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**The Mysterious World of Number Identity…**

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

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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.

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**Categories of Numbers in the REAL Number System**

Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers

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

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**Whole Numbers All of the counting numbers and zero.**

{0, 1, 2, 3, 4, 5, 6, 7, …}

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**Integers Are all of the natural numbers, their opposites and zero.**

{…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …}

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**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 =

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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 = … …

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**Venn Diagram of REAL Number System**

Rational Numbers Integers Whole Natural Irrational Numbers

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**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…

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**Classify each number as natural, whole, integer, rational, or irrational. Write as many as apply.**

… -5 ¾ -79 3 √16

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