lesson how can you describe relationships between sets of real numbers? sets of real numbers 1.2

LESSON

How can you describe relationships between sets of real numbers?

Sets of Real Numbers1.2

Texas Essential Knowledge and Skills

The student is expected to:

Number and operations—8.2.A

Extend previous knowledge of sets and subsets using a visual representation todescribe relationships between sets of real numbers.

Mathematical Processes

8.1.F

Analyze mathematical relationships to connect and communicate mathematical ideas.

ADDITIONAL EXAMPLE 1Write all names that apply to each number.

integer, rational, realA. –10

B. whole, integer, rational, real

ADDITIONAL EXAMPLE 2

No integers are whole numbers.

False; every whole number is also an integer.

Tell whether the given statement is true or false. Explain your choice.

ADDITIONAL EXAMPLE 3

the amount of time that has passed since midnight

Identify the set of numbers that best describes the situation. Explain your choice.

The set of real numbers; time is continuous, so the amount of time can be rational or irrational.

1.2 LESSON QUIZ8.2.A

1.

rational, real

2. Tell whether the given statement is true or false. Explain your choice. All numbers between 1 and 2 are rational numbers.

False; is an example of an irrational number between 1 and 2.

Write all the names that apply to the number .

3.

Integers; each number is an integer, but only three are whole numbers.

Identify the set of numbers that best describes the situation. Explain your choice.The choices on a survey question change the total points for the survey by –2, –1, 0, 1, or 2 points.

Have students consider the concept of restricted domain for the sets of numbers that describe situations. For example, the number of sisters a person has can best be described by whole numbers, but no one has ever had 1,500 sisters. An area code is an integer or whole number between 200 and 999.

Have students use a source, such as the Guinness Book of World Records, and give examples of sets of numbers that describe situations where the domain is restricted. Ask whether the restriction may be changed in the future.

How can you describe relationships between sets of real numbers?

Sample answer:Describe them as two different sets, or one set as being a subset of another.