Lesson video

Hello, I'm Miss Mia.

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 will learn about the divisibility rule for multiples of 3 and then be able to use it with 3- and 4-digit numbers.

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

So I say, then you say.

Digit sum.

Divisible/divisibility.

Multiple.

Well done, let's keep going.

Now the sum of the digits often number is called it's digit sum.

And I'll show you what that looks like and what that is in a bit.

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.

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

This lesson consists of 2 lesson cycles.

The first lesson cycle is all to do with the divisibility rule of multiples of 3.

Then we're going to take that rule and see if we can apply it to 4-digit numbers.

I'm so excited about this lesson because I can't wait to teach you about the divisibility rule for multiples of 3.

It's super interesting so let's get started.

To help us with our learning, we've got Andeep and Izzy.

They're going to be reminding us about facts and anything else that we may have forgotten.

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.

Today we will be looking at the divisibility rules for 3.

A number is divisible by 3 if it is a multiple of 3.

It can be divided into groups of 3 exactly with nothing left over.

Here's an example.

So we've got the number 36.

And Izzy says, "36 is a multiple of 3 because it is 12 groups of 3 or 3 groups of 12." Andeep challenges her, he says he can go bigger.

"90 is a multiple of 3 because it is 3 groups of 30 or 30 groups of 3." What is the largest multiple of 3 that you know? Have a think.

Now you may have said 36 because 36 is 12 groups of 3.

You may have also said 99 because 99 is 33 groups of 3.

Let's move on.

You can combine multiples of 3 to find larger multiples of 3.

For example, we've got the number 126.

Now at the beginning we might think, hang on, how do we know that's a multiple of 3? Well, we know that if we were to partition 126 into 90, which we know is a multiple of 3 and 36, which is a multiple of 3 because 12 groups of 3 is 36 and 30 groups of 3 is 90.

That gives us 126.

But also that results in 42 groups of 3 if you add the groups together.

126 is a multiple of 3 because it can be made of groups of 3.

Can you think of another one that's greater than 126? You may have said 129.

I've just added on another group of 3 there.

You may have said 150.

That could be because you know that 3 times 5 is 15, so 3 groups of 50 is 150, so it is made of groups of 3.

Now you can also find out if a number is a multiple of 3 by using the digit sum of the number.

Now on the screen you see the number 126.

Now the digits within this number are one, 2, and 6.

To find the digit sum, you add together the digits.

So we've got here the digits 1, 2, and 6.

We must add those digits together.

So your sum is one plus 2, plus 6 is equal to 9.

So the digit sum for 126 is 9.

So the number is 126 and it's digit sum is 9.

Can you repeat that after me? So the number is 126 and its digit sum is 9.

Good job.

But what now? What are we going to do with this information? Well, it's super important.

Let's find out why.

If the digit sum of a number is a multiple of 3, then the number itself is also a multiple of 3.

And here we can see that the digit sum is 9.

9 is a multiple of 3 because it is 3 groups of 3.

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

So that means the number 126 is a multiple of 3.

How cool is that? Let's carry on.

Now, Andeep and Izzy are looking at larger multiples of 3.

Izzy says, "If 24 is a multiple of 3, then 240 is a multiple of 3." Andeep says he agrees, "240 is 24 tens and 24 tens can be divided into 8 groups of 3 tens.

9 is also a multiple of 3.

So that means 249 must also be a multiple of 3.

So here we've got 249.

Great.

The digits are 2, 4, and 9.

So the digit sum of 2, 4 and 9 is 15.

What else do we know about 15? Well, we know that 15 is a multiple of 3.

So that means we know that 249 is divisible by 3.

Over to you.

I'd like you to explain why 318 is a multiple of 3 and 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, let's look at the number 318.

The digits are 3 1 8.

So that means the digit sum is 12, which is a multiple of 3.

So Izzy's partition 318.

She knows that 300 is a multiple of 3.

She knows that 18 is a multiple of 3.

So that means 318 must be a multiple of 3 as well, because if we add those groups of 3 together, we would get 106 groups of 3.

Now the divisibility rule works for all multiples of 3.

On the screen here you can see that we've got the number 846.

It's not easy to see multiples of 3 in 846.

So let's use the divisibility rule.

The digit sum is 18 'cause the sum of 6, 4 and 8 is 18, and Andeep's used number pairs there to quickly calculate that.

So instead of doing 8 plus 4 plus 6, he's added 6 plus 4 to get 10, and then he's added the eight.

So 18 is our digit sum.

Now 18 we know is a multiple of 3.

If the digit sum is a multiple of 3, then the number is too, that's amazing.

Now, 846 is a multiple of 3.

846 is divisible by 3.

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

So we've got the number 628 here.

So this time the digit sum is 16 because 8, 2 and 6 sum to 16.

We know that 16 is not a multiple of 3 because you cannot make groups of 3.

16 isn't a multiple of 3.

That means 628 isn't a multiple either.

Can you explain that in another way? Have a think.

Well, 600 is a multiple of 3 because it has 2 groups of 3 hundreds, which leaves us with 28.

Now we know 28 is not a multiple of 3.

So that means 628 isn't a multiple of 3.

Over to you, explain why 744 is a multiple of 3.

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

So how did you do? 744 is a multiple of 3 because it's digit sum is a multiple of 3.

The digit sum is 15, which is a multiple of 3 resulting in 744 also being a multiple of 3.

Onto your main task for this lesson cycle.

For question one, use the digit sum divisibility test to circle the multiples of 3, which can you say are multiples of 3 without using the divisibility test? So you've got the numbers, 643, 519, 306, 837, 958 and 693.

And then for question 2, you're going to insert a digit into these to make them a multiple of 3 using the divisibility rule.

So for question 2 A, you've got 7 gap 3 for B, you've got 9 5 gap.

And then for question C, you've got a gap and then 6 3.

And I'd like you to explain to a friend how you know they are multiples of 3.

Just a quick tip, remember the digit sum must be a multiple of 3 for these numbers to also be a multiple of 3.

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

Off you go.

Good luck.

So this is what you should have got.

Let's look at 837.

The digit sum for this number is 18.

18 is a multiple of 3 resulting in 837 also being a multiple of 3.

519 is also a multiple of 3 because the digit sum for it is a multiple of 3, and that's 15.

Now if we have a look at 306, we know that that's a multiple of 3.

We don't really need to use the digit sum for this because we know that 3 groups of 100, and 2 groups of 3 would make 306.

And lastly, 693, well 600 if we partition 693 into hundreds, tens, and ones.

All 3 numbers are multiples of 3.

Now, for question 2, you may have found different answers.

Some of these being for 2 A, 723, 753 and 783.

What was the trick here? The digit that you chose had to equate to a multiple of 3 when finding the digit sum.

So for example, 7 add 2 is 9, add 3 is 12.

12 is a multiple of 3.

Then 7, add 5 is 12, and then you're adding on another 3, which is 15, and 15 is a multiple of 3.

And lastly 7, add 8 is 15.

You are then adding another group of 3, which is 18 and 18 as you know, it is a multiple of 3.

Let's look at B.

If you got something similar, you are correct.

And that's because the digit sum for each number equates to a multiple 3.

And lastly, this is what you should have got 3, 6, or 9.

You also could have had zero as one of them because 63, when you add the digit sum for both of those, you still would've got a digit sum of 9.

Well done if you got all of those correct.

Fantastic.

You are on the way to using the divisibility rule for 3 confidently.

Let's move on to our second lesson cycle.

This is all to do with applying the divisibility rule of multiples of 3 to 4-digit numbers, exciting.

So the divisibility rule for multiples of 3 works for all multiples of 3, remember that.

Izzy says she's going to use digit cards to make a 4-digit number, and this is the number that she's made.

What number have I made? Can you say it? Well, there's 4-digits.

So we say this number as 9,036.

Andeep, is this a multiple of 3? How can Andeep check? Have a think.

Well, you may have said something like this.

"Let's find the digit sum.

So one digit is zero, so I can ignore that.

The digit sum for 9,036 is 18." So 18 is our digit sum.

18 is a multiple of 3.

So yes, 9,036 is also a multiple of 3.

Yes, 9,036 is exactly divisible by 3.

I also know it is a multiple of 3 because its parts are divisible by 3.

9 thousands can be divided into 3 groups of 3 thousands.

36 is a multiple of 3 because it is 12 groups of 3.

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

Andeep, do you think this is a multiple of 3? How can Andeep check? Again, Andeep has mentioned finding the digit sum.

He says he can use near doubles this time.

So the digit sum is 27 and he's used near doubles to efficiently calculate the digit sum, which is 27.

So 27 is a multiple of 3.

So yes, 7,956 is also a multiple of 3.

Exactly, because 7,956 is exactly divisible by 3.

Over to you, which of these 4-digit numbers is a multiple of 3? Explain how you know.

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

So what did you get? 4,194 is a multiple of 3 because the digit sum is 18, which is a multiple of 3.

So 4,194 is a multiple of 3.

8,333, on the other hand, the digit sum is 17, which means it is not a multiple of 3.

Now, Andeep has an idea about other multiples of 3.

We've got the number 7,956.

"We know that 7, 9, 5, and 6 sum to 27, which means 7,956 is divisible by 3.

What if I move the digits to make a new number?" So he's reorganised the digits, and now we've got 5,697, I think 5,697 must be divisible by 3.

What do you think? Well, the digit sum is still the same.

It is still 27 and all the numbers are divisible by 3.

if their digit sum is.

I wonder what other numbers we can make? Well, we know that 7, 9, 5, and 6 sum to 27, which means 7,956 is divisible by 3.

Andeep and Izzy makes some other numbers using the same digit cards.

And we can see that we've got 9,675, 5,679, and Izzy says that both of these are divisible by 3 too.

The digit sum is still 27.

So all of these are multiples of 3.

This is exciting because this now shows us that if we continue to reorganise the numbers, we can find more numbers that are multiples of 3, just by using the same 4-digits.

Now over to you, use the digit cards to make a different 4-digit number.

Explain how you know it is a multiple of 3.

Izzy and Andeep have said 7,956, 5,697, 9,675, and 5,679.

For example, 6,975, or you may have got 7,596.

The digit sum is always 27, which is a multiple of 3.

That's the key part there.

The digit sum has to be a multiple of 3, and in this case, it is always going to remain as 27 because the digits within the number have not changed, they've just been reorganised.

Now, Andeep has another idea about other multiples of 3.

So here we've got the number 7,956.

Now wait for this, this is really, really cool.

So I think we can use this digit sum test to swap some digits and find even more examples.

So Izzy says, "What do you mean?" What exactly are we going to swap? Hmm, what do you think about this? Well, the digit sum is 27.

2 of the digits within this are 5 and 6, and we know that 5 and 6 sum to 11.

Now, if Andeep swaps the digits for 2 other numbers, that also sum to 11.

We have a new number.

Ah, I think I see.

So 3 and 8 sum to 11.

So can we replace 5 and 6 with those? Hmm? What do you think? Yes, the digit sum is still 27.

So our new number is still divisible by 3.

How cool is that? That is super cool.

I can swap the digits 3 and 8 too.

7,983 is also a multiple of 3.

I agree there are so many combinations, 7 and 3 in the number some to 10.

I wonder if I can change those.

Can you think of numbers that some to 10 that are not 7 and 3.

Try Izzy's idea.

Explain how you know your new number is still a multiple of 3.

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

So how did you find that? Well, you may have said 4,986, 2,988 or 5,985.

You could have swapped 2,988, so the digits 2 and 8 to 8 and 2.

So you may have had 8,982.

As long as those 2 digits sum to 10, and also the overall digits sum to a multiple of 3.

Over to you.

For question one, you're going to use the digit sum divisibility test to circle the multiples of 3.

Are there any numbers you know cannot be a multiple of 3.

So you've got the numbers, 5,694, 6,613, 8,397, 3,481, 7,047 and 4,987.

And for question 2, you're going to use 4-digit cards each time to make 4-digit multiples of 3.

You are going to make the largest and smallest multiples of 3 you can.

So the digit cards that you've got are 3, 3, 4, 5, 8, 9.

You're going to choose one of your numbers and then you're going to swap 2 digits and make 3 more multiples of 3.

You can pause the video here.

Off you go, good luck.

Have fun, and I'll see you in a bit.

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

5,694 is a multiple of 3, and that's because the digit sum is 24, which is a multiple of 3.

8,397 is a multiple of 3 because the digit sum is 27.

And we know that 27 is a multiple of 3.

7,047 is a multiple of 3 because the digit sum is 18, and we know that's a multiple of 3.

Now, 6,613 is not a multiple of 3 because 13 is not a multiple of 3.

Now, for question 2, you may have made 9,843 as the largest multiple, 3345 is the smallest.

So these are some of the examples you could have had here.

And then for this part, you had to swap 2 digits and make 3 more multiples.

So in this example I've got 9,345.

I know that 3 add 4 is equal to 7.

So I swapped 3 and 4 for 1 in 6 instead because I know that 1 add 6 gives me 7 as well.

And then I know that 9 add 3 gives me 12.

So instead of having 9 and 3, I swapped that for 6 and 6, which gave me 12.

So I was able to make another number there by swapping 2 digits.

Well done if you got all of those correct and you were able to use the digit sum to help you to identify whether a number is divisible by 3 or not.

Fantastic work.

Let's summarise our learning.

In this lesson you used the divisibility rule to find multiples of 3.

You should now understand that numbers that can be divided by 3 and leave no remainder are multiples of 3.

You can use a digit sum to determine if a number is divisible by 3.

If the digit sum is a multiple of 3, then the number is also a multiple of 3.

And lastly, you should now understand that to find the digit sum of a number, add the digits in the number together so the digit sum of 17 is 1 and 7, which equals 8.

So that's just a small example there.

I hope you really enjoyed this lesson, and I look forward to seeing you in the next one, bye.