Solving One-Step Equations
GOAL: I can solve one-step equations with one variable.

 Learning Standards  Common Core Standard: 7.EE.1


RED BOOK Reference:

Pages: 128 ─ 132

Pages: 135 ─ 138

Practice on page 132,

#15-37 odds and

on page 138, #15-29 odds.

BLACK BOOK Reference:

Pages: 81 ─ 85

Practice on page 85,

#27-49 odds.

 Practices (with answers)  
  Solving 1-Step Problems (ver. 1)

 Solving 1-Step Problems (ver. 2)

Solving 1-Step Problems (ver. 3)

Lesson Vocabulary  
Equivalent Equations Equations that have the same solutions.
Addition Property of Equality Adding the same number to both sides of the equation doesn't change the equation.
Subtraction Property of Equality Subtracting the same number from both sides of the equation doesn't change the equation.
Isolate Means to get a variable all alone by itself.  You do this using the other properties mentioned in this section.  Once you have the variable all alone by itself, you have the answer to the algebra problem.
Inverse Operations Inverse operations "undo" other operations.  For example, subtraction undoes addition; multiplication undoes division; and so on.  Every mathematical operation has an inverse operation.
Multiplication Property of Equality     Multiplying both sides of the equation by the same number doesn't change the equation.
Division Property of Equality Dividing both sides of the equation by the same number doesn't change the equation.

Textbook English Video Tutorials Textbook Spanish Video Tutorials 

 Video Tutorials    
Topic Problem  Time (min: sec)
Solving One-Step Equations a + 5 = 54   1:54
Solving One-Step Equations  (x/3) = 14  2:22
Solving One-Step Equations
x + 11 = 7
7x = 21
(5x/12) = (2/3)


Strategies and Content Practice
Solving one-step equations is the most important lesson in the most important math topic in all of math.  This is no hyperbole.  Algebra is the first math class that exposes students to abstract thinking.  And solving one-step problems is the threshold through which students pass to enter the world of abstract thinking.  Solving one-steps is where students first encounter the rules of opposites (the inverse operations).  When students master one-step problems, it opens their minds to the realization that solving more challenging problems is not so much math as it is a game of chess.  Like chess, algebra has a set of movement rules that have to be followed.  Break a movement rule in chess and you're cheating.  Break a movement rule in algebra and you WILL get the wrong answer (you loose).

Write on the whiteboard "Aunt Sally's Upside Down".
Aunt Sally  (add or subtract first)
MDear (multiply or divide second)
Excuse (exponents come third)
Please (parenthesis come last)

Review the setup for the 1-step problems, all four varieties, addition, subtraction, multiplication, and division. Make sure students have this prior knowledge of the inverse operations.
Remind students that the order of operation is done in reverse for solving algebra problems;
Please Excuse My Dear Aunt Sally is up-side down.

It's important that students understand WHY Please Excuse My Dear Aunt Sally is up-side down.
In elementary/intermediate school Please Excuse My Dear Aunt Sally was used when the "thing" they were looking for was the answer and the answer was all alone on one side of the equal sign as in the following example:
2(8  5) + 7 = ?

In other words, the answer they sought was OUTSIDE the problem.
By contract, in algebra the answer that's sought is INSIDE the problem and it's called a variable, as in the following example:
2p + 18 = 6 

So in order to solve an algebra problem, it must first be turned INSIDE-OUT so that the answer sought (the variable) is again on the outside of the problem.  In order to turn the algebra problem INSIDE-OUT, we have to apply Please Excuse My Dear Aunt Sally is up-side down (not right-side-up). 
Engage Have students read pages 81  86.
Read aloud same with students, emphasize definitions and examples.
Work out the example problems on the board; solicit volunteers to try them.

Try this online Algebra Tiles App to practice solving 1-step problems.
After example problems, have students try to solve the Sample Problems below.  After students have had time to complete them, click on the Solutions link and go through the step-by-step process for solving each problem.  Repeat if necessary with additional example problems in the book and re-assess.