### Video Transcript

Relating Addition to Subtraction:
Numbers up to 20

In this video, we’re going to link
together different groups of three numbers up to 20. And we’re going to use them to
write a family of addition and also subtraction facts. To help us think about families of
numbers that we can use to make addition and subtraction facts, we need to
understand parts and wholes. We can use a part–whole model to
help us find these families. In the bottom two circles, we could
write two parts. And when we add them together, the
total or the whole amount is written in the top circle. We know that one part plus another
part equals the whole amount. Let’s put some numbers into our
part–whole model.

11 and six more make a whole amount
of 17 altogether. These are a family of numbers. They belong together because we can
use them to write additions and subtractions. Let’s start with some
additions. How many can you find? Well, perhaps, the first one, the
one that we can see straight away, is 11 plus six equals 17. But we know we could add these two
numbers the other way around and they’d still make 17. Six plus 11 makes 17 too. Look at how both our additions
contain the same three numbers. You know, we could write these
additions in two more ways because we don’t always have to end with a whole
amount. What if we start with a whole
amount? 17 is equal to what? It’s equal to 11 plus six and also
six plus 11.

Now, as well as finding this family
of addition facts, we can also use the numbers 17, six, and 11, our whole and our
two parts, to find some subtraction facts. Now, to do this, we need to start
off with 17, the whole amount. Now, we know if we start with the
whole amount and we take away one of the parts, we should be left with the other
part. So if we start off with 17 and we
take away six, we should be left with 11. One, two, three, four, five,
six. And now, if we look at how many
counters we have left, we have a full 10 frame and then one more. If we take away one part, we’re
left with the other part. 17 take away six is 11. And you guessed it. If we take away 11, we’re left with
six.

And just like before, we could
rearrange these subtractions and start with the answer first. 11 is equal to 17 take away
six. And six is equal to 17 take away
11. We found two parts that go together
to make a whole. And we’ve used these three numbers
to find a family of addition and subtraction facts. And the reason why we’ve used
different colors for each number in this video is to help us see a really
interesting fact. All of the number sentences contain
the same three numbers. But you know, it doesn’t have to be
six, 11, and 17.

10 and 10 make a total of 20. So we could’ve used those three
numbers instead, or 18, one, and 19. For each of these different
part–whole models, we could find a new family of addition and subtraction facts. And each time, all the number
sentences we could find would contain the same three numbers. Let’s try answering some questions
now where we have to look for the families of addition and subtraction facts.

Use six plus 13 equals 19 to fill
in the blanks in these number sentences. 13 plus what equals 19. 19 subtract six equals what. And what take away 13 equals
six.

To begin with, in this problem,
we’re given an addition. It’s an addition that’s a complete
number sentence. We can see the two parts that we
add together and the answer. So we could sketch a part–whole
model to represent it. Six and 13 make a total of 19. And you know, we can use these
three numbers, the two parts that go together to make the whole, to help us fill in
the blanks in some different number sentences. And the reason why we can do this
is that the three number sentences we’re given with blanks in are all related;
they’re part of a family. You’ll see why, as we go through
them.

Our first number sentence says, 13
plus what equals 19. Can you spot anything interesting
about this addition? The first thing that we can see is
that the total, the answer to our addition, is 19. It’s the same as the total in the
addition we need to use to help. And if we keep looking, we can also
see that the number we’re starting with here, which is 13, is the second number in
our addition. And so if six plus 13 make 19, then
we know that 13 plus six makes 19 too. We’ve just added the same two parts
but in a different order.

Our second calculation is a
subtraction. 19 take away six equals what. Well, we know from our last
calculation that 13 plus six more make 19. So if we start with 19 and we take
away six, we’re going to be left with 13. Each of these calculations contains
the same three numbers, 19, six, and 13. That’s what we meant when we said
they were going to be related.

Our final calculation is what take
away 13 equals six. Well, again, we can use the
addition to help us find the subtraction. If we know that six and 13 go
together to make 19, then we also know if we start with 19, the whole amount, and we
take away one of the parts ,13, we’re going to be left with six. The missing number here is 19. We’ve used six plus 13 equals 19 to
fill in the blanks and find a family of addition and subtraction sentences. 13 plus six equals 19. 19 take away six equals 13. And 19 take away 13 equals six. Our missing numbers are six, 13,
and 19.

16 plus three is 19. Which number sentence is missing
from the number sentences three plus 16 equals 19, 16 plus three equals 19, and 19
take away 16 equals three?

It seems from this question that we
got a missing number sentence here. We’re given a family of three
different number sentences, but there must be a fourth one that we need to find. To begin with, we’re given a number
fact. 16 plus three is 19. We know we could model this using
cubes. 16 plus three is 19. And if we look at our number
sentences that we’re given, the second one shows this number fact written as a
number sentence 16 plus three equals 19. Now, we can use these three
numbers, 16, three, and 19, to write a family of addition and subtraction facts
because 16 and three are two parts that make a whole amount, 19.

And you know, we could make that
whole amount in one other way. If we look at our train of cubes,
we could just swap the pink and the orange cubes around. Three plus 16 is 19 too. And this is where we get our first
number sentence from. So we start off with two
additions. Our final number sentence is a
subtraction, and we can see the same three numbers again. This time, we’re starting with the
whole amount. If we have 19 and we take away 16,
we’re left with three. So we have two additions, but we
only have one subtraction.

Let’s try and find another
subtraction that we could make using these numbers. We know the whole amount is 19. So if we’re going to take away a
number, we need to start with this whole amount. Let’s make 19 the first number in
our number sentence. And we’re going to look for another
subtraction. So we need to use the subtraction
symbol. Now, we need to take away one of
the parts. In the subtraction we’re already
given, we’ve taken away 16. So instead of taking 16, let’s take
away three.

19 take away three equals what? Well, we know from that very first
number fact that 16 and three go together to make 19. And so if we start with 19 and we
take away three, we’re going to be left with 16. We can use one addition fact to
write a whole family of addition and subtraction facts. The number sentence that’s missing
is 19 take away three equals 16.

So what have we learned in this
video? We’ve learned how to write a family
of addition and subtraction facts, linking three numbers up to 20.