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 use the divisibility rule for divisors of 6.

Your keywords are on the screen now and I'd like you to repeat them after me.

So I say, you say: digit sum, divisible/divisibility, multiple.

Fantastic.

Let's move on.

The sum of digits of a number is called its digit sum.

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

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

And lastly, a multiple is the result of multiplying a number by another whole number.

This lesson is all about the 6 times tables and actually focusing in on divisibility rules for the multiples of 6.

We've got two lesson cycles here.

Our first lesson cycle is all to do with the divisibility rule of multiples of 6, and then our second lesson cycle focuses in on 4-digit numbers.

Super exciting, and that's where we are going to apply the divisibility rule for 6 to 4-digit numbers.

To help us with our mathematical thinking and learning we have Andeep and Izzy here to join us on our journey.

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

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

In today's lesson, what we are going to be doing is actually looking at the divisibility rules for 6.

Now you may have seen a lesson to do with the divisibility rules for 3.

If you have, we are going to now build on that knowledge and see how it relates and whether we use that knowledge to help us with the divisibility rules for sixes as well.

A number is divisible by 6 if it is a multiple of 6.

It can be divided into groups of 6 exactly with nothing left over.

So no remainders.

Izzy says that "36 is a multiple of 6 because it is 6 groups of 6." Andeep says he can go bigger.

He says "360 is a multiple of 6 because it is 60 groups of 6." What is the largest multiple of 6 that you know? You may have said 366 because that's adding on another group of 6 to 360.

You may have said 72, and that's because 12 groups of 6 are 72.

Now did you know you can combine multiples of 6 to find larger multiples of 6? And I'll show you what I mean by that.

So we've got 90 here.

Now, if we were to partition 90 into the largest multiples of 6 that we know, we know that 72 + 18 is 90.

So 72 is a multiple of 6.

18 is a multiple of 6.

That's 15 groups of 6 if you add the groups together.

90 is a multiple of 6 because it can be made of groups of 6.

Can you think of one greater than 90? Well, you may have said 96.

You may have added on another group of 6 to 96 and said 102.

Now, let's move on.

If a number is even and the sum of its digits is a multiple of 3, then the number is also a multiple of 6.

That's a key takeaway there.

The number has to be even.

So the first step to knowing whether a number is a multiple, whether a number is divisible by 6, is to check that it's even.

And then if its digit sum is a multiple of 3, then it's a multiple of 6.

So let's have a look at 36.

A multiple of 6 is also a multiple of 3.

So we can use the divisibility rule.

Multiples of 6 are multiples of 3, but they are even numbers.

Now you have to remember to look at the ones to find out if it is an odd or even number.

So here we can see that our ones number is 6.

And now Andeep has pointed out that even numbers end in 0, 2, 4, 6, and 8.

So we know that 36 is even because 6 is an even number.

Now in terms of the digit sum of 36, we know that 3 + 6 = 9.

So 9 is a multiple of 3, which means 36 is an even number, and its digit sum is a multiple of 3.

So 36 is a multiple of 6.

We also know 6 groups of 6 is 36.

Now Izzy and Andeep are looking at a larger multiple of 6.

They're looking at 246.

So if 24 is a multiple of 6, then 240 is a multiple of 6.

The digits are 2, 4, and 6.

So we can add them together.

The digit sum this time is 12.

6 is an even number, and the digit sum is 12.

12 is a multiple of 3.

So we know 246 is divisible by 6.

Over to you.

You are going to explain why 432 is a multiple of 6.

Can you use the digit sum? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, the ones digit is an even number, so that's a tick.

And the digit sum is 9, which is a multiple of 3.

So 4 + 3 + 2 = 9.

That means it is a multiple of 6.

Now the divisibility rule works for all multiples of 6.

We've got the number 846 here.

It's not easy to see multiples of 6 in 846.

So let's use the divisibility rule.

The ones digit is even, and the digit sum is 18 because the sum of 6, 4 and 8 is 18.

Andeep said he used number pairs to calculate that.

So 8 + 4 + 6 gives us 18 as our digit sum.

And I can see why Andeep's used the number pairs because he can see 6 + 4 would've given him 10, which makes it far more efficient to calculate.

Now 18 is a multiple of 3.

If the digit sum is a multiple of 3, then it is a multiple of 6 too.

846 is a multiple of 3.

846 is also divisible by two because it's an even number.

Now, if the digit sum is not a multiple of 3, then the number is not a multiple of 6.

So this time the digit sum is 17 because 6, 2, and 9 sum to 17.

There you have it.

Well, 17 is not a multiple of 3.

In fact, the closest multiple of 3 would've been 18.

So because you can't make 3, 629 is not a multiple of 3 either.

Can you explain another way? Well, you may have said this: 600 is a multiple of 6 because it's 6 groups of 100.

You know that 29 is not a multiple of 6.

So 629 is not a multiple of 6.

Over to you.

You're going to explain why 846 is a multiple of 6.

Can you use a digit sum? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? 846 is a multiple of 6 because it's ones digit is even and it's digit sum is a multiple of 3.

The digit sum is 18, which is a multiple of 3.

Onto your main task for this lesson cycle.

For question one, you're going to use the digit sum divisibility test to circle the multiples of 6.

Which can you say are multiples of 6 without using the divisibility test.

So you've got the numbers 343, 618, 603, 236, 108 and 492.

And for question two, you're going to insert a digit into these to make a multiple of 6 using the divisibility rule.

Key tips here, remember that your ones digit have to be even, and the digit sum must be a multiple of 3 for it to be a multiple of 6 as well.

So two conditions there.

I'd like you to also explain to a friend how you know they are multiples of 6.

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

So how did you do? Well for question one, this is what you should have got.

618 is a multiple of 6.

So you know that 600 is a multiple of 6 and so is 18.

So 618 is a multiple of 6.

Now, for 108, it's a little bit difficult to see the multiples of 6 within 108.

So we could have used the digit sum to figure this one out.

So the digit sum is 9 and 108 is an even number.

So 108 is a multiple of 6.

Now the digit sum for 492 is 15.

So that means 492 is a multiple of 6.

And don't forget, it's also an even number.

343 is not a multiple of 6 because straight away we can see that 343 is an odd number.

603 is also not a multiple of 6 because it is an odd number.

236 is not a multiple of 6, even though it's an even number.

The digit sum is 11 and 11 is not a multiple of 3.

Right, question two.

For this question, you had to insert a digit to make them a multiple of 6.

So looking at 2a, we can see that it's an even number.

So that's a good start.

We now need to find a digit sum where all 3 numbers added together give us a multiple of 3.

So you may have had this: 732, 762, and 792.

For each number, the digit sum would have been a multiple of 3.

So for example, 7 + 3, I'm going to use my number pairs there.

So 10 + 2 is 12, which is a multiple of 3.

7 + 6 is 13, add 2 is 15, which is a multiple of 3, making it a multiple of 6, and then 7 + 9 is 16, add the 2 is 18.

18 is a multiple of 3, which means 792 is a multiple of 6.

For B, you would've had to choose an even number, and that even number would then have to be added to 8 and 5 with the condition that it has to be a multiple of 3.

So you may have had this: 852 and 858.

When you've found the digit sum for both numbers, they should be a multiple of 3, making them a multiple of 6.

And lastly, we know that the end digit is even.

So what we needed to do is again, find a digit when added to the other two digits, which are 6 and 4, to make it a multiple of 3.

So you may have gotten this.

So 264, 564, 864.

If you've got those correct, well done.

Let's move on to our second lesson cycle, and that is all to do with 4-digit numbers.

Now the divisibility rule for multiples of 6 works for all multiples of 6.

Izzy says she's going to use digit cards to make a 4-digit number.

She's made the number 5,088.

So what number have I made? Can you say it? Well, she's made the number 5,088.

"Andeep, is this a multiple of 6?" Well, let's find the digit sum.

The digit sum is 21, and that's because 8 + 8 is 16, + 5 is 21.

The last digit is 8, and 21 is a multiple of 3.

So yes, 5,088 is also a multiple of 6.

"Yes, 5,088 is exactly divisible by 6." Izzy's made another number.

"What number have I made this time? Can you say it?" If you said 7,956, you are correct.

"Andeep, is this an even number and a multiple of 3?" How can Andeep check? "Well, let's find the digit sum.

I can use near doubles.

The digit sum is 27." And this is an even number because the ones digit is a 6.

Now the digit sum is 27.

The last digit is 6, which is even.

27 is a multiple of 3.

So yes, 7,956 is also a multiple of 6.

"Yes" 7,956 is exactly divisible by 6." Over to you.

Which of these 4-digit numbers is a multiple of 6? Explain how you know.

So your two digits are 4,494 and 6,331.

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

So how did you do? 4,494 could potentially be a multiple of 6.

Let's find out why.

Well, the last digit is an even number.

The digit sum is 21, and that's because when you add all the digits in the number 4,494, you get 21.

So that means 4,494 is a multiple of 6.

Now let's look at 6,331.

Well, it cannot be a multiple of 6 because the ones digit is an odd number, and also the digit sum is 13, which is not a multiple of 3.

Well done if you got that correct.

Now, Andeep has an idea about the other multiples of 6.

He says, "We know that 4, 6, 9 and 2 sum to 21, which means 4,692 is divisible by 6.

What if I move the digits to make a new number?" Now he's got the number 2,964.

Izzy says she thinks "2,964 must be divisible by 6." What do you think? "Now, the digit sum is still the same.

It is still 21.

And all the numbers are divisible by 3 if their digit sum is." "The last digit is an even number, and 21 is a multiple of 3.

So yes, 2,964 is a multiple of 6." "I wonder what other numbers we can make." So Andeep and Izzy make some other numbers using the same digit cards.

They've got the numbers, 4,962 and 6,924.

Izzy says "Both of these numbers are divisible by 6 too." "The last digit is an even number, and the digit sum is still 21.

So all of these are multiples of 6.

This is exciting." Over to you.

You are going to use the digit cards to make a different 4-digit number.

Explain how you know it is a multiple of 6.

You've got the numbers 6, 9, 2, 4.

So the numbers that we've already covered are 4,692, 2,964, 4,962, and 6,924.

Off you go.

Good luck.

So how did you do? Well, you could have had 9,264 or 9,246.

The last digit is an even number, and the digit sum is always 21, which is a multiple of 3.

Now, Andeep has another idea about other multiples of 6.

"I think we can use this digit sum test to swap some digits and find more examples." "What do you mean?" "The digit sum is 27? Two of the digits, 6 and 6 sum to 12.

If I swap the digits for two others that also sum to 12, we have a new number." What do you think? "Ah, I think I see.

So we know that 6 and 6 sum to 12.

So we can actually replace those with 4 and 8.

4 and 8 sum to 12.

8 is an even number.

"So yes, the digit sum is still 27 and the ones digit is even.

So our new number is still divisible by 6." "That's so cool.

I can swap the digit 6 and 8 too.

8,946 is also a multiple of 6." "I agree.

There are so many combinations." "9 and 4 in the number sum to 13.

I wonder if I can change those?" Over to you.

I'd like you to try Izzy's idea.

You're going to explain how you know your new number is still a multiple of 6.

"9 and 4 in the number sum to 13.

I wonder if I can change those?" You can pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, you may have said 8,766 or 8,856.

In both multiples the last digit is even, and the digit sum is a multiple of 3, which means that both numbers are multiple of 6 Onto the main task for this lesson cycle.

So for question one, you're going to use the digit sum divisibility test to circle the multiples of 6.

Your numbers are 5,694, 6,613, 8,298, 2,480, 5,045 and 4,188.

For question two, you are going to use 4-digit cards each time to make four 4-digit multiples of 6.

You're going to make the largest and smallest multiples of 6 you can.

So the numbers that you've got to use are 3, 6, 4, 2, 8, 7.

After that, you're going to choose one of your numbers, and then you're going to swap two digits and make three more multiples of 6.

Don't forget the rules that you've learned in order to check whether a number is a multiple of 6 or not.

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

So how did you do? Well, for question one, this is what you should have got.

Now looking at 5,694, well, the ones digit is even, and the digit sum for this number is 24.

And 24 is a multiple of 3, which means 5,694 is a multiple of 6.

Then if we look at 6,613, it's an odd number.

So it cannot be a multiple of 6.

8,298, well, the ones digit is even, and the digit sum is 27, meaning that 8,298 is a multiple of 6.

Now 2,480, the digit sum here is 14.

14 is not a multiple of 3.

So the number 2,480 cannot be a multiple of 6.

5,045 is an odd number.

So unfortunately, again, it cannot be a multiple of 6.

And lastly, 4,188.

Well, the ones digit is even, and the digit sum is 21.

21 is a multiple of 3, meaning that 4,188 is a multiple of 6.

Now, for question two, 2,346 is the smallest number, and 8,742 was the largest multiple that you could have had of 6.

Now, here's an example of what you may have had.

So we've got here 8,736, 8,376.

Why does that work? Well, that's because 8,376 is an even number, and the digit sum adds up to 24.

So therefore, 8,376 is a multiple of 6.

Because the numbers have been rearranged.

Again, the numbers have been rearranged, and the last digit is even.

So we know that that's a multiple of 6 because the digit sum is still 24.

And similarly again, we've got 6,378, which is also a multiple of 6.

Now, we could have swapped some of these numbers.

Let's look at 6,378 in more detail.

We'll leave the ones alone, but let's look at 6 and 3.

Now, 6 and 3 sum to 9.

I could have swapped 6 and 3 to 4 and 5.

4,578 also would've been a multiple of 3.

Let's think of another example.

Well, let's look at the two numbers in the middle this time, 3 and 7.

3 and 7 sum to 10.

I also know 5 and 5 sum to 10.

So another number that I could have had was 6,558.

Again, my number's even, and the digit sum is 24.

So we could have also had that.

Well done if you managed to get those variations in your answer, and you managed to find different multiples of 6 using the digit sum to help you.

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

Well done.

Let's summarise our learning now.

So in this lesson, you used a divisibility rule for multiples of 6.

You should now understand that for every one group of 6, there are two groups of 3.

You also understand that for a number to be divisible by 6, it must be divisible by both 2 and 3.

In other words, it has to be an even number, and the digit sum must be a multiple of 3.

Well done.

I really enjoy teaching you this lesson today, and I hope that you can use this rule in the future.