Video: Missing Numbers in Addition Equations

In this video, we will learn how to find the missing addend in an addition equation with numbers up to 10.

10:28

Video Transcript

Missing Numbers in Addition Equations

In this video, we’re going to learn how to find the missing addend in an addition equation using numbers up to 10. Let’s start by thinking about a trick that you could do with your friends. Here’s a line of marbles. If we count them, we can see that there’s a total of five. If we were drawing a part–whole model, we could say that the whole amount is five. Now, let’s imagine that we have a plastic bowl and we say to one of our friends to turn it upside down and to cover up some of the marbles. There we are. Our friend has covered a part of the whole amount using the bowl.

But how many marbles are underneath the bowl? How can we give the answer without looking? Well, we can use what we know about addition equation and parts and wholes to help us. As we’ve said already, we know that the whole number of marbles was five. And we can see part of this whole amount. There are three marbles that aren’t covered up by the bowl. We need to use what we know to find the missing part. These are the marbles that have been covered up by the bowl. We could even write this problem as a number sentence. What plus three makes five. Five is made up of three and another number. What is that other number? We can count on to find the missing part.

Let’s use part of a number track to help us. Remember, we’re trying to find which number goes with three to make five. We could start by putting a counter on the number three and then seeing how many times we need to move our counter to get to five, one, two. We know that two goes with three to make five. So we can say our missing part in our part–whole diagram is the number two. And we can complete the missing number in our addition equation. Two plus three equals five. And that’s how we can turn to our friend without looking underneath the bowl and say, “I know that you’ve hidden two marbles underneath the bowl.” Shall we check? Here they are. Two is a part. Three is a part. The whole is five. Now let’s have a go at using what we know about addition equations to help find some missing numbers.

Find the missing number. One plus what equals four.

We can see two missing spaces here. To begin with, we’re given an addition equation. And instead of the missing number being at the end like it often is, we can see that one of the numbers we’re adding is missing. One plus what equals four. And underneath this equation, we can see the same addition shown using pictures. One ball plus how many balls equals four balls. The number that’s missing in this question is one of the parts. To help us understand this, we could sketch a part–whole model. Now we know the whole amount because the answer to the addition or the total is four. This whole amount is what happens when we add two parts together.

What else do we know? Well, we also know that one of the parts is worth one. So one is a part, another number is a part, and the whole amount is four. How can we find the missing part? Well, we could count on from the part we already know. Let’s use cubes to help us do this. This cube represents the part that we already know, which is worth one. Now let’s count on until we get to four cubes, two, three, four. We’ve counted on three more cubes to make a chain of four cubes. So we can complete our part–whole model using the number three. One and three go together to make four. Four is equal to one and three. Our missing number is three.

There are six rabbits and four of them do not have carrots. How many rabbits have carrots? What plus four equals six.

We can see that the missing number in the equation that we’re given in this problem isn’t at the end. Often we do have to find the total number if we’re adding two numbers together. But in this problem, we need to find one of the parts that we add together. Our missing number is the first number in the addition. What add four equals six. To help us find this missing number, let’s look at what the problem’s describing. To begin with, we’re told that there are six rabbits. Now, are these six rabbits part or the whole amount? Well, if we count them quickly, we can see that they are the whole amount, the total. There are six rabbits altogether.

So if we were drawing a part–whole model, we’d write the number six to represent the whole. And our whole line of six rabbits is split into two parts. We’ve got a group of rabbits that do have carrots and then another group of rabbits that do not have carrots. And we don’t need to count this second group because we’re told in the question four of the rabbits do not have carrots. So part of the whole amount is the number four. And we’re asked how many rabbits have carrots. In other words, what number goes together with four to make a total of six?

We could use counters to model the problem. We could use six counters to represent our six rabbits. Now, four of our rabbits do not have carrots. So perhaps we could use a different-colored counter, one, two, three, four. So if these pink counters represent the rabbits that do not have carrots, let’s count the white counters. These are the rabbits that do have carrots. We can see that there are one, two white counters. And of course, we could count the rabbits in the picture, one, two. The number two goes with the number four to make a total of six. Six is equal to two plus four. And so if there are six rabbits and four of them do not have carrots, the number of rabbits that do have carrots is two.

Fill in the blank. What plus three equals seven.

In this addition equation, we’ve got a missing number. Now, often with an addition equation, the missing number comes after the equal sign. We need to add together two numbers to find out what that total or the whole amount is. But what’s different about the addition equation that we have here? The missing number is one of the numbers that we’re adding together. We know what they make because we can see that the addition equals seven. The whole amount is seven. Our addition equation also shows us one of the parts that makes up seven. And that’s the number three. Something add three equals seven. And what is that something? What part goes together with three to make seven?

We could count on to help us find the answer. And to do that, we could use a number track, so let’s do that. We could start by pointing to the number three. Let’s see how many numbers we need to count on to get to a total of seven, one, two, three, four. Three and four are two parts that go together to make a total of seven. So we could complete our part–whole model to show the number four. And we could also fill in the blank in our addition equation. We can make seven out of three and four. Four plus three equals seven. The missing number is four.

So what’ve we learned in this video? We’ve learned how to find the missing addend in an addition equation with numbers up to 10.

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