Lesson video

Hi, everyone.

My name is Ms. Coe, and I'm really happy to be learning with you today.

Today's lesson is going to be jam-packed full of interesting and fun tasks for you to do.

It might be tricky or easy in part, but I will be here to help.

It's gonna be a great and fun lesson, so let's make a start.

In today's lesson under the unit Understanding Multiplicative Relationships: Fractions and Ratio, we'll be securing understanding of ratio as a multiplicative relationship.

And by the end of the lesson, you'll be able to reason about ratios in a context.

Our key words today will be looking at 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.

We'll be looking at reviewing ratio first, and then using reasoning with ratios.

So let's make a start, reviewing ratio.

Now remember, proportions relate to one number to another.

And fractions, decimals, percentages, and ratios are common forms to show proportion because proportion is a part to whole, sometimes part comparison.

For example, fractions.

Here we have one part, and we know the whole represents four parts, decimals.

Well, with decimals, we know that we have a 0.

25 is the part, and one represents the whole.

For percentages, well, we know the 25 represents the part, and the hundred represents the whole.

And for a ratio, for example, one shaded, there are three unshaded.

All of these represent the same proportion, a quarter, 0.

25, 25%, or for every one shaded, there are three unshaded.

So it's important to remember that when we're looking at ratio, sometimes we look at part to part comparison or part to whole.

For example, we're going to start looking at bar models.

And bar models and ratio tables are excellent visual ways to see that multiplicative relationship between parts and the whole.

Now I want you to have a look at this bar model and that lovely picture as well.

I want you to identify how many slices of each ingredient are needed to make this sandwich.

Well, you can either look at the bar model, or we can use a ratio table.

To make our sandwich, you can see we needed two pieces of bread, three slices of cheese, and four slices of tomato.

That makes our one sandwich.

You can look at this part to whole comparison.

For example, for every one sandwich, we need two slices of bread.

Or you could look at a part to part comparison.

For example, for every two slices of bread, we need three slices of cheese.

Or for every four slices of tomatoes, we need two slices of bread.

I want you now to have a little think, how many sandwiches and how much of each ingredient would you need if there Are 15 slices of cheese? Well, hopefully you've spotted if there are 15 slices of cheese, that means using our bar model, I've put in five, five, and five to represent our 15.

That means the whole bar model must have five in each of those little bars, thus it makes five sandwiches.

If you were to look at the ratio table, well, looking at the slices of cheese, I need to identify the multiplier.

What do I multiply 3 by to give 15? Well, it's five.

Now remember, they are in proportion.

So that multiplicative relationship is the same for each part.

Therefore, we multiply everything by five.

Thus identifying for five sandwiches, we need 10 pieces of bread, 15 slices of cheese, and 20 slices of tomato.

So you can see the bar model shows exactly the same information as our ratio table.

Now what I want you to do is have a look at a quick check question.

I want you to draw a ratio table or a bar model and calculate the following.

I want you to work out how many sandwiches can be made and how many of each ingredient is needed if you have 12 pieces of cheese.

You know to make a sandwich where you use two pieces of bread, one lettuce leaf, four pieces of cheese, and two slices tomato.

For part B, I want you to identify how many full sandwiches can you make If you only have 15 pieces of bread.

See and give it a go.

Press pause if you need more time.

Great work, everybody.

So let's see how you got on.

Well, I'm going to use our bar model first.

Hopefully, you can see from the bar model I've represented two pieces of bread, one lettuce leaf, four pieces of cheese, and two slices tomato to make my sandwich.

But the question A says, I have 12 pieces of cheese.

So that means each bar in our bar model must represent three because we have 12 pieces of cheese, that means everything is three, so it's three sandwiches.

Alternatively, you may have decided to draw a ratio table.

So here's all my information in the ratio table.

I have 12 pieces of cheese.

What is that multiplicative relationship between the 12 pieces of cheese and the four pieces of cheese? Well, I'm times-ing it by three, so that means I must multiply everything by three.

Thus giving me three sandwiches is six pieces of bread, three slices of lettuce, 12 slices of cheese, and six tomatoes.

Great work if you got that one right.

Now, let's have a look at the second part.

How many full sandwiches can you make if we only have 15 pieces of bread? So looking at our bar model, can you make those two bars in our bar model give a total of 15? Well, we can't because we're talking about full sandwiches, and that would be 7.

5 each.

So that means looking at our whole numbers, each bar should be seven.

Therefore, each number in our bar should be seven to represent seven sandwiches.

Now I'm going to use our ratio table.

Same again, we need to identify that multiplicative relationship between two slices of bread and 15 slices of bread.

Well, 15 divided by 2 is 7.

5, but the question wanted whole sandwiches, so I need to multiply by the whole number, which is seven, therefore giving us seven whole sandwiches.

Uses 14 slices of bread, seven slices of lettuce, 28 slices of cheese, and 14 slices of tomato.

Great work if you got that one right.

Now, let's have a look at a second check question.

Here, Aisha and Sofia make smoothies using this recipe below, but they only have 750 millilitres of yoghourt.

Now, to make two smoothies, you need one apple, 300 millilitres of yoghourt, a hundred millilitres of milk, and 12 berries.

Aisha says we can only make four whole smoothies because 300 times 2.

5 is our 750 millilitres of yoghourt, and we can't multiply by a decimal.

Now, Sofia says we can make five whole smoothies because 300 times 2.

5 is 750 millilitres.

Who is correct and explain.

Well done.

So let's see how you got on.

Well, Aisha and Sofia make smoothies using this recipe which are represented in a ratio table.

Now for two smoothies, we know there is one apple of 300 millilitres of yoghourt and a hundred millilitres of milk, and 12 berries.

So therefore, to make one smoothie, I'm simply dividing everything by two or multiplying by one half.

Therefore, I know for every one smoothie, I need half an apple, 150 millilitres of yoghourt, 50 millilitres of milk, and six berries.

To find out what that multiplier is, I simply do 750 divided by 150, which is five.

So multiplying each of our parts in our smoothie by five, I have five smoothies is two and a half apples, 750 millilitres of yoghourt, 250 millilitres of milk, and 30 berries.

So that means Sofia is correct because we can multiply any part in the ratio by decimals.

Well done if you got that one right.

Now let's move on to your task.

For each recipe, you need to construct a ratio table for the following recipes.

Then using that ratio table, how many cakes can you make with one kilogramme of flour and identify how much of each other ingredient is needed.

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

Well done.

Let's move on to question two.

Question two, Jacob has spilt chocolate sauce all over his ratio table for making chocolate brownies.

Can you work out those missing values? Remember that multiplicative relationship? 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 wants you to identify if the statement is true or false for the following ratio table.

See if you can give it a go.

Press pause if you need more time.

Well, for question one, your ratio table should look like this.

One vanilla cake is 250 grammes of flour, to 2 eggs, to 10 millilitres of vanilla, to 75 grammes of sugar, to 75 grammes of butter.

Now, if we had one kilogramme of flour, that means that's a thousand grammes of flour.

So what's our multiplicative relationship? Well, if you divide 1,000 by 250, we have four.

So therefore, if you multiply each part by four, we will have four cakes uses a kilogramme of vanilla, 8 eggs, 40 millilitres of vanilla, 300 grammes of sugar, and 300 grammes of butter.

So that means we can make four cakes.

Well done.

Have you got this one right? Question two, your ratio table should look like this.

For each cake, we should use 200 grammes of flour to two eggs, to three bananas, to 200 grammes of sugar, to 200 grammes of butter.

Now we've got a kilogramme of flour, so that means we have a thousand grammes of flour.

What's our multiplier? Well, our multiplier would be found by 1,000 divided by 200, which is 5.

So that means we're multiplying each part by five, thus giving us the following quantities for our cake.

So for a thousand grammes or one kilogramme of flour, we can make five banana cakes.

Well done.

And you've got this one right.

For the next one, for our grapefruit cake, our ratio table should look like this.

Same again, we have one kilogramme of flour, so that's a thousand grammes.

To identify a multiplier, we simply divide 1,000 by 125, which is eight.

So multiplying each part by eight, we now have the quantities for eight grapefruit cakes.

Great work if you've got this one right.

For question two, Jacob spilt chocolate sauce all over his ratio table.

Did you find these following amounts? Well, hopefully you've spotted that multiplicative relationship between the values.

We don't know how much flour is needed for 10 people, but we do know how much flour is needed for five people.

If five people uses 50 grammes of flour, that means 10 people would use twice that, which is a hundred grammes of flour.

Next, if you know 200 grammes of butter serves 10 people for five people, it'd be a hundred grammes, so on and so forth.

It's all about identifying that multiplier.

Great work if you got this one right.

For question three, let's see how you got on.

For one burger, we need 120 grammes of veggie patty, two lettuce slices, three slices of cheese, and four slices of tomato.

So is the statement, for every four slices of lettuce, there are six slices of cheese, is that true or false? It's true.

Think about that multiplier.

To make six slices of cheese, you're multiplying by two.

So you multiply everything by two.

Two lettuce slices times two is four, so it's correct.

Tomato slices are double the lettuce slices.

It's true.

If you look at the tomato slices, it's four.

And if you double our lettuce slices, that gives our four, so it's true.

For every 60 grammes of veggie patty, there are two slices of tomato.

That is also true.

If you know there's 120 grammes of veggie patty for every four slices, if you divide by two, 60 grammes of veggie patty makes two tomato slices.

Well done if you got this one right.

Great work, everybody.

So let's move on to the second part of our lesson where we're using reasoning with ratios.

Now, recognising the ratio shows the relative sizes of two or more values and allows you to compare a part with another part and a whole is so important.

Knowing that multiplicative relationship between the parts is constant for things in the same ratio.

For example, how many multiplicative relationships can you see with these ingredients? For every one sandwich, we need two slices of bread, three slices of cheese, and four slices of tomato.

How many multiplicative relationships can you spot? Well done.

So let's see how you got on.

I'm going to use a bar model, just to show the same information from our ratio table.

So you can see we have two pieces of bread for three pieces of cheese, for four slices of tomato, for one sandwich.

So one multiplicative relationship could be for every two pieces of bread, there are four tomatoes.

Another one would be for every one piece of bread, there are two tomatoes.

You can see that from our ratio table as well.

You're multiplying by two, or for every two pieces of bread, there are three pieces of cheese.

You can see this again in our ratio table.

You can multiply the pieces of bread by 1.

5, and it gives the slices of cheese.

There are so many multiplicative relationships.

And remember, that multiplicative relationship can be between part to part or part to whole.

Now what I want you to do is ask yourself, does the multiplicative relationship change if we're looking at three sandwiches or any multiple of sandwiches? Well, hopefully you can spot it doesn't.

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

So do you remember before, we looked at the slices of bread, multiplied by 1.

5 gave us the slices of cheese.

If I'm looking at three sandwiches, that multiplicative relationship is the same or constant.

It's the same when you're looking at slices of bread to tomato slices.

We knew two slices of bread gave four slices of tomato.

So if you're looking at three sandwiches, 6 slices of bread will give 12 tomatoes.

That multiplicative relationship remains the same.

So understanding that multiplicative relationship between the parts allows you to reason if the ratio is correct or not, and it impacts the context of the whole.

Reading the context of the question will help you identify the consequence of changing a ratio.

So now let's have a look at your task.

For question one, Laura has a recipe for lemonade.

It is the perfect mix of water, lemon, and sugar.

For every one lemon, we use 500 millilitres of water and two tablespoons of sugar.

We're asked to fill in the table to identify if the ratios below give the mixture that is too sweet.

In other words, too much sugar, too bitter, in other words, too much lemon, or perfect.

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

Well done.

Let's move on to question two.

Question two says, orange paint is made using two tins of yellow for every one tin of red.

Sam, Jacob, and Aisha are given an orange paint made in this ratio.

And they each add three more tins to the mix, only using red and yellow.

Now the results after they mix the extra tins are below.

What colours were in each of their three tins? See if you can give it a go, and press pause if you need.

Well done.

Let's move on to question three.

Question three wants you to tick if the statements are true or false.

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

Excellent work, everybody.

So let's move on to the answers to question one.

Well, for question one, for that perfect lemon mix, we need one lemon, 500 millilitres of water and two tablespoons of sugar.

So we need to have a look if the ratio below in our table is too sweet, too bitter, or perfect.

Well, for two lemons, a hundred millilitres of water and three tables with of sugar, let's find out how that impacts our mix.

Well, if we had two lemons, that means we'll need a thousand millilitres of water and four tablespoons of sugar.

If you look at what we have, two lemons, a thousand millilitres of water, but we only have three tablespoons of sugar when we should have four, so that means it's gonna be too bitter.

We should have four tablespoons of sugar, not three.

Next, 4 lemons, 2,000 millilitres of water, and nine tablespoons of sugar.

Well, using our ratio table, I'm finding what do we need for four lemons? Times everything by four means 4 lemons uses 2,000 millilitres of water and eight tablespoons of sugar.

Here, the ratio says nine tablespoons of sugar, so we have too much.

So it's going to be too sweet.

Next, 3 lemons, 1,500 millilitres of water, and six tablespoons of sugar.

Well, let's have a look at those three lemons and that multiplicative relationship.

That means we should have 1,500 millilitres of water and six tablespoons of sugar.

It's exactly the same, so it's perfect.

Well done if you got this one right.

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

Remember, each student got a big orange, tin of paint, and three mystery other tins, but we know it's either red or/and yellow.

Now, given the fact that Sam's paint turns lighter, what were those tins? Well, the ratio of paint must include more yellow than red because it got lighter.

And that means it must be a higher proportion of yellow than the original.

Since there's three cans, they must all be yellow, as one red and one yellow would maintain that original colour, so they had to be all yellow.

Next one.

For Jacob, the paint stays the same colour.

So if Jacob's paint stays the same colour, that means the ratio must be exactly the same as what was given for the orange, in other words, two yellow for one red.

Well done if you got that one right.

Aisha's paint turns darker, so that means all the paint tins had to be red, or two are red, and one is yellow.

It's impossible to tell which, but we know there are more red than yellow given the ratio of orange.

Really well done if you got that one right.

For question three, a ratio describes the relationship between values.

Is this true or false? It's true.

Ratio uses an additive relationship.

This is false.

Remember, ratios use a multiplicative relationship.

Adding the same amount to each part in a ratio keeps the ratio the same.

That is false.

Remember, it's a multiplicative relationship.

The last one, multiplying the same amount to each part in the ratio keeps the ratio the same.

That is correct because we understand that multiplicative relationship.

Great work, everybody.

So in summary.

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

That multiplicative relationship between the parts is constant for all things in the same ratio, and that multiplicative relationship between the parts of the ratio is not additive.

Adding the same amount to each part of the ratio can change that ratio.

Great work, everybody.

Well done.