1. Warm Up
Each square root is between two integers. Name the two integers.
Use a calculator to find each value. Round to the nearest tenth. 1.
10 and 11 2.
3 and 4 3.
1.4 4.
11.1

2. The Real Number System

3. Objective: In this lesson you’ll:
Differentiate between rational and irrational numbers.

4. We do the same with numbers!
Did you know????
Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko.
Animal
Reptile
We do the same with numbers!
Lizard
zzzzzz
Gecko

5. Naturals – natural counting numbers { 1, 2, 3, ….}
Words to know….
Naturals – natural counting numbers { 1, 2, 3, ….}
Wholes – natural counting numbers and zero
{ 0,1, 2, 3....}
Integers – Positive or negative natural numbers
or zero
{ -2, -1, 0, 1, 2,…}

6. Words to know…. Rational Number – any number which can be written as a
fraction.
Irrational Number –
Any decimal number which can’t be written as a fraction.
A non-terminating and non-repeating decimal.
Example –
Real – rational numbers and irrational numbers.

7. Real Numbers 4.5 -3 -1 -7 3 1 2 Irrational Numbers Rational Numbers
Integers -3 -1 -7
Whole Numbers
Natural Numbers 3 1 2

8. Sets of Numbers – (using a tree map)
Real numbers
Rationals
Irrationals
fractions/decimals
Integers
Negative Integers
Wholes
Zero
Naturals

9. Let’s practice
Directions: Identify each number below as natural, whole, integer, rational, irrational, or real. More than one answer can apply.
integer, rational, real 1.
Rational, real 3.
Whole, integer, rational, real 2. 4.
rational, real

10. Let’s practice
Directions: Identify each number below as natural, whole, integer, rational, irrational, or real. More than one answer can apply.
Natural, Whole, integer, rational, real 7. 5.
irrational, real
integer, rational, real
Natural, Whole, integer, rational, real 6. 8.

11. Use <, >, or = to compare1. = 5.
< 2.
> 6.
>
< 3. 7.
< = 4. 8.

12. 1. 2. 3. 4. Lesson Quiz real, irrational rational
Write all classifications that apply to each number. 1. 2.
real, integer, rational
real, irrational 3. 4.
rational
not a real number