Algebra Variables, Expressions and Equations
GOAL: I will understand the use of variables in Algebra expressions and equations.

 Learning Standards  Common Core Standard: 7.EE.1

Lesson Vocabulary  
 Variable A letter of the alphabet (lower or upper case) that represents the value that we are trying to find in an algebra problem.
In some problems, the Variable represents an actual thing.  For example, "D" might stand for "Dog" and "C" might stand for "Cat".  So a sentence like Mr. Tomczak has 3 dogs and 4 cats can be written as an Algebra expression like this:

3D + 4C = Mr. Tomczak's Pets

 Expression An Algebra Expression is an incomplete math sentence.
Algebra Expressions are missing equal signs (=).
Because Algebra Expressions are missing equal signs, they cannot be solved.
When it comes to Algebra Expressions, our job is usually to SIMPLIFY them.
So about half the time in Algebra you simplifying expressions.
 Equations Algebra Equations are sort of the opposite of Expressions.
Algebra Equations contain equal signs (=).
Since Algebra Equations contain equal signs, we can usually SOLVE them.
So about half the time in Algebra you solve equations.


 Strategies and Content Practice  Notes 
Begin
(prepare) 

Check for prior knowledge.

What are Variables?
Where are Variables used?

Variables are letters of the alphabet.  Variables are used to replace blank lines or the empty box in pre-algebra problems, (see notes for examples).
Replace the blank line and the empty box with variables "G" and "R".  Tell students that their old pre-algebra problems could have contained variables as shown in these demos.

2 (9 ─ 4) = ____
3(5) + 7 = [ ]

2 (9 ─ 4) = G
3(5) + 7 = R

Engage

Now write an algebra equation, (see notes for example).
Ask students, what is the difference between the pre-algebra equations with the variables "G" and "R" and the algebra equation.
Students should conclude that in the pre-algebra problems the variables are on the OUTSIDE of the problem.  In the algebra problem the variable "K" in on the INSIDE of the problem.

The "a Ha!" is...  Algebra is the mathematical game of getting the variables from the inside of the problem to the outside of the problem.  Once the variable is outside the problem, all alone by itself, the problem is solved!

Have students read pages 4 ─ 6.
Read aloud same with students, emphasize definitions and example problems.
Show demonstration videos for Lesson 1─1 (above).

 7 + 4K = 35

 I like to use some of the following ideas and phrases...

In algebra equations, the variable is INSIDE the problem.

Algebra equations have SWOLLOWED their variable(s).