Lesson Video: Multiplying by 6 Mathematics • Third Year of Primary School

Video Transcript

Multiplying by Six

In this video, we’re going to learn how to model multiplying by six. And we’re also going to recite six times table facts.

Now, I wonder, “Have you ever played a board game like this?” One where there’s a board a little bit like a number track with numbers along it, you have a counter that you need to move along the track, and then a dice that you roll to show how many spaces you need to move. If we roll our dice once, what’s the furthest number we’re going to get to? Well, if this is the sort of dice that we would normally use in games like this, then it’s got six faces, and the highest number on the dice is six. So, if we pick up the dice and then roll it once, the largest number we could roll is a six and one lot of six is six. We could write this number fact as one times six or one multiplied by six equals six.

But what if we didn’t have one dice to start with? What if we had two? And let’s imagine, we still have this incredible skill of rolling the most possible. The most we could roll this time is two lots of six. So, we need to move on our counter another one, two, three, four, five, six. Two lots of six takes us to 12. And so, we can say two times six equals 12. But you know, if we carried on increasing the number of dice, instead of counting on six every time, just like we’ve done, perhaps it might make sense to skip count in sixes and start to remember some of these six times tables facts.

Three times six equals six, 12, 18. Four lots of six are six, 12, 18, 24. Four times six equals 24. And you know the more that we repeat these multiplication facts, the more they sink in. Six, 12, 18, 24, 30. This is taking us to the end of our board now. Five multiplied by six equals 30. By the way, did you notice anything interesting about all the squares that we landed on? They’ve all been orange, haven’t they? And on this particular board, the orange squares are the even numbers. This shows us that all the multiples of six that we’re gonna be thinking about in this video are going to be even numbers.

So far, we’ve practiced up to five times six. But let’s carry on going. How many facts do you know? See if you can say each number before it appears on the screen. One times six equals six. Two times six equals 12. Three times six is 18. Four lots of six equals 24. Five times six equals 30. Six times six equals 36. Seven sixes are 42. So far, we’ve just been reciting these facts. But what if we don’t know what the next fact is? Are there any strategies that we could use to help us find eight sixes?

Well, what if we know the fact that comes before the one we want to find out? As we’ve said already, seven times six is 42. And so, if we want to find eight sixes, we just need to add another six. And 42 plus six equals 48. We’ve counted on from a fact we already knew to help us find a fact that we didn’t know. So, eight times six is 48.

But what about nine sixes? Another method we could use is doubling. Now, we know that half of six is three. Let’s imagine that we don’t know what nine times six is, but we do know our three times table and we know what nine times three is. Hopefully, you can see from the picture if we double nine lots of three, we get the same as nine lots of six. Now, we might already know nine times three is 27. And so, we could double this multiplication fact to help us find nine lots of six.

We know that double 20 is 40, and double seven is 14. So, double 27 is the same as 40 plus 14 is 54. Nine times six is 54. And we found out this fact by using a fact we already knew and then doubling it. In fact, we can do this with all of the six times table. If we know our three times table, we could double up our fact to make a six times table fact.

Let’s move on to 10 times six. Something else we could do if we’re ever stuck with a multiplication fact is to use what we know about multiplication to help us. Now, we know that 10 lots of six are the same as six lots of 10. You can do that with multiplication. You could switch the numbers around. If we think of our array as showing 10 columns of six or 10 lots of six and then just turn it slightly, can you see what we’ve got now? There are six columns of 10 or six lots of 10. And if we know our 10 times table and know that six lots of 10 equals 60, we also know that 10 times six equals 62. They’re just two ways of saying the same fact.

Now, often, we might stop at 10 times the number. But should we carry on? Let’s think of two more facts. Let’s go up to 12. If 10 lots of six are 60, 11 sixes are 66 and 12 sixes must be 72. So, all the pink numbers here are multiples of six; they’re the numbers in the six times table. Six, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72. And not only are these all even numbers, there’s a pattern to them, too. If we just take a moment to look at the ones digits in the six times table. The numbers end in six, two, eight, four, zero. And then the pattern seems to repeat itself. Six, two, eight, four, zero and then again, six, two, and so on. It’s an interesting pattern, and it can help us predict what the next multiple of six is going to be.

For example, if we know that 12 sixes are 72, we could use this idea of six, two, eight, four, zero to predict that 13 sixes are going to end in an eight. Now, we’ve gone through one or two methods that we could use to help us here. But the best way to remember our six times tables is just to learn a fact.

So, let’s go through the multiples one more time. And what we’ll do to make it a little bit more tricky, we’re going to rub some of them out. Now as we get to the facts that aren’t on the screen, we need to say them out loud and we’ll see if you’re right at the end. One time six is six, two times six is 12, three times six is 18, four times six is, five times six is 30, six times six is, seven times six is, eight times six is 48, nine times six is, 10 times six is, 11 times six is 66, and 12 times six is 72.

Did you get all the missing numbers? Four sixes are 24, six sixes are 36, seven sixes are 42, nine sixes are 54, and 10 sixes are 60. Well done! And as we’ve said already, the best thing we could ever do to learn our six times table is simply to practice it again and again. So, let’s do that. We’re gonna try answering some questions where we have to recall these six times tables facts.

We can skip count by sixes on a number chart to help us multiply by six. Use skip counting to find six multiplied by two. And then use skip counting to find six multiplied by 10.

The first part of this question tells us that we’re going to be multiplying by six. And to help us do this, we’re told that we can skip count by sixes on a number chart. Now, we could skip count by sixes on a number track or a number line, or maybe even just by thinking of the numbers in our heads. But when we use a number chart like this, we can not only seal the numbers that we’re skipping, but also we can spot patterns. If we look at this number chart, we can see that all of the multiples of six have been written in blue.

Let’s practice skip counting in sixes to begin with. Six, 12, 18, 24, 30, 36, 42, 48, 54, 60. And each of these numbers is found by adding six to the last number. But instead of saying every single number in the grid, we’ve skip counted by sixes. Now that we’ve circled these multiples of six, can you see what we meant by a pattern? We can see them in diagonal lines across the grid, can’t we? We can see that they’re all even numbers, too.

Now, the first thing we’re asked to do is to use skip counting to find the answer to six multiplied by two. Then, you might look at this multiplication and say, “Well, this is talking about a number of twos, six lot of twos, not a number of sixes.” But one thing we know about multiplications is that we can switch the numbers in a multiplication and it’ll still give the same answer.

So, we could think of this as six times two or two lots of six. We could think of six times two as meaning six repeated twice. So, let’s count in sixes twice to find the answer. Six, 12. We skip counted by sixes twice to find the answer. Two lots of six are 12.

Next, we’re asked to use skip counting to find six multiplied by 10. And again, we can think of this as 10 times six or skip counting by sixes 10 times. Well, we know how far we get when we skip count by sixes twice, so let’s carry on counting from there. 12 and then 18, 24, 30. That’s five sixes. Let’s carry on skip counting another five sixes. 36, 42, 48, 54, 60. This time, we’ve skip counted by sixes 10 times. And the last number we said was 60.

So, we use this number chart to help us skip count by sixes and find the answer to these six times tables facts. Six times two equals 12 and six times 10 equals 60.

What is six times nine?

Now, this is a very straightforward question, isn’t it? Perhaps you know the answer already. Perhaps you can recall the number fact and say six times nine is this. But if we were to make a video like this, it would be very interesting to watch. let’s try going through and answer for those of you who perhaps don’t know this fact off by heart.

If we don’t know what six times nine is, what do we know that could help us? Well, the first thing that we can say is that six times nine is exactly the same as nine times six. This is something you can do with multiplication facts. You can switch the numbers around and it still makes the same product. So, we can see that this question is asking us to find nine lots of six. Now, maybe you don’t know nine lots of six. But there is a nearby fact that you probably do know, a fact that’s easy to remember when we’re learning our times tables. And that’s 10 times six.

Now, we can use this to help. Because if we know what 10 times six is and here are 10 columns of six counters as an example, then to find nine times six, we just need to lose one of our columns. In other words, we need to subtract six. Now, 10 times tables facts are quite easy to remember. 10 times six equals 60. And so, if we take away one lot of six from 60, this is going to take us back to 54, isn’t it? And so, we can say that nine lots of six are 54. Or if we switched the numbers around, six times nine equals 54.

Now, perhaps you knew this fact already, but this is just one method you could have used if you didn’t. We’ve used a known multiplication fact to find an unknown fact. We knew 10 times six. So, we subtracted six to find nine times six. And nine times six or six times nine equals 54.

Notice how each row is six more than the previous one. One times six equals six. Two times six equals 12. Three times six equals 18. Find the result of the following: four times six equals what. And then also find the result of the following: five times six equals what.

Did you notice in this question we’ve got some six times table facts to find out? We need to find the answer to four times six and also five times six. But you know, in the first sentence, we’re given a clue that can help us. It’s pointed out to us that each row is six more than the previous one. And can you see what the rows are that this is talking about? It’s these rows of cubes. And if we look at each cube, we can see it has the number six on it. We could think of it as a dice that shows the number six.

So, what does it mean that each row is six more than the previous one? Well, our first row of cubes just shows one cube with a six on it. But our second row shows the one from before and then a new cube. In other words, it shows six more. And the next row shows the two from before. But again, one new cube, so six more. And knowing that each multiple of six in the six times table is worth six more than the last one can help us. One time six is six, and six more than six is 12. So, we know two times six is 12. Six more than 12 is 18. So, we know three times six is 18.

And now, we need to find four times six. And If we look at our cubes, we could take our three cubes that we already know from the last fact and then add one more cube. Or, in other words, take three sixes, which are worth 18, and then add one more six. And we know that 18 plus six equals 24. That’s how we know four times six is 24.

Finally then, we need to find out what five sixes are. As we’ve just said, the four sixes from our last fact are worth 24. And if we find six more than 24, we get the answer 30. So, five times six must be worth 30.

We got each answer by finding six more than the last one. Four times six is 24 and five times six is 30.

Find the missing numbers. Two times three equals what. Two times six equals what. Three times three equals what. Three times six equals what.

Did you notice anything about the multiplication facts we need to find out here? Each time we’ve got a number multiplied by three and then the same number multiplied by double three or six. How can we use a three times table fact to help us with a six times table fact? Well, as well as making us feel hungry, this array of donuts that we can see in the picture can help us.

Two times three can be shown by this group of donuts here, can’t it? Two threes are six. But if we double this amount, in other words, we include this group of donuts here, we now have a six times table fact, two rows of six. Now, we know that double six is 12. So, if two times three is six, two times six must be 12. And we can use the same idea for the next two facts. We know that three times three is nine. And if we double this, we find the answer to three times six. And double nine is 18.

We’ve used doubling to help us find six times table facts here. Two times three is six. So, two times six equals 12. Three times three is nine. So, three times six is 18.

What have we learned in this video? We’ve learned how to model multiplication by six and recite the six times table.