Lesson Video: Multiplying by 9 Mathematics • 3rd Grade

In this video, we will learn how to model multiplication by 9 and recite the times table of 9 up to 10 × 9.


Video Transcript

Multiplying by Nine

In this lesson, we’re going to learn how to model multiplication by nine. And we’re also going to practice reciting nine times tables facts.

This marks the spot where an amazing new skyscraper is going to be built. Each floor of the skyscraper is going to have nine windows. How many windows can you see at the moment? Well, construction hasn’t started yet. No floors have been built, and so there are no windows. We could write a multiplication fact to show this. Zero times nine equals zero. In fact, zero times anything equals zero. Right, let’s start work. See how many of these nine times tables facts you remember. One group of nine is, of course, nine. In fact, any number that we multiply by one stays the same. We could use doubling facts to help us with the next one. Two times nine equals 18.

You know, we need to remember that each of these facts is really two facts in one. For example, we may need a little bit of help with our nine times table and not know what three times nine is. But maybe we do know our three times table because three nines is exactly the same as nine threes. And nine times three is 27. Four times nine is 36. Five groups of nine is equal to 45. Let’s pause for a moment and think about what we’re doing here. Each time we’re finding the next number in the nine times table, we’re adding another nine.

Now we know that nine is one less than 10, and adding 10 on a number square like this is as simple as just going down to the next row. So adding nine is the same as going down a row and back one. This means that the numbers in the nine times table, what we call the multiples of nine, have a pattern to them. And just by adding 10 then taking away one, we can always find out the next multiple of nine. Let’s try this idea of adding 10 and taking away one to find the answer to six times nine.

We know that five times nine is 45, adding 10 would give us 55, and one less than this is 54. Six times nine is 54. Our skyscraper is really taking shape now. What other methods could we use to help us multiply by nine? Well, as we’ve seen already, nine is really close to 10. And we can remember 10 times tables facts really quickly. Seven times 10 is 70. So how could we use this to find seven times nine? Well, we can think of seven times 10 as being 10 lots of seven. And what we want to find is nine lots of seven. So we just need to take away seven from 70. Seven times nine is 63. And you know, we could use this method for any of our nine times tables facts.

Four times nine is the same as four times 10 take away four; six times nine is the same as six times 10 take away six. We’re building up quite a collection of methods here, aren’t we? It’s almost like we’ve been given a toolbox. If we don’t know a nine times tables fact, we could dip into our toolbox and use one of the methods we’ve talked about to help us. Now we’ve already talked about doubling when we multiplied nine by two. But we can also use doubling to find out other facts. At the moment, our skyscraper is eight floors high. And eight is double four. So if we know what four times nine is, we can double it to find out what, eight times nine is. Well, four times nine is 36. Double 30 is 60. Double six is 12. And if we add 60 and 12 together, we get 72. Eight times nine is 72.

Now what would you do if you couldn’t remember what nine times nine was worth? Well, in a way, it’s a good idea to think about the next floor up in our skyscraper, because if we know what 10 times nine is — and we do, it’s worth 90 — then nine times nine is just nine less than this. And 90 take away nine is 81. Let’s continue with these facts up to 12 times nine. 11 times nine is 99. And finally, 12 nines. Well, how are we going to work out this? We could partition the number 12 into 10 and two. And so we can think of 12 times nine as just being the sum of 10 times nine and two times nine. And 90 plus 18 equals 108. 12 nines are 108.

Now there’s a pattern with these multiples of nine. I wonder have you spotted it? Let’s skip count in nines from zero. And as we say each number, try to listen for the pattern. You should be able to hear it. Zero, nine, 18, 27, 36, 45, 54. I wonder can you hear that pattern? The ones digit of our numbers is decreasing by one each time. We start with zero, and then the ones go from nine to eight to seven to six to five to four and so on. And if we look at the tens digits, we can see that these are increasing by one each time. The first time we come across a 10 is in the number 18, and then we have two 10s in 27, three 10s in 36, four 10s in 45, and five 10s in 54.

And if we think about it for a moment, we know why the tens digits are going up and the ones digits are going down. As we’ve discussed already, every time we find another nine, it’s the same as adding 10, then subtracting one. Tens digit increases; ones digit decreases. Let’s try this skip counting method now to find some nine times tables facts.

This sequence chart will help us multiply by nine using skip counting by nines up to 10 times. Use skip counting to find nine times two, and then use skip counting to find nine times nine.

In this question, we’re given a picture of a sequence chart. If we look at it carefully, we can see it’s pretty much the same as 100 square. Each row contains 10 numbers, but instead of having 10 rows that go all the way up to 100, we have nine rows and we stop at 90. And the reason why we stop at 90 is that this sequence chart is to help us learn our nine times tables facts. The way it’s been labeled helps us skip count by nines up to 10 times. The number nine, of course, is one less than 10.

To count in tens using a chart like this, we would simply go down a row. Six becomes 16 and then 26. So if that’s how to skip count in tens using a sequence chart like this, to skip count in nines, we could move down a square and then back a square. It’s the same as adding 10, taking away one. And we can see all the multiples of nine have been labeled on this chart. They make quite a clear diagonal pattern, don’t they? In the first part of the question we’re told to use skip counting to find the answer to nine times two, or if we think of the numbers the other way around two times nine or two lots of nine. Let’s do this then.

Starting at nine, we say nine, 18. Nine times two is 18. Next, we need to use the same skip counting method. But this time, we need to count a lot further. We need to count up to nine lots of nine. So we’ll start at nine again and say nine, 18, 27, 36, 45, 54, 63, 72, 81. The whole sequence chart only shows up to 10 times nine, and we’ve said all the numbers apart from one. We’ve skip counted in nines nine times, and we’ve ended on the number 81. There are lots of patterns with a nine times table, and we can see some in this sequence chart. We followed the pattern to skip count by nines to find the answer to two multiplications. Nine times two equals 18, and nine times nine equals 81.

So far, we’ve learned about lots of strategies we can use to help us find out nine times tables facts. In our toolbox, we’ve got skip counting, using doubling to help, adding on, spotting patterns, using the much easier 10 times tables facts to help. We’re going to have a go at answering some questions now where we can use these tools. But don’t forget. The best strategy of all is simply just learning the facts. Hopefully, these questions are gonna help us remember them.

Fill in the blank: nine times three equals what.

Perhaps you know the answer to this times table and could say it straightaway. But what if you don’t? What strategy could we use to help us? The question nine times three is really asking us, what are nine lots of three or three lots of nine. Now, we may not know what nine threes are, but there is a calculation quite close to this that we probably do know. If we know what 10 times three is, we can use this to help us. 10 threes are 30. And so nine threes are just one lot of three less than this, in other words, 30 take away three. The answer is 27. We found the answer to nine times three by finding three less than 10 times three. Nine times three equals 27.

Notice how each row is nine more than the previous one. One times nine equals nine; two times nine equals 18; three times nine equals 27. Find the result of the following: Four times nine equals what. And then also find the result of the following: Five times nine equals what.

We know that learning times tables facts is all about thinking about groups of a certain number. And this question is all about nine times tables facts. We can see in the pictures that each cube is labeled with the number nine. We’re counting in nines. And the first thing that we’re told is that each row is worth nine more than the previous one. In other words, as we go through our nine times tables facts to find the next one, we just add another nine. So that’s why we have one times nine is nine, and then we’ve got a new orange cube to show that nine more’s been added. Nine add nine is 18. So that’s why we can say two times nine is 18. If we add another nine, we get 27. And that’s why we can say three times nine equals 27.

And next, we’re told to find the result of four times nine. Well, to find four lots of nine, we just need to add nine onto three lots of nine. So what’s nine more than 27? Well, we know if we had to add 10, it would be 37. And nine is one less than this. Four times nine is 36.

And in the final part of the question, we just need to do the same again because we need to find five times nine. We know what four nines are, so we just need to add one more nine. Now we know 36 add 10 would be 46. But again, nine is one less than ten, so instead of 46, the answer is 45. If we know a nine times tables fact, we can find the next fact by adding nine. And that’s how we found out that four times nine is 36 and five nines are 45.

We know that two times nine equals 18. Use this to find four times nine.

This question then is asking us to find the answer to four times nine, and we’re told how to do it. We need to use the fact two times nine equals 18 to help. Now, how can we use this first fact to help? What’s the link between two times nine and four times nine? Perhaps you’ll be able to spot the link if we model some arrays. Here’s the fact we know already, and here’s the fact we need to find. It’s double the size, isn’t it? Four is double two. So if we know what two times nine is, and we do, we can just double it to find the answer to four times nine.

So what is 18 doubled? Eight doubled is 16, and 10 doubled is 20. And if we put these two parts together, we get the total 36. We’ve used doubling to help us with our times tables facts. If we know what two times nine is, then we can double it to find four times nine. And that’s how we know four times nine is double 18. The answer is 36.

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

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