1. Ch. 4-1 Algebraic Expressions and the Order of Operations

2. Algebra Map
In the concept map below, various aspects of algebra are found, as well as how the aspects relate to different parts of "language" such as nouns, verbs, and pronouns.

3. * (asterisk, used with computers)
Different Ways to Show Multiplication:
"X"  (times sign)
3 x 5
" .  " (raised dot)
3  .  5
* (asterisk, used with computers)
3*5
(#)(#) parentheses
(3)(5)
# next to letter
3x = (3)(x)
letter next to letter
xyz = x (y)(z)
exponents
23 = 2 x 2 x 2
Different Ways to Show Division:  
Division symbol ( ÷)
2 ÷ 5
Slash symbol ( / )
2/5
Fraction bar
2 5

4. variable A symbol that stands for one or more numbers, like a pronoun
x = slope of a line
h = height
z = 22
t = -55

5. Numerical expression
mathematical phrase that uses numbers and operation symbols, like an incomplete sentence
5 – 2
2 + 2
4 x 8

6. Algebraic expression
mathematical phrase that uses numbers variables and operation symbols, like an incomplete sentence
y – 2
x + 2 4x

7. Ch. 1-1 Algebraic Expressions and the Order of Operations
-a variable is a symbol that stands for one or more numbers
Example: x = y = z = 0
-an algebraic expression is a mathematical phrase that uses numbers variables and operation symbols.
Example: x y – x
You can translate word phrases into algebraic expressions.
3 more than a number
A number increased by 3
x + 3
The quotient of a number and 8
x/8
6 times a number
The product of 6 and a number 6x
15 less than a number
15 subtracted from a number
x - 15

8. Common words used in English: Addition Subtraction Multiplication
Less... Less than... Is Less Than
Be cautious when you are translating to be exact, especially with the word phrases: "Less, Less than, and Is less than." Read the following English phrase and notice how the algebraic phrase is written.  
Common words used in English:
Addition
Subtraction
Multiplication
Division
Sum Plus Added to More*, More than* Increased by Total, totaling
Difference Minus Subtracted from Less* Less than * Decreased by
Product Times Multiply Twice, Double ( x 2) Triple ( x 3 ) Of
Quotient of Divided by Into Per    
Five less a number is two.
5 - n = 2
Five less than a number is two.
n - 5 = 2
Five is less than a number.
5 < n

9. Example 1: Write an algebraic expression for each statement below.
a.) At a ballpark, team hats are $15 each. Let n represent the number of hats purchased.
b.) You lose $5 from your wallet. Let x represent the original amount of money that you started with.
15n
x - 5
-to simplify an expression means to replace each variable with its simplest name
-to evaluate an expression, replace each variable with a number and then simplify

10. Two more than 4 times a number x1
Two more than 4 times a number x

11. 1
4x + 2
Home

12. 2
5 times a number x is 20

13. 2
5x=20
Home

14. Eight times the difference of x and y3
Eight times the difference of x and y

15. 3
8(x – y)
Home

16. The current temperature plus 20 degrees4
The current temperature plus 20 degrees

17. 4
t=temperature so t + 20
Home

18. Five dollars times the number of people, plus ten dollars5
Five dollars times the number of people, plus ten dollars

19. 5
P=people so 5p + 10
Home

20. A number x divided by the sum of 2 and another number y6
A number x divided by the sum of 2 and another number y

21. 6
x÷(2+y)
Home

22. Three times your paycheck plus $527

23. 7
P=paycheck so 3p + 527
Home

24. Two runs fewer than the other team scored8
Two runs fewer than the other team scored

25. 8
R=runs so r – 2
Home

26. Three less 2 times a number k9
Three less 2 times a number k

27. 9
3 – 2k
Home

28. Order of Operations: Basically "4" Rules (Do the rules in order):
RULE 1 - Do all operations within grouping symbols (parentheses, brackets, vinculum (fraction bar))
RULE 2 - Evaluate the number value for any exponents
RULE 3 - Multiply or divide in order from left to right
RULE 4 - Add or subtract in order from left to right
Example 3: Use the order of operations to simplify each expression below.
x = 4 and y = 2
a.) (x + 4) – 5 + x * 3 b.) 2y – x + 8/y
c.) xy/2 + 5 – d.) 18 – 3y + (x – 2)
Plug in for x and y 2(2) – 4 + 8/2
Plug in for x and y (4 + 4) – * 3
(8) – * 3
4 – 4 + 8/2
4 – 4 + 4
(8) –
0+ 4
= 4
3 + 12
=15
4(2)/
9 – 3
18 – 3(2) + (4 – 2)
8/2 + 5 – 3 =6
18 – 3(2) + 2
12 + 2
18 – 6 + 2
4 + 5 – 3
=14

29. Homework– Page 171
# 2 – 30 even

31. Example: 
When there are two or more parenthesis, or grouping symbols, perform the inner most grouping symbol first.
2 + 3[ 5 + (4 - 1)2]  2 + 3[ 5 + (3)2]    inner most parentheses are done first 2 + 3[ 5 + 9]   then work your way out 2 + 3[ 14]   44

34. Homework– Page 171
# 2 – 30 even
Go over

35. Homework Contest Teams
Reteach 4-1 and practice sheet 4-1
Homework Contest Teams

36. Two more than 4 times a number x
5 times a number x is 20
Eight times the difference of x and y
The current temperature plus 20 degrees
Five dollars times the number of people, plus ten dollars
A number x divided by the sum of 2 and another number y
Three times your paycheck plus $527
Two runs fewer than the other team scored
Three less 2 times a number k