G8

Copyright © Swun Math Grade 8 Unit 1 Lesson 3 P TE

Rational vs. Irrational Numbers

Procedural Lesson

Grade 8 · Unit 1 · Lesson 3
MC: 8 .NS. 1

Problem of the Day

Objective: I will identify rational and irrational numbers and the difference between them.

Vocabulary Teacher Resources

Squared Numbers (Perfect Square): the result

after multiplying an integer by itself

Rational Numbers: whole numbers, fractions,

and decimals represented as a ratio of two

integers; can be represented in fractional form:

풙풙

풚풚

integers and y ≠ zero

1.5 =

3

2 =^ ratio^

Irrational Numbers: the set of all numbers that

cannot be written as a ratio of two integers; it

cannot be written as a simple fraction because

the decimal is non-terminating and non-

repeating

0.101101110... , �^23 ,휋휋,√ 10 ,√1.6,−√ 123

Considerations:

Review with students how to take the square roots of

numbers. It would be helpful if they made a list of

perfect squares to keep handy. Calculator will help

students see the actual value of an irrational number.

Continue to encourage students to use the terms

“rational numbers” and “irrational numbers” in the

right context.

Steps:

1. Determine if the number can be expressed as
   a fraction.
    If so, the number is rational.
    Check for terminating/repeating
   decimals.
    Look for perfect squares.
    If not, the number is irrational.


2. Justify your answer.

Application of MPs:

MP2: How are irrational numbers related to rational

numbers?

Irrational numbers are ______________ and

rational numbers are ______________.

MP8: How would you prove that you are dealing with

a rational number?

Proof that I am dealing with a rational number

is ______________.

1 2 3 4 5 6 7 8

*  * * * *

MPs

Applied MP

* Embedded MP

Student Journal Pages

10 - 15