Lesson video

Hello, I'm Miss Miah, 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 the multiples of 2, 4 and 8.

Your keywords are on the screen now, and I would like you to repeat them after me.

Multiple, double, doubling, halving.

Well done, let's move on.

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

To double means to become twice as many or to multiply by two.

Halving means to divide into two equal parts.

This lesson is all about the 2s, 4s and 8 times tables.

And here we can see two lesson cycles.

Our first lesson cycle is all to do with identifying multiples of 2s, 4s and 8s.

And then this will help us to then explain the relationship between the 2s, 4s and 8 times tables.

So let's begin with lesson cycle one.

Are you ready? Let's get cracking.

In this lesson, you will meet Andeep and Izzy.

We are going to start off by recapping counting in multiples of two.

That means we will be adding 2 each time, starting with 0.

Are you ready? Let's begin.

3, 2, 1.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.

Fantastic.

Let's move on.

Now we're going to be recapping counting in our 4s, so multiples of fours.

That means we are going to be adding 4 each time from 0.

Are you ready? Let's begin.

I'm going to do a countdown.

3, 2, 1.

0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.

If you manage to count in multiples of four and you've got those all correct, fantastic.

Now let's recap counting on in multiples of eight.

So similarly to our multiples of 2s and multiples of 4s, we're going to be counting on, but this time counting on in 8s, starting with zero.

So let me do my countdown, get ready to join me.

3, 2, 1.

0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96.

Now this is quite a special task, so let's see what's going on.

Lucas, Andeep and Izzy are playing a multiplication game.

Izzy claps every multiple of 2, Lucas claps every multiple of 4, and Andeep claps every multiple of 8.

I am going to be counting, and these guys are going to be clapping.

Let's see what they do.

So, 1, 2, 3, 4, 5, 6, 7, 8.

Hmm, interesting.

You might want to carry this on with two friends.

Over to you.

Andeep makes a prediction about the game, "I know I'll clap every time Izzy and Lucas claps.

This is because multiples of 8 are also multiples of 2 and 4." Do you agree with Andeep? I want you to prove it.

You can pause the video here, have a go, and with your two friends and see if that's true.

So how was it? Well, it is mostly true, however, you will not clap for 2 and 4 because these are not multiples of 8.

Now what Andeep and Izzy have done is that they've recorded which multiples they count together at the same time.

So let's have a look, and you can see on this table you've got your 2s, 4s and 8s.

I am going to be counting along and we're going to see what happens.

So you've got 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

What do you notice? Well, all of the numbers said by the 8s group are also said by the 2s and 4s group.

Products in the 8 times tables are also in the 4 and 2 times table.

Products in the 4 times tables are also in the 2 times tables.

Over to you.

Identify which numbers are multiples of 2, 4, 8, or all of them.

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

This is what you should have got.

So 4 and 28 are multiples of 2 and 4, 8, 16 and 24 are multiples of all three, so 2, 4 and 8.

Now, looking at 4 and 28, we can see that these are not multiples of 8, because when counting on in 8, we will not say those numbers.

If we started at 0 and if I counted on, so 0, 8, I didn't say 4, so that's not a multiple of 8.

And then if I continued, let's see if I say 28, 0, 8, 16, 24, 32.

Onto your main task for this lesson cycle, you are going to be identifying which numbers are multiples of 2, 4, 8, or all.

And on the screen you can see the numbers that you will be sorting.

So you've got the numbers 4, 32, 24, 40, 8, 2, 19, and 42.

If you notice a number that does not fit into any of those categories, you can place it outside.

You can pause the video here and get started with this task and click play when you're ready to rejoin us.

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

So straight away we can see that 19 has not been placed in any of those.

19 is an odd number.

It's definitely not a multiple of 2, and we know that multiples of 2 are also multiples of 4 and 8, so we can eliminate 19 there straight away.

Now if we have a look at multiples of 2, we've got the numbers 2 and 42.

So that means when we are counting on in 2s, we would've definitely said those numbers.

After that we've got 4, so 4 is a multiple of 2 and 4.

And then we've got multiples of 8.

So the way I would've done this is started off by looking at my multiples of 8, and by doing that I would know that they would fall into the middle section because multiples of 8 are also multiples of 4 and 2.

And then I would've looked at multiples of 2, because not all multiples of 2 are multiples of 4 or 8.

Let's move on to the second lesson cycle.

Now this lesson cycle is all about explaining the relationship between the 2s, 4s and 8s.

Andeep and Izzy show multiples of 2, 4 and 8 using a number line.

We can show the steps really clearly this way.

So let's see, 2, 4, 6, 8, 10, 12, 14, 16.

So you can see by counting on in 2s, that those are our multiples of 2s.

Now let's look at our 4s.

So 4s, add another group of 4, add another group of 4, and add another group of 4.

Now let's see what happens when we count on in 8s.

Oh, okay, so 2, 8 times, that's 8 groups of 2.

That is the same as saying 2 x 8.

Now let's look at our 4s, over to you.

4 something times, that's the same as groups of 4.

What do you think that is? 4, 4 times.

So that's 4 groups of 4.

4 x 4 = 16.

Now Izzy has grouped 24 in different ways.

What do you notice? You may have said that for every two groups of 2, there is one group of 4.

For every two groups of 4, there is one group of 8.

So I'm hoping you can slowly start seeing a relationship here between your 2s, 4s and 8s.

So let's have a look at our 2s.

That's 2, 12 times, so 2 x 12 is 24.

That's 4, 6 times, so 4 x 6 is 24.

And that's 8, 3 times, so 8 x 3 is 24.

Have a look at your factors there, can you notice anything? Well, if one factor doubles the other halves, which means we end up with the same product.

So if we have a look at 2 x 12 = 24, now let's just look at the 4 x 6, ignore the 8 x 3, we can see that 2 has double to 4 and then 12 has halved to 6, which means our product will remain the same and we end up getting 24.

So double 2 is 4, so 12 halves to 6 and the product is the same.

Now to make 24, you need twice as many groups of 2 as you do 4.

To make 24, you need half as many groups of 8 as you do 4.

Over to you, you're going to fill in the blanks.

Three groups of 8 is equal to groups of 4, and groups of? You can pause the video here and click play when you're ready to rejoin us.

So what did you get? You should have got this.

So 3 groups of 8 is equal to 6 groups of 4, and then 12 groups of 2.

So each time a factor has halved, the other has doubled.

If you got that, good job.

Let's move on.

Now, Andeep has arranged an array.

I want you to think about how many groups of 2 are there, how many groups of 4 are there, and how many groups of 8 are there? If it helps, you can draw this array and circle the groups.

So we've got 12 groups of 2, there are 24 altogether.

Now when it comes to looking at groups of 4, if you know that there are 12 groups of 2, you also know that there are 6 groups of 4, because if we double one factor and half the other, that is what we get.

And lastly, we know that there are 3 groups of 8 because we could have circled that in the array, but we could have also used our doubling and halving methods.

So, if we know that the 6 has halved to 3, if we know that the factor of 6 in the equation 6 x 4 is 24, if we know that the 6 has halved to 3 and the 4 has doubled to 8, it will still give us the same product of 24.

Did you notice that? Well again, just a quick reminder, when one factor doubles, the product also doubles.

And when one factor doubles and the other factor halves, it will give the same product.

Back to you.

You are going to use the array to complete the questions.

So how many groups of 2 are there? Something multiplied by 2 gives us? How many groups of 4 are there? Something multiplied by 4 gives us? And how many groups of 8 are there? Something multiplied by 8 gives us? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? You should have got something like this.

So there are 16 groups of 2, which gives us 32.

Now if I know that my factor from 2 to 4 has doubled, that means I need to half 16 to get 8, which will also give me the same product of 32.

So the product has not changed.

And again, because the product has not changed, I can see that one of my factors now has doubled.

So 4 has gone from 4 to 8, which means I need to halve 8 to 4, which means my final multiplication equation that you should have got was 4 x 8 = 32.

If you manage to get all three of those correct using those rules, fantastic.

Let's move on.

Now Andeep is grouping 8 pencils.

He's written down 8 x 1 is 8.

He's also grouped the pencils like this.

And we can see that there are 4 equal groups of 2.

So 4 x 2 is 8.

And notice what we've got here, so double 4 is 8, and half 8 is 4.

And lastly, you can also group the 8 pencils into this.

So 2 groups of 4, so 2 x 4 is 8.

And it's the same relationship that we've got there.

So half of 4 is 2, and then if you double 2, it's 4.

And lastly we've got 1 group of 8.

So again, we've got the relationship of halving 2 is 1 and then doubling it is 2.

So if you halve the multiples of 8 and halve again, you get the multiples of 2.

If you double the multiples of 2 and double again, you get the multiples of 8.

Now Izzy is grouping 16 pencils, and you can see that she's grouped them like that.

So 16 x 1 is 16, 8 x 2 is 16, 4 x 4 is 16.

And then you've got your 2 groups of 8 pencils, which also gives you a total of 16.

So again, if you double the multiples of 2, you get the multiples of 4.

So for example, let's look at the equation right at the bottom, 2 x 8 is 16.

So for example, if I had 2 x 2, which is 4, if I doubled that 4, I would get 8, which is also a multiple of 2.

If you double the multiples of 4, you get the multiples of 8, and multiples of 8 are multiples of 2 and 4.

Don't forget that rule.

What you are going to do now is fill in the blanks using the relationship between the 2s, 4s and 8s.

You can pause the video here, off you go.

Good luck.

So what did you get? Well, you should have got 8 x 4 = 32, and that's because 4 doubled is 8.

And then 8 halved is 4.

Now this can also be represented as a bar model.

I love bar models because they really clearly show you the relationship between numbers.

So here we've got 16 as our whole.

So you can group 16 in many ways.

16 is equal to 2, 8 times, 16 is also equal to 4, 4 times, and lastly, 16 is equal to 8, 2 times.

Over to you.

You are going to use the bar model to complete the equations.

So your whole is 32, that is your product.

Use what you can see in your bar model to help you to fill in the gaps.

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

Well you should have got this.

So 32 is equal to 2, 16 times, 32 is also equal to 4, 8 times, and 32 is equal to 8, 4 times.

On to your main task for this lesson cycle.

So for question one, you're going to use your knowledge of the 2s, 4s and 8s to answer the following questions.

You're going to complete the bar model and then solve the questions.

You can see that 24 is your whole or the product, and then you've got different parts.

Then you've got equations to fill in the gaps for.

So 24 is equal to 2 times something, 24 is equal to 4 times something, and 24 is equal to 8 times something.

Can you think of any other facts? And then for question 2, you're going to use the array to complete the questions.

So how many groups of 2 are there? How many groups of 4 are there? And how many groups of 8 are there? Can you use any relationship facts to help you as well? You could pause the video here and click play when you are done, so then we can go through our work.

So how did you do? For question 1, this is what you should have got.

So for the first row, you should have got 12, 2 times, and that is equal to 24.

For the second row, you should have got 4, 6 times, and that is equal to 24.

And lastly, for the third row, you should have got 8, 3 times and that is also equal to 24.

So each time one of the factors doubled the other halved.

In terms of other facts, if you've got any of these facts, you are correct.

So 24 is also equal to 1 group of 24, it's also equal to 2 groups of 12, and 6 groups of 4, and then lastly, 3 groups of 8.

And for question two, you should have got 20 groups of 2 is equal to 40.

And for how many groups of 4 there are? Well, if one of my factors has doubled to 4, I know that the other factor has to halve to 10.

So 10 groups of 4 is 40.

And lastly, 5 groups of 8 make 40.

And again, we can apply the same relationship facts, so if one of the factors has doubled, the other has to halve to get the same product.

Well done, we've made it to the end of this lesson.

We are now going to summarise our learning.

So you now understand that multiples of 8 are multiples of 2 and 4.

You also understand that if you double the multiples of 2, you get the multiples of 4.

You understand that if you double the multiples of 4, you get the multiples of 8.

And lastly, if you double the multiples of 2 and double again, you get the multiples of 8.

Well done, I'm very proud that you made it to the end of the lesson and I can't wait to see you in the next one.