Lesson video

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!.