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Hi, I'm miss Kidd-Rossiter, and I'm going to be taking you today for the second lesson, on Ratio and Proportion in geometry.

Is a really great topic, and I really hope you're going to enjoy it.

Before we get started, can you please make sure that you've got something to write with, and something to write on.

It might help you today to have a ruler as well if you can.

Make sure you're in a distraction free zone, and if you're able to be, you're in a nice, quiet place.

Before we get started, if you need to pause the video now, so that you can get anything or move yourself, if not, let's get going.

So today's try this activity then, without a ruler, how could you locate the point, that is exactly 1/2 way along the green line? Which is the line that's going from this corner, all the way through the diagram to this corner? 1/3 of the way along the long blue line, so that's the one going from this corner to the top here, and 3/4 of the way along the shorter blue line.

So that's the one that goes from the top here, to the bottom here.

Pause the video now and have a go at this activity.

If you're struggling, just keep watching, and I'll give you some support.

Okay, if you're struggling, that's absolutely fine.

This is a really tricky activity to get us started.

You might want to think about, how many dots there are between the lines.

So if we look at the green line, going from the bottom corner here across, we've got 15 dots.

So what would be 1/2 way along the 15 dots? Think about that, and going, up, we've got six dots.

So what would be 1/2 of the six dots? Have a think about that, and then try and count the dots for the blue lines, that might help you out.

Pause the video now and have a go at this activity.

Well done everyone with that.

There were some tricky ideas here, so let's go through it together.

So first of all, 1/2 along the green line, well we know from the left to the right, we've got 15 dots.

So we could measure 1/2 of that, which we know would be, between the seventh dot and the eighth dot, because 1/2 of 15 is 7 1/2, so we could measure that along.

And then we've got six dots from the bottom to the top, so that would be three dots up, so we can see that that 1/2 way along our green line, would be there.

1/3 of the way along the blue line then, how many dots do we have going from here to here? Can you tell me now? Excellent, we have nine dots in there, so what's 1/3 of nine? Tell me now, excellent, it's three, isn't it? So that would mean we're going three dots along, and then we know we've got six dots going up.

So what would be 1/3 of six? Tell me now, excellent two, so from there, we'd be going two dots up so this point here, is our 1/3 along the blue line.

What about then 3/4 of the way along the shorter blue line? So we've got four dots going from here to here, so what's 3/4 of four? Tell me now, excellent, it's three, isn't it? So we go across by three, and what's 3/4 of six? Tell me now, excellent, 4 1/2, so that, that would be the point that is 3/4 of the way, along our short blue line.

So moving on to the connect part of the lesson now, we can express parts of line segments.

by the ratio of their lengths, work out the following ratios.

So before I give you any input, pause the video here, and have a think about this question, and any questions that you might have before we go forward.

So pause video now.

Excellent, right, let's first of all, just look at the red line.

So we're going to work out the following ratios.

AB to AC, and then afterwards, we're going to look at AB to BC.

So there's two ways you could do this, the first way to do it would be to count the dots.

So from A to B, I've got one, two dots, haven't I? And then from A to C, I've got one, two, three, four, five, six, seven, eight dots.

Now we can see that that's a brilliant way to do this first red line, but when we come on to doing the blue line, and the green line, that might be tricky, because our lines don't always pass through dots.

So we're going to have to think of another way to do it.

So the way that I found is to measure the line segment from A to B.

So I've used the pink, measure here from A to B is that long, and then see how many more it will take to get to C.

So I know from A to B, it's taking one at the moment, and then B from C, it's going to take another one, two, three.

So A to C is one, two, three, four of those lengths.

Can we notice anything about two to eight, and one to four? Tell me now, excellent, they're equivalent ratios, aren't they? So, that is another way this way around we do it, we get a correct answer.

What about AB to BC then? So AB we know is one, and BC we know is one, two, three.

So what fraction of the full line is AB? Tell me now, it's 1/4, isn't it? Because it's one part out of one, two, three, four parts.

What fraction of the full line then is BC? Tell me now, excellent, It's 3/4, isn't it? Well done, let's have a go at the second one then.

AP to AQ and, AP to PQ.

So again, we're going to look at measuring from A to P first of all, and then how many more of those do we need to get from P to Q? Just another one, so from A to P is one, and from A to Q is one, two.

What about from AP to P and PQ then? So, AP is one, and PQ is another one.

So AP to PQ is one to one, so what fraction of the full line is AP? Tell me now, excellent a 1/2, and PQ is also a 1/2.

And we know because it's a one to one ratio, that AP and PQ are the same length.

Finally, then AXE to AY, and AXE to XY.

So this time I found it a little bit easier to measure from X to Y first, and then to add in my extra one.

So X to Y is one part, and then A to X is another two.

So AXE is two parts, and AY is three parts.

AXE we've said is two parts, and XY is one part.

So what fraction of the full line is AXE? Tell me now, excellent, 2/3.

And what fraction of the line is XY? Tell me now, excellent, 1/3.

You're going to now have a go applying this to the independent tasks.

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.

Welcome having to go at that independent task.

There's quite a lot in there, so I'm not going to be able to go through it all fully.

I will put the answers on, and you can pause the video, whenever you need to, to check your work.

So for question one, here are all your answers, pause the video now to check.

The question two, then let's go through it together.

So point P is the midpoint of line AB, so that means it's 1/2 along the line AB.

So you should have got that it was there.

Point Q, so the AQ is 1/4 of AB.

So we want it to be a 1/4 of the way along the line, and that means it's there.

And for part c, point R, so the AR to RB is three to one.

So that means that we want point R, to be 3/4 of the way along the line.

So it's there, and then finally, we were asked to write the coordinates.

So P six four, Q is three two, and R is nine six.

If you need to pause the video to check what you've done, then please do.

Finally then we've got the explore task.

So Yasmin is saying point B has coordinates 10 eight, so the point halfway along AB, will have coordinates five four.

Do you agree with Yasmin's reasoning? Pause the video now, and have a go at this task.

What did you think, did you agree? Did you disagree? Tell me now, excellent, I disagree as well, because we can see that point A, has coordinates four two, doesn't it? So that means that the midpoint has to be 1/2 way between four two, and 10 eight.

So going across from four to 10, we've got six squares, haven't we? So we wanted it to be one, two, three across, and then going between two and eight, we've got another six square, so we would want it to be three up from there.

So this point here that I've marked, would be the mid point.

What would the other end of the line need to be, for the midpoint to be five four, that Yasmin is suggesting? What would that need to be? So for it to be here, where would the end of the line need to be? Tell me now, excellent, it would be zero zero, wouldn't it? So if we had the line go from zero zero through to B, then Yasmin would be correct.

That's it for today's lesson, so thank you so much for all your hard work, on ratio and proportion in geometry.

Please don't forget to go and take the end of lesson quiz, so that I can see how you've done.

Have a brilliant day, bye.