Making Numbers up to 20
In this video, we’re going to learn how to make numbers up to 20 in lots of different ways using both addition and also subtraction.
Let’s start by thinking about the number 15. Here’s what 15 birds look like. What are some of the ways that we can make the number 15 using addition? We know that 10 plus five makes 15. This is the addition that we see when we model this number using ten frames. We have a full ten frame, which is worth 10, and then five more. So 10 plus five equals 15. How else could we make 15? Eight plus seven equals 15. Two plus 13 equals 15. We could even add three numbers together. Two plus nine plus four makes 15.
Can you see how the number of birds in the line and the number of counters that we use on our ten frames stay the same every single time? All that’s happening is we’re splitting up or partitioning the number 15 in different ways. So these are just some of the ways that we could make the number 15 by adding. But we can also make the number 15 by subtracting. Just to remind us, here’s what 15 looks like. You know we could write a subtraction using the number 15 to start with.
Because we already have 15, we don’t need to take away anything to get 15. 15 take away zero equals 15. But what if we have 16? 16 take away one equals 15. 17 take away two leaves us with 15. And we could even say 20 take away five equals 15. We’ve had a go at making the number 15 in different ways. Now it’s time to put into practice what we’ve learned. Let’s try answering some questions where we have to make numbers up to 20 in different ways.
Which of these is not equal to nine? 14 take away five. 10 take away one. 15 take away six. 12 take away two. Or 17 take away eight.
In this problem, we’re given five different subtractions. But there’s an odd one out and we need to find it. We’re asked which of these is not equal to nine. So we’re expecting most of the subtractions will equal nine. We need to find the one that doesn’t. Let’s use a ten frame to help us. Our first calculation says 14 take away five. So let’s start by modeling the number 14. 10 and four more makes 14. Now what do we get if we subtract five? Well, we know if we take away four from 14, we’re going to be left with 10. But we don’t want to subtract four. We need to subtract five. So instead of 10, we’re going to be left with nine. 14 take away five is equal to nine. So let’s put a tick there.
You probably know what 10 take away one is without using the counters. Of course, one less than 10 is nine. What about 15 take away six? Is this our odd one out? Here’s what the number 15 looks like using our ten frames, 10 and five more. This means we can subtract five really quickly. 15 take away five leaves us with 10, but we want to subtract six, not five. So we’re going to take away one more counter. Again, this leaves us with nine. Does 12 take away two equal nine? We know we can model 12 by making 10 and two more. So if we take away those two, we’d left with 10, not nine.
It looks like we’ve found a subtraction that’s not equal to nine. And if we just check our final subtraction, we know that 17 take away seven will leave us with 10. So if we take away one more, 17 take away eight equals nine. There are lots of subtractions that make nine, but one that doesn’t and the one that’s the answer to this question is 12 take away two.
Which of these is not equal to 15? 10 plus five. 12 plus three. One plus 14. Six plus nine. Or 14 plus two.
In this problem, we can see five different additions. Now we’re asked which one of them is not equal to 15. In other words, which addition is the odd one out? Let’s find each different total by using a number track. We could count on. Now, most of our additions are going to make 15, so let’s make our number track up to 15. Our first addition then is 10 plus five, so we can start on 10 and count on five more. One, two, three, four, five. We can move the counter straight to the number 15. 10 plus five does equal 15. Let’s put a tick by this addition. What about 12 plus three? Is this our odd one out? We can start on 12 and count on one, two, three. 12 plus three also equals 15.
In our next addition, we could start at the number one right at the beginning of our number track and count on 14. But this would take quite a long time to do. And we know that we can add numbers in different ways and they still make the same total. It will be much quicker to start with the number 14 and add one because we know that 14 plus one more equals 15. Much quicker than counting on 14. Now we’ve only got two additions left. Can you spot the one that doesn’t equal 15? But if you remember in our last addition, we swapped the numbers around and we worked out that 14 plus one equals 15.
So do you think 14 plus two is going to equal 15? No, in fact, we’re gonna have to extend our number track because 14 plus two equals 16. And it’s a good habit just to check all the calculations. Six plus nine equals 15. In this problem, we’ve looked at some different ways to make 15. And the one addition that does not make 15 is 14 plus two.
Now, so far in this video, we’ve just talked about some of the ways to make these numbers. But is there a way to find all the possible answers? How do we know whether we found all the possible pairs of numbers that make 13, for example, or all the possible subtractions?
Well, to do this, we need to work systematically, which is a long word. But we can see a shorter word in there that we might recognize. It means to have a system, to have a way of doing things that will help us to find the answer. And the system that we can use is to start with one calculation and change one thing at a time. So what’s the easiest addition we could start with that makes 13? Adding zero is pretty easy, so we could say 13 plus zero equals 13. 13 orange cubes plus zero pink cubes equals 13 cubes altogether.
Now, remember, the system that we’re going to use is just to change one thing at a time. So let’s change the color of one of our cubes. We now have one less orange cube, but we have one more pink cube. 12 plus one equals 13, so does 11 plus two, 10 plus three, and nine plus four. You can see we’re just changing one little thing every time. And by doing this, it’s a way to make sure that we found all the possible additions. We haven’t missed any possibilities out. And if you look at our list of additions, you might see some interesting things.
The first numbers in each addition are decreasing by one each time. 13, 12, 11, 10, nine, and so on. Of course, this is because we’re getting rid of one orange cube each time. And if we look down the column of the second numbers in each addition, we can see that these are increasing by one each time. Zero, one, two, three, four, five, and so on. Of course, this is because the number of pink cubes is increasing by one each time. And we can also see that some of the additions contain the same numbers, but just in a different order. And you know, that’s how we know we found all the possible answers. We started with 13 orange cubes and zero pink cubes, and we ended with zero orange cubes and 13 pink cubes.
And you could look all day long for any other pairs that make 13. And you won’t find any. We know we’ve found them all because we’ve used a system. We started at the beginning and we changed one little thing every time. And, you know, we could use the same idea with subtraction. If we start with what we’ve got, we can say 13 take away zero equals 13. But if we start with 14 instead, we’re going to have to take away one to get 13. Remember the way we’re doing this, our system, is simply to change one little thing each time. And because we’re making our chain of cubes one more each time, we need to subtract one more each time to keep our answer 13.
And perhaps you can see that we could keep on adding cubes all we like. We just have to take more and more each time. But that would make for a boring video. We did say at the start that we’re going to be working within 20. So we’ll stop with 20 take away seven. So what’s a good system or a way to make sure we find all possibilities? Start with the most simple calculation and then change one small thing each time. And that’s how to find all of the addition pairs or subtraction pairs that make a number.
Now what’ve we learned in this video? We’ve learned how to make numbers up to 20 in lots of different ways, using both addition and also subtraction.