Lesson video

Welcome to our proportion problems lesson, where we'll be solving problems involving our knowledge of ratio.

All you'll need is a pencil and a piece of paper, so pause the video and get your equipment if you haven't done so already.

Here's our agenda for today's learning.

So we're solving problems involving our knowledge of quiz, then we're looking at recapping ratio, solving ratio problems and then some independent learning and a final quiz.

So, recapping ratio.

You've got four statements here that relate to the tower of cubes and you need to decide whether they are true or false and if they're false, see if you can give the correct answer.

Pause the video now and make some notes.

The first statement says that the ratio of yellow to pink cubes is two to four.

So if we have a look at the yellow cubes, we can see that there are two yellow cubes and there are four pink cubes.

So for every two yellow cubes, there are four pink cubes.

So that statement is correct.

In the second one, it says the ratio of blue cubes to pink cubes is four to eight.

So blue cubes, there's one, two, three, four, five, six, and pink cubes is one, two, three, four.

So that's actually a ratio of six to four, so that one is incorrect.

The third one, half of the cubes are blue, well, we know that there are six blue cubes and altogether there are one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, so that is correct, half of the cubes are blue.

Six out of the 12 cubes are blue.

And the final one, the ratio of yellow to blue cubes is one to three, so there are two yellow cubes and there are one, two, three, four, five, six blue cubes.

So that's a ratio of two to six, which simplifies to one to three.

If we cut this tower in half where this pink cube is and just looked at the top half of it, we could see that for every one yellow cube, there are three blue cubes and again, if we look to the bottom half from this pink one, there's one yellow cube and three blue cubes, a ratio of one to three.

Now we'll go straight into some ratio problems. So this is the type of problem that you will see when dealing with ratios.

So, Fran was planting flowers in her garden and for every four tulips she plants, she plants seven daffodils.

So Fran plants 56 daffodils, how many tulips has she planted? The first job is to think about what is the ratio of tulips to daffodils.

So go back and read the question again, for every four tulips she plants, she plants seven daffodils.

So for every four tulips, seven daffodils, that's a ratio of four to seven.

And I always like to write the word ratio as well, to help me remember which number is associated with which word.

So now we know we have our ratio of tulips to daffodils, four to seven.

So, in this question, wait.

Then now we have, well, certain So now we know our ratio of tulips to daffodils is four to seven.

So for every group of seven daffodils, a group of four tulips are planted.

Let's have a look at this pictorially.

So I plant seven daffodils and four tulips, that's how the pattern goes.

So if 56 daffodils are planted, there must be eight groups of four tulips.

Lets have a look at how this would look.

So here I have got 56 daffodils, there's seven in each group and there's eight groups altogether.

Seven times eight is 56.

So there must also be eight groups of tulips and there's four in each group, four times eight is equal to 32.

So if I count 56 tulips, then they will all.

so if Fran plants 56 daffodils, she must also plant 32 tulips.

Let's have a look at this without the pictures to help us.

So I know my original ratio is four to seven, so if Fran planted seven daffodils, she would plant four tulips but this time she's planted 56 daffodils.

So let's look at the relationship between seven and 56, seven multiplied by eight is 56 and that links back here, we have eight groups of seven, which is equal to 56.

So we must do the same to the four, the groups of four tulips and multiply it by eight, which gives us 32.

So the new ratio is 32 to 56, which simplifies to four to seven.

Now it's your turn to have a go, so I'll talk through the problem with you first and then you're going to have a go at this one independently.

So a squirrel is collecting acorns.

For every two acorns that she eats, she saves three acorns for later.

So we've got an eats to saves ratio.

So you'll want to start by working out what the ratio is, for every two she eats, she saves three for later.

Over the autumn, the squirrel saves 240 acorns, so how many acorns has she eaten this time? Pause the video and have a go at this one by yourself.

So the initial ratio of eats to saves is two to three, for every two she eats, she saves three.

And the question says that if she saves 240, how many does she eat? So we're scaling up the ratio so that she saves 240 and thinking about the relationship now, between three and 240.

So we know that the relationship between three and 24 is eight, three times eight is 24, so between three and 240, we must be multiplying by 80.

So for every 80 groups of three acorns she saves, she does the same for eating, she eats 80 groups of two acorns, which gives us 160 acorns.

So I find these diagrams really helpful when scaling up ratios.

What you needed to be really careful about on this one, was that you didn't just plunk the 240 in the first spot and made sure you did it under the saves part of the ratio, which is why I think it's really helpful to have the worded ratio at the top.

Let's look at another one together.

So Nadia is a radio DJ, all the radio DJs need to make sure that they play a mix of different genres of music.

The radio station has a ruling of three times as many pop songs as soul songs.

Nadia played 126 pop songs in her show, so how many soul songs did she play? We start off by working out the initial ratio, so the ratio is pop to soul songs.

Let's look back at this part of the question, three times as many pop songs as soul songs.

So that's a ratio of three to one.

Now she played 126 pop songs, so we're going to use our diagram that we used in the last one, the 126 is going in the pop column and we're trying to work out the number of soul songs.

So we need to think about the relationship between three and 126.

So you could do a quick bus stop division, 126 divided by three and that is equal to 42.

The ratio has been scaled up by 42, so we're multiplying three by 42 to get us to 126.

The same needs to happen to the soul songs, we need that to be enlarged by scale factor 42, which gives us 42 soul songs, one times 42 is equal to 42.

Now, here's another ratio that Nadia has to follow, so for every two old songs she plays, she must play five new songs.

If she plays 56 songs in total, how many will be new and how many will be old? So this is a slightly new type of question that we're looking at.

So the ratio of old to new is two to five, for every two old songs, she must play five new songs.

So if we have the ratio in its simplest form, two for old and five new, that means seven songs altogether.

So she plays two old songs, she plays five new songs, therefore she's played seven songs all together.

So that ratio of two to five means seven in total.

But in this one, the total is 56, so we're doing the same thing again here but this time we're looking at the totals of the ratio.

So what's the relationship between seven and 56? Seven times eight is 56, so we need to do the same to each part of the ratio.

We need to multiply, because each side has been multiplied by eight, we need to multiply two by eight to give us 16 and then five by eight to give us 40.

And then if you have a look, you can see that 16 plus 40 is equal to 56.

So you will have some questions coming up where you're being asked about the total, in which case you need to add the numbers in the ratio to find the original total and then scale up, but make sure you scale each part of the ratio up.

Now you're ready for some independent learning, so pause the video and complete the task and click restart once you're finished.

So in question one, we have a table of the ratio of songs that DJs play on different radio stations throughout the day and you were asked to fill in the missing information.

So, we'll start with Orchestra FM, they have a ratio of new to old songs, of three to one.

So we can see, that three has been enlarged by the scale factor of 22 to give us 66.

So we have to multiply one by 22, which gives us 22 and that in total gives us 88 songs all together.

So we're looking, if you have that in the diagram we've been working on, you would have three to one and then 66 to 22 below it, they've been enlarged by scale factor 22.

For Radio Rock, we've got the total number of songs and then we've got the old songs.

So to find the new songs we need to multiply the old, so we need to subtract the old from the total, 135 take away 81 is equal to 54.

And then we need to scale down the ratio, so we can look at here what's the relationship between 81, which is old, and three, which is old.

Well, 81 divided by 27 is equal to three, so we need to do the same, 54 divided by 27 is equal to two.

So they're in the ratio two to three.

In Pop Radio, the ratio of new to old is three to five and we're just given the total here.

So if we have three to five songs, that equals to eight and we multiply it by six to get us to 48, therefore we need to multiply each of these numbers in the ratio by six.

So three times six gives us 18 new songs and five times six gives us 30 old songs.

And then in Mindful Melodies, we have a ratio of 60 to 24 and we want to simplify the ratio by dividing both of them by the highest common factor.

Before we do that, we'll find the total by adding them together, that's 84.

Then we want to simplify, the highest common factor of 60 and 24 is 12, so we divide 60 by 12 to give us five and 24 by 12 to give us two, a ratio of five to two.

So the Sugar Plum Bakery makes delicious cupcakes.

There are three times as many unicorn cakes as rainbow cakes.

So the ratio here using these pictures, rainbow to unicorn, is two to six and six is three times two, so there're times as many unicorn cakes as rainbow cakes.

Now you're being asked to scale the recipe in different ways to see if there would be still three times as many, if you first of all, add two cakes to each type.

So if I add two cakes to the rainbows, I get four, if I add two cakes to the unicorns, I get eight.

And is the relationship between four and eight three times as many? No, so I can see, that the relationship between these two is that eight is two times four, so there are twice as many unicorn cakes as rainbow cakes.

So this one does not keep the ratio the same.

What about if I have the number of each type? So that will be one of the rainbows and three of the unicorns, that will be one to three.

And the relationship between one to three is still three times as many unicorn cakes as rainbow cakes, so that one would work.

What if we doubled each type of cake? That would give us a ratio of four to 12 and that still means that there are three times as many unicorn cakes as rainbow cakes, because four times three is 12.

If I add one rainbow and two unicorn cakes and I get three and eight and that is not three times as many unicorns as rainbow cakes.

In question three, Amina planted some seeds, for every three seeds she planted, only two grew.

Altogether, 12 seeds grew, how many did she plant? So the original ratio, planted to grew is three to two, if 12 grew, we're looking at the relationship between two and 12, that's multiplied by six.

So we can do the same to the other part of the ratio, which means that she planted 18 but only 12 of them grew.

Great work today, well done.

Before you leave, don't forget to complete your final quiz.