1. Where letters are numbers and numbers are letters!
Algebra
Where letters are numbers and numbers are letters!

2. Algebra Concepts Geometric Sequencing FOIL Method
Expressions as Statements
Evaluating and Simplifying Expressions
One Step Linear Equations
Two Step Linear Equations
Inequalities
Slopes, Intercepts and Graphing
Functions
Quadratic Equations
Monomials

3. Geometric Sequencing
You can use differences to find the patterns of some sequences
Patterns may be shown using shapes or numbers

4. Geometric Sequencing Examples
What is the next term in the sequence
5,15,3,53,81….
The pattern is adding 6 more to the previous number added
The next term would be….115, 155
Refer to packet for 2nd example

5. Geometric Sequencing Examples
What are the next 2 terms of the sequence 3,5,8,12….
The pattern is adding one more than previous number added
The next two terms are 17 and 23

6. Assignments Complete the 1st worksheet, I will come around and help
Tomorrow you are to complete the other 2
On the 3rd worksheet #’s 8-14 are extra credit, they are a little more difficult

7. Expressions as Statements
You can write a word equation to represent relationships before writing an algebraic equation.
For example: If the larger number is increased by the smaller, the result is 84
3x x = 84

8. Expressions as Statements Examples
9 less than the product of 6 and 8
9- (6 x 8)
Twice a number, increased by 10
2x + 10
If a number is decreased by 9 and the difference is multiplied by 3, the result is the same as twice the number decreased by 10
3(x- 9) = 2x – 10

9. Expressions as Statements Examples
Find the number (from previous example)
3(x – 9) = 2x – 10
3x – 27 = 2x – 10
3x – = 2x –
3x – 17 = 2x
3x – 17 – 3x= 2x – 3x
-17 = -1x
-1 -1
17 = x

10. Assignments
Complete the 2 worksheets that follow the examples page in the packet
1st worksheet match the expression with its statement
2nd worksheet write an expression to go with the equation

11. FOIL Method Foil stands for
First: Multiply the first term in each set of parentheses
Outer: Multiply the outer term in each set of parentheses
Inner: Multiply the inner term in each set of parentheses
Last: Multiply the last term in each set of parentheses

12. After completing with FOIL Method
FOIL Method Example
(3 + 7x) (6 + 2x)
First: 3 x 6 = 18
Outer: 3 x 2x = 6x
Inner: 7x x 6 = 42x
Last: 7x x 2x = 14x²
After completing with FOIL Method
18 + 6x + 42x + 14x² Or
x + 14x²

13. Assignments
Complete the 3 practice problems on the FOIL Method sheet in your packet

14. Evaluating & Simplifying Equations
A variable is used as a placeholder in an algebraic expression. Examples are x, y, a, and so on
A term is a number, a variable, or the product of numbers and variables. For example –2, x, and 5y
A coefficient is the numerical factor in a term, for example the –2 in –2z

15. Evaluating & Simplifying Expressions
Like terms are terms that have the same variable. For example 3z and 7z
The simplest form of an algebraic expression is the form of the expression after all like terms have been combined
3x + 7x= 10x
10x would be the simplest form

16. Evaluating & Simplifying Equations Examples
What is the value of the expression –5x when x= -2
-5x
-5(-2) 10
What is the simplest form of this expression:
4x (-6x + 4)
4x (-6x +4)
4x + 7 –12x + 8
-8x + 15

17. Evaluating & Simplifying Equations Worksheet Examples
From Worksheet #1
3a – d = 3(4) – (-3)
= 15
2. 2c + 5b = 2(5) + 5(-2)
10 – 10= 0
3. 6(c + d)= 6 ( 5 + (-3))
6(5-3)= 6(2)=12

18. Evaluating & Simplifying Equations Worksheet Examples
11c + 5d – 6c + 2c
7c +5d
3. 7(2n-3r)-8r
14n-21r-8r
14n-29r
5. 8(-4b + 2d) –12d + 2b
-32 b + 16d –12d +2b
-30b +4d
7. 12f – 6g – 12g –7f
5f –18g

19. Assignments
Complete the practice on the back of the worksheet with the examples on it
When you finish with that complete # 4, 8, 12, and 18 on worksheet #1, and # 2, 4, 6, & 8 on the 2nd worksheet

20. One Step Linear Equations
An equation is a number sentence with two expressions that are equal.
An equation with a variable is an open sentence.
When you solve an equation you find the value of the variable that makes the open sentence (original equation) true.

21. One Step Linear Equations
To solve an equation means to get the variable alone on one side of the equals sign.
Use inverse operations to “take an equation apart”
Addition and subtraction are inverse operations
Multiplication and division are inverse operations

22. One Step Linear Equations Examples
What is the solution to
2z= -10
2 2
z= -5
What is the solution to
x-8 = -3
x-8 + 8=
x = 5
m/4 = 8
m/4 (4) = 8 (4)
m = 32

23. One Step Linear Equations Examples
b – 9 = 21
b – =
b = 30
r + 17 = -5
r + 17 – 17 = -5 – 17
r = -22
12 + c = 55
12 + c – 12 = 55 – 12
c = 43

24. Assignments On worksheet # 1 complete problem #’s 4-12
We will complete the rest of the worksheets through an activity/game

25. Two Step Linear Equations
When an equation requires more than one operation, first undo addition or subtraction, then multiplication or division
Parentheses in an equation can be removed by using the distributive property
2(x – 3) + 5= 15
2x = 15

26. Solving Two Step Equations
When an equation has the variable on both sides of the equals sign get the variable terms on one side and the numerical terms on the other side
2x-7=5x-19
2x-7+7=5x-19+7
2x=5x-12
2x-5x=5x-5x-12
-3x=-12
x=4

27. Two Step Linear Equations Examples
n= 3
7(x + 2) – 10=14
7x + 14 –10 = 14
7x +4 = 14
7x +4 – 4 = 14-4
7x = 10
x= 10/7= 1 3/7

28. Two Step Linear Equations Examples
2x –7 = 5x – 19
2x – = 5x –
2x + 12 = 5x
2x + 12 – 2x = 5x – 2x
12=3x
4 = x

29. Assignments Complete the practice on the back of the page
We will complete the other worksheet through an activity

30. Inequalities
You can solve an inequality the same way you solve an equation
The exception is that you must reverse the inequality symbol when you multiply or divide by a negative number
In an inequality, two quantities are related in on of these ways
Less than <, less than or equal to <, greater than >, and greater than or equal to >

31. Inequalities
The solution set for inequalities can contain many values (more than one answer)
To graph the solution set use a number line

32. Inequalities Examples
What is the solution set for –z + 1 < 5
-z +1 – 1 < 5 – 1
-z < 4
What is the solution set for 2k – 3 > 15
2k – >
2k > 18
k > 9
Graph the inequality
y < 10
x > 4
Worksheet #1 numbers 1 & 2

33. Assignments Worksheet #1 numbers 3, 5 and 7 Worksheet # 2 even numbers
We will do worksheet #3 as a class activity

34. Slope, Intercepts, & Graphs

35. Slope, Intercepts, and Graphs Examples

36. Assignments

37. Functions

38. Functions Examples

39. Assignments

40. Quadratic Equations

41. Quadratic Equations Examples

42. Assignments

43. Monomials

44. Monomial Examples

45. Assignments

46. Algebra Review Geometric Sequencing Expressions as Statements
Evaluating & Simplifying Statements
One Step Linear Equations
Two Step Linear Equations
Inequalities
Slope, Intercepts, and Graphs
Functions
Quadratic Equations
Monomials