Lesson video

Hi everyone, it's me Mr. C.

I hope you're all okay, and I hope you are all more importantly, happy and being kind to those around you.

And of course, I do hope that you're happy to do a bit of math learning with me today.

We're going to be moving onto a new topic.

So let's take a look at what it is that we're going to be looking at.

We're moving on this time round to position and direction.

And we're going to be looking at describing the position of things on a 2D grid, and we're going to be using coordinates today.

Now, hopefully that's a word that you've heard, and if not, don't worry, we will be going through it together very, very shortly.

So you know the score, you know how things work.

If you haven't taken our knowledge quiz, you need to go and do that now, and then just come on back and rejoin us when you're ready to get on with today's learning.

Okay, I think with that time, I think you've probably done a really good job as usual.

So let's take a look at what's happening today.

But before we do, here's a little bit of a crazy thing for you to think about.

And this is another one of those ones that when I was looking at it, it made my head hurt.

I've found quite a few of those facts recently.

And this is one that seems almost unbelievable.

Now, I challenge you, once I've read this for you to not look out the window.

First thing I did after I figured out this fact was I had to look out the window and see for myself, is there any evidence of this outside? Because here's my fact for you today.

The surface of the earth where the equator is, that's the imaginary line that runs around the centre of the earth moves at a speed of 460 metres per second.

So if we scale that up to miles per hour, that's about 1,000 miles an hour.

On most roads in towns and cities, the fastest you are ever allowed to go is 40 miles an hour.

So compare that 1,000 miles an hour to the average speed of a bus that you might get around town, which is somewhere between 35 and 40 miles an hour.

That's absolute madness.

And as soon as I'd think of this factor, I had to look out my window and think, can I see things whizzing past? Can I see the stars and all the planets whizzing past out there? Why doesn't it feel that fast? Why am I not flying off? Any of you have ever been in a roundabout in a playground, where you push it and make it go faster? The faster you push it, the more you feel like you're going to fly off of it.

So why do we not all feel that we're flying off? Crazy.

That really hurt my head.

But another one of those insane facts.

This is 100% true.

I'm not lying to you, that is in fact a true fact.

So with that, we're not going to move quite as quickly as the world turning, but we are going to move quickly to what's happening today.

Making sure that you've got your pencil, a ruler and something to work on, so it may just be a book that you're working in, because the work that we're going to do today is easy enough for you to copy down into a book.

Or you may have been given these worksheets, it's up to you how you record it.

But also make sure that you find yourself somewhere quiet with no distractions, and we're ready to move on.

So knowledge quiz we've already done, that's the first thing on our agenda.

We're about to do our key learning of vocabulary, and then we're going to move on to a warm up involving symmetry, which is our last topic.

We're then going to look at what coordinates are and how we work them out.

We're going to look at our main activity, which is plotting some coordinates, and then our final knowledge quiz to see what you remembered.

So let's take a look at what's happening today.

Here's our key learning.

It is to describe position on a 2D grid as coordinates.

And remember, 2D means two dimensional.

And that will come in really handy with what we're doing today.

There are two dimensions that we're going to be looking at.

Just doing that to help.

It's not me doing a weird little dance, that will make more sense shortly.

So let's go through our key vocab together.

My turn, your turn.

2D, grid, X-axis, Y-axis.

Now, the next word is not axis, we pronounce it as axes.

Axes.

Good.

It doesn't mean that every time you see that word that's what it says, just in this case, it is the plural of the word axis.

It means we've got more than one.

Plot, vertices.

We know that word.

Origin, and coordinates.

Great.

Okay, I think you're ready to get going.

So here's the first thing.

Have a look here.

This is what we're going to be doing to start.

We have got two, four, six, eight shapes there.

All I need you to do is figure out how many lines of symmetry each of those shapes would have, and then just write that number inside the shape.

So if you think that the first shape here has 12 lines of symmetry, you'd write 12 inside.

If you thought this one had 53, you'd write 53 inside.

It's unlikely, but you might write that inside.

So that's all you need to do.

Figure out the lines of symmetry.

Remember, a line of symmetry is a mirror line, wherever you fold that shape along the line of symmetry, the two sides would then match perfectly.

Give it a go.

Come back when you're ready.

And welcome back.

So how did you fair with that? Was it pretty okay for you? I think the last few sessions we really covered symmetry well, and I think you probably did a very very good job.

So let's take a look at some of the answers then, shall we? So here we are with our answers.

I'm just going to really quickly point out where I thought that some of the lines of symmetry were.

So on this one, I figured that if we went from this vertex to this vertex that would be one.

And again, diagonal vertex to vertex, that would be two.

Through the middle, horizontal, that's three.

And from top to bottom, vertical, that's four.

Okay? Brilliant.

Here, I wonder if you spotted that one line of symmetry? There was only one place that that would work.

Yeah, from here all the way through this part and out.

Now, this shape here and this shape here are examples of what kind of shape? Regular or irregular? Hmm, they're irregular shapes.

And there's a bit of a rule we came up with with lines of symmetry on regular and irregular shapes, and I wonder if we can remember that in a moment.

Now, here we have a regular shape, and it has one, two, three, four, five sides, but it also has five lines of symmetry.

Hmm, that links back.

Here we've got an irregular shape with one, two, three, four five, six, seven sides, but I could only find one line of symmetry running down the middle.

What about this one here? Please don't forget it's not just shapes with straight edges that can have lines of symmetry.

This one has a curved edge, but it also has a line of symmetry.

And if you spotted that it ran horizontally, and you got it.

Regular or irregular? Here's one side, here's the other Yeah, I would say it was an irregular shape because those sides are not the same length.

Here we've got one, two, three, four, five, six, seven eight sides on a regular shape and eight lines of symmetry.

This one is irregular with no lines of symmetry, and the same here.

So let's look at these two.

Regular shape, five sides, five lines of symmetry.

Regular shape, eight sides, eight lines of symmetry.

Can you remember what we said the general rule was for regular shapes and their lines of symmetry? Yeah, we said that if a regular shape has six lines of symmetry, it must have six sides.

If it has seven sides, it must have seven lines of symmetry.

The lines of symmetry and the number of sides are the same in regular shapes.

Well remembered if you came up with that.

Good job.

So now that we're warmed up and ready to go, let's move ahead.

So what are coordinates? Well, coordinates are what we're looking at this week, and a coordinate is a way of recording a point or a position or where something is on a grid.

So the example I've given you here is to think of like a pirate looking for buried treasure.

You've probably heard the phrase that X marks the spot, and if you look at our little map here, X marks the spot.

Now, that means that the X marking the spot would have probably been on some kind of grid.

Now, on this we can't see it, but there may have been a grid in the background with lines going down, lines going across.

And it just means that where two of those lines intersect, we can name that point on a map.

So if there was a line coming down here in our grid, and a line going across here in our grid, this X would be on a particular position that we could name.

And we would name it using what we call coordinates.

Now, when I'm talking about it, it doesn't make it that easy to follow.

Talking about it sounds a little confusing, but when I show you what I mean using an actual grid, then it would be much clearer.

I just wanted to put into your mind this kind of image.

The idea of a map with an X marking a spot, that spot is a point on a map, that point on a map is on a grid, and that point on a grid on a map can be represented with coordinates.

That was a long string of things, but it will make sense.

So let me show you how it can make sense.

So for a grid where we are going to show something, we need a couple of things first.

We need something that looks like this one here.

Now, you can save certain features that I'm going to talk you through.

So we've got a line here that's numbered and a line here that's numbered.

One going horizontally and one going, remember the word? Vertically.

Now, the vertical one, the one that goes from top to bottom is the Y-axis.

Okay? The horizontal one is the X-axis.

Now, let me give you a little tip on how I remember which is which.

Okay, an X looks like a cross.

The X-axis goes across.

Make sense? An X looks like a cross, the X-axis goes across.

A Y has a tail that drops down, the Y-axis goes down.

I'm realising that's probably coming up backwards as I'm doing it for you because of my camera, but there is a tail on the Y, as the tail that drops down, that's like the line that drops down, the Y-axis.

So X goes across, Y, up and down.

X goes across, Y, up and down.

Easy to remember if you just think of it that way.

There are a couple of little sayings that we can use when we're looking at coordinates that will help us, okay? So the X-axis looks like a cross and goes across, the Y-axis looks like a tail dropping down, so the axis goes down.

Simple.

All right.

So I'm moving on.

So have a look at this big red cross that I've put onto my grid here.

Here on my axes.

Remember that's how we say the plural.

So we've got our X-axis and our Y-axis.

And incidentally, this bit at the middle here where they meet is zero.

That's sort of our key words, okay? We've got our numbers going along, We've got our numbers going up, but where everything is zero, so I've not gone any along and none up, zero along, zero up.

That's called the origin, okay? That's where we start our counting from the origin.

So have a look at this X.

From the origin, and we've had to go one, two, three, four, five spaces along, and one, two, three spaces up to get it.

Let me just show you how I did that again.

Watch.

One, two, three, four, five along, and one, two, three up.

Five along, three up.

Five along and three up, which means that I can write it in coordinates like this.

I use brackets.

Five, three, close the brackets.

five along, three up.

We always read the X-axis first.

So there's a way of remembering this.

We can say we go along the corridor, up the stairs.

Show you again.

Along the corridor, up the stairs.

Sometimes we might go along the corridor and down the stairs as well if we had more numbers beneath, but at the moment, we're just looking at, along the corridor and up the stairs.

X and then Y.

And you can also remember that we would do it in that order because if you think of the alphabet, X comes before Y in the alphabet.

So we would do the X-axis first.

X, Y.

Five along, three up.

five, three, okay? Now, hopefully that made sense.

There was a lot of talking, but it's very very much sticking to the same pattern every single time.

How many along have we gone? And then how many are pulled down? And we put those numbers in order, so the along number first, the up and down number second, and they're sandwiched between brackets with a comma in between.

That's it.

Really, really straightforward.

So let's have a look at another example.

So here's my X this time.

X marks the spot remember.

We read the X-axis first, so along and then up.

And just to help you remember, I'm going to just pop in the names of those axes.

So this is our X-axis, and this is our Y-axis.

So X then Y.

So we've gone one, two along and one, two, three, four, five, six up.

Two, and then six.

Two and then six.

Brackets around them, separated with a comma.

So this coordinate here is two, six.

Two along, six up.

How many times can I say two, six? I think I've probably said it enough times, and hopefully that makes sense to you now.

So have a look here.

Final one.

How many along have I gone? So I'm going to do X and then the Y-axis.

I've gone one, two, three, four, five, six, seven, eight.

And a real quick way of doing that is just to find it and drop down and see the eight.

And then I've gone one, two, three, four, five, six, seven, eight, nine up.

I've gone eight along, and nine up.

Eight, nine.

Brackets around them, separated with a comma.

Along the corridor and up the stairs.

Bish, bosh, bash, and there's my answer.

So have a think about this one.

Here's my new one.

What would the coordinates be for this one, do you think? Hmm, Hm, Hm.

How many along have I gone? Let's check, shall we? We're moving from our origin first.

One, two, three, four along, and one, two, three, four, five up.

Simple as that.

Now, guys, you can't tell me that that was tricky, right? That was a really nice straightforward, simple way to work it out.

It's just counting, okay? That's all it is.

So if you can count, which you all can, cause you're all amazing, you can do coordinates.

So have a look here.

This looks a bit overwhelming, but don't worry.

All you're going to be doing is working out the coordinates.

I've done half the job for you on each of them.

I've already given you part of each coordinate, okay? So let's just really briefly look at this together.

I've given you some of the information for each, okay? Remember, we're reading along and then up.

X and then Y.

Now, here I've given you the first value.

I've given you the X value.

We know we've gone one along, but how many have I gone? Okay? Let's look at this one.

I've gone one, two, three along, but how many up have I gone? That's what you need to fill in.

For this one I've gone how many along and four up.

So for each of those, the only one where I have not given you a helping hand is the cheeky astronauts at the end, okay? All you need to do is work out what the missing number is on each.

So just to remind you of how this works, I'm just going to write a little note.

Because I've given you a question here.

Think which axis do you read first? I'm going to give you this to remind you.

X then Y.

Here is X, here's Y.

Now, that's pretty kind of me.

I've given you those to help.

So have a go at filling in the missing digits.

Come back when you're ready.

Well, did you think you've coped with that one? Shall we take a look at the answers? That's probably a wise idea, isn't it? Let's take a look, shall we? So let me zoom in on these for you.

These are our answers, and we'll just go through them together real quick.

So remember we read X then Y, X then Y.

So we've gone one along, and then this one we haven't gone up or down, so it stayed on zero.

For here, let's go to the meteor next.

We've gone, one, two, three, four along.

This is what we needed to fill in.

And we've gone one up.

So four, one.

For this one for our astronaut, we've gone one, two, three, four, five, six along, first number, and zero up, second number.

Here we've gone none along, so we've stayed on the origin line.

We've gone up two points.

So one, two.

Here we've gone for the spaceship, one along, and one, two, three, four up.

This is a nice one.

I like this one.

Three along and three up.

So what we've actually got here if we go from this point to this point, to this point, to this point, and we've got a lovely little square.

Here we've gone three along and five up.

And five along, six up to get back to earth.

You do okay? I'm sure you did.

It's just a simple matter of remembering, which order do you need to count in.

Which one do you do first, the X or the Y-axis? And which one goes up and down? The X or the Y-axis? If the Y, think of the tail on the Y.

It drops down, the axis goes down.

Brilliant.

Little ways of remembering things are really quite helpful.

So here is your main task today.

You're going to be doing a little bit of drawing, but you're going to plot points on a grid as well.

So for example, I'm asking you here to draw on each grid, so this grid, and then this grid, two quadrilaterals on each.

Hm.

Now, here's a key thing though.

What's a quadrilateral? We've covered this in many many of our sessions before.

Quad at the beginning reminds us that it's related to a particular number.

It's a four-sided shape.

If it's got four sides, it must have four vertices, four corners, four angles.

So you're going to plot those, and then write down the coordinates for each.

So let me show you how that's going to look.

I'll give you an example, okay? So I'm going to plot four corners, one, two, three, four.

That would give me a four-sided shape.

It can be regular or irregular, it doesn't matter.

It can be named or unnamed.

Again, it doesn't matter.

And for each of these, I'm then going to write the coordinates.

So let's start with this one.

I've gone one, two along, and I've gone nine up And then don't forget you need a comma in between, and then brackets around.

So for this one, count with me.

I've gone one, two, three along, that's my first number.

And I've gone one, two, three, four, five, six, seven up.

Seven up, funny.

Okay, so that amused me, I don't know why.

For the others I've gone six along and eight up.

I can see that here, six, eight, So six along, eight up.

And I've gone for this one, six along and nine up.

What have I missed from both of these sets of coordinates? Yeah, the brackets.

Now, if you want to and you have got this on pencil and you're doing it, you can use a ruler to join those sides if you want.

You don't have to.

And then on the same grid, I'm going to do another four sided shape.

So one, two, three, four.

And I'll just repeat the process, putting in my coordinates for each.

Okay? And that's it.

So by the time you've done you'll have two shapes on each, with the coordinates written around them.

Hopefully that makes sense.

Now, like I said, you can make your shape any shape you want, as long as it's got four vertices, okay? So have a go putting those onto your grids and writing in the coordinates for each, and I'll see you when you're ready.

Well, then I think you should have had time to do that, and I'm sure you did.

Let's just recap then here are two that I did again.

Let's have a look at what we could have had for our coordinates.

For this one I've gone one along and five up.

Remember how we're looking at the presentation.

Brackets on either side with a comma separating in the middle.

So one along, five up.

Here I've gone five along, five up.

Here I've gone five along and nine up.

And here I've gone one along and nine up.

Okay? There's one of my quadrilaterals.

Here I've got another one.

One along and six up.

I've gone, Oh, six along and four up.

Seven along and seven up.

Oh, seven up again.

Making me thirsty.

And two along and nine up.

Now, a really important thing, and I should have pointed this out before, but hopefully you all spotted it.

Can you see how the points I've plotted are where two lines cross? Here and here is where they cross over each other.

It's not in the square, it's on the crosses of the lines.

So like here, where those two lines cross, or here where those two lines cross.

It's always where the lines cross when you're plotting coordinates.

So hopefully you did a good job there.

Well, there's no hopefully about it, I'm sure that you did.

So I thought I'd leave you with one final challenge before our final knowledge quiz.

I'm going to show you now a five sided shape that I've plotted, and it's here.

And I've got point A, B, C, D, and E, and you can see that in the table.

For each of those, I've given you the coordinates, but I was in a rush and I made a couple of mistakes.

Can you spot my mistakes? And can you explain what those mistakes are? So can you find my mistakes? Can you explain them? Have a go.

Okay.

Well, hopefully what you will have done is you would have gone along and worked out the coordinates for each, remembering that we do X and then Y.

So I would've gone along and counted them all.

So let's start with point A.

One, two, three along and one, two, three four up.

Ah.

Mm mh Point B.

One, two, three, along and yep, eight up.

Correct.

Point C.

Six along and eight up.

Brilliant.

Yep, good.

Great.

Point D.

Nine along, five up.

Yep.

Point E.

Hm, no, this is seven along and two up.

Hmm.

So hopefully you spotted the mistakes.

I wonder if you can explain what those mistakes were.

Let's take a look and see if you can think of how that might be explained.

What mistake did I make when I was looking at these answers? I read the wrong axis first.

Originally, I just read four, three.

So I did my Y-axis first and then my X.

So always remember, X then Y.

This is our key takeaway for today.

You need to remember X then Y, okay? Folks, well done.

Great job today.

So the final thing that you're going to need to do is just pop and take our knowledge quiz if you haven't and then come back when you're ready just for a little bye bye.

All right, guys welcome back.

Hope you did all right in your knowledge quiz.

You've certainly done all right today, I am sure, and we'll recap on more of this in the next session.

Super proud of how you've done today.

I'm really a fan of coordinates, it's one of my favourite things to do.

This kind of thing, I really enjoy it.

So we should have a lot of fun doing it.

So from me, Mr C, until next time.

Bye.

See you soon.