Lesson video

Hi, I'm Miss Kidd-Rossiter and I'm going to be taking you through today's lesson on the rule of four.

Before we get started, can you please make sure that you're in a distraction free area, a quiet place if you're able to be, you've got something to write with, and that you're completely focused and ready to go.

If you need to pause the video now to get anything sorted then please do, if not, let's get going.

So for today's try this, you've got Cala and Xavier, and they're packing boxes of sweets for some affair.

Each box has the same number of bags, and each bag has the same number of lemon and raspberry sweets.

Cala says, the ratio of lemon to raspberry is three to four.

Xavier says, there are 84 sweets in the box.

Your job it is to find out how many bags could there be, in each box.

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

If you need a couple of hints, you might want to think about some equivalent ratios to three to four, and you also might want to think about how many parts of the ratio there are in total, and whether the multiples of this number go into 84.

Have a think about that resume the video when you're ready to go through it.

How did you get on with this try this activity.

I hope you had a really good go at it.

We're going to talk about it now and then connect and try and pull out some of the important features here.

So as you can see, Cala said that the ratio of lemon to raspberry is three to four.

This could of course mean that we have three lemon sweets, and four raspberry sweets in a bag.

If that's the case, how many sweets do we have in total in each bag? Tell me now, excellent.

And we know that in a box, we have 84 sweets.

So if we have seven sweets in each bag, and 84 sweets in total, how many bags do I need to put into my box? Tell me now, excellent, 12.

So, if I have three lemon sweets in each bag, and I'm putting 12 bags into each box, how many lemon sweets will there be in total? Tell me now, excellent, 36.

And if each bag contains four raspberry sweets, and we're putting 12 bags into the box, how many raspberry sweets will I have in total? Excellent, 48.

So can we notice a relationship here, between three and 36, and four and 48 can you notice a relationship there? Excellent.

Going across the table, we're multiplying by 12, aren't we? This is our constant of proportionality that we've seen before when we've written equivalent ratios, three to four is an equivalent ratio, as 36 to 48.

And our constant of proportionality would be 12.

What about the relationship going down the table? Is there's something I can multiply three by to get four, we know about our inverse operations.

So we know that three times something equals four to find the something, we can do four divided by three which is four thirds, or 1.

3 recurring.

I prefer to leave it as a fraction.

Let's just check whether this is the same 36 and 48.

So 36 times something gives us 48.

And to find our something, we use our inverse operation, 48 divided by 36, which does simplify to four thirds when we take out a common factor of 12 from the numerator and the denominator.

So we have another multiplicative relationship going down the table, where we're multiplying by four thirds.

Now of course, Cala's ratio, doesn't mean that we have to have exactly three, and exactly four sweets in the bag.

We could have had an equivalent ratio that simplifies to three to four.

Can you tell the screen now an equivalent ratio that simplifies to three to four? The one ratio that I came up with was 18 to 24.

We can see that 18 to 24 is equivalent to three to four, what would our constant of proportionality be there? Tell me quickly, excellent six, So if I had 18 lemon sweets, and 24 raspberry sweets, how many sweets would I have all together in my bag? Tell me now, excellent, 42 and we know that we have 84 sweets in the box.

So if I have 42 sweets in each bag, how many bags do I need to put into my box? Two, well done.

I have 18 lemon sweets in each bag, and I'm putting two bags into each box so that means I will have 36 lemon sweets in the box, and if I have 24, raspberry sweets in each bag and I'm putting two bags in, that means I will have 48 raspberry sweets in each box.

Do we notice anything here? Can you notice something compared to our last example? What's our constant of proportionality here? Going from 18 to 36 or 24 to 48.

What was it? Excellent, it's two this time.

And we already know that to go from 36 to 48, we would multiply by four thirds, let's just double check that this relationship is still true for 18 to 24.

So 18 times something is 24, using our inverse operation, something is equal to 24 divided by 18, which is equal to four thirds when we take out a common factor of six from both the numerator and the denominator.

So key point of today's lesson, is that when we have a ratio table like this, we have two multiplicative relationships.

We've got the multiplicative relationship going across the table, which is our constant of proportionality, and then we also have a multiplicative relationship going down the table, which in this case is four thirds.

You are now going to apply your learning from today's lesson to the independent task.

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

Well done for giving that independent task a go.

There were some tricky questions in there.

I'm not going to go through all of the answers in full we're just going to pick out the really interesting ones to talk about.

So if at any point you need to pause the video to mark your work, then please feel free to.

Question one, I filled in the grid for you, now we need to figure out what's the ratio of squash to water.

So, squash to water we can see is 20 centilitres to 15 centilitres and if we wanted to, we could simplify this ratio to four to three.

How much bigger is bottle two than bottle one? So what do we multiply 20 by to get 60? Or the same relationship here, what do we multiply 15 by to get 45? We can see that that is three times bigger.

Question two, the answers are on your screen, so please mark those.

Question three, you can see I've already done the working out for you, it should be on your screen.

To find how high the photograph is, you first need to work out the scale factor of enlargement so that's what I've done here, and then you need to apply that, to the height of the photograph.

We've already worked out scale factor of enlargement and then we can work out our ratio.

Question four now this is a really nice question I like this one.

Gemma says that the missing number here is 35, and Ed says the missing number is 19.

Who do you agree with, and why? Tell the screen now, really good.

I hope you have really good reasons for that.

I'm going to tell you that I agree with Gemma.

She's the person that I agree with here, because, I can see that going across here, my constant of proportionality from three to 15 is multiplied by five.

So that would mean that I need to multiply by seven by five as well, to get the correct answer of 35.

What did I do wrong? Excellent.

He just added on 12, didn't he? 'Cos you can see that from three to 15.

We add 12, and he's made the error here that I think it's an additive relationship when it's not it's a multiplicative relationship.

Finally then, we're moving onto the explore task.

So we've got Cala and Xavier again, they're arranging bunches of pink and blue flowers, they've given you some statements there.

You need to figure out how many blue flowers could there be in each bunch.

What you should think about the kind of process that we used in the try this activity, and trying to apply the same kind of thinking to this explore activity.

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

That's it for today's lesson.

So thank you so much for all your hard work.

I hope you've learned loads.

I've really enjoyed teaching you this lesson, please don't forget to take the quiz, to show what you've learned, and I hope to see you again soon.

Bye.