Lesson Video: Identifying Odd and Even Numbers: Skip Counting Mathematics

In this video, we will learn how to decide whether a number up to 20 is odd or even by skip counting in twos.

14:13

Video Transcript

Identifying Odd and Even Numbers: Skip Counting

In this video, we’re going to learn how to decide whether a number up to 20 is odd or even. And we’re going to do this by skip counting in twos. Let’s start by practicing our skip counting skills. We know that when we skip count, we say a number, then skip a few, then say another number, skip a few more, and so on. And in this video, we’re going to be skip counting in twos.

Let’s build a tower out of these ice bricks. To help us skip count in twos, we’ll put two bricks down at a time. What numbers will we say? Well, there aren’t any bricks to begin with, so we can start counting at zero and then two, four, six, eight, 10, 12. What do you notice about the numbers that we’ve said? If we start at zero and skip count in twos, all the numbers that we say are going to be even: two, four, six, eight, 10, 12. Let’s carry on skip counting in twos so that we say all the other even numbers up to 20. After 12 comes 14, 16, 18, and 20. You may also have noticed that these even numbers are all numbers in the two times table. One times two is two, two twos are four, three times two is six, and so on. And so we can say all even numbers are multiples of two.

But what about the numbers in between? We could still say these numbers by skip counting in twos, but we’d have to start at one and not zero. This will be a little bit like putting one ice brick down to start with and then counting on in twos, just like before. We’d end up saying the numbers one, three, five. By the way, can you see what’s happening to our tower each time? There’s always one brick left over on the top. Seven, nine, 11. We call these numbers odd numbers. Let’s start at the last odd number that we said, 11, and let’s continue skip counting in twos so that we say all the odd numbers up to 20.

So we’ve got 11 and then 13, 15, 17, and 19. Look at how each of our odd numbers is one more than an even number. Three is one more than two, five is one more than four, seven is one more than six. That’s why when we try to make our tower, it looked so interesting. There was always one more brick left over on the top. So now that we’ve had a go at counting ice bricks in twos. Let’s have a go at entering a question where we have to count another type of object in twos. Let’s see if we can work out whether the number is odd or even.

Michael is counting his bears in twos. He gets to 12 and then sees that he only has one bear left to count. Does he have an even or odd number of bears?

It looks like Michael’s got quite a collection of toy bears here, doesn’t he? And we’re told in the first sentence of this problem that he’s counting them. But he’s not counting them in the way that perhaps we might usually count a group of objects, one, two, three, and so on. We’re told that he’s counting them in twos. And by counting them in groups of two like this, it’s a much quicker way to count. We call it skip counting because we don’t have to say every number. Some of the numbers we skip. To understand what Michael’s done here, let’s have a go ourselves.

So here’s our bear collection. Let’s start counting in twos. Two, four, six, eight, 10, 12. But wait a moment. We can’t count in twos anymore. There’s only one bear left. Let’s put her up with the others. Now by doing this for ourselves, we can understand what the next sentence in our problem tells us. We’re told that Michael gets to 12 and then sees that he has only one bear left to count. Now you might think that this question is now going to ask us, how many bears does Michael have? And to find the answer, we’d need to think about what one more than 12 is. But we’re not asked this. We don’t need to count how many bears Michael has altogether. Instead, we need to say whether he has an even or an odd number of bears.

Now, when Michael counted his bears, he started with no bears. Let’s label zero, just to show he started counting from here. Now we know that if we start at zero and we skip count in twos, every number that we say is going to be an even number. So if Michael only had two bears, he’d have an even number of bears or four bears or six, eight, 10, or 12. These are all even numbers.

But we know that Michael wasn’t able to count his bears in twos. He got as far as the number 12, but then he had one left over. Michael doesn’t have an even number of bears. He has an odd number of bears. If we skip count in twos from zero but we have one left over, we have an odd number. Another way of saying the same thing is that one more than an even number is an odd number. The number of bears that Michael has is odd.

Do you remember our number track that we colored in to show the odd and even numbers? Well, let’s cut it into squares and we’ll put all the odd numbers together and all the even numbers together. So we’ve got our odd numbers: one, three, five, seven, nine, 11, 13, 15, 17, 19. And we’ve got our even numbers: two, four, six, eight, 10, 12, 14, 16, 18, 20. Now do you notice anything about these groups of numbers now that we’ve put them all together? Let’s play a game that might help you spot something.

This bear is holding two-digit cards, and they make a number. But is this mystery number even or odd? And now comes the challenge. To find the answer, you’re only allowed to turn over one of the cards. Which is it going to be? First of all, we know that our number has two digits. But if we turned over the digit on the left here, it’s not really going to help us. Imagine we looked at it and it showed the digit one. Well, there are lots of odd numbers with a one in the tens place: 11, 13, 15, and so on. But there are also even numbers with a one in the tens place: 12, 14, 16.

Within this tens digit, there are lots of odd and even numbers sitting side by side. So to solve our challenge, the one card we need to look at is the one on the right. This is the ones digit. And the ones digit is a zero. Now we don’t know what the other digit is, but we don’t need to know. It could be a one, making the number 10, or it could be a two, making the number 20. It really doesn’t matter. And the reason why it doesn’t matter is all to do with a pattern that we can see in the numbers. If we start off by looking at our even numbers, we can see that they always end in the same set of digits. That could be the digit two like in the numbers two or 12, four as in the numbers four or 14, six, eight, or zero.

Now we know because we chose to look at that second card, the number that the bear’s showing us ends in a zero. It’s got to be even. And whilst any number that ends in a two, four, six, eight, or zero is even, we can say that any number that ends in a one, a three, five, seven, or nine is an odd number. So if our friend the bear had turned over his card and it had shown a seven instead of a zero, we’d have known that his number would have been odd.

And, you know, knowing patterns and sequences like this can help us extend our knowledge of odd and even numbers past 20. 28 ends in the digit eight. It must be an even number. We know that one is an odd digit. So any number that ends in a one must also be odd. 31 is an odd number then, as is 21. Let’s answer some questions now where we have to put into practice these two facts we’ve just learned. Even numbers always end in a zero, two, four, six, or eight. And odd numbers always end in a one, three, five, seven, or nine.

Write the next two odd numbers: seven, nine, 11, 13, what, what.

In this question, we’re given a sequence of odd numbers. We know that one way of counting in odd numbers is to start on an odd number and skip count in twos. So if we start with seven, our next odd number is nine, then 11, and 13. And can you see by skip counting in twos, we’re skipping over the even numbers in between, eight, 10, and 12? So what are the next two odd numbers in our sequence? Which odd number comes after 13? Well, if we continue skip counting in twos from 13, we get to the number 15 and then the number 17. We know that odd numbers in order always follow a pattern. The last digit is a one, then a three, five, seven, and nine.

Although we started with a digit seven, we can carry on this pattern and just check that our answer is correct. So we’ve got seven, nine, and then back to the beginning again, one, three, five, seven. We skip counted in twos to find the next two odd numbers in our sequence. The full sequence is seven, nine, 11, 13, and then our two missing numbers, 15, 17.

Find the odd number that is greater than 93 and less than 97.

In this question, we’re on the hunt for an odd number. And we’re given two clues about our number. We’re told that it’s greater than 93 and also less than 97. If we say this a different way, we need to find the odd number that is between 93 and 97. Now there are lots of numbers in between 93 and 97 but only one odd number. To find out what it is, we can use our knowledge of some of the patterns that we can see in even and odd numbers. How could we identify an even number if we saw one? We’d be able to tell just by looking at the final digit, because even numbers always end in zero, two, four, six, or eight.

So what does this tell us about odd numbers? Well, they always end in the digits in between. Odd numbers always end with the digits one, three, five, seven, or nine. So if we look at the two odd numbers that we’re given in our question, 93 ends in a three, 97 ends in a seven. That’s how we know they’re odd. You know, it might be helpful to label the digit three and the digit seven in our list over here because if we look at our odd digits in order, we can see a digit in between them. In between three and seven is five. And so the odd number in between 93 and 97 is 95.

If we know what the last digit in a number is, we can always tell if it’s even or odd. Even numbers always end in zero, two, four, six, or eight. And odd numbers always end in one, three, five, seven, or nine. And that’s how we know the odd number that is greater than 93 and less than 97 is 95.

What have we learned in this video? We’ve learned how to decide whether a number is odd or even by skip counting in twos.

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