Identifying Addition Patterns Over Increasing Place Values

Instructor: T.J. Hoogsteen

T.J. is currently a grade 5 teacher and Vice-Principal. He has a master's degree in Educational Administration and is working toward an Ed.D. in Educational Leadership.

In this lesson, you will learn how to take a basic addition fact that you know and use it to figure out patterns of addition when place values increase.

First Steps in Math

Think back to the first time you took a step. You likely wouldn't remember that moment, but your parents sure would. Before you could do that, though, you probably developed other skills first. You probably learned to crawl. Then you figured out how to stand up. Next, maybe you were able to walk around furniture if you had something to hold onto. Finally, after practicing each of these movement skills, you took your first step without anything or anyone to help you. Once a first step has been taken, there is no stopping that baby.

That is much like addition. Before adding, a person learns to count, then identifies numbers, then uses manipulatives to help in adding, before finally learning addition facts. Once the basic addition facts are known, there is nothing stopping you from learning how to add numbers with increasing place values.

Addition Patterns Over Increasing Place Values

Very early in our math learning, we learn how to add a set of numbers like 1 + 1. Of course the answer is 2. But what about 10 + 10? That is a little bit harder, but if you know how the patterns in numbers work, solving 10 + 10 and even larger numbers becomes simple.

So as I said, I know 1 + 1 = 2, but I don't know 10 + 10. What if I said, though, that if I know 1 + 1, then 10 + 10 is easy, and so is 100 + 100. Well, it's true. I just have to follow the pattern. What's the pattern you ask? Look below:

Example 1

Looking at the picture, you may have noticed that from the first row to the third row, the major difference is the added zeroes. In the second row, each addend, a number that is added to another number, has a zero, and the answer has a zero. In the third row, each addend has two zeroes, and the answer has two zeroes. You may also notice that each addend starts with 1, and the answer starts with 2.

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