# Ch 1: Common Core Math Grade 8 - The Number System: Rational & Irrational Numbers

### About This Chapter

**Standard**: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. (CCSS.MATH.CONTENT.8.NS.A.1)

**Standard**: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. (CCSS.MATH.CONTENT.8.NS.A.2)

## About This Chapter

Upon mastering this standard, students will have a good grasp of rational and irrational numbers, comprehend how decimal expansion occurs in rational numbers and understand how to convert a decimal expansion. They will also be able to analyze irrational numbers by comparing sizes, finding them on a number line and more. Through these lessons, your students will learn how to do the following:

- Recognize the difference between rational and irrational numbers
- Describe decimal expansion of numbers
- Show the repetition and conversion of decimal expansion
- Exhibit how to graph rational numbers on a number line
- Detail how to estimate square roots

Once your students showcase their comprehension of decimal expansion, successfully graph on the number line diagram and exhibit their knowledge of estimating square roots, you will know they are grasping these Common Core standards for their grade level. The lessons and standards can help students get closer to achieving long-term goals like attending a quality college and securing jobs in fields that use math, such as computer science, operations research and finance.

### How to Use These Lessons in Your Classroom

Below are some suggestions to consider as you decide how to implement rational and irrational numbers into your curriculum and meet the Common Core standards.

#### Play the 'Rational or Irrational Number?' Game

You can have the students watch the 'What are Rational Numbers?' and 'What are Irrational Numbers?' lessons. After watching the videos, break the students into teams and have them compete by successfully identifying the number you write on the board or have written on a card. Is the number rational or irrational? The team with the most correct answers can receive a reward of your choosing. This is a great way to ensure students fully understand the difference between the two types of numbers.

#### Create a Group Graphing Exercise

After having your students watch the 'Graphing Rational Numbers on a Number Line' lesson, break them into groups of 2-3. Have them elect one team member to draw a number line on a piece of paper using a ruler. Any range of numbers is fine as long as there is an odd number of digits represented (ex. -3, -2, -1, 0, 1, 2, 3). Then, you can have students graph a variety of rational numbers of your choosing by having them place dots on numbers you choose. You can also have them graph numbers not represented on the line, challenging them to find fractions between whole numbers, whole numbers between fractions and more.

#### Use Quizzes to Gauge Comprehension

You can use the assessment quiz with each lesson as a way to gauge your students' comprehension of rational and irrational numbers after watching the video lessons. The answers on their quizzes can give you an idea of the areas your students might need to review. Have your them revisit any lessons they don't fully grasp.

### 1. What are Rational Numbers? - Definition & Examples

In this lesson, we will learn about rational numbers and their characteristics. We'll discover what they are, what they aren't and how to distinguish them from other types of numbers.

### 2. Decimal Expansion of Rational Numbers

Numbers can be represented in several different forms, including fractions and decimals. In this lesson, learn about decimal forms of numbers and how to convert repeating decimals to rational numbers.

### 3. Graphing Rational Numbers on a Number Line

Number lines have many uses both in mathematics and everyday life. This lesson will teach you how to graph numbers on a number line and give real-world examples of how to use number lines.

### 4. What are Irrational Numbers? - Definition & Examples

Irrational numbers may not be crazy, but they do sometimes bend our minds a little. Learn about common irrational numbers, like the square root of 2 and pi, as well as a few others that businessmen, artists, and scientists find useful.

### 5. Estimating Square Roots

Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.

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### Other Chapters

Other chapters within the Common Core Math Grade 8 - The Number System: Standards course