### 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.