Warm-up: 8/25/14Explore: You can use emoticons in text messages to help you communicate. Here are six emoticons. How can you describe a set that includes five of the emoticons but not the sixth?           Questions: What are some features that only one emoticon has? What sets could you define that include only five emoticons?

Standard: N.RN.3: Explain why sums and products of rational numbers are rational, that the sum of a rational number and an irrational number is irrational, and that the product of a non-zero rational number and an irrational number is irrational.

Objective: To classify real numbers and identify properties of real numbers.

Date:

Now classify numbers into subsets.

Discuss with your team andwrite down what the diagramrepresents.

Share.

Real Numbers:All numbers in the set of real numbers that are not imaginary.

Rational numbers:

•are all numbers you can write as a quotient of numbers a/b.

•includes terminating decimals. 1/8 = 0.125

•includes repeating decimals. 1/3 = 0.333333…

Irrational numbers:

•Have decimal representations that neither terminate nor repeat.

...414213.12

•Cannot be written as a quotient of integers.

With your group discuss the classification of the following information.

1. Your school is sponsoring a charity race. Which set(s) of numbers describes the amount of people who participate?  2. From the same charity event, each participant made a donation of $15.50 to a local charity. Which set(s) of numbers describes the amount raised? 3. Now create a real life scenario for the classification of an irrational number. Discuss the challenges your group is facing. 4. Is it true that the sum and product of a rational number is still rational? Prove. Explain. 5. Is it true that the sum of a rational numberand an irrational number is irrational? Prove. Explain. 6. Is it true that the product of a non-zero rational number and an irrational number is irrational? Prove. Explain.

Properties of real numbers: are relationships that are true for all real numbers (except in one case, zero)

Additive inverse of any number a is –a. The sum of a number and its opposite is zero.

Multiplicative inverse of any non-zero number a is 1/a. The product of a number and its reciprocal is 1.

Commutative Property: for addition a + b = b + a. For multiplication: ab = ba.

Associative Property: Addition (a + b) + c = a + (b + c). Multiplication (ab)c = a)bc)

Identity Property: Addition a + 0 = a. Multiplication

Distributive Property: a(b + c) = ab + ac

Closure Property: a + b and ab are real numbers.

With your group come up with examples of all the properties listed and prove the properties are always true. Can you find any counterexamples?

Closure:

Homework:Properties of Real NumbersAssignment (hand-out)