Lesson Video: Multiplying by 2 Mathematics • 3rd Grade

Video Transcript

Multiplying by Two

In this video, we’re going to learn how to model multiplication by two and also how to recite the two times table.

Ethel here is about to start watering her plants. Can you see how she’s planted them in groups of two or pairs? This is useful because this video is all about groups of two. Let’s turn the hose on. The water is only going as far as one pair of flowers to begin with. And one group of two is worth two. Let’s turn the hose up a little more. Now, she’s watering another group of two. This is the same as four flowers. Each time Ethel turns up the water, she waters another two flowers.

Three lots of two is the same as six flowers. Four twos are the same as eight flowers. And five lots of two equals 10 flowers. Did you notice anything about the numbers that we said? They’re numbers in the two times table. We’re counting in twos. And this means that every number we say is even, two, four, six, eight, 10. Do you remember all of the two times table facts?

Let’s practice them. Why don’t you try to be quick and say each fact before the answer appears on the screen. One times two equals two. Two times two equals four. Three times two is six. Four twos are worth eight. Five times two equals 10. Now, before we continue, let’s stop for a moment. Let’s imagine we’ve been asked to find six times two. Don’t quite remember what it is. We don’t want to start all the way back at one times two and count up to six times two.

Now, one fact we do know is the one that comes just before it, five times two equals 10. How can knowing five times two help us to work out six times two? Well, if we know that five lots of two are worth 10, then all we have to do is add two more to find six lots of two. 10 plus another two equals 12. We didn’t need to start all the way back at one times two to find the answer. Instead, we used a fact we knew already and we counted on from there.

Your brain is like a tool kit. It’s full of different tools that we can use to solve different problems. And what we’ve just done is used one of the many tools that we can use to multiply by two. Let’s try some of the others.

Let’s imagine that we’ve been asked to find the answer to seven times two this time and we don’t know what that is. But one thing we do remember is that seven lots of two is exactly the same as two lots of seven. This means we can use a doubles fact to help us. Multiplying by two is the same as doubling. Seven add another seven equals 14. To find seven times two, we could just double seven. Seven times two equals 14. So, there’s another tool we can use to help us.

Eight times two equals... What other tools could we use? What about skip counting? We could skip count in twos eight times, two, four, six, eight, 10, 12, 14, 16. Eight times two equals 16.

Nine times two equals 18. Let’s imagine we don’t know the answer to 10 times two. We’ll try one last tool to help us. Although we’re not quite sure what 10 times two is, we do remember that fact from earlier on, five times two equals 10. Is there a way we could use this to help? So, we know what five times two is, and we want to find out what 10 times two is.

Do you notice something about the numbers five and 10? If we double five, we get 10. And in the same way, if we double our answer to five times two, we should get the answer for 10 times two. As we’ve said already, five times two is 10. And if we double this answer, we’ll get 20. It worked! We took the answer to five times two and doubled it to help us find 10 times two.

And you know this works with other pairs of times tables too. Three doubled is six, so if we take the answer to three times two and we double it, this will give us the answer to six times two. Or if we double the answer to four times two, we can use it to help find the answer to eight times two. What a lot of doubling facts we got flying around in this video!

Although we’ve learned lots of tools here to help us, probably the best thing we could ever do to help us with our two times table, or any times table, is just to learn the facts. And the two times table is perhaps one of the easiest times tables to remember because these numbers are all even.

Let’s practice our two times table facts one more time. And just to really test you, we’re going to start rubbing them out from one end as we start saying them at the other. Let’s see if you can remember them if they’re not on the screen anymore. Ready? One times two equals two. Two times two equals four. Three times two equals six. Four times two equals eight. Five times two equals 10. Six times two equals 12. Seven times two equals 14. Eight times two equals 16. Nine times two equals 18. And 10 times two equals 20.

How did you get on? Hopefully you remembered the ones that were missing. Let’s answer some questions now where we have to put into practice all the tools that we’ve learned about to help us multiply by two.

Try the following method to calculate multiplications by two. Two times four equals four plus four, which equals eight. Complete the following: Two times five equals five plus five, which equals what. And then, use the same method to complete the following: Two times six equals what.

In this question, we’re shown several calculations to do with multiplying by two. But we can’t just find the answer however we like. We’re shown a method or a way of doing things. And once we’ve understood it, we need to try it for ourselves to help us find the answers. To begin with then, we’re shown an example. And this example is all about finding out two times four.

What does this mean? Well, one way we can think of this is as two groups of four. Here’s one group of four. Now, we have two groups of four. We could write this as the addition four plus four. We could even say double four. And we know that four plus four, or double four, is equal to eight. So, we’ve used this doubling fact to help us find that two times four equals eight.

Now that we understand this doubling method, we can use it again to help us fill in the blanks in these other calculations. Two times five is the same as two groups of five or five plus another five. And we know that five plus five, or double five, equals 10. That’s how we know two times five equals 10.

Finally, we need to find the answer to two times six. Two times six is the same as two groups of six or six plus six. And we know that six plus six, or six doubled, equals 12. So, two times six equals 12.

In this question, we recognized that multiplying numbers by two is the same as doubling them. And so, we’ve used addition facts to help us solve multiplication facts. Two times five is the same as five plus five, which equals 10. Two times six is the same as six plus six, which equals 12. Our two missing numbers are 10 and 12.

Fill in the blank: Two times three equals what.

In this question, we’re given a multiplication fact to complete. Now, when you see this fact, what do you think? Perhaps you think of the number two repeated three times. Or perhaps you think of it as two lots of three. Maybe you know this fact already, but what could we do if we don’t? We could skip count along the number line to help us.

Now, we did say that one way we could think about this multiplication is as two repeated three times or three lots of two. So, let’s try this method. We’ll start at zero, and we’ll skip count in twos three times. Zero, two, four, six. Skip counting twos three times, we reach the number six. And just to show that we found the correct answer, let’s try the other method. Let’s skip count two lots of three, zero, three, six. Whether we think of this calculation as three lots of two or two lots of three, we’ll still get the same answer. Two times three equals six.

In multiplying by two, each row is two more than the previous one. One times two equals two. Two times two equals four. Three times two equals six. Complete the following: Four times two equals what. And then, complete the following: Five times two equals what.

In maths, there are often patterns everywhere we look. And in questions like this, we can use the patterns that we find that help us find the answers. Perhaps one of the best sentences we could ever say in maths is “I don’t know the answer, but I do know this fact, and I’m going to use it to help.” And in a way, this is what this question is all about, using facts that we already know to help us find facts that we don’t.

Our first sentence tells us about a pattern. In multiplying by two, each row is two more than the previous one. In the model, we can see some rows of cubes. And each cube has a value of two. We can see the number two written on them. The first row shows one lot of two. And of course, we know one times two equals two. But then, look what happens in our second row. We’ve taken the answer from before, and we’ve added one more lot of two, the yellow cube on the end. We now have two lots of two. And two times two equals four.

The pattern continues with our third row. This is made up of the answer from before and then two more. We know from the last fact that two times two equals four. So, if we find two more than this, we get the answer six. And that’s how we know three times two equals six. Now, we’ve got some times tables facts to complete. Perhaps you know the answers already. But in case you don’t, let’s continue using this method.

We’ll use facts that we already know, and we’ll build on them. So, the first fact we need to find is four times two. And if we look at our row of cubes, we can see that there are three red cubes. We know where these are from, don’t we? These are the three cubes that made up the answer to the last fact. And just like all our other facts, we’ve got a new cube on the end. These are the two more that we need to add.

We know from our last fact that three times two is six. So, to find four times two, we simply need to add another two. We need to find two more than six. And six plus another two is eight, so four times two must equal eight.

In the last part of the question, we need to find five times two. So, we can do the same thing again. Take the answer from the last question, which is eight, and then add another two. Eight add two equals 10. And so, we know five times two equals 10. Even though we may not have known all the multiplication facts in this question, we took the facts we did know and we used them to help. If we know what three times two is, we simply add two to find four times two. And if we know what four times two is, we do the same again to find five times two. Four times two equals eight. And five times two is 10. Our two missing numbers are eight and 10.

What are the two missing numbers in this table?

Can you see where the two missing numbers belong? They’re both in the bottom row, here and here. Now, for us to understand what these two missing numbers might be, we need to understand how this table works. Can you see a clue that might help us? This table is all about multiplying by two. We take a number from the top row, multiply it by two, and then that gives us the number in the bottom row. It’s a little bit like the idea of a multiplying machine, where a number goes in, it gets multiplied by two, and then a different number comes out. This is exactly what’s happening in our table.

Number one on the top row gives us number two on the bottom row. One times two equals two. And number two on the top row gives us four on the bottom row because two times two equals four. So, we can see then that our two missing numbers are going to be what we get when we multiply three by two and what happens when we multiply six by two.

Now, we could think about each of these facts completely separately. We could think about three times two and then six times two. But these two facts are linked. Can you see what the link is between three and six? We know that if we double three, we’d get six. So, do you think if we double the answer to three times two, we might find the answer to six times two? Let’s see whether multiplications work like this.

Three times two is worth two, four, six. So, we know that our first missing number is six. Can you predict what our second missing number’s going to be? We can take the answer for three times two and then double it. And six doubled is 12. Let’s count in twos and see whether the number 12 fits in the pattern. Two, four, six, eight, 10, 12. It worked!

We multiplied three by two to find our first missing number. And we knew that we could double the answer to three times two to find the answer to six times two. This gave us our second missing number. Three times two is six. And six times two is 12. Our two missing numbers are six and 12.

So, what’ve we learned in this video? We’ve learned how to model multiplication by two and practice reciting two times tables facts.