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# Operation Rational Irrational Numbers

Lesson 6 of 15

## Objective: SWBAT know when the sum or product of rational and irrational numbers is rational or irrational.

## Big Idea: Real numbers are either rational or irrational. But do we know the nature of sums and products of these real numbers?

*75 minutes*

#### Accessing Prior Knowledge

*20 min*

At the start of class, I hand each student an Entrance_Card. I intend students to work independently on this task. When students are done, I go over the questions with them and then I allow the students to play an rational or irrational number game on the computer for a few minutes. After they have several minutes to play the game, I call on a student to explain the difference between a rational and an irrational number using examples.

**Teacher Note about Entrance card question 1b: **Students tend to define rational numbers as :”numbers that can be written as a fraction” The problem with this is that irrational numbers such as the square root of 3 are also fractions. A better definition is that rational numbers are “numbers that can be written as a fraction of integers”.

Before moving on to the main activity for the day, I use the **thumb rule **to assess the students on their ability to identify rational and irrational numbers. The site below may help those students who need it the extra help.

**Additional Resources:**

*expand content*

I have one section of 8th grade Algebra, this will be an excellent resource to use with them. It flows very nicely and encourages the students to use higher level thinking.

| 2 years ago | Reply*Responding to stacey rose*

Really though, it's my first year in 8th, and I studied to teach elementary school! Am I overlooking answer keys? I'd hate to be making a mistake in my work and mess up my students' understanding because of it! Thanks :) -Miss Impagliatelli

| 2 years ago | Reply*Responding to Filiberto Santiago-Lizardi*

Hi Filiberto, your comment on my lesson is priceless to me. Thank you. It was done while I was still getting the "hang of it". Later lessons I think get a little user friendlier. Good luck to you and thanks again!

Mauricio

| 2 years ago | Reply

Hi Mauricio,

Thank you for sharing this lesson plan for teaching rational and irrational numbers. Your lesson is a true student-centered learning experience. All three components are intuitive and provide multiple points of entry. Your ideas are great! Thank you.

Filiberto Santiago-Lizardi.

| 2 years ago | Reply

*expand comments*

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- UNIT 1: Number Sense
- UNIT 2: Solving Linear Equations
- UNIT 3: Relationships between Quantities/Reasoning with Equations
- UNIT 4: Powers and Exponents
- UNIT 5: Congruence and Similarity
- UNIT 6: Systems of Linear Equations
- UNIT 7: Functions
- UNIT 8: Advanced Equations and Functions
- UNIT 9: The Pythagorean Theorem
- UNIT 10: Volumes of Cylinders, Cones, and Spheres
- UNIT 11: Bivariate Data

- LESSON 1: Linear Patterns
- LESSON 2: Algebra Match
- LESSON 3: In Linear Relationships
- LESSON 4: Making It Clear
- LESSON 5: Calendar Clever
- LESSON 6: Operation Rational Irrational Numbers
- LESSON 7: Absolutely
- LESSON 8: Discovering Slopes
- LESSON 9: Transforming Formulas
- LESSON 10: Inequality Connection
- LESSON 11: Slope Intercept Scenarios
- LESSON 12: Separate the Radicals
- LESSON 13: Two Variable Inequalities
- LESSON 14: Graphing Inequalities (Vertical and Horizontal Boundaries)
- LESSON 15: Round Robin Review ( Unit 3 )