Lesson video

Hi there, how are you today? I hope that you're having a really good day.

My name is Ms. Coe, and I'm really excited to be working with you on this maths lesson today.

In this lesson, we're going to be thinking more closely about our 2, 4, and 8-times table, and I hope that you're becoming more and more familiar with some of those times table facts.

If you're ready to get going, let's get started.

This lesson is part of the unit focusing on the 2, 4, and 8-times table, and hopefully you're becoming increasingly more familiar with those times table facts.

By the end of this lesson, you will be able to say that you can solve problems using knowledge of the divisibility rule for 8.

So, we have a few key words in this lesson today.

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

Are you ready? My turn, half, your turn.

My turn, half, your turn.

My turn, divisible, your turn.

My turn, divisibility, your turn.

Let's take a look at what those words mean.

A half is one of two equal parts of a whole.

Divisibility is when division of a number results in another whole number.

A number is divisible by another if it can be shared exactly with no remainder.

In our lesson today, we're going to be using the knowledge of the divisibility rule for divisors 8 to solve problems, and you may be familiar with divisibility rules for other numbers like 2 and 4.

In the first part of our lesson, we're going to be looking at the divisibility rule for 8, and then we're going to be solving problems. Let's get started with the first cycle of our learning.

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

So, let's start here.

Divisibility rules can help you figure out if a number can be divided by another number without having to do too much calculation.

They are helpful to test whether a number is a multiple of another.

Today, we're going to be focusing on the divisibility rules for 8.

You may be familiar with some other divisibility rules and also may be familiar with other multiples.

It's useful in this lesson to remember that a multiple of 4 is a number in the 4 times table.

Andeep is reminding us of the divisibility rule for 4.

If you halve a number and the result is even, then it is a multiple of 4.

So, if we halve 8, we get 4.

Two groups of 4 is equal to 8.

Half of 8 is 4.

4 is an even number, so therefore 8 is divisible by 4.

It's a multiple of 4.

8 is a multiple of 4 because it's divisible by 4.

It's also divisible by 2 because it's an even number.

Izzy is going to use arrays and counters to see if numbers are multiples of 8.

A multiple of 8 is a number that can be made of groups of 8.

So, if we look at the number 8, there are 8 counters here.

8 is a multiple of 8 because it is one group of 8.

Just like 4, which you may have some recent experience of, we can use a divisibility rule to check if a number is a multiple of 8.

A number is a multiple of 8 if you can halve it and halve it again, and the result is an even number.

Let's take a look with 8.

Half of 8 is 4.

Half of 4 is 2.

So, we've halved it once, and if we halve it again, we have 2.

2 is an even number, which means that 8 is divisible by 8.

Izzy continues to make arrays using counters to look for multiples of 8.

She knows that 16 is an even number, but is it divisible by 8? I wonder.

Remember, if we halve a number twice and the result is even, then it is divisible by 8.

Half of 16 is 8.

We can see that if we divide the counters into two equal groups, half of 16 is 8, half again is 4.

4 is an even number, so that means that 16 is a multiple of 8.

And Andeep is reminding us of that numbers that are divisible by 8 are also divisible by 4 and 2.

So that can be a useful way to think about whether a number is a multiple of 8.

So, Izzy knows that 16 is a multiple of 8, and it is divisible by 8.

If we skip counting 8, 0, 8, 16, we say 16, so it's a multiple of 8.

That means that 8 is a factor of 16.

We can also write a division equation.

16 divided by 8 is equal to 2.

8 is the divisor, because it's the divisibility rule for 8 that we're thinking about.

Time to check your understanding.

Which of these numbers is a multiple of 8? Think carefully about our divisibility rule for 8.

If you can halve the number and halve it again, and the result is even, then that number is divisible by 8.

Pause the video here and have a think about these three numbers.

Welcome back.

How did you get on? In this case, B, 40, is divisible by 8.

If you halve 40, you get 20.

20 is a multiple of 4.

If we halve it again, we get 10.

10 is an even number.

This means that it's divisible by 8.

43 is an odd number.

We know that halving it once is not going to result in an even number, so we can't halve it twice.

If we halve 44, we get 22.

If we halve 22, we get 11.

11 is not an even number, so 44 is not divisible by 8.

Izzy continues to make arrays to look for multiples of 8.

She's made the number 23 using counters.

I wonder, is 23 a multiple of 8? Is it divisible by 8? She says, well, it's not an even number, so does that mean it can't be divisible by 8? Half of 23 does not give a whole number.

If we show half of 23, we can see that half of 23 is 11, but we have one left over.

So, it's a remainder of 1.

If you can't halve a number, then it can't be a multiple of 8.

That means that only even numbers have a chance of being divisible by 8.

So, Izzy carries on.

This time she looks at the number 26.

Is 26 a multiple of 8? Well, she says it's an even number, so therefore it must be a multiple of 8.

What do you think? Do you agree? Well, it is an even number, says Andeep.

Half of 26 is 13.

We can divide 26 into two equal groups, but if we need to halve it again to get an even number, half of 13 is not even.

It would leave a remainder.

That means that 26 is not divisible by 8.

Time to check your understanding.

Circle the multiples of 8.

Explain how you know.

Think about what we've learned so far about multiples of 8.

Pause the video here and have a think.

Welcome back.

How did you get on? Did you remember that if you halve the number twice and the result is even, then the number is a multiple of 8? For example, if we halve 88, that's 44.

If we halve 44, that's 22.

22 is an even number.

That means that 88 is a multiple of 8.

32 is also a multiple of 8.

If you halve 32, you get 16.

Half of 16 is 8.

8 is even, therefore, 32 is a multiple of 8.

72 is also a multiple of 8.

Half of 72 is 36.

Half of 36 is 18.

18 is an even number.

Therefore, 72 is a multiple of 8.

56 is also a multiple of 8.

Half of 56 is 28.

Half of 28 is 14.

Therefore, 56 is a multiple of 8.

28, however, is not a multiple of 8.

Half of 28 is 14.

Half of 14 is 7.

7 is an odd number, which means 28 is not a multiple of 8.

And hopefully you spotted that 41 is an odd number.

Odd numbers are not multiples of 8.

Well done if you identified those four multiples of 8.

Izzy continues to think about numbers to see whether they are multiples of 8.

She has the number 104, and she says, I'm not sure how to solve this.

104 is not in my times tables.

She could count in eighths to find out if it's a multiple of 8, but I think she'd be there for quite a long time, and she might lose her place and have to start again.

Izzy can halve and halve again to find out if it's a multiple of 8.

Remember, if that results in an even number, it's a multiple of 8.

To help her halve, she can partition 104 to halve it more efficiently.

Let's see.

104 can be partitioned into 100 and 4, so we can halve both of those to see if that so far is an even number.

Half of 100 is 50.

Half of 4 is 2.

50 plus 2 is 52.

We've halved 104 once, and we have 52.

So far, so good.

What happens if we halve it again? Do we get an even number? Half of 52 is 26, says Izzy, and 26 is an even number, which means that 104 is divisible by 8.

Now Izzy tries to work out whether 104 is a multiple of 8, and she says she can also use her multiplication facts to help her.

I wonder what she means.

Let's find out.

Andeep is reminding us that if we halve the number and it's a multiple of 4, then it's divisible by 8.

104 halved or divided by 2 is equal to 52.

So Andeep says that that means 104 is a multiple of 8.

I wonder how he knows.

Well, 52 is a multiple of 4 because he knows that 4 times 12 is 48.

52 is 4 more than 48, which means it must be 13 groups of 4, or 4 multiplied by 13.

So, we can sometimes use our multiplication facts to help us work it out without having to halve again.

We could also halve 52 again.

Half of 52 is 26.

26 is an even number, so that's further proof that 104 is a multiple of 8.

Izzy is now trying to calculate whether 200 is a multiple of 8.

She knows that 100 is not a multiple of 8, because if you halve 100, you get 50.

Halve it again, you get 25.

25 is odd.

So, she says that if 100 is not a multiple of 8, then 200 can't be a multiple of 8 either.

What do you think? Do you agree? Andeep decides to use some base 10 equipment to show his understanding of this.

He says if you halve the number twice and it's even, it's divisible by 8.

So, if we halve 200, we get 100.

And if we halve it again, we get 50.

50 is an even number.

So that must mean that 200 is a multiple of 8.

200 divided by 8 is equal to 25.

You can make 8 groups of 25 from 200.

Time to check your understanding.

Calculate whether 300 is a multiple of 8.

You might want to use base 10 blocks to help you here.

Andeep is reminding us that if you can halve the number twice and it is even, it is divisible by 8.

Pause the video here and have a think.

Welcome back.

How did you get on? Well, you may have thought that because 200 is divisible by 8, then 300 is also divisible by 8.

However, if you halve and halve again, then you get 75.

75 is not even.

So, while 200 is a multiple of 8, 300 is not a multiple of 8.

Well done if you spotted that.

Another quick check of your understanding here.

Which three-digit number is divisible by 8? 423, 100, 240.

Andeep is reminding you that to halve and halve again, you might need to partition some of these numbers to check to see if that results in an even number.

Pause the video here and have a think.

Welcome back.

How did you get on? 240 is divisible by 8.

Half of 240 is 120.

Half of 120 is 60.

60 is an even number.

Therefore, 240 is divisible by 8.

423 is an odd number, so we know that's not divisible by 8.

And if you halve 100 and halve it again, you get 25.

And we know 25 is an odd number, so 100 is not divisible by 8.

Well done if you said C, 240 is divisible by 8.

Izzy continues to look at numbers to see if they are multiples of 8, and she has the number 390.

And she says, I'm not sure how to solve this.

If I use an array of counters, well, that's 390 counters.

That's gonna take her a very long time.

Andeep is reminding us of the divisibility rule for 8.

If you can halve the number and it's a multiple of 4, then it's divisible by 8.

Or we can halve it again and check that it's even.

Half of 390 is 195.

Now you may do that by partitioning.

Half of 300 is 150.

Half of 90 is 45.

Add those together, you get 195.

195 is an odd number.

It's not a multiple of 4 because it's not even.

That means that 390 is not a multiple of 8.

That was a bit quicker than trying to halve it and halve it again.

Time to check your understanding.

Circle the multiples of 8.

So, we have 152, 208, 245, 173.

Which of these are multiples of 8? Can you discount some instantly? Pause the video and have a think.

Welcome back.

How did you get on? 152 and 208 are multiples of 8.

For example, if you halve 208, you get 104.

104 is a multiple of 4 because we know 100 is a multiple of 4 and 4 is a multiple of 4.

We could also halve it again.

104 divided by 2 is 52.

52 is an even number.

Therefore, 208 is a multiple of 8.

Did you notice that 245 and 173 are odd numbers, which means they are not multiples of 8? Well done if you spotted those.

Time for your first practise task.

For question one, I'd like you to circle the numbers that are divisible by 8 and explain how you know that they're divisible by 8.

So, a selection of numbers there.

Good luck with that.

Pause the video here and come back shortly for some feedback.

Welcome back.

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

24 and 96 are divisible by 8.

You may have noticed that 96 is divisible by 8 because it is made up of 80 and 16.

Both of those are multiples of 8.

10 times 8 is 80.

2 times 8 is 16.

Therefore, 96 is a multiple of 8.

232 and 224 are also multiples of 8 and divisible by 8.

You may have noticed that half of 224 is 112.

We know that 112 are both divisible by 4.

Therefore, 224 must be divisible by 8.

What about the others? Well, if we halve 42, we get 21.

21 is an odd number, so we can't halve it again without a remainder.

That means 42, 242, and 142 are all not divisible by 8.

What about 108? Well, it looks like it could be divisible by 8.

However, half of 108 is 54.

Half of 54 is 27.

27 is an odd number, so 108 is not divisible.

For 106, we know that 100 is not divisible by 8, and we also know that 6 is not divisible by 8, which means that 106 must also not be divisible by 8.

Well done if you identified those four numbers that were divisible by 8 and if you gave really good reasons for why you knew that they were divisible by 8.

Let's move on to the second cycle of our learning, where we're solving problems using this divisibility rule.

So, we can also solve worded problems thinking about this divisibility rule.

Here is an example of a problem that you could solve in this way.

A bakery has baked 33 cupcakes.

It packs them into full boxes of 8.

But can 33 cupcakes be packed into full boxes of 8? I wonder.

Izzy is reminding us that we can use the halving and halving method to solve this.

So, we have 33 cupcakes.

Half of 33 is not an even number.

It has a leftover or a remainder, which means that it's not a multiple of 4.

And that also means that it is not a multiple of 8.

So, you can't pack 33 cupcakes into equal groups of 8.

As you can see from the picture, we have one cupcake left over.

That means that 33 is not a multiple of 8.

Time to check your understanding.

Is 35 a multiple of 8? Use the halving method to determine whether it's a multiple of 4 first.

Pause the video here and have a think.

Welcome back.

Well, if we half 35, we do not get a whole number answer.

We have a remainder.

We can't make 4 equal groups if we have 35 cupcakes.

So that means if you can't make 4 equal groups, you can't make 8 equal groups.

So, 35 is not a multiple of 8.

And we can see here that if we try and divide it into equal groups of 8, we end up with 3 left over.

Well done if you spotted that.

Let's look at another worded problem.

A bakery has baked 120 cupcakes.

It packs them into boxes of 8.

Can 120 cupcakes be packed into boxes of 8? So, we have an example there of what a box of 8 might look like.

What do we know? What do we not know? So, what is unknown? How else could you represent this problem? Well, we know that there are 120 cupcakes, and that is our dividend.

And they're going to be packed into boxes of 8.

8 is our divisor.

I think we know a divisibility rule for 8 that's going to help us here.

We don't know our quotient, which is the amount of boxes required.

This problem can also be represented as a bar model.

So, we can see that we have 120 cupcakes.

We know that one box is 8, but we don't know how many boxes or how many groups of 8 we're going to need.

Izzy is reminding us that to solve this problem, we can use our knowledge of the relationship between the 4s and 8s and divisibility rules to help us.

So, we could try halving 120.

If the result is a multiple of 4, then we also know that 120 will be a multiple of 8, which means we could pack 120 cupcakes into boxes of 8.

Remember, if the number is a multiple of 4, it's also a multiple of 8, because the multiples of 8 are double the multiples of 4.

Half of 120 is 60.

60 is made up of 40 and 20, so I can partition 16 into 40 and 20.

40 and 20 are both multiples of 4, so that means 60 must be a multiple of 4.

If 60 is a multiple of 4, then 120 must be a multiple of 8.

So, you can pack 120 cupcakes into boxes of 8 equally.

120 is a multiple of 8.

Time for your second practise task.

Complete the questions.

You can use a bar model to help you represent the problem if you need to.

A bakery bakes buns and sells them in packs of 8.

Can 320 buns be divided into packs of 8? What about 200 buns? What about 420 buns? How many buns will be left over if there are any left over in C? Pause the video here, have a go at those questions, and come back when you're ready for some feedback.

Welcome back.

How did you get on? For question one, you may have drawn a bar model.

You knew that there were 320 buns all together.

One box is 8 buns, so we needed to know how many boxes we would need.

And we needed to know if we could actually make full boxes of 8 buns with 320.

Well, if we half 320, that's 160.

160 is a multiple of 4, which means it's also a multiple of 8.

We know 160 is a multiple of 4 in lots of different ways, but I knew that is 16 tens.

I know 16 is a multiple of 4, so 16 tens is also a multiple of 4.

That means that 320 buns would be divided into packs of 8.

For B, we asked whether 200 buns could be divided into packs of 8.

And the answer to that is also yes.

Half of 200 is 100.

100 is a multiple of 4, which means that 200 is also a multiple of 8.

For C, 420 buns this time.

Well, no, they can't be divided into packs of 8.

Half of 420 is 210.

210 is not a multiple of 4.

We could also half 210 again.

Half of 210 is 105.

105 is odd.

That means that it is not a multiple of 8.

We could not make full boxes of 8 buns from 420 buns.

4 buns would be left over.

Well done if that's what you said.

We've come to the end of the lesson, and I know how hard you've worked using your knowledge of the divisibility rule for divisors of 8 to solve problems. Let's summarise our learning.

To check divisibility by 8, we can half twice.

If the result is even, the number is a multiple of 8 and divisible by 8.

We also know that if we half a number and the result is a multiple of 4, then the number is also divisible by 8, because multiples of 8 are double multiples of 4.

We also know that odd numbers are not divisible by 8.

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