variables and expressions order of operations real numbers and the number line objective: to solve...
TRANSCRIPT
![Page 1: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/1.jpg)
Variables and ExpressionsOrder of Operations
Real Numbers and the Number Line
Objective: To solve problems by using the order of operations.
![Page 2: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/2.jpg)
Variables
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Variables
![Page 4: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/4.jpg)
Problem 1
![Page 5: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/5.jpg)
Got it?
• What is an algebraic expression for 18 more than a number n?
![Page 6: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/6.jpg)
Got it?
• What is an algebraic expression for 18 more than a number n?
n + 18
![Page 7: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/7.jpg)
Writing Expressions with Multiplication and Division
![Page 8: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/8.jpg)
Got it?
![Page 9: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/9.jpg)
Got it?
nb
na
18)
6)
![Page 10: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/10.jpg)
Got it?
nb
na
18)
6)
6
6
)
y
y
Noc
![Page 11: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/11.jpg)
Writing an Expression with Two Operations
![Page 12: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/12.jpg)
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![Page 13: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/13.jpg)
Got it?
84) xa
![Page 14: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/14.jpg)
Got it?
84) xa )8(2) xb
![Page 15: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/15.jpg)
Got it?
84) xa )8(2) xbx
c12
5)
![Page 16: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/16.jpg)
Writing a Rule to Describe a Pattern
![Page 17: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/17.jpg)
Writing a Rule to Describe a Pattern
![Page 18: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/18.jpg)
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![Page 19: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/19.jpg)
Got it?
2n
![Page 20: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/20.jpg)
Class Work
• Top of Page 7 (lesson check)• 1, 2, 7, 8
![Page 21: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/21.jpg)
Homework
• Pages 7-8• 9-25 odd• 39, 41, 43
![Page 22: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/22.jpg)
Exponents
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Exponents
• An exponential is expressed in the following:
• is read 5 to the second power or 5 squared.• is read 5 to the third power or 5 cubed.• is read 5 to the fourth power.• is read 5 to the fifth power.• Etc….
35
25
4555
![Page 24: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/24.jpg)
Simplifying Powers
![Page 25: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/25.jpg)
Got it?
![Page 26: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/26.jpg)
Got it?
813333
![Page 27: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/27.jpg)
Got it?
813333 27
8
3
2
3
2
3
2
![Page 28: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/28.jpg)
Got it?
813333 27
8
3
2
3
2
3
2 125.5.5.5.
![Page 29: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/29.jpg)
Order of Operations
![Page 30: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/30.jpg)
Order of Operations
• Please• Excuse• My• Dear• Aunt• Sally
![Page 31: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/31.jpg)
Order of Operations
• Parenthesis• Exponents• Multiplication• Division• Addition• Subtraction
![Page 32: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/32.jpg)
Order of Operations
• Parenthesis- Always simplify everything inside of any grouping symbol before doing anything else.
![Page 33: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/33.jpg)
Order of Operations
• Parenthesis- Always simplify everything inside of any grouping symbol before doing anything else.
• Exponents- After simplifying everything in the grouping symbol, you then apply the exponent.
![Page 34: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/34.jpg)
Order of Operations
• Parenthesis- Always simplify everything inside of any grouping symbol before doing anything else.
• Exponents- After simplifying everything in the grouping symbol, you then apply the exponent.
49)7()43( 22
222 43)43(
![Page 35: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/35.jpg)
Order of Operations
• Multiplication• Division.• These operations are equal. You do not always
multiply before you divide. These operations are done from left to right.
![Page 36: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/36.jpg)
Order of Operations
• Multiplication• Division.• These operations are equal. You do not always
multiply before you divide. These operations are done from left to right.
• Let’s look at the following. What do you think the answer is?
248
![Page 37: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/37.jpg)
Order of Operations
• Multiplication• Division.• These operations are equal. You do not always
multiply before you divide. These operations are done from left to right.
• Let’s look at the following. What do you think the answer is?
• Wrong!• Right!
188248
422248
![Page 38: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/38.jpg)
Order of Operations
• Addition.• Subtraction.• These operations are equal. You do not always add
before you subtract. These operations are done from left to right.
![Page 39: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/39.jpg)
Order of Operations
![Page 40: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/40.jpg)
Got it?
• Solve the following:
2475 2
52512
27
34 4
![Page 41: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/41.jpg)
Got it?
• Solve the following:
27835216352475 2
52512
27
34 4
![Page 42: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/42.jpg)
Got it?
• Solve the following:
27835216352475 2
751252512
27
34 4
![Page 43: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/43.jpg)
Got it?
• Solve the following:
27835216352475 2
751252512
175
85
5
814
27
34 4
![Page 44: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/44.jpg)
Evaluating Algebraic Expressions Using Substitution
![Page 45: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/45.jpg)
Evaluating Algebraic Expressions Using Substitution
![Page 46: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/46.jpg)
Got it?
• Solve the following if a = 3 and b = 4.
23 ab ab 72 2
![Page 47: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/47.jpg)
Got it?
• Solve the following if a = 3 and b = 4.
3912
)3()4(3
32
2
ab ab 72 2
![Page 48: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/48.jpg)
Got it?
• Solve the following if a = 3 and b = 4.
3912
)3()4(3
32
2
ab
112132
21)16(2
)3(7)4(2
722
2
ab
![Page 49: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/49.jpg)
Class Work
• Top of page 13 (lesson check)• 1-7 all
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Homework
• Page 13• 9-33 odd• 37, 39, 41• 45, 47, 49
![Page 51: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/51.jpg)
Square Roots
![Page 52: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/52.jpg)
Simplifying a Square Root
![Page 53: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/53.jpg)
Perfect Squares
14412
12111
10010
819
648
497
366
255
164
93
42
2
2
2
2
2
2
2
2
2
2
2
![Page 54: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/54.jpg)
Perfect Squares
14412
12111
10010
819
648
497
366
255
164
93
42
2
2
2
2
2
2
2
2
2
2
2
12144
11121
10100
981
864
749
636
525
416
39
24
![Page 55: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/55.jpg)
Got it?
![Page 56: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/56.jpg)
Got it?
648
864)2
a
255
525)2
b
![Page 57: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/57.jpg)
Got it?
648
864)2
a
255
525)2
b
3612
61
61
361
)(
)
c
121812
119
119
12181
)(
)
d
![Page 58: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/58.jpg)
Real Number System
![Page 59: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/59.jpg)
Graphing and Ordering Real Numbers
![Page 60: Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649e6a5503460f94b687d3/html5/thumbnails/60.jpg)
Homework
• Page 20• 9-17 odd• 45, 47, 49