Algebra: Solving Addition and Subtraction Equations

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SWBAT use the inverse operations to find the missing number.

Big Idea

The inverse operation is used to undo an operation so that the students can find a missing number.

Whole Class Discussion

15 minutes

In today's lesson, the students learn how to find the value of a variable.

I have the Teaching Tool - Addition and Subtraction Equations.pptx displayed on the Smartboard. The students sare sitting at their desks with paper and pencil.  I ask the students to write M + 5 = 12 on their papers. I let the students know that this is an equation with a variable.  The variable represents the missing number.  When we have an equation with a missing number, we can use the inverse operation to solve the equation.  I ask, "What is the inverse of addition?"  Student response:  subtraction.  

To solve this problem, we need to get the variable on the side by itself.  In this problem, we have M + 5.  The inverse of addition is subtraction.  To get M on the side by itself, we need to subtract 5.  To give the students a visual, I draw 5 circles.  To show subtraction, I mark an "x" through each of the circles to take them away.  On the other side of the equation, we have the number 12.  To model, I have the students draw 12 circles.  I explain to the students that if we take 5 away from one side, we must take 5 away from the other side.  I have the students draw an "x" through 5 of the circles.  I ask, "How many circles do we have left?"  Student response: 7.  Therefore, M = 7. 

I tell the students that they must always check their answers to see if they are correct.   On the board, I write the equation M + 5 = 12.  I tell the students that in place of the M, write a 7 because we said that m = 7.  The new equation is 7 + 5 = 12.  I ask, "Is this true?"  Student response: yes.  Therefore, our answer is correct.

Let's try another one.  (For the subtraction problems, the models did not work appropriately.  Therefore, the students only use the inverse operation to solve the subtraction problems.)  I ask the students to write, Q - 17 = 6.  I explain to the students that because this is a subtraction problem, we should use addition to get the variable on the side by itself. We must add 17 to both sides.  This leaves us with Q = 23.  To check the equation, we replace Q with 23.  The new equation is 23 - 17 = 6.  I ask, "Is this correct?"  Student response: yes.

Skill Building/Exploration

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others.

For this activity, I put the students in pairs.  I give each group an Addition and Subtraction Equations.docx.  The students must work together to find the value of the variable.  They must communicate precisely to others within their groups. They must use clear definitions and terminology as they precisely discuss this problem. 

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students.  As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6).  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.  

As they work, I monitor and assess their progression of understanding through questioning. 

1.  What is the variable in this equation?

2.  What is the inverse operation for this problem?

3.  When you check your answer, is the equation true?


 Early Finishers:  Practice the skill at the following website:


15 minutes

To close the lesson, I call on different pairs of students to share their answers.  The students must explain why they worked the problem in the order that they did (Video - Addition and Subtraction Equations).  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples (Student Work - Addition and Subtraction Equations and Student Work 2 - Addition and Subtraction Equations), as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.