1. Order of Operations notebook2.notebook September 18, 2012
Start with p. 50 as a groupwork assignment for day 1
Unit 1:
Chapter 1 & 2
Sep 18­7:40 AM May 14­7:50 AM
Warm Up
Order of Operations
May 14­7:50 AM May 8­1:02 PM
Why is following the order of something important?
Does order really matter?
Order Matters!!!!
May 8­1:05 PM May 8­1:09 PM
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2. Order of Operations notebook2.notebook September 18, 2012
May 8­1:09 PM May 8­1:09 PM
May 8­1:09 PM May 8­1:09 PM
May 8­1:09 PM May 8­1:09 PM
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3. Order of Operations notebook2.notebook September 18, 2012
Which method is correct???
May 8­1:03 PM May 8­3:03 PM
The method where you do the division first is correct!!!
Complete
Multiplication and
Division from left
to right.
WHY???
Complete Addition
and Subtraction
from left to
right.
May 8­1:03 PM May 8­3:03 PM
List all symbols that would be used for:
P:
E:
M/ D:
A/ S:
Jun 27­9:31 AM May 8­3:03 PM
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4. Order of Operations notebook2.notebook September 18, 2012
Try this one:
Jun 15­8:12 AM May 8­1:07 PM
p. 19 #4- 84 every other even!!!
Show work in your notebooks.
Use your cell phone to help with
easy calculations.
Sep 6­8:07 AM Jun 15­8:12 AM
Try these examples:
1.
2.
3.
Jun 15­8:12 AM Jun 15­8:12 AM
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5. Order of Operations notebook2.notebook September 18, 2012
Pull a balloon and
solve the equation
justifying each step.
Remember to use your rules and Justify!
Pull
2 82­22 8 (4 3)2
2 8 35­(1+102)
9+3
29­3(9­4)
5 5 ­ 3 3
{(6 ­9)÷23}4
3
Jun 15­8:12 AM Jul 28­8:33 AM
HOMEWORK:
p. 10- 11
#52- 72 evens
May 8­3:07 PM Jun 15­8:12 AM
Warm Up
More Order of Operations
May 8­3:08 PM May 8­3:08 PM
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6. Order of Operations notebook2.notebook September 18, 2012
May 8­1:10 PM May 8­3:19 PM
May 8­3:04 PM May 8­3:19 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 Do the problems and show a
justification for each step
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
May 8­3:20 PM Mar 19­7:45 AM
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7. Order of Operations notebook2.notebook September 18, 2012
Re­arrange these sentences so that the
Answers expression is simplified correctly.
24+4/2­6
20.
24+2­6
4(3+3)+4/2­6
26­6
4(6)+4/2­6
Mar 19­7:45 AM Mar 19­7:45 AM
Answers to p. 19 #4- 84 eoe
HOMEWORK: 4. -21
8. -14
48. -2/5
52. 7
p. 19- 20 12. -68
16. -15
56.
60.
-7/2
-45
20. 41/6
64. -43
#4- 84 eoe 24. -4
28. 0
68.
72.
73
25
32. 3.3
76. -42
(every other even) 36. -22.8
40. -9
80.
84.
0
16.9
44. -7/24
May 8­3:07 PM May 8­3:07 PM
Warm Up
Do you understand the
Write in your journal about something you do
where you follow and "order." Please list the
correct order of
order.
(Think about the S'mores cartoon)
operations for this?
Example: (and do not use this one) To make a sandwich
Yum...
you get out the bread, use a knife to spread the peanut
butter, etc.)
May 8­3:16 PM May 8­3:16 PM
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8. Order of Operations notebook2.notebook September 18, 2012
Integer Practice Integer Practice
Pull
Pull
Answers
-8 + 5 -3 -3 - 7 -10 5 + (-16) -11 -8 + 5 -3 -3 - 7 -10 5 + (-16) -11
12 - 13 -1 12 + 6 18 -8 - 9 -17 12 - 13 -1 12 + 6 18 -8 - 9 -17
-4 + (-4) -8 -9 - (-8) -1 13 - 21 -8 -4 + (-4) -8 -9 - (-8) -1 13 - 21 -8
Click to reveal Click to reveal
More Practice:
1. [(74 + (­36)] + 36 2. ­3[5 ­ (­2)] ­ 2(­4 ­ 9)
3. ­6(­3 ­9 ­1) 4. ­5 + (­2)(7) ­ (­3)(8)
May 8­3:26 PM Sep 7­7:42 AM
Warm Up Remember...
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.
Today we are going to focus on Exponents.
May 8­3:16 PM May 8­3:26 PM
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9. Order of Operations notebook2.notebook September 18, 2012
EXPONENTS
May 8­3:26 PM May 8­3:30 PM
EXPONENTS What is the difference between
If you know thatCan you fill in this chart correctly? (-5)2 and -52
May 8­3:30 PM May 8­3:39 PM
Simplify each problem using your knowledge Simplify each problem using your knowledge
of order of operations. of order of operations.
1. (-3)2 - 42 = -7 4. -3(-2)3 + 4(-1)5 = 20
2. -32 - 52 = -34
5. (-3)2 - 3(-2)(5) + 42 = 55
3. 23 - 33 = -19
May 8­3:42 PM May 8­3:42 PM
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10. Order of Operations notebook2.notebook September 18, 2012
Simplify each problem using your knowledge
of order of operations.
6. (3 + 4)3 - 1 = Homework:
p. 28
7. [3(-2)2 - 2(-3)2 ]3 = #28­ 46 evens
May 8­3:42 PM May 10­7:58 AM
p. 28 #28­ 46 evens Warm Up
28. ­7 30. ­24
32. ­18 34. ­35
36. ­28 38. 22
40. 15 42. 4
44. 25 46. 169
May 10­7:58 AM May 9­11:38 AM
Combining and Evaluating Expressions
May 9­11:38 AM May 9­11:36 AM
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11. Order of Operations notebook2.notebook September 18, 2012
How do you evaluate an expression???
May 9­11:35 AM May 9­12:11 PM
What is the difference between an How do you evaluate an expression???
expression and an equation? Move each
oval into the appropriate box.
Expression ­7x ­ 8x = 15 Equation
­x ­ y ­ z 2x ­ 3
3x ­ 2 = 10 2y ­ y = ­7
14x + 9x + 2y
Jun 18­2:17 PM May 9­12:11 PM
Evaluate 5y2 ­ y + 7 if y = 3.
May 9­12:12 PM May 9­12:10 PM
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12. Order of Operations notebook2.notebook September 18, 2012
In the second basketball game of the season, Wesley
scored two fewer points than three times the number of
Evaluate ­x 2 ­ x ­ y + y2 if x = 2 and y = ­2.
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 May 9­12:10 PM
Kenan borrowed four books from the library each month for Evaluate 2x 2 + 3y + 6 if x = ­2 and y = 9.
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 9­12:10 PM May 9­11:36 AM
Combining Like Terms Combining Like Terms
What are "like terms?"
Terms with the exact same variables or variables
raised to the same power.
Examples:
4x and -10x 15xy and 17xy
-2x2y and 7x2y -9xy3 and 13xy3
May 9­11:35 AM May 9­12:22 PM
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13. Order of Operations notebook2.notebook September 18, 2012
Combining Like Terms - Important Note Determine whether the terms are LIKE or UNLIKE terms.
Drag the correct word to each box.
NOTE: The subtraction sign and the negative sign mean the same
thing.
-4x and -10x 13xy and 5y 5x2 and 9x
Examples:
• 4 - 9 becomes 4 + (-9) as an addition problem so the
subtraction symbol tells you that the 9 is negative 9x2y and 4x2y 3xy2 and 7x2y 17ab and -21ab
• 5a - 4 becomes 5a + (-4) as an addition problem so the
subtraction symbol tells you the 4 is negative. LIKE UNLIKE
Feb 25­9:32 PM Feb 25­9:19 PM
Work with your partner to complete the following problems.
The expressions on the right have had their like terms combined. Match each
Are these 2 expressions the same?
expression on the left with an expression on the right. When done move the red
check inside the green box to reveal the answers. 9 ­23x ­ 9x + 23
b
8x - 3x a. 5x y + 2xy
2 2
e
3x + 9y - 5x b. 5x Are these 2 expressions the same?
g
-4x - 5x - 7xy c. 3x + 9y
­9 + 10x ­ 12 6x ­ 3 + 4x
d
6xy + 4yz - 3xy + yz d. 3xy + 5yz
a
7x2y - 2x2y + 5xy2 -3xy2 e. -2x + 9y Are these 2 expressions the same?
f
-4x - 7xy + 8y f. -4x -7xy + 8y
c
7y2 + 4y 11y2
8x + 9y - 5x g. -9x - 7xy
May 3­3:31 PM May 10­10:40 AM
Simplifying Expressions by Combining Like Terms More Examples
You can combine like terms by adding their numerical coefficients.
3. 9a2 - 6ab - 11a2 + 10ab
Examples:
1. 5x + 9x - 12x 2. 14x + 9 + 6x
4. -6a + 7 - 3b - 4 + 2a + b
Feb 25­9:25 PM Feb 25­9:28 PM
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14. Order of Operations notebook2.notebook September 18, 2012
Guided Practice Guided Practice - Answers
Simplify each expression. Simplify each expression.
1. -6x + 7x + 13x 2. 5x2 - 9 - 7x2 + 16 1. -6x + 7x + 13x 2. 5x2 - 9 - 7x2 + 16
(5x2 + (- 7x2)) + (-9 + 16)
14x
-2x2 + 7
3. 3xy + 7x - 8xy + 9x 4. 8a2 + 9a - 9a2 - 17a 3. 3xy + 7x - 8xy + 9x 4. 8a2 + 9a - 9a2 - 17a
(3xy + (-8xy)) + (7x + 9x) (8a2 + (-9a2)) + (9a + (-17a))
-5xy + 16x -a2 - 8a
Answers
Back
May 3­12:21 PM May 3­12:21 PM
What expression represents the perimeter What expression represents the perimeter
of this rectangle? of this rectangle?
x 3m + 1
x + 9 7m - 9 +n
May 10­10:35 AM May 10­10:35 AM
p. 36- 37
18. 34.
Homework:
p. 36- 37
42. 54.
#2- 54 eoe
May 9­12:56 PM Sep 13­7:51 AM
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15. Order of Operations notebook2.notebook September 18, 2012
p. 36 #2­ 54 eoe
2. ­2x 6. 4n
Warm Up
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 9­12:26 PM May 9­12:53 PM
Solving Equations
May 9­12:53 PM Jun 18­2:49 PM
Solving equations is
something you have done
before. You must keep both
sides equal without throwing
one side off balance. ­3 ­3
We all know how to solve this
equation. What is the first
step? x = 5
Do you understand HY you
W
must subtract 3 from BOTH Check:
sides to keep the balance? 5 + 3 = 8
8 = 8
Both sides are
still balanced!
May 9­12:53 PM Dec 26­6:01 PM
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16. Order of Operations notebook2.notebook September 18, 2012
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Jun 18­2:51 PM Jun 18­2:52 PM
Jun 18­2:53 PM Jun 20­7:59 AM
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17. Order of Operations notebook2.notebook September 18, 2012
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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18. Order of Operations notebook2.notebook September 18, 2012
p. 50 #2­ 50 eoe
14. 22.
Homework:
p. 50
# 2- 50 eoe 30. 46.
May 10­8:27 AM Jun 21­12:32 PM
p. 50 #2­ 50 eoe QUIZ #1
2. 5 6. 10
CR #1 due tomorrow at the
beginning of class!
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
Sep 13­8:40 AM May 8­3:16 PM
Warm Up
CR #1 is due NOW
When 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 May 10­12:45 PM
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19. Order of Operations notebook2.notebook September 18, 2012
Consecutive Integer Word Problems Let's watch this video to see if you can
explain the meaning of
CONSECUTIVE
May 10­12:45 PM May 10­12:45 PM
How do you represent integers for these word problems???
What does Consecutive Integers: Consecutive Even/ Odd Integers:
x = 1st integer x = 1st even/ odd integer
CONSECUTIVE x + 1 = 2nd integer x + 2 = 2nd even/ odd integer
x + 2 = 3rd integer x + 4 = 3rd even/ odd integer
mean to you? x + 3 = 4th integer x + 6 = 4th even/ odd integer
and 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 10­12:45 PM May 11­8:24 AM
Examples:
Example: Find 3 consecutive integers whose sum is 147.
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?
May 10­12:48 PM May 11­8:31 AM
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20. Order of Operations notebook2.notebook September 18, 2012
4. What three consecutive negative integers have a sum of ­36? 6. What two consecutive odd integers have a sum of ­28?
7. What four consecutive integers have a sum of ­34?
5. What four consecutive integers have a sum of 66?
May 11­8:35 AM May 11­8:36 AM
2. Hank went to Shop Rite and purchased some roast beef
Word Problems 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
1. A number problem states "­5 times a number, minus 22 gives a pounds of roast beef did he buy? Round your answer to the
result of 23." What is the number? nearest tenth if necessary.
Jul 9­9:17 AM Jul 9­9:22 AM
3. A plumber charges a $35 fee on all house calls plus an
More
hourly rate for labor. If the total bill for a job takes 3 hours
is $110, what is the plumber's hourly rate? practice...
Jul 9­9:22 AM May 10­12:48 PM
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21. Order of Operations notebook2.notebook September 18, 2012
More
practice...
Homework:
Worksheet
May 10­12:48 PM May 11­10:45 AM
Warm Up
Jun 21­12:33 PM May 10­12:52 PM
Equations with Fractions
May 10­12:52 PM May 10­12:54 PM
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22. Order of Operations notebook2.notebook September 18, 2012
Answer on next slide...
May 10­12:59 PM May 10­12:59 PM
Answer on next slide...
May 10­1:00 PM Jun 21­12:45 PM
May 10­1:04 PM May 10­1:04 PM
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23. Order of Operations notebook2.notebook September 18, 2012
Solve each of the following:
1. 2. Homework:
p. 58
#2- 12 even, 16 and
18
May 10­1:08 PM May 10­1:11 PM
Warm Up
May 10­1:12 PM May 10­1:44 PM
Interval Notation ( 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).
May 10­1:44 PM May 10­12:48 PM
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24. Order of Operations notebook2.notebook September 18, 2012
[ is called the left hand parenthesis symbol. ( ) is equivalent to < or >
] is called the right hand parenthesis [ ] is equivalent to
symbol.
Inequality NotationInterval Notation
Written in interval notation [­8, 7] means
the set of numbers between ­8 and 7 2 < x < 15 (2, 15)
including ­8 and 7. (2, 15]
[2, 15)
[2, 15]
May 10­12:48 PM May 10­1:59 PM
How would you write the following
inequalities in interval notation?
May 10­2:24 PM May 10­1:43 PM
How would you write the following
intervals into inequalities? Solve the following inequalities and
write your answer in interval notation.
May 10­2:24 PM May 10­2:30 PM
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25. Order of Operations notebook2.notebook September 18, 2012
Homework:
p. 85
#2- 20 evens
May 10­1:47 PM Jun 21­12:51 PM
Review for Unit 1 Exam
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?
May 10­12:48 PM May 10­12:48 PM
Jun 27­9:34 AM May 11­11:06 AM
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26. Order of Operations notebook2.notebook September 18, 2012
Jul 9­9:29 AM
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