Unit 1 class notes

Order of Operations notebook2.notebook

1

September 18, 2012

Sep 187:40 AM

Start with p. 50 as a groupwork assignment for day 1

May 147:50 AM

Unit 1:Chapter 1 & 2

May 147:50 AM

Warm Up

May 81:02 PM

Order of Operations

May 81:05 PM

Why is following the order of something important? Does order really matter?

May 81:09 PM

Order Matters!!!!


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September 18, 2012

May 81:09 PM May 81:09 PM




3

September 18, 2012

May 81:03 PM

Which method is correct???

May 83:03 PM

May 81:03 PM

The method where you do the division first is correct!!!

WHY???

May 83:03 PM

Complete Multiplication and Division from left

to right.

Complete Addition and Subtraction from left to

right.

Jun 279:31 AM

List all symbols that would be used for:P:

E:

M/ D:

A/ S:

May 83:03 PM


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September 18, 2012

Jun 158:12 AM May 81:07 PM

Try this one:

Sep 68:07 AM

p. 19 #4- 84 every other even!!!

Show work in your notebooks. Use your cell phone to help with

easy calculations.

Jun 158:12 AM

Jun 158:12 AM

Try these examples:1.

2.

3.

Jun 158:12 AM


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September 18, 2012

Jun 158:12 AM Jul 288:33 AM

293(94)35(1+102)

Pull a balloon and solve the equation justifying each step.

2 8222 8 2 8

(4 3)29+3

5 5 3 3{(639)÷23}4

Pull

PullRemember to use your rules and Justify!

May 83:07 PM

HOMEWORK: p. 10- 11

#52- 72 evens

Jun 158:12 AM

May 83:08 PM

Warm Up

May 83:08 PM

More Order of Operations


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September 18, 2012



May 83:20 PM

Try these examples. Check your answers with your group.

1. 9 12 8 + 5 6 = 12 2. [14 (16 18)] [32 (8 9)] = 17

3. 6(3 9 1) = 78 4. 6 {(2+7)/3 (2)(3 5)} = 1

5. 14.1 (17.2 13.6) = 10.5 6. 7(6.2 7.1) 6(1.4 2.9) = 19.5

Mar 197:45 AM

Do the problems and show a justification for each step


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Mar 197:45 AM

Answers

Mar 197:45 AM

Rearrange these sentences so that the expression is simplified correctly.

24+4/26

20.

24+26

4(3+3)+4/26

266

4(6)+4/26

May 83:07 PM

HOMEWORK: p. 19- 20

#4- 84 eoe(every other even)

May 83:07 PM

Answers to p. 19 #4- 84 eoe

4. -218. -1412. -6816. -1520. 41/624. -428. 032. 3.336. -22.840. -944. -7/24

48. -2/552. 756. -7/260. -4564. -4368. 7372. 2576. -4280. 084. 16.9

May 83:16 PM

Warm Up

Write in your journal about something you do where you follow and "order." Please list the order.

(Think about the S'mores cartoon)

Example: (and do not use this one) To make a sandwich you get out the bread, use a knife to spread the peanut butter, etc.)

May 83:16 PM

Do you understand the correct order of

operations for this?Yum...


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September 18, 2012

Click to reveal

Integer Practice

-8 - 9

-8 + 5

12 - 13

-4 + (-4)

-3 - 7

12 + 6

-9 - (-8)

5 + (-16)

13 - 21

-3

-1

-8

-10

18

-1

-11

-17

-8

Pull

Pull

Click to reveal

Integer PracticeAnswers

-8 - 9

-8 + 5

12 - 13

-4 + (-4)

-3 - 7

12 + 6

-9 - (-8)

5 + (-16)

13 - 21

-3

-1

-8

-10

18

-1

-11

-17

-8

Pull

Pull

May 83:26 PM

More Practice:

1. [(74 + (36)] + 36 2. 3[5 (2)] 2(4 9)

3. 6(3 9 1) 4. 5 + (2)(7) (3)(8)

Sep 77:42 AM

May 83:16 PM

Warm Up

Write in your journal about something you do where you follow and "order." Please list the order.

(Think about the S'mores cartoon)

Example: (and do not use this one) To make a sandwich you get out the bread, use a knife to spread the peanut butter, etc.

May 83:26 PM

Remember...

Today we are going to focus on Exponents.


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September 18, 2012


EXPONENTS

May 83:30 PM

EXPONENTSIf you know thatCan you fill in this chart correctly?

May 83:39 PM

What is the difference between

(-5)2 and -52

May 83:42 PM

Simplify each problem using your knowledge of order of operations.

1. (-3)2 - 42 = -7

2. -32 - 52 = -34

3. 23 - 33 = -19

May 83:42 PM


4. -3(-2)3 + 4(-1)5 = 20

5. (-3)2 - 3(-2)(5) + 42 = 55


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May 83:42 PM


6. (3 + 4)3 - 1 =

7. [3(-2)2 - 2(-3)2]3 =

May 107:58 AM

Homework:p. 28

#28 46 evens

May 107:58 AM

p. 28 #28 46 evens

28. 7 30. 24

32. 18 34. 35

36. 28 38. 22

40. 15 42. 4

44. 25 46. 169

May 911:38 AM

Warm Up

May 911:38 AM

Combining and Evaluating Expressions

May 911:36 AM


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September 18, 2012

May 911:35 AM May 912:11 PM

How do you evaluate an expression???

Jun 182:17 PM

EquationExpression

3x 2 = 10

x y z

2y y = 7

7x 8x = 15

14x + 9x + 2y

2x 3

What is the difference between an expression and an equation? Move each

oval into the appropriate box.

May 912:11 PM

How do you evaluate an expression???

May 912:12 PM May 912:10 PM

Evaluate 5y2 y + 7 if y = 3.


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September 18, 2012

May 912:10 PM

In the second basketball game of the season, Wesley scored two fewer points than three times the number of points he scored in the first game. Let p represent the number of points Wesley scored in the first game.

• Write an expression that can be used to find the number of points scored in the second game.

• If p = 11, find how many points Wesley scored in the second game.

May 912:10 PM

Evaluate x2 x y + y2 if x = 2 and y = 2.

May 912:10 PM

Kenan borrowed four books from the library each month for m months in a row. Write an expression to find the number of books he borrowed from the library during this time period.

Evaluate the expression if m = 6.

May 911:36 AM

Evaluate 2x2 + 3y + 6 if x = 2 and y = 9.

May 911:35 AM

4x and -10x 15xy and 17xy

-2x2y and 7x2y -9xy3 and 13xy3

Examples:

What are "like terms?"

Terms with the exact same variables or variables raised to the same power.

Combining Like Terms

May 912:22 PM

Combining Like Terms


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September 18, 2012

Feb 259:32 PM

Combining Like Terms - Important Note

NOTE: The subtraction sign and the negative sign mean the same thing.

Examples: • 4 - 9 becomes 4 + (-9) as an addition problem so the

subtraction symbol tells you that the 9 is negative

• 5a - 4 becomes 5a + (-4) as an addition problem so the subtraction symbol tells you the 4 is negative.

Feb 259:19 PM

Determine whether the terms are LIKE or UNLIKE terms. Drag the correct word to each box.

-4x and -10x 13xy and 5y 5x2 and 9x

9x2y and 4x2y 3xy2 and 7x2y 17ab and -21ab

LIKE UNLIKE

May 33:31 PM

Work with your partner to complete the following problems.The expressions on the right have had their like terms combined. Match each expression on the left with an expression on the right. When done move the red check inside the green box to reveal the answers.

8x - 3x

3x + 9y - 5x

-4x - 5x - 7xy

6xy + 4yz - 3xy + yz

7x2y - 2x2y + 5xy2 -3xy2

-4x - 7xy + 8y

8x + 9y - 5x

a. 5x2y + 2xy2

b. 5x

c. 3x + 9y

d. 3xy + 5yz

e. -2x + 9y

f. -4x -7xy + 8y

g. -9x - 7xy

b

e

g

d

a

f

c

May 1010:40 AM

Are these 2 expressions the same?

9 23x 9x + 23


9 + 10x 12 6x 3 + 4x


7y2 + 4y 11y2

Feb 259:25 PM

Simplifying Expressions by Combining Like Terms

You can combine like terms by adding their numerical coefficients.

Examples:

1. 5x + 9x - 12x 2. 14x + 9 + 6x

Feb 259:28 PM

More Examples

3. 9a2 - 6ab - 11a2 + 10ab

4. -6a + 7 - 3b - 4 + 2a + b


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September 18, 2012

May 312:21 PM

Guided PracticeSimplify each expression.

1. -6x + 7x + 13x 2. 5x2 - 9 - 7x2 + 16

3. 3xy + 7x - 8xy + 9x 4. 8a2 + 9a - 9a2 - 17a

Answers

May 312:21 PM

Guided Practice - AnswersSimplify each expression.

1. -6x + 7x + 13x

14x

2. 5x2 - 9 - 7x2 + 16

3. 3xy + 7x - 8xy + 9x 4. 8a2 + 9a - 9a2 - 17a

Back

(5x2 + (- 7x2)) + (-9 + 16)

-2x2 + 7

(3xy + (-8xy)) + (7x + 9x)

-5xy + 16x

(8a2 + (-9a2)) + (9a + (-17a))

-a2 - 8a

May 1010:35 AM

What expression represents the perimeter of this rectangle?

x

x + 9

May 1010:35 AM

What expression represents the perimeter of this rectangle?

3m + 1

7m - 9 +n

May 912:56 PM

Homework:p. 36- 37

#2- 54 eoe

Sep 137:51 AM

p. 36- 3718. 34.

42. 54.


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September 18, 2012

May 912:26 PM

p. 36 #2 54 eoe

2. 2x 6. 4n

10. 9xy 6z 14. 10xy + 2x y

18. 16a 43 22. x +5y

26. 15x 2 30. 13x + 30y

34. 12x 21 38. 62

42. 26 46. 84

50. 16 54. 21

May 912:53 PM

Warm Up

May 912:53 PM

Solving Equations

Jun 182:49 PM

May 912:53 PM

Check:5 + 3 = 8

8 = 8Both sides are still balanced!

3 3

x = 5

Solving equations is something you have done before. You must keep both sides equal without throwing

one side off balance.

We all know how to solve this equation. What is the first

step?

Do you understand WHY you must subtract 3 from BOTH sides to keep the balance?

Dec 266:01 PM


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Jun 182:49 PM Jun 182:51 PM

Jun 182:51 PM Jun 182:52 PM

Jun 182:53 PM Jun 207:59 AM


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Jun 182:53 PM Jun 182:54 PM

Jun 182:54 PM May 108:30 AM

Dec 266:01 PM May 1010:52 AM


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September 18, 2012

May 108:27 AM

Homework:p. 50

# 2- 50 eoe

Jun 2112:32 PM

p. 50 #2 50 eoe

14. 22.

30. 46.

Sep 138:40 AM

p. 50 #2 50 eoe

2. 5 6. 10

10. 11/5 14. 5/2

18. 13/5 22. 15

26. 7 30. 2

34. 7/5 38. 18/7

42. 23/4 46. 2

50. 12/11

May 83:16 PM

QUIZ #1CR #1 due tomorrow at the

beginning of class!

May 1012:45 PM

CR #1 is due NOWWhen you get anything back (quiz,

CR, test), if you are pleased with your score, feel free to give it back to me so

I can post it on the wall!

May 1012:45 PM

Warm Up


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September 18, 2012

May 1012:45 PM

Consecutive Integer Word Problems

May 1012:45 PM

Let's watch this video to see if you can explain the meaning of

CONSECUTIVE

May 1012:45 PM

What does CONSECUTIVE

mean to you?

May 118:24 AM

How do you represent integers for these word problems???

Consecutive Integers: Consecutive Even/ Odd Integers:x = 1st integer x = 1st even/ odd integerx + 1 = 2nd integer x + 2 = 2nd even/ odd integerx + 2 = 3rd integer x + 4 = 3rd even/ odd integerx + 3 = 4th integer x + 6 = 4th even/ odd integerand so on...and so on...

Notice you always add 2 (+2) to get to the next even or odd integer.

Think about it. What do you add to 5 to get to the next odd integer ?

What do you add to 24 to get to the next even integer ?

May 1012:48 PM

Example: Find 3 consecutive integers whose sum is 147.

May 118:31 AM

Examples:

1. Two consecutive integers have a sum of 91. What are the two integers?

2. What two consecutive odd integers have a sum of 88?

3. Two consecutive even integers have a sum of 26. What are the two integers?


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September 18, 2012

May 118:35 AM

4. What three consecutive negative integers have a sum of 36?

5. What four consecutive integers have a sum of 66?

May 118:36 AM

6. What two consecutive odd integers have a sum of 28?

7. What four consecutive integers have a sum of 34?

Jul 99:17 AM

Word Problems

1. A number problem states "5 times a number, minus 22 gives a result of 23." What is the number?

Jul 99:22 AM

2. Hank went to Shop Rite and purchased some roast beef and a loaf of bread for a total of $11.54. If the bread cost $3.44 and the roast beef sells for $5.40 per pound, how many pounds of roast beef did he buy? Round your answer to the nearest tenth if necessary.

Jul 99:22 AM

3. A plumber charges a $35 fee on all house calls plus an hourly rate for labor. If the total bill for a job takes 3 hours is $110, what is the plumber's hourly rate?

May 1012:48 PM

More practice...


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September 18, 2012

May 1012:48 PM

More practice...

May 1110:45 AM

Homework:Worksheet

Jun 2112:33 PM May 1012:52 PM

Warm Up

May 1012:52 PM

Equations with Fractions

May 1012:54 PM


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September 18, 2012

May 1012:59 PM May 1012:59 PM

Answer on next slide...

May 101:00 PM Jun 2112:45 PM

Answer on next slide...

May 101:04 PM May 101:04 PM


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September 18, 2012

May 101:08 PM

Solve each of the following:

1. 2.

May 101:11 PM

Homework:p. 58

#2- 12 even, 16 and 18

May 101:12 PM May 101:44 PM

Warm Up

May 101:44 PM

Interval Notation

May 1012:48 PM

( is called the left hand parenthesis symbol.

) is called the right hand parenthesis symbol.

Written in interval notation (8, 7) means the set of numbers between 8 and 7 (does not include 8 or 7).


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September 18, 2012

May 1012:48 PM

[ is called the left hand parenthesis symbol.

] is called the right hand parenthesis symbol.

Written in interval notation [8, 7] means the set of numbers between 8 and 7 including 8 and 7.

May 101:59 PM

Inequality NotationInterval Notation

2 < x < 15 (2, 15)

(2, 15]

[2, 15)

[2, 15]

( ) is equivalent to < or >

[ ] is equivalent to

May 102:24 PM

How would you write the following inequalities in interval notation?

May 101:43 PM

May 102:24 PM

How would you write the following intervals into inequalities?

May 102:30 PM

Solve the following inequalities and write your answer in interval notation.


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May 101:47 PM

Homework:p. 85

#2- 20 evens

Jun 2112:51 PM

May 1012:48 PM

The formula for converting degrees Celsius (C) to degrees Fahrenheit (F) is: F = 9/5C + 32

If the temperature in Celsius is 17 degrees, what is the temperature in Fahrenheit?

Review for Unit 1 Exam

May 1012:48 PM

Jun 279:34 AM May 1111:06 AM


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Jul 99:29 AM

Unit 1 class notes

Technology

Transcript of Unit 1 class notes