Classifying The Real Number System

Math Response

BELL-RINGER QUESTION

The graph of a linear function is shown

on the coordinate grid.  What is the

slope of the linear function displayed?

Type answer here

Correct Answer: \frac{1}{4}

Deg^°

Rad

Directions: Following along with the video provided, take notes with illustration for the categories of the real-number system.

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VIDEO NOTES: Understanding the Categories of The Real Number System

Multiple Choice

PARTNER PRACTICE
1. In which section of the diagram does the number -⁶/₃ belong?

• Rational Numbers

• Counting Numbers

• Whole Numbers

• Integers

Multiple Choice

PARTNER PRACTICE
2. Which of the following statements is always true?

• All integers are counting numbers.

• All rational numbers are integers.

• All integers are whole numbers.

• All counting numbers are whole numbers.

Multiple Choice

PARTNER PRACTICE
3. Which best describes all possible classifications of the following set of numbers?

{0, 4, √25, 32}

I - Counting Numbers

II - Integers

III - Rational Numbers

IV - Whole Numbers

• IV only

• I and IV only

• II, III and IV only

• I, II, III and IV

Categorize

Options (9)

An irrational number can also be a real number.

The square root of 4 is a real number.

The number 0 is considered a real number.

Pi is an irrational number.

Every real number can be represented on the number line.

All real numbers are rational numbers.

The square root of -1 is a real number.

The number 1/0 is a real number.

The number 2.5 is not a real number.

PARTNER PRACTICE

4. Determine if the following statements are true or false. 

TRUE

FALSE

Multiple Choice

PARTNER PRACTICE

5. Which of the following statements is false regarding The Real Number System and subsets? 

• An irrational number can also be a real number.

• A whole number is also an integer.

• A negative decimal can still be considered an integer.

• A radical (square root) is always an irrational number.

Categorize

Options (18)

$$\frac{22}{11}$$  

$$-3$$  

$$\frac{0}{5}$$  

$$\sqrt{9}$$  

$$-\frac{3}{4}$$  

$$2.5$$  

$$0.75$$  

$$\frac{8}{3}$$  

$$\sqrt{2}$$  

$$e$$  

$$\sqrt{3}$$  

$$\sqrt[3]{5}$$  

\sqrt{-1}

$$2+\sqrt{3}i$$  

$$\frac{1}{0}$$  

$$e^{\pi i}+1$$  

$$\sqrt[3]{125}$$  

$$1.414114111411114...$$  

PARTNER PRACTICE

6. Classify the given number using DESMOS to convert if necessary.

Integers

Rational Numbers

Irrational Numbers

Non-Real Numbers

Multiple Choice

EXIT TICKET 02/10 - TEK 8.2A

Which Venn-diagram correctly represents the relationship between rational numbers and irrational numbers?