1. 1.3
Ordering Real Numbers
How do you order a set of real numbers?

2. Texas Essential Knowledge and Skills
The student is expected to:
Number and operations—8.2.D
Order a set of real numbers arising from mathematical and real-world contexts.
Number and operations—8.2.B
Approximate the value of an irrational number, including and square roots of numbers less than 225, and locate that rational number approximation on a number line.
Mathematical Processes
8.1.D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

3. ADDITIONAL EXAMPLE 1
Compare. Write <, >, or =. A.
< B.
>

4. ADDITIONAL EXAMPLE 2
Order , and 3.25 from greatest to least.

5. ADDITIONAL EXAMPLE 3
The diameter of a meteorite in millimeters is calculated by four different methods. Order the results from least to greatest.
Joe mm, Lisa mm,
Pablo 4.6 mm, Julien mm
Julien: mm, Joe: mm,
Lisa: mm, Pablo 4.6 mm

6. 1.3 LESSON QUIZ 8.2.B, 8.2.D 1. Compare. Write <, >, or =. <
Order 10.5, , and from greatest to least.

7. 3.
A length in centimeters is calculated differently by four different people. Order their calculations from least to greatest.
K.D. cm, Silvio cm, Paula cm, Luis

8. Sample answer: 4.5 is between 4.1 and 4.8
Have students investigate whether there are infinitely many numbers between two numbers by giving examples for each of the following.
Between any two rational numbers there is at least one other rational number.
Sample answer: 4.5 is between 4.1 and 4.8
Between any two irrational numbers there is at least one rational number.
Sample answer: 4.5 is between and

9. Sample answer: is between 3.1 and 3.6
Have students investigate whether there are infinitely many numbers between two numbers by giving examples for each of the following.
Between any two rational numbers there is at least one irrational number.
Sample answer: is between 3.1 and 3.6
Between any two irrational numbers there is at least one irrational number.
Sample answer: is between and

10. How do you order a set of real numbers?
Sample answer:
Find their approximate decimal values and order them.