## Topic outline

• #### Course Introduction

"Why is math important? Why do I have to learn math?" These are typical questions that you have most likely asked at one time or another in your education. While you may learn things in math class that you will not use again, the study of mathematics is still an important one for human development. Math is widely-used in daily activities (e.g. shopping, cooking, etc.) and in most careers (e.g. medicine, teaching, engineering, construction, business, statistics in psychology, etc.). Math is also considered a "universal language." One of the fundamental reasons why you learn math is to help you tackle problems, both mathematical and non-mathematical, with clear, concise, and logical steps. In this course, you will study important fundamental math concepts.

This course begins your journey into the "Real World Math" series. These courses are intended not just to help you learn basic algebra and geometry topics, but also to show you how these topics are used in everyday life. In this course, you will cover some of the most basic math applications, like decimals, percents, and even the dreaded "f-word," fractions. You will not only learn the theory behind these topics, but also how to apply these concepts to your life. You will learn some basic mathematical properties, such as the reflexive property, associative property, and others. The best part is that you most likely already know them, even if you did not know the proper mathematical names.

Let's start with fractions. Have fractions ever been bothersome to you? Do you think that there is no purpose for them? In this course, you will learn that fractions are all around us in the forms of measurement, ratios, and proportions-and we think you might change your tune on the subject. You will see how to solve those sometimes troubling fraction problems, like the ones that use 1 2/3 and 3 1/5, which don't divide as evenly as you'd like. In case you're not yet familiar with fractions, let's offer a common every day example: a recipe for making chocolate chip cookies. You see a recipe that calls for 2 1/3 cups of flour, 3/4 cup of sugar, and 1/2 teaspoon of vanilla, and you need to make 2 1/2 times the recipe amount. Each of these measurements involves fractions. If you want to make the right amount of cookies, you have to determine how much you need of each ingredient.

This course will also introduce you to decimals and percentages, which are widely used in money, finances, and measurement. Decimals are all around you, including when you download applications for your smart phone. Say, for example, you've just purchased the newest Angry Birds application for $0.99. The number 0.99 is a decimal. If you want to spend no more than$10.00, then you will have to determine how many other applications you can download without going over budget. In this course, you will learn how to solve complex decimal problems, such as 13.4561 - 21.03 and 301.21 x 140.31.

You will also learn to write ratios and solve proportions in the course. You are probably already very familiar with ratios, even if you're not aware of it. A recipe that calls for "2 parts milk to 1 part flour," or a speed limit sign that reads "55 miles per hour," or a newspaper ad listing apples at a cost of $2.99 per pound -- these are all examples of ratios. Ratios and proportions are particularly useful when doing an everyday activity like planning a party: "If I need two hams for nine guests, how many hams will I need for thirty guests?" Learning how to set up and solve problems like this is a very useful mathematical concept that is applicable to real life situations. Finally, have you wondered how graphs and charts are created with certain data? Data can be visually represented in various forms (bar graphs, circle graphs, etc.) to convey information to a reader. In this course, you will see data in common forms and will have to interpret data (for example, reading a chart of the most downloaded songs from iTunes or interpreting football statistics for your fantasy league). The final unit of the course pertains to charts and graphs and includes the interpretation and creation of various charts and graphs. • #### Unit 1: Number Properties Just as in life, there are certain things in math that make you shrug and say, "Well, duh. I knew that; it's common sense." This unit will discuss some of the basic algebraic properties which you already know, but may not necessarily know the names of, because they are what some math teachers refer to as the "common sense" properties. The really neat thing about these properties is that you can see their uses in everyday, non-mathematical ways. For example, if you drive to work, you "commute." Whether you are driving to work from home, or to home from work, you are making the same trip. (Ignoring those times you take a back road because you do not want to spend two hours sitting on the interstate, of course!) In math, the commutative property tells us when we can move numbers around and still get the same answer. Another example is the associative property. The people you hang out with are also known as your "associates." If you are hanging out with two friends, but one of them is in a different room, you still have the same group of friends. The same applies to certain mathematical situations. If you are grouping numbers, depending upon the situation, the grouping is not going to change anything. Completing this unit should take you approximately 9 hours. • #### 1.1: Laws and Properties of Addition • #### 1.1.1: Commutative Law of Addition • #### 1.1.2: Associative Law of Addition • #### 1.1.3: Identity Property of Addition • #### 1.1.4: Property Recognition Activity • #### 1.1.5: Inverse Property of Addition • #### 1.2: Laws and Properties of Multiplication • #### 1.2.1: Commutative Law of Multiplication • #### 1.2.2: Associative Law of Multiplication • #### 1.2.3: Identity Property of Multiplication • #### 1.2.4: Property Recognition Activity • #### 1.2.5: Inverse Property of Multiplication • #### 1.2.6: Multiplication by Zero • #### 1.3: Dividing by Zero Is Undefined • #### 1.4: Distributive Property • #### Topic 18 • #### Unit 2: Order of Operations In life, we often have procedures that everybody uses to avoid problems. When driving a car, for example: if you want to change lanes, you have to first look to make sure the lane is clear, activate your turn signal, check the lane again, move into the lane, and deactivate your turn signal. You do not move into the lane, activate your signal, make sure the lane is clear, and deactivate your signal. That can, and eventually will, cause a serious accident. In order to avoid costly errors, mathematicians had to agree on the series of steps that are needed to simplify expressions involving the four basic operations, grouping symbols, and exponents. This series of steps is known as the "order of operations" and is more commonly known as either PEMDAS or "Please Excuse My Dear Aunt Sally, she Left to Right." This tells us in which order to simplify the expression. (Tip: it is multiply OR divide and add OR subtract - whichever you see first.) Mathematicians also needed a way to quickly write out a repeated multiplication problem, like 2 x 2 x 2 x 2 x 2, so they invented the use of exponents. This unit will introduce you to the process of working with basic exponents. As you go higher, you will learn more about exponents. Another topic you will learn about in this unit is the concept of "greatest common factor." Mathematically, the greatest common factor (GCF) is the largest number you can divide two or more numbers by. In real life, it also makes appearances, both mathematical and non-mathematical. A detective trying to make connections between an arrested criminal and a suspected accomplice is going to be less interested in the facts that they have both eaten at McDonald's and both like strawberry milkshakes than in the fact that the suspected accomplice has been the criminal's best friend for twenty years. That fact is far greater to the investigation. The last topic you will cover is related to greatest common factor but is different. It is known as "least common multiple." Here, you are trying to determine the smallest number that two numbers can both divide into. Again, it appears in life. Let's say your favorite radio station is running a promotion: every fifth caller receives free concert tickets, and every twelfth caller receives a free gas card. How long will it take before they have a caller who receives both prizes on the same phone call? This is an example of using the least common multiple. (In case you are wondering, it would be the 60th caller who won both prizes.) Completing this unit should take you approximately 22 hours. • #### 2.1: Greatest Common Divisor/Factor • #### 2.2: Least Common Multiple • #### 2.3: Negative Numbers • #### 2.3.1: Negative Numbers Introduction • #### 2.3.2: Adding Negative Numbers • #### 2.3.3: Adding Integers with Different Signs • #### 2.3.4: Adding/Subtracting Negative Numbers • #### 2.3.5: Multiplying Positive and Negative Numbers • #### 2.3.6: Dividing Positive and Negative Numbers • #### 2.4: Exponent Basics • #### 2.4.1: Understanding Exponents • #### 2.4.2: Level One Exponents • #### 2.5: Order of Operations • #### 2.5.1: Introduction to Order of Operations • #### 2.5.2: Order of Operations • #### Unit 3: Fractions Fractions are very easy to work with if you learn the rules. After all, fractions are everywhere. Have you ever eaten a Hershey's chocolate bar? It is conveniently broken up into little pieces, allowing you the option to devour in big bites or to savor tiny little morsels. Let's say you have a Hershey's bar sitting on your dining room table. Your oldest child cheerfully announces that she has eaten half of the bar, and her younger brother has eaten a quarter of the bar. If you know how to work with fractions, you can quickly calculate how much of the bar is left. Fractions appear in many other situations such as sale prices, measurements, money, gardening; the list of applications is virtually endless. In this unit, you will learn to work with fractions. You will learn how to reduce them, how to add/subtract/multiply/divide them, and how to apply them to real-world situations. Completing this unit should take you approximately 38 hours. • #### 3.1: Fraction Basics • #### 3.1.1: Identifying Fraction Parts • #### 3.1.2: Equivalent Fractions • #### 3.1.3: Fraction Types • #### 3.1.3.1: Proper and Improper Fractions • #### 3.1.3.2: Mixed Numbers and Improper Fractions • #### 3.1.3.3: Converting Fractions • #### 3.1.3.3.1: Changing Improper Fractions to Mixed Numbers • #### 3.1.3.3.2: Changing Mixed Numbers to Improper Fractions • #### 3.1.4: Fractions in Lowest Terms • #### 3.1.5: Fractions in Highest Terms • #### 3.1.6: Finding Common Denominators • #### 3.2: Fractions Operations • #### 3.2.1: Adding and Subtracting • #### 3.2.1.1: Adding Fractions with Like Denominators • #### 3.2.1.2: Subtracting Fractions with Like Denominators • #### 3.2.1.3: Adding Fractions with Unlike Denominators • #### 3.2.1.4: Subtracting Fractions with Unlike Denominators • #### 3.2.1.5: Adding and Subtracting Fractions with Different Signs • #### 3.2.2: Adding and Subtracting Mixed Numbers • #### 3.2.2.1: Adding Mixed Numbers with Like Denominators • #### 3.2.2.2: Subtracting Mixed Numbers with Like Denominators • #### 3.2.2.3: Adding Mixed Numbers with Unlike Denominators • #### 3.2.2.4: Subtracting Mixed Numbers with Unlike Denominators • #### 3.2.3: Applications of Adding and Subtracting Fractions • #### 3.2.4: Multiplying • #### 3.2.4.1: Multiplying Fractions • #### 3.2.4.2: Multiplying Mixed Numbers • #### 3.2.5: Dividing • #### 3.2.5.1: Dividing Fractions • #### 3.2.5.2: Dividing Mixed Numbers • #### 3.2.6: Applications of Multiplying and Dividing Fractions • #### 3.3: Order of Operations • #### 3.3.1: Order of Operations with Fractions • #### 3.3.2: Complex Fractions • #### Unit 4: Decimals In this unit, you will turn your attention to the "fraternal twin" of fractions: decimals. Yes, decimals are really just fractions in disguise! Who knew? For example, look at (American) money. A dollar is 100 cents; a quarter is 25 cents, or in decimal form,$0.25. The fraction 25/100 reduces to 1/4, which is read as "one-quarter." Decimals are fractions, and fractions are decimals. It's all in how you write them.

Decimals are everywhere, just like fractions. You cannot go shopping without encountering decimals. Whether you are adding up totals on your shopping list, calculating your change, or even just measuring the length of something, you will use decimals. If you add up all your purchases, find that your total comes to $17.31, and you hand the cashier$20, you need to know how to determine your change to make sure the cashier gives you back the correct amount of money. If you are measuring the length of your wall in order to fit a couch there, you might find that the wall's length is in between two lengths, measuring at, say, 11.5 ft. You have to know how to deal with decimals to approximate distances.

In this unit, you will learn how to add/subtract/multiply/divide decimals as well as how to convert between fraction and decimal form.

Completing this unit should take you approximately 26 hours.

• #### Unit 5: Ratios and Proportions

In this unit, you will study ratios and proportions. These are mathematical concepts you use all the time, probably without even realizing it. Have you ever been in line at a donut store, comparing the number of chocolate donuts to the number of customers? That's a ratio. Perhaps you are telling your vet how many times a week your dog drags you outside for an extended walk. That's also a ratio. Have you ever been driving on a trip, going around 75 mph, and wanted to know how long it would take to reach your destination, which was only 35 miles away? You would find the answer using a proportion. In sports, statisticians use proportions to predict an athlete's production, based on what they've done up to that point. In this unit, you will learn how to write ratios, how to set-up and solve proportions, and how to apply these skills to real-world experiences.

Completing this unit should take you approximately 9 hours.

• #### Unit 6: Percentages

In this course, you have already studied fractions and decimals. In this unit, you will study the other "fraternal twin" of fractions: percents, which are actually fractions and decimals in disguise. (Perhaps we should call them "fraternal triplets.") Going back to our example with decimals: we established that a dollar is 100 cents, a quarter is 25 cents, and the fraction form would be 25/100, which reduces to 1/4. A percentage is simply a fraction whose denominator is 100. Therefore, 25/100 becomes 25%. Because it is also 0.25, the percent is a fraction which is a decimal, which in turn is a percent. It's the Circle of Math. (Cue music from "The Lion King.")

Percents appear all over the place in life, especially when it comes to buying products. If you are considering whether to buy clothes at one store that has a sale with 65% off or a second store that has a sale with 50% off and an additional 15% discount off the sale price, you might be surprised to learn that the two sales are not the same. For those who follow the stock market, you might see the news talking about how your stock has had an increase of 70%. What does that mean?

In this unit, you will learn the rules of percentages and how to apply them. You will learn to convert percentages to and from fractions and decimals. You will learn about percent increase and decrease, which comes into play when you are out shopping. You will also learn (to the delight of shoppers everywhere) exactly how to calculate sale prices, restaurant tips, and other similar items.

Completing this unit should take you approximately 17 hours.

• #### Unit 7: Graphs and Charts

The list of available graph and chart applications is endless. You may have seen applications such as trying to understand voting trends and demographics for presidential campaigns and elections. Or, a business may require graphs and charts to forecast employment growth for a specific time period. Or, you may belong to a fantasy football or baseball team, and you may need to analyze the history of points that players have against certain teams as well as other statistics. In reading a news article that provides a chart, you may want to determine what information the chart provides. Using graphs and charts is a way to convey data that is easy to understand for a specific audience. Knowing how to read and interpret these items is of utmost importance in life, because charts and graphs can be manipulated to misrepresent the data.

This unit discusses various topics when using graphs and charts in mathematics. For each type of graph in the unit, you will need to create a graph as well as interpret the results of this type of graph. You will learn to create charts and graphs (stem-and-leaf plots, line graphs, bar graphs, box-and-whisker plots, circle or pie graphs, and pictographs), read charts, and work with the measures of central tendency for a data set.

Completing this unit should take you approximately 17 hours.