Lesson video

Hello there.

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

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

Now, you've probably already done some learning about the 3 and the 9 times table, and hopefully you're able to start to recall some of those key facts for those times tables.

Well, in this unit we're going to be really looking carefully about how those facts are connected and how we can use one to find the other.

By the end of this lesson today, you will be able to say that you can explain the relationship between pairs of 3 and 9 times table facts that have the same product.

We have one keyword in our learning today.

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

My turn, multiple, your turn.

Great job.

Now, let's just check we know what that word means.

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

In our lesson today, we're going to be explaining the relationship between pairs of 3 and 9 times table facts and thinking about those that have the same product.

And our learning today splits up into two cycles.

In the first cycle, we're going to be thinking about how many 3s and how many 9s, so thinking about groups of 3 and groups of 9.

And then in the second cycle, we're going to be looking at common multiples of 3 and 9.

Remember, multiples are partly numbers that we can find in our 3 and 9 times table.

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

In this lesson today, you're going to meet Andeep and Izzy, and they're going to be helping you with your learning and asking you some interesting questions throughout the lesson.

So let's start here.

Izzy is looking at some counters.

You might want to use some counters to make the same pattern that Izzy has made here.

How can you describe these counters using groups of 9 and groups of 3? Hmm, I wonder.

Well, that's right, Izzy.

We can see 1 group of 9.

If we count the individual counters, 1, 2, 3, 4, 5, 6, 7, 8, 9, I can see that we have 9 counters.

There is 1 group of 9.

We can write that as a multiplication equation.

We can say that 1 x 9 = 9.

We can also see 3 groups of 3.

I can see one group, two groups, three groups, and each group has 3 counters in it.

We can write that as a multiplication equation as well, 3 x 3 = 9.

And we can say that 1 x 9 = 3 x 3.

They have the same value.

We can see that the product, the answer, is 9.

That's the total number of counters that we have.

So whether we think about this as 1 group of 9 or 3 groups of 3, the product is still the same, it's 9.

Let's take a look at a second example.

Take a close look at the counters.

How could you describe these using groups of 9 and groups of 3? I wonder if we can apply what we've just thought about to this example.

Well, this time we have 2 groups of 9.

We can see that the horizontal rows are made up of 9 counters each.

So we can say that there are 2 groups of 9, and we can represent this as an equation, 2 x 9.

There are 18 counters altogether, so our product is 18.

2 x 9 = 18.

How many groups of 3 can we see? We can also see 6 groups of 3.

Have we removed any counters? Have we added any counters? No, so we still have the same number of counters, but we can write a different multiplication equation.

We can say that 6 x 3 = 18.

And we know that because they have the same product, they are equal.

So we can write this as 2 x 9 = 6 x 3.

We can say that 2 groups of 9 is equal to 6 groups of 3.

Time to check your understanding.

Use what we've just done to think about how you might describe these counters using groups of 3 and groups of 9.

You have some equations and some sentence stems to fill out.

So for example, mm x 9 = mm.

So how many groups of 9 can you see? The sentence stems are there are mm groups of 9, there are mm groups of 3.

Pause the video here and have a think.

Welcome back.

Well, let's see, what can we see in the counters? Well, I can see 3 horizontal rows, and each of them have the same amount of counters.

Each row has 9 counters, so I can see 3 groups of 9.

And I can write this as 3 x 9.

Now I can skip count in 9s, 9, 18, 27, to find out that our product, the number of counters we have altogether, is 27.

So I can write 3 x 9 = 27.

Well done if you got that first equation.

How many groups of 3 have we got? Well, we can see that there are 9 groups of 3, and we can write the equation 9 x 3 = 27.

Remember, the product is the same.

We haven't added any counters or removed any counters, we've just grouped them differently.

And well done if you've recognized that therefore we can write 3 x 9 = 9 x 3.

Let's take a closer look at those equations then.

We have 1 x 9 = 9, 3 x 3 = 9, then we have 2 x 9 = 18, 6 x 3 = 18, 3 x 9 = 27, and 9 x 3 = 27.

What do you notice? Hmm.

Well, that's right, Izzy.

If we look at the first factor in each pair of equations, that represents the number of groups.

So if we look at the first pair of equations, 1 x 9 = 9, the 1 represents the number of groups.

There is 1 group of 9.

In the second equation, 3 x 3 = 9, that first 3 represents the number of groups.

There are 3 groups of 3.

And the same applies for the second pair and the third pair of equations.

Let's look closely at those factors.

Do you notice a relationship between them? Is there a link between 1 and 3, 2 and 6, and 3 and 9? Hmm.

Well, yes, we can multiply the top 1 by 3 to get to the second one.

1 x 3 = 3.

2 x 3 = 6.

3 x 3 = 9.

And that's because there are 3 times as many groups of 3 as there are groups of 9 for the same product.

Can we try and say that together? There are 3 times as many groups of 3 as there are groups of 9 for the same product.

If we think about that third example, 3 groups of 9 is equal to 27, 9 groups of 3 is equal to 27, we can use the array in the corner to help us think about it.

The first factor, 3 and 9, shows us the number of groups.

3 groups of 9, 9 groups of 3.

The product, the number of counters, is the same, and we can see that there are 3 times as many groups of 3 because 3 x 3 = 9.

Each extra group of 9 adds 3 groups of 3, and you can see that in the counters.

If we add an extra row of 9, we have to add 3 extra groups of 3.

Time to check your understanding.

Complete the final pair of equations.

So we have the equations that we've just looked at and then we've got one set, mm x 9 = 36, mm x 3 = 36.

The product is the same.

And then say the stem sentence.

There are mm times as many groups of 3 as there are groups of 9 for the same product.

There's an array there to help you think about those equations.

Pause the video here and have a think.

Welcome back.

How did you get on? Well, you might have spotted a pattern going across each one.

So we had 1 x 9, 2 x 9, 3 x 9, so the next one would be 4 x 9.

And remember, there are 3 times as many groups of 3 as there are groups of 9 for the same product.

So if we want to find that missing number, we could do 4 x 3, which gives us 12.

4 x 9 = 36, therefore 12 x 3 = 36.

Let's say that stem sentence together again.

There are 3 times as many groups of 3 as there are groups of 9 for the same product.

Well done if you got those equations.

Time for your first practice task.

How many groups of 9 can you see and how many groups of 3? You can use what we've learned to think about this efficiently.

So for A, we have 4 groups of 9.

I can see that because there are 4 groups of 9 strawberries.

How many groups of 3 is that? You have B, C, and D to think about as well.

Remember to fill in the gaps in the stem sentence and the equations.

For question 2, apples come in boxes of 3 or in boxes of 9.

Fill in the blanks of the table.

So let's take a look at that first row.

The total number of apples in the first row is 9.

How many boxes of 3 apples would that be? If you have counters, you could get 9 counters and see how many groups of 3 you could make with 9 counters.

Then how many boxes of 9 apples would that be? Again, you might want to use counters.

Be really careful because sometimes you're not told the total number of apples.

Sometimes you're told the boxes of 3 apples or the boxes of 9 apples.

Remember that there are 3 times as many groups of 3 as there are groups of 9 for the same product.

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

Welcome back.

How did you get on? So for question 1, let's look closely at 1A.

There are 4 groups of 9, and we know that there are 3 times as many groups of 3, so 4 x 3 = 12.

So there are 4 groups of 9 and 12 groups of 3, and we can write that 4 x 9 = 12 x 3.

For B, there are 2 groups of 9, and so there are 6 groups of 3.

For C, there are 3 groups of 9, which means there are 9 groups of 3.

And then for D, there are 6 groups of 9 and 18 groups of 3.

Remember, there are 3 times as many groups of 3, so I can do 6 x 3, which is 18, to find out the number of groups of 3.

Well done if you completed all of those stem sentences and the equations.

Let's take a look at this table.

So for the first row we had 9 apples altogether.

I know that that is 1 box of 9, so I could put 1 in the boxes of 9 apples column.

I know that there are 3 times as many groups of 3, so there'd be 3 groups or boxes of 3 apples.

If we looked at the second row, we didn't know the total number of apples to begin with, but we knew that there were 9 boxes of 3 apples.

I know that 9 groups of 3 is equal to 27, so that is the total number of apples.

If I wanted to work out how many boxes of 9 apples, I could skip count in 9s until I got to 27.

9, 18, 27.

That means there are 3 boxes of 9 apples.

Remember that there are 3 times as many groups of 3 as there are groups of 9 for the same product.

So take a look at your boxes of 3 apples and boxes of 9 apples, and you should notice that the boxes of 3 apples is 3 times as many as the box of 9.

Well done if you correctly filled out this table.

Let's move on to the second cycle of our learning where we're thinking about common multiples of 3 and 9.

This number line shows the multiples of 3 and 9.

As you can see, along the top row we have 0, 9, 18, 27, 36.

These are the multiples of 9.

And underneath we have 0, 3, 6, 9, 12, and so on.

These are the multiples of 3.

Andeep has suggested that we look more closely at the number 18.

"What do you notice about the number 18?" he asks.

Hmm.

Well, Izzy has spotted that there are 2 jumps of 9 and we can see that on the number line.

We have done 2 jumps to get to the number 18.

Now, Izzy knows a lot about the relationship between the 3 and the 9 times table, so she's also said there must be 3 times as many jumps of 3.

Do you agree? Let's take a look.

1, 2, 3, 4, 5, 6.

Well, there were 2 jumps of 9, and 2 x 3 = 6, so Izzy is absolutely right.

There were 3 times as many jumps of 3.

We can see that 2 x 9 = 18, and we can also see that 6 x 3 is 18.

And that's right, Andeep.

There are 6 jumps of 3, which is 3 times as many as the 2 jumps of 9.

Time to check your understanding.

Complete the statements for the product 27, which you can see on the number line.

Mm x 9 = 27 and mm x 3 = 27.

Think about the jumps.

So you have some statements here to fill out as well.

I can see mm jumps of 9, so there must be mm jumps of 3.

Think about the relationship between the 3 and the 9 times table.

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

Welcome back.

How did you get on? Well, I can see that there are 3 jumps of 9.

9, 18, 27.

I did 3 jumps.

So 3 x 9 = 27.

I know that there are 3 times as many jumps of 3, so 3 x 3 = 9, so that must mean there are 9 jumps of 3.

And we could count them if we wanted to, but there are definitely 9 jumps of 3 there.

Let's take a look at our stem sentences.

I can see 3 jumps of 9, so there must be 9 jumps of 3.

There are 3 times as many jumps of 3 as there are jumps of 9 for each product in the 9 times table.

Well done if you got all of that correct.

Andeep and Izzy are thinking about continuing their number line.

So you can see on their number line now that they have additional multiples of 9.

Let's count them together, are you ready? 0, 9, 18, 27, 36, 45, 54, 63, 72.

Those are all multiples of 9.

Andeep's wondering what it would look like for 7 x 9.

Hmm, how many jumps do I need to do for 7 x 9? Which of these numbers is the product of 7 x 9, or 7 groups of 9? That's right, Izzy.

There will be 3 times as many jumps of 3.

So 7 x 9 is the same as 21 x 3, so we'd have to do 21 jumps of 3 to be the same as 7 jumps of 9.

We can see here that 7 x 9 = 63.

We've done 7 jumps of 9 on our number line.

And to get to 63 if we're jumping in jumps of 3, we would need 21 jumps to make 63.

If you look really carefully, you could take a moment to count if you wanted to.

There are 21 jumps of 3 to equal 63.

Remember, there are 3 times as many jumps for 3 as there are for 9.

And we can show that on the number line.

1 group of 9 is equal to 3 groups of 3.

And Andeep is really challenging us.

"What would it look like for 100 groups of 9?" Goodness me.

Well, I wouldn't want to draw a number line to show that because my number line would be very long, and if I had to do 100 groups of 9, I'd be there for a long time.

But I think I'd be there for even longer if I had to do the same amount for jumps of 3.

There would still be 3 times as many jumps of 3, so 100 groups of 9 would be 300 groups of 3.

Goodness me, that would be a lot of jumps.

I'm not sure I'd be able to keep count.

And Andeep's absolutely right, a number line like that would just fall off this slide, it wouldn't fit.

Time to check your understanding.

Fill in the blanks in this table and the sentence.

So you've got a multiple of 9, the number of 9s and the number of 3s.

So let's take a look at 36.

How many groups of 9 are equal to 36? You could skip count in 9s or use the number line to help you.

And remember that there are always mm times as many 3s as there are 9s in a multiple of 9, and that's because there are mm 3s in 9.

That will help you find the second column.

Good luck with that and I'll see you shortly for some feedback.

Welcome back.

How did you get on? Well, let's look at a couple of these rows.

For 36, that is 4 groups of 9.

I can skip count in 9s.

9, 18, 27, 36.

That is 4 groups of 9.

And I know that there are always 3 times as many 3s as there are 9s in a multiple of 9, and that's because there are 3 3s in 9.

So if I want to find out how many groups of 3 there are in 36, I can multiply 4 by 3.

4 x 3 = 12, so there'd be 12 groups of 3.

Let's look at that bottom row.

The multiple of 9 is 81, but if I skip counted in 9s, I would have to say 9 groups of 9 to make 81.

9 x 9 = 81.

And we know that there are 3 3s in 1 group of 9, so I'd have to multiply 9 by 3.

9 x 3 = 27, so there'd be 27 3s in 81.

Well done if you got all of that.

Time for your second practice task.

You have a bit of a challenge here, we've got a bit of a maze for you.

Make your way across the grid of multiples of 3 and 9 from start to finish, and I want you to describe the next step by giving the number of 3s or the number of 9s in the next number.

You must take turns in giving a number of 3s and 9s.

So let's see what that might look like.

If you start on start, Andeep says, "Go to 12 3s." Now, 12 x 3 = 36, so he would go on to 36.

Izzy would then have a go.

Where is she going to direct Andeep to? She says, "Move on to 7 9s." 7 groups of 9 is equal to 63, so Andeep would move on to 63.

Andeep would then have a go.

How can you get across to the finish line? Can you find different ways to do it? Good luck with that and I'll see you shortly for some feedback.

Welcome back.

How did you get on? I wonder if you found different ways of describing the numbers and also different ways of making it from the start to the finish line.

There are lots of possibilities for doing this, so you might have done something like this route that Andeep and Izzy did.

They started off by saying 2 9s.

I know that 2 groups of 9 is equal to 18, so I moved to 18.

And then Izzy said 24 3s.

Goodness me, now I don't know 24 3s, but I know that for every 1 group of 9 there are 3 groups of 3, so I know that 24 3s is the same as 8 groups of 9, which is 72.

That's a really good clue.

The children then continued taking turns thinking about groups of 3 and groups of 9 until they ended up with 15 3s, which is 45, and got to the finish line.

Well done if you managed to get to the finish line in different ways.

We've come to the end of the lesson and we've been explaining the relationship between multiples of 3 and multiples of 9.

Let's summarize what we've learned.

In a multiple of 9, there are 3 times as many 3s as there are 9s.

So if we think about the number 18, that is 2 groups of 9, and we can see that there are 3 times as many 3s as there are 9s.

So if there are 2 groups of 9, there must be 6 groups of 3.

Thank you so much for all your hard work today and I hope to see you in another math lesson soon.