Numbers and numerals

Axioms and arrays

Factors and multiples

Order of operations

Positive and negative numbers

Expressions, equations and inequalities

Angles

Classifying 2-D shapes

Constructing triangles and quadrilaterals

Coordinates

Area of 2-D shapes

Transforming 2-D figures

Prime factor decomposition

Conceptualising and comparing fractions

Manipulating and calculating with fractions

Ratio

Percentages

Different number systems

Sequences

Forming and solving equations

Forming and solving inequalities

Linear graphs

Accuracy and estimation

Algebra and problem solving

Ratio (8.6a)

Ratio, real life graphs, and rates of change

Direct and indirect proportion

Univariate data

Bivariate data

Famous maths problems

Angles and parallel lines

Angles in polygons

Bearings

Volume and surface area of prisms

Area review

Circles

FDP review (9.1a)

Probability

Sets and Venn Diagrams

Solving linear simultaneous equations algebraically

Solving linear simultaneous equations graphically

Angle review (9.5a)

Constructions, congruence, and loci

Pythagoras's theorem

Ratio review (9.7a)

Similarity and enlargement

Surds and trigonometry

Quadratic expressions (9.9)

Quadratic equations (9.10)

Indices and standard form

Growth and decay

Finance

Shape and patterns

Angles and shape

Faces, shapes and patterns; lines and turns

3D Shape

Shape and pattern

Transformations

2-D Shape and Symmetry

Missing angles and lengths

Coordinates and shape

Shape and sorting

2-D and 3-D shape

Maths

Y9 Maths

Key Stage 3

Year 9

Geometry

THEME

UNIT

In this lesson, we will learn about different representations of ratio, including the relationship between fractions and ratio. These are mostly seen in the context of shape.

Representing ratio

﻿Hi, I'm Miss Kidd-Rossiter, and I'm going to be taking the lesson today on representing ratio. We're going to do it mainly in the context of shape, and it's a really exciting topic. So I hope you really going to enjoy it. Before we get started, can you make sure that you're in a nice quiet space, you're free from all distractions and that you've got something to write with and something to write on. If you're able to, it'd be really great if you have a ruler for this lesson as well. If you need to pause the video here to get anything that you need, then please do, if not, let's get going. So today let's try this activity. Then Antoni, Binh, Cala and Xavier are drawing rectangles. Antoni says the side lengths of my rectangles are in the ratio 5:2. Binh says the side lengths of my rectangles are in the ratio 6:2. Cala says the shorter sides of my rectangles are 1/3 of the length of the longer sides. And Xavier says the longer side of my rectangles are 2 1/3 times the length of the shorter sides. You've got to draw an example rectangle for each student. If you've drawn one, can you draw another, can you draw another, can you draw another? And then how could you compare the rectangles that they've drawn? Pause the video now and have a go at this task. Excellent work. Which side did you draw first for each of these? Did you draw the longer side or the shorter side first? Can you draw one starting the other way round? So if you started with the longer side, this time can you start with the shorter side. Pause the video now and have a go at that. Excellent. We're going to go through this in the connect part of the lesson. So let's go. So we're going to compare Antoni and Binh first of all. So can you tell me a rectangle that you drew for Antoni? Excellent. So there are loads of different ones here, so I'm just going to give you one example. So Antoni could have drawn his rectangle and he could have had the longer side is 10 centimetres and the shorter side is four centimetres. Do you agree that that's in the ratio 5:2? So let's just double check. Longer to shorter, 10:4. Does that simplify to 5:2, tell me now? Excellent, it does, doesn't it? So that was one example that we could have had. What faction of the longer side is the shorter side here? So we've got our longer side, which is 10 centimetres, and if we draw our shorter side underneath it, which is four centimetres, what fraction of the 10 centimetres is the four centimetres? Tell me now. Excellent. It's 4/10, isn't it? Or can we simplify that? Excellent, 2/5. Can we see a relationship here between the fraction and the ratio? Could we write the longer side as a fraction of the shorter side? Tell me now. Yes we could. What would that fraction be? Tell me now. Excellent. So the longer side as a fraction as the shorter side would be 10/4, which simplifies to 5/2, or if you prefer to write it as a decimal 2.5. So the longer side is 2 1/2 times the shorter side. Is there a relationship here with the ratio? What about Binh's rectangle then? So her side lengths are in the ratio 6:2. So again, there's loads of different rectangles that you could have drawn. Here's one that I've drawn and they're going to have, you should have drawn yours with a ruler because they would be much neater than mine. So I'm going to say that Binh has done hers 18 centimetres here to six centimetres here. Is that in the ratio 6:2? Let's just double check. So longer side to shorter side, 6:2. Do we have the same constant of proportionality to get from two to six and from six to 18? What would it be? Tell me now. Excellent. It's three, isn't it? So therefore, yes, these are in the same ratio. So what fraction of the longer side is the shorter side here? So if we've got 18 and we've got our six centimetres, what fraction is that? Tell me now. Excellent, the shorter side is 6/18 of the longer side, isn't it? Which simplifies to 1/3, brilliant. How does a third relate to the ratio 6:2? Think about that for me. What about the other one then? So, what fraction of the shorter side is the longer side? Well it would be 18/6, which is three. So the longer side is three times the length of the short side. Again, can we see a relationship with the ratio here? Moving on then to Binh and to Cala. So we've already looked at one of Binh's and we said that hers was 18 and six centimetres. And we said that the shorter side is 1/3 of the longer side. And we also said that the longest side is three times the shorter side. So what does that mean about Binh's statement and Cala's statement? Tell me now. Excellent. They could be describing the same rectangle, couldn't they? Let us do another example just to check for Cala. So we've got a longer side and let's call this one 300 metres. Cala's shorter side would be 1/3 of this, wouldn't it? So it'd be 100 metres. So that would be an example of Cala's. Is that in the ratio 6:2? So it could, I have the same constant of proportionality here to get from six to two, to 300 to 100. Yes I could, what would it be? Tell me now. Excellent. It would be a multiply by 50, wouldn't it? Is there a simpler ratio here than 6:2 that we could write? Tell me now. Excellent. It's 3:1, isn't it? So all of the rectangles for both Binh and for Cala are in the ratio longer side to shorter side 3:1. Finally, then we've got Xavier. Xavier's is a bit of a tricky one I think to think about. So let's have a go at drawing one. What did you come up with here? I'm going to draw my shorter side as being 12 millimetres. What would that mean my longer side is? So 2 1/3 times 12. So let's think about that as 12 times two is 24 millimetres. 12 millimetres remember I should include my units. And 12 millimetres times 1/3 is the same as saying, what is a 1/3 of 12, which is four millimetres. So all together 2 1/3 times 12 is 28 millimetres. So Xavier's rectangle could look like that. There's also lots of other options again it could look like. So let's have a look then of the ratio of our longest side to our shorter side here. So the longest side is 28 millimetres and the short side is 12. Can I simplify this ratio? What would it be? Excellent. I could simplify it, 7:3. What fraction of the shorter side is my longer side? We already know that, don't we? We know it's 2 1/3 times. So let us think about what fraction of the longer side is the shorter side? So can you tell me now? Excellent, it'd be 12 millimetres out of 28 millimetres, wouldn't it? And what does that simplify to? Excellent, 3/7. So the shorter side is 3/7 of the longer side. Really good work. You are now going to apply everything that you've learned to the independent task. So pause the video here, navigate to the independent task. And when you're ready to go through some answers, resume the video. Good luck. Excellent work on the independent task, well done everyone. So let's go through these then. So side lengths of a triangle are in the ratio 3:5:2. What fraction of the perimeter is the longest side? So the longest side has to be the part that's represented by the biggest part of the ratios. It has to be represented by the five. So it has to be five out of something. And how many parts of our ratio do we have in total? Excellent, 10. So that means that the fraction of the perimeter that is the longest side is a half or 5/10. Side lengths of a triangle are in the same ratio. What fraction of the longest side is the shortest side? Well, we know that the shortest side must be represented by the two. So it has to be two out of five. Excellent. And the sidelines of the triangle still in the same ratio. What fraction of the shortest side is the longest side? So again, this will be the opposite way around, 5/2. Good work. Here are your answers for question four, pause the video if you need to check them. And here comes your answers for question five. Pause the video now if you need to check them. Now, just be careful here, because you might have been caught out a little bit because we were told that the side lengths were in the ratio 4:3. So if we had 4:3 and the longer side was eight, then the constant of proportionality here is two. So our shortest side would be six, which I bet most of you got six metres. But then remember that the perimeter is the whole distance around the outside of the shape. So if this is eight metres and this is six metres, then this is also six metres and eight metres. So you would need to do eight metres add six metres, add eight metres add six metres, which gives us our 28 metres or the other way you could have done was two times the eight metres add the six metres, okay? So just be careful there. Pause the video if you need to check these answers. So moving onto the explore task now then. So Yasmin and Zaki each draw a triangle with an angle of 30 degrees. Can they draw triangles that meet the following conditions, so that their side lengths are in the same ratio, but are not identical? So could they both draw right angled triangles? Could they both draw triangles that have the same area? And could they both draw triangles that have the same perimeter. Pause the video now and have a go at this task. Excellent work that absolutely loads here. So I'm sure you've had a good go at it. There are lots of different ways to approach this, but one way might be to draw a right angled triangle here and then make sure that this is 30 degrees either angle. This is my 90 degrees. And then we will say that this is six centimetres and this is three centimetres. So the ratio here would be 1:2, wouldn't it? Could we draw another triangle that's maybe a bigger or smaller. You would use a ruler. Where this is still a right angle. This is still 30 degrees. And these are still in the same ratio. I'll leave you to think about that. So you could have put anything here. We could have got that this is 4.5 centimetres, which would mean that this is what? Excellent, it would be nine centimetres. Good work. So keep going with this activity. I hope you can draw absolutely loads of great triangles. Because we've gone like the rectangles and triangles today, if you'd like to share your work with Oak National, then please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak. That's the end of today's lesson. So I hope you've enjoyed it. And I really have enjoyed teaching you. Don't forget to go and take the end of lesson quiz so that you can show me what you've learned and hopefully I'll see you again soon. Bye.

In this lesson, we will divide oblique line segments into specified ratios by dividing the segment's horizontal and vertical displacements in the same ratio.

Ratio and proportion in geometry

﻿Hi, I'm Miss Kidd-Rossiter, and I'm going to be taking you through today's lesson on ratio and proportion in geometry. It's part of this ratio review unit, and I hope you're really going to enjoy it. Before we get started, can you make sure that you're in a nice, quiet place if you're able to be, you've got no distractions, and that you've got something to write with and something to write on. You also might find a ruler helpful for today's lesson. If you need to, pause the video here to get anything that you need, if not, let's get going! So today's try this activity then, you've got three lines, AC, AQ, and AY, which are on the diagram just below me. You need to choose a point on one of the lines. So for example, you might draw a point and call it H on line AC. Then I want you to work out the ratios AH to AC, AH to HC, and also the fractions AH over AC and AH over HC. What's the same and what's different about these when you've written them? And then choose a new point on one of the other lines and continue to investigate. If you feel confident with this activity, pause the video now and get going with it. If not, just stay tuned and I'll give you a little bit of support. Excellent, if you need a little bit of support, that's absolutely fine, that's what I'm here for! And let's choose our point, then, on AC. So I'm going to choose this point here on AC, and I'm going to call that H. I want to know how far it is between A and H, so let's work that out first of all. So that's 1, 2, 3 if we count the spaces between the dots. So let's say that that is three. So we're going to do AH to AC here first. So AH is 3. What is AC? 1, 2, 3, 4, 5, 6, 7, 8. So AH to AC is in the ratio 3 to 8. Can you work the same thing out for AH to HC? Then AH over AC. And then AH over HC. Can you work those three things out for me, please? Pause the video. Excellent, what did you get for AH to HC, tell me now. Excellent, you got 3 to 5, that's what I like to hear. What did you get for the fraction AH over AC? Tell me know. Excellent, 3/8. And what did you get for the fraction AH over HC? Tell me now. Excellent, 3/5. So pause the video here, and tell me what's the same and what's different about the things that we've written down. And then choose another point on a different line and work the same thing out. Good luck! Excellent work, everyone! You can see one example that I've done there on the screen. What's the same about these? Well the same about them is the relative size of the parts to the whole. So we can see that AC is 3/8 of the whole line, isn't it? And we can see that here from the ratio, it's 3 parts out of the 8 parts. And we can also see it here in the fraction. And for AH to HC, we can see that AH is 3/5 of the size of HC. If you picked a different point on one of the other lines, you should have got a similar relationship. These are both different representations, so we've got ratios and fractions that were different representations that we're comparing. Well done on that task! Moving on to the connect activity now then. We've got a line segment here, AB, and we're being asked to work out what is the midpoint of that line segment, what is the ratio AM to AB, and what is the ratio AM to MB? So pause the video here and have a think about that. M represents the midpoint, pause now. So to work out the midpoint, we can see that our full line going from A to B is 4 across and then 6 up. In the middle of that, well we, the midpoint we know is half of the distance. So instead of going from 0 to 4, the midpoint will be half of that distance, so it will be from 2. And then from 0 to 6 up to B, we know that half of that distance would be three up. So that means that our midpoint would be this coordinate here. So I'm just going to write the coordinate of M. So M is 2, 3, so that's the midpoint of the line segment. What's the ratio AM to AB? Well if we say that this distance here between A and M is 1, what's the distance between A and B? Well we've got another line segment that is the same length as the distance between A and M from M to B. So AM will be 1 and AB will be 2. So the ratio AM to AB is 1 to 2. What's the ratio of AM to MB, tell me now. Excellent, 1 to 1. So we know that if we've got a midpoint of a line segment, then the first part of the line segment to the midpoint and the second part of the line segment, from the midpoint to the end, will always be in the ratio 1 to 1. So what fraction of the full line is AM? So what fraction of the full line is AM, tell me now. Excellent, so AM is half of AB. So here we are, how can I extend the line, so that the ratio AB to AD is 1 to 4? So we've got to extend this line, so that we get the final line in that ratio. So we can see that our one part, because we're told that AB is one part of our ratio, is 3 across and 2 up. So what would four parts be, starting from 0, 0? Well instead of 3 across, four lots of 3 across would be 12 across, wouldn't it? So 3, 6, 9, 12. And then instead of 2 up, we've got four lots of 2 up, so we would be going 8 up, 2, 4, 6, 8. So this point here will become point D. And that is how we will extend our line! Then we were asked to plot point C on the line so that the length CD is 1/3 of the length AC. So if it's 1/3 of the length AC, we know that CD to AC would be 1. And AC would be 3, because 1 is 1/3 of 3. Pause the video now and work out where that point would go. Excellent, well done, it goes here doesn't it, at 9, 6. So this is point C, cause we can see here that this is one part, and then if we have the same 1. 2. 3. So we can see that CD is 1/3 of the length AC, good work. Going to pause the video now and navigate to the independent task, and when you're ready to go through some answers, resume the video. Good luck! Well done on that independent task. There were some tricky questions in there, so I hope you've had a really good go at it! Let's go through some answers. So the first one then, we're asked to find the coordinate of A if M is 5, 4. So first thing I would do, is I would draw my line segment of B, which I know is 10, 8. And then I know that this is my midpoint here. I know that I've got to extend this line by the same length, because we said previously that if we've got a midpoint, then the length AM to MB will always be in the ratio 1 to 1. So this length here needs to be repeated, so we add it on, and we would do it with a ruler and you get this here. So that tells me that the coordinate of A for the first question here is 0, 0. Second one then, M is 7, 5. So I do this in exactly the same way, draw on B and M and then extend my line to find out where A would be. So A is 4, 2. And again for the third one, label on B and M and then extend the line to find out where A would be. So for this one, A is 10, 3. And then same again for the last one. We draw on our line segment, label B and M and then extend to find our coordinate of A. So A is 11, 4.5. Second question then, the line AQB is drawn on the axes to the left, where Q is a point on the line, B has coordinate 10, 8, what are the coordinates of... So first one, Q if A is 1, 2 and AQ to QB is 1 to 2. So the first thing I would draw on is I would draw on my line AB and label it A and B. Then I would find where Q is, so Q will be here for the first one, because I can see that this length here is 1 and this length here is two parts of the same length. So the coordinate for Q is 4, 4. Second one then, Q if A is 1, 2 and AQ to AB is 2 to 3. So we've got the same line this time. So I've still got my labels A and B, and this time I want to find where Q is, and Q is here, because I can see that A to Q is two parts and A to B is three of the same sized part. So this time, Q has a coordinate 7, 6. Next one then, A if Q is 4, 5 and AQ to AB is 2 to 5. So this time I'll draw my line segment, I'll label Q and B, and I know that this has got to be three parts longer than A to Q. So here's my size of one part, two parts, three parts. So I want to go two parts in the opposite direction. So I find that A is there, and the coordinate of A is 0, 3. And then finally, A if Q is 11, 6 and AQ to QB is 1 to 1. So we draw on our line again, label on Q and B, and if it's 1 to 1, we know that Q is the midpoint this time, so we extend our line by the same distance and label on A, and we know that A is the coordinate 12, 4 here. Excellent work, well done. Moving on to the explore task, then. Choose any three coordinates with integer values that form a straight line and write all the ratios you can associated with this line segment. If you can write any fractions as well, that would be great. Can you find three integer coordinates that form a straight line, for which these ratios might describe the relationship between points? And then what about if the coordinates no longer have to be integers? Pause the video here and have a go at this activity. Excellent, there were so many different line segments that you could have drawn here. Let's have one look at one for 2 to 3. So I could start here, and I could say that a second point was here and a third point was here. So let's call these A, B, and C, and you would join them with a ruler, I don't have one, so I'm going to try my best. There we go, and I can see that this is in the ratio 2 to 3, cause I've got one part there and a second part there and then 1, 2, 3 here. What other ratios could be associated with this, then? Tell me. Excellent, so I know that AB to BC is 2 to 3, but I could have also said that AB to AC is 2 to 5. And there are some other ones there that you could've figured out, too. I could've said that AB is 2/5 of AC. So I'm going to leave that with you. Keep going with it, there are loads of things that you can find here, so good luck with that! That's the end of today's lesson, so thank you so much for all your hard work! I hope you've learned a lot about line segments and ratio. Hope to see you again soon. Don't forget to go and take the quiz for this lesson, so you can show me what you've learned. See you soon, bye!

In this lesson, we will review how to divide amounts into a ratio and find part or whole amounts from given information.

Dividing into a ratio

﻿Hi, I'm Miss Kidd-Rossiter and I'm going to be taking today's lesson on dividing into a ratio. Before we get started, it'd be really helpful if you could have a pencil and a ruler, because you going to be drawing some diagrams in today's lesson. Make sure you're in a nice quiet space so that you can fully concentrate and that you've got no distractions. If you need to pause the video now to sort anything out then please do, if not let's get going. So for today's try this activity, you've got a statement here about three rectangles. I'm going to read it to you. Rectangle A's perimeter is twice the length of rectangle B's perimeter, which is three times the length of rectangle C's perimeter. Quite tricky statement there, so pause the video and reread it if you need to. You're asked to find the ratio of their perimeters. If the sum of the three perimeters is a hundred centimetres, find each individual perimeter. And then finally if rectangle A's perimeter is 75 centimetres longer than rectangle C's, find the perimeter of rectangle B. Pause the video now and have a go at this activity. When you're ready to go through some answers, resume the video. Excellent effort, well done everyone. Let's first of all look at the first part. So find the ratio of their perimeters. So the way I'm going to do this is I'm going to write it in the form A to B to C. So for me, it's easiest to start with C here. You can pick any length at all for C. So I'm going to pick the C is 30 centimetres long in perimeter. Then we're told that B is three times the length of rectangle C. So if C is 30, then B is three times that. So tell me what all that would be now? Excellent, it would be 90 centimetres, won't it? And then I'm also told that A's is twice the length of B's. So if B's is 90 centimetres, what will A's be? Tell me now. Excellent, 180 centimetres. Now you can see here, you could have come up with loads of different lengths for those perimeters. So what we need to do now is to simplify this ratio as much as possible. So can I identify a common factor of 30, 90, and 180? Tell me now. Excellent, there's loads of different ones. So whatever you said, I'm sure it was great. I'm going to divide by the highest common factor, which in this case is 30. So 30 divided by 30 is one, 90 divided by 30 is three, and 180 divided by 30 is six. So the ratio of their perimeters is six to three to one. Pause the video here and check that your ratio simplifies to this. Excellent, let's look then at, if the sum of the three perimeters is a hundred centimetres, find each individual perimeter. So I've still got the ratio on the screen there, 'cause that's going to help us. The way I'm going to do this is I'm going to draw it as a bar model. You might have been shown a different way to do it, and that's absolutely fine, but this is the way I'm going to go with today. So here is my bar model representing A, B and C. You'll notice that each part of the ratio is the same width and the same height. This is really important because each part of a ratio is equal. So we've got our one part here, our three parts here and our six parts here. And we know that the sum of these three perimeters is a hundred centimetres. So I'm dividing equally my hundred centimetres into the parts of my ratio here. How many parts do I have in total? Tell me now. Excellent, I have 10 parts, don't I? So I'm dividing a hundred centimetres by the 10 parts to get what one part would be, which is what? Excellent, 10 centimetres. So I know that each part of my ratio is 10 centimetres. If I know that to be the case, because I've worked it out, what does that mean then that the perimeter of rectangle A is? Tell me now. Excellent, what does that mean that the perimeter of rectangle B is? Tell me now. Excellent, and what does that mean that the perimeter of rectangle C is? Tell me now. Excellent, so a has A perimeter of 60 centimetres. B has a perimeter of 30 centimetres and C has a perimeter of 10 centimetres. Well done there. What fraction of A's perimeter is C's perimeter? What fraction of A's perimeter is C's perimeter? Pause the video and think about that. Excellent, so A's perimeter is 10 centimetres, isn't it that? And no, it's not sorry that's my fault. C's perimeter is 10 centimetres. A's perimeter is 60 centimetres. So as a fraction, it's 10 of 60, which we know simplifies to one sixth. So C is one sixth of A's perimeter. Or I should be more clear. C's perimeter is one sixth of A's perimeter. What fraction of B's perimeter is C? Tell me now. Excellent, it's a third, isn't it? Because it's 10 centimetres of 30 centimetres, which simplifies to a third and let's just do one more. What fraction of A's perimeter is B's perimeter? Tell me now. Excellent, it's three sixths, isn't it? Or we could be even more clever and simplify that down to a half. Really good work, well done. Final part then that you were asked to do. If rectangle A's perimeter is 75 centimetres longer than rectangle C's, find the perimeter of rectangle B. So I'm going to use the same diagram here for A, B and C. And this time I'm told that rectangle A's perimeter is 75 centimetres longer than rectangle C's. So I can see that C's perimeter is one part and A's is six. So that means that the 75 centimetres that is longer must be represented by these five parts here. So that must be my 75 centimetres. So if five parts are represented by 75 centimetres, how could I find one part? Tell me now. Excellent, I could do 75 divided by five and I shouldn't forget my unit, should I? So let's just do that again. 75 centimetres divided into five parts gives me 15 centimetres. So this time each part of my ratio is 15 centimetres. And if I know that these parts are all 15 centimetres, then that means that every part of my ratio must also be 15 centimetres. I've then asked you to work out B's perimeter. So B's worth three parts of this ratio. So B's perimeter so I'm just going to say P for perimeter. So perimeter of being is 15 centimetres multiplied by three, or you could have done 15 add 15 add 15, absolutely fine. So 15 centimetres multiplied by three, which gives me 45 centimetres. Pause the video here and navigate to the independent task when you're ready to go through some answers, resume the video, good luck. So here's the first question of the independent task then. So the first thing I want to redo is I would draw my bar model. Then I think what do I know about angles in a trapezium? Interior angles in a trapezium. Well I know that interior angles in a trapezium add up to 360 degrees. So I know that this full ratio here must represent 360 degrees. I've got how many parts to my ratio? Tell me now. Excellent, I've got 18, haven't I?. So I'm doing 360 degrees divided into my 18 parts this tells me that one part must be worth 20 degrees. Now I'm not going to write them all in here because it will take me a while. But you know that every part of this ratio is worth 20 degrees. So that means then that the first angle here is how many degrees? Tell me now. Excellent, 60 degrees. This angle here represented by the four parts is how big? Tell me now. Excellent, 80 degrees. The angle here represented by the five parts is how big? Tell me now. Excellent, a hundred degrees. And then the final one represented by the six parts is worth how many degrees? Tell me now. Excellent, 120 degrees. Don't forget your units here. Then we were asked to sketch the trapezium. So here's a trapezium that you could have sketched and we're going to label on the angles. So we've got two acute angles, haven't we? So we know that this angle here could either be 60 degrees or 80 degrees 'cause it's only a sketch. So it's not super accurate. So let's call this one 60 degrees and other acute angle here would be 80 degrees. How do I know which angle this will be here? Pause the screen and think about that. Excellent, this one will be 120 degrees it, which means that this one will be a hundred degrees because these two angles here are co-interior, aren't they? Which means that they sum to 180 degrees. And we have the same here at pair of co-interior angles. Next question then. So the first thing you would identify is that these five parts here are 10 centimetres, which means that one part has to be two centimetres. And if each of those parts is two centimetres, then that means that every part of my ratio must be two centimetres. So to calculate the length of each side, I would just look at my ratio here. So I know that each side, the first one is 8 centimetres, the second one is 12 centimetres, and the third one is 18 centimetres. And you're asked to calculate the perimeter. So to do that, you would just add up your eight centimetres, your 12 centimetres and your 18 centimetres, and get 38 centimetres. And then finally, what fraction of the perimeter is the longest side? Well, the longest side we know is 18 centimetres, and we know that the perimeter is 38 centimetres. So we know that 18 over 38 simplifies to 9 over 19. We didn't actually need to work all that out though, did we? There's another way that we could have worked that fraction out, can you tell me? Excellent, we could have used the ratio at the top, couldn't we? So we can see that we've got our nine parts of our ratio out of the total 19 parts, excellent work. Right, we moving finally then onto the explore task. Pause the video here and have a go at this activity. If you're struggling a little bit with this activity, think about what you could use to represent that one. So I'm going to give you an example. I could say that this is 30 degrees, then N would be, let's say 60 degrees, and M would be 90 degrees. So I've got what type of triangle here, tell me now. Excellent, it's a right angled triangle, isn't it? Because I've got a 90 degree angle. Think about what other value I could use. So I could use this time, I could use one to N to M. This time I could say that this is 45 degrees. This is 55 degrees and M is 80 degrees. What type of triangle would it be this time, tell me now. Excellent, it would be scalene, wouldn't it? Because all the angles are not equal. So we've got three different types of angle there. Pause the video now and have a go at this activity. Excellent work everyone. I hope you've had a really good go at that explore task. There's a couple of answers there on the board that I've given. So feel free to look at those, but there are absolutely loads here. So I hope you've had a really good mess with it. That's the end of today's lesson. So thank you so much for all your hard work on dividing into a ratio. I hope you've learned a lot. Please don't forget to go and take the end of lesson quiz so that you can show me what you've learned, and I'll hopefully see you again soon, bye.

In this lesson, we will solve problems involving ratio, fractions and percentages.

Ratio problems

﻿Hi, I'm Miss Kidd-Rossiter and I'm going to be taking you through today's lesson on ratio problem solving, where we're going to look at some problems that involve ratios with fractions and percentages. And we're also going to look at combining ratios too. It's a really great topic and I hope you're really going to enjoy it. Before we get started, please make sure that you're in a nice, quiet area if you're able to be, and you're free from all distractions. You're going to need something to write with and something to write on. So if you need to, pause the video now to get yourself sorted. If not, let's get going! So, for today try this activity then. You've got Zaki and Binh, and they've collected some seashells. Which of the statements on the right are correct? Can you improve or add to any of the statements? And, can you write any statements of your own that we haven't covered already? So, pause the video here and have a go at this task. What did you think? Did you agree? Did you disagree? Are any of them wrong? Let's go through it then. For every shell Zaki has, Binh has three. Do you agree with this one or not? Let me know. Excellent. I agree as well. For every shell that Zaki has, Binh has three. We can say that one's correct. Zaki has one quarter of the total number of shells. Well how many shells does Zaki have? Tell me now. Excellent. He has three, doesn't he? Out of a total of how many? Tell me now. Excellent, 12. So, he has three shells out of 12 shells which does simplify to 1/4. So this one is correct as well. Zaki has 3/9 of the shells. Well, we know this one's wrong, don't we? Because we've just worked out that Zaki has 1/4 of the shells. And 3/9, does that simplify to 1/4? Let's just double check. So 3/9, simplifies to what? Tell me now. Excellent, 1/3. So that one cannot be right. Binh has three times as many shells as Zaki. So, we know Zaki has three and Binh has nine. So, does she have three times as many? Tell me now. Excellent. Yes, she does, so that one's correct. And the ratio of Zaki to Binh's shells is 3:9. Well, we know that's correct, don't we? Cause we've already worked out how many each of them have. Could we make this statement even better? Could we simplify this ratio? What would it be? Tell me now. Excellent. We could say that this ratio is 1:3 and that links in with our very first statement, doesn't it? Excellent. So that one is correct. Well done on that. So we've got a question on the screen here. The ratio of roses to violets is 5:4 and the ratio of violets to daisies is 3:2. You are asked, what is the ratio of roses to violets to daisies? Now, before I can get started on a question like this, I find it really, really helpful to draw myself a diagram. So I'm going to represent the roses to violets like this, where the roses are, the five pink parts on the left hand side, and the violets are the four purple parts on the right hand side. And then I'm going to do the same for violets to daisies and show it like this. So violets to daisies. The three parts on the left hand side of the bottom bar are my violets and the two parts on the right hand side of my bottom bar are my daisies. Now I've got the same amount of violets in both ratios. So that's why I've overlapped those there. I need to find common, multiple here that I can use to compare these ratios, to get the ratio of roses to violets to daisies. So, first of all, can you think of a common multiple of four and three, pause the video now and tell me. Excellent, 12. So we've gotten from 5:4 and 3:2. So we've got roses to violets and violets to daisies. And you told me that the common multiple of both four and three is 12, which is correct. So I'm going to change these four parts here to 12 parts. What have I multiplied four by to get 12? What's my constant of proportionality? Tell me now. Excellent, three. And what would I multiply my three by to get 12? Tell me now. Excellent, four. And so I'm going to multiply my violets here by four to get my 12 parts there. But I know that if I scale one side of my ratio, I have to do the same to the other, don't I? So I'm also going to multiply my five by three and get what? Excellent, 15. And here I'm also going to multiply my two by four. And what will I get? Tell me now. Excellent, eight. So now I have a ratio that I can compare all of these, can't I? Because these now, the parts in both ratios are an equal size. So that means that roses to violets to daisies will be 15:12:8. In a moment, you're going to have a go at doing a question like this. So my face is going to disappear and you need to pause the screen and have a go at the question. When you're ready to go through an answer, resume the video. So you can see we've got the same question on the screen here. The first thing I did was I wrote out my two ratios. So I had them clearly in front of me. So peas to tomatoes, 5:3. And tomatoes to carrots, 6:5. Then I looked for the common part of both ratios. So here, our common part is the tomatoes. So I'm looking for a common multiple of three and six. What's a common multiple of three and six? Tell me now. Excellent, I'm sure you all shouted different things. I'm going to use the lowest common multiple, which in this case is six. So I'm going to change my tomatoes to be six in both ratios. You'll notice that for the tomatoes to carrots ratio, that means I don't need to change it because I've already got six parts that are tomatoes. So for my peas to tomatoes, I need to change my tomatoes to be six. So what would my constant of proportionality be here? Tell me now. Excellent, two. And if I multiply one part of my ratio by two, I also need to multiply the other part of my ratio by two, well done. So that will become 10:6. Now I have parts of my ratio that are equal. I can write my final ratio of peas to tomatoes to carrots as 10:6:5. Look at that ratio on the screen help me with the next part. And I'm told that there are 50 carrots grown. So I know that that part of my ratio will be 50. And I'm looking for my constant of proportionality here. So what do I multiplied five by to get 50? Tell me now. Excellent, 10. And I'm looking for how many peas are grown. So I have to also multiply this by the same constant of proportionality to get 100. I don't need to do the middle part of my ratio here because the question hasn't asked it, but I will do it anyway. And that will give me 60 tomatoes. And then my final answer to the question will be a lovely sentence that says, 100 peas are grown, well done on that. So moving onto the second connect part of the lesson today, then. There are only yellow, blue, and purple counters in a bag. 20% of the counters are yellow, 9/20 of the counters are blue. And you're asked to write down the ratio of yellow counters to blue counters to purple counters. So here we're going to have to move quite flexibly between percentages, fractions, and ratios. So first of all, we know that yellow is 20%. I'm going to convert everything to percentages here before I write my ratio. You could choose to do everything as fractions first. That's absolutely fine. And then I know that blue is 9/20. And I know to convert that to a percentage, I first need to convert it to an equivalent fraction out of a hundred. What would I multiply 20 by to get a hundred? Tell me now. Excellent, five. So that means I also need to multiply my nine by five to get 45/100. So that means that my blue counters are 45%. Therefore my purple counters will be 100% take away the other two percentages added together. Well then say 20%, add the 45%. What's 20% add 45%? Tell me now. Excellent, 65%. So I've got 100% take away 65%. And that gives me what? Tell me now. Excellent, 35%. So that means my ratio of yellow to blue to purple would be 20%:45%:35%. And then I can simplify this ratio, can't I? So this would be 4:9:7. Can we see that? Excellent, well done. So now I've got some questions for you to try in the independent task that involve working with percentages and fractions and ratios. So pause the video here, navigate to the independent task. And when you're ready to go through responses, resumed the video. Good luck. Excellent work, well done. So first question then, I'm not going to go through in full, but your answer is 52%. The second one then, the ratio of that age is Antoni:Binh:Calala is 12:4:1. And the fraction of the total ages that Binh represents is 4/17 because her part is four parts of a total of 17 parts. Let's go through this one then. I love this question, there's so much in it. It's really exciting for me, right? So the first thing we have to do is write down the ratio of Antoni to Cala and Xavier. So we know if they get 150% of the amount that Antoni gets, that means they get 1 1/2 times as much. So in our ratio, if we write it as one for Antoni, that means that Cala and Xaier will get 1.5. And you can see if I've written that as an equivalent ratio, there 2:3:3, where my constant of proportionality is 2, just so that I've avoided the decimals. And also it's going to help me again in a little bit. Now we need to look at Antoni and Binh. So I'm going to write the ratio, Antoni to Binh. If Antoni gets 2/7 of the amount that Binh gets, then the ratio must be 2:7, because two is 2/7 of seven. Now we can see that in all of our ratios that we've written so far here and here, this two represents Antoni. And because that two is the same in both ratios, it means that our ratios must be the same size. The parts of the ratio must be the same size, I'm sorry. So that means we can write a final ratio of Antoni to Binh to Cala to Xavier as 2:7:3:3. Now we've got to divide this 1,440 pounds into this ratio. So I've drawn a bar model for it where we've got Antoni at the top, Binh here, Cala here, and Xavier here. And we know that this bar model represents in total 1,440 pounds. So let's work out what one part of our ratio is. Tell me how many parts of the ratio there are in total now, please. Excellent, there are 15. So we're dividing our 1,440 pounds by 15 to find out what one part will be. And what's the answer to that. Pause the video and work it out. Excellent, it's 96 pounds. So that means that each part of our ratio is 96 pounds. I'm not going to write them all in, but you understand that every one of these boxes represents 96 pounds. We then need to work out how much money each one of them get before we can work out how much more money Binh gets. So I've done these all already for you. So I'm just going to tell you those answers now. So Antoni gets 192 pounds. Binh gets 672 pounds and Cala and Xavier get the same amount. Don't know if we can see that here. And they both get 288 pounds. Now, of course you didn't have to work this out first. You could have seen how many more parts it was than each of them and work it out that way. That would be absolutely fine. So Binh, how much more money does she get than Antoni? Tell me now. Excellent, 480 pounds, more than Antoni. And it's really nice to write these in full sentences. And then Binh gets how much more than Cala and Xavier? Tell me now. Excellent, she gets 384 pounds more than Cala and Xavier. Excellent work on that one. There was so many steps there. So I'm super impressed if you managed to get all the way through to the end, well done. Moving on to the explore task now then. A jar contains red, yellow, and green jelly beans. 20% of the beans are green. The ratio of red beans to yellow beans is 5:3. Write down everything, you know, based on this information about the jar of jelly beans. There's loads here that you could write down. So good luck with that activity. What did you say? Did you figure it out anything here? Did you figure out the ratio of red to yellow to green? Did you figure out the percentage of red? Did you figure out the percentage of yellow? Did you figure out what fraction of the full amount they were? There's some prompts there if you didn't manage to get started I'm not actually going to go through this at all, because I want to know what you worked out. Well done on this task. That's the end of today's lesson on ratio problems. We crumb loads in there, so well done for making it all the way through to the end. I'm really, really impressed. Thank you so much for all your hard work. Please don't forget to go and take the end of lesson quiz so that you can show me what you've learned and hopefully I'll see you again soon. Bye.

I draw a rectangle and the side lengths are in the ratio 5:7. What fraction of the perimeter are the longer sides?

I have a bag of pink and brown cubes. 5/11 of the cubes are pink. What is the ratio of pink cubes:brown cubes?

A triangle has side lengths in the ratio 5 : 5 : 3. What fraction of the perimeter is the shortest side?

A rectangle has side lengths in the ratio 4:3. How long would the longer side of this rectangle be, if the shorter side is 24m?

Fill in the gap: The _____________ of proportionality of ADE to ABC is 1.5.

Fill in the gap: The ratio of 𝐴𝐸: 𝐴𝐶 = 6: 9 = 2:___

A line segment ABC is split in the ratio AB to BC as 3 : 5. What fraction of the line segment is AB?

The angles in a triangle are in the ratio 3 : 4 : 5. What type of triangle is it?

The ratio of Adam’s height to Tony’s height is 7 : 9. Adam is 154 cm tall. How tall is Tony?

A box contains caramel and toffee chocolates. 3/10 of the chocolates are caramel. What is the ratio of caramel to toffee chocolates in the box?

At a bake sale 25% of the cupcakes on sale are chocolate.  3/5 of the cupcakes are vanilla and the rest are peanut butter. What is the ratio of chocolate:vanilla:peanut butter?

The ratio of roses to violets is 3 : 4.  The ratio of violets to daisies is 6 : 5. What is the ratio of roses to violets to daisies, in its simplest form?

Unit Overview: Ratio review (9.7a)

Lessons:

Representing ratio

Ratio and proportion in geometry

Dividing into a ratio

Ratio problems