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LESSON
1.3 Ordering Real Numbers
How do you order a set of real numbers?
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.
ADDITIONAL EXAMPLE 1
Compare. Write <, >, or =.
A.
B.
<
>
ADDITIONAL EXAMPLE 2
Order
, and 3.25 from greatest to least.
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
Pablo 4.6 mm, Julien
Julien:
Lisa:
mm, Joe:
mm,
mm
mm,
mm, Pablo 4.6 mm
1.3 LESSON QUIZ
8.2.B, 8.2.D
1. Compare. Write <, >, or =.
<
2. Order 10.5,
least.
, and
+ 1 from greatest to
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
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
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
How do you order a set of real numbers?
Sample answer:
Find their approximate decimal values and order
them.