Lesson video

Howdy? It's me, Mr. C, how are we all? We are here at the end point of our last few sessions, seeing how much we remember and how much we can put together.

So exciting times today.

So shall we move straight ahead, hey? Alright.

Make sure you've taken a knowledge quiz and then as soon as you are ready, come on back and join us.

Lots to get through.

Lots of skipping backwards and forwards.

Welcome back.

Alright.

So here's our math trick for today.

How to square a two digit number that ends in five.

Remember when you square a number, it means that you multiply it by itself, and that can be tricky.

So this is how you can find a real quick way of doing it for any number that ends in five, any two digit number that ends in five.

So if you need to square a two digit number ending in five, this is what you do.

You're going to multiply the first digit by itself, plus one.

So for example, if we were doing 65 squared, I would do six times six plus one.

So six times seven basically, which gives me 42.

And then all I need to do is drop a 25 at the end.

And then 4225 is 65 times 65.

Should we try it with 45 together? So we do the first digit, four times the first digit add one.

So four plus one.

So that's four times five, which equals five, ten, fifteen, twenty, and we drop a two five at the end, 2025 is 45 squared, and it works for any two digit number that ends in five.

So give it a go.

That is a real quick way of being able to say, I know what 45 times 45 is.

Or I know what 75 times 75 is.

Give it a go and impress people.

Show off your mathematical prowess, your expertise and your genius.

Brilliant.

Alright.

So we're going to need a pencil, a ruler, paper or book and today you are going to need some paper, if you've got it for an extension.

Just a sheet of rectangular paper and somewhere quiet with no distractions.

So we've done on all this quiz, we're going to move on to our key learning of vocab in a minute, and then we're going to have our go, our number fit, know this is a new born, we've not done this and I'll explain it as we get to it.

Then we're going to recap on all types of shape covered so far, our main activity which is a variety of shape-based investigations, activities and things.

And then a final knowledge quiz to see what you've remembered over the course of these last five sessions, which I'm sure is a huge event.

Okay, so key learning today is to solve problems based on quadrilaterals and triangles.

Remember quadrilateral is four sided.

So here's our key vocab, quadrilateral, triangle, regular, irregular, parallel, vertices, sides, and angles.

Now two of those words here could mean the same thing.

I wonder which two of those words are meaning the same.

Yeah, vertices and angles, they're basically the same thing, corners in this case.

Alright.

So this is our number fit.

It's a bit like a crossword but with numbers not letters.

And we've been given all the numbers that go into it, we've just got to put them in the right place.

So I'm going to show you where to start.

And this could be frustrating, it's a trial and error sometimes.

But that's the beauty of it.

You can spend quite a bit of time working through this and I would suggest you do.

Now we've got three digit numbers, four digit numbers, five digit numbers and six digit numbers.

And all that means is, if there are four white squares, so one, two, three, four, I need to put a four digit number in here.

If there are one, two, three white squares, it's a three digit number and so on.

So for example, one, two, three, four, five, six, that was one of our six digit numbers, 725 692.

Seven, two, five, six, nine, two.

Now the beauty of this is, you don't have to do any additional subtraction at all.

You're just slotting the numbers in the right place.

Wonder where you might start.

I'll give you a clue, look for the least number of options.

So, three digit numbers, least number of options? Well, no.

I've got one, two, three, four, five more to put in.

Four digit numbers.

One, two, three, four, five, six of those.

Mmh, not going to start there.

Five digit numbers? Mmh, which might you start with? Yeah, I would agree.

I would start with the six digits because I've only got one left, 'cause I've crossed these two out.

So can you spot where the other six digit number would go? I'll give you a clue, it goes down.

Think you got it? Alright, so it's two, one, zero, four, nine, six.

Okay, here it is, two, one, zero, four, nine, six.

Now what do you think I'm going to do to make sure I don't reuse that number? Yup.

Cross it out, goodbye, see ya.

Didn't need that one.

Now I'm going to look at these two because I've only got about two digits in.

Let's see one, two, three, four, that's a four digit number and it starts with seven.

Here's my four digit numbers and these both start with seven.

It can only be one of them though because look, I've got a two here as well.

So it's got to be seven, something, two, something.

Seven, something, two, something, seven, something, one, no.

So it's got to be this one.

Seven, one, two, nine.

Seven, one, two, nine.

Do you get the idea? Do you see what I'm doing? So I would next then go to this one.

Something, five, something, zero.

So I'm now going to look at three, four, five digits, four digits.

Something, five, something, zero.

So I'm going to look see, basically I'm going to look for the zero now.

Do any of them end in zero? Oh yes, one of them does.

3580.

Three, five, eight, zero.

Now I think I've helped quite enough.

So now it's up to you.

Can you slot in the rest of the numbers in there? Another thing I might be tempted to do, if you look here, I've used all my six digit numbers, so I might just be tempted to, do that so I don't use any of them again.

Cross them out once you've used them, give it a real good go 'cause I think you're going to do do brilliantly on this.

Alright, we are coming back, three, two, one, hello? Brilliant.

So not too bad, right? I think you would have managed brilliantly.

I wonder if you had a little system you were using, shall we see the answers? Well here they are.

Pause the screen if you need to just to check your answers, see if you've got them all in the right place.

I'm very confident that you did because you're amazing.

Alright.

Shall we move ahead and see what we're looking at today? Lots of separate activities today.

So we'll do one, come back, do one, come back.

So here is our first activity that I would like you to have a go at.

I wonder if you can remember the properties of various shapes.

So we're going to do draw it, name it and describe it basically.

So we'll draw it in the first column, we'll name it in the second column, we'll describe whether it has parallel sides, the features of those sides and the angles and vertices, the corners.

So I've done the first one as an example, let me just write that in for you.

This is an example.

So the square, look, I've drawn my square that's there to help me, okay? And I've named it.

And that was a nice, straightforward square.

I can say it's got two sets of parallel sides.

Remember, parallel sides are pairs of lines that no matter how long they are will never meet, they stay the same distance apart the whole time.

Parallel lines, okay? All four sides are equal and it has four equal angles, they're all right angles.

So the next one is an oblong.

How would you do that? How would you describe the oblong? You're going to draw it using a ruler and a pencil and then you're going to do tell me parallel sides, features of those sides, now it will be different to the square, and then what type of angles or vertices does it have.

Then we've got trapezium.

You're going to draw it, describe it.

And then we have something where all three sides are equal.

Well, you should be able to work out the rest of that by going backwards.

What shape has three sides? And what one of those would have three equal sides? You've also got second set there, right.

I think you're going to do brilliantly.

Well not that I think, I know you're going to do brilliantly because I know how much focus you're putting into this.

Be really careful with spellings of the names of certain shapes, okay? And be really precise with your description of the properties.

Give it a good go.

And just think, if you were trying to describe this shape to someone who had no idea what it is, how would you describe it? That's all you need to think of and just use those headings as a little bit of a help.

Off you go.

Let's come back together in five seconds.

Hello? Brilliant.

Alright.

See how you did, shall we? Take a look over then.

The oblong has two sets of parallel sides and the opposite sides are equal.

So it would look like this.

And remember if you want to be real professional, you might even do this.

These are equal.

These are equal.

And if you wanted to make it look really profesh.

It's got four right angles so you can mark those in as well.

Brilliant.

A trapezium has one set of parallel sides, one set of equal sides and two pairs of equal angles.

So these are the same, and so are these, okay? Has no particular kind of angle though what kind of angle does it definitely not have? Yeah, right angle.

So if all three sides were equal, it's a three sided shape where they're all equal, I know that's an equilateral triangle.

One, two, three, and each of the angles measure 60 degrees.

It has no parallel sides.

Here are the other ones.

Scalene triangle.

No parallel sides, three different length of sides and three different angles.

Parallelogram.

Two sets of parallel sides, opposite sides are equal, opposite angles are equal and there are no right angles.

A rhombus.

Two sets of parallel sides, all sides are equal but there are no right angles and opposite angles are equal and it's not a diamond.

And our last one is an isosceles triangle because two of the three sides are equal, one, two, and two equal angles, okay.

Brilliant.

Well done folks.

Are you now ready then for activity number two? I think you are.

More dots guys.

Sorry about it.

So this time we're investigating quadrilaterals, how many different quadrilaterals can you make by, with a ruler and pencil, joining four dots on the outside of a circle.

Now when you create a shape, can you name it? And only use straight lines.

So here I have joined one, two, three, four, together.

I've got my quadrilateral 'cause remember quad means four, and this is a, trapezium.

What others can you do? Can you make a square? Can you make an oblong? Can you make a parallelogram? What can you make? So really think about it and see how many variations you can come up with.

Alright.

I think you're going to do brilliantly.

Now if you finished, can you make overlapping patterns on one circle with different quadrilaterals in the same one? I wonder.

I'm sure you could.

Alright, off you go.

See you soon.

And we're coming back in a few seconds, three, two, one, welcome back.

Hello.

Alright.

Let's have a look then at our next activity.

Now guys, you are really doing an amazing job so far today.

And before we do go onto our next activity actually, I wonder if you came up with any others for the previous one.

I wonder if you could guess then, if I were to join up this one, this one, this one and this one, what shape would that create? Amazing.

Yeah, you would have gotten a square there.

What about this one, this one, this one and this one? Yup, that would have been another trapezium.

Now here's an interesting one for you.

This is one we haven't talked about, but I'm going to uh, do the best I can.

See look, this is why we need rulers.

We know this shape.

I'm giving you a clue.

Yeah, that one's a kite and there are lots of others we could have made on there so very well done.

Let's look then at our next activity.

Okay.

Here it is.

This is our triangles investigation.

Now this time, more dots, sorry, sorry, sorry.

It's going to be like Dalmatians in front of your eyes, isn't it? How many different triangles can you make that just have the one dot in the middle? Alright.

How many different ones? See how many you can make.

Give yourself a time limit.

Maybe say, six minutes.

How many can you do in six minutes? Alright.

They all need to have that one dot left over in the middle.

You see there's one left there.

How many can you do? I'm sure you can do quite a large number.

So remember, they have to have how many dots left in the middle each time? Yep.

One dot left each time.

Alright, give it a go because your time starts.

now.

You manage? Too bad, right? Quite nice little investigation.

Shall we take a little look at some other examples? I'm just going to circle the dots then and tell me, would I be right or wrong? So you got to use your visualisation skills here.

So if I did this one and this one and this one, would that fit the criteria? Yeah, 'cause I've got my dot in the middle.

What about this one, this one and this one, would that fit the criteria? No because there's no dots in the middle this time.

What about this one, this one and this one? Yes, 'cause I have my dot in the middle.

So some of them are much bigger than others.

Alright, well done.

So we've really got one more little bit of investigating to do today, okay? And this is our challenge.

And for this, I'm going to give you no visuals, I'm just going to give you the instructions, okay? Because I want you to really cope well.

I don't want to do anything in front of you that might influence you, I want you to go and explore, okay? So challenge.

You're going to be exploring shapes by folding paper.

Now you need a piece of rectangular paper, and few terms just for you.

How small can you make that paper by folding it? How many different sorts of triangle can you make by folding that paper? Now do you remember when we went, when we were back a few sessions ago, when we made our little angle finders, where we had the rectangular and we folded a bit, so we had small angle, large angle, right angle, acute, obtuse, and right angle on it? Use that as a starting point.

How many different triangles can you make? Can you do it where you fold it and then when you open it out again, you've got four identical triangles? Can you make a square? Can you make any other quadrilaterals by folding? Just explore.

Now if you've got a larger piece of A4, it makes it easier.

If you have smaller rectangular paper and you've got different colours, even better, you can make patterns.

But how many different triangles can you make? How many different quadrilaterals? And can you meet any of these criteria? This is your run and play with it kind of activity now.

Just explore.

Have an amazing time doing that and I will see you when you're finished.

Hello? We're back.

Brilliant.

Okay.

I think you did an amazing job and I wonder if any of you managed to make any really interesting quadrilaterals? I find it quite easy to make some rather irregular ones, not my regular ones I find trickier, that can end up folding just right.

But if you're any good at origami then you probably did brilliantly at that.

So pop off now, this is the final bit.

You need to make sure you've taken our knowledge quiz for today.

And if you haven't, do it and then come back and see us in just a few seconds.

We will be here waiting.

I'm going to freeze now.

No, I couldn't do that for much longer.

That was quite exhausting, off you go.

Well, welcome back guys.

I think you've had a really phenomenal set of sessions so far, so very well done.

Really enjoyed doing it with you.

All I meant to say is this, well done for all your hard work today and I'm going to see you next time.

Keep an eye out around you over the next few days and just see what shapes can you see.

I wonder if you can spot one shape that you've seen more than any other, what could that be? Well, have a wonderful rest of the day.

I've been lovely working with you and we will work together again very, very soon.

So from me, Mr. C, bye bye.