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(^) Copyright © Swun Math Grade 8 Unit 1 Lesson 2 C TE

Rational vs. Irrational Numbers

Conceptual Lesson

Grade 8 · Unit 1 · Lesson 2
MC: 8 .NS. 1

Problem of the Day

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

Vocabulary Teacher Resources

Whole Numbers: t he natural numbers, including 0

0, 1, 2, 3, ...

Integers: the set of all counting numbers, including

0, and their opposites

... ─3, ─2, ─1, 0, 1, 2, 3, ...

Squared Numbers (Perfect Square): the result after

multiplying an integer by itself

Real Numbers: both rational and irrational numbers

Rational Numbers: whole numbers, fractions, and

decimals represented as a ratio of two integers; can

be represented in fractional form:

where 푥푥푦푦 are integers and y ≠ zero.

1.5 =

3

2 = ratio^

Irrational Numbers: the set of all numbers that

cannot be written as a ratio; cannot be written as a

simple fraction because the decimal is non-

terminating and non-repeating

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

Considerations:

Students can draw a representation of rational

numbers or come up with a scenario where a rational

number would be needed. Have student share

findings with one another and explain their thinking.

Review with students how to take the square root of a

number from Grade 8, Unit 1. Perfect squares are

rational numbers. Calculators 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 or 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 _______.

MP5: Is there a tool you can use to help you find

your answer?

A tool I can use to help me find my answer is

______________.

MPs

Applied MP

* Embedded MP

1 2 3 4 5 6 7 8

*   *

Student Journal Pages

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