Number Map Notes Handout NUMBER MAP NOTES
Project: Real Number Classification (TEKS 7.1.2A)
Name: __________________________
Date: ___________________________
THE REAL NUMBER SYSTEM
All the numbers we work with in 7th grade are part of the Real Number System . We can organize these numbers into specific groups, or "subsets," based on their characteristics.
SUBSET BLUEPRINTS
Neighborhood Definition & Key Characteristics Examples Natural Numbers The "counting" numbers. Start at 1 and go up by 1. 1, 2, 3, 4... Whole Numbers All natural numbers PLUS the number __________. 0, 1, 2, 3... Integers Whole numbers and their opposites (negative whole numbers). No decimals or fractions! -3, -2, -1, 0, 1, 2... Rational Numbers Any number that can be written as a ratio (fraction) \( \frac{a}{b} \). Includes terminating or repeating decimals. 1/2, -0.75, 5, 0.333... Irrational Numbers Numbers that CANNOT be written as fractions. Decimals that never end and never repeat. \( \pi \), \( \sqrt{2} \), 1.23456...
THE REAL NUMBER MAP
Rational Numbers
Integers
Whole
Natural
Irrational
Disconnected from Rational numbers
REAL NUMBERS
PRO TIP:
If a number can be simplified, simplify it BEFORE you classify it! For example, \( \sqrt{25} \) is actually 5, so it is a Natural number!
Check Your Understanding
Is 0 a Natural number? Why or why not?
Category Catch Worksheet CATEGORY CATCH
Field Practice: Real Number Classification
Name: __________________________
Date: ___________________________
PART 1: THE SORTING BIN
-12 0 \( \pi \) 15 \( \frac{2}{3} \) \( \sqrt{49} \) -3.5 \( \sqrt{11} \) 0.666... -1 8.4
RATIONAL
INTEGERS
WHOLE
NATURAL
IRRATIONAL
PART 2: BLUEPRINT SPECIFICATIONS
Check ALL boxes that apply to each number.
Number Natural Whole Integer Rational Irrational -25 \( \sqrt{100} \) 0.45 \( \pi \) 0
PART 3: SURVEY THE SITE
1. All whole numbers are integers. True or False?
Explain your reasoning:
2. A number can be both rational and irrational at the same time. True or False?
Explain your reasoning:
3. List a number that is a Rational Number but NOT an Integer.
Number Neighborhoods Slides Number Neighborhoods
TEKS 7.1.2A: Real Number Subsets
The Big Picture
Just like houses are organized into neighborhoods , numbers are organized into subsets .
"Every number has a specific address where it belongs based on its properties."
The inner core
Natural Numbers
Numbers we use for counting .
1, 2, 3, 4...
Whole Numbers
Natural numbers PLUS ZERO .
0, 1, 2, 3...
Is 2.5 a whole number? NO! No decimals allowed here!
The Integers
Integers include all Whole Numbers and their Opposites (negatives).
...-3, -2, -1, 0, 1, 2...
Warning
Still no fractions or decimals that aren't equivalent to whole numbers!
Rational Numbers
The word Rational contains the word RATIO .
Any number that can be written as a FRACTION \( \frac{a}{b} \).
Terminating Decimals (0.5)
Repeating Decimals (0.333...)
Mixed Numbers (\( 1\frac{1}{2} \))
All Integers (since \( -5 = \frac{-5}{1} \))
\( \frac{2}{3} \)
The Outskirts: Irrational
Cannot be written as a fraction!
These decimals never end and never repeat .
\( \pi \) 3.14159...
\( \sqrt{2} \) 1.41421...
\( \sqrt{7} \) 2.64575...
The Blueprint Summary
RATIONAL
INTEGERS
WHOLE
NATURAL
Irrational
QUICK CHALLENGE!
Where does this number belong?
\( \sqrt{49} \)
Is it 49?
It simplifies to 7!
Where does 7 go?
NATURAL, WHOLE, INTEGER, and RATIONAL!
Real Number Key ANSWER KEY
Project: Real Number Classification (TEKS 7.1.2A)
Teacher Resource
NOT FOR STUDENTS
NUMBER MAP NOTES: KEY
Guided Definitions
Whole Numbers: Natural numbers PLUS the number ZERO.Rational Numbers: Any number written as a ratio or fraction.Irrational Numbers: Decimals that never end and never repeat.
Check Your Understanding
Is 0 a Natural number? NO. Natural numbers start at 1 (counting numbers). 0 is a Whole number.
CATEGORY CATCH: KEY
PART 1: THE SORTING BIN
RATIONAL
2/3 -3.5 0.666... 8.4
INTEGERS
-12 -1
WHOLE
0
NATURAL
15 sqrt(49)
IRRATIONAL
pi sqrt(11)
PART 2: BLUEPRINT SPECIFICATIONS
Number Natural Whole Integer Rational Irrational -25 X X \( \sqrt{100} = 10 \) X X X X 0.45 X \( \pi \) X 0 X X X
PART 3: SURVEY THE SITE
1. All whole numbers are integers. True or False?
TRUE. Every number in the "Whole" circle is inside the larger "Integer" circle. Whole numbers (0, 1, 2...) are all part of the integer set.
2. A number can be both rational and irrational at the same time. True or False?
FALSE. These are two separate categories. A number is either rational (can be a fraction) or irrational (cannot be a fraction). They don't overlap.
3. List a number that is a Rational Number but NOT an Integer.
Answers vary: 2.5, 3/4, -0.1, etc. (Any fraction or decimal that does not simplify to a whole number).
