Lesson video

Hi, everyone, my name is Ms. Kuh, and today we're going to have a really interesting and fun lesson.

I'm so happy to be learning with you today, and it might be hard in places, but I will be here to help.

You're going to come across some keywords that you are familiar with, as well as some new keywords to build on that previous knowledge.

It's going to be a great lesson, and I'm really happy to be learning with you today In today's lesson, from the unit properties of number, factors, multiple squares and cubes, we'll be looking at divisibility tests for 2 and 3.

And by the end of the lesson, you'll be able to identify and explain whether or not a number is a multiple of a given integer.

So let's have a look at some keywords, starting with the word divisibility.

Now, divisibility is a number's ability to be exactly divided by another number, leaving no remainder.

So let's look at an example.

Here, 24 is divisible by 3 because 24 divided by 3 is 8 and there's no remainder.

Another example would be 12 is divisible by 4 because we know 12 divided by 4 is 3 and there is no remainder.

A non-example would be 12 is not divisible by 8 because if you divide 12 by 8, the answer is 1.

5.

It's not an integer and we have a remainder.

So divisibility is a number's ability to be divided exactly by another number, leaving no remainder.

There are two parts to our lesson today, so let's have a look at our first part by identifying any even number is a multiple of 2.

Divisibility tests are quick processes to identify even number is divisible by another number.

We use divisibility tests instead of dividing the number as it often saves time.

So let's start by doing a test for divisibility by 2 for all even numbers.

I'm gonna identify all the even numbers up to and including 30, which you can see here: 2, 4, 6, 8, 10, all the way up to 30.

Can you see a pattern with these numbers? Hopefully, you can spot the digit in the ones column is always a 0, a 2, a 4, a 6, or an 8.

So all our even numbers or multiples of 2 will always end in a 0, 2, 4, 6, or 8.

So the question I'll ask now is: Is 58 divisible by 2? And the trick is to look at the digit in the ones column.

Well, yes it is because the digit in the ones column is 8.

Let's have a look at a check.

We have a huge number here, 489,215,478,384.

Is that a multiple of 2? So you can see why we don't want to be doing any working out here.

We just want to identify a quick and easy way to see: Is it a multiple of 2? Hopefully, you can spot, yes it is.

But the reason, what is the reason why it's a multiple of 2? Is it because all even numbers have the digit 0, 2, 4, 6, or 8 in the ones column, or is it because the number begins with a 4 from left to right? Hopefully, you've spotted it's because all even numbers have the digit 0, 2, 4, 6, or 8 in the ones column.

Well done.

Moving on to our second check question.

Which of these numbers are divisible by 2? And can you justify your answer? See if you can give it a go and press Pause if you need.

Let's go through these answers, and hopefully you didn't divide everything by 2 and looked for that little shortcut.

Well, we know our answer is B simply because the digit in the ones column is an 8, and anything which is divisible by 2 always has a digit of 0, 2, 4, 6 or 8 in that ones column.

Well done.

So let's move on to your task.

Using a divisibility of 2 test, identify all the multiples of 2 from the list below.

We have some huge numbers here, 2,478,349, 3,284,738, 999,111,333, 445,534, 390, 1,115, and 222,222,222.

Big numbers.

Let's see if you can identify which ones are multiples of 2.

Well done.

So let's move on to the second question.

Izzy's calculator has broken, and she knows the number on the screen is a multiple of 2, has exactly five 10s, is a four-digit number, which is greater than 8,600 but less than 8,660.

What could her number be? See if you can give it a go and press Pause if you need.

Well done, so let's go through these answers.

Using a test of divisibility by 2, we're going going to identify all these multiples of 2.

Hopefully, you've spotted it's all of these numbers because the digit in the ones column is either a 0, 2, 4, 6, or 8.

Well done.

For Question 2, we know Izzy has broken her calculator and she has a number on the screen.

It has to be a multiple of 2.

So that means we know the digit in the ones column is either a 0 2, 4, 6, 8.

Now, we know it has exactly five 10s.

So think about your place value table, there should be a five in that 10s column.

We know there's four digits which is greater than 8,600, but less than 8,660.

There's quite a few answers here, so I'm going to list them all.

We have 8,650, 8,652, 8,654, 8,656, and 8,658.

A huge well done if you've got any or all of those answers.

Great work so far.

So let's move on to the second part of our lesson, which looks at the divisibility test for multiples of 3.

So the divisibility test for multiples of 3 is very different from the divisibility test for multiples of 2.

All I'm going to do is list some multiples of 3: 3, 6, 9, 12, all the way up to, let's say, 711,381.

And what we have to do is we have to spot: Is there a way in which we can identify a number is divisible by 3 without doing long, arduous calculations? So I'm just going to randomly pick any multiples of 3 from my list: 12, 18, and 27, for example.

And from these numbers, I just want you to look at the individual digits, and you may spot a method to identify if a number is divisible by 3.

Can you see it? Well, let's have a look at these individual digits.

For 12, it has the digits 1 and 2.

one 10 and two 1s.

For 18, it has the digits 1 and 8, one 10 and an 8.

And for 27, we have the digits 2 and 7, two 10s and a 7.

But how does this help us identify if a number is divisible by 3? Well, I'm going to sum our numbers up.

So the 12, I've broken into two separate digits, 1 and 2.

Now, if I summed them and I have 3.

For 18, I'm going to separate the digits 1 and 8 and sum them to make 9.

For 27, I'm going to separate those digits, 2 and 7, and add them to make 9.

Now, I'm gonna do the same with this huge number, 711,381.

And summing these digits, I have 7, 1, and 1, and 3, and 8, and 1, which is 21.

Now, there's something important about the sum of these digits.

If you sum the digits, the sum is always a multiple of 3.

So that means if you sum the individual digits and it's divisible by 3, we know it is a multiple of 3, and that's the divisibility test for multiples of 3.

Let's move on to a check, where I'm going to do the first part and you'll do the second part.

Jun has a huge number, 345,394,191, and he says it's divisible by 3.

We need to identify is he correct and we have to show our working out using the divisibility test for 3.

Divisibility tests are great because they save us so much time.

So let's have a look at these individual digits.

Well, he is correct because if you sum these individual digits, 3, add 4, add 5, add 3, add 9, add 4, add 1, add 9, add 1, they sum together to make 39, and 39 is a multiple of 3.

So that means we know this huge number, 345,394,191, is divisible by 3.

Let's see if you can try a question.

Sophia says, "We have 254,622," and she says it's divisible by 2 and 3.

Is she correct? And you must show you are working out using the divisibility tests.

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

So let's find out how you did.

Well, she is correct.

254,622 is divisible by 3 because if you sum up those individual digits, 2 add 5, add 4, add 6, add 2, add 2, it makes 21, and 21 is a multiple of 3.

We also know 254,622 is divisible by 2 because the digit in the ones column is a 2, and we know any number with the digit 0, 2, 4, 6, or 8 in the ones column is a multiple of 2.

A huge well done if you've got that one correct.

Now, let's move on to your task.

Question 1a wants you to identify all the multiples of 3 from the list.

We have 234, 1,398, 20,495, 593, and 56,576.

Question 1b wants you have to identify all the multiples of 2 and 3 from the list.

We have 325, 139, 120,490, 594, and a big number, 656,578,452.

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

Well done, so let's move on to Question 2.

Question 2 shows us five cards each with a digit 6, 1, 1, 5, and 4.

Now, only using 4 cards, you're asked to make a four-digit number which is a multiple of 3.

For part B, using only 4 cards, it wants you to make four-digit number, which is a multiple of 3 and 2.

See if you can try and find as many answers as you can to part A and part B.

Give it a go and press Pause if you need.

Well done.

So let's move on to the next question.

Question 3 shows a Venn diagram, and we're asked to insert the following numbers in our Venn diagram.

Now, if you look at our diagram, you can see the multiples of 2 are on the left and the multiples of 3 are on the right.

You need to insert the numbers 248, 4,343, 4,350, 312,492, 892,091, 111, 7, 77, and 555,555 See if you can give it a go and press Pause if you need.

Well done.

Let's move on to our next question, Question 4.

Question 4 gives us an integer with lots of digits.

Using the divisibility test, how do you show that this is a multiple of 3? This is a great question and you can only use the divisibility test for multiples of 3 in this question.

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

Well done.

So let's go through our answers.

For Question 1, we needed to identify all the multiples of 3 from the list.

So all I'm going to do is sum up our individual values.

234, the individual digits are 2, 3, and 4, which make 9.

So that means I know 9 is divisible by 3.

So 234 is divisible by 3.

Next, we have 1,398.

Summing those individual digits, I have 21.

21 is divisible by 3, so that means 1,398 is divisible by 3.

So our next number is 20,495.

Now, summing the individual digits up, we have 20.

20 is not divisible by 3.

So that means we know 20,495 is not divisible by 3.

Our next number is 593.

Looking at the individual digits, we have 5, 9, and 3.

Summing them together gives 17.

17 is not a multiple of 3.

So that means we know 593 is not a multiple of 3.

Looking at our last number and summing these digits, we have 29.

29 is not a multiple of 3.

So for Question 1a, we know there are only 2 numbers which are multiples of 3, are 234 and 1,398.

Question 1b want you to identify multiples of 2 and 3 from the list.

So we're going to firstly look at the digit in the ones column, as this will tell us if it's a multiple of 2 or not.

Immediately, I know 325 is not a multiple of 2, 139 is not a multiple of 2, but we know 120,490 is.

So let's see if it is a multiple of 3 as well.

I'm going to sum up these individual digits and I have an answer of 16.

16 is not a multiple of 3, so that means I know 120,490 is not a multiple of 3.

Now, 594 has a 4 in the ones column, so I know it is a multiple of 2.

So let's find out is it also a multiple of 3 by summing these digits.

If I summed them together, I have 18, so that means I know 594 is a multiple of 2 and 3.

Lastly is this huge number, 656,578,452.

Because it has a 2 in the ones column, I know it's a multiple of 2, but let's sum these digits to find out.

Is it a multiple of 3? Summing these digits gives me 48 and 48 is a multiple of 3, so that means I know the two numbers which are multiples of 2 and 3 are given here.

Well done if you've got this one right.

Now, let's have a look at Question 2.

We have to make a four-digit number, which is a multiple of 3 using only 4 of these five cards.

Only 4 cards you could have used to make a multiple of 3 would be using the 1, the 1, the 4, and a 6 in any order to make a four-digit number.

I've just put some examples here.

6,114, 4,116, 6,141, 4,161, but there are many more examples.

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

Now, for part B, we had to make a four-digit number which is a multiple of 2 and 3.

So same as before.

We can only use those digits 1, 1, 4, and 6, as we know as we sum them together, we make a multiple of 3.

But remember, to make a multiple of 2, it must end in a 0, 2, 4, 6, or 8.

So some examples would be 6,114.

I've used the digits 1, 1, 4, and 6, and the digit in the ones column is a 4.

Another example is 4,116.

I've used the digits 1, 1, 4 and 6.

And the digit in the ones column is a 6.

1,146 is another example and another 1 is 1,164.

There are a few more examples out there, but the key thing is making sure you use the digits 1, 1, 4, and 6.

And the digit in the ones column should only be a 6 and 4 given the context of the question.

Well done if you got this 1 right.

Question 3 was a great question because we had huge numbers here.

Let's see how you got them.

248 should have only been positioned here.

4,350 should be here because it's a multiple of 2 and a multiple of 3.

312,492 is a multiple of 2 and 3.

892,091 is neither a multiple of 2 or 3.

111 is a multiple of 3, but not a multiple of 2.

7 is not a multiple of 2 or 3, 77 is not a multiple of 2 or 3, and 555,555 is a multiple of 3 only.

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

Our last question was a great question.

We had a massive number and we could only use a divisibility test for multiples of 3.

So how could we show this huge number is a multiple of 3 only using this divisibility test? Well, let's sum up the individual digits.

Summing up all these digits gives us 135.

We can then sum the digits of 135 to make 9, thus identifying this massive number is divisible by 3.

A huge well done if you did this question.

So in summary, we looked at divisibility tests and we use them because they're a quick process to identify if a number is divisible by another number.

A number is divisible by 2 if the digit in the ones column is a 0, 2, 4, 6, or 8.

And a number is divisible by 3 if we sum those individual digits and the sum is a multiple of 3.

A huge well done today.

It was great learning with you.