# Lesson: Equations: Addition using Variable

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

SWBAT solve addition equations with variables (letters or pictures)

### Lesson Plan

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

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Do Now (3 -5 min): Teacher writes 102 + 3 _<__ 100 -3 on the board and says, all of you saw a problem similar to this one in the beginning of the lesson yesterday. I explained to you that inequalities, like equations, have two parts which are vocabulary words that you need to know for this new unit: expression, inequalities, and variables. We learned about inequalities and expression yesterday. I would like two volunteers to come to the front of the class and circle these two parts.” Teacher gives selected students two different colored markers and says, “__________, could you please circle the expression? [102 + 3 and 100 -3 should be circled] Very good, and ___________, could you please circle the inequality? [< should be circled] Great job, you all did awesome!”

Opening (2 -3 min): Teacher says, “Yesterday, we learned about inequalities. They are very similar to the equations we learned about the day before. However, they do not include an equal sign. Today we are going to work on setting up and solving addition equations. To be successful at this independently we need to know two things: 1) Signal Words that tell us it is an addition problem and 2) How to set up and solve the equation. I know you are all thinking, Oh.. that is easy. It can be, if we follow the steps I am about to teach you. By the end of this lesson, you will all be able to set up and solve one-step addition equations with variables. Are there any questions?”

Direct Instruction (10 – 12 min): Teacher then writes the following equation on the board x +7 = 12 and says,  “Ok, I bet you are all sick of this equation and on top of that, I bet you can all solve this without even blinking! While I am happy you know that you need to add 5 to 7 to get 12, I want to teach you the steps to solving an equation with a variable using the algebraic process. Watch as I solve this equation using the algebraic process.”

Step 1: Write out equation as is         x+7 = 12
Step 2: Get the variable by itself x = 12 -7
Step 3: Solve for the variable x = 5
Step 4: Check variable answer 5 + 7 = 12
12 = 12

Teacher then continues, “Alright, did everyone see how I did that? The trickiest step 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 – 7. 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 winter break, Justin earned \$25 for helping out around the house and watching his sister. By the end of the school year Justin had \$89. How much money did Justin earn between winter break and summer?

Teacher should reference the Which Operation Chart, and point out that ‘how much’ is a signal for an addition problem. The teacher should also point out that the equation should always begin with the variable.

Step 1: Write out equation         x+25 = 89
Step 2: Get the variable by itself x = 89 -25
Step 3: Solve for the variable x = 64
Step 4: Check variable answer 64 + 25 = 89
89 = 89

Teacher then continues, “Now, lets look at how this question. What if the question asked Which number sentence could be used to find m, the amount of money Justin earned? Did I just do more work than I needed to? [Yes] So now, who can tell me what the answer would be if the question was just to set up the number sentence using the variable m? [m + 25 = 89] Great job! Most of the time the DC-CAS will just ask you to set up the number sentences, but we are mathematicians, so we are going to follow all the steps to solve!”

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: Ms. Winter planted 50 flowers in her garden. Then next morning she only had 27 flowers left. How many flowers have gone missing from Ms. Winter’s garden?

Step 1: Write out equation         x+27 = 50
Step 2: Get the variable by itself x = 50 -27
Step 3: Solve for the variable x = 23
Step 4: Check variable answer 23 + 27 = 50
50 = 50

Example 3: Mr. Plum loves to eat donuts. He purchases 36 donuts a week. His wife says can’t eat that many donuts a week. Mr. Plum reduces the number of donuts he eats a week to 20. How many donuts did Mr. Plum cut out of this diet?

Step 1: Write out equation as is         x+20 = 36
Step 2: Get the variable by itself x = 36 - 20
Step 3: Solve for the variable x = 16
Step 4: Check variable answer 16 + 20 = 36
36 = 36

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.