Lesson video

Hi everyone, my name is Ms. Ku 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 5 and 10" and by the end of the lesson you'll be able to identify and explain whether a number is or is not a multiple of 5 and 10.

So let's go through some of our keywords starting with divisibility.

Now remember, divisibility is a mathematical concept that refers to one number's ability to be divided exactly by another number, leaving no remainder.

A divisibility test for 2 states that the digit in the ones column must be a 0, 2, 4, 6, or 8.

For example, 794 we know is divisible by 2 because the digit in the ones column is a 4.

9,351 is not divisible by 2 because the digit in the ones column is a 1, so that means it is not divisible by 2.

Let's look at the divisibility test for 3.

Remember, if you sum the digits and it's a multiple of 3, therefore we know the number is divisible by 3.

For example, 1,389.

Summing those individual digits gives us 21 and 21 is a multiple of 3, so that means we know 1,389 is divisible by 3.

A non-example would be 673.

If you sum those individual digits, it makes 16, and 16 is not a multiple of 3, so therefore we know 673 is not a multiple of 3.

Our lesson today will consist of two parts.

The first one is looking at the divisibility test for 5, and the second will be looking at the divisibility test for 10.

So let's start with the divisibility test for 5.

Now remember, a divisibility test checks if a number can be divided into another number without a remainder.

They're really important, as divisibility tests are quick processes to identify if a number is divisible.

It saves us a lot of time and we don't want to be using long division or short division to identify if a number is divisible by another number.

So let's start with a test for divisibility by 5.

I'm going to identify all the multiples of 5 less than or equal to 50, so I've listed them here.

5, 10, 15, 20, 25, 30, 35, 40, 45, and 50.

And what I want you to do is see if you can spot a pattern.

Can you see? Is there a way in which you can identify if a number is divisible by 5? Well, hopefully you can see it's the digit in the ones column.

Now if the digit in the ones column is a 5 or 0, this means we know the number is divisible by 5.

So let's have a look at the number 5,345.

Do you think this is divisible by 5? Well, hopefully you can see it is because the digit in the ones column is a 5.

This is our test for divisibility by 5.

If the number has a digit in the ones column which is a 5 or 0, then we know it is divisible by 5.

So let's check this knowledge using a question.

Using a test of divisibility by 5, identify all the multiples of 5 from the list below.

We have some huge numbers here, so press pause if you need.

Well done if you spotted them.

We have these big numbers which are all divisible by 5 because the digit in the ones column is a 5 or 0, well done.

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

Andeep shows the following working out to test if 349,895 is a multiple of 5.

He shows these two types of working out.

The working out on the left shows short division and the working out on the right shows a multiplication to give our answer of 349,895.

Give an advantage and disadvantage in using division to discover if a number is a multiple.

Have a little think and press pause when you're ready.

While an advantage would be, if a number is a multiple, using division also calculates the factor.

A disadvantage is it takes much longer than a divisibility test for 5.

Let's move on to your practise questions.

Here you need to identify all the multiples of 5 from the list.

234, 1,390, 20,495, 593 and 56,570.

From that list, you need to identify the multiples of 5.

Question 1B wants you to identify the multiples of 3 and 5 from the list.

327, 139, 143,490, 594, and a huge number of 246,578,445.

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 gives us a table and from the table you can see the column headings.

"Multiple of 2," "Multiple of 3," "Multiple of 5" and "Multiple of 9." We have the numbers 2,788,904, 16,740, 15,498, and 44,701.

Question 2A says place a tick in the cell of the table above if the number is a multiple of 2, 3, 5, or 9.

Part B asks you to look at the table and identify, what do you notice about the number 16,740? And part C wants you to use the table and see if you can notice something about the number 44,701.

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

Great work, so let's go through our answers, starting with our answers to question 1.

We had to identify all the multiples of 5.

All you need to do to identify multiples of 5 is look at the digit in the ones column, and if it ends in a 0 or 5, we know it's a multiple of 5.

So question 1A, our multiples of 5 are simply 1,390, 20,495 and 56,570.

For 1B, we needed to identify the multiples of 3 and 5 from the list.

Now remember, to identify multiples of 5, the digit in the ones column must end in a 0 or 5, and to identify multiples of 3, we know we have to sum the individual digits and it will give us a multiple of 3.

So let's start with looking at 327.

This is not a multiple of 5 because the digit in the units column is a 7.

139 is not a multiple of 5 because the digit in the units column is a 9.

This means we're looking at 143,490.

Summing these digits gives us 21.

This is a multiple of 3, so this means we know 143,490 is a multiple of 3 and a multiple of 5.

Moving on, 594 is not a multiple of 5.

But moving to our last number, 246,578,445, you can see it is a multiple of 5, so let's find out if it's a multiple of 3 as well.

Summing these digits gives us 45, so that means we know it is a multiple of 3 and a multiple of 5.

Question 2 is a great question and hopefully you've identified the multiples of 2, the multiples of 3, the multiples of 5, and the multiples of 9.

If you've got this table right, a huge well done.

Let's have a look at 2B.

What do you notice about the number 16,740? Well, hopefully you can see it's a multiple of 2, 3, 5, and 9.

So therefore, what do you notice about the number 44,701? Well, it's not a multiple of 2, 3, 5, or 9.

Well done if you got this one correct.

Great work so far, so let's move on to the second part of our lesson, divisibility test for 10.

Well, in order to do a divisibility test for 10, let's identify all the multiples of 10 up to and including 50.

10, 20, 30, 40, 50.

Now can you see a pattern? How can we identify if a number is divisible by 10? Hopefully you can spot the digit in the ones column is always a 0.

This is our test for divisibility by 10.

And this is one of the easiest tests for divisibility.

So let's use this in a Venn diagram.

In this Venn diagram we'll be looking at the multiples of 2, multiples of 3 and multiples of 5.

And what I want you to do is insert all the numbers from 1 to 30 into the Venn diagram.

Give it a go and press pause if you need more time.

Well done, let's go through these answers.

First of all, starting with 1.

Well, 1 is not a multiple of 2, 3, or 5.

2 is a multiple of 2.

We have 3 is a multiple of 3.

4 is only a multiple of 2.

5 is a multiple of 5.

6 is a multiple of 2 and 3.

I'm going to insert all the rest of our numbers from 1 to 30 into our Venn diagram.

If you've got these correct, a huge well done.

Now we have our Venn diagram complete, what do all the numbers here represent? 6, 24, 12, 18, and 30? Well, if you look at our Venn diagram, you can see they are the numbers which are both multiples of 2 and 3.

So if a number is a multiple of 2 and 3, this means it's a multiple of 6.

Now let's have a look at this region.

What do you think these numbers here represent? Well, hopefully you've spotted they are multiples of 3 and 5.

Now these numbers are multiples of both 3 and 5.

This means they're also multiples of 15.

Now let's have a look at another region.

What do you think all the numbers here represent, 10, 20, 30? Well, hopefully you can spot from our Venn diagram they represent multiples of 2 and 5.

But multiples of 2 and 5 also mean they're multiples of 10.

So let's move on to a check question.

In this question, a student says, "5,083 is a prime because I did a divisibility test for 2, 3, 6, 5, 9, and 10 and it shows they're not factors." Is that true or false? And see if you can select a reason to justify your answer.

Well done, so this was a hard question and hopefully you've identified it's false because 2, 3, 5, 9, and 10 are not the only factors of every number.

In actual fact, 13 is a factor of 5,083, so that means 5,083 is not a prime.

Next I'd like to look at function machines.

Now the output of function machines do not always need to be calculated when identifying if a number is a multiple, and multiples can be seen through the operations.

For example, if we have an input, we multiply by 2 and then multiply by 3 and get an output.

Is the output always even? Yes, because the product of 2 and 3 is 6, therefore all the outputs will be multiples of 6 which are even numbers as 2 is a factor of all evens.

Let's look at another example.

Here we have a function machine where we have an input.

We multiply by 3, then we multiply by 10, then we divide by 2 and get our output.

Do you think the output is always a multiple of 6? This is a great question and the answer's no because the product of 3 and 10 is 30, and 30 divided by 2 gives 15, therefore all the outputs will be multiples of 15, and 6 is not a factor of 15.

Great work, so let's move on to our task.

Firstly, in this particular question we're asked to shade in all the multiples of 10.

Once you shade in all the multiples of 10, a number will reveal itself.

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

Great work, so let's move on to question 2.

Question 2 shows us a four-digit number, but we're missing a digit.

We're asked to insert a digit below to make the statement true.

For question 2A, it wants us to put in a digit so that the number is a multiple of 10.

For part B, it wants us to put in a digit so the number is a multiple of 5.

For question 3, it shows a four-digit number but we're missing two digits now and we're asked to insert two digits below to make the statements true.

It wants us to insert two digits so our four-digit number is a multiple of 10.

It wants us to insert two digits so our four-digit number is a multiple of 3 and 5.

It wants us to insert those two digits so our number is a multiple of 9 and 10.

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

Question 4 is a great question as it wants us to fill the table incorrectly.

Now, Laura uses integers as her inputs into a function machine.

We're asked to place a tick in the cell if every single number will be a multiple of 2, 3, or 10.

For example, we have a function machine with an integer input, then we multiply by 6 and multiply by 5.

Will every single output be a multiple of 2? Will every single output be a multiple of 3? And will every single output be a multiple of 10? For the second function machine, we have an integer input, then we multiply by 8, then we multiply by 7.

Will every single output be a multiple of 2? Will every single output be a multiple of 3? Or/and will every single output be a multiple of 10? The next function machine states if we have an integer input, then multiply by 10, multiply by 6, then divide by 5, will every single output be a multiple of 2? Will every single output be a multiple of 3? Will every single output be a multiple of 10? The last part states, if we have an integer input, we multiply by 6, then multiply by 5, and then divide by 2, will every single output be a multiple of 2? Will every single output be a multiple of 3? And will every single output be a multiple of 10? This is a great question.

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

Great work, so let's go through our answers, starting with question 1.

We were asked to shade in all the multiples of 10.

Once shading in all the multiples of 10, can you see the number? Yes, it's the number 3.

Huge well done if you've got this one correct.

For question 2, we had a four-digit number and we needed to insert one digit to make the following statements true.

So for 2A, there was only one answer, which was 4,170.

For 2B, to identify a multiple of 5, you could have one of two answers.

4,170 or 4,175.

Well done if you got those correct.

For question 3, we needed to insert two digits into our four-digit number for part A to make a multiple of 10.

There were lots of different answers here, so I'm going to give you an example, 8,950.

You could have even had 8,960, 8,990.

It doesn't really make a difference as long as you have the digit in the ones column to be a 0.

For 3B, it states that we have to have a multiple of 3 and 5.

Well, we have 8,900 and a number which is a multiple of 3 and 5 is 8,910, 8,925, 8,940, 8,955, 8,970, and 8,985.

A huge well done if you got any one of those.

For part C, we had to identify if it's a multiple of 9 and 10, and the only answer we would've got is 8,910.

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

So let's go through our answers for question 4.

Now, question 4, we know Laura uses integers as the inputs into her function machine and we're asked to place a tick in the cell if every output number will be a multiple of 2, 3, or 10.

So the first function machine states we have an in integer input, then we multiply by 6 and multiply by 5.

This means we are multiplying by 30, so our output will always be a multiple of 30.

Now we know that 2 is a factor of 30, so that means every number will be a multiple of 2.

We also know 3 is a factor of 30, so that means we know every number will be a multiple of 3.

We also know 10 is a factor of 30, so that means every output value will be a multiple of 10.

For the second function machine, it states that we have an integer input, we multiply by 8 and multiply by 7.

So this means every single output will be a multiple of 56.

Now we know 2 is a factor of 56, so that means we know every number will be a multiple of 2.

3 is not a factor of 56, so that means every number will not be a multiple of 3.

10 is not a factor of 56, so every number will not be a multiple of 10.

Now let's move on to the next function machine.

We have our integer input, multiply by 10, multiply by 6, and then divide by 5.

So what does this mean? Well, 10 multiplied by 6 is 60, divide by 5 is 12.

So that means our output values will always be multiples of 12.

Well, 2 is a factor of 12, so that means we know every number will be a multiple of 2.

3 is a factor of 12, so that means we know every number will be a multiple of 3.

10 is not a factor of 12, so that means we know every number will not be a multiple of 10.

The last function machine we're multiplying by 6, then multiplying by 5, then dividing by 2.

While 6 multiplied by 5 is 30, divided by 2 is 15, so we know every output will be a multiple of 15.

Well, 2 is not factor of 15, so that means every number will not be a multiple of 2.

3 is a factor of 15, so therefore we know every number will be a multiple of 3.

And 10 is not a factor of 15, so that means we know every number will not be a multiple of 10.

That was a great question.

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

A number is divisible by 5 if the digit in the ones column is a 5 or 0, and a number is divisible by 10 if the digit in the ones column is a 0 only.

A huge well done today.

We did a lot of work and it was great learning with you.