Lesson video

Hi, everyone.

My name is Ms. Ku, and I'm really excited to be learning with you today.

It's gonna be an interesting and fun lesson.

We'll be building on some previous knowledge, as well as looking at some keywords that you may or may not know.

It might be easy or hard in some places, but I'll be here to help.

I'm really excited to be learning with you, so we can learn together.

Hi, everyone.

In today's lesson, from the unit Properties of number: factors, multiples, squares, and cubes, we'll be looking at the divisibility test for 4 and 8, and by the end of the lesson, you'll be able to identify and explain whether a number is a multiple or 4 or 8.

So let's start by looking at our keywords.

The first keyword that we'll be looking at is divisibility, and divisibility is a mathematical concept that refers to one number's ability to be exactly divided by another number, leaving no remainder.

For example, the divisibility test for 2.

That means we can test if a number is a multiple for 2 by simply looking at the digit in the ones column.

And if the digit in the ones column is a 0, 2, 4, 6, or 8, then we know it's divisible by 2.

For example, 794.

This is divisible by 2 because the digit in the ones column is a 4.

A non-example would be 9,351.

This is not divisible by 2 because the digit in the ones column is a 1.

Our lesson today will consist of two parts, so let's have a little look at the first part, divisibility test for 4.

We know the divisibility test for 2 states that the digit in the ones column has to be a 0, 2, 4, 6, or 8.

So given that 4 is a multiple of 2, does this mean all the multiples of 4 are also multiples of 2? So let's identify by listing the first ten multiples of 4.

We have 4, 8, 12, 16, 20, 24, 28, 32, 36, and 40.

Now, let's identify the first ten multiples of 2.

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

So the question is, does this mean all multiples of 4 are also multiples of 2? Well, let's identify all our multiples of 4.

Are these multiples of 4 also multiples of 2? Yes, they are.

So that means yes, we know that all the multiples of 4 are also multiples of 2.

So let's change the question a little bit.

Does this mean all the multiples of 2 are also all multiples of 4? Well, let's identify all our multiples of 2.

Are all these multiples of 2 also all multiples of 4? Well, hopefully, you can spot 2, 6, 10, 14, and 18 are multiples of 2, but they're not multiples of 4.

So the answer is no, because 2 is not a multiple of 4.

So let's move on to the divisibility test for 4.

All I've done is identify all the multiples of 4 up to and including 100.

Now, do you notice a pattern? There are lots of lovely patterns with the multiple of 4, but there's something very important about 4 being a factor of 100, or 100 being a multiple of 4.

And what I want you to do is see if you can figure out if 38,834,864 is divisible by 4 by simply using the information that I've put on the screen.

This is quite tough.

See if you can figure it out.

Well, hopefully, you've spot it.

Knowing that 4 is a factor of 100, that means we immediately know that 4 is a factor of the 38,834,800, so we know for sure 4 is a factor of that big number.

So that means we need to only look at the last two digits, which are 64, and we know 64 is a multiple of 4.

So that means we know that 38,834,864 is a multiple of 4.

That's because we only look at the last two digits of any integer number.

So the divisibility test for 4 states that a number is a multiple of 4 if the last two digits are a multiple of 4.

So let's check for understanding.

In this question, it wants us to identify which of the following is a multiple of 4, and there can be more than one answer.

I'd also like you to justify your answer.

We have 4 numbers.

A is 44,898,434, B is 378,432, C is a huge number, 5,984,438,424, and D is 389,308.

You can see why we use divisibility tests, as they're a quick and easy process compared to something like long division or short division.

See if you can give this a go, and press pause if you need.

Well done.

So let's have a look at the last two digits of each of our numbers.

For A, we have 34, for B, we have 32, for C, we have 24, and for D, we have 8.

Hopefully, from this, you've spotted that we have B is a multiple of 4 because we know the last two digits are 32, and 32 is a multiple of 4.

You also would've spotted C is a multiple of 4, as the last two digits are 24, and 24 is a multiple of 4.

You may have also got D is also a multiple of 4.

The last two digits are 08, or just 8, and 8 is a multiple of 4.

A huge well done if you got this one right.

So let's have a look at another check question.

Here, we have three trucks, and each truck is transporting fruit to supermarkets.

Now, fruit is sold in multiples of 4, and unfortunately, one truck has lost six pieces of fruit.

Which truck lost the fruit, and can you explain your answer? We have three trucks here.

Truck A has 8,384 pieces of fruit, Truck B has 9,162 pieces of fruit, and C has 7,228 pieces of fruit.

See if you can give it a go, and press pause if you need.

Well done.

So hopefully, you've identified we have to use our divisibility test for 4.

Because if we find which trucks have a multiple of 4, that means we know they haven't lost any fruit.

Looking at the last two digits, 84, 62, and 28, 62 is not a multiple of 4, so Truck B is the truck that lost the six pieces of fruit.

Well done if you got that one correct.

Now, let's move on to your task.

For part A, it wants you to identify the multiples of 4 from the list.

Now, question two wants you to identify multiples of 4 and 5 from the list.

Use those divisibility tests for 4 and the divisibility test for 5 to work out the answers.

Press pause if you need more time.

Well done.

So let's move on to the next question.

Here, we have a table, and in our table, we need to identify if the statements are sometimes true, always true, or never true.

So let's have a look at our first statement.

A multiple of 4 is a multiple of 2.

Is that sometimes true, always true, or never true? Our next statement is a multiple of 2 is a multiple of 4.

Is that sometimes true, always true, or never true? Our next statement is a multiple of 10 is a multiple of 2.

Do you think that's sometimes true, always true, or never true? The next statement is a multiple of 9 is also a multiple of 3.

Do you think that's sometimes true, always true, or never true? The next one is a multiple of 8 is odd.

Do you think that's sometimes true, always true, or never true? And lastly, are multiples of 40, are they also multiples of 5, 8, and 10? Is that sometimes true, always true, or never true? See if you can give this a go, and press pause if you need.

Well done.

So let's go through these answers.

For question one, you should have circled the following answers.

Remember, for question 1a and b, you're only looking at the last two digits.

From these last two digits, if it's a multiple of 4, that means you know the number is a multiple of 4.

Now, let's have a look at question two.

For question two we needed to identify if it's a multiple of 4 and 5.

Now, remember, if something is a multiple of 5, it will always end in a 0 or 5.

Looking at all our numbers, that doesn't really help us out.

So we have to identify multiples of 4 by looking at the last two digits.

A huge well done if you got that one right.

Let's have a look at question three, and looking at our statements, we had to identify if it's sometimes true, always true, or never true.

So our first statement was a multiple of 4 is a multiple of 2.

That is always true.

Well done.

We looked at that at the start of the lesson.

So that means is the statement a multiple of 2 is a multiple of 4, is that sometimes true, always true, or never true? Well, it's sometimes true.

Remember our examples.

2, 6, and 10, they're all multiples of 2, but they are not multiples of 4, but we do have multiples of 2 which are multiples of 4, so that's why it's sometimes true.

The next statement says a multiple of 10 is a multiple of 2.

That's always true because we know 2 is a factor of 10.

So that will always be true.

Think about all your multiples of 10.

10, 20, 30, 40, so on and so forth.

Every single multiple of 10 is a multiple of 2.

Next, a multiple of 9 is a multiple of 3.

That's always true.

Same again.

Think of your multiples of 9.

9, 18, 27, so on and so forth.

All of these numbers are multiples of 3.

This is because 3 is a factor of 9, or 9 is a multiple of 3.

Next, we have the statement a multiple of 8 is odd.

This is never true.

This is because we know 8 is an even number.

Therefore, all multiples of an even number will always be even.

Lastly, multiples of 40 are multiples of 5, 8, and 10.

That's always true.

That's because 5, 8, and 10 are factors of 40.

A huge well done if you got this one right.

Fantastic work so far.

So let's move on to the second part of our lesson, which is divisibility tests for 8.

Now, divisibility tests for 4 works when the last two digits are divisible by 4.

Now, this is because we know 100 is a multiple of 4.

However, 100 is not a multiple of 8.

But what I want you to do is have a look at all of these multiples of 8, up to and including 1,000.

How do you think we might test for divisibility by 8? Well, we certainly know 8 is not a factor of 100, so that means we can't look at the last two digits.

However, what we do know is 8 is a factor of 1,000.

So this means as 8 is a factor of 1,000, if we look at the last three digits of a number, if it's a multiple of 8, then we know a number is divisible by 8.

So let's have a look at an example.

Well, we have 7,160.

So we know 8 is a factor of the seven-thousands because 8 is a factor of 1,000.

So that means we need to have a look at the last three digits, 160.

Is 160 a multiple of 8? Yes, it is.

So that means we know 7,160 is a multiple of 8.

Let's have a look at another example, a bigger number.

We have 138,293,144.

Well, we know 3,000 is a multiple of 8 because 8 is a factor of 1,000.

So that means we know 90,000 is also a multiple of 8, as we know 200,000, so on and so forth.

So we just simply need to look at the last three digits.

Is 144 a multiple of 8? Yes, it is.

So that means we know this huge number, 138,293,144, is a multiple of 8 by simply looking at those last three digits.

Now, let's have a look at a non-example.

Well, we have 293,666.

We know 3,000 is a multiple of 8, as 8 is a factor of 1,000.

So that means we know 90,000 is a multiple of 8, and we know 200,000 is a multiple of 8.

So looking at the last three digits, we have 666.

Is 666 a multiple of 8? No, it's not.

So that means we know 293,666 is not a multiple of 8.

Now, let's have a look at a check for understanding question.

Which of the following shows 385,248 is divisible by 8? Now, Jun says, "I know my 8 times table, "and I know 248 is a multiple of 8, "so that means I know 385,248 is divisible by 8." Andeep did some working out.

He used short division, and from the short division, he's identified that the last three digits are divisible by 8.

So 385,248 is divisible by 8.

Alex also did some working out.

He did some long division.

He divided the last three digits by 8.

So the 248 does divide by 8, so that means he knows 385,248 is divisible by 8.

So which one shows that this number is divisible by 8? Well, hopefully, you can spot they all do.

They are all really good ways in identifying if a number is divisible by 8.

By knowing your 8 times table, or by just simply dividing those last three digits by 8 and getting a, and achieving a whole number answer after division.

A huge well done if you identified all three methods are absolutely fine.

Another way in which you can identify if a number is divisible by 8 is by using partitioning.

Aisha uses a different method.

She uses a partitioning method to check if the same number, 385,248, is divisible by 8.

So what she does is she focuses on those last three digits, 248, and then she breaks it into its parts.

We have 200 and 40 and the 8 sums together to give our 248.

From here, she knows, well, 200 is made by multiplying 8 by 50, and 40 is made by multiplying 8 by 5, and 8 is made by multiplying 8 by 1.

As each of these parts has a factor of 8, that means we know 8 is a factor of 200, 40, and 8, so that means 385,248 is a multiple of 8.

So this is the method Aisha uses.

So let's have a look at another check question.

Can you identify which of the following is a multiple of 8? We have some huge numbers here.

You can choose any method you prefer and you're comfortable with to identify if those last three digits are a multiple of 8.

See if you can give it a go, and press pause if you need.

So looking at our last three digits, 348, 360, and 498, hopefully you've identified that B is the only answer, which is a multiple of 8.

So I'm going to use partitioning.

I'm breaking 360 into 300 and 60.

Now, these two numbers don't really help me out.

So what I'm gonna do is break them into 160, 160, and 40.

I've chose these numbers because I can identify factors of 8 more readily.

8 times 20 is 160, 8 times 20 is 160, and 8 by 5 is 40.

So immediately, I know 8 is a factor of 160 and 40, so that means we know this huge number, 789,483,839,360, is a multiple of 8, simply by looking at those last three digits.

Well done.

So now, let's move on to your task.

Here, you're asked to circle all the multiples of 8.

We have some big numbers here, so remember that divisibility test for 8.

So question two gives you two statements and a question.

It states all multiples of 2 and 3 are multiples of 6.

It states all the multiples of 3 and 5 are multiples of 15, and it wants you to explain why all the multiples of 2 and 8 are not all multiples of 16.

These are great questions.

Press pause if you need more time.

Well done.

So let's move on to the next part of our task, question three.

Question three wants you to fill in the missing information.

Some have been done for you.

You can see our Venn diagram, but we don't know what the multiples are, but we do know we have one number in our Venn diagram is given to be 160.

Can you complete our Venn diagram? See if you can give it a go, and press pause if you need.

Well done.

So let's go through our last question.

So question four states that you're playing a board game, and a multiple of 5 can move you 2 to the right, and a multiple of 3 can move you 3 up, a multiple of 8 can move you 4 to the left, and a multiple of 11 can move 1 left or right.

So question 4a wants you to pick a starting number in order for you to finish at the exit.

Do you start at 26? Do you start at 13? Do you start at 440? For B, it wants you to draw a path to win the game in as few moves as possible.

And part C, see if you can design your own game using multiples of 2, 3, 4, 6, 8, 9, or 10.

See if you can give this a go, and press pause if you need more time.

Well done.

So let's go through these answers.

We're going to start with question one.

Identifying all our multiples of 8.

you should've had something like this.

A huge well done.

Remember, only focus on those last three digits to identify if it's a multiple of 8.

For question two, the statement was all multiples of 2 and 3 are multiples of 6, all multiples of 3 and 5 are multiples of 15, and you had to explain why all multiples of 2 and 8 are not multiples of 16.

Well, this is because 2 is a factor of 8.

So this means all multiples of 2 and 8 are actually multiples of 8.

So that means not all multiples of 2 and 8 are multiples of 16.

For example, 8 is a multiple of 2, and 8 is a multiple of 8, but 8 is not a multiple of 16.

A huge well done if you got that one right, as it very much embeds your understanding of multiples.

For question three, we had lots of numbers to fill in here, so a huge well done if you got this one right.

Now, I put the multiples of 5 to the left, and the multiples of 8 to the right.

You may have got them the other way round.

It doesn't make a difference, as long as you have got these numbers in the right circle.

A huge well done if you got this one right.

And four was a great question, as you're using strategy as well as knowledge.

So 4a asks you, which starting number would you choose? The only starting number would be starting at 440, which is starting number three.

This is the best path that you could choose in order to win the game.

A huge well done if you've identified this path.

So in summary, divisibility tests are quick processes to identify if a number is divisible by another number.

We know a number is divisible by 4 if the last two digits are a multiple of 4, and this is because we know 4 is a factor of 100.

A number is divisible by 8 if the last three digits are a multiple of 8, and this is simply because we know 8 is a factor of 1,000.

Remember, there are a few different ways to identify those last three digits are divisible by 8.

Long division, short division, or partitioning, for example.

A huge well done.

It's been great learning with you, and I hope you've enjoyed this lesson.