Course Introduction

Time: 116 hours

Free Certificate
For example, we use fractions when we make measurements, configure ratios, and calculate proportions. We use decimals and percentages in finance, measurement, and weight. In this course we also study how to represent data visually, such as in bar and line graphs, and pie charts to convey data information quickly and accurately to an audience. We also explore how to interpret data, to help you make sense of a chart that outlines the current mortgage interest rates, so you can calculate how much money you will need to earn to pay off a bank loan. In the same way, you need to understand the latest statistics to create a winning fantasy football team.
First, read the course syllabus. Then, enroll in the course by clicking "Enroll me in this course". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.

Unit 1: Number Properties
In this unit we discuss some basic algebraic properties you may already know, which math instructors call "common sense" properties. We see uses of these properties every day.
For example, the commutative property tells us we can rearrange the order of the numbers and still get the same result: 3 + 2 = 5, and 2 + 3 = 5. The same is true for multiplication: 2 × 3 = 6, and 3 × 2 = 6. Other algebraic properties are less intuitive. For example, what happens when we multiply or divide a number by zero? Understanding these number properties provides the foundation for this course.
Completing this unit should take you approximately 6 hours.
Unit 2: Order of Operations
To avoid making errors, mathematicians follow a series of steps to simplify expressions that use the four basic operations, grouping symbols, and exponents. We call these steps the "order of operations." In this unit, we explore how to use exponents and grouping symbols to perform mathematical operations in the correct order.
For example, we can use exponents to write out a repeat multiplication, such as 2 × 2 × 2 × 2 × 2, or 2^{5}. We also examine the concept of the greatest common factor (GCF), the largest positive integer that divides evenly into a group of numbers with zero remainder. For example, for the set of numbers 18, 30, and 42 the GCF = 6. We also use the least common multiple (LCM) to determine the smallest number that two numbers can both divide into. For example, for the set of numbers two, and six, the LCM is six. Finally, we learn how to perform mathematical operations with negative numbers.
Completing this unit should take you approximately 23 hours.
Unit 3: Fractions
Fractions allow us to perform calculations with numbers that are not whole. For example, imagine you baked a pie. If your family eats half the pie for dessert one day, we use fractions to determine half a pie remains. If you eat another slice, you would use fractions yet again to see how much is left. We use fractions every day to calculate sale prices, measurements, money, gardening, and in many other situations. In this unit, we explore how to add, subtract, multiply, divide, and reduce fractions.
Completing this unit should take you approximately 33 hours.
Unit 4: Decimals
In this unit, we study decimals, which are simply another way to write fractions. For example, let's study some American currency. One dollar equals 100 cents; a quarter is 25 cents, or in decimal form, $0.25. We can write the meaning of a quarter as 25/100. This reduces to 1/4, which we read as onequarter. Decimals are everywhere, just like fractions. We use them in money, and in measuring lengths and amounts. In this unit, we study how to add, subtract, multiply and divide decimals and 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, we study ratios and proportions – mathematical concepts we use all the time, often without realizing it. For example,
 At the grocery store, have you ever compared unit prices for different packages of the same type of food? That is a ratio.
 When driving 65 mph (miles per hour) on the highway, have you ever determined how long it will take you to get to your destination? That is a proportion.
 In sports, statisticians use proportions to predict an athlete's performance, based on what they have accomplished in the past.
Here we explore how to write ratios, setup and solve proportions, and apply these skills to realworld experiences.
Completing this unit should take you approximately 8 hours.
Unit 6: Percentages
Now that we have studied fractions and decimals, we are ready to explore percents. Percents are just fractions and decimals written in a different way. For example, we can say 0.5 as a decimal, 1/2 as a fraction, and 50% as a percent. They all mean the same thing!
We see percents all the time in the real world, such as in sales at stores. For example, a sale on shirts may say that they are 50% off. So, a $10 shirt would be reduced to $5. A week later, the store may post a sign saying that there is an addition 20% off the sale price of the shirts. How do you determine the new discounted price of the shirt?
In this unit, we explore how to apply the rules of percentages. We convert between percents and fractions or decimals, and learn about percentage increases and decreases. We also examine how to calculate realworld uses of percents, such as restaurant tips and sale prices.
Completing this unit should take you approximately 13 hours.
Unit 7: Graphs and Charts
Once we have gathered data or performed calculations, we need to visualize the information to make sense of it. If you are making a presentation, it is much easier for your audience to read a graph or chart than to interpret meaning from a long list of numbers.
We use graphs and charts in almost every field. Businesses use them to show trends in growth. Politicians use them to explain demographics and voting trends in campaigns and elections. Since we use graphs and charts so often, it is important to know how to read and interpret them.
In this unit we discuss different types of graphs and charts used in mathematics. We explore how to create charts and graphs, interpret the results for each type of graph or chart, and work with the measures of central tendency for a data set.
Completing this unit should take you approximately 7 hours.
Course Feedback Survey
Please take a few minutes to give us feedback about this course. We appreciate your feedback, whether you completed the whole course or even just a few resources. Your feedback will help us make our courses better, and we use your feedback each time we make updates to our courses.
If you come across any urgent problems, email contact@saylor.org or post in our discussion forum.
Certificate Final Exam
Take this exam if you want to earn a free Course Completion Certificate.
To receive a free Course Completion Certificate, you will need to earn a grade of 70% or higher on this final exam. Your grade for the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again as many times as you want, with a 7day waiting period between each attempt.
Once you pass this final exam, you will be awarded a free Course Completion Certificate.