Subtracting from Six and Seven
In this video, we’re going to learn
how to use pictures and subtraction equations to show all the ways to take away from
the numbers six and seven. Here are six bottles of water. Let’s put them in a ten frame so it
makes them easier to count. Now, what happens if we’re feeling
hot and we drink one of the bottles?
We’ve taken one bottle away from
the group of six. And now we’re left with five
bottles. We know there are five left because
it’s the top row of our ten frame. We don’t need to count them. Now, we could write we’ve just done
as a subtraction sentence. Another word for the same thing is
Now, we started off with six
bottles of water. So let’s write the number six to
begin with. And then we took away one. So we can use the subtraction
symbol and then the number one. This shows six subtract one. And then we’re left with five. So we can use the equal symbol to
show that six take away one is equal to or the same as five.
We said at the start this video is
about finding lots of ways to take away from six and from seven. So being as we’re thinking about
the number six here, how else could we take away from six? What if we drink another bottle of
Our picture shows a different
subtraction now. It shows six take away two. And if we count the number of water
bottles left, there are one, two, three, four. Six take away two leaves us with
four. And you know, we know this, don’t
we? Because two and four are a pair
that go together to make six. As well as a picture, we could
write another number sentence. This time, we’re going to write six
take away two bottles of water equals four bottles of water.
Now, we seem to be subtracting in a
sort of order here. How many could we subtract now? We’ve already subtracted one and
then two. Let’s drink one more bottle of
water. Now, we’ve taken away three. Now, what number goes with three to
make six? Well, we know three plus three
makes six. And so if we start off with a group
of six and we take away three, we’re going to be left with one, two, three. So we’ve found another subtraction
sentence we could write. Six take away three equals
Now, if we look at our
calculations, we can see a pattern going on here. The first number in each
subtraction is always a six. This is because we’re exploring
different ways to take away from six. We always want to start with
six. So we know that our next
subtraction is going to definitely begin with a six.
Now, let’s look at the second
number in each subtraction. This is the number that we’re
taking away each time: first one, then two, then three. Can you see the pattern? We’re taking away one more each
time. And so after three, we’d expect to
take away four. It’s helpful to follow this pattern
if we want to find all the possible ways to take away from six.
And you know, there’s also a
pattern when we look at the answer to our subtractions: five, then four, then
three. These numbers are going down by one
each time. If we think about it, that’s what
we expect them to do. Each time we’re drinking one more
bottle of water. So the number of full bottles of
water is going down by one each time. We’ve got as far as three bottles
of water. So if we take away four, we’re
going to be left with one less than three, which is two.
Now, let’s see if we can change our
picture to show this subtraction. Six take away four now leaves us
with two. And we know this because four and
two are a pair that go together to make six. We’ve said this already. Let’s keep drinking bottles of
water until we’ve got no more to drink. Six take away five leaves us with
one. And six take away six, if we drank
all the bottles of water, will leave us with zero.
We’ve found lots of different ways
to take away from six. We started by taking away the
smallest amount, which was one. And then we took away one more each
time so that we made sure we’ve found all the different possibilities. Now, let’s try answering some
questions where we have to both take away from six but also seven.
Liam is subtracting from seven. Write the missing number
sentence. Seven take away one is six. Seven take away two is five. Seven take away three is four. Seven take away four is three. What? Seven take away six is one.
In this question, Liam is taking
away or subtracting from the number seven. We know this because we’re told
this in the first sentence. We can also see that on each of his
ten frames, he’s put seven black counters to start off with. And we can also see that the first
number in every number sentence is seven. It’s the number Liam is starting
off with each time. And so the first thing we can say
about our missing number sentence is it’s going to begin with the number seven. What’s the next thing we can
Well, because this is a subtraction
number sentence, we need to take away a number. But how many should we take
away? If we look carefully at Liam’s
pictures, we can see that he’s taking away in a certain order. In the first ten frame, he’s
crossed out or taken away one counter, then two counters in the second ten
frame. Then he takes away three, then
four. He’s taking away one more each
time, isn’t he? And one more than four is five. Our missing number sentence shows
seven take away five.
Now, we could find the answer by
counting the number of black counters that haven’t been taken away. But we could also find the answer
by looking at our number sentences, in particular, the answers. Our first answer is six, then five,
four, three. Can you see a pattern here? Liam is taking away one more
counter each time. And so his answer is getting one
less each time. His last answer was three. So his next answer, the one we’re
looking for, is going to be one less than three. We would expect it to be two.
Now, does that number sentence make
sense? Is five and two a pair that make
seven? Yes, they are. Liam’s missing number sentence is
seven take away five is two.
Ethan is subtracting from six. Write the missing sentence. Six take away one is five. Six take away two is four. What? Six take away four is two. And six take away five is one.
In this question, we’re told that
Ethan is subtracting from six. And if we look carefully, we can
see he’s trying to find all the possible ways to take away from six. He starts with a very small number,
so he takes away one. Then he takes away one more, so he
takes away two. In our third example, we can see
that Ethan takes away one, two, three counters. Of course he does. This is one more than two. So he starts off with six and he
takes away three. And he continues going through all
the different subtractions, taking away four and finally five.
But we want to think particularly
about this middle subtraction. Six take away three is what? You know, we could use a part
whole–model to help us here. In each of these pictures and each
of these number sentences, the whole amount is six. This is the amount that Ethan
starts with. Now, when Ethan takes away one
counter to begin with, he’s left with five. And we know this because one and
five are two parts that go together to make six. He takes away two then. He’s left with four because two and
four go together to make six.
So now he wants to take away
three. All we have to do is think about
what part goes with three to make six. And we know that three and another
three make six. And so we can complete our number
sentence. Six take away three is three. We’ve followed Ethan’s pattern to
find the missing number sentence. And that was six take away three is
So what have we learned in this
video? We’ve learned how to show all the
ways to take away from six and from seven using pictures and subtraction