Lesson video

Hi there, welcome to our proportion problems lesson, where we'll be looking at solving problems involving the relative size of two quantities.

You'll just need a pencil and piece of paper for today's lesson.

So pause your video and get your things if you haven't done so already.

In today's lesson, we'll be looking at solving problems involving the relative size of two quantities.

Specifically looking at Recipes Today, you'll see a multi-step scaling before you do some independent learning and then a final quiz.

So in our first recipe, we have a recipe that makes 4 cookies, and these are the quantities of each of the ingredients.

Now Iman wants to use this recipe to make 6 cookies for her friends.

So we need to think about how can we adapt this recipe to make 6 cookies, and is there more than one way to do this? So I'd like you to start off by pausing the video and having a think about the relationship between 4 and 6, how much bigger is 6 and 4.

But what we know about 6 is that 6 is half as big as 4 again.

So if you think about 4, 4 divided by 2 is 2, and if we add that on to 4, we get 6.

So 6 is one and a half times 4.

We can also think about to get to 6 from 4, we can have 4 to get 2, and then multiply by 3 to get 6.

Or we could divide 4 by 4 to get 1 and then multiply by 6 to get to 6.

Now let's have a look at what the strategies actually look like because that was a lot of different ways of getting there.

So here's our first strategy.

In strategy One what we're going to do is we're going to enlarge by a scale factor of one half by dividing by 2.

So 4 cookies divided by 2 will get us to 2 cookies.

And then we're going to look at the recipe for 2 cookies.

And we're going to enlarge by a scale factor of 3 to get 6 cookies.

So we're doing two steps to get from 4 to 6 divided by 2 times by 3.

And therefore we have this, this happens to all of the ingredients, they all get divided by 2, they all get enlarge by a scale factor by half, and then they become 3 times greater.

They're enlarged by a scale factor of 3.

So that's strategy One.

In strategy Two, what we're going to do is we're going to go from 4 cookies down to 1 cookie.

By dividing by 4 or enlarging by a scale factor of one quarter, and then we get from 1 to 6 by multiplying by 6 or enlarging by a scale factor of 6.

So each of the ingredients in the original recipe will be divided by 4 to get to 1 cookie, and then multiply by 6 to get to 6 cookies.

So I want you to have think about these two strategies.

And I would like you to look at the Paste sauce recipe that serves 6 and scale the recipe to serve 9 people.

Pause the video now and have a go.

So for strategy One, what we can do to 6 is we can divide it by 2, or enlarge it by a scale factor of one half to give us 3 servings and then to get from 3 to 9, we're going to multiply by 3, or enlarge by a scale factor of 3.

And we need to make sure that we do the same to all of the ingredients.

So we divide everything by 2 first to get to 3 servings, then we multiply by 3 to get us to 9 servings.

In your second strategy, you're getting 1 serving first and then scaling up, so we're going to divide by 6, so that we have the recipe for 1.

So every of the every one of these ingredients has been divided by 6, and then we're going to multiply by 9.

1 multiplied by 9 gives us 9 or enlarge it by a scale factor of 9.

And we do the same to each of these ingredients.

So half a tablespoon of olive oil becomes 4 and a half tablespoons of olive oil and so on.

Now we're going to look at another one together, Metila is making her own cereal bars, the recipe is below.

So here's the original recipe, she needs 50 grammes of oats, 20 grammes of raisins, 10 grammes of chocolate chips and 40 grammes of nuts.

But if she uses 60 grammes of oats, what quantity of raisins and chocolate chips and nuts are needed.

So we're trying to think about the relationship between 50 and 60.

So have a quick thing, how are we going to get from 50 to 60.

So the first strategy, we can divide 50 by 5, which will give us 10 and multiply that by 6 to give us 60.

And then our second strategy, we could divide 50 by 10 to give us 5 And multiply by 12 5 times 12 gives us 60.

So you've got two strategies to use.

And I would like you now to work out the quantities using both strategies.

Pause the video now and work them out.

So using strategy one, we're dividing by 5 and multiplying by 6.

So if we divide everything by 5 50 grammes of oats becomes 10 grammes of oats 20 grammes of raisins becomes 4 10 grammes of chocolate chips becomes 2 and 40 grammes of nuts becomes 8, then we multiply by 6 to scale the recipe up to having 60 oats.

10 times 6 is 60, and so on.

So that's our strategy one.

In strategy Two, we were dividing by 10 and then multiplying by 12.

So 50 divided by 10 gives us 5 20 gives us 2 10 gives us 1 and 40 gives us 4.

And then we know that 5 multiplied by 12 gives us 60.

And the same with every other one.

So what you're looking for is a route to getting from one number to another.

And you can either scale it down to having one of that quantity and then scale back up.

Or if you can see a different relationship then you can go in any route that you want to.

Now it's time for you to complete some independent learning.

So pause the video and complete the task and then click Restart once you're finished.

So in question one, we've got a recipe for ice cream.

Ronaldo is making his own ice cream.

And although the recipe calls for 400 millilitres of cream, he actually only have 300 millilitres of cream.

So we need to think about how much of each ingredient he should use.

How do we get from 400 to 300.

I'm going to show you one strategy, you may have got that differently.

That's absolutely fine.

It's all about what your final quantities are.

So what I've decided to do is to find 100 millilitre by enlarging by a scale factor of one quarter or dividing by 4.

So 400 millilitres divided by 4 gives me the recipe using 100 millilitres of cream, and I've divided every other ingredient by 4, but actually he has 300 millilitres, so I need to enlarge this recipe by scale factor 3, which means that he needs to have 300 millilitres of cream which he's got 375 of milk, 3 eggs, 90 grammes of chocolate and 75 grammes of sugar.

So you may have gone about this in a different way and that's fine as long as you have ended up with these quantities.

In question 2, Jannah is making two pies using her mother's recipe.

But the recipe is for 80 pies.

So we need to scale the recipe down.

And this is one hint on that.

So in the recipe it says that it uses 10 dozen eggs, a dozen is 12.

So 10 dozen and is 10 times 12 which is 120 eggs.

Now to go from 80 to 2 we need to divide by 40.

So everything every quantity needs dividing by 40 we'll start with the eggs.

So that's actually 120 eggs 120 divided by 40 is 3 eggs.

And then every of the other ingredient has been scaled down by a oh sorry enlarged by a scale factor of one fortieth to give us these new quantities.

Tasnia has a recipe for buttercream icing and for a party she has to ice 10 cakes.

So what quantity of each ingredient will she need.

So she's got a recipe for icing 6 cakes, but she wants to scale it to 10.

So let's think about how to do this what I can see is that if I divide 6 by 3, that gives me 2 and then I can get to 10 from 2 by multiplying by 5.

So I've enlarged by a scale factor of one third, I've divided everything by 3.

So this gives me 2 cakes.

Now I'm going to enlarge it by scale factor 5 to give me 10 cakes.

What you might have done is enlarge by a scale factor of one sixth, so divided by six to give you 1 cake and then enlarge by a scale factor of 10 multiplied by 10 to give you 10 cakes.

Your journey that doesn't matter as long as you end up with these quantities in the end.

For Question four, we've got Novie's recipe for breakfast.

So she uses 50 grammes of oats, 30 grammes of raisins and 40 grammes of nuts.

But if she has 125 grammes of oats, what are the quantities that she need.

So I can already see a relationship, I know that half of 50 is 25 and then I can easily multiply 25 to get to 125.

So I'm going to enlarge it by a scale factor of one half, divide everything by 2.

And then I'm going to multiply by 5 25 times 5 gives me 125 grammes of oats and so on with the other ingredients.

Again, you might have gone about it in a different way.

But these are the end results that you needed to come up with.

Well done for your hard work in today's lesson, I hope you go on to use some of the recipes I've given you and make some tasty treats in the kitchen.

Before you go.

Don't forget to complete your final quiz.