# Lesson Video: Relating Addition to Subtraction: Numbers up to 20 Mathematics • 1st Grade

In this video, we will learn how to write a family of addition and subtraction facts linking three numbers up to 20.

10:50

### Video Transcript

Relating Addition to Subtraction: Numbers up to 20

In this video, we’re going to link together different groups of three numbers up to 20. And we’re going to use them to write a family of addition and also subtraction facts. To help us think about families of numbers that we can use to make addition and subtraction facts, we need to understand parts and wholes. We can use a part–whole model to help us find these families. In the bottom two circles, we could write two parts. And when we add them together, the total or the whole amount is written in the top circle. We know that one part plus another part equals the whole amount. Let’s put some numbers into our part–whole model.

11 and six more make a whole amount of 17 altogether. These are a family of numbers. They belong together because we can use them to write additions and subtractions. Let’s start with some additions. How many can you find? Well, perhaps, the first one, the one that we can see straight away, is 11 plus six equals 17. But we know we could add these two numbers the other way around and they’d still make 17. Six plus 11 makes 17 too. Look at how both our additions contain the same three numbers. You know, we could write these additions in two more ways because we don’t always have to end with a whole amount. What if we start with a whole amount? 17 is equal to what? It’s equal to 11 plus six and also six plus 11.

Now, as well as finding this family of addition facts, we can also use the numbers 17, six, and 11, our whole and our two parts, to find some subtraction facts. Now, to do this, we need to start off with 17, the whole amount. Now, we know if we start with the whole amount and we take away one of the parts, we should be left with the other part. So if we start off with 17 and we take away six, we should be left with 11. One, two, three, four, five, six. And now, if we look at how many counters we have left, we have a full 10 frame and then one more. If we take away one part, we’re left with the other part. 17 take away six is 11. And you guessed it. If we take away 11, we’re left with six.

And just like before, we could rearrange these subtractions and start with the answer first. 11 is equal to 17 take away six. And six is equal to 17 take away 11. We found two parts that go together to make a whole. And we’ve used these three numbers to find a family of addition and subtraction facts. And the reason why we’ve used different colors for each number in this video is to help us see a really interesting fact. All of the number sentences contain the same three numbers. But you know, it doesn’t have to be six, 11, and 17.

10 and 10 make a total of 20. So we could’ve used those three numbers instead, or 18, one, and 19. For each of these different part–whole models, we could find a new family of addition and subtraction facts. And each time, all the number sentences we could find would contain the same three numbers. Let’s try answering some questions now where we have to look for the families of addition and subtraction facts.

Use six plus 13 equals 19 to fill in the blanks in these number sentences. 13 plus what equals 19. 19 subtract six equals what. And what take away 13 equals six.

To begin with, in this problem, we’re given an addition. It’s an addition that’s a complete number sentence. We can see the two parts that we add together and the answer. So we could sketch a part–whole model to represent it. Six and 13 make a total of 19. And you know, we can use these three numbers, the two parts that go together to make the whole, to help us fill in the blanks in some different number sentences. And the reason why we can do this is that the three number sentences we’re given with blanks in are all related; they’re part of a family. You’ll see why, as we go through them.

Our first number sentence says, 13 plus what equals 19. Can you spot anything interesting about this addition? The first thing that we can see is that the total, the answer to our addition, is 19. It’s the same as the total in the addition we need to use to help. And if we keep looking, we can also see that the number we’re starting with here, which is 13, is the second number in our addition. And so if six plus 13 make 19, then we know that 13 plus six makes 19 too. We’ve just added the same two parts but in a different order.

Our second calculation is a subtraction. 19 take away six equals what. Well, we know from our last calculation that 13 plus six more make 19. So if we start with 19 and we take away six, we’re going to be left with 13. Each of these calculations contains the same three numbers, 19, six, and 13. That’s what we meant when we said they were going to be related.

Our final calculation is what take away 13 equals six. Well, again, we can use the addition to help us find the subtraction. If we know that six and 13 go together to make 19, then we also know if we start with 19, the whole amount, and we take away one of the parts ,13, we’re going to be left with six. The missing number here is 19. We’ve used six plus 13 equals 19 to fill in the blanks and find a family of addition and subtraction sentences. 13 plus six equals 19. 19 take away six equals 13. And 19 take away 13 equals six. Our missing numbers are six, 13, and 19.

16 plus three is 19. Which number sentence is missing from the number sentences three plus 16 equals 19, 16 plus three equals 19, and 19 take away 16 equals three?

It seems from this question that we got a missing number sentence here. We’re given a family of three different number sentences, but there must be a fourth one that we need to find. To begin with, we’re given a number fact. 16 plus three is 19. We know we could model this using cubes. 16 plus three is 19. And if we look at our number sentences that we’re given, the second one shows this number fact written as a number sentence 16 plus three equals 19. Now, we can use these three numbers, 16, three, and 19, to write a family of addition and subtraction facts because 16 and three are two parts that make a whole amount, 19.

And you know, we could make that whole amount in one other way. If we look at our train of cubes, we could just swap the pink and the orange cubes around. Three plus 16 is 19 too. And this is where we get our first number sentence from. So we start off with two additions. Our final number sentence is a subtraction, and we can see the same three numbers again. This time, we’re starting with the whole amount. If we have 19 and we take away 16, we’re left with three. So we have two additions, but we only have one subtraction.

Let’s try and find another subtraction that we could make using these numbers. We know the whole amount is 19. So if we’re going to take away a number, we need to start with this whole amount. Let’s make 19 the first number in our number sentence. And we’re going to look for another subtraction. So we need to use the subtraction symbol. Now, we need to take away one of the parts. In the subtraction we’re already given, we’ve taken away 16. So instead of taking 16, let’s take away three.

19 take away three equals what? Well, we know from that very first number fact that 16 and three go together to make 19. And so if we start with 19 and we take away three, we’re going to be left with 16. We can use one addition fact to write a whole family of addition and subtraction facts. The number sentence that’s missing is 19 take away three equals 16.

So what have we learned in this video? We’ve learned how to write a family of addition and subtraction facts, linking three numbers up to 20.