Lesson video

Hi, my name's Miss Kidd-Rossiter.

I'm a maths teacher from Hull.

I'm going to be taking you through today's lesson, which is called "In the Same Ratio." It's going to build on the work that we've already done on groups.

Before we get started, make sure you've got a pen and something to write on and you're free from all distractions.

If possible, get yourself into a nice, quiet place, so that you can fully concentrate on today's lesson.

If you need to pause the video for any reason, then please do now but if not, let's get going.

So for today's Try this, you've got four students on your screen and they're going to colour in the patterns for the grid in the centre.

I want you to read the four student statements and then have a go at answering this question: How many tiles of each colour does each student use? And once you've figured that out, can you notice anything about the number of tiles that they use? If you feel confident with starting this activity, then pause the video now and have a go.

If not, keep listening and I'm going to give you a little bit of support.

Okay, so if you need a little bit of support, it will really, really, really help you to draw this grid out, if you don't have it in front of you already and then go through and try and colour in the different patterns that the students are speaking about.

If you're struggling with Anthony's statement, all it means is that in each group of five tiles, there'll be one red tile and four blue tiles.

So that hopefully will help you a little bit.

So pause the video now and have a go at this activity.

Well done for giving that Try this activity a go.

Let's go through some of them.

So first of all, Carla said, "I'm going to use two red tiles and four blue tiles in each row." So you can see on the diagram that I've shaded in the two red and the four blue in the first row and that would repeat in every row.

So if we just look at the ratio for the first row, how could we write that in ratio notation? Tell me now.

Excellent, we could write it as 2:4, couldn't we? So one row is in the ratio 2:4.

So if we continued that pattern and shaded all the grid in, how many red tiles would we have? Tell the screen now.

10, excellent.

And how many blue tiles would we have if we shaded that in? Tell me now.

Excellent, 20.

So we can see here that we would have 10 red tiles and 20 blue tiles in the final pattern.

Can we notice something about these two ratios? Pause the video now and think about that.

Excellent.

We can get from one to the other by multiplying both parts by the same constant.

What do I multiply four by to get 20? Tell me now.

Excellent, five.

And what do I multiply two by to get 10? Excellent, five.

So these two are in the same ratio.

Let's talk now about Yasmin's statement.

She says she's going to use 10 red tiles and the rest will be blue.

So how many blue tiles does that mean that she has? Tell me now.

Excellent, 10 red tiles and 20 blue tiles.

Do we notice anything about this ratio and the last ratio? Excellent, they're the same, aren't they? We've just gone about it in a slightly different way.

Well done.

What about Anthony, then? Anthony says he's going to use red tiles and blue tiles in the ratio 1:4.

So I've done that on the screen for you there and the little hint I gave you is on the screen too.

If he's talking about groups of five, how many groups of five do we have in this grid? Tell me now.

Excellent, we have six groups of five, don't we? So if we have one red square in each group of five and we have six groups, how many red squares will we have in total? Tell me now.

Excellent, six.

And if we have four blue squares in each group of five and we have six groups of five, how many blue squares will we have in total? Tell me now.

Excellent, 24, well done.

Do we notice anything about 1:4 and 6:24? Really good, these are also in the same ratio, aren't they? What do we multiply our first ratio by to get our second? Tell me now.

Excellent, it's six, isn't it? So we've got another two equivalent ratios here.

These are in the same ratio.

Finally then, we've got Javier and he says he's going to use 20 more blue tiles than red tiles all together.

So you should've worked out that that meant he was using five red tiles and 25 blue tiles.

Could you find another ratio that's in the same ratio as this? Tell me now.

Excellent, there are loads of answers there but one that you could have had is 1:5, or you could've had 10:50.

There's lots of different ratios that you could've found there that would have been in the same ratio.

We're now going to look at the key points from that Try this activity in the Connect task.

So we've got red cubes and blue cubes on our screen.

On the first one, the ratio of red cubes to blue cubes is what? Tell me now.

Excellent, it's 5:10, isn't it? Well done.

On the second one, the ratio of red to blue cubes is what? Tell me now.

Excellent, it's 3:8.

And on the third one, the ratio of red to blue cubes is what? Tell me now.

Excellent, it's 3:6.

So for the ratio 5:10, that is like saying for every five red cubes, I have 10 blue cubes.

Can you think of a smaller group, that if I put five groups together would give me this ratio? Tell me now.

Excellent, we could have red to blue in the ratio 1:2, couldn't we? For every one cube, we have two blue cubes.

We can see that clearly here and that's just five groups of that give us 5:10.

What about here, then? Does the ratio 1:2 give us 3:8 if we were to put multiple groups together? Well, let's have a look.

One red cube, two blue cubes, that's one group.

The second red cube with two blue cubes, that's a second group.

And then a third red cube with two blue cubes, that would be our third group.

But that should be it, shouldn't it? We've got two spare blue cubes here, so this cannot be in the same ratio as 1:2 or 5:10 because we've got spare cubes there.

What about this one, then? Two red cubes and four blue cubes are taken away and we're left with the ratio 3:6.

So one red cube, two blue cubes, one red cube, two blue cubes, one red cube, two blue cubes.

Yes, that works, doesn't it? So 3:6 is in the same ratio as 5:10 and interestingly, 2:4, the number of cubes that we took away is also in the same ratio as 1:2 and obviously, we've got our 5:10 there as well.

So you can notice that it has to be a multiplicative relationship to give us a ratio that is the same as the other.

So here, we've multiplied by two to get to there, we've multiplied by three to get to there, we've multiplied by five to get to there.

The 3:8, it was just an additive relationship, wasn't it? Or actually, we were taking away.

So we took away two cubes of each colour from the original ratio and because we didn't involve a multiplicative relationship, that's why it didn't give us an equivalent ratio.

We're now going to apply this to some quick true or false questions.

So first one, true or false? 1:5 and 2:10 are in the same ratio.

Tell me now.

Answer in three, two, one.

Excellent, that one is true.

Well done.

Second one then, true or false? 1:5 and 5:9 are in the same ratio.

Tell me now.

Answer in three, two, one.

That one is false.

They are not in the same ratio.

Third one then, true or false? 6:15 and 2:5 are in the same ratio.

Tell me now.

Answer in three, two, one.

That one is true, well done.

Excellent work.

So now you're going to have a go at the independent tasks.

So pause the video, navigate to the independent task and when you're ready to go through some answers, come back and resume the video.

See you soon.

Right, we're going to go through the answers to be independent tasks now.

I'm not going to go through all of the answers in full, some of them will just appear on the screen but we will talk about some of the answers.

So for the first one, your answer here is C and D will make the same shade of orange.

If you need to at any point, pause the video to check your working out.

If not, just keep watching.

The second one, then, we will talk about this one.

I mix 12 litres of yellow paint and six litres of blue paint to make green.

I need more of the same colour.

I have eight litres more yellow.

How much more blue paint should I use? So there's lots of ways of answering this question and I'm sure you could tell me the different methods that you've done.

So don't worry if it's different to the way that I do it, that's absolutely fine.

So, first of all, I'm going to write my ratio of yellow, to blue as 12 litres to six litres, because that's what I'm told in the question.

I had been told that I need to make the same colour, so I need to make the same colour.

So that means that my ratio has to be in the same ratio as the one that I'm given here.

So if I've got 12 litres of yellow paint and six litres of blue paint, I could think about that and I might've drawn a diagram here to help me If I needed to but for every two litres of yellow paint, I've got one litre of blue paint.

Yeah, can you see that? So then, if I have yellow to blue in that ratio, 2:1, for every two litres of yellow paint, I need one litre of blue paint, if I have eight litres of yellow paint, how much more blue paint do I need? Excellent, it's four, isn't it? So that means I also need to multiply my one by four to get my answer of four.

So how much more blue paint should I use? Remember to answer the question.

Even better if you wrote it in a full sentence.

So I should use four litres more blue paint and remember your units there.

Question three, then.

Pink paint is made with red and white paint in the ratio 4:3.

You were asked to copy and complete the table.

Here are your answers.

Pause the video now and double-check them.

And then finally, here are the answers to question four.

So again, pause the video now and check these.

So we're moving on to the explore task now.

Beth mixes a pot of red paint and a pot of yellow paint to make orange paint.

She then mixes another pot of red paint and a pot of yellow paint and makes the same shade.

What size pots could Beth have picked and what about if she can use multiple pots? Pause the video now and have a go at this activity.

Well done on that, there are absolutely loads of answers here, so I can't possibly go through them all.

I will talk about a couple, though.

So I decided that Beth was going to mix 12 litres of red paint with eight litres of yellow paint.

I then found another shade that would be the same would be by mixing three litres of red paint with two litres of yellow paint.

But then I realised, oh no, I don't have a three litre pot of red paint, so what could I do here? Well, I'm going to have to use multiple pots, aren't I? I'm going to have to use a one litre pot and a two litre pot.

Did you manage to find any where she didn't have to use multiple pots? Well done if you did and when you use multiple pots, there are even more solutions, so well done for having a go at that activity, I'm really impressed with all your hard work.

That's it for today's lesson, so thank you so much for all your hard work.

Don't forget to go and take the quiz to show me what you've learned and I hopefully will see you again soon for some more fun with ratio.

Bye!.