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Hello, and welcome to today's lesson about bearings on isometric grids.

For today's lesson, all you need is a pen and paper or something to write on and with.

Please take a moment now to clear away any distractions, including turning off any notifications.

If you can, please find a quiet space to work where you will not be disturbed.

Okay, once you're ready, let's begin.

Okay, so I'd like you to try this.

Workout as many angles as you can.

Can you find a way to check the sum of the angles? So, I'd like you to pause the video and have a go.

Pause in three.

Two.

One.

Okay, welcome back.

So.

you might have noticed that either this is 360 split into six sections, so each one is an angle of 60 degrees, or you might have noticed these are equilateral triangles, so each angle is 60 degrees.

Or you might have looked Carla's statement and halved this angle.

So half of 120 is 60.

Now, if you know that one of these corners is 60, you can work out lots of things.

This is 60.

That is 300.

This is 60, also 300.

This is 120, 240, 240 there as well, 120- two sections, 240, 120, 240, and 60 and 300.

Can you find a way to check the sum of these angles? Well, we can check the sum of all the interior angles.

We can add them all up.

Then we can count how many sides our shape has.

One, two, three, four, five, six, seven.

So, because we know our shape has seven sides, we know that some of the interior angles should add up to 900 and you know, you might want to think about how could we check the ones on the outside? All right, so that's something you can have a think about.

Okay.

Make a path from A to B using bearings and steps.

You are only allowed to move along the lines.

So, imagine you are at A, or someone is at A, and you want to give them instructions about how to get to B.

I'm just going to make any path.

I'll make this one.

Okay, I'm trying to keep my line as straight as I can.

Okay, so there we are.

Not perfectly straight, but it doesn't matter.

Now we're on an isometric grid.

We need to work out that barrier.

What is that angle? Well, before, we worked out that that was 60 and that was 60.

So, the whole thing is 120.

So, we have a bearing of 120 from A for one, two, three, four, five steps.

But then we're not at B, so we need to do another set of instructions are another instruction, which is going that way.

So if we went off there, that would be an angle of 60.

So it would be 060, not forgetting the zero, like I almost did, for one step.

Okay, so start at 120 travel a bearing of 120 degrees for five steps, and then travel a bearing of 060 degrees for one step.

And that would get me to B.

Well, is there another way? And yes, there is; in fact, there's lots of different ways.

And you don't just have to use two steps, as in two separate instructions, you could have a really crazy path like this.

Okay? So there's loads of different ways you can do it.

I'm just going to do one more.

In fact, I'll start off and I'll go down to here.

So that would be so, start as A, and then we've got 180 degrees for.

one, two, three, four, five steps.

And then we've got one, two, three, four, five, six.

So we've got six steps.

And what is that bearing? That is a bearing of, well if that's North, that is 60, so 060.

for six steps.

Okay, and there are two separate instructions of how we could get from A to B.

And I slightly preferred how I set it out here.

So if you could set it out the same as that, that would be great.

Okay.

Which of these is not a path from A to B.

Pause the video if you need some more time.

Five.

Four.

Three.

Two.

One.

Why isn't this a path? Well, that's try.

Four steps from zero.

Four steps, 060, so that's that way.

One, two, three, four.

Remember, now off clockwise, and then three steps bearing of 180.

One, two, three.

I wouldn't quite reach.

I'd need an extra four steps.

Okay.

Now, I'd like you to have a go at the independent task.

Pause the video to complete your task, resume once you've finished.

Okay, so here are some possible answers from me.

Now, these are not the only answers.

These are just some possible ones.

So we've got from A to B.

So you've got 060 and five steps, which is like that.

We've got 120 for two steps, 060 for three steps, and 000 for two steps.

And here are two possible paths from B to A.

Now I'm just going to talk about it for one second, because look at this one, and look at this one.

They are kind of like the opposite of each other.

That path goes that way.

This one goes that way.

That one goes that way.

Then look at this one, 180, two steps, 240 for three steps, and 300 for two steps.

That's really cool, isn't it? Do the bearings mean anything? I just want you to have to think.

Okay, what do you notice? And then finally, two possible solutions for this, and remember there is many.

So from C to B, so we're at C, 00 for four steps, and then 060 for four steps.

Or we could have done it the other way around.

060 for four steps, 00 for fast steps.

Ooh, what shape does this form? That's four diagonal.

That's four up.

That's four diagonal.

That's far up.

Are those lengths the same? Is that the same as that? Well, it's an equilateral triangle, so they are the same.

So that, and that, and that, and that are the same length.

So that means we have a rhombus.

Okay, and you didn't have to make a rhombus.

I just thought that was really cool.

I thought it was really cool how you could make a rhombus.

You might've been able to make a parallelogram as well, I think.

No, you might have actually gone off the grid.

but, I just want to explore them and find different ways, find cool ways.

Did you do it in more than two steps? Did you do it in like 10 steps? This is all great practise of bearings, so well done, however you did it.

Okay, so the final task for today.

This robot here, he starts at X.

I move a bearing of, choose one, for one space, then I move a bearing of for two spaces.

Where am I now? Okay, what happens if you can only use them once? Can you get to all of them? What happens if you're allowed to use them twice? Can you get to all of them? You might want to just spell something, okay.

Just have a play around, have an explore.

See what you can work out.

So pause the video and have a go.

Pause in three.

Two.

One.

Okay, so I could not have possibly worked out all the things you might have explored here, but hopefully you found something interesting and I would have been very impressed if you managed to find a way to all of the different points.

That would have been a really good use of your time and a really, really good way to practise bearings.

So, that is it for today's lesson.

If you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you very much for your participation in today's lesson, and I look forward to seeing you next time.

Thank you.