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You can describe the relationship between two factors in a ratio context.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

The language \"For every __ __ there are __ __ \" can be used to describe ratio.
Objects and diagrams can be used to represent ratio relationships.

Common misconception

Using addition and subtraction to connect the parts and whole in a ratio context.

Model all relationships at this stage using the language and notation of multiplication and division.

Keywords

Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole
For every - For every allows you to talk about the relative sizes of the values e.g. for every 2 squares there is 1 triangle

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Hello and welcome to this lesson on ratio and proportion.

At the end of this lesson, you should be able to describe the relationship between two factors in a ratio context.

Now there might be some words in there that are a bit less familiar.

I think this may be the first time we've come across the word ratio.

And what we're going to be looking at in this lesson is how we can look at parts in a whole and describe the relationship between those two parts, those two factors which make up this whole.

Let's look at the words we're going to be using in this lesson.

We're going to be using the word ratio and we're going to be using the little phrase for every.

So ratio is a new word, we'll look at what that means and we'll discover what that means over the course of this lesson.

And for every is going to be a really useful phrase to help us to describe what we see and then to create our own patterns and scenarios based around a given ratio.

So let's have a look at what those words mean.

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

So we've got a whole here of three shapes made up of two squares and one triangle.

So within our whole, we've got those two parts, those two factors, two squares and one triangle.

So let's look at how that language we talked about is gonna help us to describe that.

For every, allows us to talk about the relative sizes of those two values.

So we can say that for every two squares there is one triangle.

We could always say for every one triangle there are two squares, but we've looked at it in the order in which we can see it on the screen.

So for every two squares there is one triangle.

Our whole is those three shapes, our parts are the squares and the triangle and we can talk about how they relate to each other.

So in this lesson we are going to be thinking about other scenarios to describe and then creating our own scenarios given the language first.

So let's have a look and see if we can use that language together.

So in the first part of our lesson, that's exactly what our focus is going to be, using the language for every to describe ratio.

But we've got three images here on the screen, A, B, and C and we're going to use that language to help us.

So let's put up a stem sentence just so that we're thinking about how we're using that language.

So for every something there are something.

So you might want to just pause for a moment and think about how you would describe those images using that language.

Okay, let's have a have a look together.

So that was our stem sentence we were going to use.

So let's have a think about how that relates to those images.

So what can we see in A? We can see a beetle and I'm gonna focus in on its legs.

How many legs has the beetle got? So I can see it's got six legs.

So we could say for A, that for every one beetle there are six legs.

What we can see there is a beetle and six of its legs.

So for every one beetle there are six legs.

Let's move on to B.

What can we say about B? What can we see to start with? Well, we can see a pack of 10 pens.

So let's think about how we can use that language for every to describe what we can see there.

So we could say that for every one pack there are 10 pens.

We could also say for every 10 pens there's 1 pack.

But we're gonna go that way round and say, for every 1 pack there are 10 pens.

Like we said, for every one beetle, there are six legs.

Okay, what about C? We haven't got an obvious sort of one thing that we are describing here.

So we're getting that idea of thinking about what is our whole? Our whole is a small group of children here.

So what can we see in C? Or we can see that for every one girl, there are two boys.

We could say again, for every two boys, there's one girl.

But if you look at those three each time we've started with the one thing first, for every one beetle there are six legs, for every 1 pack there are 10 pens, for every one girl there are two boys.

Let's have a look at these images.

One might look a bit familiar to you, but look really carefully.

Again, you might want to pause and have a think about how we can use our stem sentence to describe what we can see here in A, B, and C.

For A, we've moved things around a bit, haven't we? From the previous slides.

So this time we can say that for every two girls there is one boy and I've kind of said that the way the picture is there.

So for every two girls there is one boy.

Okay, what about B? What can we see there? We can see two balloons and two party hats.

So we can say for every two balloons there are two party hats.

But let's have a look at that again.

Can we make those numbers a bit smaller? How else could we say that? So we could look at it, look at one sort of pair at a time.

And we could say for every one balloon there is one party hat.

But this time we've got that same number happening each time.

So if we are describing the parts within a whole, sometimes those parts might be equal.

For every two balloons there are two party hats.

Let's have a look at C.

And what can we see here? We can see that there are two bicycles and there are three cars.

So our sentence this time could say, for every two bikes there are three cars.

We haven't got a one involved this time in all the others we've managed to get to a one, but we can't really split that up any other way.

So this time our comparing of our parts, the two factors that make up our whole, within this image, we're gonna say that for every two bikes there are three cars.

Time for you to check to see if you are really comfortable with that language of for every.

So what we've got here is some images and we've also got some partly filled in sentences.

So this time I've given you the numbers but I haven't given you the objects.

So you've got sort of two jobs to do here.

We're gonna complete the statements and then match the statement to the images.

So can you find a statement that would fit for every one something there are five somethings and so on.

So pause the video, have a go at both completing those statements and then matching them up to an image.

Well, how did you get on? First one said for every one there are five.

So let's have a look at the picture.

We've matches that middle picture, that for every one squirrel there are five birds.

So the middle was for every two somethings there are four somethings.

And in our bottom image there, we've got two squirrels and four birds.

So we can say for every two squirrels there are four birds.

And then our bottom statement was a three somethings and three somethings.

And that top image shows us that there are three squirrels, three acorns.

So we can say that for every three squirrels there are three acorns.

How did you get on? Are you getting more familiar with that language of for every to describe the way these things are made up? I hope so because it's gonna be your turn to have a go at some practise.

So in this task, task one, we're going to ask you to describe what you see using that language for every something there.

And I've left it blank because it might be a there are or it might be a there is.

So have a look at those three images and complete that stem sentence for each image A, B, and C.

Now in task two, I'm going to ask you to be creative and to ask you to draw an image to match this description.

So the description I'm going to give you is that, for every three circles, there are four ticks.

So can you draw an image to match that description and maybe you could draw another one.

See how many different images you could draw that allow you to match that description.

So how did you get on? Here's task one.

So you were using that for every to describe what you could see in those images.

So in A, we've got our car, so we can say that for every one car there are four wheels.

In B, we've got two possibilities here 'cause our image showed two leaves and there are two beetles on each leaf.

So we could say for every one leaf there are two beetles or we could say for every two leaves there are four beetles.

And when we can describe a picture in two different ways, that's gonna be quite useful to us going on as we move on and think about ratio in different contexts.

And then in C, we've got our children back again and we can say here that for every three boys there are four girls.

At the moment, I'm not sure I can say that in a different way to describe that picture.

That's what we can see for every three boys there are four girls.

You might've gone the other way round and said, for every four girls there are three boys, that's absolutely fine.

It's describing that same way that those two factors within this group are related.

So how did you get on with task two where we asked you to be creative to draw an image to match the description? So we've got, for every three circles there are four ticks.

So you could have drawn it perhaps like that first one, just the three circles and then the four ticks.

But do we agree that the bottom image also matches that description, for every three circles there are four ticks.

Well, I can still see my three circles and I can still see my four ticks, but I've arranged them in a slightly different way.

So I wonder if you came up with any other images that represented the description that were different from the ones that I came up with.

We're going to carry on with a bit more and develop the ideas in that last task about creating and describing patterns with a given ratio.

So rather than just describe what we can see, we're going to take some descriptions and be a bit more creative with them.

Okay, so let's make a start.

A bit of a recap to start us using for every, to describe this pattern.

For every two circles, there's one square.

We're getting really confident with that now.

So let's take this on a little bit further.

Is it still true, for every two circles there is one square? That is, but we've got more circles and squares now.

But if we sort of section it up, we can still see two circles, one square, two circles and one square, two circles and one square.

So we are starting to think now about where the pattern that we're creating starts and stops.

So in this case, our basic pattern is that idea that for every two circles there is one square, but this time we've repeated it.

So we are beginning to think that this way of describing the way these two factors link together can help us when describing a pattern containing more objects or more symbols.

So what about this image? What can you see? How could you use that sentence using for every and where does our pattern start and stop this time? You might want to pause now and have a think about it before we share our thinking together.

So this time we can see that for every two triangles there are three stars.

So our pattern sort of starts and stops around those two triangles and our three stars.

And then we can see that it repeats with the same ratio.

So we are identifying the sort of basic pattern, the simplest part, for every two triangles there is three stars.

Well, what about this one then? Where does the pattern start and stop this time? Again, you might want to pause.

So this time for every three squares there is one hexagon.

We could say for every nine squares there are three hexagons.

But we can simplify that and look at the basic pattern where it starts and stops and then realise that we are repeating it.

So the simplest way we can describe that is to say that for every three squares there is one hexagon.

Time to just check and have a think about how we're getting on with this.

So there's an image there, some circles lit up and with some bits shaded and there are three statements there.

So which of these statements are correct and why do you think that's the case? So pause the video and have a think decide which of these statements are correct.

So I think we can say that B is correct is if we think about that sort of basic pattern bit, one of those circles.

For every two shaded parts there are three unshaded parts.

Definitely true.

A, I'm not sure is true.

It says for every one shaded part there are two unshaded parts that I don't think that works, does it? Because we've got two shaded parts there and three unshaded parts.

So we can't really link the one to anything.

So we saying that A is false, but B is true.

What about C then? For every eight shaded parts there are 12 unshaded parts.

Well, there's our basic pattern.

But actually C is true as well, isn't it? Because if we look at those four shapes as our whole, we do have 8 shaded parts and 12 unshaded parts.

And you might want to have a little look at those numbers of shaded parts.

For every two shaded parts there are three unshaded parts in statement B.

And then in statement C, for every 8 shaded parts there are 12 unshaded parts.

I wonder if there's anything you notice about how those numbers have changed.

Time for you to do some practise.

So having a think about completing the statements to describe the images.

There may be more than one way that you can describe them, but can you describe them thinking about what very the basic pattern is that is repeating? So you might write two statements for each of them but try to think about what's the basic pattern that's repeating in each case.

We said we were gonna get more creative in this part of the lesson.

So task two is gonna ask you to create and describe patterns with a given ratio.

So you're going to draw some images to match these statements and there are three statements there for you to have a look at.

And again, thinking about that basic repeat, what do you notice? So how did you get on with task one? Completing those statements.

For every one shaded square there is one unshaded square.

You might have said for every two shaded squares there are two unshaded squares.

But did you spot that that basic repeat, the repeating part is one shaded and one unshaded square.

The middle image of the circles, for every four shaded parts there are two unshaded parts.

So if we take the one circle as our pattern that's repeating, that's the simplest way we can look at it.

I wonder if there's a simpler way though.

I wonder if anybody came up with that one.

But equally we could have looked at the all five circles as a whole and said that for every 20 shaded parts there are 10 unshaded parts.

And the bottom image got some tens and ones equipment here, some Dienes Based 10 resources and our basic pattern says that, for every three tens there are two ones.

But we could have taken the whole and said, for every nine tens there are six ones.

So task two asked you to be creative and to create some patterns this time.

So the statement you were given for every two squares there are four circles and there's one where you might have drawn it, you might have arranged them differently but the ratio is saying that for every two squares we have four circles.

Middle statement there, we're thinking about a pot of flowers.

So for every pot there are five flowers.

So did you draw a pot of flowers? You might have drawn just a figurative pot of flowers.

That's absolutely fine.

And the bottom one, for every three triangles there are three stars.

And again, you might have arranged your triangles and stars differently.

But the important thing is that for every three triangles there are three stars.

Is there anything you notice about these? The images within those green boxes? Do you notice something about the total number of objects in each box? I've got two squares and four circles, for every two squares there are four circles.

I've got six shapes, for every one pot there are five flowers.

They're not all the same, are they? I've got a pot and five flowers, but I've got that idea of six again.

And then for every three triangles there are three stars.

Again I've got that six being my total.

How interesting to have a think about what we've got in our whole as well as what we've got in our parts.

Hopefully that's given you a bit more practise at spotting what the basic ratio is and describing and creating patterns to meet a given description.

Okay, and we're into the final part of this lesson, thinking about that idea of the total.

And we just started to think about that in that second practise task, didn't we? Looking at that total of six as we went through.

So this time we're going to look at some ratios and we are going to see if we can work out and think about the total number of items or objects that are being described in these different scenarios.

So let's have a look at this then.

So no images at the moment.

We might want to draw something to help us to think about it.

But let's have a thing we're asked to say, is this possible? There are 15 shapes.

So our total is 15 shapes and the ratio we are given is that for every two triangles there is one circle.

So if that's our ratio, can we have 15 shapes in total? Might want to pause and have a little think, draw yourself a picture before we share our thinking together.

Did you have a think? Let's see if we can draw something to help us.

So we've got this idea that for every two triangles there is one circle.

So how many does that give us all together in our basic repeat? Yeah, that's right, three.

So we've got two triangles and one circle, but we are told that there are 15 shapes in total.

So we've got three shapes there, what would happen, what would we have to do for there to be 15 shapes in total? Well, we could repeat this pattern.

Will we get to 15 shapes in total? So two groups are gonna give us six, three repeats will give us nine 'cause we've got three lots of the three shapes.

Have you predicted that this is what's gonna happen here? 4 repeats, there'll be 12 shapes in total and in 5 repeats there'll be 15 shapes because we've got five groups of the three.

Five lots of the basic pattern of three shapes.

So is it possible? Yes, it is possible.

If we repeat the pattern and we have five repeats of five versions of the pattern, then we can still say that for every two triangles there's one circle but we have 15 shapes in total and we can represent this using an equation.

So I can say that 3 times five is 15.

Times table fact that I'm sure you're very familiar with.

But how does this relate to the picture that we've drawn? How does this relate to the image? How does this relate to that description of the ratio? So where's the three from our equation in the image? Where's the five from our equation in the image? And where's the 15 from our equation in the image? Might want to pause and have a think before we discuss the answers to those together.

Okay, so let's think about the three and the five.

What do we know about the three? Well, where's the three? Three is the number of shapes in that basic pattern.

We were told for every two triangles there's one circle.

Two triangles and one circle gives us the three shapes in our basic pattern, so that's our three.

Whereas the five? Well, the five is the number of times that the basic pattern has been repeated.

I've got five lots of my three shapes.

So my other factor in my equation is five.

Five lots of those three shapes.

So where is the 15 then? Well the 15 is that total number of shapes that we were given in the problem.

There are 15 shapes for every two triangles as one circle, can this be true? And yes, we've proved that it can because if we've got three shapes in our basic pattern, we've got five times that number of shapes, we've got 15 altogether.

So yes, that can be true.

Okay, so having thought about that and thought about how we can represent this as an equation as well as a picture, we'll stick with our two, for every two triangles there's as one circle.

So that's our basic pattern.

We've got three other totals here.

We've got a statement to say there are 14 shapes in total, there are 21 shapes in total there are 99 shapes in total.

Can we explain if these totals are possible or not and why they are possible or not? Again, you might want to pause and just have a think to yourself before we discuss them together.

So let's have a think.

14 hasn't got a tick.

Why is 14 do we think not possible? Well the one we looked at was 15, wasn't it? And 15 was possible and we know that there's a basic repeat of three and I'm not sure that we can make groups of three and get to a total of 14 because 14 is not a multiple of 3.

3 is not a factor of 14.

So 21 we've given a tick.

Is 21 a multiple of 3? Yes it is, 3 times 7 is 21.

So if we had 7 repeats of our pattern, we'd have 21 shapes in total.

And I'm not gonna suggest we draw the (indistinct) 'cause we might be drawing for a while, but what about 99? I'm liking the 99, 9s and 3s are good together, aren't they? Is 99 a multiple of 3? Yes it is.

How many repeats would we need? I think we'd need 33 repeats of our pattern and then we would've used 99 shapes.

So we can say that it will be possible if the total number of shapes is a multiple of three, a number in the three times table.

So that's something to think about as we go on and just have a bit of a check and then do some practise ourselves.

So we've got a new pattern here, patterns made from two squares and three circles and we've got three statements and decide if they're true or false and tick the statements that are true.

So you might want to pause for a moment and just have a think and then we'll have a look at the ones that are true or false together.

So we had two squares and three circles.

So our first statement said for every two circles there are three squares.

That's not right, is it? It should be for every two squares there are three circles.

So A is not correct.

B says you could make this pattern with 50 shapes in total.

So what have we got in our basic pattern? We've got five shapes.

So when we looked to the threes, the total had to be a multiple of the number that we had in our pattern.

So is 50 a multiple of five? Yes it is.

And you might have got as far as working out that we'd need 10 repeats of the pattern.

We'd need the pattern 10 times in order for there to be 50 shapes in total.

Now C is asking us to think about a part and not just the whole.

So C says if there are six squares there will be 15 shapes in total.

Let's have a think about that.

So six, if there were six squares, I'd have three versions of the pattern.

I'd have the pattern three times.

There's three lots of two is equal six, three times two is six.

So if I had the pattern three times, I'd have three lots of five, three times five in total.

So yes, I would have 15 shapes in total.

So by thinking about that pattern, thinking about the way those numbers have been multiplied, I can see that actually C is true.

That if there were six squares and I imagine that pattern three times, I would have 15 shapes in total.

Okay, time for you to do some practise.

So task one is saying that you can use two shapes or two colours of cubes.

So we're gonna use.

Like we've been using squares and circles or triangles and stars, pick two shapes or if you've happen to have some cubes or some bricks in front of you, just pick two colours.

So they're going to be two parts to our whole our ratio will be for every something of this colour there's something of this colour.

Or for every this number of this shapes, there's this number of the other shape.

But this time you're gonna have a total number.

So you're going to use 24 shapes in total or 24 cubes or bricks if that's what you've got in front of you.

And I'd like you to explore the different ratios you can create using all 24 shapes or cubes.

So I wonder how you got on.

I had a go and I used triangles and circles and I looked at that basic pattern of ratios that would work remembering that we had 24 in total, I've discovered that the ratio will work if the number of shapes in the pattern is a factor of 24, all those factors of 24.

Is three a factor of 24? Yes, because there are 8 threes in 24, 3 times 8 is 24.

And so if I had 8 repeats of that pattern, I would have 24 shapes.

Is 4 a factor of 24? Yes it is.

4 times 6 is equal to 24.

If I repeated my middle pattern 6 times, I would use 24 shapes.

And if 4 times 6 is equal to 24, then 6 times 4 must be equal to 24 because I know that multiplication is commutative.

So if I've got six in my basic pattern, I would need 4 repeats in order to have 24 in total.

We've come to the end of our lesson.

Thank you for all your hard work, for all your descriptions and for all your creating of patterns.

I hope you are feeling really confident now about the fact that ratios allow us to describe the relationship between parts in a whole, that we can use that language for every to describe those two parts in the relationship.

We can use that within repeating patterns and we can use that language to describe the basic pattern and how it repeats.

And that if we know the ratio and we know about the parts in the whole, we can work out how many parts there would be in a given whole.

So again, thank you very much for all your work in this lesson and I look forward to seeing you another time.

Thank you.

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3 \\times 4 = 12

3 \\times 4 = 12

3 \\times 4 = 12

represent in relation to this image?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1692016545%2Fztbqzxdsbk6zmtfhvgbn.png&w=2048&q=75", "imageKey": "d3ab27cb-9903-c220-362c-64e8b5cb7197/question/5a879a25b0aea50af362254882ac49ec.png" }, "questionType": "Multiple choice", "correct": [ { "text": "The number of times the pattern is repeated" } ], "choices": [ { "text": "The number of triangles in the image" }, { "text": "The number of circles in the image" }, { "text": "The number of times the pattern is repeated" } ], "id": "2e42af35-8672-4a49-f65e-ee48b2f081ad", "lessonId": "02dc5992-0667-45c3-5860-064d612298d3" }, { "type": "Question", "question": { "text": "Look at the pattern and tick all the statements that are true", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1692016545%2Fnnh4wmh9vm5xxtbqjacu.png&w=1080&q=75", "imageKey": "d3ab27cb-9903-c220-362c-64e8b5cb7197/question/2a62293a01f744750a3ea9e61ffe363c.png" }, "questionType": "Multiple choice", "correct": [ { "text": "For every 1 square there are 3 stars" }, { "text": "You could make this repeating pattern with 44 shapes in total" } ], "choices": [ { "text": "For every 1 star there are 3 squares" }, { "text": "For every 1 square there are 3 stars" }, { "text": "You could make this repeating pattern with 44 shapes in total" }, { "text": "If you repeated the pattern 8 times you would use 30 shapes in total" } ], "id": "26c14ad9-f7c3-6116-75cd-77d40dfd4445", "lessonId": "02dc5992-0667-45c3-5860-064d612298d3" } ], "lessonId": "02dc5992-0667-45c3-5860-064d612298d3", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 6", "topic": null, "unit": "Ratio and proportion", "lessonCount": "10", "age": [ 10, 11 ], "gradeId": "age_10_11", "gradeStage": "Key Stage 2", "lesson": "Describe the relationship between two factors in a ratio context" } } ] }