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.

In this lesson, you'll be able to solve problems using the relationship between pairs of three and nine times tables facts, including those with the same product.

Your key word is on the screen now, and I'd like you to repeat it after me.

Triple.

Fantastic.

Let's find out what triple means.

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

Now, this lesson is made up of two lesson cycles.

The first lesson cycle consists of solving worded problems, and then we'll be moving on to solving problems. So let's begin.

In this lesson, you will meet Andeep and Izzy, who will help us with our mathematical thinking.

Now, when you solve problems, you need to decide what operation and calculation is needed.

So two things, operation, calculation.

Now, the language in a worded problem can help us decide on the calculation.

Sometimes, you may come across worded questions which involve multiplication or division.

So the ultimate question here is to divide or to multiply.

Equal parts usually means you need to divide.

Groups of usually means you need to multiply.

Halving means dividing by two.

Double and twice often mean you are multiplying by two.

Split and cut often means a division question.

Times and lots of mean we will be multiplying our factors.

Now, one more phrase that I'd like to throw in there is three times as many and triple.

Both mean we need to multiply by three.

Identifying the keywords will help you to find which operation to use, so let's have a look at the question that's on the screen.

Andeep has nine packets of guinea cards.

Izzy has three times as many.

How many guinea packs does Izzy have altogether? So let's look at the language.

In this example, we will have to multiply to find the answer, and the reason being is because we've got the words three times as many, which means we will be multiplying by three, or tripling.

Another clue here is altogether tells us we are finding the whole or total, which also tells us that we are multiplying.

So nine times three is 27 because nine tripled is 27.

Over to you, look at the word problem, which word suggests we must divide? A baker baked 36 cupcakes.

He splits them equally into boxes of nine.

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

Well, split usually means we have to divide, so well done if you've got that.

Equally tells us that we need equal groups.

Let's move on.

Identifying the key words will help you to find which operation to use.

So we've got a question here and I'm going to read it to you.

For every three metres a tabby cat is able to run, a jaguar runs nine metres.

If the cat ran 21 metres, how far did the jaguar run in total? Hmm, there's quite a bit going on in this question, but don't worry, we will break it down.

In this example, what we can do is multiply or divide to find the answer.

So let's look at it in more detail.

We've got some key numbers here, so we've got the fact that a tabby cat is able to run three metres, and for every three metres a tabby cat runs, a jaguar runs nine metres.

So already, there's a relationship between the three and the nine.

I know that three multiplied by three is nine, so let's keep that information in our head.

Now, if the cat runs 21 metres, we need to figure out what the jaguar's run in total.

So if you know that three times seven is 21, then you also know that nine times seven is 63, and that's because 21 tripled is 63.

And how did we know we were multiplying? Well, total tells us that we are finding the whole or total, which tells us we are multiplying.

Now, do remember when one factor triples, so does the product.

So we used our multiplication method there.

We could have also used division to help us to answer this question.

So we know that 21 divided by three is seven and then we multiply seven by nine, and that would've given us a product of 63.

So the Jaguar ran 63 metres in total.

Over to you.

What calculation is correct for this worded problem? Justify your thinking to your partner.

If Izzy sliced a ribbon into six nine centimetre pieces, how many three-centimeter slices would she be able to cut? Is it A, three times six is equal to 18, so 18 three-centimeter pieces, B, nine times six is equal to 54, so 54 three-centimeter pieces or C, nine times three is equal to 27, so 27 three-centimeter pieces.

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

So how did you do? Well, you should have got A.

Well done if you managed to get that correct.

Onto the main task for this lesson.

So for question 1a, you got to solve the following word problems. Explain how you can use the relationship between the three and nine times table facts for each answer.

1a, Andeep is comparing how fast cats run.

For every three metres a tabby cat is able to run, a Jaguar runs nine metres.

If the cat ran 15 metres, how far did the Jaguar run in total? 1b, if Izzy sliced the pizza into four nine-centimeter pieces, how many three-centimeter slices would she be able to cut? Question two, Andeep's grandfather caught 90 fish on his recent trip to Osley Lock.

If he puts the fish into boxes of nine, how many boxes will he need? 2b, if he puts them into boxes of three, how many boxes will he need? 3a, a baker baked 54 pastries and cakes all together.

If he puts them into boxes of nine, how many boxes will he need? And if he puts them into boxes of three, how many boxes will he need? Right, you could pause the video here and click play when you're ready to rejoin us.

Off you go.

Good luck.

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

So five times three metres gives us 15 metres, so five times nine metres is equal to 45 metres.

The jaguar ran 45 metres altogether.

You may have noticed that the jaguar runs three times as far, so we can triple 15 to get 45.

Well done if you managed to do that.

For question B, well, three times four is equal to 12.

Izzy would be able to cut 12 three centimetre pieces.

You may have noticed that three is one-third of nine, and so she would be able to cut triple the amount of pieces.

2a, 90 divided by nine is equal to 10 boxes, or nine times 10 is equal to 90.

So 10 boxes were needed altogether.

And lastly, 2b, if nine is triple three, then triple 10 is 30.

Andeep's grandfather will need 30 boxes.

And question three, a baker baked 54 pastries and cakes altogether.

If he puts them into boxes of nine, how many boxes will he need? Well, we know that nine multiplied by six is 54, or 54 divided by nine is equal to six, so six boxes will be required altogether.

And lastly, if you put them into boxes of three, well, we know that three is one-third of nine, so he'll need triple the amount, so 18 boxes altogether.

Well done if you managed to get all of those questions correct.

Let's move on to the next lesson cycle.

For this lesson cycle, we are going to be solving problems. Let's go.

Here's a quick recap.

So on the screen, I can see a triangle, and it has three sides.

I can also see a nonagon.

It has nine sides.

Andeep and Izzy are creating triangles and nonagons using straws to make the sides of the shapes.

Each bundle has 10 straws.

Now, Izzy has 90 straws.

Andeep has 36 straws.

Izzy says that she can make four nonagons.

Can you make the same? Andeep says yes, I know I will need 36 straws because if one nonagon needs nine straws, then four nonagons is the same as four times nine, which is equal to 36 straws.

This time, Izzy makes 13 triangles.

Can Andeep make the same? Izzy says I've got so many straws, I could make more.

Hmm, I don't think I'll have enough.

13 triangles is equal to 13 times three, which is equal to 39 straws.

I need 13 groups of three to make 13 triangles.

As Andeep only has 36 straws, he will not be able to make 13 triangles.

13 triangles requires 39 straws, so he is three straws short.

Now, if Izzy makes six triangles, how many nonagons must Andeep make to have used the same amount of straws? Have a think.

Well, Andeep says he can use his knowledge of the threes and nines to help him.

So he knows that three times six is equal to 18, and that's how many straws are required for six triangles.

One triangle needs three straws, so six triangles is six times three, which is equal to 18.

Andeep needs 18 straws.

I know that one nonagon will need triple the number of straws, so I can make a third of the amount of shapes.

So here we are, nine times two is equal to 18.

Andeep's made two nonagons.

Now if Andeep makes four nonagons, how many triangles does Izzy need to make to use the same amount of straws? Your turn.

Off you go, good luck.

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

So how did you do? Well, Izzy needs to make 12 triangles to use the same amount of straws as Andeep, and that's because four nonagons is equal to using 36 straws, so if one triangle uses three straws, which is one-third of the amount, then 12 triangles will use 36 straws.

Back to you.

If Izzy makes nine triangles, how many nonagons must Andeep make to have used the same amount of straws? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, one nonagon will need nine straws, so three nonagons means you will need 27 straws because nine tripled is 27.

One triangle needs three straws, so nine triangles is nine times three, which is equal to 27 straws.

Onto the main task for this lesson cycle.

So for question one, you're going to use some straws, lolly sticks, or other straight objects and you're going to make some nonagons.

Now turn the nonagons into triangles.

What happens if you make one more nonagon? How many triangles can you make now? What patterns do you notice? Question two, you're going to answer the following questions using your knowledge of the three and nine times tables.

So for 2a, Izzy makes nine triangles.

How many nonagons can Andeep make using the same number of sticks? 2b, now, Izzy makes four nonagons.

How many triangles can Andeep make using the same number of sticks? C, Izzy is given 90 sticks.

How many nonagons can she make from this? How many triangles can she make from this? D, Andeep is given 81 sticks.

How many nonagons can he make and how many triangles can he make? E, if Izzy is given 900 sticks, she knows she can make 100 nonagons.

Using this information, how many triangles can she make? You could pause the video here, click play when you're ready to rejoin us.

So how did you do? Well, for question one, you may have tried something like this.

Now, she turned three nonagons into nine triangles, and she still has 27 straws.

Four nonagons made 12 triangles.

She ended up using 36 straws.

So for every one nonagon, she made three triangles.

And I think you may have found the same as well.

The number of triangles is always triple the number of nonagons.

Let's move on to question two.

So for 2a, you should have got three nonagons, and that's because nine times three is equal to 27.

For 3b, you should have got 12 triangles, and that's because three times 12 is equal to 36.

For question C, you should have got 10 nonagons, and that's because we know that one nonagon is made of nine sticks, so if you're given 90 sticks, 90 divided by nine means we will end up with 10 nonagons.

Now, if Andeep was given 81 sticks, we could use our knowledge of multiplication to help us with this, so we know that nine times nine is equal to 81, so Andeep would've been able to make nine nonagons.

We can then use this information to calculate how many triangles he made.

We know that we will have to triple the amount.

So nine tripled is 27, so Andeep would've been able to make 27 triangles.

And lastly, so if we know that 900 sticks allows us to make 100 nonagons, we know that triple the amount of triangles would be made.

So that's 300 triangles, because one-third of nine is three so we would need to triple the amount to use the same amount of sticks.

Well done if you managed to get that correct.

Amazing.

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

Well done.

I hope you really enjoyed it.

So let's summarise our learning.

In this lesson, you were able to explain the relationship between multiples of three and multiples of nine, and you did this by solving problems. So you should now understand that there is a triple relationship between multiples of three and multiples of nine.

You should now be able to use this knowledge to solve problems. Well done.

I'm super proud of you.

Good job and I look forward to seeing you in the next lesson.

Bye.