1. CLASSIFYING NUMBERS 8 th grade Math – Numeration Unit 7 π -√36 ¾ 0 2.12122….

2. Number Types  Whole  Integers  Rational Numbers  Irrational Numbers  Which is which?  How can you tell them apart?

3. Whole Numbers  The Counting Numbers including 0.  Ex: 0,1,2,3,4,5…… 235 9 12 101 43

4. Integers  Positive and negative whole numbers.  -3,-2,-1,0,1,2,3…….  How are integers and whole numbers related? -27 19 -132

5. Whole Numbers = Integers  All whole numbers are integers because integers include both positive and negative whole numbers. Integers Whole Numbers

6. Rational Numbers  Numbers that can be written as a fraction a/b.  Numbers that have terminating decimals.  Numbers that have repeating decimals.  4.375 = 4 375/1000 = 4 3/8  2.5 = 2 5/10 = 2 1/2  0.3 repeating = 3/9 = 1/3  How do rational numbers relate?

7. Rational Numbers = Integers = Whole Numbers  All rational numbers are integers and whole numbers because you can make them into a ratio (or fraction) by putting a 1 under it.  24/1, -8/1, 567/1, -76/1, 24/3, -64/8 Rational Number Integer Whole

8. Irrational Numbers  Numbers that cannot be made into a simple fraction; they have a decimal that keeps going and going.  π, √2, 4.23233…., -√8 Pi

9. Are Irrational Numbers Related?  Irrational Numbers are by themselves because they cannot be made into fractions (rational numbers) or cannot be a positive or negative whole number since there is no decimal. Irrational Numbers Rational Number Integer Whole

10. Let’s Practice!  State which type of number these examples are: Type of Number 0 47 24/8 56/1 279 Type of Number 2.454554555…. √6 π -3.4224222…. -√10

11. Practice Continued  State which type of number these examples are: Type of Number 2.45 -.6 repeating 34 ½ ¾ -7.5 Type of Number -4 -√100 -12 -81/9 -√25

12. Answers Whole 0 47 24/8 56/1 279 Irrational 2.454554555…. √6 π -3.4224222…. -√10 Integer -4 -√100 -12 -81/9 -√25 Rational 2.45 -.6 repeating 34 ½ ¾ -7.5

13. Quiz  Place these numbers into the correct category on the chart to prove your understanding.  -3, 27/3, π, 4.68, √13, -√49, 3.14144…, 8, ¼, 3.25, 61,.8 repeating, √144, -30/5, 244/2, 0 Irrational Numbers Rational Number Integer Whole

14. How did you do? Rational Number Integer Whole Irrational Numbers -3 27/3 π 4.68√13 -√49 3.14144… 8 ¼ 3.25 61.8 repeating √144 -30/5 244/2 0

15. Explanation Time!  Explain with a chart how these types of numbers are related and give examples of each:  Whole numbers  Integers  Rational Numbers  Irrational Numbers  Which is which?  How can you tell them apart?

16. Conclusion Rational Number Can be made into a fraction a/b. ¼, 4.25, 8, -3,.7 repeating Integer Any + o r – whole number. -712, -53, -4/2, -√9, Whole Number The counting numbers. 0, 3, 5, 18, 53, 721, 8943 Irrational Number Any number that cannot be made into a fraction. 2.34344…., √11, π Remember: All whole #’s are integers and all integers and whole #’s are rational #’s

17. References  http://www.examiner.com/math-education-in- dallas/history-of-pi http://www.examiner.com/math-education-in- dallas/history-of-pi  Pi picture  Microsoft PowerPoint SmartArt  Graphic organizers