Lesson video

Hi, everyone.

My name is Miss Ku, 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 as looking at some key words 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.

In today's lesson, from the unit Properties of number: factors, multiples, squares, and cubes, we will be listing multiples, and by the end of the lesson, you'll be able to state what a multiple is and list multiples and common multiples of two or more numbers.

So let's look at our keywords for our lesson today.

The first keyword that we'll be looking at is a multiple, and a multiple is the product of a number and an integer.

The next keyword that we'll be looking at is a common multiple, and a common multiple is a number that is a multiple of two or more numbers.

Our lesson will be broken into three parts.

So let's start the first part by listing multiples.

So let's start by looking at an example because there are lots of different ways to list a multiple of a number.

Here, the example wants us to list the first six multiples of five.

So I'm going to use an array.

Now, because I'm looking for this first six multiples of five, I'm going to have my first row being five dots.

Now, the second row will be adding another five dots, so I have 10 dots.

The third row is adding another five dots, so I have 15 dots.

The fourth row is adding another five dots, so I have 20 dots.

The fifth row has another five dots, so I have 25 dots.

And lastly, the sixth row has 30 dots, so now I have my six multiples of five.

Using an array is one example of how you can identify multiples.

Let's have a look at another way by counting on.

Well, starting with the number five, let's simply add on another five, thus giving us 10.

Now, I'm gonna simply add another five to give me 15.

Adding another five gives me 20.

Adding another five gives me 25, and finally, adding another five gives me 30.

So you can see, we can find the first six multiples of five by simply counting up.

Let's have a look at another way using a multiplication table.

Identifying the first six multiples of five simply means we need to look at the five times table, and identify the first six numbers from that five times table.

So you can see we have 5, 10, 15, 20, 25, and 30.

So here are our six multiples of five.

You may have chosen to use the multiplication table going across, which is absolutely fine, and still gives you those first six multiples of five.

Lastly, and my favourite way, is simply using products.

So identifying the first six multiples of five, we simply do five multiplied by one, which is our five, because this is our first multiple of five.

To identify the second multiple of five, we do five times two, which is 10.

To identify the third multiple of five, we do five times three, which is 15.

To identify the fourth multiple of five, we do five times four, which is 20.

What do you think the calculation would be for the fifth multiple of five? Well done.

It'd be five times five, which is 25, and the sixth multiple of five would simply be five times six, which is 30.

For me, this is my favourite way to identify the first six multiples of five.

Now, let's have a look at a checking question.

Which of the following set of numbers are the first six multiples of eight? And explain what the other sets of numbers represent.

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

Well done if you spotted the answer is D.

So let's go through each answer, and understand what do these set of numbers represent.

Looking at A, we have the first six multiples of six, 6, 12, 18, 24, 30, and 36.

For B, we have the factors of 8, 1, 8, 2, and 4.

C was a hard one to identify because these are all multiples of eight.

However, they are not the first six multiples of eight.

D represents the first six multiples of eight.

Eight times one is eight, eight times two is 16, eight times three is 24, eight times four is 32, eight times five is 40, and eight times six is 48.

Well done if you got that one right.

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

Laura wrote a list of consecutive multiples.

Can you work out the missing multiples? See if you can give it a go.

Press pause if you need more time.

This was a great question.

Well done.

Well, if you know the first multiple is 131, that means 131 times one is 131.

The second multiple would be 131 times two, which is 262.

The third multiple works out to be 131 times three, which is 393, and the fourth multiple is 131 multiplied by four, which is 524.

Well done if you got that one right.

So now, let's move on to the practise questions.

Question one wants you to list the first five multiples of eight, then the first five multiples of 10, then the first five multiples of 12, and then the first five multiples of 15.

Question two states that Alex says 30 is a multiple of four because four multiplied by 7.

5 is 30.

Now, is Alex correct? Explain your answer.

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

Well done.

So let's move on to the next question.

The next question has lots of inkblots, Jacob started listing the first multiples of some numbers.

He then spilled ink all over his work.

Now, we're asked to find the multiples Jacob was working out, and we're asked to find those missing numbers.

So question 3a states, well, this represents the multiples of 111, but we have two numbers that we can't see.

Can you figure them out? B, well, we don't know what those multiples are, but we do have some multiples listed.

The second multiple is 46, the fourth multiple is 92, the fifth multiple is 115, and we're missing some other multiples.

Can you see what you have to do here? On C, we're given the multiples of 324, but we're missing the second multiple, the third multiple, and the fourth one.

Part D, this one is a tough one.

You don't know what the multiples are.

We're missing the first, second, third, and fourth multiple, but we do have the fifth multiple, which is 4,225.

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

Great work.

These were tough questions, so let's go through our answers.

For question one, we're asked to list the first five multiples of 8, 10, 12, and 15.

So our first five multiples of eight are 8, 16, 24, 32, and 40.

The first five multiples of 10 are 10, 20, 30, 40, and 50.

The first five multiples of 12 are 12, 24, 36, 48, and 60.

The first five multiples of 15 are 15, 30, 45, 60, and 75.

Well done if you got those right.

Question two states that Alex says 30 is a multiple of four because four times 7.

5 is 30.

Is he correct? Then, you have to explain.

Well, hopefully, you spotted he's not correct because four has not been multiplied by an integer.

Let's have a look at question three.

Now, Jacob spilled ink all over his work, and we're missing some numbers.

We're asked to find the multiples Jacob was working out, and identify those missing numbers.

For A, we know they're multiples of 111, so we're simply going up by 111 each time.

One times 111 is 111, two times 111 is 222, three times 111 is 333.

Well done if you got that one right.

B, well, we don't know what those multiples are, but we do know the second multiple is 46.

So two times what gave us that 46? Hopefully, you would've spotted it's 23.

So that means we know the multiples of 23 start with 23, then 46, then 69, 92, 115 onwards.

Well done if you got that one right.

C, multiples of 324.

So we know we're going up by 324 each time.

The first multiple is 324, the second is 648, the third is 972, the fourth is 1,296, and it works out for the fifth to be 1,620.

That was a good question.

D is an excellent question.

So a huge well done if you got any of these right.

We don't know what the multiples are, but we do know the fifth multiple is 4,225, so that means something times five gives us 4,225.

Working it out, you may have figured out it's 845, because 845 multiplied by five is 4,225, so we're increasing by 845 each time.

Our first multiple is 845.

Our second multiple is 1,690.

Our third multiple is 2,535, and our fourth multiple is 3,380.

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

Great work so far.

So let's move on to the second part of our lesson, using listing to find common multiples.

Well, a common multiple is a number that is a multiple of two or more numbers.

So let's have a look at an example.

In this example, it wants us to list the first 10 multiples of three, and it wants us to list the first 10 multiples of four.

So the first 10 multiples of three are 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30.

You can use anywhere you want to get to those first 10 multiples of three.

The first 10 multiples of four are 4, 8, 12, 16, 20, 24, 28, 32, 38, and 40, so we've listed our first 10 multiples of four.

Now, we're going to look at this word, common multiple.

Remember, common multiple is a number that is a multiple of two or more numbers.

So can you see a common multiple in these two lists? In other words, what number appears in the first 10 multiples of three, and it also appears in the first 10 multiples of four? Well, hopefully, you spotted 12 and also 24, so this means 12 and 24 are common multiples of three and four.

There's actually an infinite number of common multiples, and remember we've only looked at the first 10 multiples of three and four here.

So let's check your understanding.

Jun lists multiples of eight and seven.

The multiples of eight are 8, 16, 24, 32, 40, 48, and so on and so forth.

The multiples of seven are 7, 14, 21, 28, 35, 42, 47, and so on and so forth.

Now, Jun says there are no common multiples of eight and seven.

Is Jun correct? And you have to explain.

Press pause if you need more time.

Hopefully, you've spotted that Jun is incorrect.

He needed to continue listing the multiples, and he would've found 56 is a common multiple of both seven and eight.

Just remember there are an infinite number of common multiples.

Let's have a look at another check question.

I'll do the first part.

I'd like you to try the second part.

First, we're asked to list all the common multiples of three and five that are less than 50.

So I'm going to start listing the multiples of three which are less than 50.

You can see them here.

Then, I'm going to list the multiples of five which are less than 50, so you can see them here.

Now, we need to look at our multiples and identify what number is in both the multiples of three and the multiples of five.

Hopefully, you've spotted all the common multiples.

Now, it's your turn.

The question wants you to list the common multiples of six and four that are less than 50.

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

Well done.

So let's have a look.

Firstly, the multiples of four which are less than 50 are listed here.

Then, let's list our multiples of six which are less than 50.

So I've listed them here.

Now, let's have a look at our lists and see can we identify a number that is in both the multiples of four and the multiples of six? Yes, we can.

A huge well done if you got that one right.

Now, let's move on to your task.

Question one wants you to find all the common multiples of 7 and 5 which are less than 100.

Question two wants you to find all the common multiples of 5, 8, and 10 which are less than 100.

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

Well done.

So let's move on to the next task.

Question three wants you to use the numbers and fill in the missing gaps.

Now, you can only use each number once.

We have the numbers 5, 6, 9, 10, 12, 12, 27, 27, and 50.

Can you fill in those gaps to identify something is a common multiple of something and something? Give it a go, and press pause if you need.

Let's move on to the last task in this section.

Question four.

Now, a path is made up of 100 steps, numbered 1 to a 100.

Our first robot, Robot A, steps on every eighth step.

Our second robot, Robot B, steps on every third step, and our third robot, Robot C, steps on every sixth step.

Now, the question wants you to identify which numbered steps will all three robots have stepped on? And the second part asks, well, if Robot D steps on every second step, will this change your answer to part A? And you have to explain why.

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

A huge well done.

So let's go through these answers.

Well, for question one, we were asked to identify the common multiples of 7 and 5 which are less than 100.

Hopefully, you spotted it's 35 and 70.

For question two, we get asked to identify the common multiples of 5, 8, and 10 which are less than 100.

Hopefully, you've worked out it to be 40 and 80.

Well done.

Now, let's have a look at question three.

Now, don't worry about the ordering of your answers as long as the correct common multiples are paired with the correct number.

So this is what you should have had.

12 is a common multiple of 6 and 12, 50 is a common multiple of 5 and 10, and 27 is a common multiple of 27 and 9.

That was a great question.

Well done if you got that one right.

Now, let's have a look at question four.

Now remember, we have our steps, numbered 1 to 100.

Robot A steps on every eighth step, Robot B steps on every third step, and Robot C steps on every sixth step.

So when we're asked to identify which number step have all three robots stepped on, we're asked to identify the common multiple of 8, 3, and 6 which is less than 100.

Hopefully, you would've worked it out to be 24, 48, and 72.

For part B, we have another robot, and it steps on every second step.

Will this change our answer to part A? And we have to explain why.

No, it wouldn't change our answer because multiples of 2 are also common multiples of 8 and 6, so it won't make any difference whatsoever.

That was a great question.

Well done.

Great work so far.

So let's move on to the last part of our lesson, which is using common multiples to compare fractions.

We can use common multiples to compare fractions by writing the equivalent fraction where the denominator is that common multiple, and when there is a common denominator, we can make comparisons more easily.

So let's have a look at example to see what I mean.

Well, here, we have Sofia and Jacob.

Sofia is a good tennis player, and she generally wins two out of three games played.

Jacob is also a good tennis player, and he generally wins three out of five games played.

We have to compare in order to identify who is the better tennis player, and we have to show our working out.

Now, you might notice with these two fractions, we have different denominators, which makes the comparison difficult.

So in making our denominators the same, we can compare more effectively.

So I'm going to use my knowledge on equivalent fractions, as well as listing multiples to find out our common multiple.

Starting with Sofia.

Well, we know 2/3 is the same as 4/6, which is also the same as 6/9, which is also the same as 10/15.

These are all equivalent fractions.

And for Jacob, we know 3/5 is the same as 6/10, which is the same as 9/15.

Now, you can see we have a common denominator of 15, so now we can make our comparison more easily.

Sofia generally wins 10 out of 15 games, and Jacob generally wins nine out of 15 games.

Now, we can make an easy comparison.

It's clear that Sofia is the better tennis player because if they played 15 games, Sofia would be expected to win 10, and Jacob would be expected to win nine.

Let's have a look at another check question.

Aisha does the following working out to find out which fraction is smaller.

She's given 2/3 or 5/9.

You can see her working here, and she has identified the equivalent fractions of 2/3 to be 4/6, 6/9, 8/12, 10/15, and 12/18.

She's also identified the equivalent fractions of 5/9 to be 10/18, 15/27, and 20/36.

Which equivalent fractions should she use to compare? And using this, which fraction is the smallest? Well, you can see from the question, we've got a bit of a choice.

We could use the 6/9 and the 5/9, as both of them have a denominator of nine.

Thus, identifying the smallest fraction would be 5/9.

Alternatively, you could have also compared 12/18 and 10/18 because we have both of the denominators are the same, 18, so therefore, we know the smaller fraction is still 5/9.

Lastly, let's have a look at our last check question.

Andeep compares 3/4 and 7/10, and he does the following working out.

Which is the correct working out, and can you explain? Well, hopefully, you've spotted A is correct.

Unfortunately, B shows incorrect working out of equivalent fractions.

So you can see how important equivalent fractions are when comparing fractions.

Now, let's move on to the task.

Question one wants you to use common multiples to compare fractions, and identify the largest fraction.

It's important that you do show your working out.

For part A, you need to identify the largest fraction out of 3/5 and 2/7.

For part B, you want to identify the largest fraction out of 4/5 and 5/6.

For part C, you want to identify the largest fraction out of 7/10 and 3/8.

Question two shows we have three students, and they play a computer game, and they have the following success rates.

Sam has a good success rate of 2/3, Lucas has a good success rate of 11/15, and Alex has a good success rate of 3/5.

But who is the best player? And we have to show our working out.

The second part wants us to state a fractional success rate in between Sam's and Alex's success rates.

This is a great question.

If you need more time, press pause.

Well done.

So let's go through our answers.

For question one, hopefully, you've listed the equivalent fractions of 3/5 and 2/7.

I've decided to pick a denominator of 35, so that means 21/35 is equivalent to 3/5, and 10/35 is equivalent to 2/7, so the largest fraction is 3/5, as that is equivalent to 21/35.

For part B, hopefully, you've listed the equivalent fractions of 4/5 and 5/6.

Looking at a common denominator, I'm going to choose 30.

So this means the equivalent fraction to 4/5 is 24/30, and the equivalent fraction to 5/6 is 25/30.

Now, I can compare, so I know 5/6 is the biggest fraction.

For part C, listing the equivalent fractions for 7/10 and 3/8, I can spot, I can use a common denominator of 40.

This makes my comparison much easier, so I can see that 7/10 is the largest fraction.

Well done if you got those correct.

Let's have a look at question two.

We have three students with very good success rates, and we have to identify who is the best player, and we've got to make sure we show our working out.

Now, we have different denominators, so I'm going to identify a common denominator of 30.

So 2/3 is equivalent to 20/30, 11/15 is equivalent to 22/30, and 3/5 is equivalent to 18/30.

Now, I can compare more easily, and spot that Lucas is the best player.

The second part of the question wants us to state a fractional success rate in between Sam's and Alex's success rates.

Well, hopefully, you can spot Sam has a success rate of 20/30, and Alex has a success rate of 18/30, so that means an example success rate in between 20/30 and 18/30 is 19/30.

There's lots of different answers there, but this is the easiest to calculate.

So in summary, a common multiple is a number that is a multiple of two or more numbers.

Common multiples can be found by listing multiples of each number, and then identifying the common multiple from each list.

Common multiples can be used to compare fractions too.

A huge well done.

It was great learning with you today.