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Hi, my name is Miss Kidd-Rossiter, I'm a maths teacher in Oak, and I'm going to be taking your lesson today on representing ratio.

Take a minute now to clear away any distractions and find a quiet place to work if you can, okay? Are you ready? Let's get started.

We're going to start today's lesson with the try this.

In a moment, you'll see four students appear on the screen.

They've been mixing green and white paint in different ways.

Your job is to compare the shades that they've made.

Pause the video now and have a go at this activity.

When you're ready, resume the video.

If you're struggling, it might help you to draw a diagram.

Okay, so we going to have a look at the connect part of the lesson now.

We going to start by comparing Antoni and Binh from the try this.

So we know that Anthony has mixed his green and white paint in the ratio five to two.

So that's five parts green and two parts white.

We can represent this using a bar model, like the one on your screen.

Similarly Binh has mixed her pain in the ratio six to two, where six parts are green and two parts are white.

We could also show this using a bar model.

Pause the video now and think about how you could use these bar models to compare the proportion of green paint in Antoni and Bihn's mixtures.

So one way that I thought about doing it, was to put one on top of the other.

When I do this, I can clearly see that Antoni's got less green paint in his mixture proportionally than Bihn has.

Right, we going to have a look now comparing Bihn's paint mixture with Cala's paint mixture.

We've already got on the screen one representation that we could use for Bihn.

So we need to think about how we could represent Cala's.

Three quarters of Cala's paint is green.

So that means there are three parts of green and one part is white.

So we could represent this in a bar model like this.

Pause the video now and have a think about how you could compare these two bar models.

Is there anything that you notice this time? Okay, so again, I'm going to compare mine by putting one on top of the other.

So this time I've got Bihn's on the top and Cala's underneath.

I can quite clearly see that the proportion of green paint in each of these mixtures is the same.

Two parts of Bihn's mixture, is equal to one part of Cala's mixture.

This means that six to two and three to one are equivalent ratios.

We can represent this in a table also.

So Cala's paint is mixed in the ratio three to one, which we know is equivalent to six to two.

And we can find the constant of proportionality.

So that's what we've multiplied the ratio three to one by, to get six to two.

And in this case, we've multiplied by two.

We have to remember that it's both parts of our ratio, both sides of our ratio that have multiplied by two.

Okay now we're going to compare Bihn's paint mixture to Xavier's paint mixture.

We've still got Bihn's representation on the screen.

Xavier's paint mixture has three tenths of it being white.

So that means that seven parts must be green, and three parts are white.

So we could represent it in this way.

Pause the video now and have a think about how we could compare these two bar models.

Also, can you think about when a bar model might become a bit tricky to use.

Brilliant, so again, I can compare these by putting one on top of the other like this.

And I can see that six to two has more green paint proportionally than seven to three.

I also asked you to think about the limitations of bar models.

So when we might be able to not use a bar model to represent what we're wanting to see.

If we get into having really big numbers, like 42 to seven or 127 to nine, it would be really tricky to draw those bar models.

So you need to think about is there another way, that we could compare ratios? The one way that I've thought about doing it, is making one part of the ratio the same.

So if we look here, we've got Bihn's ratio is six to two, Xavier's ratio is seven to three.

Could I make one part of those ratios, either the green or the white the same? Pause the video now and think about how you could do that.

So I'm going to do it.

I'm making the white part of the ratio the same.

But you could do it by making the green the same as well.

They both work.

So I know that six is a multiple of two and three.

So I'm going to make the white paint in each ratio become six.

So for Bihn's paint, this means that the constant of proportionality is three.

So I've multiplied the white paint by three to get six here.

So that means that I also need to multiply the green paint by three to create the equivalent ratio.

So six multiplied by three gives me 18.

For Xavier's paint my constant of proportionality this time is two.

I've multiplied the three by two to get six.

So that also means that I need to multiply the seven by two to create the equivalent ratio.

So seven multiplied by two, we know is 14.

So now we can compare these ratios because the white is the same in each case, six parts.

We know that proportionally, this one has more green paint because 18 is a higher number than 14.

Now you're going to apply what you've learned to the independent task.

So pause the video and navigate to the worksheet, to have a go at the questions.

We're now going to go through the answers to the independent task.

Well done for persevering with it, some of the questions on there were quite tricky.

So your answer to question one is five eights.

Your answer to question two is five to three, and your answer to question three is five tens.

And then extra well done if you remembered that you should simplify five tenths to one half.

The question four, here are your answers.

I'll let you have a look at those and I'm going to read them all out.

So pause the video if you need to.

And the question five, this was really tricky.

There were loads of correct answers here.

So well done if you managed to think about it in lots of different ways.

One way that I thought about it, was that four to eight is an equivalent ratio to one to two.

That would mean that the black part of my bar is one third of the whole bar.

And the white part of the bar is two thirds of the whole bar.

But as I said there's loads of different answers here that you could have come up with.

So extra well done if you came up with loads of that.

So the last thing that we going to do in today's lesson, is have a go at this explore task.

Antoni has lots of tins of green and white paint.

He is mixing up to seven tins together.

How many different shades can he make? And what if he could mix eight tins or nine tins? Pause the video now and have a go at this task.

Okay so hopefully you've had a really good go at this explore activity now, and I'm just going to talk you through one approach that I chose to use.

You could have done it a different way and that's absolutely fine.

So what I did was I listed all the possible ratios of tins of green paint to tins of white paint for seven tins.

So I could have had one tin of green paint to one tin of white paint.

I could have had one tin of green paint to two tins of white paint and so on.

You'll notice that the parts of my ratio never exceed seven because I've only got seven tins.

And then I thought, well, all of these options, different, so all of these different shades of green paint.

Well I don't think they are in fact they're not, because I've got some equivalent ratios here.

So if you look, I've got the ratio one to one, which is equivalent to the ratio two to two, and that is also equivalent to the ratio three to three.

So there's several pairs or trios of equivalent ratios here.

So again, I've got the ratio one to two that is equivalent to the ratio two to four.

And you can continue to go through my answer if you like and find other equivalent ratios in there.

That brings us to the end of today's lesson.

So I hope you've had a really good learning experience and I look forward to seeing you again in the future, bye.