1. Tennessee Adult Education Mathematics Level 3 Curriculum 2011
Lesson 8
Algebra

2. Input/ Output Tables
When given an input/output table, the question is usually asking for what operation was used to achieve the output number.
Input
Output 3 1 4 2 5 7
How does 3 get to 1?
Subtract 2
How does 4 get to 2?
Subtract 2
It is important to test all inputs and outputs by the rule before selecting an answer.
How does 5 get to 3?
What is the rule for this table?
Subtract 2
How does 7 get to 5?
Subtract 2
Subtract 2
* This is the rule for this specific table.

3. Guided Practice Directions: Find the rule for each input/output table.1. 2.
Input
Output 1 6 11 10 15 5
Input
Output 2 4 3 6 8 16 5 10

4. Guided Practice Directions: Find the rule for each input/output table.1. 2.
Input
Output 1 6 11 10 15 5
Input
Output 2 4 3 6 8 16 5 10
1 + 5 = 6
2 x 2 = 4
6 + 5 = 11
3 x 2 = 6
= 15
8 x 2 = 16
5 + 5 = 10
5 x 2 = 10
Rule: Add 5
Rule: Multiply by 2

5. Integers What are integers?
Integers include all whole numbers (all positive numbers) and their opposites. The opposite of a whole number is the negative of that number. In other words, integers include both positive and negative numbers.
For example: 1 is positive, and its opposite is -1.
Why do I need to know about integers?
People use integers everyday for things such as banking or temperature. On the GED test, there will be algebra problems. You must have the basic understanding of how integers work to solve algebra problems.

6. Adding Integers Rules:
If the signs are the same, add and keep the sign.
Example:
2 + 7 = 9
= -9
If the signs are different, subtract and keep the sign of the larger number.
= -2
= 2

7. Guided Practice -5 + -8 = ____ 2. -9 + 4 = _____
= ____ = _____
= ____ = ____
= ____ = _____
= _____ =____

8. Guided Practice -5 + -8 = ____ 2. -9 + 4 = _____
-13 -5
= ____ = _____
= ____ = ____
= ____ = _____
= _____ =____ 4
-15
-67 11
-23
-24

9. Subtracting Signed Numbers
Rewrite the problem, using the following steps:
Keep It - Keep the first number as it is.
Change It - Change the operation.
Switch It – Switch the sign on the second number.
Follow the addition rules.
Example: Original Problem Revised
-6 – = -10
-8 - (-72) = 64

10. Guided Practice -8 – 6 = _______ -5 - 4 = _______ -5 - -2 = _______
= _______
= _______
= _______
-7 – 6 = _______

11. Guided Practice -8 – 6 = _______ -5 - 4 = _______ 5 - -2 = _______
= _______
= _______
= _______
-7 – 6 = _______
-14 -9 7 9
-13

12. Multiplying & Dividing Signed Numbers
Rules for Multiplying and Division are the same:
When the signs are the same, the answer is positive.
When the signs are different, the answer is negative.
Examples:
Same Signs Different Signs x 7 = x 7 = -42
-6 x -7 = x -7 = -42
42 ÷ 6 = ÷ -6 = -7
-42 ÷ -6 = ÷ 6 = -7

13. Guided Practice -2 x -6 = _____ -3 x -10 = _____ -20 ÷ 5 = _____
-20 ÷ 5 = _____
-9 x 12 = _____
12 ÷ -4 = _____

14. Guided Practice -2 x -6 = _____ -3 x -10 = _____ -20 ÷ 5 = _____12
-2 x -6 = _____
-3 x -10 = _____
-20 ÷ 5 = _____
-9 x 12 = _____
12 ÷ -4 = _____ 30 -4
-108 -3

15. Order of Operations Purple Elephants Marching Down A Street
When expressions have more than one operation, we have to follow rules for the order of operations:
Purple Elephants Marching Down A Street
Parenthesis
Exponents
Multiplying or Division
Addition or Subtraction
First, do all operations inside parentheses.
Next, solve the exponents.
Working from left to right, do all multiplication and division (whichever comes first)
Finally, working from left to right, do all addition and subtraction. (whichever comes first)

16. Order of Operations (2 x 4)² x (5 – 1) +1 8² x 4 + 1 x 4 + 1 256 + 1
Purple Elephants Marching Down A Street
(2 x 4)² x (5 – 1) +1
Step 1: Parenthesis
Step 2: Exponents
Step 3: Multiply or Divide
Step 4: Add or Subtract 8²
x 4
+ 1 64 x
256
+ 1
257

17. Guided Practice ORDER! (1 x 2) + (6 - 3)² = 2. (4 – 5)³ x 3 x 9 =

18. Guided Practice ORDER! (1 x 2) + (6 - 3)² = 2. (5 - 2)³ x 3 x 9 =
2 + 3²
3³ x 3 x 9
2 + 9
27 x 3 x 9 11
81 x 9
729
72 ÷ 6²
2(1+ 54)
72 ÷ 36
2(55) 2
110
(30)(15) ÷ 2
450 ÷ 2
225

19. Substitution
What is a substitute? In mathematics, a variable is a substitute for a number in algebraic expression. What does substitute mean?
A substitution is a replacement for something else.
What is a variable?
It is a letter that represents an unknown value or number.

20. b + 3(t – 4); solve if b = 7 and t = 6
In most problems there will be more than one variable. In this case, a number will be assigned to each variable.
For example:
b + 3(t – 4); solve if b = 7 and t = 6
Simply substitute the numbers in place of each variable:
7 + 3(6 – 4) = 13
**Before solving, remember to use the Order of Operations

21. Guided Practice!! y + z + 2 if y = -6, z = 5
(n + 4)² - (3 + 2)(n) if n = 4
2. (p + 65)(4 – 2) + p if p = 10
y + z if y = -6, z = 5

22. Guided Practice!! (n + 4)² - (3 + 2)(n) if n = 4
2. (p + 65)(4 – 2) + p if p = 10
3. y + z if y = -6, z = 5
(4 + 4)² - (3 + 2)(4)
8² - 5(4)
64 – 5(4) 44
( )(4 – 2) + 10
(75)(2) + 10
160
-1 + 2 1

23. Algebraic Equations Terms:
Equation – both sides of an equal sign must be equivalent = 10
10 = 10
Variable – a letter that represents an unknown value or number.
n + 7
Coefficient – a number connected to a variable
3 x + 4

24. Solving Algebraic Equations
An algebraic equation is like a balance. The left side of the equation must equal the right side of the equation. Ex. x + 3 = 5 What number can we replace “x” with? HINT: You can replace the variable/letter with an empty box.

25. Solving Algebraic Equations
The overall goal in solving equations is to get the variable by itself. To get the variable by itself, use the inverse (opposite) operation.
Inverse Operations:
Addition Subtraction
Multiplication Division
For example:
X + 12 = 26
x = 14
Steps for solving:
Throw the number to the other side of the equal sign and use the inverse operation.
Perform the operation.
- 12 X =

26. Guided Practice x + 6 = 9 2. 32 = x + 3 4x = 16 4. 2x = 12

27. Guided Practice x + 6 = 9 2. 32 = x + 3 4x = 16 4. 2x = 12