Chapter 1: Probability, Percent, and Rational Number Equivalence

What This Chapter Is About

This chapter starts by looking at probability, which is a way of figuring out how likely something is to happen. As you learn about probability, you'll also review math you already know—like working with whole numbers and fractions.

You'll practice basic counting skills and learn how to list all the possible results of an event, called the sample space. You'll also learn the difference between two types of probability:

• Theoretical probability – what should happen based on math and reasoning
• Experimental probability – what actually happens when you try something out and collect data

We start the year with probability for two reasons. First, it helps you see math as a tool for exploring the real world. Second, these activities help your class learn to talk about math together and work as a team.

Next, you'll review and get better at working with fractions, percents, and decimals. These are all different ways of showing a part of a whole. You'll also practice comparing and putting fractions in order, including both positive and negative fractions.

Finally, the chapter ends with a section on solving problems using percents and fractions. This includes real-life situations like discounts (price reductions), interest (extra money earned or owed), taxes, tips, and percent increase or decrease.

Key Vocabulary

chance, decimal, experimental probability, fraction, frequency (how often something happens), outcome (a possible result), percent, probability, ratio (a comparison between two numbers), theoretical probability

Connecting to What You Already Know

What You've Learned Before:

You've already learned about ratios, which compare two amounts. Ratios can compare a part to a whole, or a part to another part. In this chapter, we'll focus only on part-to-whole comparisons. That's because probability, fractions, decimals, and percents are all part-to-whole relationships. (Later, in Chapter 4, you'll learn about part-to-part comparisons, called "odds.")

You've also used addition, subtraction, multiplication, and division with fractions and decimals before. You've probably used number lines and bar models to show fractions, percents, and decimals.

In 6th grade, you placed both positive and negative numbers on a number line. But you didn't do math with negative numbers yet—that starts in 7th grade, in Chapter 2.

What's Coming Next:

This chapter is just an introduction to probability. You'll dive deeper into it later, in Chapter 7. The ideas you learn now about chance, theoretical probability, and experimental probability will help you understand more advanced topics later on.