# Lesson: Equations: Subtraction Using Variables

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### Lesson Objective

SWBAT solve subtraction equations with variables

### Lesson Plan

Materials Needed: dry erase markers, white board, DN Worksheet, IND Practice worksheet
Vocabulary: addition, operations, equations, variables, signal words, inequalities

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Do Now (3 -5 min): Students are given their DN worksheet to complete independently.

Opening (2 -3 min): Teacher says, “Yesterday, we learned about solving addition equations with variables. Today, we are going to continue solving equations with variables. By the end of the lesson, you will be able to solve subtraction problems with variables. “

Direct Instruction (10 – 12 min): Teacher then writes the following equation on the board x - 14 = 27 and says,  “Ok, you saw a problem that was set up in a similar way yesterday. The difference is that this problem is asking you to subtract. Watch as I solve this equation using the algebraic process.”

Step 1: Write out equation as it is x - 14 = 27
Step 2: Get the variable by itself x = 27 + 14
Step 3: Solve for the variable x = 41
Step 4: Check variable answer 41 - 14 = 27
27 = 27

Teacher then continues, “Alright, did everyone see how I did that? Remember that the hardest part is Step 2.  When you get the variable by itself move the number on the other side of the equal sign. When you do that you have to change the operation. So in this case, it became + 14. Now let me practice this with a word problem. I will leave these steps on the board so we can use them as reminders. When we tackle a word problem we have to do more than just solve the equation. We have to determine the variable, set up the equation, and then solve. Watch as I do this one.”

The teacher writes the following problem on the board and then works through with these steps:

Example 1: Over Spring Break, Gerard earned \$97 dollars for taking care of his neighbor’s cats. After finishing the job, Gerard bought some candy and ice cream at the store. After leaving the store, Gerard had \$85 dollars. How much money did Gerard spend at the store?

Before beginning, the teacher says, “Pay attention, this equation is not going to begin with the variable, because we already know the total amount of money that Gerard made. In subtraction problems, you have to solve for the remaining amount.

Step 1: Write out equation 97 – x = 85
Step 2: Get the variable by itself 97 = 85-x
97 - 85 = x
Step 3: Solve for the variable x = 12
Step 4: Check variable answer 97 - 12 = 85
85 = 85

Teacher then continues, “Now, lets look at how I solved this problem. It is a little bit different from solving addition problems, because there are actually two different things that you need to do to get the variable by itself. First, you must move the x to the other side of the equal sign by adding it to the other side. Then, you must subtract the 85 in order to get the x to be by itself. This might seem a little bit confusing at first, but with some practice, it will get easier!”

Guided Practice (8 -10 min): Teacher then completes Example 2 for guided practice. An additional problem can be added if students are having difficulty.

Example 2: Tara planted 50 flowers in her garden. When they bloomed, Tara gave most of her flowers to her friends. If Tara ended up keeping 15 flowers, how many did she give away?

Step 1: Write out equation 50 - x = 15
Step 2: Get the variable by itself 50 = 15 – x
50 – 15 = x
Step 3: Solve for the variable x = 35
Step 4: Check variable answer 50 - 35 = 15
15 = 15

Example 3: Ron loves to eat donuts. He makes a point of eating 45 donuts a week. However, after learning about cholesterol, he decides that he can only eat 30 donuts a week. How many fewer donuts is Ron eating?

Step 1: Write out equation as is 45 - x = 30
Step 2: Get the variable by itself 45 = 30 – x
45 – 30 = x
Step 3: Solve for the variable 15 = x
Step 4: Check variable answer 45 – 15 = 30
30 = 30

Independent Practice (10 min): Teacher gives each student their own copy of the Independent Practice (IND) worksheet. Teacher circulates the room to answer individual student’s questions.

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 Practice subtraction problems   Classwork 3 DN_single_step_algebra_problems.pdf 1