# Lesson Video: Adding in Any Order Mathematics • 1st Grade

In this video, we will learn how to find sums up to 20 by adding two numbers in any order.

09:57

### Video Transcript

Adding in Any Order

In this video, we going to learn how to find sums up to 20 by adding in any order. Here are two ten frames. These two robots have been programmed to paint the ten frames, five blobs of orange and nine blobs of pink. Let’s start with the orange robot first. One, two, three, four, five. Now, we need to add nine more. We know that a row of a ten frame is worth five. So we can count the blobs from five. Six, seven, eight, nine. We found the sum of two numbers here.

Remember, sum means total. It’s what we get when we add two numbers together. We started with five, and then we added on another nine. What’s the sum? Well, we know that a full ten frame is always worth 10. So we can just count on from 10. 11, 12, 13, 14. Five plus nine equals 14.

But what if we programmed the pink robot to go first? We’ll use the same numbers, but we’re going to add them in a different order. So we’ll start off with nine pink blobs. We can do this quickly because we know it’s one less than a full ten frame. And now we just need to paint our five orange blobs. One, two, three, four, five.

The two robots were programmed to paint in a different order this time. So the addition that this shows is nine plus five. We’re adding the same two numbers together, but they’ve just been swapped around. What do you notice about the total?

Once again, we have a full ten frame and then four more. The robots have painted 14 blobs again. Both additions give the same answer. And these two robots have taught us something very important about adding numbers. It doesn’t matter which way around we add numbers together. Seven and two is exactly the same as two and seven. Five more than 15 makes 20. And if we swap the numbers around and find 15 more than five, we get exactly the same answer. Whether we find the answer to five plus 13 or 13 plus five, the total of a sum will stay the same.

Let’s have a go at answering some questions now where we have to put into practice what we’ve learned. And remember what we’ve learned, it doesn’t matter which way around we add numbers together.

Do these sums have the same answer?

Under the question, we can see two lines of cubes. And they both represent different additions or sums. When we find the sum of something, we find the total. And in our first addition, we’re finding the sum or the total of 10 and seven. We know this because there are 10 yellow cubes, and then another seven blue cubes are added onto it.

Let’s have a look at our second addition. What’s the same and what’s different? Well, what’s the same is that the addition contains the numbers 10 and seven again. Only this time they’re added together in a different order. This time, we start with seven and we add 10 more. So our question is asking us, is 10 plus seven the same as seven plus 10?

Can you think of a way to answer this question without doing any adding. We could just look at the picture and say to ourselves that the two lines of cubes are exactly the same length. So it looks like the total of the cubes whether we add 10 and then seven or seven and then 10 is the same. But as well as looking at the picture, it’s probably a good idea to work out the answer.

To begin with, let’s count on seven more than 10. 10, 11, 12, 13, 14, 15, 16, 17. The sum of 10 and seven is 17. Now, let’s start with seven and count on another 10. Seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17. Just like we thought, both sums have the same answer. It doesn’t matter which way around we add two numbers together. They’ll always give the same total. Do the sums 10 plus seven and seven plus 10 have the same answer? Yes, they do.

On Monday, Isabella got two stickers for her reward chart. And on Tuesday, she got three stickers. On Monday, Mason got three stickers for his reward chart. And on Tuesday, he added two more. Who has more stickers?

This question is about two reward charts for two different children, Isabella and Mason. Let’s look at Isabella’s reward chart first. We’re told that on Monday, she got two stickers for her chart. And if we look at the row for Monday on Isabella’s chart, we can see those two stickers that she got. We’re then told that on Tuesday, she got three stickers. And again, we can look on her chart and we can see those three stickers.

Now, the question that we’re asked at the very end of this is, who has more stickers? So let’s think about how we might find the total of Isabella’s stickers. She started off with two on Monday and then was given another three. So we’re going to need to find the answer to two plus three. But before we do that, let’s have a look at Mason’s reward chart. On Monday, he got three stickers for his chart. And then we’re told that on Tuesday, he added two more. So which two numbers are we going to need to add together to find the total of Mason’s stickers?

He starts off with three and then adds two more. Can you see something interesting about these two additions? They both contain the same numbers. They’re just added in a different order, two plus three and then three plus two. Now, what do we know about numbers if they’re added in a different order?

Well, they give the same total. It doesn’t matter which order we add two numbers. Two plus three is the same as three plus two. So if Isabella starts with two and then counts on three, four, five, this is exactly the same as if Mason starts with three and counts on another four, five. They both have five stickers. And so who has more stickers? They have the same number.

Find the missing number. Nine plus seven equals what plus nine.

You know we can find the answer to this question without doing any adding at all. But to do this, we need to look very carefully at what the question tells us. We’re given two additions here with an equal sign in between. This shows that they’re worth the same. Nine plus seven is the same as something add nine. Now, if we look at these two additions, we can see something very similar. They both contain the number nine. Now, in the first addition, the number that’s added to nine is seven. In the second addition, nine is added on to a number. But we don’t know what that number is. And so nine and seven make exactly the same number as nine and seven. This is the only answer that makes sense. The additions are the same. It’s just the numbers have been swapped around. And we know that if we add two numbers in a different order, they make the same total.

If you have time, try working out the answer in the two different ways. But we don’t need to actually do this to answer the question. Nine plus seven gives exactly the same answer as seven plus nine. The missing number is seven.

What have we learned in this video? We’ve learned how to find sums up to 20 by adding two numbers in any order. And we’ve also learned a really important fact. We can add in any order, and it makes no difference. The total will be the same.

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