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Today, we will be learning to use ratio to express relationships.

Just a pencil and piece of paper needed for today's lesson so pause the video and get your things if you haven't done so already.

This is the agenda for today's lesson, no knowledge quiz today we're going straight into describing patterns using ratio.

Then we'll look at applying ratio to word problems before you do some independent learning and then a final quiz.

So let's go straight into looking at the same pattern that we started with yesterday.

I'd like you to think about how you can describe the pattern.

And this time think about how you can compare the number of squares to triangles, and how you can compare the number of triangles to squares.

Pause the video now and make some notes.

So when we're comparing the triangles and squares, we can ask ourselves a follow up question.

So in this pattern for every three triangles we have, how many squares are needed? So we can see that for every three triangles, six squares are needed.

And if we look at it the other way round, if we say for how many, for every six squares, how many triangles are needed, we would say for every six squares, three triangles are needed.

Then let's zoom in on one section of the pattern.

Now we're just looking at one of those parts.

So for every two squares, how many triangles are needed? We can see that for every two squares, one triangle is needed.

Now let's make a bit more sense of why we're looking at these questions.

So I want you to think about these four questions.

What proportion are triangles in this pattern? What proportion are squares? What's the ratio of triangles to squares? And what's the ratio of squares to triangles? And you've got a hint here.

The proportion compares one part to the whole.

So think back to the previous lesson, and a ratio compares one part to another part.

So pause the video now and try and make some notes around these questions.

So the first one, what proportion are triangles? We can see that the proportion of triangles is one third, one out of the three shapes are triangles.

So the proportion of squares therefore is two thirds.

And we're comparing this to the whole, we're comparing the parts to the whole.

Now in ratio, we're comparing one part to another part.

So the ratio of triangles to squares is this, there is one triangle for every two squares.

So the ratio of triangles to squares is one to two.

One triangle for every two squares comparing the two different parts.

Then we look at it the other way around.

What's the ratio of squares to triangles? So for every two squares, there's one triangle.

So the ratio of squares to triangles is two to one.

Now we're going to explore this a little bit further.

Have a look at the whole pattern again, and we're going to think about what is the ratio of triangles to squares.

Look at the order in which we're looking at the shapes.

We're going to start with the triangles and compare it to the squares.

So that is one triangle for every two squares.

So the ratio of triangles to squares is one to two.

Now what if there were 10 triangles in the pattern? How many squares would that be? Let's have a look at how that pattern would actually look.

So here I have my pattern now with 10 triangles, and I'm thinking about how many squares would that be? So if there are 10 triangles, there's 10 groups of one triangle, then there'll be 20 squares because there'll be 10 groups of two squares with the ratio of one to two.

There is one triangle for every two squares.

So the ratio of triangles to squares is one to two.

And if you looked at the ratio of this whole pattern, there are 10 triangles, 20 squares that's 10 to 20, which simplifies to one to two, if you zoom in on one section of the pattern.

So let's have a look at another pattern together, and then you're going to have a go at one independently.

So here I have a pattern of pentagons and trapezia.

So I'm going to use the sentence structure to help me.

And I'm going to start with the pentagons just because that's the first shape here.

And you can see that this pattern has two repeated sections, okay? So I can see that for every three pentagons here, there are two trapezia.

So three pentagons two trapezia.

So therefore, the ratio of pentagons to trapezia is three to two.

Let's look at it the other way round.

We can also say that for every two trapezia, there are three pentagons.

the ratio of trapezia to pentagons is two to three.

So use that logic now and apply it to this pattern here.

So you can use these sentence structures to help you pause the video now and complete the sentences.

So we'll start with the parallelograms. So for every one parallelogram there are four hexagons.

One parallelogram four hexagons, one parallelogram four hexagons and so on.

Therefore, the ratio of parallelograms to hexagons is one to four.

We can say then looking at it the other way round that for every four hexagons, there is one parallelogram.

So the ratio of hexagons to parallelograms is four to one.

Now we're going to have a look at applying this ratio to word problems to develop our understanding.

So Jannah and Aleeyah share their football cards.

They share the cards in the ratio of three to one.

So for every three cards, Jannah has Aleeyah has one card.

Now we need to scale it up.

If Jannah has 24 football cards, how many cards does Aleeyah have? So we're looking at the ratio of Jannah to Aleeyah.

When I'm working with ratio, I often find it helpful, to write the words that represent a ratio first.

So Jannah to Aleeyah is three to one.

If we're going to scale it up so that Jannah has 24 cards, we've multiplied the three by eight to get 24.

So you need to do the same for Aleeyah you multiply one by eight to get eight.

Then if we think about other numbers if Jannah had 15 cards, we would multiply the three by five to get 15.

And the one by five to get five.

Then we could say, if Aleeyah had seven cards, that would be one multiplied by seven.

So you would multiply three by seven to get 21.

So whatever you do to one part of the ratio to scale it up, you have to do to the other sub-part of the ratio.

Now I think you're ready for some independent learning.

So I'd like you to pause the video and complete the tasks and then click restart once you're finished and we'll go through the answers together.

So for question one, Janiya has drawn a picture of a caterpillar.

And she says that her picture is in the ratio of five to one.

So for every five centimetres of her picture, it represents one centimetre of a real caterpillar.

So her picture is 35 centimetres long it's five times bigger than the actual caterpillar.

How long is the real caterpillar? So again, as I said before, I like to use the words to represent my ratio.

So the picture versus the real caterpillar that is in the ratio of five to one.

So if the picture is 35 centimetres long, how long is the caterpillar? So five has been multiplied by seven to get to 35.

So the same happens to the other side.

So the real caterpillar is seven centimetres long.

So, as I said, the picture is five times greater than the real caterpillar.

And you can see that relationship here as well.

The real caterpillar is seven centimetres long.

The picture's 35 centimetres long that's 35 is five times greater than seven.

So you can see relationships going in multiple ways with ratio.

The question to Alex is planting tulips in the school garden.

He has bulbs for red and purple tulips.

And for every red five red tulips, he plants three purple tulips.

Therefore there's a ratio of five to three red to purple.

So he plants 15 purple tulips.

We need to know how many red tulips he planted.

So we've got our ratio red to purple five to three.

He planted 15 purple.

Make sure you had that on the correct side there, which means that three was multiplied by five it was scaled up he did five times as many.

So you do the same to the other side, which gives us a ratio of 25 to 15.

So in the end he planted 25 red tulip bulbs and 15 purple tulip bulbs.

In question three Becca is making chocolate chip cookies.

For every three milk chocolate chip cookie she makes, she makes two white chocolate cookies.

So the first part is what is the ratio of milk chocolate to white chocolate? So for every three milk she makes two white, so the ratio is three to two.

If she makes 12 white chocolate cookies, how many cookies does she make altogether? So here we can look at the ratio scaled up.

So we see that she made 12 white chocolate cookies so we multiply two by six.

So we do the same to the other side.

So she made 18 milk and 12 white.

The question was, how many did she make altogether? That is equal to 30 all together, 18 plus 12.

In question four, we have two friends with bags of sweets, of different ratios of fizzy to sour.

So Pippa's bag has a ratio of fizzy to sour of one to two.

Vicky's bag has a ratio of fizzy to sour of two to three.

If each bag has 30 sweets who has more fizzy sweets? So Pippa has fizzy to sour is one to two, so if we say that that was three sweets for every three sweets, one is fizzy and two are sour.

So we scale that up to 30 sweets that would mean that she would have 10 fizzy and 20 sour, 10 to 20.

And Vicky, her fizzy to sour ratio is two to three, and that will be five sweets so two out of the five fizzy and three out of the five sour.

And then we scale that up to be out of 30 by multiplying both by six, which gives us a ratio of 12 to 18.

And then the question was who has more fizzy sweets? Well, that would be Vicky.

Well done for working so hard in today's lesson, before you go, make sure you complete your final quiz, to test everything you've learned today.