### Video Transcript

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.