Using the Inverse Operation for Addition and Subtraction

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SWBAT use inverse operations to find the missing numbers in addition and subtraction problems.

Big Idea

Inverse operations can help you find missing numbers.

Direct Instruction

10 minutes

In this Introductory Video Using Inverse Operation, I explain our objective for today.

The students have already learned how to add and subtract by using place value.   In today's lesson, they learn to find a missing number in an addition or subtraction problem by using the inverse operation.  This aligns with 4.NBT.4 because the students are adding and subtracting multi-digit whole numbers using the standard algorithm. 

This is a very important skill for the students.  They need to know that if you have a missing number, you can take the numbers that they give you and do an operation that helps you figure out the missing number.  That operation is the "inverse" operation.

I let the students know that today we learn a strategy that will help us add if there is a missing addend, and even find the difference if one of our numbers is missing.  

I like to use my Smart board for a whole class discussion.  The students come to the carpet so that they can be near as we discuss the skill together.  My students know that they can ask questions or give input throughout the whole class direct instruction.  As we discuss the skill, I ask questions throughout the lesson.  By doing this, it allows the students to think about the answer instead of me just giving them a lot of information.  I feel that students learn better when they come up with things on their own.  

The Using Inverse Operation power point is displayed on the Smart board.  For this particular lesson, I will begin by reviewing place value and how we use it to add and subtract.  


1.  When we add or subtract, we line our numbers up according to place value.  The numbers in the ones place should line up under each other, the tens place, etc.  

2.  Some numbers need to be regrouped.  When we regroup, we put the number in the ones place at the bottom, and regroup the number in the tens place at the top of the tens place.  For example, with the number 15, the 5 would go in the ones place and the 1 would be regrouped to the tens place because it is valued at 10

3.  When we subtract, we may have to regroup as well.  If the top number is smaller than the bottom number, we need to take 1 away from the place to the left and add it to the place to the right.  For example, 17 - 8.  The 7 is smaller than the 8, so we take one away from the tens place (that becomes a zero), then we add that one to the ones place.  We now have a 17.  


Let’s Practice!

 45 + ___ = 87


To find the missing addend for this addition problem, we can use the inverse operation of subtraction.


Because we have two numbers, we can take those 2 numbers and make a math problem. 

87 – 45 =  42

The missing addend is 42.


Let’s try it with subtraction!

___ - 53 = 28

To find the missing number, we can use the inverse of subtraction.   Let’s add to find the missing number.


28 + 53 = 81

 How does using the inverse operation help find missing numbers?

Group or Partner 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 (MP3).

For this activity, put the students in pairs.  Give each group an Inverse Operation Group Activity.    The students must work together to find the missing number by using the inverse operation. They must communicate precisely to others within their groups (MP6), using vocabulary and definitions that relate to addition and subtraction.  They must justify their answers, as well as critique the reasoning of their partner (MP3).

As the students work together, I monitor their progress.  If the students are having a difficult time, I ask guiding questions to help lead the students to the answer.  

Possible Questions:

1.  What operation did they give you in this problem?

2.  What is the inverse operation?

3.  How can you check your answer?



Independent Assignment

10 minutes

To give me a clear understanding of what each student knows, the students will do an Independent Assignment Inverse Operation.  As a teacher, I need to assess students independently to make sure they are all receiving the help they need.  I put a problem on the Smart board for the students to work (see attached resource).  The students use paper and pencil to solve the problem.  I walk around to visually assess the students understanding, keeping track of all students who I will work with in small group for remediation.



78 + _____ = 103

Find the missing number.

How does using the inverse operation help you solve this problem?




10 minutes

To close the lesson, I have one or two students share their answers.  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, 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 student independent and partner sharing will be addressed whole class.  

Possible Misconception:

1.  If the second number is missing in a subtraction problem, you can use the inverse operation of addition.


To address this misconception, within the powerpoint whole class discussion, we discuss that if the second number is missing, the students must subtract the two numbers to find the missing number.