Relating Addition to Subtraction: Numbers up to 10
In this video, we’re going to learn how to write a family of addition and also subtraction facts, where we link together three numbers up to 10. In this picture, we can see some monsters. There are four orange monsters and three of these friendly looking blue monsters. The total of the monsters is seven because four plus three equals seven.
We could model this number fact using colored cubes. The total number of our colored cubes is four plus three equals seven. We could also use these three numbers in a part–whole diagram. The whole amount is seven, and the two parts that go together to make up seven are four and three.
Now, these three numbers are part of a family. They’re related to each other. We know this because we can use them to write some addition facts. As we’ve already said, four plus three equals seven. But also, we could add the two numbers the other way around and they’re still going to make seven. Three plus four equals seven. Another way of writing these same number facts is to start with the total; seven is equal to four plus three and seven is equal to three plus four. We found four addition facts using the same three numbers: seven, four, and three.
But we can also use these numbers to write some subtraction facts. They’re part of the family, too. Let’s imagine we want to find how many monsters are blue. Well, we start off with the total number of monsters, which is seven, and we take away the number of monsters that are orange, which is four. Seven take away four leaves us with three. And there’s another subtraction we could find. Seven take away three leaves us with four.
And then, just like before, we could start with the answers. Three is the same as seven take away four. And four is the same as seven take away three. These addition and subtraction facts are all linked together because they all contain the same three numbers. They’re part of the same family.
Let’s have a go at answering some questions where we have to think about the family of addition and subtraction facts.
Daniel has four yellow balloons and five green balloons. Write an addition equation to represent the total number of balloons. And write a subtraction equation to show how many balloons are yellow.
There are two parts to this question. We’re asked to write an addition equation, or number sentence, and a subtraction equation. And you know we can look at the picture of balloons that we’re given, and we can write both an addition and a subtraction number sentence because the two are linked together. Let’s have a think about how.
Firstly, we’re told that Daniel has four yellow balloons and also five green balloons. And of course, we can see these in the picture. In the first part of our problem, we’re asked to write an addition number sentence to represent the total number of balloons. And we know that if we’re finding the total of something, we need to add to find it.
We could use a ten frame to help us model this. Let’s put on four yellow counters and then one, two, three, four, five green counters. There’s only one more space left in our ten frame, so we can see what the total is. Four and five make a total of nine, one less than 10. So, let’s write this as an addition equation. We start off with four. We add another five and we get a total of nine. Four plus five equals nine. We could also represent this on a part–whole model, where four and five are the two parts that go together to make a whole of nine.
Now, these three numbers are part of a family. They go together. We can also use them to come up with a subtraction. And in the second part of our question, we’re told to write a subtraction equation or a number sentence to show how many balloons are yellow. Well, we’re already told that there are four yellow balloons. But how can we show this as a subtraction?
Well, we need to start with the whole amount, which is nine. And then we need to take away the part that represents the number of green balloons. We know that there are five green balloons, so we need to take away five. One, two, three, four, five. So, how many balloons are we left with? One, two, three, four. The number sentence that shows us how many balloons are yellow is nine take away five equals four.
We can use the numbers nine, four, and five to write both addition and subtraction facts. Four plus five gives us the total number of balloons, which is nine. And then nine take away five gives us the number of balloons that are yellow, which is four.
There are four red birds and two yellow birds. Fill in the blanks. Four plus two equals what. Six take away what equals two. Two plus what equals six. And six take away what equals four.
This question is getting us to think about how addition and subtraction facts are linked. We’re told that the picture shows four red birds and two yellow birds. These are two parts that go together to make a whole amount. And in our first question, we can find out what that whole amount is because we’re asked to add the two parts together, four plus two equals what.
To find the answer, we can just count on another two from four: four, five, six. Four plus two equals six. These three numbers belong in a family together because the two parts go together to make a whole. And we’re going to use the numbers four, two, and six in each of the number facts that we need to fill in.
Our second number fact says six take away what leaves us with two. Well, if we look at the model we’ve made out of cubes, we can see the two that we want to have left over at the end. So how many cubes are we going to take away to leave us with this two? One, two, three, four. Six take away four leaves us with two. And we know this because four and two are two parts that go together to make six.
We could keep our model as it is for a moment because our next question says two plus what equal six. Perhaps you can see which one of our three numbers is going to be the answer. But let’s use cubes to model this. What are we going to add to two that gives us a total of six? One, two, three, four. Of course, the number that goes together with two to make six is the number of red birds. Two plus four equals six.
Our final number sentence says six take away what equals four. So, at the end of the subtraction, we want to be left with four. How many do we need to take away? One, two. Two and four are two parts that go together to make a total or whole amount six. And we’ve used these numbers, two, four, and six, to write down some different addition and subtraction facts that are all in the same family. Four plus two equals six. Six take away four equals two. Two plus four equals six. And six take away two equals four.
Now what have we learned in this video? Firstly, we’ve learned that addition and subtraction are related. And we’ve learned how to write a family of addition and subtraction facts that link together three numbers.