# Lesson: Variables: Using them to solve equations

Tara Smith E.l. Haynes Pcs Washington, DC
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### Lesson Objective

SWBAT use a variable to solve an algebraic expression

### Lesson Plan

Materials Needed: DN Worksheet, Math manipulatives for GP (baggies with movable pieces of the following: H +5, -5, -9, +9, =, 27, 36, 31 – it could be paper pieces) white board, dry erase markers, and IND Practice Worksheet.
Vocabulary: input/output table, variable, operation

……….
Do Now (2 - 3 min): The teacher passes out the DN worksheet. The DN focuses on finding the rule (2 step) of input/output table.

Opening (2 -3 min): Teacher opens by reviewing the answers to the DN. The teacher then states the objective, “Yesterday was our final day with input/output tables. We learned how to find both the input and output numbers with our rule. Today we are going to be solving expressions. Expressions have variables. By the end of the lesson, you will be able use a variable to solve an algebraic expression.”

Direct Instruction (10 min): Teacher explains, “We’ve been working with input/output tables for a few days now. Today we are going to switch gears and learn how important a variable can be to solving an equation. By the end of this lesson, you will all be able to solve this problem.

Carmen put a number into the "START" box of the sentence below.

[Refer to IND WORKSHEET QUESTION 2 for GRAPHIC]

The "END" number was 20. What number did Carmen put into the "START" box?

Now watch as I walk you through the steps to solving a problem like this. I have a problem like this on my test. The first thing I think is, what the heck is a box doing in my math equation? What I have to train myself to think when I see shapes in math equations is variables. A variable is a letter, shape, or symbol that represent a value in an equation. What is a variable? [a letter, shape, or symbol that represent a value in an equation.] Ok, now I know that this square is a variable. Then what? Well, I need to solve the equation. Yes, you jump right from looking at the equation to solving it. Watch as I do it!

1:  J + 6 - 3  = 18

2: J + 6 – 3 =  18
+ 3 =  +3
0 21

3: J + 6 = 21
- 6 = - 6
0     15

4:  J = 15

15 + 6 - 3 = 18
18 = 18

The teacher should walk through each step in the following manner, “ Ok I see that J is my variable because it is a letter in my equation. I need to get my variable all by itself. I want to see J = ____ and no other operation signs. Watch as I show you how to do that. First I want you to watch closely as I do this step something tricky is going to happen.” Teacher completes item 2. “I moved the 3 over to the other side of the equal sign. When I did that I changed the operation. We all know that addition is the inverse of subtraction, so instead of -3 it becomes + 3. We need to be thinking of our operations and numbers are partners when we are solving problems like this. The operation accompanies the number.” The teacher then continues to model until the checking of the work is complete.

The teacher should then challenge a student to explain the process just completed, before Guided Practice.

Guided Practice (10 min): The teacher then moves to guided practice and hands out materials to each student (little baggies with manipulatives) and writes the following equation on the board. The teacher should call on student volunteers to come to the board to write the operation and numbers in order, and then have each student at their desk modify their equation with the manipulatives. For example, the students would set up the equation as it is written on the board. Then they would look for their +9 piece and put that next to the 27. They would continue this until they only had pieces H = 31.

H + 5 – 9 = 27

Independent (10  min): The teacher hands out the IND worksheet. Students are asked to complete the worksheet independently and turn it in.

Closing (2-3 min): Teacher calls the attention of the students back toward the front of the class to quickly review the answers to the Independent Practice worksheet/ ask what we learned about.

### Lesson Resources

 IND Lesson 15   Classwork 280 DN Lesson 15   Starter / Do Now 221