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.

This lesson is all about explaining the relationship between pairs of three and nine times tables facts that have the same product.

So in other words, all about the three and nine times tables, but in a little bit more detail.

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

Multiple.

Triple.

Great, let's find out what these words mean.

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

So for example, three times five is equal to 15.

15 is a multiple of three and five.

Now, the next definition we've got here is triple.

So to triple means to become three times as many or to multiply by three.

So for example, three tripled is nine.

So this lesson is all about our threes and nine times tables.

We've got two lesson cycles today.

Our first lesson cycle is all to do with tripling, and our second lesson cycle then moves on to finding out about pairs of facts.

Are you ready? Let's begin.

And joining us on our lesson journey today, we've got Andeep and Izzy.

They're going to be helping us with our mathematical thinking.

Now, triple means three times as many.

For example, we've got one ice cream cone here, and now I've got three ice cream cones.

So there is one group of one ice cream.

Triple means I have three groups of one ice cream.

It is three times as many.

This is the same as saying one times three.

Now I've got two sweets, and this has become six sweets all together.

So there is a group of two sweets.

Triple means I have three groups of two sweets.

It is three times as many.

This is the same as saying two times three.

Over to you.

I'd like you to fill in the blanks.

Triple three sweets is something sweets.

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

So how did you do? Well, you should have got nine because triple three is nine.

That's the same as saying three times three is equal to nine.

Now, Izzy has arranged nine counters.

How many groups of nine are there? One times nine is equal to nine, nine times one is equal to nine.

There is one group of nine.

One times nine is equal to nine.

Now, there are nine counters.

How many groups of three are there? There are three groups of three.

Three three times is equal to nine.

So there's one group of three, two groups of three and three groups of three.

You can say triple three is equal to nine.

Triple means three times.

There are three times as many threes as there are nines.

There are 18 counters on the screen.

How many groups of three are there? There are six groups of three.

Three six times is equal to 18 and we can represent this as a multiplication equation as well.

So six times three and three times six, which gives us a product of 18.

How many groups of nine are there? Well, there are two groups of nine.

That's nine two times.

There are two groups of nine, two times nine is 18.

And to represent this as a multiplication equation, we can write two times nine or nine times two, and they both give us the same product of 18 as well.

The product 18 is in both the three and nine times tables.

You can say triple six is equal to 18.

You can also say that 1/3 of 18 is equal to six.

Now, pairs of facts can help us to quickly solve multiplication equations.

What do you notice between these multiplication equations? So you've got two times three is equal to six and two times nine is equal to 18.

Well, when one factor triples, so does the product.

18 is triple six.

And now we're going to look at the multiplication equations.

Do you notice anything there? One factor stayed the same, which is two, but the three has tripled to nine.

So the product has also tripled.

Six is 1/3 of 18, which means nine has been divided by three.

Over to you.

Fill in the gap and I'd like you to use what you know about tripling.

So if you know that four times three is equal to 12, then you also know that four times nine is equal to? You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, without using your times tables facts, all you had to do was triple 12 to get 36.

Well done if you got that.

I'd like you to fill in the gap.

If you know that four times nine is 45, then you also know that five times three is? You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, you should have got 15 because 1/3 of 45 is 15.

Sometimes finding 1/3 of a number may not always be the most efficient method to calculate a multiplication equation, but in this sense, it's just good to know how the relationship of numbers work between the nines and threes.

So pairs of facts can help us to solve multiplication equations.

What do you notice? Well, when one factor triples, so does the product and it's easy to see here that the 30 has tripled to 90.

And that's because we can see that the factor three has tripled to nine, meaning that the product also tripled.

Finding 1/3 the amount means dividing by three.

So here what we would've done is divide nine by three, which means 30 is 1/3 the amount of 90.

Andeep says he can now use this to spot patterns.

We're now going to look at larger numbers.

So three times 100 is 300.

Nine times 100 is 900.

What do you notice? Now, remember, when one factor triples, so does the product.

So in this case, the three has tripled to nine, which means the product has tripled to 900.

And finding 1/3 the amount means dividing by three.

So we would've had to divide nine by three in order and we would've got three.

So three would've been our factor and it is there.

So three times 100 is 300.

And 1/3 of 900 is 300.

So 300 is 1/3 the amount of 900.

So Andeep says that "if I know that nine is three three, then I also know that 900 is triple 300." Onto your main task for this lesson cycle.

So for question one, Andeep and Izzy are setting up a sweet store for a fete.

Izzy needs three times as many items as Andeep.

Use the information below to fill out the table.

One has been done for you.

So you can see Andeep's items there are two sweets.

Izzy needs three times as many, so that would be six because two tripled is six.

The equation there is two times three, which is equal to six.

I'd like you to complete the rest of the table.

Then for question two, using the information from above, answer the following questions.

2a, if Andeep has 60 bars of chocolate, how many will Izzy need? 2b, if Izzy starts with 270 lollipops, how many lollipops will Andeep start with? C, if Izzy has 360 mini chocolate bars, how many will Andeep have? And D, Izzy has 240 mini choco-desserts.

How many will Andeep have? You could pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, this is what you should have got.

Let's have a look at this table in more detail.

We can see with Andeep's items, he's got four chocolate ice creams there.

So three times as many as that is four times three, which is 12.

So you could have written your equation as three times four or four times three.

Next, he has five sweets.

So five tripled is 15.

You could have recorded this as three times five or five times three.

Now, for this question, Izzy started off with three times as many.

She's got nine sweets there.

So nine divided by three is three.

So that's how many items Andeep would've had and that is also your equation.

Next, Andeep has seven lollipops.

Seven tripled is 21? So Izzy would've needed 21 lollipops and the equation for this is three times seven or seven times three.

And lastly, there's eight choco-desserts there.

So eight tripled is 24.

That's how many Izzy would've started with and then our equation would've been three times eight or eight times three.

Well done if you got all of those correct.

Let's move on to our word problems now.

So for question 2a, you should have got 180 and that's because 60 tripled is 180.

For question 2b, we needed to find 1/3 the amount and use the fact 27 divided by three.

So if we know that 27 divided by three is nine, we also know that 27 tens divided by three is 9 tens, which is equivalent to 90.

Andeep will start with 90 lollipops.

Question C, Izzy has 360 mini chocolate bars.

Now, if Andeep has 1/3 the amount, we know we're still dividing by three.

So then again, I would've used a division fact that I know to help.

So if I know that 36 divided by three is 12, then I also know that 36 tens divided by three is 12 tens, which is equivalent to 120.

So if you've got 120, you are correct.

And lastly, for question D, Izzy starts off with 240 mini chocolate desserts.

Now, Andeep has 1/3 the amount, so that means we're dividing by three.

If I know that 24 divided by three is eight, then I know that 24 tens divided by three is eight tens, which is equivalent to 80.

So Andeep would've started with 80 mini-choco desserts.

Well done if you've got all of those questions correct, I'm super proud of you.

Now let's get ready to move on to lesson cycle two.

Now, lesson cycle two is all to do with pairs of facts.

Let's get started.

So Andeep and Izzy are comparing one three and one nine.

Andeep says there are many ways to represent this.

One group of three.

One times three is three.

One three is three.

Three times one is three.

Three one time is three.

And Izzy says that she can represent nine the same way too.

So she's got one group of nine.

One times nine is nine.

One nine is nine, nine times one is nine and nine one time is nine.

What do you notice? Well, you may have said something along the lines of nine is triple three.

So one nine is triple one three.

Let's move on.

This is three groups of three.

Three times three is equal to nine, three threes is nine, three times three is equal to nine.

Three three times is nine.

Now let's look at our second array.

Three groups of nine, three times nine is equal to 27, three nines is 27, nine times three is equal to 27, nine three times is 27.

So you may have noticed that the product has always stayed the same.

The groups which represent the factors changed order.

Is there anything else that you may have noticed? Well, nine is triple three.

So three nines is triple three threes.

Now, Izzy says she can use this to quickly solve multiplication questions.

Over to you.

I'd like you to fill in the blanks using the relationship between the threes and nines.

Have a look at the arrays, you can pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, 45 is something 15.

Well, if you got 45 is triple 15, you are correct.

Good job.

I'd like you to fill in the blanks again using the relationship between the threes and the nines.

The arrays are three groups of five and five groups of nine, 15 is something 45.

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

So how did you do? Well, you should have got 15 is 1/3 of 45.

And we know this because 15 tripled gives us 45.

We can use the inverse to help us.

Now, let's move on.

Andeep and Izzy are comparing other groups.

So I can see two arrays here.

I've got four groups of three, which is 12.

That's on the left-hand side and on the right-hand side, I've got four groups of nine, which is 36.

Now, we can represent this as four groups of three and the second array, we can represent as four groups of nine.

What do you notice? Now, nine is triple three.

So four nines is triple four threes.

This is a fact pair.

By tripling, we've uncovered a new fact.

Over to you.

I'd like you to use the relationship between the threes and nines to fill in the blanks.

So Andeep says if he knows that three times seven equals 21, then Izzy also knows that nine times seven is? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? I'm hoping you did not count on from nines to help you with this.

I'm hoping you used your knowledge of the threes to help you.

So nine is triple three.

So seven nines is triple seven threes.

In other words, if you multiplied your product of 21 by three, you would've got 63, which is also an efficient way to calculate what nine times seven is.

Let's move on.

Andeep is filling in the missing numbers.

He's got two equations here, three times six, which is equal to 18, and nine times six and there's a gap.

Andeep says, "I don't know my nine times tables.

I could count on in nines." What advice would you give to Andeep? Have a think.

Now, Izzy says she thinks there is an easier way.

You may have said that nine is triple three.

So six nines is triple six threes.

That means we need to multiply 18 by three.

Now, that could give us more work to do than we initially wanted to.

So in order to calculate what 18 times three is, you could use a repeated addition to help you.

So that's 18 add 18 add 18.

Now, if I was to compare the two methods, yes, I could use my knowledge of the threes and nines to help me with this question, but I think a more efficient way of calculating what nine times six is would be to just know my multiplication fact for that.

But because we're looking at the relationship between the threes and nines, this is also a super cool method to use.

So this would've given you a product of 54.

So nine times six is 54.

Now, Andeep's filling in more missing number questions.

This time he knows that nine times nine is equal to 81.

So using that, how can we calculate what nine times three is? He says he doesn't know his three times tables, but he could count on in threes.

What advice would you give to Andeep? Izzy again says she thinks there's a more efficient way.

Now, remember, three is 1/3 of nine.

Nine threes is 1/3 of nine nines.

So that means we can divide 81 by three.

And to make this easier, we can partition 81 into 60 and 21, which are both multiples of three.

And then we divide both of them by three, which gives you a quotient of 27.

Andeep says, "Yes, that's correct." So nine times three is 27.

Onto the main task.

You're going to use what you know about the relationship between the three and nine times tables.

Find triple and 1/3 of the numbers below without calculating.

So you've got the numbers 99, 9, 27, 270, 36, 360, 15, 150 and 180.

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

So how did you do? Now, one way I would've tackled this question was to start off by finding 1/3.

Now, let's look at 99.

I know that 99 divided by three is 33 and that's because I can partition 99 into 90 and three and I know both are divisible by three.

So that would've given me 33.

1/3 of nine is three.

Now, if I know that 1/3 of 27 is nine, then I also know that 1/3 of 270 is 90.

If I know that 1/3 of 36 is 12, then I also know that 1/3 of 360 is 120 because 36 tens divided by three is 12 tens.

If I know that 1/3 of 15 is five, then I also know that 1/3 of 150 is 50, and that's because 15 tens divided by three is five tens.

And lastly, if I know that 18 divided by three is six, then 18 tens divided by three is six tens, which is equivalent to 60.

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

Now let's move on to tripling.

So let's look at nine first.

I know that nine tripled is 27.

I can then use that to help me calculate what 99 tripled is.

So let's partition 99 into nine tens and nine ones.

Nine tens tripled is 27 tens.

Nine tripled is 27 ones.

If I add them together, I get 297.

Next, I've got 27.

27 tripled, you should have got 81.

Then if I know that 27 tripled is 81, then I also know that 27 tens tripled is 81 tens, which is equivalent to 810.

36 tripled is equivalent to 108.

Now, if I know that 36 tripled is 108, then I also know that 36 tens tripled is 108 tens, which is equivalent to 1,080.

Now, 15 tripled is 45.

So 150 or 15 tens tripled is 45 tens, which is equivalent to 450.

And lastly, if I know that 18 tripled is 54, then I also know that 18 tens tripled is 54 tens, which is 540.

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

I'm super proud of you.

Let's move on.

We've made it to the end of the lesson.

Well done.

Let's summarise our learning.

So today you explained the relationship between multiples of three and multiples of nine.

You should now understand that there are three times as many threes as nines, and we can say that triple three is equal to nine.

You should also understand that triple means three times.

Well done.

I'm very proud of you and I look forward to seeing you in the next lesson.

Bye.