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 multiples of 4 and multiples of 8.

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

Multiple, double/doubling, halving.

Now we're going to see what the definitions of these words are.

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 our 4s and 8s times tables, and I can't wait to begin this.

We have two lesson cycles here.

So, the first lesson cycle is all about identifying multiples of 4s and 8s.

And this is really important because this will then help us with our second lesson cycle, which is to explain the relationship between our 4s and 8s.

And you'll be surprised as to see what that relationship is.

Can't wait.

So let's begin with our first lesson cycle.

And in this lesson, you will meet Andeep and Izzy.

Let's begin by recap in counting in multiples of four.

Chant with us.

Are you ready? Three, two, one, zero.

Four, eight, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.

What did you notice? Well, from zero we counted on in fours, which means we were adding four each time.

These are all numbers which are multiples of four, so that means they're in the four times tables, and we can carry on adding four to 48.

This will also reveal all the other multiples of four.

And we can keep going with that.

Now, this time what we're going to do is I'll have a turn then it's your turn.

Okay? Let's begin.

Zero, eight, 16, 24, 32, 40, and 48.

Well done if you've got those correct.

Let's move on to our eight times tables now.

So, when counting on in multiples of eight, we're going to be adding eight each time to zero.

Let's begin.

Zero, eight 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96.

Now, I'm going to have a turn then it will be your turn.

Are you ready? Let's begin.

Zero, 16, 32, 48, 64, 80, and lastly, 96.

Well done if you got that correct.

This is really going to help us with the next stage now.

Let's go.

Now, Andeep and Izzy are counting in multiples of four and eight.

They record which multiples they count together at the same time.

So, as you can see on the table here, we've got our 4s and the top row, and then we've got our 8s.

Now, let's look at zero.

When counting on in multiples of four and eight, they both will say zero, because they're both starting with zero.

And then we're going to say the rest of the numbers.

So one, two, three, four, five, six, seven, eight, nine, 10 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

What do you notice? All of the numbers said by the 8s group, they're also said by the 4s group.

Products in the eight times tables are also in the four and two times tables.

Products in the four times tables are also in the two times tables.

Over to you.

You're going to be identifying which numbers are multiples of four, eight, or both.

So you've got the numbers 4, 20, 28, 16, 36, 8, and 48.

You can pause the video here to sort the numbers.

Off you go.

Good luck.

And click Play when you're ready to rejoin us.

So, how did you do? These are the multiples of four that you should have got.

four, 20, and 28.

And that's because when counting on in fours, if I started at zero.

Let's see if we say these numbers.

So, 0, 4.

Yes, that's correct.

Let's carry on.

8, 12, 16, 20, so we've got 20 there as a multiple of four, 24, 28.

And I've said 28 as well, so that's a multiple of four.

Some multiples of four are not multiples of eight.

Now, Andeep and Izzy are playing with dominoes.

So this domino represents two, this domino represents four, and this domino represents eight.

How many groups of 4 can you see? There's one group of 4, and there's two groups of 4.

So there are two groups of 4.

Now, how many groups of 8 can you see? Well, there's one group of 8.

How many groups of 4 are there? That's one group of 4, two groups of 4, three groups of 4, four groups of 4, five groups of 4, and six groups of 4.

That means there are six groups of 4 altogether.

That's 4 six times.

How many groups of 8 are there? So that's one group of 8, two groups of 8, three groups of 8.

So there are three groups of 8.

And that is also the same as saying there are 8 three times.

This can also be represented as a bar model.

And a bar model can really clarify or show clearly the relationship between the 4s and the 8s.

So let's have a look.

Here we are.

So we've got our groups of 4 at the top, and our groups of 8 at the bottom.

And we can notice here for every two groups of 4 there's one group of 8.

Now there's six groups of 4, which is 6 times 4.

This is also equal to three groups of 8, which is 3 times 8.

So 6 times 4 is equal to 3 times 8.

What do you notice? So four groups of 8 is equal to 32.

8 times 4 is equal to 32.

This means for every two groups of 4, there is one group of 8.

One pair of dominoes with four spots each is the same as one domino with eight spots.

Over to you.

Represent this image as a bar model.

You can pause the video here.

Off you go.

So, how did you do? If you got something like this, you are correct.

So you should have had four groups of 8.

It doesn't matter which, whether it was on the top or at the bottom, as long as you had four groups of 8.

Followed by eight groups of 4.

If you got that, well done.

Let's move on.

Back to you.

I'd like you to fill in the blanks.

So, five pairs of four-spot dominoes is the same as groups of eight-spot dominoes.

Four times is the same as eight times.

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

So, what did you get? Well, five pairs of four-spot dominoes is the same as five groups of eight-spot dominoes.

And that's because when we multiply both 5 by 8, we get 40.

So that's 40 spots altogether.

Four 10 times is the same as 8 five times.

Back to you.

I'd like you to fill in the blanks.

So, how did you do? Well, you should have got 4 times 10 is equal to 8 times 5.

Onto the main task for this lesson cycle.

So for question 1, what I would like you to do is circle the multiples of four, eight, or multiples of both.

Which is the odd one out? And what you can see here is a Key.

So, for multiples of four, select one colour, for multiples of eight, select a different colour, and then for multiples of both, I'd like you to select a different colour for that as well.

And then what you're going to do is circle which are multiples of four, which are multiples of eight, or both.

And then for question 2, you're going to be completing the missing number and writing an equation to identify whether it's a multiple of four or eight.

The first question has been done for you as an example, and we'll have a look at that.

So, if there are eight legs, there are spiders.

Well, I know a spider has eight legs, so there is one spider.

That is the same as saying, eight one time is eight, or 8 times 1 is 8.

So eight is a multiple of eight in this question.

I want to read you out the other questions and then you can get started.

So if there are 16 legs, there are amount of spiders.

Something multiplied by something gives you.

So, 16 is a multiple of.

Now, if there are 16 legs, there are amount of cats.

Something multiplied by something gives you amount of legs.

So that means 16 is multiple of.

Now, let's look at the other questions.

There are 48 legs, which means there are amount of cows.

Something multiplied by something is.

So, 48 is a multiple of.

Next question.

There are 32 tentacles, there are octopuses.

So, 32 is a multiple of.

And lastly, there are 96 tentacles, which means there are amount of octopuses.

96 is a multiple of.

When you're ready, click Pause, and I'd like you to get started with this task.

So, how did you do? Now, the way I would've tackled this question is using the rule that I know.

So, I know that multiples of eight are also multiples of four.

So I would've started off with that.

And I would've circled the multiples of both first.

So, I would've circled eight, 16, 24, 32, and 48 first, leaving me to just find the multiples of four separately, and I would've done that by counting on in 4s and circling the rest.

And then lastly, 1 is the odd one out because it isn't a multiple of four or eight.

We'll skip the first one because we've already spoken about it.

So, if there are 16 legs, there are two spiders, and that's because I know a spider has eight legs.

So 8 times 2 is 16, 16 is a multiple of 8.

If there are 16 legs, there are four cats.

And I know that because one cat has four legs.

That means four cats, 4 times 4 is 16, 16 is a multiple of 4.

So, in this case, 16 is a multiple of 4, because that is the context of the question.

We're looking at cats.

If we were looking at cats and octopuses, I would've also said that 16 is a multiple of 4 and 8.

For the next question, there are 48 legs, which means there are 12 cows, and that's because I know one cow has four legs, that means 12 cows will have 48 legs.

And the multiplication equation that you should have got there was 4 times 12, 48, in this context is a multiple of 4.

There are 32 tentacles, which means there are four octopuses, because one octopus has eight legs, which means four octopuses would have 32 legs.

Your equation here is 8 times 4, which is 32, 32 is a multiple of 8.

And lastly, there are 96 tentacles, goodness me, that's a lot, which means there are 12 octopuses, because one octopus has eight legs.

That's 96, because 8 times 12 is 96, 96, in this context, is the multiple of 8.

Well done if you've got all of that correct.

Let's move on to the second lesson cycle.

For this lesson cycle, you're going to be explaining the relationship between 4s and 8s.

How many groups of four and eight are there? And we're going to use our number line to identify this.

So that's one group of 4, two groups of 4, three groups of 4, four groups of 4, five groups of 4, six groups of 4.

So 6 times 4 equals 24.

That's six 4s.

Then we've got one group of 8, two groups of 8, three groups of 8.

3 times 8 equals 24.

That's three 8s.

Now let's have a look at this example.

How many groups of four are there? One group of 4, two groups of 4, three groups of 4, four groups of 4, five groups of 4, six groups of 4, seven groups of 4, and eight groups of 4.

So there are eight groups of 4.

Four, eight times.

Or in other words, 8 times 4, which means there are 32 spots.

Now let's have a look at how many groups of 8 there are.

So that's one group of 8, two groups of 8, three groups of 8, and four groups of 8.

So there are four groups of 8.

So that's 8 four times.

Four times 8 equals 32.

Over to you.

How many ways can you group 24? So you can see that there are spots.

There are 24 spots altogether.

You can use the number line to help you.

So, how did you do? Well, these are the ways that you could have grouped 24.

You've got 1 times 24, one group of 24 which is 1 times 24.

2 times 12, 2, 12 times.

4 times 6, so 4, six times.

And then 8 times 3, that's 8, three times.

Now, Andeep has arranged an array.

Now arrays are super useful when it comes to multiplication, but they show us how many groups we can make.

So over to you.

How many groups of 4 do you think there are, and how many groups of 8 do you think there are? And is there a relationship between both? Well, we can see that there are six groups of 4, which means 6 times 4 is 24, we've got 24 altogether.

And there are three groups of 8.

What do you notice? When one factor doubles, the product also doubles.

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

And that's exactly what's happened here.

So, if we started off with 6 times 4, which is equal to 24, we can see that the six has halved to three, and the four has doubled to eight, which means we still end up with the same product and I think that's amazing because we can now use this rule to figure out so many other calculations.

But that's only if we apply this rule.

Over to you.

You're going to use the array to complete the questions, and I'll read the questions up to you.

How many groups of 4 are there? And how many groups of 8 are there? You can pause the video here and click Play when you're ready to rejoin us.

So, how did you do? For the first equation, you should have got eight groups of 4, which gives us 32.

Now, thinking about the rule we just learned.

If we halve eight to four, and then we can see that the four has doubled to eight, we should also get the same product which is 32.

So if you had the array in front of you, you would've circled eight groups of 4 and then four groups of 8.

Let's move on.

Andeep and Izzy are comparing the 4s and 8s times tables.

What is the same and what is different? Well, we can see that the products in the eight times tables are also in the four times tables Apart from multiplying by zero, multiples of eight are double the multiples of four.

And apart from multiplying by zero, multiples of four are half the multiples of eight.

Over to you.

Andeep believes that if all multiples of eight are multiples of four, then all multiples of four must be multiples of eight.

Do you agree? I'd like you to justify your thinking to your partner.

So, what did you discuss? Well, you may have said that Andeep is incorrect.

And that's because not all multiples of four are multiples of eight.

So let's have a look at this example.

12 is not a multiple of eight.

Four times 3 is 12, but we can see in our eight times tables, 12 is not there.

The closest multiples we have to 12 are 8 and 16.

So we do not say 12.

Let's move on.

So, Andeep is saying that if he knows 4 times 13 is 52, then he also knows that 8 times 13 is 104.

Do you agree? Justify your thinking to your partner? Think about what has happened to one of the factors and what's happened to the product.

So, what did you discuss? Well, Andeep is correct.

Because if we double a factor, then the product also doubles.

So we can see here that the 4 has doubled to 8.

The other factor is still the same.

So if we've doubled four to eight, that means our product must also double.

So 52 doubled is 104.

Now, Izzy is saying if we know that 8 times 12 is 96, then we also know 8 times 13 is equal to 8 times 12 add 4.

Do you agree? I'd like you to justify your thinking to your partner.

In this case, Izzy is incorrect, and that's because 8 times 13 is the same as they saying 13 groups of 8? Izzy has said that 13 groups of 8 is equal to 12 groups of 8, add 4.

She's added four instead of adding eight.

So, she should have added eight.

Over to you.

If Andeep knows that 8 times 8 is 64, then he says that he knows 4 times 8 is 32.

Do you agree? I'd like to justify your thinking to your partner.

So, how did you do? Well, Andeep is correct.

Because if we halve one of the factors, then the product also halves.

And we can see here that we've halved eight to four, which means 64 as our product will also need to be halved, and half of 64 is 32.

Back to you.

So if 8 times 11 is 88, then 4 times 11 is 44.

Is this true or false? You can pause the video here and then click Play when you're ready to rejoin us.

So what did you get? Well, it is true and that's because if we halve a factor, then the product also halves.

So we can see that 8 has been halve to 4, the other factor is the same.

So, we then need to halve 88, which gives us 44.

Izzy's completing the questions below.

We can see that there are numbers on the left, in the middle, and then on the right.

And we need to calculate the numbers that are in the middle.

Now, there's two sets of equations happening here.

We can see that Izzy has started by following the instructions on the arrows.

We need to help her complete the table.

So let's look at the top number.

Zero times 4 is equal to 0 times 8, which is 0.

Two times 4 is equal to 8.

So, 1 times 8 is also equal to 8.

Four times 4 is equal to 2 times 8.

That's 16.

Six times 4 is equal to 3 times 8.

That's 24.

Eight times 4 is equal to 4 times 8.

That's 32.

And 10 times 4 is equal to 5 times 8.

That's 40.

What do you notice? An even number times 4, gives you a product in the eight times tables.

And that's why we've got our even numbers on the left, so you can see that it goes up in twos.

These are all our even numbers.

So now I'd like you to use your knowledge of the 4s and 8s to complete this question.

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

How did you do? If I was solving this question, I'd look at my equation.

So I've got 12 times 4 and I've got 8 times 6.

Now, I can see that one of my factors has doubled.

So, 4 has doubled to 8, and one of my factors has halved, so 12 has halved to 6.

So, with this type of question, I know the product has to remain the same for both.

So I can actually just look at one side and calculate that.

So if 12 groups of 4 is 48, then six groups of 8 is 48.

Onto your main task for this lesson cycle.

For question 1, you're going to be using the array to complete the questions, how many groups of 4 are there and how many groups of 8 are there? And then what have you noticed? And then for question 2, you're going to be using the images to help you to fill in the gaps.

And then I'd like you to also fill in the gaps for the sentence below.

So products in the eight times tables are also in the.

And you can pause the video here, off you go, good luck with these tasks and click Play when you're ready to rejoin us.

So, how did you do? For question 1, you should have got 10 groups of 4 which is equal to 40.

And for the next part of this question, you should have got five groups of 8 is equal to 40.

And that's because we can see that because 4 has doubled to 8 and the product stayed the same, the other factor must have halved to get 40.

And what you should have noticed is that if you double a factor, then the product also doubles.

If you halve one factor and double the other, the product stays the same.

And for question 2, this is what you should have got.

So 6 times 4 is 24, 6 groups of 4 is 24.

So that means three groups of 8 is 24.

If you know that 10 groups of four is 40, then you know that five groups of 8 is 40.

So we've halved one of the factors and doubled the other, which gives us the same product.

And then if you know 12 groups of four is 48, then you also know that six groups of eight are 48.

And that's because, again, we've halved one factor and doubled the other, and it's given us the same product.

Lastly, products in the eight times tables are also in the four, and don't forget, the two times tables.

Well done.

We've made it to the end of this lesson.

And now we're going to summarise our learning.

So in this lesson, you explain the relationship between the multiples of four and multiples of eight.

By the end of this lesson, you should now understand that multiples of eight are double the multiples of four, and multiples of four are half the multiples of eight.

You also understand multiples of eight are all multiples of four, but not all multiples of four are multiples of eight.

Well done.

I really hope you enjoy this lesson.

You remember these facts so that they can help you to tackle other multiplication questions in the future.

I'll see you in the next lesson.