1. Algebra

2. ALGEBRA Algebra is finding the unknown It uses letters for numbers
Algebraic equation has a letter
- has an equal sign
- eg. 5 + y = 8

3. ALGEBRA
one side of the equal sign must equal the other.

4. Using Variables VARIABLES
You can use any letter to represent a variable without changing the meaning of the equation or expression
Use a short cut to show multiplication
3n = 3 x n
When you solve an equation you find the value of the variable
Short cut
Wherever there is a pencil that means they have to write out the notes. We have gone over 2(3) and how that can be written many different ways but they will probably forget!!!

5. 2y-7
Coefficient
Constant
Variable

6. Reading Equations and Expressions
The cup contains an unknown amount of counters
Write the expression 1. X +
I would like them to write it ALL even the instructions. They have to draw the cup on the paper. Then have them try to figure out what the equation/expression is. The answer will be on the last click of the button.
X + 4

7. X X 2X + 2 X+X + 2 2. + + Write the expression
The coefficient is . . .
The constant is …
2X + 2
X+X + 2
There is a text box hiding behind the 2x+2 it says x + x+ 2. Have them try to figure out a different way to write it, then the next click has 2x +2

8. X X + 3 = 7 3. = + Write the equation
How many counters must be in the cup to make both sides equal?
X + 3 = 7
They should write it all down on their paper. If they are being good the last questions they don’t have to write but just put the answer

9. Do – Reading Equations and Expressions practice.

10. BIG IDEAS… so far
In ALGEBRA we are trying to find out how much the UNKNOWN is
Both sides of the equal sign are in balance
Variables represent the part that is unknown in the equation

11. When we Know what “x” is Equal To
When we have a value for the variable and we put it into the equation or expression and solve.
Called SUBSTITUTION
eg #1. Solve if x = 5
x + 8 =
Write the equation down
Substitute the value in for the variable
5 + 8 =
5 + 8 = 13
Solve – Find the answer

12. Ratio Tables
We can use a RATIO TABLE to solve equations when we know the value of “x”
eg. 5 + x =
Input (x)
Output (Answer) 1 6
5 + x = 20 2 5 1 6 10 25 7 2 7 5 10 20 25

13. eg. 2x + 1 = 2 x + 1 = (4) (2) (3) (1) 3 5 7 9 1 3 2 5 3 7 4 9 BEDMAS
Multiply
Input (x)
Output (Answer) 1 3
2 x + 1 =
(4)
(2)
(3)
(1) 3 5 7 9 2 5
BEDMAS 3 7 4 9

14. Do – Substitution Practice.

15. X – 1 = 3 x What is the equation? x Modeling Algebra -1 1
PRESERVATION OF EQUALITY x -1 1 1 1
What is the equation?
X – 1 = 3

16. What is the equation?
3X + 7 = -6

17. What is the equation?
X - 3 = 3

18. What is the equation?
-3 = 2x - 2

19. When we do not know the value of “x”
What is the equation?
X + 1 = 2

20. The Equality UNBALANCED
Goal – Get “x” by itself
What happens when we move ? x 1 1 1 x 1 1 1
The Equality UNBALANCED

21. BUT
We have to do something that keeps the balance AND gets “x” by itself 1 -1 x x 1 -1 1 1
X + 0
What can you do to +1 that will leave “x” by itself?
What can we do to this side to balance it?
WHAT YOU DO TO ONE SIDE YOU MUST DO TO THE OTHER
We want X + 0 on one side. What can we do to balance the scale? x 1 -1

22. How much is “x” ? x 1 -1
X = 1

23. Remember what you do to one side you must do to the other
What is the equation?
We want x alone – What do we have to do? 1 1 x -1 1 1 1 1 1 1 1 1
x + 0
Want this to equal zero
x = 2
X -5= -3
Remember what you do to one side you must do to the other

24. Modeling Algebra – Finding “x”
Goal –
- to get “x” alone on one side of the equal sign
- What you do to one side of the equal sign you must do to the other

25. Do
Modeling Algebra: Finding “x”