8th grade Math – Numeration Unit 7 -√36 ¾ π Classifying Numbers 2.12122…. 0
Number Types Whole Integers Rational Numbers Irrational Numbers Which is which? How can you tell them apart?
Whole Numbers The Counting Numbers including 0. Ex: 0,1,2,3,4,5…… 9 43 12 101 235
Integers Positive and negative whole numbers. -3,-2,-1,0,1,2,3……. How are integers and whole numbers related? -132 -27 19
Whole Numbers = Integers All whole numbers are integers because integers include both positive and negative whole numbers.
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?
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
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 Pi
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. Rational Number Integer Whole Irrational Numbers
Let’s Practice! State which type of number these examples are:
Practice Continued State which type of number these examples are:
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
How did you do? Irrational Numbers ¼ .8 repeating π 3.25 4.68 √13 -3 -√49 -30/5 27/3 3.14144… 8 61 244/2 √144 0
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?
Conclusion Remember: All whole #’s are integers and all integers and whole #’s are rational #’s
References http://www.examiner.com/math-education-in-dallas/history-of-pi Pi picture Microsoft PowerPoint SmartArt Graphic organizers