unit 1, week 3

RATIONAL & IRRATIONAL NUMBERS

Unit 1, Week 3

Do Now – August 20th, 2012

Solve for the variable.1. 3x – 12 = -242. -10x – 7 = 133. 25 = -x -154. -40 = -7x - 5

Do Now – August 20th, 2012

Please pick up your guided notes and sit down SILENTLY.

Respond to the following on your guided notes:

1. How did you prepare for your quiz?2. What could you have done to better

prepare your for your quiz?3. What is your goal for this week’s quiz?

Today’s Objective

SWBAT review and track last week’s quiz.

SWBAT obtain a class intern position if necessary.

SWBAT define rational and irrational numbers and add to the number diagram.

Today’s Agenda

Do Now – 6 minutesAgenda Review – 2 minutesReview Quiz – 20 minutesTrack quiz – 7 minutesClass Interns – 5 minutesNumber Diagram INM – 8 minutesClose – 2 minutes

Student of the Week!

Willie White

Willie is…• Enthusiastic

about learning!

• Engaged in the material!

• Positive in his thought!

• Very kind!

• A math rockstar!

This could be

you!

Quiz Averages

3rd Period 5th Period 6th Period 7th Period0

102030405060708090

100

85 85 85 85

74

92

72 73

Big GoalQuiz 1

Class Interns

Chief of Staff

Supplies Distributor

Document Filer

Attendance Monitor

Homework DistributorWhiteboard Distributor

Expo Marker Distributor

Time Keeper

Line Leader (5th only)

Calculator Manager

Number Diagram

Last week, we categorized numbers into our number diagram.

Today, we will add more to the diagram.

IntegersWhole

Natural

IntegersWhole

Natural

Rational

IrrationalCopy this onto your

notes!

Rational and Irrational Numbers

1. Rational Numbers Any number that can be converted into a fraction.

Including: mixed numbers, percents, improper fractions, repeating decimals, and terminating decimals.

Example: 5 ½ , 10/5, 0.33333…, 0.515, 25%2. Irrational Numbers

Any number that can’t be converted into a fraction. Including: nonrepeating decimals, imperfect squares,

and pi (π). Example: √57, 0.521257392…,

Academic Enrichment Do Now – August 21st

Please complete the following SILENTLY & INDEPENDENTLY:

Solve for the variable.1. 12x – 60 = -24

2. -5x + 10 = -50

3. 0.5 = 0.5x + 3.5

Do Now – August 21st, 2012

Please respond to the following SILENTLY on your guided notes:1. EXPLAIN the difference between rational and

irrational numbers.

2. Is every whole number a rational number?

3. Name an integer that is not a whole number.

Today’s Objective

SWBAT identify numbers as rational and irrational.

Agenda

Do Now – 6 minutesAgenda Review – 2 minutesFoldable Review – 10 minutesIdentifying Numbers as Rational or Irrational

Numbers GP – 25 minutesExit Ticket – 5 minutes

Identifying Numbers as Rational or Irrational.

Before we start to classify numbers, we will make a foldable and recall what we introduced yesterday.

You must WATCH to make your foldable, I will not verbally give you directions!

Identifying Numbers as Rational or Irrational

Rational Irrational

Types of Numbers

Identifying Numbers as Rational or Irrational

Rational Numbers

Irrational Numbers

Identifying Numbers as Rational or Irrational

In order to determine whether or not a number is rational or irrational, we must convert it into a decimal.

Identifying Numbers as Rational or Irrational

Example 1: ¾ Converted to a decimal it is 0.75

Is this rational or irrational? Why?

Example 2: 53% Converted to a decimal it is 0.53

Is this rational or irrational? Why?

Identifying Numbers as Rational or Irrational

Example 3: -5 ½ Converted to a decimal it is -5.5

Is this rational or irrational? Why?

Example 4: √5 Converted to a decimal it is 5

Is this rational or irrational? Why?

Identifying Numbers as Rational or Irrational

Example 5: 2/3 Converted to a decimal it is 0.6666666….

Is this rational or irrational? Why?

Example 6: √150 Converted to a decimal it is 12.247448…..

Is this rational or irrational? Why?

Identifying Numbers as Rational or Irrational

Example 7: √100 Converted to a decimal it is 10

Is this rational or irrational?

Example 8: 0.71711711171111…. Is this rational or irrational?

Example 9: -0.5% Converted to a decimal it is -0.005

Is this rational or irrational?

Identifying Numbers as Rational or Irrational

Example 10: 152

Converted to a decimal it is 225 Is this rational or irrational?

Identifying Numbers as Rational or Irrational

Work on examples 11 – 15 with your partner.DO NOT MOVE ON TO EXAMPLES 16-20!11. π12.√3913.⅙14.∞15.-35%

Identifying Numbers as Rational or Irrational

Please work on the following on your own SILENTLY & INDEPENDENTLY.

16.√4917.-32

18.0.41423414341424…19.7π20.-⅛21.CHALLENGE: Name a rational number that

is NOT an integer

Exit Ticket

Each of you will receive an exit ticket. The exit ticket has 10 problems on it.You will complete the exit ticket in 5

minutes and it must be turned in before you can exit the classroom.

You must work SILENTLY and INDEPENDENTLY

HOMEWORK – Worksheet!

Academic Enrichment – Do Now – August 22nd

Simplify the following expressions:1. -6(-8m – 7)

2. 3(2 – 5)

3. -1(-m – 11)

4. 4 ( 3 + 8)

5. -5(x + 2) = 20

Do Now - August 23rd, 2012

Please respond to the following SILENTLY & INDEPENDENTLY on your guided notes:

1. What is the fundamental difference between a rational and irrational number?

2. Identify these numbers into their most specific subset:

-⅔ π 0 102

√80

Today’s Objective

SWBAT simplify expressions and identify as rational or irrational.

Agenda

Do Now – 6 minutesAgenda – 2 minutesSimplifying Expression INM – 12 minutesSimplifying Expressions GP – 10 minutesSimplifying Expressions IP – 10 minutesExit Ticket – 5 minutes

Simplifying Expressions

Before we can identify expressions as rational or irrational, we must simplify them.Depending on the number, we simplify in different ways.

Simplifying Expressions

Example 1:

This problem is actually saying √100 divided by √25. To solve, take the square root of the top number, take

the square root of the top number, and then divide. √100 = 10 √25 = 5 10/5 = 2

Is 2 rational or irrational? Rational

€

10025

Simplifying Expressions

Example 2:

This problem is actually saying √49 divided by √10. To solve, take the square root of the top number, take

the square root of the top number, and then divide. √49 = 7 √10 = 3.162… 7/3.162… = 0.4517…

Is 0.4517… rational or irrational? irrational

€

4910

Simplifying Expressions

Is there an easier way to determine whether or not these type of expressions are rational or not? Write your rule below! Think with your partner for 1 minute.

Easy rule to follow when determining rational or irrational:

€

40049

€

205

Simplifying Expressions

Work on example 3 – 5 with your partner. DO NOT MOVE ON TO EXAMPLES 6 – 8.

3.

€

169225

€

3619

€

8048

Simplifying Expressions

Work on examples 6 – 8 ON YOUR OWN!6.

7.

8.

€

40010

€

22525

€

259

Simplifying Expressions

Sometimes, you will see expressions like this:

Example 9: 3√25 This problem is telling you to multiply the

square root of 25 by 3. In order to solve this, you do what was stated

above √25 = 5 x 3 = 15 OR identify if the square is perfect or imperfect. If the square is perfect, the answer will be

rational. If the square is imperfect, the answer will be

irrational.

Simplifying Expressions

Example 10: √3 + 2 The same rule applies to any number that has a

square root in it. Based off of what we discovered earlier and applied in

the previous example, is the answer to this expression rational or irrational?

Try example 11- 13 with your partner.11.4√10012.√39 + 713.-7√16

Simplifying Expressions

Complete examples 14 – 18 on your own.14. √50 – 1015.4√16916.√144 + 617.½ √518.-3√36

Simplifying Expressions

The last type of expressions you might see include those with squares and π. Example 19: (√15) 2

According to PEMDAS, you take the square root of 15 and then square your answer. Determine if its rational or irrational.

However, there is an easier way to solve this.• Think with your partner for 1 minute.• Rule for solving these problems:Squaring and square root are opposite. So they simply

cancel each other out so determine if the number in the radical is I or R!

Example 20: (√-10) 2

Rational or irrational?

Simplifying Expressions

Work on examples 21 – 24 with your partner. DO NOT MOVE ON TO EXAMPLES 25 – 27.

21.(√17) 2

22.(√100) 2

23.(√½) 2

24.(√π) 2

25.(√39) 2

Simplifying Expressions

If you see a problem with π (pi), you must make sure it is not being cancelled out before you assume its irrational. Example 26:

Pi on top cancels pi on bottom so your problem is √10/√15. When you simplify your answer is irrational.

This will not always happen. Example 27:

Rational or irrational?

€

10π15π

€

100π25π

Simplifying Expressions

Work on examples 28 – 29 with your partner and then do examples 30 – 31 on your own.

28.

29. 10π30.½π31.

€

9π36π

€

25400π

Exit Ticket

Each of you will receive an exit ticket. The exit ticket has 4 problems on it.You will complete the exit ticket in 5 minutes

and it must be turned in before you can exit the classroom.

You must work SILENTLY and INDEPENDENTLY

HOMEWORK – Worksheet!

Academic Enrichment Do Now – August 23rd

Please work these on the back of your homework.

1. -5x (3 – 10)

2. 20(-x – 2)

3. 7(-x-6)

4. -10(-2x + 4)=-100

Do Now - August 23rd, 2012

Please respond to the following SILENTLY & INDEPENDENTLY on your guided notes:

Identify as rational or irrational:1.

2. (√-7π)2

3. 4√37

€

100400

Today’s Objective

SWBAT identify numbers as rational or irrational.

Agenda

Do Now – 6 minutesAgenda – 2 minutesHomework Review – 10 minutesGuided Practice – 30Close – 3 minutes

Homework Review

Please get out your homework and we will go over it to check for your understanding.

Rational and Irrational Numbers Game

The class will be broken up into teams.Each team will get a group of note cards

indicating the different types of numbers.Each team will get a chance to identify

numbers shown to the class by me. If the expression is rational, each team will then

determine the more specific subset it could go into.Afterward, a student will come up to the

board and put it into our number diagram.

Irrational

RationalIntegers

WholeNatural

Friday’s Quiz

Classifying numbers as rational and irrational

Simplifying expressions then classifying numbers

Real number diagram

BE SURE YOU ARE ABLE TO EXPLAIN YOUR ANSWERS!