Lesson video

Hi there.

How are you today? I hope you're having a really good day.

My name is Ms. Coe, and I'm really excited to be working with you on this unit, looking at the relationship between the 3 and 9 times table.

Now, you may already have done some work around the 3 and the 9 times table, and hopefully you're able to start recalling some of those facts from those tables.

In this unit, we're going to be looking really carefully and thinking about how those two times tables, the 3s and the 9s, are connected.

By the end of this lesson, you will be able to say that you can explain the relationship between multiples of 3 and multiples of 9.

In this lesson today, we have one key word.

I'm going to say it, and I'd like you to say it back to me.

Are you ready? My turn.

Multiple.

Your turn.

Great job.

Let's think about what that word means.

A multiple is the result of multiplying a number by another whole number.

This lesson today focuses on explaining the relationship between multiples of 3 and multiples of 9.

Now, you might not be familiar with the term multiple, but we're really focusing on our 3 times table and our 9 times table, and I hope you've got a few facts of those in your head at the moment.

Our lesson today has two cycles.

In the first cycle, we're going to identify multiples of 3 and 9.

And then in the second cycle, we're gonna really focus on the relationship between those multiples.

If you're ready to get going, let's get started with our first cycle.

In this lesson today, you're going to meet Andeep and Izzy, and they are going to be helping us with our learning, and asking us some questions along the way.

So let's start here.

Let's count in multiples of 3 from zero.

Remember, multiples of 3 is like skip counting in 3.

So before we start counting with Andeep and Izzy, let's just check we know what we mean.

If we start at zero, the next multiple of 3 will be 3 more than zero.

So have a think.

That's it.

1, 2, 3.

So our first multiple that we're going to say is 3.

Then, the next one will be 3 more than that.

So have a think.

That's right.

4, 5, 6.

So let's see if we can count with Andeep and Izzy.

Are you ready? Let's go.

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36.

Let's stop there.

Remember, the multiples of 3 keep going, so we could keep going in steps of 3, but let's stop there for now.

Now, let's count up in multiples of 9 from zero.

So if multiples of 3 was counting up in steps of 3, what do you think multiples of 9 will be? That's right.

We're going to count up in steps of 9.

So our first step will be zero, and then the next step will be 9.

Let's see if we can count with Andeep and Izzy.

Let's count together.

Are you ready? Let's go.

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108.

Again, let's stop there.

We could keep going, but let's stop there for now.

Well done if you managed to keep up with all that counting.

So this time, Andeep and Izzy are looking at the 3 times table on a number line.

Andeep is asking us to count in 3s with them.

Let's do that together.

Are you ready? 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36.

Great job.

Well done.

Now, Izzy's saying something interesting.

She says although we've counted in multiples of 3 and we've used our 3 times table, she thinks she can see some multiples of 9 on that list too.

What do you think? Can you spot any of those numbers that we said when we counted in multiples of 9? Time to check your understanding.

Which multiples of 9 can you see on the number line? What do you notice about them? Pause the video here.

Take a moment to have a think.

Welcome back.

What did you notice? "Well, let's try counting in 9s," says Andeep.

That's a really great suggestion.

We're going to count in 9s from zero and see which of these numbers we can select.

Are you ready? 0, 9, 18, 27, 36.

Our number line ends at 36.

Now, remember we could keep counting in multiples of 9, but these are the multiples of 9 that we can see on the number line.

0, 9, 18, 27, and 36.

Well done if you circled all of those.

Did you notice anything about them? Well, the multiples of 9 are also the multiples of 3.

So we had multiples of 3 on this number line, but we've circled multiples of 9.

So we can see that those multiples of 9 are also multiples of 3.

Well done if you spotted that.

You might have also spotted that there are two multiples of 3 between the multiples of 9.

Let's take a look at what Andeep meant.

If we take 18 and 27, we've circled them, we know that they are multiples of 9 'cause we say them when we skip count in 9s.

Between those two, we have 21 and 24.

21 and 24 are multiples of 3.

They are not multiples of 9, and there are two of them in between the multiples of 9.

And if you look, you can see the same is true for any of the two multiples of 9 on this number line.

Well done if you spotted that as well.

Andeep and Izzy both count from 0 in ones.

Andeep is going to clap on the multiples of 3, and Izzy is going to clap on multiples of 9.

They use this table to record which multiples they clap together at the same time.

So let's count together and see what happens.

0.

Well, both Andeep and Izzy say zero.

Remember, Andeep is identifying multiples of 3, and Izzy is identifying multiples of 9.

Let's carry on counting in ones.

1, 2, 3.

Andeep would clap for 3.

4, 5, 6.

He would clap for 6.

7, 8, 9.

9 is the first multiple of 9, and both Andeep and Izzy clap.

Let's carry on.

10, 11, 12.

Another clap from Andeep.

13, 14, 15.

Andeep claps again.

16, 17, 18.

Notice how both of them have clapped for 18.

19, 20.

Take a look at that completed table.

What do you notice? Let's take a closer look at the numbers where both Izzy and Andeep clapped together.

You can see them because they have two ticks rather than one tick.

So in our table, we can see that they both clapped for 9 and 18.

What do you notice about those numbers? Well, that's right, Izzy.

All the numbers she clapped were the numbers that Andeep clapped as well.

That's because multiples of 9 are multiples of 3 as well.

Time for another check of your understanding.

If Izzy and Andeep carry on clapping up to 36, which numbers will they both clap together? So we can see so far that they've both clapped on 0, 9, and 18.

Can you work out which numbers they will both clap together, and explain why? Pause the video here and have a think.

Welcome back.

Let's check together by counting on from 21.

You ready? 21 is a multiple of 3, so Andeep would clap.

22, 23, 24.

Andeep would clap again.

25, 26, 27.

Both Andeep and Izzy would clap.

28, 29, 30.

Andeep would clap again.

31, 32, 33, 34, 35, 36.

So 27 and 36 are the numbers where both Andeep and Izzy would clap.

Why is that? Well, that's because all multiples of 9 are multiples of 3.

I wonder if you can say that sentence with me.

Are you ready? All multiples of 9 are multiples of 3.

Great job.

Time for your first practise task.

I would like you to play a game called Oak Tree with the 3 and 9 times table.

You're going to take it in turns to count on in ones from the number one.

If your number is a multiple of 3, instead of saying the number, you're going to say oak.

If the number is a multiple of 9, instead of saying the number, you're going to say tree.

Andeep and Izzy are going to show you how to play.

So Andeep starts counting by saying the number one, and then it's Izzy's turn, so the next number after 1 is 2.

Now, it's Andeep's turn.

The next number is 3.

But as he's correctly identified, 3 is a multiple of 3.

So instead of saying 3, he would say oak.

So so far, our counting has gone 1, 2, oak.

Izzy says the next number, which is 4.

Andeep would say 5.

I wonder if you can predict what Izzy's going to say.

That's right.

She's going to say oak instead of 6 because 6 is a multiple of 3.

Andeep would say 7.

Izzy would say 8.

And ah, for number 9, well, 9 is a multiple of 3 and 9, so instead of saying 9, Andeep would say oak tree, and they would carry on in counting.

So that's the game you're going to play with a partner.

For question two, this is a Venn diagram.

I would like you to sort the numbers correctly.

So you have a list of numbers there, and you have two circles, multiples of 3 and multiples of 9.

And where the circles overlap in the middle, that's where you put numbers that are both multiples of 3 and multiples of 9.

Any numbers that are not multiples of 3 or 9 should go outside of the hoops or circles.

What do you notice when you've completed this? Good luck with those two tasks.

Pause the video here, and come back when you're ready for some feedback.

Welcome back.

How did you get on with those two tasks? I hope you really enjoyed playing Oak Tree with a partner.

Did you notice that for every multiple of 3, you said oak, just like Andeep has done here instead of saying the number 3? Hopefully, you continue taking it in turns, saying oak for every multiple of 3.

But what did you notice for every multiple of 9? Hopefully, you realised that every time you said a multiple of 9, so 9, 18, and so on, you had to say oak tree, both of those words together.

There was no point where you just said tree, and that's because all multiples of 9 are also multiples of 3.

For question two, this is how your Venn diagram should have looked.

Let's take a closer look at some of those numbers.

The number 8 goes outside the hoops.

8 is not a multiple of 3, nor is it a multiple of 9.

If we count up in 3s, 3, 6, 9, we didn't say 8.

8 is not a multiple, so it goes outside.

Numbers like 30 are multiples of 3.

If we skip count in 3s, we say 30.

If we skip count in 9s, we do not say 30.

So numbers like 30 are just a multiple of 3.

Now, I think I've spotted something interesting about this Venn diagram.

Did you spot it? That's right.

All of the numbers in the middle, such as the number 36, are multiples of 3 and 9, so they go in the middle of the Venn diagram, where the two hoops overlap.

But did you notice that there were no numbers in that right-hand side where it says just multiples of 9, and that's because all multiples of 9 are also multiples of 3.

Well done if you identified that, and well done if you organised the numbers correctly.

Let's move on to the second cycle of our learning, where we're focusing on the relationship between multiples of 3 and multiples of 9.

Take a close look at my collection of strawberries.

How many groups of 3 are there? Hmm, I wonder.

Well, I can see 3 groups of 3.

If I look at the rows in my array going horizontally, I can see that there is 1, 2, 3 rows.

There are 3 groups of 3 strawberries.

How many groups of 9 can you see? Hmm.

Well, I can see one group of 9.

If I count the strawberries, 1, 2, 3, 4, 5, 6, 7, 8, 9, there is one group of 9 in this array.

So I can see both 3 groups of 3 and 1 group of 9.

And we can say that when there are 3 groups of 3, there is one group of 9.

So it's possible for this array to show both 3 groups of 3 and one group of 9.

We can also write that as a multiplication equation.

3 groups of 3 can be written as 3 multiplied by 3, or 3 times 3, and 1 group of 9 can be written as 1 multiplied by 9 or 1 times 9, and we can use the equal sign to show that they are equivalent or equal.

We can say that 3 times 3 is equal to 1 times 9 because 3 groups of 3 are the same as 1 group of 9.

Let's take another look at a different problem.

How many groups of 3 are there? Well, here we know that we have 3 groups of 3.

So so far, we have 3 groups of 3.

How many groups of 9 are there? That's right.

There is 1 group of 9.

Remember, if there are 3 groups of 3, then there is also 1 group of 9.

We can show that as a bar model, and we can show that they are equal.

So in my bar model, I have 3 equal groups of 3, and I can see that it is the same as, it is equal to 1 group of 9.

And remember, we can write this as an equation.

3 times 3 is equal to 1 times 9.

How many groups of 3 are there this time? How many strawberries can you see? Well, we have 3 groups of 3 there, and another 3 groups of 3.

How many groups of 3 do we have altogether? That's right.

There are 6 groups of 3 here.

How many groups of 9 are there? We have 1 group of 9 and another group of 9.

So altogether, that is 2 groups of 9.

I wonder what relationship you can say, or you can start to see in this.

We can draw another bar model and connect it to the first bar model.

So now, we have 6 groups of 3, and we can see that that is equal to how many groups of 9? That's right, there are 2 bars with a value of 9, so that is 2 groups of 9, and we can write another equation.

6 groups of 3 is equal to 2 groups of 9.

So we can say that 6 times 3 is equal to 2 times 9.

How many groups of 3 are there this time? Hopefully, you can start to see a pattern here.

Let's check.

We had 3 groups of 3, another 3 groups of 3, and another 3 groups of 3.

That is 9 groups of 3 altogether.

So we had 3 groups of 3, then we had 6 groups of 3, and now we have 9 groups of 3.

I can see a pattern there.

Can you? How many groups of 9 are there? We have 1 group of 9, another group of 9, and another group of 9, so that is 3 groups of 9.

So first, we had 1 group of 9, then we had 2 groups, now we've got 3 groups.

There is definitely a pattern here.

Can you predict what the bar model will look like now? That's right.

We can add another 3 groups of 3 and another 1 group of 9.

So if we look at our bar model now, we can see that there are 9 groups of 3, and that is equal in length to the 3 groups of 9.

So we can say that 9 groups of 3 is equal to 3 groups of 9, and we can write that as 9 times 3 is equal to 3 times 9.

Now, I am sure you can see the pattern now.

How many groups of 3 are there this time? We've got 3 groups of 3, another 3 group of 3, another 3 groups of 3, and another 3 groups of 3.

How many groups of 3 is that altogether? That's right.

There are 12 groups of 3.

Now, I bet you can predict how many groups of 9 there are.

Let's check.

1 group of 9, another group of 9, another group of 9, and another group of 9.

That means there are 4 groups of 9 altogether.

And as always, we can show that in our bar model by adding another 3 groups of 3 and adding 1 more group of 9.

So we can say that 12 groups of 3 are equal to 4 groups of 9, and we can write that as an equation.

12 times 3 is equal to 4 times 9.

What do you notice here? What relationship can you see with the multiples of 3 and 9? So first, we said that 3 groups of 3 strawberries is the same as 1 group of 9 strawberries, and we can also now say that 12 groups of 3 strawberries is the same as 4 groups of 9 strawberries.

And remember, we can show that as an equation.

12 multiplied by 3 is equal to 4 multiplied by 9.

Time to check your understanding.

Take a really good look at the groups of strawberries and fill in the blanks.

So we have mm groups of 3 strawberries is the same as mm groups of 9 strawberries, and then you have the equation there.

Something multiplied by 3 is equal to something multiplied by 9.

Pause the video here and take a moment to have a think.

Welcome back.

How did you get on? Well, I can see 1, 2, 3, 4, 5 groups of 9.

Each of those groups has 3 groups of 3 strawberries.

So I could skip count in 3s.

3, 6, 9, 12, 15.

So I can say 15 groups of 3 strawberries is the same as 5 groups of 9 strawberries.

Hopefully, you spotted that.

How did you get on with filling in the equation? That's right, we can say that 15 multiplied by 3 is the same as, is equal to 5 multiplied by 9.

Well done if you got that.

This table here is another way to look at the 3 and 9 times table.

So in the first column, you can see that we have written the facts of the 3 times table.

3 multiplied by 0 is equal to 0, 3 multiplied by 1 is equal to 3, and so on.

And in the second column, we have the 9 times table.

9 multiplied by 0 is 0, 9 multiplied by 1 is equal to 9, and so on.

What do you notice about that table? Take a good look.

Can you see any patterns? Hmm, I wonder.

Well, you may have noticed that some of the numbers appear in both columns.

9, 18, 27, and 36 are the first multiples of 9 after 0, and they appear in the column for the 3 times table as well, and that's because multiples of 9 are also multiples of 3.

But you may have also noticed that not every multiple of 3 is a multiple of 9.

If we look at some of the products or the answers to our times tables in the first column, like 3, 6, 12 or 15, we don't see those appearing in the 9 times table column, and that's because while all multiples of 9 are also multiples of 3, not all multiples of 3 are multiples of 9.

And we can also say that every third multiple of 3 is a multiple of 9.

Do you remember that we looked at that on a number line, and we noticed that there is a gap of two multiples of 3 between each multiple of 9.

We can see the same here in the column for the 3 times table.

Every third one is a multiple of 9.

Well done if you spotted that.

And Izzy is reminding us that when there are 3 groups of 3, there is one group of 9, which explains why all multiples of 9 are also multiples of 3.

Time for your second practise task.

For question one, I'd like you to fill in the gaps using the images to help you.

Let's take a closer look at the first image.

We have two groups there, and I can see that each group has 9 strawberries in it.

Think about how many groups of 3 you have altogether.

So for the first equation, mm multiplied by 3 is equal to mm, how many groups of 3 can you see? That would be your first factor.

And what is it equal to? You have the second and third image there as well.

For question two, I'd like you to play a game.

Choose a number from the grid and cross it out.

So pick any one and cross it out.

That's your number.

However, you score one point if you say the number when you count in 3s, two points if you say the number when you count in 3s and 9s, and no points if you don't say that number when you count in 3s or 9s.

So if I were to pick the number 10, for example, I'd choose it, I'd cross it out, and then I would think, if I was counting in 3s from 0, would I say the number 10? If I was counting in 9s from 0, would I say the number 10? I'd get one point if I say it when I count in 3s, two points if I say it when I count in 3s and 9s, but I don't get any points if I don't say it when I count in 3s or 9s.

Good luck with those two tasks, and I'll see you shortly for some feedback.

Welcome back.

How did you get on? Let's take a look at those strawberries.

So for the first one, we had 2 groups of 9, and for every 1 group of 9, there are 3 groups of 3 strawberries, so that means we had 6 groups of 3 strawberries.

So our equations, which are equal, are 6 multiplied by 3, which is equal to 18, and 2 multiplied by 9, which is equal to 18.

For the second one, we had 4 groups of 9 strawberries, and I know that there are 3 times as many groups of 3 because for every one group of 9, there are 3 groups of 3.

So I can say that there are 12 groups of 3.

So the equations here are 12 multiplied by 3 is equal to 36, and 4 multiplied by 9 is equals to 36.

Now, the final one was a bit tricky.

We had 7 groups of 9, and therefore, we had 21 groups of 3 strawberries.

Remember, the product is still the same.

So 7 multiplied by 9 is equal to 63, which meant that 21 multiplied by 3 is also equal to 63.

Well done if you wrote down all of those equations correctly.

For question two, you may have played this game in lots of different ways, but let's take a look.

The numbers with one tick are multiples of 3.

So if you crossed out 6, for example, it's something that you'd say when you count in 3s, 0, 3, 6.

It's not something you'd say when you count in 9s, so you would score one point.

The numbers that have two ticks would get you two points because they're multiples of 3 and 9.

So for example, the number 36, if I was going to count in 9s, I would say 36, and we know that all multiples of 9 are multiples of 3, so that would get me two points.

Numbers that don't have any ticks are not multiples of 3 or 9.

So the number 10 that I chose earlier would've scored me zero points because it is not a multiple of 3 or 9.

Well done if you correctly gave yourself points for those numbers.

We have come to the end of our lesson, and today we've been learning about the relationship between multiples of 3 and multiples of 9.

Let's summarise what we've learned.

Numbers in the 9 times table are also in the 3 times table, which means that multiples of 9 are also multiples of 3, and we know that when there are 3 groups of 3, there is 1 group of 9.

You can build the 9 times table using the 3 times table, and we looked at that both with pictures and thinking about it as a bar model.

Thank you so much for all of your hard work today, and I look forward to seeing you in another maths lesson soon.