Lesson video

Hi everyone, my name is Ms Coul and I'm really happy and excited to be learning with you today.

It's going to be a fun lesson full of some words maybe that you may or may not know, and we'll build on that previous knowledge too.

Super excited to be learning with you.

So let's make a start.

In today's lesson under the unit understanding multiplicative relationships, fractions and ratio, we'll be looking at multiplicative relationships in context.

And by the end of the lesson you'll be able to appreciate that any 2 numbers can be connected via a multiplicative relationship.

Today's key words, we'll be looking at the word ratio.

And a ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

Today's lesson will be broken into 2 parts.

Firstly, we'll be looking at that multiplicative relationship in context, and the second we'll be looking at converting money.

So let's make a start at multiplicative relationships in context.

Well to start with, I want you to have a look at this ratio table, and I want you to identify how many multiplicative relationships can you see between these ingredients.

See if you can give it a go and press pause if you want more time.

Well done.

So let's see how you got on.

Well, here are just some examples.

Maybe you did the number of smoothies multiply by 8 gives you the slices of apple.

Maybe you did the slices of apples multiply by a half gives you the slices of bananas.

Maybe you did the slices of bananas multiply by 25 gives you the amount of milk.

Or maybe you did the slices of banana multiply by 50 gives you the amount of yoghourt.

There are lots of multiplicative relationships here.

So here are just a few.

Now I'm going to ask, does this multiplicative relationship change if we look at 3 smoothies? What do you think? Well hopefully you spotted, it doesn't.

The multiplicative relationship remains the same or constant for the parts in the ratio.

You can use those formulas to double check.

It doesn't matter if you're looking at 3 smoothies or 30 smoothies, that multiplicative relationship remains the same.

So there are lots of ways to show multiplicative relationships when using ratio tables.

What multiplicative relationships can you use here to fill in this table? Copy it down, fill in what you can, and let's see how you found it using those multiplicative relationships.

Press pause for more time.

Well done, let's see how you got on.

Well, you could have done it a number of ways.

I'm going to look at identifying that multiplicative relationship between eggs and sugar.

Well to find it I'm gonna simply do 3 divide by 2 which is 1.

5.

So that means I can multiply all the quantities of eggs by 1.

5 and that'll give me the quantity of sugar.

For 10 eggs, it's 15 grammes of sugar.

For 7 eggs, it's 10.

5 grammes of sugar.

And I can even find out what that missing value is for eggs as 6 multiply by 1.

5 is 9.

Another way you could have done it is identify the multiplicative relationship between the rows.

Well, I could multiply the sugar by 3 to give me 9.

And that means I have to multiply the eggs by 3 to give me 6.

I could have multiplied the eggs of 2 by 5 to give me 10.

So that means I need to multiply the quantity of sugar by 5 to give me 15.

I could have multiplied the quantity of eggs by 3.

5.

Therefore I have to multiply the quantity of sugar by 3.

5 to give me 10.

5.

I get exactly the same answer.

Super important that you recognise that multiplicative relationship do parts to parts or parts to whole.

So now let's have a look at a check question.

Here we have a recipe for vegetable soup.

We need 8 carrots, 4 potatoes, 200 millilitres of water, and 2 stock cubes.

Now Andeep used 10 carrots, 5 potatoes, 400 millilitres of water, and 1 stock cube.

And Andeep, unfortunately made a mistake when making the soup and is trying to fix it so the ratio is correct according to that recipe.

I want you to figure out what is the least amount of ingredients he could add to the correct ratio.

Assuming you can only have an integer amounts of each ingredient.

So you can give it a go and press pause if you need more time.

Let's see how you got on.

I'm gonna put this in a ratio table for carrots, potatoes, water, and stock.

So to find out the least amount of ingredients we can add to our ratio, let's divide what Andeep has by our recipe.

So if Andeep has 10 carrots, divide that by 8 carrots gives us 1.

25.

Well, we know we can only add an inch in integer number of amounts.

So let's round up to 2.

Let's check with potatoes.

5 divided by 4 gives us 1.

25.

For water, 400 divided by 200 gives us 2.

And for stock cubes, 1 divided by 2 is a half.

So that means the lowest number of ingredients that we can have is when we double what we have in our ratio, 16, 8, 400 and 4.

So the lowest number of carrots needed are 6 carrots, three potatoes, and 3 stock cubes.

Well done if you got this one right.

Now let's have a look at Jun.

Jun using the same recipe, but he has 39 carrots, 19 potatoes, a 1,000 of water and 6 stock cubes.

What is the least numb amount of ingredients he could add to make the ratio correct? Same again, we're assuming we can only have integer amount of each ingredient.

See if you can give it a go and press pause if you need more time.

Well done.

Let's see how you got on.

So let's divide what Jun has by what's in our recipe.

Well, if you divide 39 carrots by 8 carrot, that would give you around about 4.

8, et cetera, et cetera.

So rounding up, that would be a multiplier of 5.

19 potatoes divided by 4 gives us around about 4.

75.

Same again, rounding up gives us a multiplier of 5.

A 1,000 millilitres of water divided by 200 gives us a multiplier 5 and 6 stock cubes divided by 2 is 3.

So that means we have to multiply each part of our recipe by 5.

Multiplying this means we need 40 carrots, 20 potatoes, a 1,000 millilitres of water and 10 stock cubes.

So that means Jun needs 1 carrot, 1 potato, and 4 stock cubes.

Great work if you got this one right.

Now it's time for your task.

Here you need to fill in the table recognising the following multiplicative relationships.

See if you can give it a go and press pause if you need more time.

Well done.

Let's move on to question 2.

Question 2.

Most bread doughs start with flour and water.

And to make chapati, for every 2 cups of flour, you add 1 cup of water.

And to make pizza bases, you have 3 cups of flour, you need 2 cups of water.

Now in each bowl, is it a chapati dough, a pizza dough, or neither? See if you can give it a go and press pause if you need more time.

Well done.

Let's move on to question 3.

Question three, to make the perfect meringue for every 3 eggs, you add 150 grammes of sugar.

But what is the minimum needed to add to each mixture below to make the meringue correct? See if you can give it a go and press pause if you need more time.

Well done.

Let's see how you got on.

Well, for question one, we know the multiplicative relationship between eggs and sugar.

You multiply the number of eggs by 75 to get the sugar, thus giving the following amounts.

Flour is twice as many grammes as butter.

So therefore we have these following amounts.

And butter multiplied by 1.

5 is sugar.

So we have our completed table.

Great work if you've got this one right.

Let's have a look at question 2.

Now remember that ratio.

To make chapati for every 2 cups of flour, you add 1 cup of water.

And to make pizza you have 3 cups of flour to every 2 cups of water.

If we for part A have 9 cups of flour, what does that mean? Well, putting our information in a ratio table, 9 cups of flour would mean we need to multiply by 4.

5.

Thus meaning we'd have 4.

5 chapatis, we'd use 9 cups of flour and 4.

5 cups of water.

So we know it's not a chapati.

Now for pizza, if we have 9 cups of flour, we multiply by 3.

So that means for 9 cups of flour it's 3 pizzas, which is 6 cups of water.

So this ratio is a pizza base ratio.

Well done if you got this one right.

For B, well let's see what we have.

We have 12 cups of flour and 8 cups of water.

So to make 12 cups of flour, we multiply by 6.

Thus that means we have 6 chapatis, would mean 12 cups of flour with 6 cups of water.

So we know it's not a chapati.

For the second part, let's see, to make 12 cups of flour, we're multiplying by 4.

So that means we have 8 cups of water to make 4 pizzas.

So yes, it's a pizza with the 12 cups of flour with the 6 cups of water.

You can see from our ratio table it has to be a chapati.

Well done if you got those right.

For D, 18 cups of flour to 12 cups of water.

So let's make our cups of flour 18.

A multiplier would be 9.

Thus we'd need 9 cups of water.

For pizza, a multiplier would be 6.

So we'd need 12 cups of water.

So that means it has to be a pizza.

For E and F, we have 24 cups of flour multiply by 12, we need 12 cups of water.

And 24 cups of flour, multiplying by 8 gives us 16 cups of water.

So that means we know E must be to chapati and F is neither.

Great work if you got this one right.

For question 3, for every 3 eggs you add 150 grammes of sugar.

Well, if we have 200 grammes of sugar and 6 eggs so let's identify our integer multiplier by simply doing 200 divided by 150 and 6 divided by 3.

Well our multiplier would have to be 2, thus giving us 300 grammes of sugar and 6 eggs.

So that means we only need to add a 100 grammes of sugar.

For B, let's identify our multiplier.

450 divided by 150 and 7 divided by 3.

A multiplier has to be 3, thus giving us 450 grammes of sugar and 9 eggs.

So I need to add 2 eggs to make our ratio correct.

For C, 400 grammes of sugar divided by 150 and not all 9 divided by 3.

This gives us a multiplier 3 to give us 450 grammes of sugar and 9 eggs.

So that means we add 50 grammes of sugar.

Next we have 500 grammes of sugar and 9 eggs, so we divide.

So identifying our multiplier, we do 500 divided by 150, then 9 divided by 3.

So our multiplier must be 4.

So our recipe needed to be multiplied by 4 to give us 600 grammes of sugar and 12 eggs.

That means we need to add 200 grammes of sugar or 3 eggs.

You may have also spotted if you divide the sugar by 50, it'll give us the eggs.

So you could also spot, we could need 500 grammes of sugar and 10 eggs.

So that means we can add 1 egg as well.

That was a good question.

Next we have 500 grammes of sugar and 10 eggs.

So 500 divide by 150.

Then 10 divided by 3 gives us the same multiplier.

So that means we should have no change as it is perfect.

Great work everybody, so let's move on to converting money.

Now there are lots of different countries across the world.

I want you to have a look at this map and see if you can identify the currencies used in these countries.

Well done.

Let's see how you got them.

Well, in America, they use dollars.

In Spain, they use euros.

Argentina use pesos.

Japan use yen.

China use renminbi and India use rupees.

Amazing work if you knew this.

There are so many different currencies in the world and it's important to know how to convert between them.

And converting money into another currency is proportional and users a multiplier.

So for example, what do you think is the multiplicative relationship using our ratio table? And can you fill it in? Copy it down, see if you can give it a go.

Great work.

Let's see how you got on.

You could find some missing values by multiplying the top row by 3.

So thus giving us £3 to represent $3.

75.

And you could have multiplied £1 by 10 to give us the converting dollars to $12.

50.

Alternatively, you could have spotted that multiplier.

What do you multiply pounds by to give dollars? Well by 1.

25.

So you multiply everything by 1.

25, thus giving you exactly the same quantities.

Looking at a check.

Every £1 converts to €1.

16.

What I'd like you to do is look at these answers.

And from here, which of the following show the same ratio? See if you can give it a go and press pause if you need more time.

Well done.

Let's see how you got on.

Well for A, I'm going to use a ratio table.

If we know £1 represents €1.

16, that means £20, we have a multiplier of 20.

So that means it would be €23.

20.

So yes, A has the same ratio.

Let's have a look at B.

Using my ratio table at- Again, we've got £110.

Well, the multiplier would be multiplying that £1 by 110.

Do the same to the euros.

Gives me a €127.

60.

So yes, it follows the same ratio.

And for C, what we have €0.

29 converts to £0.

25.

So let's have a look at our euros.

Our euros, if you divide by 4, it gives me €0.

29.

So that means I'm going to divide my pounds by 4 to give me 0.

25.

So yes, they are the same.

This is one way to identify if they share the same ratio.

You may have also identified the multiplier from pounds to euros is 1.

16.

That would give you exactly the same answers.

Huge well done if you got that one right.

Let's have a look at another check question.

3 shops provide 3 different conversions, which is the best deal, and I want you to explain why.

See if you can give it a go and press pause if you need more time.

Well done.

So let's see how you got on.

Well, using a ratio table for every £2 you get €2.

28.

That means to find that multiplier, I'm going to divide the euros by pounds to give me 1.

14.

This means that to convert pounds to euros, I multiply by 1.

14.

For B, for every £12 you get €24.

But to get my ratio table, identifying what my multiplier is means I have a multiplier of 2.

So that means if I multiply the pounds by two, I get my euros.

For shop B, writing it as a ratio table I have £30 to €45.

Well, identifying that multiplier, I have a multiplier of 1.

5.

This means if I multiply my pounds by 1.

5 I have euros.

So which is the best deal? Well, shop B is the best because the multiplier from pound to euros is the greatest.

In other words, you get more euros per pound.

Great work if you got this one right.

Now it's time for your task.

I want you to fill in the currency conversion table using the following ratios.

See if you can give it a go and press pause if you need more time.

Great work, everybody.

Let's move on to question 2.

For question 2, a group of 3 friends are going on holiday and they all exchanged some pounds for euros.

So Sofia got €120 for a £100 and Laura got €30 for £20 and Sam got €90 for £60.

Who got the best deal? Poppy says Andeep decided to come along too and exchanged €110 for a £100.

Whose deal was it most similar to? See if you can give it a go and press pause for more time.

Well done.

Let's move on to these answers.

For question one, you should have had these values here.

This converts our euros to dollars using that same multiplicative relationship.

Well done if you got that one right.

For question two, let's have a look at what Sofia got.

Well using a ratio table, a £100 is a €120.

So identifying what our multiplier is, 120 divided by a 100 is 1.

2.

That means pounds multiplied by 1.

2 gives us our euros for Sofia.

For B, using our ratio table, let's identify that multiplier.

30 divided by 20 is 1.

5.

So multiplying those pounds by 1.

5 gives us €30.

Pounds times 1.

5 gives us euros for Laura.

For C, to find out the multiplier, we simply do 90 divided by 60, which is also 1.

5.

So that means pounds times 1.

5 is equal to euros.

Who got the best deal? Well, Laura and Sam get the best deal.

Look at that multiplier.

They got more euros per pound because the multiplier is larger.

Well done if you got that one right.

Now let's have a look at Andeep.

Well, what was the multiplier for Andeep? To work it out, 110 divided by a 100 is 1.

1.

This means his deal was most similar to Sofia.

Great work if you got that one right.

Well done everybody.

So in summary, recognising that ratio shows the relative sizes of 2 or more values and it allows you to compare a part with another part in a whole is important.

That multiplicative relationship between parts is constant for all things in the same ratio.

And this multiplicative relationship applies to lots of real life context, including currencies.

Great work everybody.

Well done.