Lesson video

Hi, everyone.

My name is Miss Coo 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 at 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 four and eight, and by the end of the lesson, you'll be able to identify and explain whether a number is a multiple or four or eight.

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 two.

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

And if the digit in the ones column is a zero, two, four, six, or eight, then we know it's divisible by two.

For example, 794, this is divisible by two, because the digit in the ones column is a four.

A non-example would be 9,351.

This is not divisible by two because the digit in the ones column is a one.

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

We know the divisibility test for two states that the digit in the ones column has to be a zero, two, four, six, or eight.

So given that four is a multiple of two, does this mean all the multiples of four are also multiples of two? So let's identify by listing the first 10 multiples of four.

We have four, eight, 12, 16, 20, 24, 28, 32, 36, and 40.

Now, let's identify the first 10 multiples of two.

Two, four, six, eight, 10, 12, 14, 16, 18, 20.

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

Are these multiples of four also multiples of two? Yes, they are.

So that means, yes, we know that all the multiples of four are also multiples of two.

So let's change the question a little bit.

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

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

So the answer is no, because two is not a multiple of four.

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

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

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

And what I want you to do is see if you can figure out if 38,834,864 is divisible by four 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 spotted knowing that four is a factor of 100, that means we immediately know that four is a factor of the 38,834,800.

So we know for sure four 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 four.

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

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

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

So let's check for understanding.

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

I'd also like you to justify your answer.

We have four numbers.

a is 44,898,434, b is 378,432, c is a huge number, 5,000,984,438,424, and d is 389,308.

You can see why we use divisibility tests, as there are 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 eight.

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

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

You may have also got d is also a multiple of four.

The last two digits are 08, or just eight, and eight is a multiple of four.

A huge well done if you've 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 four, 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 four, because if we find which trucks have a multiple of four, 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 four, 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 four from the list.

Now, question two wants you to identify multiples of four and five from the list.

Use those divisibility tests for four and the divisibility test for five 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 four is a multiple of two.

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

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

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

Do you think that's sometimes true, always true, or never true? The next one is a multiple of eight 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 five, eight, 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 four, that means you know the number is a multiple of four.

Now let's have a look at question two.

For question two, we needed to identify if it's a multiple of four and five.

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

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

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

A huge well done if you've 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 four is a multiple of two.

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 two is a multiple of four, is that sometimes true, always true, or never true? Well, it's sometimes true.

Remember our examples, two, six and 10, they're all multiples of two, but they are not multiples of four, but we do have multiples of two which are multiples of four.

So that's why it's sometimes true.

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

That's always true because we know two 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 two.

Next, a multiple of nine is a multiple of three.

That's always true.

Same again, think of your multiples of nine, nine, 18, 27, so on and so forth.

All of these numbers are multiples of three.

This is because three is a factor of nine, or nine is a multiple of three.

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

This is never true.

This is because we know eight is an even number.

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

Lastly, multiples of 40 are multiples of five, eight, and 10.

That's always true.

That's because five, eight, and 10 are factors of 40.

A huge well done if you've 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 eight.

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

Now, this is because we know 100 is a multiple of four, however, 100 is not a multiple of eight, but what I want you to do is have a look at all of these multiples of eight up to and including 1,000.

How do you think we might test for divisibility by eight? Well, we certainly know eight is not a factor of 100.

So that means we can't look at the last two digits.

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

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

So let's have a look at an example.

Well, we have 7,160, so we know eight is a factor of the seven thousands because eight is a factor of a thousand, so that means we need to have a look at the last three digits, 160.

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

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

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 eight, because eight is a factor of a thousand.

So that means we know 90,000 is also a multiple of eight, 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 eight? Yes, it is.

So that means we know this huge number, 138,293,144, is a multiple of eight 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 eight, as eight is a factor of 1,000.

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

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

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

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

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

Which of the following shows 385,248 is divisible by eight? Now, Jun says, "I know my eight times table and I know 248 is a multiple of eight.

So that means I know 385,248 is divisible by eight." 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 eight.

So 385,248 is divisible by eight.

Alex also did some working out.

He did some long division.

He divided the last three digits by eight.

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

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

They are all really good ways in identifying if a number is divisible by eight, by knowing your eight times table or by just simply dividing those last three digits by eight and getting a and achieving a whole number answer after division.

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

Another way in which you can identify if a number is divisible by eight 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 eight.

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

We have 200 add 40 add the eight sums together to give our 248.

From here, she knows, well, 200 is made by multiplying eight by 50, and 40 is made by multiplying eight by five, and eight is made by multiplying eight by one.

As each of these parts has a factor of eight, that means we know eight is a factor of 200, 40, and eight.

So that means 385,248 is a multiple of eight.

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 eight? 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 eight.

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 eight.

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 eight more readily.

Eight times 20 is 160, eight times 20 is 160, and eight by five is 40.

So immediately I know eight is a factor of 160 and 40, so that means we know this huge number, 789,483,839,360, is a multiple of eight 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 eight.

We have some big numbers here.

So remember that divisibility test for eight.

So question two gives you two statements and a question.

It states all multiples of two and three are multiples of six.

It states all the multiples of three and five are multiples of 15, and it wants you to explain why all the multiples of two and eight 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 five can move you two to the right and a multiple of three can move you three up.

A multiple of eight can move you four to the left, and a multiple of 11 can move one 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 two, three, four, six, eight, nine, 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 eight, you should have had something like this.

A huge well done and remember, only focus on those last three digits to identify if it's a multiple of eight.

For question two, the statement was, all multiples of two and three are multiples of six, all multiples of three and five are multiples of 15.

And you had to explain why all multiples of two and eight are not multiples of 16.

Well, this is because two is a factor of eight.

So this means all multiples of two and eight are actually multiples of eight.

So that means not all multiples of two and eight are multiples of 16, for example, eight is a multiple of two, and eight is a multiple of eight, but eight is not a multiple of 16.

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

For question three, we add lots of numbers to fill in here.

So a huge well done if you got this one right.

Now, I put the multiples of five to the left and the multiples of eight to the right.

You may have got them the other way around.

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

A huge well done if you've got this one right.

Four was a great question as you are 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, and 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 four if the last two digits are a multiple of four, and this is because we know four is a factor of 100.

A number is divisible by eight if the last three digits are a multiple of eight, and this is simply because we know eight is a factor of a thousand, and remember there are a few different ways to identify those last three digits are divisible by eight, 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.