1. Chapter 1 - Foundations of Algebra
Algebra I

2. Table of Contents 1.6 - Order of Operations
1.7 - Simplifying Expressions
1.8 - Introduction to Functions

3. 1.6 - Order of Operations
Algebra I

4. 1-6
Algebra 1 (bell work)
The first letter of these words can help you remember the order of operations.
Please
Excuse My
Dear
Aunt
Sally
Parentheses
Exponents
Multiply
Divide
Add
Subtract
Order of Operations
Perform operations inside grouping symbols.
First:
Second:
Evaluate powers.
Third:
Perform multiplication and division from left to right.
Perform addition and subtraction from left to right.
Fourth:

5. 1-6
Example 1
Simplifying Numerical Expressions 1 2
A. 15 – 2 · 3 + 1
8 ÷ · 3
15 – 2 · 3 + 1
16 · 3
15 – 6 + 1 48 10
B. 12 – ÷ 2
–20 ÷ [–2(4 + 1)]
12 – ÷ 2
–20 ÷ [–2(4 + 1)]
12 – ÷ 2
–20 ÷ [–2(5)]
12 – 9 + 5
–20 ÷ –10 8 2

6. Evaluate the expression for the given value of x.
1-6
Example 2
Evaluating Algebraic Expressions
Evaluate the expression for the given value of x.
10 – x · 6 for x = 3
42(x + 3) for x = –2
10 – x · 6
42(x + 3)
10 – 3 · 6
42(–2 + 3)
10 – 18
42(1) –8
16(1) 16

7. 14 + x2 ÷ 4 for x = 2 (x · 22) ÷ (2 + 6) for x = 6 14 + x2 ÷ 4
1-6
14 + x2 ÷ 4 for x = 2
(x · 22) ÷ (2 + 6) for x = 6
14 + x2 ÷ 4
(x · 22) ÷ (2 + 6)
÷ 4
(6 · 22) ÷ (2 + 6)
÷ 4
(6 · 4) ÷ (2 + 6)
14 + 1
(24) ÷ (8) 15 3

8. Math Joke Q: Why are the parentheses wearing blue ribbons?
1-6
Math Joke
Q: Why are the parentheses wearing blue ribbons?
A: Because they always come first

9. Simplify. –8 + 22 –8 + 22 1-6 Example 3
Simplifying Expression with Other Grouping Symbols
Simplify.
2(–4) + 22
42 – 9
3| ÷ 2|
3| ÷ 2|
–8 + 22
42 – 9
3| ÷ 2|
3|16 + 4|
–8 + 22
16 – 9
3|20| 14 7
3 · 20 60 2

10. 5 + 2(–8) (–2) – 3 |4 – 7|2 ÷ –3 |–3|2 ÷ –3 32 ÷ –3 9 ÷ –3 –3 1-6 3
(–2) – 3
|4 – 7|2 ÷ –3 3
|–3|2 ÷ –3
5 + 2(–8)
–8 – 3
32 ÷ –3
9 ÷ –3 –3
5 + (–16)
– 8 – 3
–11 1

11. A. the sum of the quotient of 12 and –3 and the square root of 25
1-6
Example 4
Translating from Words to Math
Translate each word phrase into a numerical or algebraic expression.
A. the sum of the quotient of 12 and –3 and the square root of 25
B. the difference of y and the product of 4 and the quotient of y and 2

12. 1-6
Translate the word phrase into a numerical or algebraic expression: the product of 6.2 and the sum of 9.4 and 8.
6.2( )

13. 1-6
Example 5
Application
A shop offers gift-wrapping services at three price levels. The amount of money collected for wrapping gifts on a given day can be found by using the
expression 2B + 4S + 7D.
On Friday the shop wrapped
10 Basic packages B,
6 Super packages S,
5 Deluxe packages D.
Use the expression to find the amount of money collected for gift wrapping on Friday.
2B + 4S + 7D
2(10) + 4(6) + 7(5) 79
The shop collected $79 for gift wrapping on Friday.

14. HW pg.43
1.6
14-23, (Odd), 50-54, 67, 85-88
Ch: 65, 66

15. 1.7- Simplifying Expressions
Algebra I

16. 1-7
Algebra 1 (bell work)
Pg. 46
Pg. 47

17. 1-7
Example 1
Using the Commutative and Associative Properties
Simplify.
( ) + (16 + 4)
(100) + (20)
11(5)
120 55

18. 1-7
Simplify. 1 2 •
7 • 8 1 2 •
8 • 7
( ) + (58 + 2) ( ) 1 2 • 8 7
(500) + (60) 4 • 7
560 28 21

19. 1-7
Example 2
Using the Distributive Property with Mental Math
5(59)
8(33)
5(50 + 9)
8(30 + 3)
5(50) + 5(9)
8(30) + 8(3)
295
264

20. 1-7
The terms of an expression are the parts to be added or subtracted.
Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms.
Like terms
Constant
4x – 3x + 2
A coefficient is a number multiplied by a variable. Like terms can have different coefficients.
A variable written without a coefficient has a coefficient of 1.
Coefficients
1x2 + 3x

21. Math Joke Q: Why was the math teacher upset with Cupid?
1-7
Math Joke
Q: Why was the math teacher upset with Cupid?
A: He kept changing “like terms” to “love terms”

22. 1-7
Example 3
Combining Like Terms
0.5m + 2.5n
7x2 – 4x2 = (7 – 4)x2
= (3)x2
0.5m + 2.5n
= 3x2
0.5m + 2.5n

23. 1-7
Example 4
Simplifying Algebraic Expressions
Just Watch
Simplify 14x + 4(2 + x). Justify each step.
Procedure
Justification 1.
14x + 4 (2 + x)
Distributive Property 2.
14x + 4(2) + 4(x)
Multiply. 3.
14x x
Commutative Property 4.
14x + 4x + 8 5.
(14x + 4x) + 8
Associative Property 6.
18x + 8
Combine like terms.

24. 1-7
Simplify 6(x – 4) + 9. Justify each step.
Procedure
Justification 1.
6(x – 4) + 9 2.
6(x) – 6(4) + 9
Distributive Property
Multiply. 3.
6x –
Combine like terms. 4.
6x – 15

25. HW pg. 49
1.7
21-35 (Odd), 45, 52-54, (Odd)
Ch: 57, 58

26. 1.8 - Introduction to Functions
Algebra I

27. Points on the coordinate plane are described using ordered pairs.
1-8
Algebra 1 (bell work)
Points on the coordinate plane are described using ordered pairs.
An ordered pair consists of an x-coordinate
and a y-coordinate and is written (x, y).
Points are often named by a capital letter.

28. Graph each point. A. T(–4, 4) B. U(0, –5) C. V (–2, –3) 1-8 Example 1
Graphing Points in the Coordinate Plane
Graph each point.
A. T(–4, 4)
B. U(0, –5)
C. V (–2, –3)
Go over using graph paper,
Vs accurate graphs on notebook

29. A. E Quadrant ll B. F no quadrant (y-axis) C. G Quadrant l D. H
1-8
Example 2
Locating Points in the Coordinate Plane •E •F •H •G y
A. E
Quadrant ll
B. F
no quadrant (y-axis)
C. G
Quadrant l
D. H
Quadrant lll

30. 1-8
When you substitute a value for x, you generate a value for y.
The value substituted for x is called the input, and the value generated for y is called the output.
Output
Input
y = 10x + 5

31. Write a rule for the engraver’s fee.
1-8
Example 3
Application
An engraver charges a setup fee of $10 plus $2 for every word engraved.
Write a rule for the engraver’s fee.
Write ordered pairs for the engraver’s fee when there are 5, 10, 15, and 20 words engraved.
Let y represent the engraver’s fee and x represent the number of words engraved.
Engraver’s fee is
$10
plus $2
for each
word y = 10 + 2 x
y = x

32. Number of Words Engraved Rule Charges Ordered Pair x (input)
1-8
Number of
Words
Engraved
Rule
Charges
Ordered Pair
x (input)
y = x
y (output)
(x, y) 5
y = (5) 20
(5, 20) 10
y = (10) 30
(10, 30) 15
y = (15) 40
(15, 40) 20
y = (20) 50
(20, 50)

33. Math Joke Q: Why was the math teacher upset with one of the students?
1-8
Math Joke
Q: Why was the math teacher upset with one of the students?
A: He kept asking, “What’s the point?”

34. Input Output Ordered Pair
1-8
Example 4
Generating and Graphing Ordered Pairs
Generate ordered pairs for the function using the given values for x. Graph the ordered pairs and describe the pattern.
y = 2x + 1; x = –2, –1, 0, 1, 2 •
Input
Output
Ordered Pair x y
(x, y) –2
2(–2) + 1 = –3
(–2, –3) –1
2(–1) + 1 = –1
(–1, –1)
2(0) + 1 = 1
(0, 1) 1
2(1) + 1 = 3
(1, 3)
2(2) + 1 = 5 2
(2, 5)
The points form a line.

35. Input Output Ordered Pair
1-8
y = x2 – 3; x = –2, –1, 0, 1, 2
Input
Output
Ordered Pair x y
(x, y) –2
(–2)2 – 3 = 1
(–2, 1) –1
(–1)2 – 3 = –2
(–1, –2)
(0)2 – 3 = –3
(0, –3) 1
(1)2 – 3 = –2
(1, –2)
(2)2 – 3 = 1 2
(2, 1)
The points form a U shape.

36. HW pg. 57 1.8 17-20 (Use 1 Graph), 21-27, 29, 36, 37, 67-71 (Odd)
Ch: 41, 42-47