Real Numbers (Irrational) Students will be able to identify numbers as irrational based on the rules of real numbers. Wednesday, September 3rd

WARM UP Find the 64. Convert -2 1 20 to a decimal fraction. Is 𝜋 a rational or irrational number. Write a sentence to justify your answer. 4. What is 5 2 ? 5. 5 – 3x = - 10

Real Number Hexagon

Activity - Real Number Hexagon Each person will need a copy of the Real Number Hexagon Each table will be assigned a specific set of numbers and a color Each person at the table will need to color their own specific set of numbers, using their assigned color (15 minutes) Now, in your group, compare your hexagons. (You can hold one sheet behind the other to make comparisons) (about 5 minutes) Discuss any differences and determine which is correct (5 minutes) Let’s compare groups now (10 minutes) – what do you notice about the different sets of numbers?

Let’s recall what we know about Rational Numbers Recall that rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals. 4 5 23 3 = 3.8 = 0.6 1.44 = 1.2

What are irrational numbers? Irrational numbers are numbers that CANNOT be written as a fraction. They are non-repeating, non-terminating decimals. Can you think of some irrational numbers? Let’s look at a more formal definition….

Remember this Venn Diagram that displays the sets of Real numbers? Reals, Rationals, Irrationals, Integers, Wholes, and Naturals. Reals Type equation here. Rationals Integers -3 -19 -2.65 Wholes Irrationals Naturals 1, 2, 3...

Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so 2 is irrational. A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits. Caution!

Additional Example 1: Classifying Real Numbers Write all classifications that apply to each number. A. 5 5 is a whole number that is not a perfect square. irrational, real B. –12.75 –12.75 is a terminating decimal. rational, real 16 2 = = 2 4 2 16 2 C. whole, integer, rational, real

whole, integer, rational, real Check It Out! Example 1 Write all classifications that apply to each number. A. 9 9 = 3 whole, integer, rational, real B. –35.9 –35.9 is a terminating decimal. rational, real 81 3 = = 3 9 3 81 3 C. whole, integer, rational, real

TICKET OUT… What is the difference between a rational and an irrational number? Put your name and your answer on an index card and place in the basket by the front door BEFORE you leave!!!

Homework Who do you agree with? You will be asked to agree/disagree with what 5 students say about a certain number. Then, you will have to say whether the number they are discussing is rational or irrational and explain how you know.