Lesson video

Hi everyone, my name is Miss Ku and I'm really happy to be learning with you today.

Today's lesson's 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, we'll be looking at 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.

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 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 to part comparison.

For example, fractions.

Here, we have 1 part and we know the whole represents 4 parts.

Decimals, well, with decimals we know that we have 0.

25 is the part and 1 represents the whole.

For percentages, well, we know the 25 represents the part and the 100 represents the whole.

And for a ratio, for example, 1 shaded, there are 3 unshaded.

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

25, 25%, or for every 1 shaded there are 3 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 2 pieces of bread, 3 slices of cheese, and 4 slices of tomato, that makes our 1 sandwich.

You can look at this part to whole comparison.

For example, for every 1 sandwich, we need 2 slices of bread.

Or you could look at a part to part comparison.

For example, for every 2 slices of bread, we need 3 slices of cheese.

Or for every 4 slices of tomatoes, we need 2 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 5, 5, and 5 to represent our 15.

That means the whole bar model must have 5 in each of those little bars, thus it makes 5 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 5.

Now remember, they are in proportion, so that multiplicative relationship is the same for each part, therefore, we multiply everything by 5.

Thus identifying for 5 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, we use 2 pieces of bread, 1 lettuce leaf, 4 pieces of cheese and 2 slices of tomato.

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

So you can 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 2 pieces of bread, 1 lettuce leaf, 4 pieces of cheese and 2 slices of 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 3 because we have 12 pieces of cheese.

That means everything is 3, so it's 3 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 4 pieces of cheese? Well, I'm timesing it by 3, so that means I must multiply everything by 3, thus giving me 3 sandwiches.

It's 6 pieces of bread, 3 slices of lettuce, 12 slices of cheese and 6 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 2 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 7.

Therefore, each number in our bar should be 7 to represent 7 sandwiches.

Now I'm going to use our ratio table.

Same again, we need to identify that multiplicative relationship between 2 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 7, therefore giving us 7 whole sandwiches uses 14 slices of bread, 7 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 2 smoothies, you need 1 apple, 300 millilitres of yoghourt, 100 millilitres of milk and 12 berries.

Aisha says we can only make 4 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 5 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 2 smoothies, we know there is 1 apple, 300 millilitres of yoghourt and 100 millilitres of milk and 12 berries.

So therefore, to make 1 smoothie, I'm simply dividing everything by 2 or multiplying by 1/2.

Therefore, I know for every 1 smoothie, I need half an apple, 150 millilitres of yoghourt, 50 millilitres of milk, and 6 berries.

To find out what that multiplier is, I simply do 750 divided by 150, which is 5.

So multiplying each of our parts in our smoothie by 5, I have 5 smoothies is 2 1/2 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, 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, Jacobs 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.

Great work.

Let's move on to question three.

Question three wants you to create your own recipe for a Crazy Cake, which serves 4 people.

Ensure to write the correct unit of each measurement.

I want you to fill in your ratio table to make the ratios between each ingredient 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, your ratio table should look like this.

1 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 1 kilogramme of flour, that means that's 1000 grammes of flour.

So what's our multiplicative relationship? Well, if you divide 1000 by 250, we have 4.

So therefore if you multiply each part by 4, we will have 4 cakes uses a kilogramme of flour, 8 eggs, 40 millilitres of vanilla, 300 grammes of sugar and 300 grammes of butter.

So that means we can make 4 cakes.

Well done if 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 2 eggs to 3 bananas to 200 grammes of sugar to 200 grammes of butter.

Now we've got a kilogramme of flour, so that means we have 1000 grammes of flour.

What's our multiplier? Well, our multiplier would be found by 1000 divided by 200, which is 5.

So that means we're multiplying each part by 5, thus giving us the following quantities for our cake.

So for 1000 grammes or one kilogramme of flour, we can make 5 banana cakes.

Well done if you've got this one right.

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 1000 grammes.

To identify a multiplier, we simply divide 1000 by 125, which is 8.

So multiplying each part by 8, we now have the quantities for 8 grapefruit cakes.

Great work if you 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 5 people.

If 5 people uses 50 grammes of flour, that means 10 people would use twice that which is 100 grammes of flour.

Next, if you know 200 grammes of butter serves 10 people, for 5 people, it'd be 100 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 1 burger, we need 120 grammes of veggie patty, 2 lettuce slices, 3 slices of cheese and 4 slices of tomato.

So is the statement for every 4 slices of lettuce, there are 6 slices of cheese.

Is that true or false? It's true.

Think about that multiplier.

To make 6 slices of cheese, you're multiplying by 2.

So you multiply everything by 2.

2 lettuce slices times 2 is 4, so it's correct.

Tomato slices are double the lettuce slices.

It's true.

If you look at the tomato slices, it's 4, and if you double our lettuce slices, that gives our 4, so it's true.

For every 60 grammes of veggie patty, there are 2 slices of tomato.

That is also true.

If you know there's 120 grammes of veggie patty for every 4 slices, if you divide by 2, 60 grammes of veggie patty makes 2 tomato slices.

Well done if got this one right.

Now, creating your own Crazy Cake can have any ingredient you want as long as you are consistent with that multiplier.

So whatever your quantities were, to change the serving of 4 people to 2 people, you divide by 2 or multiply by 1/2.

To change the 2 people to 14 people, for example, you could have multiplied those quantities by 7 or you could have multiplied the serving 4 by 3.

5.

This is a really nice task, making sure you are embedding that understanding of that multiplicative relationship.

Well done.

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 1 sandwich, we need 2 slices of bread, 3 slices of cheese and 4 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 2 pieces of bread for 3 pieces of cheese for 4 slices of tomato for 1 sandwich.

So one multiplicative relationship could be for every 2 pieces of bread, there are 4 tomatoes.

Another one would be for every 1 piece of bread, there are 2 tomatoes.

You can see that from our ratio table as well.

You're multiplying by 2 or for every 2 pieces of bread, there are 3 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 3 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, multiply by 1.

5 gave us the slices of cheese.

If I'm looking at 3 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 2 slices of bread gave 4 slices of tomato.

So if you're looking at 3 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 1 lemon, we use 500 millilitres of water and 2 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.

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 says, orange paint is made using 2 tins of yellow for every 1 tin of red.

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

And they each add 3 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 3 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 1 lemon, 500 millilitres of water and 2 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 2 lemons, 100 millilitres of water and 3 tablespoons of sugar, let's find out how that impacts our mix.

Well, if we had 2 lemons, that means we'll need 1000 millilitres of water and 4 tablespoons of sugar.

If you look at what we have, 2 lemons, 1000 millilitres of water, but we only have 3 tablespoons of sugar when we should have 4.

So that means it's gonna be too bitter.

We should have 4 tablespoons of sugar, not three.

Next, 4 lemons, 2000 millilitres of water, 9 tablespoons of sugar.

Well, using our ratio table, I'm finding what do we need for 4 lemons.

Times everything by 4 means 4 lemons uses 2000 millilitres of water and 8 tablespoons of sugar.

Here, the ratio says 9 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 6 tablespoons of sugar.

Well, let's have a look at those 3 lemons and that multiplicative relationship.

That means we should have 1,500 millilitres of water and 6 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 you got.

Remember, each student got a big orange tin of paint and 3 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's got lighter and that means it must be a higher proportion of yellow than the original.

Since there's 3 cans, they must all be yellow as 1 red and 1 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, 2 yellow for 1 red.

Well done if you got that one right.

Aisha's paint turns darker, so that means all the pink tins had to be red, or 2 are red and 1 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.