Lesson video

Hello, I am 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 explain the relationship between multiples of three and six.

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

Multiple.

Doubling.

Halving.

Fantastic.

Let's move on.

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

So for example, four times four is equal to 16.

16 is a multiple of four.

Doubling is the act of becoming twice as many.

So if I were to double three, I'd get six.

So six is double three.

Halving means to divide into two equal parts.

So if I had 22 sweets and I had to halve that amount, I would end up with 11 sweets.

Now this lesson is all about our three times tables and our six times tables, and we are going to be exploring the relationship between our threes and sixes further in this lesson.

This lesson is made up of two lesson cycles.

Now our first lesson cycle is all to do with identifying multiples of three and six.

Our second lesson cycle is to then be able to explain the relationship between the threes and sixes and answer questions to do with those.

I'm really excited about this.

Let's get started.

So in this lesson you'll meet Andeep and Izzy, who will help us with our mathematical thinking.

We are going to start off by recapping counting in multiples of three, and I'd like each to chant with me.

So we're going to start off at zero, and if you're a bit stuck, think what is the next number if every time I add on three to my previous number.

Are you ready? Let's do a small countdown.

Three, two, one, zero.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36.

Did you manage to count all your multiples of three in order from zero to 36? If so, well done.

Now we're going to count in multiples of six, and I'd like you to chant with us again.

We're going to start from zero and each time we're going to be adding on six to the previous number.

Let's go.

0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72.

If you managed to do that, well done because that shows me that you know what your multiples of six are from zero all the way up to 72.

Good job.

Now, Andeep and Izzy are counting in multiples of three and six.

They record which multiples they count together at the same time.

So we've got a table here.

We've got our threes and our sixes on the left-hand side, and we've got numbers going from zero all the way up to 20.

Now let's see what happens when they start to count the multiples of three and six together.

We're gonna start off at zero.

So 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

So what do you notice? I can see a bit of a pattern emerging here.

All of the numbers said by the sixes group are also said by the threes group.

Hmm, that's interesting.

Do you notice anything else? Well, not all of the numbers said by the threes group are said by the sixes group.

Okay.

Now, for every number said by the sixes group, the threes group says two numbers.

Quite a lot of you may have picked up on that.

If you want to do this activity again, I would recommend that you do so with a friend.

So one friend can count on in threes, the other friend can count on in sixes, and each time if you clap together, that means it's a multiple of six.

Over to you.

I'd like you to identify which numbers are multiples of three, six, or both.

Now you've got only multiples of three on the left-hand side, then you've got both in the middle, and then only multiples of six on the right-hand side.

You've got the numbers 9, 27, 30, 36 and 80.

You can pause the video here and click play when you're ready to rejoin us after you've sorted the numbers, off you go.

So how did you do? Well, multiples of three are 9 and 27 because these are numbers that you would've counted on in threes.

So I know nine is a multiple of three because if I count on from zero, here we go, 3, 6, 9, I count that number.

And if I were to count on from 24 in multiples of three, I would say the number 27.

But let's check that.

24, add on another three, 27.

So that's a multiple of three.

Now interestingly, the multiples of six, we don't only multiples of six, we have nothing there.

However, when it comes to both, we've got 36, 18, and 30.

That means if we were to count on in multiples of three and six, we would say those numbers.

If you managed to get all of that correct, well done.

Let's move on.

Ooh, I've got two dice here and they've got three spots each.

How many groups of three are there? Well, here's one group of three, there's two groups of three.

So that means there are two groups of three.

Now, how many groups of six are there? Well, I can see one group of six.

Back to you.

How many groups of three are there? Let's count it together.

There's one group of three, two groups of three, three groups of three, four groups of three, five groups of three, six groups of three, seven groups of three, eight groups of three.

So there are eight groups of three.

We can also write this as eight times three, which is 24 spots all together.

Now how many groups of six are there? Hmm, I wonder if there's a way that we could use the information we already have to help us.

Let's have a look.

Well, there's one group of six.

There's two groups of six, three groups of six and four groups of six.

So there are four groups of six, which means we can also represent this as six times four or four times six, which also gives us the same amount of spots all together, which is 24.

This can be represented as a bar model.

Let's have a look at what that looks like.

Okay, so we've got eight groups of three and four groups of six.

Can you spot a relationship here between the threes and sixes? Well, for every one group of six, I can see that there are two groups of three.

Two pairs of three spots is the same as one group of six spots.

Over to you.

I'd like you to fill in the blanks.

10 lots of three spots is the same as something groups of six spots.

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

So how did you do? Well, 10 lots of three spots is the same as five groups of six spots.

Back to you.

Three times 10 is equal to six times.

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

So what did you get? Well, three times 10 is equal to six times five.

10 groups of three, that means we must have five groups of six.

Onto the main task for this lesson cycle.

For question one, you are going to be sorting the numbers correctly.

Numbers that are neither multiples of three or six need to go outside of the circles.

So you've got the number 0, 3, 6, 8, 15, 18, 27, 36, 42, and 48.

You are going to be sorting them into multiples of three, both, or multiples of six.

For question two, Andeep has created two designs for a maths competition.

So we can see two shapes here.

A triangle has three vertices and a star has six vertices.

So for one triangle, there are three vertices.

For one star, there are six vertices.

Using this information, you are going to complete the sentences.

So if three triangles have nine vertices, three stars will have vertices.

If five triangles have something amount of vertices, five stars will have.

vertices.

If six stars have.

vertices, six triangles will have.

vertices.

And lastly, if something amount of stars have 72 vertices, then triangles will have.

amount of vertices.

Use the images to help you.

You can pause the video here, have a go.

Good luck.

So this is what you should have got for the first question.

Eight is not a multiple of three or six because when counting on in multiples of three and six, eight is not counted.

However, 3, 27, and 15 are multiples of three.

Now, 18, 42, 36, 6, 0, and 48 are multiples of both three and six because when we count on in three and six, those are the multiples that we do say, which means they're also in both of those times tables.

Did you notice anything else? You may have noticed that it's the even multiples of the multiples of three that are also multiples of six.

Well done if you figured that out.

Let's move on.

Now for question two, this is what you should have got, and I'm going to read you out the answers and explain the answers in a little bit more detail.

So for question one, if we know that three triangles have nine vertices, then three stars will have 18, and that's because stars have double the amount of vertices than a triangle has so that means we need to double the product, and that gives us 18.

Now, if five triangles have 15 vertices, five stars, again we are doubling the amount, would have 30 vertices because 15 doubled is 30.

Now if six stars have 36 vertices, so you would've got that because you know that one star has six vertices.

So six stars is six times six, which is equal to 36 vertices.

Six triangles would've had 18 vertices.

Now that's because triangles have half the amount of vertices as stars, so if we know that six stars have 36 vertices, triangles would have half the amount, so half of 36 is 18.

Well done if you got that correct.

And for the last question, we know that 12 stars would have to have 72 vertices because using my multiplication facts, I know that six times 12 would give me 72, so that means there must be 12 stars.

And for the last part, 12 triangles would mean that there would be 36 vertices all together because 72 halved is 36.

Well done if you've got all of those questions correct.

Let's move on to the second lesson cycle.

For this lesson cycle, you are going to be explaining the relationship between threes and sixes.

Now Andeep and Izzy are comparing the three and six times tables.

On the left-hand side you've got your three times tables, and on the right-hand side you've got your six times tables.

I want you to think about what is the same and what is different.

Let's have a look together.

Well, products in the six times tables are also in the three times tables.

And we can see that there.

We can see that six times two is 12 and three times four is 12.

We can also see that six times seven is 42 and three times seven is 21.

So apart from multiplying by zero, multiples of six are double the multiples of three.

So if we have a look at the next row down, six times eight is 48, but three times eight is 24, 24 is half of 48.

Now apart from multiplying by zero, multiples of three are half the multiples of six.

So for example, let's have a look at three times 11 and that's 33.

And then if we look across, six times 11 is 66, so multiples of three are half of multiples of six.

Now Andeep says that if all multiples of six are multiples of three, then all multiples of three must be multiples of six.

Do you agree? Justify your thinking to your partner.

You can pause the video here.

So what did you guys discuss? Well, Andeep is incorrect because not all multiples of three are multiples of six.

Let's have a look at three times five.

Three times five is equal to 15, 15 is not a multiple of six.

In fact, the closest multiple of six to 15 is 18 or 12.

Let's move on.

Now, Andeep says that using this information, he knows that three times 13 is 39, and if he knows that, then he also knows that six times 13 must be 78.

Do you agree? I'd like you to justify your thinking to your partner.

Well, Andeep is correct because if we double a factor, so in this case the three has doubled to six, then the product also doubles.

So 39 doubled is 78.

Over to you.

If Andeep knows that six times nine is 54, then he also knows that three times nine must be equal to 27.

Do you agree? Justify your thinking to your partner.

You can pause the video here.

So how did it go? Well, Andeep is correct because this time we've halved a factor.

So the six has halved to three, which means the product also halves.

So half or 54 is 27.

So if you've got that, well done.

Andeep has arranged an array.

How many groups of three are there and how many groups of six are there? Well, there's three groups of four, so that's three times four, which is 12.

So how many groups of six are there? Let's have a look.

There are two groups of six.

This can be represented as two times six or six times two.

So you may have noticed that the product remains the same, the factors have changed.

What do you notice about the factors that have changed? Well, I can see that the three has doubled to six, but whilst the three has doubled to six, the other factor has halved to two, which means that our product remains the same.

Over to you.

I'd like you to identify how many groups of three there are and how many groups of six there are.

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

So how did you do? So there are eight groups of three, which is 24, and there are four groups of six, which also gives us 24.

And you may have noticed a pattern there as one factor doubles and the other halves, the product still stays the same as 24, but our relationship between the threes and sixes and actually the fours and eights as well helps us to answer this question.

Let's move on.

How many groups of three are there all together? Well, we've got one group of three, two groups of three, three groups of three, four groups of three, five groups of three, six groups of three, seven groups of three, and lastly, eight groups of three.

And each time we've added on three or counted on in three on our number line.

So this can be represented in this many ways.

So there are eight groups of three, eight threes, and eight times three is equal to 24.

Now how many groups of sixes are there? Can you use your relationship between the threes and sixes to help you? Let's have a look.

One group of six, two groups of six, three groups of six, and four groups of six, which can be represented as four groups of six, four sixes, or four times six, which is equal to 24.

Now using these facts, we can gather more facts.

Let's have a look at what those facts might be.

If we know that four times six is equal to 24, double four times six would give us 48.

So in other words, eight times six.

We can then look at how we can use the relationship of halving to give us another multiplication fact.

So if we know that eight times three is equal to 24, half of eight times three would be 12.

So that is the same as saying four times three is 12.

You have a representation on the screen.

How many ways can you group 18? 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 got this: six groups of three is equal to 18, three times six is equal to 18, or one times 18 is equal to 18.

There are so many ways we can group our numbers to give us different multiplication facts with the same product.

Let's move on.

Now Izzy is completing the question below.

So on the left-hand side we can see even numbers that have been multiplied by three, and then on the right-hand side we can see the numbers going from zero all the way up to five and they've been multiplied by six.

We've got the first two that have been filled up, so we've got zero and six.

Now Izzy started by following the instructions on the arrows.

Can you help her to complete the table? Let's have a go together.

So we've got zero and six already filled in.

Now the next product is four times three, but four times three is all is also equal to two times six.

I wonder what that could be? If you've got 12, well done.

Now the next number is another even number multiplied by three.

So six times three is equal to three times six.

If you've got 18, well done.

Now the next question is eight times three is equal to six times four.

If you got 24, good job.

And lastly, if you got 30, you are correct.

So 10 times three is equal to six times five.

What do you notice? Well, an even number times three gives you a product in the six times tables.

Now, that's key information there because if it was an odd number, I wonder if it would still be a multiple of six.

Let's have a think about that now.

So over to you.

An odd number multiplied by three gives a product in the six times tables.

Is it true or false? And I'd like you to then justify your answer.

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

Well, it's false.

Why do you think that is? Have a think.

That's because five times three, so an odd number multiplied by three, gives us 15 and 15 is not a multiple of six.

Onto your main task for this lesson cycle.

So for question one, you're going to use the array to complete the questions.

How many groups of three are there and how many groups of six are there? And I wonder if you can use the relationship between the threes and sixes to help you with that.

And for question two, you're going to fill in the gaps using the images to help you.

So when you double a factor, the product.

And when you halve one factor, the product.

And for question three, you're going to fill in the gaps using the bar model to help you.

So if something multiplied by three gives you.

that means something multiplied by six.

You can pause the video here.

Off we go, good luck, 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.

12 groups of three or 12 times three is equal to 36, and knowing that, if you halve the factor and also double the other factor, you should also get the same product.

So six times six is also equal to 36.

Well done if you managed to get that correct.

For question two, this is what you should have got for the first image.

So there are six groups of three.

That's equal to 18.

That also means that three times six is equal to 18.

If you know that 10 times three is equal to 30, then you also know that five times six is equal to 30 because for every two groups of three, there's one group of six.

And lastly, 12 groups of three is equal to 36, so that means six groups of six is equal to 36.

When you double a factor, the product also doubles.

When you halve one factor, the product halves.

And for question three, this is what you should have got.

So there are six groups of three that's equal to 18.

So that means three times six is equal to 18.

Eight groups of three is equal to 24, so that means four groups of six is equal to 24.

And lastly, 12 groups of three is equal to 36, which means six groups of six is equal to 36.

Give yourself a tick if you managed to get all of those correct.

Well done, you finished this lesson and I'm now going to help you summarise this learning.

In this lesson, you are able to explain the relationship between multiples of three and six.

You should now understand that all multiples of six are multiples of three, but not all multiples of three are multiples of six.

You should also understand that multiples of six are double the multiples of three and multiples of three are half the multiples of six.

Don't forget that it's the even numbers multiplied by three that give you a multiple of six.

Well done.

I'm so glad you made it to the end of this lesson.

I can't wait to see you in the next one.

Bye.