Lesson video

Hello, I'm Miss Mia, and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

In this lesson, you'll be able to explain the relationship between multiples of three and multiples of nine.

So your times tables facts of the threes and nine times tables will definitely help, and I hope you've been practising them.

So your key words are on the screen now and I'd like you to repeat them after me.

Multiple, triple.

Great, let's find out what these words mean.

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

To triple means to become three times as many or to multiply by three.

We're going to find out how we can do that throughout this lesson.

So this lesson is all about our threes and nine times tables, and there's two lesson cycles here.

Our first lesson cycle is all to do with identifying the multiples of three and nine, and then we're going to move on to explaining the relationship between the threes and nines.

Are you ready? Let's get started.

And of course, to join us, we've got Andeep and Izzy who will help with our mathematical thinking.

So we are going to recap counting on in multiples of three, and I'd like you to chant with me, are you ready? We're going to start off with zero.

Now remember, when you're counting on in threes, you are adding three each time to the previous number.

Are you ready? Let's go, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, well done if you managed to chant all of those correctly.

And by doing that we've just chanted our multiples of three.

Now, let's recap counting on in multiples of nine, we're going to start off at zero, and this time, instead of counting on in threes and adding three to our previous number, we are going to be adding on nine, that's correct.

So we're going to add on nine to the previous number that we say.

When you're ready, let's begin.

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

Well done if you managed to chant all your multiples of nine.

Let's move on.

Now, Andeep and Izzy are counting in multiples of three and nine, they record which multiples they count together at the same time.

So let's have a look at what happens when they're doing this.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, so what did you notice? Well, all of the numbers said by the nines group are also said by the threes group.

Not all the numbers said by threes group are said by the nines group.

So what we found out here is that for every number said by the nines group, the threes group say three numbers.

So Andeep claps the multiples of three.

Izzy claps the multiples of nine.

Andeep says, "For every three times I'll clap, you'll clap once." Izzy says, "Let's check." Do you agree? Prove it, you can pause the video here, have a go with your partner, click play when you're ready to rejoin us.

So what did you all find out? Well, Andeep is correct, because for every three multiples of three you clap one multiple of nine.

Hmm, how many groups of three are there? So we've got an array of nine strawberries.

What can you see? Well, there's one group of three, two groups of three, three groups of three.

So if you said three groups of three, well done.

There are three groups of three.

Now, how many groups of nine are there? Have a think.

Well, there's one group of nine.

Hmm, we've definitely got more strawberries here, so how many groups of three are there? There are 12 groups of three.

And we know that 12 times three is equal to 36.

Now I want you to think about how many groups of nine there are.

Have a think.

There's one group of nine, two groups of nine, three groups of nine, and four groups of nine.

So that can be represented as four times nine, which is equal to 36 strawberries altogether.

Now, another way to represent this is through using a bar model.

We can see here that we've got three threes, which make one group of nine, altogether we've got 12 lots of threes, which is 36.

But when we look at the relationship between the threes and nines, we can see that for every three groups of three, there's one group of nine.

To further break this down, we can also say, for every one group of nine, there are three groups of three.

So three rows of three is the same of one group of nine strawberries.

Over to you, I'd like you to fill in the blanks.

You can see an array there, 15 lots of three strawberries is the same as something groups of nine strawberries.

You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, 15 lots of three strawberries is the same as five groups of nine strawberries.

Back to you, I'd like you to fill in the blanks.

Three times 15 is five times.

You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, three times 15 is equal to five times nine, and that's because five times nine is 45.

Onto your main task for this lesson cycle.

So for question one, you're going to be sorting the numbers correctly.

Your numbers are 0, 3, 6, 8, 15, 18, 27, 36, 42, and 48, and you are going to be sorting them into multiples of three or multiples of nine.

Now, numbers that are neither multiples of three or nine need to go outside the circles, and is there anything that you notice once you've done that? For question two, you're going to fill in the gaps using the images to help you, so you've got some arrays there, and you are going to closely look at how many groups of three there are and how many groups of nine there are.

You can pause the video here to start your tasks, off you go, good luck, and click play when you're ready to rejoin us.

So how did you do? So this is what you should have got.

For multiples of three, you should have got 3, 6, 15, 42 and 48.

And that's because when we count on in multiples of three, we would've chanted these numbers.

Now, if we look at eight, eight is neither a multiple of three or nine, because we do not chant it when we are counting on in either three or nine.

Multiples of three and multiples of nine are 0, 18, 27 and 36.

Now, you may have noticed that there are no multiples of just nine, and that's because multiples of nine are multiples of three.

And that's because no numbers go in this section, because all of the multiples of nine are multiples of three.

Now let's move on to question two.

So we've got images here that are presented as arrays and we were going to use this to help us answer the questions and fill in the gaps.

So for the first question, you should have got six groups of three, which is 18, and then two groups of nine, which is also 18.

Secondly, you should have got 12 groups of three, which is equal to 36, and four groups of nine, which is equal to 36.

And lastly, you should have got 24 groups of three, which is equal to 72, and eight groups of nine, which is equal to 72.

Now you may have noticed here for each equation set, the product was the same, so for example, if we look at the first question, we can see that 18 is our product, our factors are different.

But even though our factors are different, we still have the same product, and that's because for every three groups of three there's one group of nine.

Well done if we manage to get all of those questions correct.

Let's move on.

So for lesson cycle two, we are going to be looking at explaining the relationship between the threes and nines now, let's go.

Now Andeep and Izzy are comparing the three and nine times tables.

We can see that on the left hand side we've got the threes, and then on the right hand side we've got the nine times tables.

I want you to think about what is the same and what is different.

Now, you may have thought of something like this.

Products in the nine times tables are also in the three times tables, and we covered that in the previous lesson cycle.

Now, apart from multiplying by zero, multiples of nine are triple the multiples of three.

Hmm, wonder what triple means.

Ah, did you remember? It means that it is three times as many, so that means 54 is three times as many as 18.

Apart from multiplying by zero, multiples of three are one third the multiples of nine.

So for example, 18 is one third of 54.

That means I'd have to triple 18 to get 54.

Now, Andeep has arranged an array, so we can see that he's got three rows of three.

This shows one group of nine.

Three is one third of nine, and that's what that looks like.

We can represent that as one times three, which is equal to three.

Now, nine is triple three.

So another way to say that nine is triple three, this can be represented as three times three is equal to nine.

Now, Andeep has arranged another array, and this time he's got one group of 18, but here we've got three groups of six, which is also equal to 18.

Six is one third of 18, so we can see that there.

So that means we would need two more groups of six to get 18.

One way to represent three groups of six is three times six, which is equal to 18, or six times three, which is equal to 18.

18 is triple six.

Now, Andeep has arranged an array, how many groups of three are there and how many groups of nine are there? Well, there's three groups of three, and this gives us nine altogether.

And there's one group of nine, which gives us nine.

Over to you.

There's an array on the screen, how many groups of three are there and how many groups of nine are there? Can you use the language of tripling to help you? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, this is what you should have got.

There are nine groups of three, nine times three equals 27.

And there are three groups of nine, so three times nine is equal to 27.

That means nine is one third of 27 and 27 is triple nine.

To you, is Andeep correct? All multiples of three are also multiples of nine.

You could pause the video here and click play when you're ready to rejoin us.

So how did you do? Andeep is incorrect, one times three equals three.

Three is not a multiple of nine, remember that.

Now, Andeep and Izzy continue to spot patterns.

If I know that three times four is equal to 12, then I know nine times four is equal to 36.

I just have to triple the product in the three times tables.

Do you agree with this? Well, Andeep is correct, because if one factor triples, then so does the product.

Back to you, I'd like you to fill in the gaps.

So using what Andeep said in the previous slide, he said that if one factor triples, so does the product.

So we've got here, if three times six is equal to 18, then nine times six is equal to, oh, I can see one of the factors has tripled.

Use this to help you, you can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, multiples of nine are triple the multiples of three.

So 18 tripled is 54, that's 18 three times.

18 times three is equal to 54.

Well done if you've got that correct.

Let's move on.

Andeep and Izzy continue to spot patterns.

He says, "If I know nine times five equals 45, then I know three times five is equal to 15." Do you agree? Let's see what Izzy says.

She says that Andeep is correct, and that's because we know multiples of three are one third of the multiples of nine.

So you must divide the product by three.

Back to you, I'd like you to fill in the gaps.

Andeep knows nine times 10 is 90.

Izzy says, "Well, then three times something must be 90." A fact that Andeep knows is three times 10, so use that to help you.

You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, knowing that our nine times tables is triple the three times tables, you should have got this.

So multiples of nine are triple the multiples of three, which means that you need to multiply the missing factor by three.

So if you know that three times 10 is 30, three times 30 equals 90.

So you would've multiplied 10 by three.

Back to you, if three times three equals nine, then nine times three equals 27.

Is that true or false? You could pause the video here and click play when you're ready to rejoin us.

Well, it is true.

This time, I'd like you to justify your answer.

Is this because, A, multiples of three are triple the multiples of nine, or B, multiples of three are one third of the multiples of nine? So what did you get as your justification? You should have got B, and that's because multiples of three are one third of the multiples of nine, and we could have used this to help us with this fact here, let's move on.

This is your main task for this lesson cycle.

So question one, use the array to complete the questions.

How many groups of three are there? How many groups of nine are there? Something is triple, and something is one third of.

So what you're going to do is use the answers from the questions before to help you answer the last couple of questions.

Question two, desserts come in packs of three or nine, using this information, answer the following.

So you've got a pack of nine desserts there and a pack of three desserts.

So question 2a, Andeep's mom buys one pack of nine, how many packs of three is this? B, if Andeep's mom has a total of 27 desserts, how many packs of nine is this? And how many packs of three is this? C, if Andeep's mom has a total of 36 desserts, how many packs of three is this? And how many packs of nine is this? D, Izzy's mom wants to buy 81 desserts, but the shop only has packs of three left.

How many packs will she need to buy? If 90 desserts are bought, how many packs of three is this? You could pause the video here and click play when you're ready to rejoin us, off you go, good luck.

So how did you do? Well, for question one, this is what you should have got.

Now, I can see that there are 12 groups of three, 12 times three is equal to 36.

I can see that there's four groups of nine, so four times nine is equal to 36.

So we then know that 36 is triple 12 and 12 is one third of 36.

For question 2a, well, Andeep's mom bought one pack, to calculate what three packs are, if you know that one pack is nine, three packs will be needed, because three times three is nine.

For question B, you should have got three packs of nine and nine packs of three.

Now, we're going to look at C in a little bit more detail.

So if Andeep's mom has a total of 36 desserts, how many packs of three is this? Let's start with that first.

Now using your knowledge of the three times tables, you know that three times 12 is 36, so that means we will need 12 packs.

And when working out how many packs of nine we'd need, again, we could use our nine times tables to help us or we could use the information that we got from before.

So if I know I need 12 packs of three, and I also know that I'd only need four packs of nine, because four is one third of 12.

For question D, this is what you should have got.

If nine times nine is 81, then three times 27 is equal to 81, because you need to triple one of the factors to get the same product.

So Izzy's mom will need to buy 27 packs.

And lastly, if 90 desserts are bought, how many packs of three is this? Well, if you know that nine times 10 is equal to 90, then three times 30 is equal to 90, so 30 packs would be bought.

Well done if you got all of those answers correct, and it's super good if you managed to use your knowledge of the relationship between the threes and nines to help you answer those questions.

Let's summarise our learning.

Today, you explained the relationship between multiples of three and multiples of nine.

You should now understand that multiples of nine are three times the multiples of three and that multiples of three are one third of the multiples of nine.

You should also understand that multiples of nine are all multiples of three, but not all multiples of three are multiples of nine.

And now you can use this knowledge to solve problems. Thank you very much for joining me in this lesson and I look forward to seeing you in the next one, bye.