Video Transcript
Adding Zero
In this video, we’re going to be
learning how to add zero to numbers up to 10 using models and equations.
Let’s start off by reminding
ourselves what zero means. It’s the symbol that we use to
represent nothing. Here’s a picture of a plate with
zero doughnuts on it. And here’s a picture of zero
elephants. Of course, we can’t see any
elephants because zero means nothing. So, what happens if we add zero to
a number? And what happens if a number is
added to zero? Let’s find out.
Here’s a group of three
trumpets. Now, what happens if we add a group
that doesn’t contain any trumpets at all? We can say that this group has zero
trumpets in it. To find the total of both groups,
we just need to count all the trumpets we can see. So, that’s one, two, three. And there aren’t any more to count
in this group. So, we can say three plus zero
equals three. We’ve ended with the same number of
trumpets as we started with.
Adding zero to a number means that
the number doesn’t change. And this rule works if we start
with zero too. Here’s a picture of zero
sweets. What if we add two sweets to our
group of zero sweets? We can see straightaway that the
number of sweets we have altogether is two. So, if we start with zero and add a
number to zero, again that number doesn’t change. Let’s try answering some questions
that involve adding zero.
What is four plus zero? Hint, count to find the answer.
In this question, we need to work
out the answer to four plus zero. You know, plus is another way of
saying “add.” This is an addition question. And we can see the addition symbol
too, four plus zero. This calculation is also shown as a
picture. First, we have a group of four
cats. Then, we have an empty space, which
is the same as saying a group of zero cats. Remember, zero is the same as
nothing.
We’re given a hint in the
question. And it tells us to count to find
the answer. So, let’s count all of the cats in
both groups. There are one, two, three,
four. And then, we haven’t got any more
to add on in this group. Four plus zero equals four.
If I have four marbles and you give
me zero marbles, then I still have four marbles. So, four plus zero equals four. If I have zero marbles and you give
me four marbles, how many marbles do I have? Write an addition sentence to show
the answer.
This problem is a little bit like a
story. And we could use maths equipment to
help us find out what the answer is. Let’s read it through again from
the very start. Firstly, we’re told that we begin
with four marbles. It says, if I have four
marbles. So, let’s start by taking four
counters. These can represent our four
marbles.
In the problem, we’re told that you
do something to my four marbles. You give me another zero
marbles. We know that zero is the same as
nothing. That’s why the hand at the top of
the picture hasn’t got anything in it. And that’s also why if we’re using
counters to show this problem, we don’t need any. Zero means no more.
The sentence goes on to tell us
that if you give me zero marbles, I will still have four marbles. And this story is also represented
by an addition sentence or an equation. Four plus zero equals four. We can also see this by looking at
the part–whole model we’ve made using counters. Four counters plus no more counters
makes a total of four counters. When we add zero to a number, it
stays the same.
The next part of our story problem
ends in a question. If I have zero marbles and you give
me four marbles, how many marbles do I have? We can see this being shown in the
picture, too. Here’s my hand. It has zero marbles in it. And here’s your hand giving me four
marbles. To find the answer, we need to add
together zero and four. We could even write these numbers
as part of our addition sentence straightaway. We know that what we need to do is
to add zero, that’s the number that I have to begin with, and four, that’s the
number that you give me. Let’s use counters again to model
what we’re being asked.
I start off with zero marbles. So, we don’t need to draw any
counters there. Then, you give me four marbles. Now, we need to combine both sets
of counters to show what the total is. The total is four. The number of marbles that I have
now is four. If we add a number to zero, the
answer’s going to be the same as the number we added. The addition sentence or equation
that shows the answer to this problem is zero plus four equals four.
Is eight the answer to both these
sums? Eight plus zero equals what? And zero plus eight equals
what?
This is a really interesting
question because, in a way, we’re given the answer before we start. We’re given two addition sentences
and then asked, is eight the answer? It’s our job to look at the sums
and to think to ourselves, is the answer eight both times?
To begin with, let’s look at our
additions. What do we notice? Well, the first thing that we can
see is that they both contain the same two numbers being added together. There’s a number eight and there’s
a zero. Remember that zero has a value of
nothing; it’s not worth anything. We can also see that both number
sentences are additions. That’s why the word sums is used in
the question. It means additions, two numbers
added together.
So, they both contain the same
numbers. They both contain addition
symbols. But the numbers in each sum are the
other way around. Did you notice this? In the first calculation, we start
with eight and then we add on zero. And in the second sum, we start on
zero and we add eight. So, do you think eight is gonna be
the answer to both these sums?
Let’s use a number track to help us
model what they’re asking us. In our first sum, we need to work
out the answer to eight plus zero. So, the number we’re going to start
on is the number eight. We’ll put a counter next to the
number eight to show where we’re starting from. And now, we need to move on another
zero places because we’re adding zero. Watch the counter. We’re about to move it zero
places. There we are. It hasn’t moved at all. We know it’s not going to move
because zero is the same as nothing, no places.
If we add a zero to a number, it
stays the same. So, if we start on eight and we add
nothing to it, we get an answer of eight. So, we know that eight is the
answer to the first sum. But is it the answer to both of the
sums? Let’s check out the second sum.
In this addition, we need to start
on zero and count on another eight because we need to add eight to it. Our number line has the number zero
on it already, so let’s put a counter next to it. Now, let’s move it eight places as
we add eight. We’ve moved it one place, two
places, three, four, five, six, seven, eight. If we start with zero and add
eight, we get an answer of eight.
This question shows us a really
interesting fact about adding with zero. If we start off with a number and
we add zero, the number stays the same. And if we start on zero and we add
a number, the answer is going to be the same as the number we added. Eight plus zero equals eight. And if we add the two numbers the
other way around, zero plus eight also equals eight. Our counters ended up in exactly
the same place. Is eight the answer to both these
sums? Yes, it is.
So, what have we learned in this
video? We’ve learned how to add zero to
numbers up to 10. And we’ve done this using models
and equations or number sentences. But, you know, we also found out
something interesting about what happens when we add zero. We’ve learned that if we add zero
to a number, the number doesn’t change. We’ve also learned that if we start
with zero and add a number to it, the answer will be the same as the number we
added.
