Question Video: Comparing Two Groups of Pence and Identifying the Group That Has More Money Mathematics

Video Transcript

We have two groups of coins as shown in the picture, two-pence coins and 10-pence coins. Which group has more coins? Which group has more money?

We’re told that we have two groups of coins. Let’s spend a moment to look at them. The first group is labeled two-pence coins. Do you know why this is? Well, each of the coins in this group is the same, and they’re all worth two pence. Perhaps you remember that by the way that these coins look or by the way that it says at the top of each coin two pence. Now, our second group is a little bit shorter, isn’t it? There are less coins in this group, and this group is labeled 10-pence coins. Each of the coins in this group is worth 10 pence. And again, perhaps you knew this already. They’re silver colored, they’re circular, and if you look really closely, you’ll be able to make out the words 10 pence at the top of each coin.

So we’ve been given these two groups of coins to look at. Let’s take a look at the questions that we need to answer. But perhaps you notice when we very first read these questions, they do sound quite similar. Which group has more coins? Which group has more money? That’s the same thing, isn’t it? Let’s begin with the first question, which group has more coins? Now, when we ask this, what we’re talking about is how many bits of metal are there in this group. How many actual coins are there? We’re not worried about what each one is worth, what their value is. We’re just worried about how many there are. And as we’ve said already, the line of 10-pence coins looks a little bit shorter, doesn’t it, than the line of two-pence coins. Perhaps, we’d better count each group just to be safe.

In the group of two-pence coins, we can see one, two, three, four, five, six coins altogether. And in the group of 10-pence coins, there are one, two, three, four coins altogether. It’s just like we thought. The group that has more coins is the group of two-pence coins, isn’t it? In the second question, we’re asked which group has more money? You might think to yourself, well, we’ve just seen which group has more coins, and that’s the group of two-pence coins. So surely this group has more money. More coins means more money, doesn’t it? Well, it doesn’t because what this question is asking us is which group is worth the most, and this depends on what sort of coins we’re looking at. In the first group, all of the coins are worth two pence each, so we can skip count in twos to find the total, two, four, six, eight, 10, 12. The two-pence coins altogether are worth 12 pence.

Now, if we stop and think about this, we can probably answer the question now. We know that each of the coins in the second group are worth 10 pence, and we have four coins in the second group, four lots of 10 pence. All those two-pence coins in the first group only added up to 12 pence. Do you think the second group is going to add up to more than 12 pence? I think so, don’t you, especially as each coin is worth 10 pence already. But there’s only one way to find out, and that’s to skip count in 10s, 10, 20.

Well, we’re already more than 12, aren’t way? So we know that this group has more money. Let’s carry on counting from 20, 30, 40. Our 10-pence coins are worth 40 pence altogether. This question has taught us something interesting about coins. Just because we have more coins doesn’t always mean that we have more money. It depends on what our coins are worth. The group that had more coins in our question was the group of two-pence coins. But when we counted the value of each group, we found that the group that had more money was the group of 10-pence coins.