Lesson video

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

My name is Miss Coe.

And I'm really excited to be working with you on this math lesson today.

In this lesson, we're going to be thinking more closely about our two, four, and eight 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.

By the end of this lesson today, you will be able to say that you can solve problems using knowledge of the divisibility rules for two and four.

We have a few keywords in our lesson today.

I'm going to say them.

And I'd like you to say them back to me.

Are you ready? My turn, divisibility.

Your turn.

My turn, divisor.

Your turn.

My turn, multiple.

Your turn.

My turn, half.

Your turn.

My turn, halve.

Your turn.

Great job.

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

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

A divisor is a number that divides an integer, or whole number, exactly with no remainder.

So in the example six divided by three is equal to two, the three is the divisor.

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

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

This lesson is from a unit focusing on our two, four, and eight times table.

And hopefully, you're becoming more familiar with those multiplication facts.

In this lesson, we're going to be using the knowledge of divisibility rules for divisors of two and four to solve problems. And we have two cycles in our learning.

The first cycle we're going to be looking at the divisibility rules for two.

And then, the second cycle, we're going to be looking at the divisibility rules for four.

So if you are ready, let's get going with our first cycle.

In this lesson today, you're going to meet Andeep and Izzy.

And as always, they're going to be helping us with our math learning.

So let's start here.

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

So they can be super efficient.

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

Today, we're going to be focusing our attention on the divisibility rules for two and four.

Izzy is sorting out number cards into multiples of two.

So you can see there, she has number eight.

And she has represented that using eight counters.

She says that eight is a multiple of two because it is an even number.

All multiples of two are even.

Andeep is giving us a divisibility rule here.

If you could halve a number with no remainder, then it is a multiple of two.

So if we take eight and divide it into two equal groups, we can see that there is four in each group.

There is no remainder, none left over.

Therefore, eight is a multiple of two.

Eight is divisible by two.

It's s time for a quick check of your understanding.

Which of these numbers is a multiple of two? Explain how you know.

So we have 11, 12, and 13.

And we've represented them with counters.

Remember, think about what Andeep said about what happens when you halve a number to see if it's divisible by two.

Pause the video here.

Welcome back.

How did you get on? In this case, 12 is a multiple of two.

You can halve 12 with no remainder, so it is divisible by two.

12 is a multiple of two because this is an even number.

If I divide 12 into two equal groups, that is six.

11 and 13 are odd numbers.

If I was to halve 11 or 13, I couldn't do it without splitting one of the counters or leaving a remainder.

They are not multiples of two.

Izzy continues to look at different cards.

Now, she has the number 12.

Izzy knows that 12 is a multiple of two because you can halve 12 with no remainder.

And she knows that 12 is an even number.

We can see there that we've divided 12 into two equal groups.

12 halved, or 12 divided by two, is equal to six.

There is no remainder.

There are no counts left over.

This means that two is a divisors of 12.

So we can write an equation, 12 divided by two is equal to six.

In this case, two is the divisor.

Time to check your understanding.

Andeep says, "If the ones digit is an even number, it can be divided by two." Do you agree or disagree? You might want to try some numbers out.

Pause the video here and have a think.

Welcome back.

What did you think? Well, if we take a couple of examples here, we have 11 and 14.

14 has a ones digit of four, which is an even number.

14 is divisible by two because if you halve 14, you get two groups of seven, 11 ends in a one.

One is an odd number.

It is not divisible by two because you cannot halve 11 equally.

You end up with a remainder.

So Andeep is correct in saying that if the ones digit is an even number, then the whole number is divisible by two.

Izzy continues to think about numbers.

Now, she's thinking about whether 48 is a multiple of two.

So she's thinking about whether 48 is divisible by two.

Izzy isn't sure how to solve this.

48 isn't in her times tables.

She could start by counting in twos.

So she could go two, four, six, eight to see if it's a multiple of two.

But I wonder if there's a quicker way.

Ah, yes, thank you, Andeep.

Andeep is reminding us that if the ones digit is an even number, then the number is divisible by two.

In this case, the ones digit is an eight.

Eight is an even number.

That means that 48 is divisible by two.

And that also means that 48 is a multiple of two.

Now, Izzy here is looking at a larger number.

She's looking at the number 242.

She thinks she might be able to make an array to see if she can divide for 242 into two equal groups.

But, hmm, it would take ages.

You'd also need a lot of counters.

I think I'd lose count.

I wonder if there is a more efficient way to see if it's divisible by two.

Ah, that's right, Andeep.

If the one's digit is an even number, then it is divisible by two.

In 242, the one's digit is a two.

Two is an even number.

So that means that 242 is a multiple of two.

242 is divisible by two.

What about this one then? Izzy is now thinking about the number 340.

Again, she knows she can't really make an array because making an array of 340 counters would take a long time.

And she's probably going to lose count.

But, hmm, I'm not sure about that ones digit.

What do you think? Ah, Andeep is reminding us multiples of 10 end in a zero.

And multiples of 10 are even.

So if it is a multiple of 10, it ends in a zero, that means this is an even number.

So that means that 340 is also a multiple of two.

340 is divisible by two.

So to find out if the number is divisible by two, we can just look at the ones digit.

If it's an even number, then the whole number must be divisible by two.

Time to check your understanding.

Take a close look at these six numbers.

Circle or point out the multiples of two.

Think carefully about how we've been identifying multiples of two.

Pause the video here.

Welcome back.

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

148 is a multiple of two.

The ones digit is eight.

Eight is an even number, which means 148 is divisible by two, meaning it's a multiple of two.

390, remember, if it ends in a zero, it is a multiple of 10.

390 is a multiple of two.

298 also ends in an eight.

The ones digit is an eight.

Eight is an even number, so 298 is divisible by two.

Are there any others? That's right, you should have circled 206 as well.

Six is an even number.

It is divisible by two.

Therefore, 206 is a multiple of two.

245 and 173 and in odd numbers, five and three.

That means they are not multiples of two.

Time for your first practise task.

For question one, I'd like you to sort the number cards according to whether they can be divided by two equally or not.

Is the number two a multiple of two? If it's a multiple of two, it can be divided by equally by two.

If it's not multiple of two, it cannot be divided equally by two.

Think about how Andeep identifies multiples of two to help you out here.

For question two, I'd like you to think about some worded problems. A toy factory makes robot figurines and sells them in packs of two.

Can 488 figurines be divided into whole packs of two? What about 231 figurines? If either of them cannot be divided equally into whole packs of two, how many will be left over? Good luck with those two tasks.

And I'll see you shortly for some feedback.

Welcome back.

How did you get on? Question one, here are the numbers sorted correctly.

Let us take a closer look at a couple of them.

Hopefully, you remembered that if the ones digit was even, then that meant the number could be divided equally by two.

For 150, we know that that's a multiple of 10 because it ends in zero.

And we know that all multiples of 10 are also even numbers.

So it can be divided equally by two.

In the second column, all of the ones digits are odd.

If we look at 429, nine is in the ones place.

Nine is an odd number, which means there would be a remainder if you divided it by two.

These numbers are not multiples of two.

Well done if you sorted them correctly.

Let us take a look at question two.

If the toy factory puts robot figurines into packs of two, then 488 can be divided into whole packs of two.

This is because the ones digit is eight.

That's an even number.

So that means 488 is divisible by two.

231, however, is not divisible by two.

The one digit is a one, which is an odd number.

So that cannot be divided by two.

230, however, can be.

So there would be one figurine left over.

Well done if you answered those correctly.

Let us move on to the second parts of our learning where we're looking at the divisibility rule for four.

This time we're going to be thinking about multiples of four.

So we've thought about multiples of two, or numbers that are by two.

Now, we're thinking about multiples of four.

A multiple of four is a number that can be made exactly from groups of four.

So Izzy uses her counters again to see if she can find some multiples of four.

We can see that four here is one group of four and eight is two groups of four.

Four and eight are both multiples of four because they can be made exactly from groups of four.

Like we've been looking at for multiples of two, there is also a divisibility rule for multiples of four.

If half of the number is an even number, then the number is a multiple of four.

Let us take a closer look at what that means.

If we take four, we know four is a multiple of four.

Half of four is two.

Two is an even number.

That means that four is divisible by four.

Four is a multiple of four.

Half of eight is four.

Four is an even number.

So we also know that eight is divisible by four and eight is a multiple of four.

Izzy continues to use counters to see if she can find multiples of four.

She has the number 21.

So she's represented 21 with counters.

Andeep is reminding us that if we halve a number and the result of that is an even number, then the whole number is divisible by four.

Hmm, can we halve 21 into two equal parts? Well, no, 21 is an odd number.

Halving it to results in a remainder.

And we can see that here.

If you divide 21 counts into two equal groups, we have two equal groups of 10.

But we have one counter left over.

So we have a remainder of one.

So therefore, we don't have an even result.

That means that the number is not a multiple of four.

Izzy says that no odd numbers can be halved without a remainder.

So that means that no odd numbers are a multiple of four.

21 is not a multiple of four.

So it's not divisible by four.

Izzy looks at 22.

She says, "Well, 22 is an even number." So she thinks it's going to be divisible by four.

Hmm, do you agree Andeep? What do you think? Do you agree that because 22 is an even number, it will be divisible by four? Let's see.

Andeep is reminding us that if we halve a number and we get an even result, the number itself is divisible by four.

What happens when we halve 22? We know we can halve 22 because it's even.

But half of 22 is 11.

And we can show that by rearranging the counters.

I've divided 22 into two equal groups.

And there are 11 counters in each group.

Hmm, 11 is an odd number.

So that means 22 is not divisible by four.

If we tried to make four equal groups from 22 counters, we wouldn't be able to do it.

We would have a leftover.

So we can say that 22 is not a multiple of four.

So it is not divisible by four.

Time to check your understanding.

Using the halving method that we've just looked at, find the number that is divisible by four.

So we have nine, 16, and 22.

Use counters if you need to.

Pause the video here.

Welcome back.

How did you get on? The number here that is divisible by four is 16.

Half of 16 is eight.

Eight is an even number.

So that means that 16 is a multiple of four.

Well done if you spotted that.

Another check for your understanding here.

Why aren't all even numbers divisible by four? Can you find some examples? Pause the video here and have a think.

Welcome back.

What did you find? Well, some even numbers have an odd number answer when they are halved.

For example, half of 26 is 13.

Half of 42 is 21.

13 and 21 are odd numbers.

Remember, a multiple of four is only when halving results in an even number.

So 26 and 42 are even numbers to start with.

But halving them gives an odd answer, which means that they are not divisible by four.

Well done if you said that.

And well done if you found some examples.

Izzy continues to source number cards into multiples of four.

She has the number card 100.

Hmm, she says, "It's a large number." She's not sure she has 100 counters.

And as before, finding 100 counters would be time-consuming.

And she perhaps wouldn't be very efficient or accurate.

Andeep is reminding us that we can use the Divisibility rule on larger numbers as well.

He knows that double 50 is 100, which means that half of 100 is 50.

Now, we know that if we halve a number and the answer is even, it must be divisible by four.

Is 50 an even number? Absolutely right, Andeep.

50 is an even number.

So that means 100 is a multiple of four.

But we can always halve it again to check.

So we're dividing it into four equal groups.

Half of 50 is 25.

25 is a whole number.

There's none left over.

So 100 divided into four equal groups is 25, which means that 100 is a multiple of four.

And it's divisible by four.

Andeep and Izzy decide to play a game.

They're trying to find multiples of four.

Izzy goes, "Well, I've already circled the multiples of four.

And she circles 104 and 328 immediately.

"How did you do that so quickly," asks Andeep.

I was pretty impressed as well, were you? How does she do it so quickly? "Well," says Izzy, "I know 100, it's divisible by four.

So any number of hundreds will be two." 100 is divisible by 4, 200, 300, 400, and so on.

This means that she only needs to look at the last two digits.

So we've got four in 104.

And she knows that four is a multiple of four.

So 104 is a multiple of four.

With 328, the last two digits are two tens and eight ones, or 28.

Andeep is reminding us that we can use our times table flats here.

Seven multiplied by four is equal to 28.

So 28 is a multiple of four, then 328 is a multiple too.

28 is divisible by four.

So 328 is divisible by four.

Did you spot anything else about the two numbers that Izzy circled? Ah, that's a great strategy, Izzy.

She says 825 and 621 are odd numbers.

And we know that odd numbers are not divisible by four.

Therefore, they can't be.

So they're easy to rule out.

Time to check your understanding.

Which three digit number here is divisible by four, 825, 626.

288? Remember, a good way to check is the last two digits need to be divisible by four.

Pause the video here and have a think.

welcome back.

How did you get on? 288 is the three digit number that is divisible by four.

If we look at the last two digits, which is 88, 88 is a multiple of four because if you halve it, you get 44.

44 is an even number.

We know the hundreds are divisible by four.

So that means that 288 is also divisible by four.

825 definitely isn't because this is an odd number.

626 is an even number.

But if I halve 26, I get 13.

13 is an odd number, which means 626 is not divisible by four.

Well done if you spotted that.

We can also solve worded problems using these divisibility rules.

Here is an example.

A bakery has baked 26 desserts and it packs them into boxes of four.

Can 26 cupcakes be packed into boxes of four? Hmm, I wonder.

Can we use our divisibility rules? Izzy says, "We can use our halving method to solve this." Half of 26 is 13.

13 is not an even number.

So that means there would be some cupcakes left over, as we can see in the picture.

If we divide 26 into groups of four, we have six groups of four with two left over.

That means that 26 is not divisible by four.

So 26 cupcakes can't be boxed up in full boxes of four.

There'd be a couple of cakes left over.

Time to check your understanding.

Is 34 a multiple of four? Use the halving method that we've been using.

Pause the video here.

Welcome back.

Now, you may have thought that 34 was a multiple of four because it is an even number.

However, if we halve 34, we get 17.

17 is not an even number.

It couldn't be halved again without a remainder.

That means that 34 is not a multiple of four.

Well done of you said that.

Time for your second practise task.

For question one, I'd like you to circle the numbers that are divisible by four.

So think about the strategies that we've used so far.

For example, if you think 48 is divisible by four, then you can circle it.

If you think 109 is, circle it.

Take care to look carefully at the digits in each number, particularly, the ones digits.

For question two, there are some worded problems for you to think about.

A factory sells desserts in packs of four.

Can 364 desserts be divided into whole packs of four? What about 486 desserts? What about 789 desserts? And the last question, how many desserts will be left over from question C, 789 desserts? Good luck with those two tasks.

Pause the video here.

And I'll see you shortly for some feedback.

Welcome back.

How did you get on? Let us take a look at question one where we're thinking about the numbers that are divisible by four.

Did you halve 48 and 96 to check? Half of 48 is 24, half of 96 is 48.

Both of those are even numbers, which means 48 and 96 are divisible by four.

These other numbers are also divisible by four, 220, 208, 148, 312, and 116.

For these ones, you could just half the tens and ones.

So for example, half of 48 is 24, which is even.

So that means that 148 is a multiple of four.

It is divisible by four.

Did you notice that 109, 251, and 241 are odd? So they just can't be multiples of four.

And finally, if you halve 106, you get 53.

53 is an odd number.

So that means that 106 is not divisible by four.

Well done if you circled all of those numbers to show that those ones are divisible by four.

For question two, a factory cells desserts impacts a four.

Can 364 desserts be divided into whole packs of four? Well, yes.

We can just look at 64.

Remember, three hundreds can always be divided into four equal groups.

Half of 64 is 32.

32 is an even number.

So that means 364 desserts can be divided into whole packs of four.

What's about 486? Well, again, we can look at the last two digits.

86.

86 is not a multiple of four.

Because if we have 86, we get 43.

43 is an odd number.

So 486 desserts cannot be divided into packs of four.

What about 789 desserts? Well, 789 is an odd number.

The digit nine is odd.

That means that it can't be a multiple of four.

For D, 788, however, is a multiple of four because 88 divided by two, or 88 halved, is 44.

So that means there would be one dessert left over.

Well done if that's what you've got.

We've come to the end of the lesson where we've been using the knowledge of the divisibility rules for divisors of two and four to solve problems. And I know how hard you've worked.

Let's summarise our learning.

We understand that if you can halve a number and get a whole number, it must be a multiple of two and divisible by two.

We also know that if you halve a number and the result is even, then that number is a multiple of four and divisible by four.

We also know that if a number is divisible by four, then it must be divisible by two.

But not all multiples of two are multiples of four.

So watch out for that.

Thank you so much for all of your hard work in this lesson.

I've really enjoyed working with you.

And I hope to see you in another maths lesson soon.