Question Video: Deciding If a Number Is Odd or Even by Counting in Twos Mathematics

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?

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Video Transcript

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.

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