# Lesson Video: Making Two-Digit Numbers Mathematics • 1st Grade

In this video, we will learn how to decompose two-digit numbers into 10s and ones in different ways, using patterns to find all the ways.

13:13

### Video Transcript

Making Two-Digit Numbers

In this video, we’re going to learn how to decompose or split up two-digit numbers. We’re going to split them up into 10s and ones in different ways. And we’re going to use patterns to make sure we find all of the ways.

Let’s start with a two-digit number. We’ll begin with the number 39. Now, how could we split up the number 39 into 10s and ones? Our first idea is probably going to be the most common way. We can make 39 using three 10s and also nine ones. We know that three 10s are the same as 30. And so we could say we’ve split 39 into 30 plus nine. We could use the word decompose here. You know when leaves fall from the trees? Eventually, over time, they break up, won’t they, into smaller and smaller parts. We can say that they decompose. It’s a word that simply means break up or split up. And that’s what we’ve done here to our number 39. We’ve broken it up or decomposed it into three 10s and nine ones.

But this video is about splitting up numbers in different ways. How else could we show 39 in 10s and ones? Well, there’s not a lot we can do with our nine ones because they don’t make a full 10. Perhaps we can do something with our 10s blocks though. We know that each of our 10s blocks is equal to 10 ones. They’re worth the same. So why don’t we take one of our 10s blocks and exchange it for 10 ones? There we go. Now, instead of three 10s, we only have two 10s. But we have more ones, don’t we? Instead of nine ones, we now have another 10 ones. So we have 19 ones altogether. We know that two 10s are worth 20. And so we’ve decomposed or split up the number 39 a different way. We’ve broken it up into 20 plus 19.

Shall we keep going? We’ve got more 10s that we could break up. We could take another 10s block and exchange it for 10 more ones. Instead of two 10s, we now only have one 10. But we’ve now got 10 more ones, haven’t we? So instead of 19 ones, we now have 29 ones. As we know, one 10 is worth 10. So we can say we’ve decomposed the number 39 another way, 10 plus 29. Now, what’s going to happen if we exchange our last 10 for 10 ones? If we do this, it’s going to be interesting because we’ll have made the number 39 completely out of ones. We’ve broken up 39 into zero 10s. And instead of 29 ones, there are now 39 ones. 39 is equal to zero plus 39.

Did you know we’ve found all the possible ways to make 39 using 10s and ones? How do we know that we found all of them? If we look at the ways that we’ve split up 39, we can see some patterns. To begin with, we made 39 using the most number of 10s that we could, which was three 10s or 30. All we needed then was another nine ones. From then on, we took one 10 each time and exchanged it for 10 ones. That’s why our pattern goes from 30 to 20 to 10 and then zero where we have no more 10s that we can exchange.

We can also see a pattern in the number of ones. We start with nine ones and then, because we’re exchanging one 10 each time for 10 more ones, we can see that the number of ones increases by 10 each time until we make the whole number completely out of ones. And that’s how we know we found all the possible ways to break up 39 into 10s and ones. Let’s try answering some questions now where we have to decompose or break up two-digit numbers into 10s and ones in different ways.

Which place-value table also shows 74? Hint, regroup 10s into ones. We’re given three possible answers to choose from, 40 10s and 34 ones, four 10s and three ones, or four 10s and 34 ones.

Underneath the question, we can see a large place-value table. And in it, a two-digit number has been modeled using 10s and ones blocks. Underneath each of the pictures of blocks, we can see how many blocks there are. The number contains seven 10s and four ones. We know that the seven 10s have a value of 10, 20, 30, 40, 50, 60, 70. And of course, four ones are worth four. So our place-value table shows 74, and it’s being broken up into seven 10s, which we said will worth 70, and also four ones. 70 plus four equals 74.

Now, as we’ve said at the start, there are some smaller place-value tables at the bottom. These are our possible answers. These place-value tables don’t show the blocks. They just tell us how many 10s and ones there should be. And our question asks us which one of these place value tables shows 74 just like the one in the middle. To help us solve the problem, we’re given a hint. We’re told to regroup 10s into ones. You know, there’s something important that we know about 10s blocks. Each lot of one 10 is worth exactly the same as 10 ones. So, we could take one of our 10s blocks and regroup it into 10 ones, just like this. Instead of seven 10s, we now have six 10s. And instead of four ones, we now have 10 more ones. So we have 14 ones.

Six 10s are worth 60, and we know that 14 ones have a value of 14. And because 60 plus 14 equals 74, we know that six 10s and 14 ones make 74. If we look at our possible answers, though, none of them have six 10s in them. Maybe we ought to try exchanging another 10. Let’s swap this 10 here for 10 ones. Remember, each time we do this, we’re not making the number get bigger or smaller. It still shows 74. Instead of six 10s, we now have five 10s. And we have another 10 ones. So instead of 14 ones, we have 24 ones. We know that 50 plus 24 equals 74, so we can split up 74 into five 10s and 24 ones. Now, none of our possible answers say five 10s. But two of them have four 10s in the tens place.

Let’s regroup one more 10 into ones. Instead of five 10s, we now have four 10s. And we have another 10 ones. So instead of 24 ones, we have 34 ones. Four 10s are worth 40, and we’ve split 74 into 40 plus 34. Can you see the answer now? By regrouping 10s into ones, we’ve found another place-value table that also shows 74. Four 10s are worth 40, and 34 ones are worth 34. And we know that 40 and 34 go together to make 74. The place-value table that shows 74 is the one that shows four 10s and 34 ones.

Which of the following is the wrong model to decompose 43?

There’s an interesting word in this question: decompose. Do you know what it means? When something decomposes, it breaks up or splits up. And so we use this word in math to describe when we split up a number. So we could really read our question as which of the following is the wrong model to break up the number 43? We’re given three models to choose from, and each model contains two parts. Firstly, there’s a place-value table where we can see a number has been modeled using 10s and ones blocks. And next to each one of these tables is a part–whole model which shows us how the number of 43 has been split up or decomposed.

This is an interesting question really because we’re not being asked for the right answer here. The question asks us, which of the following is the wrong model to decompose 43? In other words, which one is the odd one out? Two of these models show different ways to split up the number 43 and one of them doesn’t, and we need to find that one. Let’s start then by looking at our first model. In the tens part of our place-value table, we can see four 10s. We know that four 10s have a value of 40. This is where the number 40 comes from in our part–whole model. We can also see three red ones blocks. And we know, don’t we, that we can split up the number 43 into four 10s or 40 and three ones.

If you were told to make the number 43 out of 10s and ones, this is probably the way you do it. So we know this first model is correct. You know, we can use this first way of showing 43 to help find other ways. If we look at the remaining two models, we can see that there’s something similar about them. Instead of four 10s, they both have three 10s. Something’s happened to one of the 10s. Well, if we just took away one of the 10s like this, the number would stop being worth 43. It would actually be worth 33. We know that one 10s block is the same as 10 ones. So if we’re going to get rid of one of our 10s blocks, we need to exchange it for 10 ones. That’s better.

Now, instead of three ones, we have another 10 ones, so we have 13 ones altogether. We can decompose 43 into 30 and 13. And if we look at our possible answers, we can see that this is the same as the bottom model. By finding the two models that are correct, we’ve identified the wrong one. It contains three 10s, which are worth 30, but only four ones, which are worth four. And what do we get if we put 30 and four together? This model shows 34 not 43. It’s almost as if the person that’s made it has swapped the digits around. The wrong model to decompose 43 is the one that shows three 10s and four ones, or 30 plus four.

What have we learned in this video? We’ve learned how to break up or decompose two-digit numbers into 10s and ones in different ways. We’ve also used patterns to find all of the ways.