In this video, we will learn how to add zero to numbers up to 10 using models and equations.

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### Video Transcript

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.