Lesson video

Hi everyone.

My name is Ms. Ku 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 two numbers can be connected via a multiplicative relationship.

Today's key words will be looking at the word ratio.

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

Today's lesson will be broken into two 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 eight 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 three smoothies? What do you think? Well, hopefully, you've spot it.

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 three 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 three divide two, 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 seven eggs, it's 10.

5 grammes of sugar.

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

5 is nine.

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

Well, I could multiply the sugar by three to give me nine, and that means I have to multiply the eggs by three to give me six.

I could have multiplied the eggs of two by five to give me 10.

So that means I need to multiply the quantity of sugar by five 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 through 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 eight carrots, four potatoes, 200 millilitres of water, and two stock cubes.

Now Andeep used 10 carrots, five potatoes, 400 millilitres of water, and one 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 eight carrots gives us 1.

25.

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

So let's round up to two.

Let's check with potatoes.

Five divided by four gives us 1.

25.

For water, 400 divided by 200 gives us two.

And for stock cubes, one divided by two is 1/2.

So that means the lowest number of ingredients that we can have is when we double what we have in our ratio.

Sixteen, eight, 400, and four.

So the lowest number of carrots needed are six carrots, three potatoes, and three 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, 1,000 millilitres of water and six stock cubes.

What is the least amount of ingredients he could add to make the ratio correct? Same again, we're assuming we can only have integer amounts 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 carats by eight carat, that would give you around about 4.

8, etc.

etc.

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

19 potatoes divided by four gives us around about 4.

75.

Same again, rounding up gives us a multiplier, five.

1,000 millilitres of water divided by 200 gives us a multiplier of five.

And six stock cubes divided by two is three.

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

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

So that means your needs, one carrot, one potato, and four 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 two.

Question two.

Most bread dough start with flour and water.

And to make chapati, for every two cups of flour, you add one cup of water.

And to make pizza bases, you have three cups of flour, you need two 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 three.

Question three.

To make the perfect meringue for every three 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 multiply 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 two.

Now remember that ratio.

To make chapati, for every two cups of flour, you add one cup of water and to make pizza, you have three cups of flour to every two cups of water.

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

5.

Thus meaning, we'd have 4.

5 chapatis would use nine cups of flour and 4.

5 cups of water.

So we know it's not a chapati.

Now for pizza, if we have nine cups of flour, we multiply by three.

So that means for nine cups of flour, it's three pizzas, which is six 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 eight cups of water.

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

Thus that means we have six chapatis would mean 12 cups of flour with six 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 four.

So that means we have eight cups of water to make four pizzas.

So yes, it's a pizza.

With the 12 cups of flour, for the six 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 nine.

Thus, we'd need nine cups of water For pizza.

A multiplier would be six.

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 eight 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 three, for every eggs, you add 150 grammes of sugar.

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

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

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

For B, let's identify our multiplier.

450 divided by 150 and 70 divided by three.

Our multiplier has to be three.

Thus giving us 450 grammes of sugar and nine eggs.

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

For C, 400 grammes of sugar divided by 150 and that all nine divided by three.

This gives us a multiplier three to give us 450 grammes of sugar and nine eggs.

So that means we add 50 grammes of sugar.

Next, we have 500 grammes of sugar and nine eggs.

So we divide.

So identifying our multiplier, we do 500 divided by 150, then nine divided by three.

So our multiplier must be four.

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

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

You may have also spotted if you divide by 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 one egg as well.

That was a good question.

Next, we have 500 grammes of sugar and 10 eggs.

So 500, you add by 150, then 10 divided by three 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 on.

Well, in America, they use dollars.

In Spain, they use euros.

Argentina use pesos.

Japan use yen.

China use renminbi, and India used 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 three.

So thus, giving us three pounds to represent $3 75.

And you could have multiplied the one pound 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 one pound converts to one euro 16.

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

And from here, which of the following show the same ratio? So 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 one pound represents 1.

16 euros, that means 20 pounds, we have a multiplier of 20.

So that means it would be 23 euros 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 pounds.

Well, the multiplier would be multiplying that one pound by 110.

Do the same to the euros gives me 127.

60 euros.

So yes, it follows the same ratio.

And for C, what we have nor 0.

29 euros converts to nor 0.

25 pounds.

So let's have a look at our euros.

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

29 euros.

So that means I'm going to divide my pounds by four 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.

Three shops provide three 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 two pounds, you get two euros 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 pounds, you get 4.

24 euros.

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

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

Writing it as a ratio table, I have 30 pounds to 45 euros.

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 two.

For question two, a group of three friends are going a holiday and they all exchanged some pounds for euros.

So Sofia got 120 euros for 100 pounds and Laura got 30 euros for 20 pounds, and Sam got 90 euros for 60 pounds.

Who got the best deal? For B says Andeep decided to come along too and exchanged 110 euros for 100 pounds.

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, 100 pounds is 120 euros.

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

2.

That means pounds, multiply 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 euros.

Pounds times 1.

5 gives us euros for Laura.

For C, to find out the multiplier, we simply do 90 divide 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 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 two 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.