach you about best fitting lines and scatter plots. This topic is really a key application of everything we have learned about in finding the equation of lines. You want to have graph paper when you learn and practice this skill because you will need to estimate data from a graph. Also I would suggest using the point-slope formula to find the actual equation of the line once you determined the best data to use. This topic has a lot of real world application in business and science so it s a nice example of how math is so important in many areas of study. Copyright 2013 TabletClass.com, LLC 29

30 Ch. 7 Section 7 Linear Models/Word Problems This section is about linear equation word problems- very common in algebra. Before you start the lesson you want to make sure you have mastered all the previous sections as we will be using various linear equation skills. Of course the best part of this lesson is it s about word problems examples of how math really helps us solve problems in the real world. You want to take excellent notes as linear models are very important and used in many applications. Also pay attention to the steps on how to solve a word problem they will help you in other topics as well. Copyright 2013 TabletClass.com, LLC 30

31 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 8 Chapter 8: Introduction to Systems Understanding systems and the methods to solve them are vital in algebra. This chapter introduces the student to systems and what their solutions represent. Techniques to solve systems will build from the student s prior knowledge of solving linear equations. Upon completion of the chapter a student will have a solid skill set in systems that prepares them for Algebra 1 and 2. Section Summary (circle / complete after chapter is finished): 1. Solving Systems by Graphing 2. Solving Systems Substitution Method 3. Solving Systems by Elimination/Linear Combination Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 31

32 Ch. 8 Section 1 Solving Systems by Graphing In this section I will introduce the concept of systems to you. A system is a mathematical way of describing the behavior of something using two or more equations. The subject of systems is HUGE in math so you want to embrace the study of systems by learning the fundamentals in this lesson. Now the type of systems we will study are linear - where we use line equations like y=mx + b. Hence it s important you know a lot about linear equations to include graphing them. As you will see the solution to a basic system is the point where two lines intersect. As such you will be graphing lines to find the point of intersection so make sure you have graph paper and a ruler for the lesson. Ch. 8 Section 2 Solving Systems Substitution Method This section will be about solving systems using the substitution method. You want to really practice and make sure you master this skill as it will come up over and over again in algebra and beyond. I will be teaching you various ways to solve systems but for now you really want to master the graphing method, the substitution method and the combination method. Many students have problems with the equation solving steps in this topic so you might want to review literal equations and formulas if needed (the lesson is in the equations chapter). Take great notes and you must practice solving systems a lot to really be confident about your skills. Example Set D Copyright 2013 TabletClass.com, LLC 32

33 Ch. 8 Section 3 Solving Systems by Elimination/Linear Combination In this section I will teach you the elimination/ combination method to solve a system. The method gets its name because you will take steps to eliminate one variable in the equation to solve the system. Like many things in math the name sounds more complex than the actual concept- so as long as you follow the steps I teach, you will be fine. The elimination/ combination method and the substitution method are the two main system methods you need to master at the pre-algebra / algebra 1 level. It s important that you practice a wide variety of problems to really master the skill. Example Set D Copyright 2013 TabletClass.com, LLC 33

34 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 9 Chapter 9: Absolute Value Absolute value problems can be challenging for some students to grasp. Time is taken to teach students core concepts and build understanding. Students will learn how to graph absolute value functions and apply the steps to solve absolute value equations/inequalities. Section Summary (circle / complete after chapter is finished): 1. Introduction to Absolute Value 2. Graphing Absolute Value Equations 3. Solving Absolute Value Equations 4. Absolute Value Inequalities Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 34

35 Ch. 9 Section 1 Introduction to Absolute Value In this section I will introduce you to absolute value functions. The concepts are extremely important to learn as absolute value is everywhere in algebra and more advance math courses. Basically the absolute value is the distance a number is from zero on a number line. You will learn how to evaluate absolute value expressions and understand the exact definition. Once you master this lesson you can move onto learning about absolute value equations, inequalities and graphs. Ch. 9 Section 2 Graphing Absolute Value Equations In this section we will explore the graphs of absolute value equations. Understanding how to graph various functions in algebra is a key skill you need to learn. Graphs help us interpret data and make conclusions when problem solving. The absolute value graph is easy to identify as it s always V shaped. I will be teaching you how to find the vertex (the point of the tip of the V ) and how to sketch a basic graph. Also I really suggest that you use graph paper when practicing as it will help you keep your work neat and organized. Example Set D Copyright 2013 TabletClass.com, LLC 35

36 Ch. 9 Section 3 Solving Absolute Value Equations In this section I will teach you how to solve absolute value equations. Once you understand the concepts of absolute value I think you will find solving absolute value equations easy. However make sure to take your time and really understand the concepts in the lesson as it s the best way to retain your skills. Remember, developing a real understand of a concept is what you want to strive to do in order to master math. If you are going through the lessons quickly and trying to use rote memorization to solve problems this will cause you trouble over the long term. Take your time and review the lesson as much as you need to in order to gain mastery of the skill. Ch. 9 Section 4 Absolute Value Inequalities In this section you will learn how to solve absolute value inequalities. Unlike solving absolute value equations where you have 2 solutions, absolute value inequalities have solutions that are inequalities and graphs. Some students have a difficult time with this topic because they are weak in inequalities- so make sure you review linear and compound inequalities if you need to. As you can tell the concept of absolute value has many sub-topics you need to master to include: absolute value equations, absolute value graphs and absolute value inequalities. Make sure you take good notes and practice as much as you can. Copyright 2013 TabletClass.com, LLC 36

37 Chapter 10: Powers and Exponents TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 10 This chapter covers the rules of powers and exponents a student needs to learn in algebra. Also, important applications of these rules are covered to include scientific notation, compound interest and exponential growth and decay. Section Summary (circle / complete after chapter is finished): 1. Product and Power Rules of Exponents 2. Negative and Zero Exponents Rules 3. Division Rules of Exponents 4. Scientific Notation 5. Compound Interest 6. Exponential Growth and Decay Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 37

38 Ch. 10 Section 1 Product and Power Rules of Exponents In this section I will teach you the product and power rules of exponents. To be successful in algebra you must know how to work with and simplify expressions with powers. There are a few different rules of exponents so there is more to learn than just this rule. Make sure you take good notes and practice as much as you- I can t stress this enough. Also as you gain more experience you will see that you can simplify a problem using different steps- as long as the steps you take are proper and you get the correct solution is all that matters. Lastly make sure to show all your work while practicing and use pencil so you can easily erase mistakes. Ch. 10 Section 2 Negative and Zero Exponents Rules In this section I will be teaching you about negative exponents and zero powers. The good news is the zero power rule is easy; anything to the zero power is always 1. So the real focus in this lesson is how to work with negative exponents. Because we will be working with negative numbers make sure you know how to add real numbers (positive and negative numbers). Also in algebra we never leave our final solutions with negative exponents- so you re not done with your problem until the expression has all positive exponents. Take your time with the lesson as it can be a little confusing and of course practice is a must. Copyright 2013 TabletClass.com, LLC 38

39 Ch. 10 Section 3 Division Rules of Exponents In this section I will teach you how to divide powers. The rule is pretty straight forward but you need to be careful as it s easy to make an error. The key to most of the exponent rules is identifying powers with the same base- so make sure you have a really good grasp on the different parts of a power. Also you may notice that you can simplify a division of powers problem using other rules of exponents not just the division rule. Remember you can take different steps to simplify an expression involving powers and exponents. However you need to first master and understand all the rules of exponents. Ch. 10 Section 4 Scientific Notation In this section I will teach you about scientific notation. The topic has to do with very large and small numbers- those that we often find in science. What we will be doing in the lesson is rewriting these very big/small numbers as a power of 10. Then we will use the rules of powers and exponents to simplify and solve problems. You want to have a scientific calculator when doing this lesson as it will make some of the basic arithmetic easier. Scientific notation is a great example of how math is used in the real world and I m certain you will see it in most of your math and science courses so learn it well! Example Set D Copyright 2013 TabletClass.com, LLC 39

40 Ch. 10 Section 5 Compound Interest In this section I will teach you about compound interest. Compound interest is used everywhere in the real world. In the lesson I will explain the differences between compound and simple interest. To solve compound interest problems you need to know how to work with powers and exponents. Hence if you need to review the rules of powers and exponents go ahead before watching the lesson. One last interesting thing about compound interest, Albert Einstein once called it the most powerful force in the universe - I hope that inspires you to work hard to master the topic. Ch. 10 Section 6 Exponential Growth and Decay In this section I will introduce you to the topic of exponential growth and decay. As you study more math you will learn about different types of functions that model how fast something grows or decays. An example of exponential growth would be the rate population grows- over time it can grow faster and faster. An example of exponential decay would be how slow radioactive material decays- it gets smaller and smaller over longer periods of time. You want to have a good understanding of powers and exponents for this lesson. In future chapters we will explore exponential functions in much more detail. Copyright 2013 TabletClass.com, LLC 40

41 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 11 Chapter 11: Polynomials Polynomials are the key building blocks of algebra. The chapter starts by covering the parts of a polynomial and related terminology. Students then learn how to perform various polynomial operations, and a special focus is placed on avoiding common mistakes. Lastly, there is a section dedicated to introduce quadratic equations which are extremely important in more advance topics in algebra. Section Summary (circle / complete after chapter is finished): 1. Introduction to Polynomials 2. Adding and Subtracting Polynomials 3. Multiplying Polynomials 4. Introduction to Quadratic Equations Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 41

42 Ch. 11 Section 1 Introduction to Polynomials In this section I will introduce you to polynomials. Algebra is filled with polynomials and I can t stress how important polynomials are in mathematics- you will be studying them in great detail! As such you want to pay extra attention to everything in this lesson. Remember in order to master a topic you need to start with a great understanding of the fundamentals. In the lesson I will explain the precise definition of a polynomial (which you need to know) and many other details about the basics of polynomials. If you want to master algebra you must have a total understanding of polynomials. So work hard, take good notes and practice, practice. Ch. 11 Section 2 Adding and Subtracting Polynomials In this section I will teach you how to add and subtract polynomials. You want to make sure you remember how to add/subtract like terms- you may want to review the topic in the real numbers chapter. If you have an excellent grasp on like terms then this lesson will not be too difficult. Students seem to make more mistakes with subtracting polynomials because you have to change signs so be careful. Also you need to practice this skill way beyond a few problems. The worst thing you can do is watch the lesson, say I get it and move on without practice- remember in math there are no short cuts for truly mastering the subject. Example Set D Example Set E Copyright 2013 TabletClass.com, LLC 42

43 Ch. 11 Section 3 Multiplying Polynomials In this section I will teach you how to multiply polynomials. Make sure you understand the distributive property and the rules on powers before starting this lesson. Just to be clear this lesson is a continuation of learning the various operations we can do with polynomials, namely: adding, subtracting, multiplying and dividing. These are the basic operations and as you advance in math you will learn other things about polynomials like factoring. Please practice multiplying polynomials as much as possible- you want to attempt a wide variety of problems to ensure you have the procedures down. Ch. 11 Section 4 Introduction to Quadratic Equations In this section I will introduce you to quadratic equations. The topic of quadratic equations is really a study of polynomials where the highest power (degree) is 2. Quadratic equations are very important in algebra and advance math so you want to work extra hard to master the concepts. As I was saying a quadratic equation is a type of polynomial. It goes without saying that you want to know about polynomials before studying quadratic equations. As you continue your study of algebra you will learn how to solve quadratic equations, graph quadratic equations/inequalities and a host of other skills that demonstrate why quadratic equations are so important in mathematics. Copyright 2013 TabletClass.com, LLC 43

44 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 12 Chapter 12: Rational Expressions This chapter takes the student through fundamental rational expressions to include ratios, proportions, percent and variation. Students will learn different methods to solve rational expression problems. The section on simplifying rational algebraic expressions starts by reviewing basic examples using numbers before introducing variable examples. Section Summary (circle / complete after chapter is finished): 1. Ratios and Proportions 2. Percent 3. Direct and Inverse Variation 4. Simplifying Rational Expressions Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 44

45 Ch. 12 Section 1 Ratios and Proportions In this section I will teach you the basics of ratios, rates and proportions. Rates and ratios are nothing more than fractions and proportions are two equal fractions. Before you get into this lesson make sure you have a solid understand of fractions and solving equations. Like I was saying rates and ratios are fractions but the key thing we will be focusing on with rates and ratios are there units of measure. For example, I can have the fraction 1/3 no big deal. But if I take that same fraction and write it as 1 teacher / 3 students I now would have a ratio- see the difference? Also ratio and rate problems are very common on tests like the SAT, ACT and even the GED- so make sure you practice everything I go over in the lesson. Example Set D Ch. 12 Section 2 Percent In this section I will teach you about percent. Of course percent is one of those math skills that we use all the time. For example when you are walking around the store and see the XBOX 360 you want is 25% off- I m sure many of you would be doing some quick mental math. Hey Mom and Dad lets buy the game as it is such a great deal- look how much we would be saving! In all seriousness percent is an extremely important topic and in my experience many students are not as good at it as they think. If I asked you to find 30% of $100 that should be easy for most students. However if I asked you 118 is 16% of what number? I would be impressed if you could answer the question quickly and confidently. My goal in this lesson is to get you to master percent not just the easy problems but the more difficult problems as well. As always it s critical that you practice this skill as percent is everywhere in math and real life. Copyright 2013 TabletClass.com, LLC 45

46 Ch. 12 Section 3 Direct and Inverse Variation In this section we will be studying direct and inverse variation. The concept of variation is simply how two or mare variables relate to one another. For example let s look at the formula A=BH the formula gives us the area of a rectangle. Now given the formula A=BH, what would happen to the area (A) if I made the base of the rectangle (B) larger and larger- the area would get larger and larger as well, correct? You see as I increase the value of B in this equation the value of A goes up as well- this is an example of direct variation. My lesson will go over many details about variation so make sure you take good notes and practice, practice, practice. Ch. 12 Section 4 Simplifying Rational Expressions In this section I will teach you how to simplify a rational expression. This is a big topic and requires many skills to master to include a strong understanding of fractions, powers and exponents and polynomials. Recall, that a rational number is a fraction where the numerator and denominator are integers. A rational expression (not number) is a fraction where the numerator and denominator are polynomials. When we simplify a fraction (rational number) we reduce it- example, simplify the fraction 3/9. Of course 3/9 = 1/3 so my answer is 1/3 the fully simplified fraction equivalent to 3/9. The concept is no different when we are talking about simplifying rational expressions- we simply look to write the expression in its simplest form. I can t state over state how important it is for you to master this skill as you will need it in the study of future algebra topics. Copyright 2013 TabletClass.com, LLC 46

47 TabletClass Math Pre-Algebra Course Follow Along Guidebook Chapter 13 Chapter 13: Introduction to Functions and Relations Functions and relations transcend all through mathematics. This chapter explains core concepts at the Pre-Algebra level and prepares the student for more advance study of the topic. Time is taken to explain the difference between a function and relation; and introduce the student to the language of functions to include the domain, range and linear/nonlinear functions. Section Summary (circle / complete after chapter is finished): 1. Introduction to Functions and Relations 2. Graphing Functions 3. Linear and Nonlinear Functions Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2013 TabletClass.com, LLC 47