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!