Lesson video

Hi everyone, my name is Ms. Coo and today I'm really excited to be learning with you as we'll be looking at the wonderful unit ratio.

I hope you enjoy the lesson, so let's make a start.

Hi everyone and welcome to this lesson.

I'm checking and securing understanding of sharing in a ratio and it's under the unit ratio and by the end of the lesson you'll be able to use a ratio fluently in the context of sharing.

Let's have a look at some keywords, just to quickly recap.

Variables are in proportion if they have a constant multiplicative relationship 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 three parts.

We'll be looking at sharing in a ratio first, then sharing in a ratio given the difference and then solving ratio problems. So let's make a start sharing in a ratio.

Now in sharing an amount according to a ratio, it's so important to read the question carefully so you know what each part of the ratio means.

For example, I want you to have a look at these two questions.

I want to see if you can see the difference between these two questions.

The one on the left says the ratio of flour to butter to sugar in a cookie recipe is three to two to one and 120 grammes of flour is used.

How much butcher is used and the one on the right says the ratio of flour to butter to sugar in a cookie recipe is three to two to one.

The cookie is 120 grammes, how much butter is used? Can you see the difference between these two questions? Well, hopefully you can spot the question on the left states that the flour is 120 grammes.

So using a bar model, we know three parts as this represents our flour makes 120 grammes.

That means we can work out what each part is, 120 divided by three means each part has to be 40 grammes.

So putting 40 grammes into our bar model shows that flour is 120 grammes, butter is 80 grammes and sugar is 40 grammes.

Now the question on the right states that the whole cookie is 120 grammes.

So if you're using a bar model, you can see we have a total of six parts and these six parts must equal the 120 grammes.

So therefore if you divide 120 by six, that gives us each part to be 20 grammes.

That means we can spot flour is 60 grammes, butcher is 40 grammes and sugar is 20 grammes.

So it's always important to read the question carefully so you understand what ratio represents what quantity.

Let's have a look at a quick check question.

I'm going to do the one on the left and I'd like you to do the one on the right.

Lucas and Aisha share a packet of sweets in the ratio of seven to five.

Now Aisha has 25 sweets and we need to work out how many sweets does Lucas have.

Well, drawing our bar model, you can see a represented Lucas's seven parts here and Aisha's five parts here.

Now we know Aisha has 25 sweets, so that means Aisha's bar model must be 25.

So we can work out what each part in Aisha's bar model to be, it has to be five.

So now we know what one part represents, we can work out how many sweets Lucas has.

Well Lucas has seven parts, each part is five sweets, so that means Lucas has 35 sweets.

Now it's time for your question.

Lucas and Aisha share a packet of sweets in the ratio of four to seven, Lucas and Aisha have 22 sweets.

How many sweets does Aisha have? So you can give it a go, press pause one more time.

Well done, well hopefully you can spot that we know Lucas and Aisha both have 22 sweets, so that means the total parts has got to be 22.

If you count, you might notice we have 11 parts in total.

So 22 sweets divided by 11 parts means each part must be two sweets, filling in our bar model you can easily work out that Aisha has 14 sweets.

Really well done if you've got this.

So we've looked at bar models, but it's also important to recognise that ratio tables are another effective way to share an amount according to a ratio.

For example, the ratio of cats to dogs is three to seven and if there are 35 dogs, how many cats are there and how many animals would there be in total? So let's put this in a ratio table.

Cats is three parts and dogs is seven parts.

Now reading the question, we know there are 35 dogs.

I'm gonna extend my ratio table and put 35 here.

Now ratio tables clearly show that multiplicative relationship so you can see I'm simply multiplying the seven by the five to give us 35 dogs and we can easily work out the number of cats when we know the number of dogs is 35, so we know it's 15.

This means we know the total animals can be found, when there's 35 dogs, that means there has to be 15 cats giving us a total of 50, slightly change the question.

For example, we know the ratio of cats to dogs is three to seven, but if there are 40 animals in total, how many cats and dogs are there? And we're going to start by putting this in a ratio table.

Once again, we know the ratio of cats to dogs is three to seven, but reading the question, we now know that the total of animals is 40.

So if we know the ratio of parts is three to seven, that means the total parts would be 10.

Identifying that multiplicative relationship again, we can work out the number of cats and dogs quite easily.

I'm simply multiplying by four, so that means I have 12 cats to 28 dogs.

So that means when there are 40 animals we know there are 12 cats and 28 dogs.

Now it's time for a quick check.

I'll do the question on the left and I'd like you to do the question on the right.

The ratio of red to blue to black cars in a car park is eight to five to 12.

Now we know there are 75 cars.

How many red and blue cars are in the car park? Well let's put it in a ratio table.

We know the ratio of red to blue to black is eight to five to 12, thus giving us a total parts of 25.

But the question told us that there are 75 cars parked in total, so that means I'm adding that extra row to our ratio table making a total of 75.

Because of that multiplicative relationship we know we're simply multiplying by three.

So I now know that the number of red cars is 24 blue cars is 15, black cars is 36, summing them up gives us that 75.

So that means there are 24 red and 15 blue cars in the car park, now it's time for your question.

The ratio of red to blue to black cars in the car park is eight to five 12, but there are 35 blue cars.

What I want you to do is work out how many red and how many black cars there are in the carpark, so you can give it a go.

Press pause more time.

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

While drawing our ratio table again, you can see the ratio red to blue to black is eight to five to 12.

We know there are 35 blue cars, so I've highlighted that, so you can see that multiplicative relationship was simply multiplying by seven.

Multiplying by seven means there are 56 red and 84 black cars in the car park, really well done if you got this.

Now it's time for your task.

There are lots of questions here, so please do take your time, fill in the cross number given the ratio of A to B.

Read the question carefully, make sure you know which amount represents which parts.

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

Great work, let's move on to these answers.

Massive well done if you have these answers, great work everybody.

Now it's time to look at sharing in a ratio, given the difference.

Here are three questions all sharing an amount according to a ratio.

Can you explain the difference between them? The first question says Aisha and Sam share 240 pounds in the ratio of eight to three, work out how much Aisha receives.

The second question says, Aisha and Sam share some money in the ratio of eight to three.

Sam gets 240 pounds, work out how much Aisha receives.

And the third question says Aisha and Sam share some money in the ratio of eight to three.

Sam gets 240 pounds more than Aisha work out how much Aisha receives.

Can you explain the differences between these three questions? Well done, let's see what you've got.

Well hopefully you recognise 240 pounds represents the total parts in our first question.

The second question states that 240 pounds is three parts as this is from Sam's ratio and the third question states that 240 pounds is the difference between Aisha and Sam's ratios.

Well done if you spotted the difference between these questions.

So let's look at the last question and represent it in a bar model first.

We know Aisha gets eight parts and Sam gets three parts as you can see represented in the bar model.

Now it states that Sam gets 240 pounds more than Aisha.

So this means this part of our bar model represents 240 pounds.

In other words, five parts of our bar model represent 240 pounds.

So we can work out what each part is by simply dividing 240 pounds by five, that means each part has to be 48.

Knowing each part is 48, we can complete the rest of the bar model and then from here we can work out how much Aisha receives.

It's 48 multiply by the eight parts, gives us 384 pounds.

Well done if you spotted this.

Now it's time for another check.

A piggy bank holds copper and silver coins in the ratio of seven to 15.

Laura has 40 more silver coins than copper coins.

Can you work out how many copper coins Laura has? A bar model has been drawn for you if you need? See if you can give it a go.

Press pause if you need more time.

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

Well we know the difference between copper and silver coins is 40 coins.

So looking at the difference between the bar models, you can count there are eight parts different.

So 40 coins divided by the eight parts means each part has to be five coins.

Knowing this, we can fill in the rest of our bar model and we can identify that Laura has seven multiply by five, which is 35 copper coins.

Really well done if you've got this.

Next I want you to try this check question, I want you to match each problem to its corresponding bar model.

Question one states that the ratio of red to blue is five to three, there are 120 red, how many are there in total? Question two says the ratio of red to blue is five to three, there are 120 in total.

How many reds are there? Question three says the ratio of red to blue is five to three, there are 120 fewer blue.

How many red are there? Question four says the ratio of red to blue is five to three, there are 120 blue.

How many reds are there? See if you can match up the question with the correct bar model, press pause one more time.

Really well done, let's see how you match them up.

Well we should have this question three is matched with A, question Four is matched with B.

Question two is matched with C and question one is matched with D.

Very well done if you match those questions with those bar models.

So we've looked at representing the difference using bar models.

So now let's look at representing the difference using a ratio table.

For example, the ages of the Oak teacher and Lucas are currently in the ratio of 15 to seven.

The Oak teacher is 16 years older than Lucas.

How old is Lucas? So let's represent this in a ratio table first, drawing our ratio table, you can see the ratio between the teacher's age and Lucas's age.

Now from here let's add another column.

Identifying the difference between these ratios.

So the difference between the ratio of 15 and seven is eight.

Now we know from the context of the question we're looking at a difference of 16.

So using that multiplicative relationship, we are simply multiplying by two.

Therefore we know the teacher is 30 years old and Lucas is 14 years old.

Really well done, have you spotted this? Now it's time for a quick check.

Jun and Andeep share some gaming cards in the ratio of four to nine.

Now Andeep has 30 more cards than Jun.

Can you work out how many cards there are in total? See if you can give it a go draw a bar model or ratio table to help.

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

Well I'm going to use a ratio table.

So I'm going to represent Jun as four and Andeep as nine as that stated in the question.

Now it does state that and Deep has 30 more cards than Jun.

So we're going to find the difference.

We know the difference between Jun and Andeep's ratio is five, but the difference between the cards is 30.

So let's identify that multiplicative relationship.

We know where multiplying by six.

So I know Jun has 24 cards and Andeep has 54 cards and you can see we have a difference of 30.

From here we can answer the question.

The question wants us to identify how many cards there are in total, we're 24 and 57 is 78 cards in total.

Really well done if you've got this.

Let's have a look at another check question.

We're looking at our ratio tables now and I want you to match the question with the correct ratio table and answer, see if you can give it a go.

Press pause if need more time.

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

Well hopefully you've matched these ones we should know for question one, using this ratio table 240 millilitres of juice was needed for question two, it should be this ratio table.

Hopefully you've spotted that we've got 400 millilitres of juice is needed.

And for the last one, hopefully you've spotted 80 millilitres was needed using this ratio table.

Really well done if you've got this great work everybody, now it's time for your task.

Read the question carefully, take your time and press pause as you'll definitely need more time for these questions.

Well done, let's move on to question four.

Question four says there are three ratio tables here and I want you to form a question and work out the answer, given these ratio tables be as creative as you want.

Well done, let's go through these answers.

Well for question one you can see how I've constructed the ratio table here giving us an answer of 121 pounds.

For question two same again, you can see how I've constructed the ratio table giving us our answer of 125 grammes for flour, 200 grammes for sugar and 50 grammes for butter.

Press pause if you need to look at that working out a little bit more.

Well done.

Question three, hopefully you spotted we need an agility level of 575 and for the second part the minimum strength is 804 and the minimum agility is 1005.

Once again, press pause if you need to have a look at this working out.

Well done.

Now for question four you could have formed any questions you want as long as they are in line with the context of the ratio.

So here's some questions that I've thrown together just as an example.

Great work and this is why I like ratio, because you can create and event so many different questions.

Excellent work everybody.

So let's have a look at solving ratio problems. Now, ratio problems can appear with other topics of mathematics and it's important to carefully read the question, extract what facts are needed and then share the amount according to the ratio.

For example, a spinner can land on a one, two, three or four.

Now the spinner is bias and the probability that it lands on a one or four is 50%.

The probability of a two or three is in the ratio of seven to three and we're asked to work out the probability it lands on a three, so let's have a look.

Well this question refers to probability.

So have a little think about what do you know about the sum of these mutually exclusive events.

Well hopefully you spotted that the some of probabilities is always one if it's represented as a fraction or decimal or a hundred percent.

So reading the question, we know the probability of one or the probability of four is 50%.

So what do you think is the remaining probability for the numbers two and three? Well, we know the probability of two and three must sum to 50%.

So this means we can draw a ratio table knowing that the sum of parts or the probability of two and the probability of three must equal 50%.

As you can see here, the ratio parts is 10 because we have the ratio of seven add the ratio of three must give us a total of 50%.

Now we can find the probability of one part by simply dividing by 10, so that means we know one part is 5%.

Given that the probability of two is seven parts, I know the probability of two is 35% and the probability of three is three parts.

So therefore, given that the question wants us to work out the probability it lands on three, it's simply the probability of three is 15% or 0.

15 or three over 20, well done if you spotted this.

Now it's time for a check.

A triangle has three angles in the ratio of three to eight to one.

Now the difference between the largest angle and the smallest angle is 105 degrees.

Sophia says that the largest angle is 128 degrees is Sophia correct? And I want you to explain, you can draw a bar model, but ideally a ratio table if you want to help you answer this question, press pause for more time.

Great work, so let's see how you got on.

Well, there are a few different ways to show if Sophia is correct, using the largest angle of 128 degrees, her ratio would look like this.

Given the fact that we know the the ratio between the angles is three to eight to one.

If she says the largest angle is 128 degrees, that means the medium angle must be 48 and the small angle must be 16.

And this is not possible.

It's not possible because we know if we to sum all those angles it should give us 180 degrees.

But summing all of these gives us 192.

And also if the largest angle was 128 degrees, the difference between the largest and the smallest is not 105 degrees.

Alternatively, let's see if we can work out the correct answer using a ratio table, using the ratio table.

You can see I've written the ratio of medium to large to small as three to eight to one.

Now given the fact that we know the difference between the largest angle and the smallest angle is seven parts, we're going to multiply this by 15.

Thus giving goes a difference between the largest angle and the smallest angle to be 105 degrees.

Multiplying each of the parts by 15 gives us 45 degrees, 120 degrees and 15 degrees.

From here, we know the largest angle is 120 degrees and the smallest angle is 15 degrees, therefore, Sophia is incorrect.

Great work everybody, so let's move on to your task.

Question one and two, good problem solving questions.

Think about what other topics of mathematics have been incorporated with ratio here.

Give it a go, press pause if you need more time.

Well done for question three and four, same again, read the question carefully, give it a go.

Press pause if you need more time, well done.

Let's have a look at these answers.

Well, for question one, you can see my ratio table here and I've worked on the probability of even to be 62.

5%.

Press pause if you need more time to look at the working out.

Question two, hopefully you can spot for my ratio table that the angles are 60 degrees, 80 degrees and 40 degrees.

Really well done, if you've got this, press pause if you need more time to look at the working out.

For question three, here is my quadrilateral.

This was a great question and you had to identify that the quadrilateral is a kite.

Very well done if you've got this.

And for question four, here's the working out and you should have got an answer of 60 pound.

Once again, press pause if you need to have a look at this working out.

Great work, everybody.

So in summary, when sharing an amount according to a ratio, it's important to carefully read the question to know which parts of the ratio equals which amount.

For example, here are three very different ratio scenarios.

The ratio of red to blue is five to three, and there are 120 red.

The ratio of red to blue is five to three, but there are 120 in total and the ratio of red to blue is five to three, but there are 120 fewer blue, three very different ratio scenarios.

So ratio problems can appear with other topics of mathematics and it's important to carefully read the question, extract what facts are needed, and then share the amount according to the ratio.

Massive well done everybody, it was great working with you.