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Unknown Numbers in Addition And Subtraction

OA.8
Answer Keys Here

Aligned To Common Core Standard:

Grade 1 Measurement - OA.8

This is going to be the first time that students will be confronted with algebraic thinking. This can be very overwhelming for them, or they could embrace it. The best way to approach this new subject matter with them is to present it as a mystery. I usually call this my Math Detective unit. I tell students that now that we have a good on the basic math operations (addition and subtraction), we can now check the work of others. I tend to start this process visually as you will see in the progression of the worksheets. Using word problems that can easily be drawn is a good place to start. Once they get the basic concept of finding missing addends or subtrahends, you are ready to jump into working with actual equations. These worksheets will have students complete problems that undergo an addition or subtraction operation. This is an algebra primer for students. Again, this is most likely the first time that they have seen problems like this and it will require some patience on the part of the teacher. This is not a unit that you will fly through and it will need extra time set aside for it. We encourage you to give them as much practice as is possible within your time frame.

Guided Lessons

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Practice Worksheets

I created this section as a primer section for word problems.



How to Find Unknown Numbers in Addition and Subtraction Equations

Solving Unknowns in Addition Equations

5 + __ = 8 Mountain Format

Example Problem: Find the unknown value in the equation: 5 + __ = 8

Math Based Solution

Step 1) A good way to approach this is to rewrite the problem in what we call mountain format. In this format we write the sum or difference at the top and the parts that create it at the bottom. In this case, 8 at the top and 5 and the unknown (noted by the blank square) at the bottom.

Step 2) Since the unknown is being added to 5. We can count up from 5 until we hit our sum. In this case, it requires us to count 3 times.

Step 3)This tells us our missing addend is 3.


Solving Unknowns in Addition Equations

5 + __ = 8 Model

Example Problem: Find the unknown value in the equation: 5 + __ = 8

Model Based Solution

Step 1)You can also model this problem with the use of simple shapes. In this case, I will use a circle. We know the sum is 8. As a result, we will draw 8 circles.

Step 2) The sum indicates that you already have 5. We will model this by separating the first five circles. We then just need to count how many circles remain to make the total (8). We can see from the diagram that it is 3.

Regardless of the method that you chose to use to solve the problem. The answer should follow as:
5 + __ = 8 | 5 + 3 = 8


Solving Unknowns in Subtraction Equations

7 - __ = 5 Mountain Format

Example Problem: Find the unknown value in the equation: 7 - __ = 5

Math Based Solution

Step 1) We can once again apply the mountain format. In this format we write the sum or difference at the top and the parts that create it at the bottom. In this case, 5 at the top (difference) and 7 and the unknown (noted by the blank square) at the bottom.

Step 2) Since the unknown is being subtracted from 7. We can count down from 7 until we hit our difference (5). In this case, it requires us to count down 2 times.

Step 3)This tells us our missing addend is 2.


Solving Unknowns in Subtraction Equations

7 - __ = 5 Model

Example Problem: Find the unknown value in the equation: 7 - __ = 5

Model Based Solution

Step 1)You can also model this problem with the use of simple shapes. In this case, I will use a circle. We know the starting value is 7. As a result, we will draw 7 circles.

Step 2) The difference indicates a result of 5. We will model this by separating the last five circles. We then just need to count how many circles remain to make the total (7). We can see from the diagram that it is 2.

Regardless of the method that you chose to use to solve the problem. The answer should follow as:
7 - __ = 5 | 7 - 2 = 5