DO NOW: Use long division to change 3/4 to a decimal. What is the decimal representation of pi? What is the square root of 2? What is the decimal representation of 1/9, 2/9, 3/9? Explain in complete sentences the pattern you see.

CORRECT ANSWERS: …,0.222…,0.333…

My Goal for Class Today: I can tell the difference between rational and irrational numbers. I understand that any number that can be written as a fraction is a rational number and I can convert a repeating decimal into a fraction. By the end of class I should be able to answer: What is the difference between a rational and irrational number?

TODAY’S AGENDA I Do: The Real Number System Venn Diagram We Do: Skittles Challenge You Do: Intendent Practice and Teach the Class Exit Ticket

Whole Numbers Counting Numbers Integers Rational Numbers Irrational Numbers The Real Number System

SKITTLES CHALLENGE I will call out a number On your white board write down if the number is a counting number, whole number, integer, rational number or irrational number If you’re correct you win a skittle! If every member of the team is correct the team gets a point The Team with the most points at the end wins!

IS ….RATIONAL OR IRRATIONAL?

IT IS RATIONAL! BUT WHY?

YOU DO: CONVERT THESE TO FRACTIONS WITH YOUR TABLE PARTNER … … …

EXIT TICKET 1.Convert the following into a fraction: …. 2.Is the answer from number one rational or irrational? 3.Write down one “ah-ha” moment from today or one question you still have about rational and irrational numbers.

DO NOW:

My Goal for Class Today: Is to be able to use rational approximations to define and compare irrational numbers. By the end of class I should be able to: locate and graph irrational numbers on the number line and estimate the value of those numbers.

TODAY’S AGENDA I Do: Estimate irrational numbers We Do: Compare rational and irrational numbers You Do: Laundry Line Activity- Locate irrational numbers on a number line Independent Practice Exit Ticket

I DO: HOW WE ESTIMATE IRRATIONAL NUMBERS Rational approximation: using a sequence of rational numbers to get closer and closer to a given number to estimate the value of a number.

WE DO: LAUNDRY LINE We will be creating “special laundry” to hang on the clothesline. Rational numbers will be placed on tee shirts and irrational numbers on pants. You will each chooses a number from the bag and then cut out a pair of pants or a shirt from the construction paper provided Once you are finished, it is time to hang the laundry. Come up and pin your laundry items on the clothesline. As more clothing is added you may need to move laundry to accurately place yours on the number clothing line.

INDEPENDENT PRACTICE Determine what is the interval of numbers √28 will lie between, Why? Classify the following numbers as rational or irrational. Be prepared to explain your reasoning. √ … √

HOME LEARNING Watch the following Khan Academy Videos and complete the practice problems with notes: math/cc-8th-numbers-operations/cc-8th- roots/v/introduction-to-square-roots math/cc-8th-numbers-operations/cc-8th- roots/v/introduction-to-square-roots Or Complete the Provided Worksheet

EXIT TICKET Summarize 3 main points from today’s lesson

DO NOW:

My Goal for Class Today: Is to understand squares and square roots, to realize that imperfect squares are irrational, and to be able to plot imperfect squares on the number line using rational approximation. By the end of class I should be able to answer: What does a square root represent?

AGENDA I Do: Perfect Squares Notes You Do: Khan Academy Square Roots Video We Do: Discovering Squares and Square Roots Activity You Do: Powers and Roots Worksheet Exit Ticket

HOME LEARNING Complete your Powers and Roots Worksheet

EXIT TICKET Place the following numbers on a number line: √16, √9, √11,

DO NOW: Evaluate the following equations: 1 x 1 x1= 2 x 2 x2= 3 x 3 x 3 =

My Goal for Class Today: I can evaluate cube exponents, and I can identify cube roots. By the end of class I should be able to answer: What is the relationship between cubes and cube roots?

AGENDA I Do: Perfect Squares Notes You Do: Perfect Squares Video We Do: Discovering Cubes Activity You Do: Cubes and Cube Roots Independent Practice Exit Ticket

I Do: What does cube root mean? The cube root of a number is… …the value when multiplied by itself three times gives the original number.

CUBE ROOT VOCABULARY index radicand radical sign

If a number is a perfect cube, then you can find its exact cube root. A perfect cube is a number that can be written as the cube (raised to third power) of another number. Perfect Cubes

WHAT ARE PERFECT CUBES? 1 3 = 1 x 1 x 1 = = 2 x 2 x 2 = = 3 x 3 x 3 = = 4 x 4 x 4 = = 5 x 5 x 5 = 125 and so on and on and on…..

Examples: because

Not all numbers or expressions have an exact cube root as in the previous examples. If a number is NOT a perfect cube, then you might be able to SIMPLIFY it. Simplify Cube Roots

2 Extract the cube root of the factor that is a perfect cube. 1 Write the radicand as a product of two factors, where one of the factors is a perfect cube. To simplify a cube root... 3 The factors that are not perfect cubes will remain as the radicand.

perfect cube Examples: 1)2) 3)

Not all cube roots can be simplified! 30 is not a perfect cube. 30 does not have a perfect cube factor. Example: cannot be simplified!

AGENDA I Do: Perfect Squares Notes-DONE You Do: Perfect Squares Video We Do: Discovering Cubes Activity You Do: Cubes and Cube Roots Independent Practice Exit Ticket

USING YOUR CUBES FIND THE ANSWERS FOR THE FOLLOWING CHART REMEMBER THE VOLUME OF A CUBE IS LENGTH X WIDTH X HEIGHT Side LengthVolume of CubeTherefore…That Means the Cube Root is …

HOME LEARNING

EXIT TICKET

DO NOW: Pulse Check: How has your first two weeks of school gone? How do you feel? What fun plans do you have this weekend?

My goal for you today is that you will all become masters at square and cube roots by the end of class, and that you will enjoy your weekend and come in next week with a positive attitude, ready to start fresh and learn.

AGENDA We Do: Cube and Square Roots Jeopardy Competition- Winning team gets homework passes! You Do: Cube Roots Coloring Project Enjoy your weekend!

JEOPARDY Square & Cube Roots Rational/ Irrational Simplifying Radicals Estimating Roots Misc

$100 SQUARE AND CUBE ROOTS

$100 ANSWER SQUARE AND CUBE ROOTS 169

RETURN

$200 SQUARE AND CUBE ROOTS 5³

$200 ANSWER SQUARE AND CUBE ROOTS 125

RETURN

$300 SQUARE AND CUBE ROOTS

$300 ANSWER SQUARE AND CUBE ROOTS 14

RETURN

$400 SQUARE AND CUBE ROOTS

$400 ANSWER SQUARE AND CUBE ROOTS 256

RETURN

$500 SQUARE AND CUBE ROOTS

$500 ANSWER SQUARE AND CUBE ROOTS 17

RETURN

$100 RATIONAL OR IRRATIONAL 1.25

$100 ANSWER RATIONAL OR IRRATIONAL Rational

RETURN

DAILY DOUBLE

DAILY DOUBLE RATIONAL OR IRRATIONAL …

DAILY DOUBLE ANSWER RATIONAL OR IRRATIONAL Rational

RETURN

$300 RATIONAL OR IRRATIONAL

$300 ANSWER RATIONAL OR IRRATIONAL Irrational

RETURN

$400 RATIONAL OR IRRATIONAL …

$400 ANSWER RATIONAL OR IRRATIONAL Irrational

RETURN

$500 RATIONAL OR IRRATIONAL

$500 ANSWER RATIONAL OR IRRATIONAL Rational

RETURN

$100 SIMPLIFYING RADICALS

$100 ANSWER SIMPLIFYING RADICALS

RETURN

$200 SIMPLIFYING RADICALS

$200 ANSWER TOPIC 3 6

RETURN

$300 SIMPLIFYING RADICALS

$300 ANSWER SIMPLIFYING RADICALS

RETURN

$400 SIMPLIFYING RADICALS

$400 ANSWER SIMPLIFYING RADICALS

RETURN

$500 SIMPLIFYING RADICALS

$500 ANSWER SIMPLIFYING RADICALS

RETURN

$100 ESTIMATING ROOTS

$100 ANSWER ESTIMATING ROOTS

RETURN

$200 ESTIMATING ROOTS

$200 ANSWER ESTIMATING ROOTS

RETURN

$300 ESTIMATING ROOTS

$300 ANSWER ESTIMATING ROOTS 3.3

RETURN

$400 ESTIMATING ROOTS

$400 ANSWER ESTIMATING ROOTS

RETURN

$500 ESTIMATING ROOTS

$500 ANSWER ESTIMATING ROOTS 2.6

RETURN

$100 MISC. What are the square roots of 81?

$100 ANSWER MISC.

RETURN

$200 MISC. What kind of decimals are rational?

$200 ANSWER MISC. Repeating and Terminating

RETURN

$300 MISC.

$300 ANSWER MISC. 16

RETURN

$400 MISC.

$400 ANSWER MISC.

RETURN

$500 MISC. Area = 100 ft squared What are the side lengths?

$500 ANSWER MISC. 10 ft.

RETURN

THANK YOU FOR PLAYING