### Video Transcript

Making Six and Seven

In this video, we’re going to learn
how to use pictures and addition equations to show all the ways to make the numbers
six and seven.

Here we have seven birds sitting on
a wire. At the moment, they’re all on the
right-hand side of the wire. At this end, there are no birds or
zero. And all seven of the birds are
huddled up together at the other end. We can write the number of birds at
either end of our wire as an addition. And it’s going to make a total of
seven. Zero plus seven equals seven. You know, we can record this number
fact in lots of different ways, as a number bond in this part–whole diagram. If we like the idea of birds on a
wire, we could use counting beads on a piece of string. We could also write out the
addition as a number sentence.

How else could we make seven? Well, let’s imagine that one of our
birds gets fed up being part of a large group and wants to hop off to the other end
of the wire on his own. There we go. We could model this by pushing one
of our beads along the string. What addition can we see now? We now have one bird at this end of
the wire. And although we did have seven
birds on the other end, we now have one less. We have six birds, but we still
have seven birds altogether. We can say that one plus six equals
seven. It’s another way of making the same
total.

What if another bird decides to
move? This shows another way to make
seven. Two and five make seven too, so do
three and four. You know, changing one thing at a
time, whether it’s a bird on a wire or a bead on a string, is a good strategy that
we can use to make sure we find all the possible ways to make a number. And if we look carefully at our
number sentences, we could spot some patterns.

Firstly, we can see that the answer
each time is seven. This is because we’re finding
different ways to make seven. If we think about beads on a
string, the number of beads aren’t going to change. What pattern can we see with the
first number in each number sentence? Zero, one, two, three. These numbers are increasing by one
each time. What number would you expect to
come next? Zero, one, two, three, four.

If we look at the second number in
each number sentence, we have seven, six, five, four. These numbers are going down, and
they’re decreasing by one each time. Seven, six, five, four, three. We’d expect the next number to be
three. Four plus three equals seven. And we can continue that
pattern. Five and two make seven. Six and one make seven. And finally, if we move all the
beads to the other side, seven and zero make seven too. We found eight different ways to
make the number seven. Let’s have a go at answering some
questions now. We can use this strategy in some
different models and answer some questions how to make six and seven.

Find the missing addition
sentence. Zero plus six is six. One plus five is six. Two plus four is six. Three plus three is six. Four plus two is six. What? And we have four possible
answers. Four plus one is six. Four plus two is five. Five plus one is six. And four plus one is five.

In this question, we’re given
some addition sentences. These are written using
numbers, but they’re also modeled using cubes. And we can see both orange and
green cubes here. The first line of cubes shows
no green cubes and six orange cubes. That’s where we get our number
sentence zero plus six from. We can think of the first
number as being the number of green cubes that we can see and the second number
as being the number of orange cubes that we can see. And because the length of each
line of cubes is the same each time, these are always going to make six. Zero plus six is six.

We can also see that one plus
five is six. Two green cubes and four orange
cubes make six. If we add together three of
each type of cube, we get six. Four plus two make six. But then we come to a missing
addition sentence. And the question asks us to
find out what it is. What can we say about this
missing addition sentence? Well, firstly, we can say that
we’re looking for two numbers that we need to add together, just like all the
other addition sentences. We can also say that we’re
looking for a number sentence that gives the answer six.

If we look at our line of
cubes, we can see that there are six cubes just like all the others. So which two numbers can we
find that make six? If we look at the numbers in
each addition, we can see some patterns. The first number in each
addition, which is the number of green cubes, increases by one each time. If we read each of the first
numbers, we can see zero, one, two, three, four. If we’re increasing by one each
time, what’s going to come after four? We’d expect to see the number
five. Should we count our green
squares to see whether that’s correct? One, two, three, four. Yes, there are five green
squares.

And if we look at the second
number in each addition, which is the number of orange squares, we can see that
these decrease by one each time. They get smaller. Six, five, four, three,
two. What comes after two? One. How many orange squares are in
our line of cubes? One. So we would expect our missing
addition sentence to say five and one is six. Can you see that as one of our
possible choices? Yes, here it is. Five plus one is six.

Using cubes like this is a
really good way to model all the possible ways to make a number. In fact, there is only one
other way that isn’t shown. A line of just green cubes
would show us that six plus zero is six too. But we don’t need to know this
to answer the question. The missing addition sentence
from the picture that we were shown is five plus one is six.

Which of these has a different
answer? Three plus three. One plus five. Three plus four. Or two plus four.

We can see that these four
different additions are also shown as a model using both blue and orange
rectangles. Can you see what the first
number in each addition represents? It’s the number of blue
rectangles, isn’t it? For example, in the first
addition sentence or equation, we have three blue rectangles. That’s why our first number is
three. And we also have three orange
rectangles. That’s why the second number in
our equation is three. So what is three plus
three? Let’s start by saying the first
number and then counting on another three. So we’ll say three, four, five,
six. There are six rectangles in our
first model. Three plus three equals
six.

In our second model, we can see
that we have one blue rectangle and five orange rectangles, so we can start with
the number one and count on another five. One, two, three, four, five,
six. Our second number sentence also
shows six. And if we compare the length of
our models, we can see they’re both the same length. They both contain six
rectangles, don’t they?

What about our next number
sentence, three plus four. We’ll start with three and
count on four. Three, four, five, six,
seven. This number sentence has an
answer of seven. And if we look at the length of
the model, we can see that this is longer than the rest. The number sentence with a
different answer is three plus four. We know this because if we
start on two and count on another four, we’re going to arrive at six. Two, three, four, five,
six. The addition that has a
different answer is the one that shows three plus four.

There are six cats. Three plus three is six. Find out the missing numbers to
have another way to get six. What plus what is six.

We’re told in this question
that there are six cats, and this question is all about different ways to make
six. To begin with, we’re shown a
number sentence made out of pictures. In the first picture, we can
see three cats. And in the second picture, we
can see another three cats. Then, in the final picture, we
can see six cats. This shows us that three plus
three is six. We could actually draw a line
across our group of six cats to show us that three and three make six.

But then we’re shown another
picture number sentence. This time we’ve got some
missing numbers, and we’re told to find out the missing numbers to have another
way to get six. How else could we make six? Well, if we look carefully at
our first picture, we can see that, instead of three cats, this now shows two
cats. Let’s write the number two
above that picture. Two plus what make six. But if we want to make the same
total, which is six, we need to do something with the cat that’s walked
away. Instead of three cats to begin
with, we have two. So the cat that’s gone away is
gonna have to join the second group to keep the answer the same.

If you remember, we did have a
group of three cats as a second group. We now need to have a group
with one more cat in it. Let’s count them to see whether
there are four cats in our second group. One, two, three. Yes, there are. There are four cats in our
second group. Two plus four is six. And again, we can draw a line
on our group of six just to show that two and four make six. We know that three plus three
is six, and we can use this to help us find that two plus four is six too.

What have we learned in this
video? We’ve learned how to use pictures
and equations or number sentences to show all the ways to make the numbers six and
seven.