Adding and Subtracting Numbers up to 10
In this video, we’re going to learn how to solve problems by deciding whether to add or subtract. And then once we’ve decided, we’re going to learn how to complete equations by adding and subtracting within 10. Now, if we’ve been given a number sentence to solve, we might look at the symbol that’s in that number sentence. And it’s gonna tell us what to do. We might see this symbol, which shows that we need to add to find the answer. Or we might see this symbol, which tells us we need to take away or subtract. But what if we’re given a problem that’s written all in words and we’re not given a number sentence at all? How do we know whether we need to add to find the answer or take away?
Well, problems where we need to add to find the answer are often about putting groups or numbers together or adding on to something. We might come across words like what is the “total,” how many “altogether,” or any words that’s mean the same as adding like “combine.”
What about problems where we need to subtract to find the answer? These are often about taking away a group or a number from the whole amount and seeing what’s left behind. We need to keep our eyes open for words like “take away” or questions that ask us how many we’ve got left. Let’s have a go at answering some word problems now. We’re going to be able to solve them by either adding or subtracting. And the very first question we need to ask ourselves each time is, how can we tell whether to add or subtract?
A fisherman caught two fish. Then, he caught one more. Which of these tells you how many fish he caught in total. Two plus two, two plus one, or two take away one.
In this question, we’re given a word problem. To begin with, we’re told that the fisherman caught two fish. And in the picture, we can see those two fish. We’re then told that he caught one more. This is the red fish that we can see in the picture. We’re then asked to choose an answer which tells us how many fish the fisherman caught in total.
Now, if we look at our possible answers that we have to choose from, we can see that two of them are additions and one of them is a subtraction. So the first question we need to ask ourselves is, do we need to add to find the answer here? Or do we need to take away? If we look at the words in our word problem, we can see some clues.
Firstly, there’s the word “more.” A fisherman caught two fish. Then he caught one more. If we find one more than something, we need to add to find the answer. The word “total” is another clue. If we want to find the total of some numbers, we add them together. So we’re going to need to add to find the total number of fish the fisherman caught. Let’s cross out the subtraction. We know this isn’t the right answer. Now, which of our two possible additions is correct? Two plus two or two plus one?
Well, we know that the fisherman caught two fish and one more. And to find one more than two, we need to add two and one together. Two plus one is one, two, three. We know the fisherman caught three fish in total. And of course, we can see that in the picture. And so the expression that tells us how many fish he caught in total is two plus one.
Eight children are at a party, but then two have to leave. Which of these tells you how many children are left at the party? Eight plus two, six plus two, or eight take away two.
If we look at our three possible answers in this word problem, we can see that two of them have addition symbols, where we need to add to find the answer. And one that has a subtraction symbol, where we need to take away to find the answer. But which of these is correct? Do we need to add to find the answer? Or do we need to take away?
Let’s read the word problem more carefully to try to find out. The first thing we’re told is that eight children are at a party. And if we count the children in the picture, we can see that there are eight of them. But the next piece of information we’re told is that two of the children have to leave. Must be these two children here because they’re separated from the rest.
Now, our question asks us to find a way to show how many children are left at the party. So we start off with eight children at the party. Now, if two of them leave, is the number eight going to get bigger or smaller? Well, because two children have left the party, we know that there’ll be less than eight children in the party. The number is going to get smaller. This means this is a subtraction question.
Now, out of our three possible answers, only one of them is a subtraction. So we know the answer must be eight take away two. Let’s use this and see whether it does tell us how many children are left at the party. Eight take away two should leave us with one, two, three, four, five, six children left at the party. And if we count the children in the picture just to check, we can see that there are six children left at the party.
When we need to find how much of something is left, we often have to subtract to get there. So the expression that tells us how many children are left at the party is eight take away two.
You have four blue sweaters and three red ones. How many sweaters do you have?
If we read this problem quickly, we might say you’ve just told me the answer. I’ve got four blue sweaters and three red ones. But if we think more carefully about the question, we know that when it asks us how many sweaters we have, it’s talking about the whole amount. How many sweaters do you have in total? How many altogether?
Now, apart from two numbers, this problem is written in words. There aren’t any symbols to tell us whether to add or to take away to find the answer. The first thing we can do then is to decide. Is this an addition problem or a subtraction problem?
Well, the question tells us we have four blue sweaters and three red ones. You know, it’s very easy to miss that little three-letter word in between. You have four blue sweaters and three red ones. In other words, you’ve put together a group of four blue sweaters and three red ones to make one big group. And when numbers or groups are combined like this, we know we have to add to find the answer.
Let’s model the problem using cubes. Four blue cubes to represent four blue sweaters and then three red cubes. We can write this as an addition sentence or equation. Four plus three equals what? Let’s count on from the four we already have to see how many we have altogether. Four, five, six, seven. If you have four blue sweaters and three red ones, the way to find the answer is to add four and three together. So how many sweaters do you have? Four plus three equals seven.
This garden had five flowers. Then, Jennifer picked two flowers. How many flowers are left in the garden?
To solve this problem, it would be helpful if we had a number sentence or equation. Then we’d know what to do with the numbers. Should we add them? Or should we take them away? The first thing we need to do is to read the problem carefully and to think to ourselves, is this an addition or a subtraction problem?
The first thing we’re told is that the garden had five flowers. We could use five counters to represent our five flowers. Then we’re told that Jennifer picked two flowers. Now, does this mean that Jennifer added another two flowers to the five flowers that were already there? If so, we need to work out the answer to five add two. Or does it mean that Jennifer took away two flowers from the five that were already there? In which case we need to work out five subtract two.
Well, of course, if somebody picks some flowers, the group of flowers is going to get less. We know this because the question asks us how many flowers are left in the garden. When something’s left behind, it’s after we’ve taken something away. So to find the answer, we need to work out five take away two. And if we look at our counters, we can see that we have three left. Five take away two equals three. We can use the picture to check. There are three flowers left behind.
Because this problem was all about somebody picking flowers out of a garden, we decided it was going to be a subtraction sentence that we needed to write. The number of flowers that are left in the garden is the same as five take away two, which equals three.
So what have we learned in this video? We’ve learned how to solve problems by doing two things. Firstly, by deciding whether to add or subtract to find the answer. And then actually finding the answer by completing equations, by adding or subtracting.