Whats In A Number The Mysterious World of

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

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 0 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.

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

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

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

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

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 = 0. 333333333333

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 = 1. 4142… • π = 3. 1415… • 45. 9492…

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

Tree Diagram of Real Number System 0. 5, 1. 4, 0. 256 0. 3, 0. 45 1/ -5, -80 1, 2, 3… 4 2 5, /11, 1 /3 0. 6392518… Π, √ 2

Classify each number as natural, whole, integer, rational, or irrational. Write as many as apply. 1. 2. 3. 4. 5. 6. 7. 4569594… -5 ¾ -79 3 0 √ 16