1. The Mysterious World of Number Identity…
What’s In A Number?
The Mysterious World of
Number Identity…

2. Focus 4 - Learning Goal #1: Students will know that there are numbers that are not rational, and approximate them with rational numbers. 4 3 2 1
In addition to level 3.0 and above and beyond what was taught in class, students may:
-Make connection with other concepts in math.
- Make connection with other content areas.
Students will know that there are numbers that are not rational, and approximate them with rational numbers.
- Convert a decimal expansion that repeats into a fraction.
- Approximate the square root of a number to the hundredth & explain the process.
- For all items listed as a 2, students can explain their process.
Students will know the subset of real numbers.
- Know that all numbers have a decimal expansion.
- Compare the size of irrational number.
- Locate approximately irrational numbers on a number line.
With help from the teacher, I have partial success with level 2 and 3.
Even with help, students have no success with the unit content.

3. Categories of Numbers in the REAL Number System
Natural Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers

4. Natural Numbers
Are the counting numbers
{1, 2, 3, 4, 5, 6, 7, 8, …}

5. Whole Numbers All of the counting numbers and zero.
{0, 1, 2, 3, 4, 5, 6, 7, …}

6. Integers Are all of the natural numbers, their opposites and zero.
{…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …}

7. Rational Numbers Numbers that can be expressed as a fraction (a/b).
This set includes the integers, terminating decimals, and repeating decimals.
Some examples:
2 = 2/1
3 ¼ = 13/4
-0.25 = -25/100
1/3 =

8. Irrational Numbers
Numbers that CANNOT be expressed as a fraction of integers.
In decimal form, they are the numbers that go on forever without a repeating pattern.
Some examples:
√2 = …
π = … …

9. Venn Diagram of REAL Number System
Rational Numbers
Integers
Whole
Natural
Irrational Numbers

10. Tree Diagram of Real Number System
0.5, 1.4, 0.256
0.3, 0.45 …
Π, √2
1/5, 4/11, 12/3
-5, -80
1, 2, 3…

11. Classify each number as natural, whole, integer, rational, or irrational. Write as many as apply.…
-5 ¾
-79 3
√16