1. Expressions and Equations
Define expression:
A number, variable or the combination of numbers and variables with symbols.
Define equation:
Two expressions that equal each other.

2. What do expressions look like
What do expressions look like? 15 3x+4 y2 a2+b2 What do equations look like? 3x+14 = 15 a2+b2=c2 3y=9 What’s the difference?

3. Expression or Equation?
7x =5x-1
19=11+8y 4x=3+9
26+6x x

4. Like terms have the same variable to the same power
Like terms have the same variable to the same power. Examples: 15, 3, and -6 are all like terms. 12x, 4x and -2x are all like terms. 2a2, -a2, a2 are all like terms.

5. We simplify expressions by combining like terms
We simplify expressions by combining like terms. What property are we using to “move” terms? Simplify the following expressions: 3x + 4x y + 3 3x + 5y -7x + 21x 2x3 + 4y 2 – 5x3 + 7y 5 -23a 4 – 14a2 + 3f 5 – 5a 4 + 6f 5

6. Today’s Expression is 12x Which representations are equivalent to 12x?
20x – 8x
+ x
Today’s Expression is 12x Which representations are equivalent to 12x?
24x 2x
2(6x)
Jane has $x more than Ellie, Ellie has $12. How much money does Jane have?
12 + x
X * X * X * X * X * X * X * X * X * X * X * X
Jane earns $x in allowance each week. How much money would she have in 12 weeks.
If there are certain representations that you want to have come out of the activity and you are worried they won’t, examples vs. non-examples might be a nice way to introduce them. It emphasizes the student reasoning through the situation, rather than being told. 36 12
100 – 88x
(x)
3x + 9x
x + x + x + x + x + x + x + x + x + x + x + x
3x(4x)

7. We solve equations by isolating the desired variable.
The golden rule of algebra: Any operation done on one side of an equation must also be done on the other side. 
3x – 5 = 10
3x – =
3x + 0 = 15
3x = 15
3x ÷ 3 = 15 ÷ 3
x = 5
We can also think of it as: to move something across the equal sign, the operation has to flip (become its inverse).
3x – 5 = 10 => move the 5 to the other side by adding 5
3x =
3x = => move the 3 to the other side by dividing by 3
x = 15 ÷ 3
Why can’t we divide by 3 as the first step, then add 5?

8. Solve for x: Check your answer! 2) 32 + x = 28 -7x = 63

9. Combine like terms then solve for y:
5) 3y + 2y = 50
7) -2y + 3y = 20
6) 33 + y + 3 = 124
8) 14y + y=
Check your answer!

10. Write each sentence as an algebraic equation:
The product of five and a number increased by fifteen is ten.
The quotient an unknown number and 7 decreased by 3 is 18.
Twelve less than three times a number is three.

11. My teenage neighbor, Cassie, babysits in her spare time
My teenage neighbor, Cassie, babysits in her spare time. She charges $3 to travel to any job and $4 per hour. Calculate how much she will earn for a 2 hour job. 3 hours? 4 hours? x hours? She got paid $13 last night. How many hours did she babysit?