1. Warmup Group the following numbers by similar characteristics. 6, ½, 3.2, 7, -5, , 3.1714…, 4, ¼, ¾, 0.75, 9, -1, 4, 0.5, 0.3, 2, 0.6, -9, 7.1, 1/3, 0.25

2. Number Sense AIMS Math Spring, 2009

3. Number Sets Real Numbers Rational Numbers Irrational Numbers Anything that can be written as a ratio Non-Repeating IntegersNon-Ending IntegersNon-Ending positives and negatives Decimals positives and negatives Decimals Whole NumbersRoots that are not Whole NumbersRoots that are not 0 Perfect 0 Perfect Numbers that Natural or Counting cannot be Natural or Counting cannot be Numbers written Numbers written as ratios as ratios 1, 2, 3, 4, … 1, 2, 3, 4, …

4. Definitions Real Numbers: Any number that can name a position on a number line is a real number. Every position on a number line can be named by a real number in some form. Irrational Numbers: Is a number that cannot be written as the quotient of two integers. Rational Numbers: Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions.

5. Definitions Integers: The counting numbers (1, 2, 3,...), their opposites (-1, -2, -3,...), and zero are integers Whole Numbers: Zero and the positive integers are the whole numbers. Natural or Counting Numbers: This set includes all of the whole numbers except zero (1, 2, 3,....)

6. Definitions Finite - having limits, a beginning and an end. Infinite: having no limits, no beginning and no end. Set: A collection of distinct elements as in the set of real numbers. Subset: A set contained within another set, as in as in the set of integers contained within the set of rational numbers Distance: Difference between locations. Usually found by subtracting. Cannot be negative.

7. Video Lesson Khan Academy – Number Sets #1 Khan Academy – Number Sets #1

8. To what number set does this belong? Number of people in Casa Grande Amount of carpet needed for this room Amount of oil in a car Sand on a Beach {-2, -5, 3, 1} {1/2, ¾, 7/8, 0, 16} {1, 2, 3, …} {0, 1, 2, 3, …}

10. Square Roots Is each rational or irrational? Give its value (if rational) or approximation (if irrational). √81 √ 36 √ 85 √ 225 √ 10 √ 9 √ 400 √ 100 √ 1 √ 1,000 21 √ 21 140 √ 140 172 √ 172 356 √ 356 400 √ 400 0 √ 0 625 √ 625 25 √ 25 28 √ 28 35 √ 35

11. Perfect Squares 02=02=02=02= 12=12=12=12= 22=22=22=22= 32=32=32=32= 42=42=42=42= 52=52=52=52= 62=62=62=62= 72=72=72=72= 82=82=82=82= 92=92=92=92= 10 2 = 11 2 = 12 2 = 13 2 = 14 2 = 15 2 = 16 2 = 17 2 = 18 2 = 19 2 = 20 2 = 25 2 =

12. What is a Square Root? Visual of Square Roots & Estimations Visual of Square Roots & Estimations