Lesson video

Hi, my name's Miss Kidd-Rossiter, and I'm going to be taking you through today's lesson on equivalent ratios.

It's going to build on the work that we've already done in the same ratio and groups.

Before we get started, can you make sure that you're in a nice, quiet place, if you're able to be, and that you're free from distractions.

You're also going to need something to write with and something to write on.

So if you need to pause the video now to get any of that sorted, then please do.

If not, then let's get going.

So for today's Try This activity, you've got a strip of paper on your screen that has been folded into 4 equal parts.

One of the parts has been coloured green, as you can see.

Then you've got some identical strips of paper, and these are also folded into an equal number of parts.

Your job is to find out how many parts would be coloured green so that each strip looks the same as the first strip when the strip is folded into 8 equal parts, 20 equal parts, 6 equal parts, and 2 equal parts.

It might help you to have some strips of paper to try this with, or if not, it would definitely help if you could draw the diagrams. Pause the video now and have a go at this activity.

Let's look at the answers then.

So if we folded our strip of paper into 8 equal parts, then 2 of these parts would need to be green so that it looks the same as the first diagram.

If we folded it into 20 equal parts, then 5 parts would need to be shaded green so that it looks the same as the first diagram.

If we did it into 6 equal parts, then 1.

5 or one and a half of these parts would need to be shaded green so it looks the same as the first diagram.

And for the final one, half of a part would need to be shaded green so it looks the same as the first diagram, or obviously that's the same as 0.

5 So we're moving on to the Connect part of the lesson now.

What's the ratio of pink to green in each of these strips.

And what do the strips show about these ratios? Pause the video now and have a go at answering those questions.

Excellent, what's the ratio of pink to green in the first strip then? Tell me now.

Excellent, it's 2:3.

What's the ratio of pink to green in the second strip? Tell me now.

Excellent, it's 4:6.

So first of all, what do we notice? What can we see from the strips about these ratios? Tell me now.

Excellent.

We can see that they're equivalent, can't we? We've got the same amount of pink here and the same amount of green here as we have in the top strip.

So that means that we must have a constant of proportionality that we can multiply our first ratio by to get our second ratio.

Can you tell me now what that would be? Excellent, it's 2.

So for our constant of proportionality for these two strips, it's 2.

What fraction of the top bar is pink? Pause the video now and think about that.

Excellent.

The pink is 2/5, isn't it? We can see it's two parts out of a total of five parts.

So that means what fraction is green on the top bar? Tell me now.

Excellent, it's 3/5, isn't it? Well done.

On the second bar then what fraction is pink? Tell me now.

4/10.

Well done.

And what fraction is green? Tell me now.

Excellent.

6/10.

What do we know about 4/10 and 2/5? Tell me now.

They're equivalent fractions.

Well done.

What do we know about 6/10 and 3/5? Tell me now.

Excellent.

Well done.

They're equivalent fractions as well.

So let's now look at creating what we call a unit ratio.

So we touched on this previously, but we're going to talk about it a bit more now.

So for every one pink part, how many green parts do we have? So remember our ratio is 2:3.

What would our constant of proportionality be from going from 2:1? Excellent.

It's a half isn't it.

So that means that we also need to multiply our 3 by a half.

So that gives us 1.

5.

So our unit ratio pink to green is 1:1.

5.

What would our unit ratio be of green to pink? So unit just means for every one green part, how many pink parts do I have? So let's write our ratio first of green to pink.

That would be 3:2 wouldn't it? So what do I need to multiply 3 by to get to 1? Well, that would be a third.

Wouldn't it? That would be our constant of proportionality.

So we also need to multiply two by a third, to get a unit ratio there.

Right.

I'm going to take this writing off the screen now, and I'm going to put some more strips onto the screen.

I want you to have a think about everything that we've just done there.

Can you write the ratio of pink to green? Can we find the fraction that is green and the fraction that is pink? Can you find the unit ratio for each strip? Do you notice anything there? If you can also draw some different strips that are representing the same ratio.

Pause the video now and have a go at that task.

Excellent.

So you should have realised that all of our ratios were equivalent and the fractions that were pink were equivalent and the fractions that were green were equivalent.

Did you notice anything about the unit ratios? Excellent.

Those were equivalent as well, well done.

We're now going to apply your learning to the independent task.

So pause the video here, navigate to the independent task, and when you're ready to go through it, resume the video.

See you soon! So we're going to go through the answers to the independent task now.

You'll notice that I've given you some of the answers and we'll talk through some of them.

So first of all, you had to complete the equivalent ratios.

Those are on the screen now for parts B and E.

If you wrote them as decimals instead of fractions, that's absolutely fine.

So for part D instead of 3/2, you could have had 1.

5 and for part E instead of 2/3, you could have had 0.

6 recurring.

It's really important though, that you did have that recurring.

It's not 0.

6, it is 0.

6, recurring.

We've also got the answers for the equivalent ratios on your screen there.

So remember that it doesn't have to be integers.

We could have decimals and that could come into play when we're using different units, for example.

So if we were using centilitres and litres or millimetres and centimetres, that might play in there.

So pause the video if you need to just check your work.

Then for question 3, we've got all the answers on the screen there again.

So just pause the video and check what you've done.

We're moving on then finally, to the explore task Zacki has 24 gold counters and 36 silver counters.

He wants to share the counters into piles with the following rules.

There must be the same number of counters in each pile and each pile can only have one colour of counter.

He has given you an example there of what you could do.

So I'll let you read that, and I'll also let you read the questions that you need to complete.

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

Okay, If you need a little bit of support, I've just kept the key point on there, that Zacki has 24 gold counters and 36 silver counters.

One way that I thought about doing this was organising my thoughts into a table.

So you could have a look at the table that I've drawn there and have a go at answering some of the questions.

So if he's got 12 counters in each pile, and he's got 24 gold counters, and how many piles of gold counters would he have? Tell me now.

Excellent.

He would have two wouldn't he? If he had 36 silver counters and he's got 12 in each pile, how many silver piles would he have? Tell me now.

Excellent.

He would have 3 silver piles.

So our ratio here would be 2 gold piles to 3 silver piles.

Pause the video now and have a go at completing the rest of this table.

When you're ready, resume the video.

Excellent work everyone.

There were some tricky concepts in here.

So I'm really glad that you've grappled with those.

I'll give you the answers that you could've come up with.

This is how you could have organised your thoughts.

So you could have drawn a table.

What if Zaki lost one silver counter and tried this again.

So that would mean that he had 24 gold counters and 35 silver counters.

Did you manage to find different ways that he could do this? I hope that you thought about the highest common factor here and what number of counters he could have in each pile.

I'm not going to tell you the answer to that.

I'm going to leave you to puzzle on it, but think about what I've said about highest common factor.

That's it for today's lesson.

Thank you so much for all your hard work.

I hope you've learned a lot.

Please don't forget to go and take the quiz to show me what you've learned and I hope to see you again soon.

Bye!.