Lesson video

Hello everyone it's me Mr. C.

Hope you're well and hope you're ready to learn.

It's great to have you with us today, we're starting a new topic for our learning, so let's take a look at what that topic is.

We're going to be looking, in the next few sessions at reasoning with patterns and sequences.

And today we're going to be investigating the place value from different number systems. That will make more sense as we plod along.

So, before we do anything else please make sure that you've taken our knowledge quiz and that you're ready for the rest of the session.

When you've done the knowledge quiz, come back and join us and let's move on.

Welcome back everybody.

Hopefully you did alright in that knowledge quiz and your brain is now warmed up and you're ready to get going with our learning.

So before we do anything, I'd like to share with you a little riddle.

And this is our riddle today, take a look at this one here.

So, Andrew is a greengrocer.

He's got size 10 shoes, he's 180 centimetres tall, and his trousers have a waist of 32 inches.

So what does Andrew weigh? Hmm, lots of information there.

When we're looking at these kinds of things remember, we're always looking for key information.

Well, let's have a look at some of that key information shall we? Some of the key information we have here, well, it's going to to be the numbers, isn't it? So size 10 shoes, 180 centimetres tall, and his treasures have a waist size of 32 inches, hmm, so what does he weigh? Maybe there's some kind of formula we need to do, would I need to do maybe something like 10 times 180 plus 32? Or would I do 10 add 180 and times by 32? Hmm, it's quite a tricky one.

Any suggestions I wonder, what would you do to work that out? A few seconds of thinking time, give you five.

What did you come up with? Anybody got an answer? I'm finding this really tricky, so I'm going to give you another bit of information, it's going to be helpful.

Oh, well look here, all of this information, well, almost all of it, is completely useless.

But this is important.

It's his job that tells us the answer.

So let me just read this question to you again.

Andrew is a green grocer.

He has size 10 shoes, he's 180 centimetres tall and his trousers have a waist size of 32 inches.

What does Andrew weigh? And it's his job that tells us the answer, by the way, this, that's Andrew, right here.

Hmm.

Okay, I'm going to confess to something.

I was trying to catch you out, this is completely and utterly a trick question.

Should I explain how? I'm asking you what Andrew weighs, he's a green grocer, so if he's a green grocer he weighs fruit and vegetables, sorry.

If I caught you out, yay me.

If I didn't catch you out, yay you, well done.

So yeah it was a trick question.

We can't work out how much he weighs by knowing his shoe size, his height and the waistband of his trousers, but we do know that for a living, he weighs fruit and vegetables for people, so it was a trick question.

So, yeah that's a cheesy one but maybe try it out on someone at home and see if you can catch them out.

Alright, in all seriousness though, let's move on.

Make sure then for today you've got your pencil, your ruler, something to write on.

If you've printed out the worksheets brilliant, if you've got paper they're easy enough to just write down on the paper and you're going to need somewhere quiet with no distractions.

And today in particular, I would suggest you have enough paper to make a few mistakes.

You'll understand why when we get to the main activity.

So our agenda for this lesson, starting with our knowledge quiz, you've done that already, then moving on to our key vocab and learning, with our multiplication warm up today, not speedy times tables, a different type of multiplication warm up.

Then we're going to learn a bit of history actually, so it's a bit of a maths history type lesson, we're going to learn today what numbers are, where did they come from and why do we use them.

Then our main activity is going to be matching number scripts.

Then I'm going to move on to a challenge where we're going to write in different number scripts.

It will make more sense as we go along.

And then a final knowledge quiz to see what you've remembered.

So play along with me, here is our key learning, to investigate the place value of different number systems. My turn, your turn.

Scripts, patterns, similarities, differences, Roman numerals, and Arabic numerals.

Now hopefully you'll know what Roman numerals are, you've probably talked about this at some point before, and they are around us all the time.

You just don't always notice them.

And if you know what they are, and they are around you all the time, your brain probably already translates them into what we know anyway.

So let's move ahead shall we? To start with, you have some calculations here, four of them, they're multiplications you're multiplying a three-digit number by a single-digit number.

Now you've got some space here, if you need to, to do the calculations or if you're writing it out you can give yourself as much space as you need, and then there's space for the answer.

Have a go, use whatever method works for you, okay? It won't always be the same method, but use whatever method works for you.

Have a good go at it and come back when you are ready.

Welcome back.

Hopefully you've managed to use a really successful and an effective and efficient method, efficient means that it doesn't take you forever, it should be quick and to the point, hopefully you've used a method that works for you.

So let's take a look at some of those answers.

So for the first couple here, here are your answers, take a look.

And I want to just spend a bit of time looking at how I would have done one of them.

And I'm going to look at this second one here, okay? If I wanted to be really quick with it, I would have probably used some partitioning, and multiplying everything by 7.

I would have probably done 100 times 7, 40 times 7, and 3 times 7.

And then I always remind myself I would have put thousands, hundreds, tens and ones at the top to help me.

Now I'm going to start with the one that I know is easiest, the one that I can manage quickest, and that's the 7 times 100, that's really easy.

7 times 100 if I didn't know 7 times 100 I could do 7 times 1, make it 10 times bigger, 10 times bigger again.

7 times 100 I know is 700.

And then I'd look at 7 times 40, well, if I didn't know 7 times 40, what could I do? Think about it, if I didn't know 7 times 40, what could I do? Yeah I could do, 7 times 4 and then make my answer 10 times bigger, so let's do that.

7 times 4 is, well, if you're not sure do 7 times 2 and double it, 7 times 4 is 28, and making it 10 times bigger would make it 280.

Okay, and now down to my last one, 3 times 7, that's nice and straightforward, 21.

Now that I've got all of these numbers, what do you think I would do next? I would find the total.

So I'm going to add all of those numbers together.

So I'll start with my ones column 0 add 0 add 1 is 1.

And then to my tens column, am I right to say 0 add 8 add 2? Hmm hmm because it's my tens column is eight tens and two tens.

So 80 add 20.

80 add 20 as we know is 100.

And I'm going to carry over to here and just regrouping, and then 700 add 200 is, 900 yeah.

Add another 100, yeah, is 1000.

And that's how I would have worked it out, if I needed to do it in an efficient way that I knew was going to make it right.

So, if that's what you did do, fantastic.

If you did it just in the column method and you were amazing at doing it that way, even better, 'cause that's quicker than me.

So let's just take a look then at the next two answers.

Okay then, let's move on.

So, today I said we were going to be learning about numbers in different scripts.

But before we can do that let's learn a little bit about what numbers actually are.

Well, numbers are insanely important.

We all know that.

But we want to think about now really, how did they start? Well, thousands of years ago, thousands and thousands of years, four thousands of years, people lived in really small communities, little tribes or villages, but then as time went on these communities began to interact with each other, so they would meet and they would trade and they would try to communicate with each other.

They might not even talk the same languages so that would make it difficult.

Now, in terms of counting, why would you need to be able to count when you're meeting other people? Well, if you're selling things or swapping things, you might need to know how many of one thing is worth, how many of another? So for example, two cattle might be worth seven sheep.

You need to be able to know and put a value on what you're looking at.

So to start with people could only count the cattle, the cows that they had, or the days by using a tally system.

Now, when we tally things, we see something that looks like this.

And that actually hasn't changed very much for thousands and thousands of years.

Just out of interest, remind me what does this bit of a tally mean? How many is that worth? Yeah, that would be worth five, and that would be worth another three, so altogether here, we've got how many? Yeah, eight.

Now, tallies are great, but they're quite long winded and they waste a lot of time.

And if you've got huge amounts of tallies for working at a large number of things, that's a lot of lines to count your way through.

So the larger the number the harder it is to make a tally for it.

So ancient civilizations had to come up with better ways more efficient ways of recording numbers.

And a really good example that you probably all know about are the Egyptians.

Now the Egyptians used pictures to help them represent numbers and we know that those pictures are called hieroglyphs or hieroglyphics.

So they were being used in around about 3000 BC.

So 3000 years before the year zero.

And if you take a look at the bottom here, you can see some examples of the kind of images that might've been used to count using hieroglyphs.

I think my favourite has to be the very last one that looks like someone really happy jumping up in the air with a celebration.

And some of those images you might recognise what they are.

For example, one of them to me looks a little bit like a whale.

So what number would a whale represent do you think? It's written underneath, how would you say that number? Let's start from this side shall we? So I have a line, represents one we have a kind of an arch for 10, a swirl for a hundred, this looks almost to me like almost like something growing, that's 1000, looks like a pointing finger here for 10,000, whale for 100,000 and then a leaping person a very happy excited leaping person for six zeros, and then yeah, yeah.

So think we used as far back as 3000 BC.

And then in around 2,600 BC, so 400 years later, there are people living in Babylonia, the Babylonians, they use something similar to the Egyptians, their pictures though were slightly different.

And if you notice, the number six was 60 is involved a lot more in that system.

Now I can think of a system that we still use now whether number 60 is used a lot, in time.

Now they had pictures like the ones at the top, but they also represented something called a positional system.

Where they had little symbols like these almost like a Y with a hat on.

And depending on the position that they were pointing in or the position they were lying in they would represent something different.

So we can see really clearly we've got one represented by one of these marks two is to the next of each other, three there, and I quite like how four has now I've got three on top of the extra one underneath five, six and so on.

And then 10 would be represented by a shape on its side.

Then two of them for 20, three of them for 30, and I'm guessing four for 40, five for 50 and so on.

And we can see that because this number here is 59 we've got five tens and nine ones.

So actually, not a million miles away, from when we look at things using Dienes blocks.

It's quite similar isn't it? So have a look here, before we move on to our main task, there are some numbers here in what we call different scripts.

Now a script is basically a style of writing something, okay? A script just like these ones here, they're all scripts.

They represent the same thing, but they're written in different ways.

It's almost like I guess on a computer, you can have lots of different fonts for how you write something.

Comic sounds or Times New Roman.

All of those are fonts.

They're scripts.

Ways of writing the same thing but different styles.

And that's all we mean by number script.

It's a style of writing a number.

So, when we look at the next slide you'll see that there are a few examples of different scripts.

I'm going to disappear so you can see them more clearly on the screen.

So take a look.

You've got lots of different scripts there, okay? I've circled four of them.

And I'm assuming that some of these might look familiar to some of you, hopefully some of those will look familiar to all of you.

If you look at this one here, well okay, we see numbers like that every day.

And also here.

Some of you will see all those of these every day.

I think these ones would be quite popular for some of you to see on a daily basis.

Well, they're actually what we would call Arabic numerals.

The numbers we use in everyday school, they come from Arabic backgrounds.

They originated in India and made their way over to Europe, Western Europe in about 1,200 AD.

So that's after the year zero.

And they would have slowly changed from something that looked like this into the numbers that we would hopefully all recognise now.

Okay? I wonder if any of you recognise any of the others.

There are different examples there.

Hmm well, these are going to come in real useful for your investigation and your main activity today.

So let me explain that to you.

Now here you've got six different styles of writing numbers.

And for each of those six different styles, there are five numbers.

Let me illustrate 'cause this sounds tricky, it's not I promise you, it's not tricky to get your head around it's just you'll play with them a little bit in a moment.

So there are six different ways and five different numbers for each.

Let me show you.

Look here, there's one, two, three, four, five, and look there we go there's a sixth one.

So we've got six numbers in one script.

They're all very similar.

I might be tempted to write them in size order when I write them out.

There are other scripts where you can find six numbers from the same script.

So there'll be six numbers in this kind of style, there'll be six numbers in this kind of style, and so on.

Your task is to try and group them into their scripts into the same styles.

Now, if there is a 13 in this script, there's a 13 in all the others.

So you've got to try and figure out which ones are worth 13.

There are lots of them, there is an example for each of the number two so find the one that could mean number two in all of the other scripts.

Again, there's an example of a hundred for each of those scripts.

58, 83, 25.

Your job is to play super detective and see if you can figure them out.

Two is quite simple I can tell you for starters there's definitely one in this row that also represents two.

And it's really obvious.

So I wonder if you'll be able to match them up.

Now, this is where one of our key words comes in useful.

Well two of our keywords actually.

We were talking about similarities and differences.

Similarities means things that are the same, differences means that things are not the same, that look different.

Look for similarities that will help you work out what each number is.

Okay? So what you're going to need to do is try to find all of the right numbers from each script.

So what I would be tempted to do here, I might put it into a table.

So for example I might put them from smallest to largest I'm going to use the numerals I definitely recognise it to, 13, what was coming next? Oh yeah, 25, yeah 58, 83, and 100.

And I would probably create a table like so and try and find some others that would fit in.

Now, I can see a couple of others that already look like two.

They may help you.

If you recognise some of those other scripts and you can read them, you have got a super advantage.

And I'm very jealous 'cause I wish I could read more than one script.

So, have a go at finding all the twos, all the 13s, all the 25s, all the 58s, all the 83s and all the 100s.

And I will say, take your time with it, what you might want to do, if you've printed it out you could cut them up and move them around or you could draw them down, cut them up and move them around, or you could just write them by looking at the screen it's entirely up to you, good luck, fingers crossed, everything crossed for you, I think you're going to do a phenomenal job, so give it a great go, I'm crossing everything, come back and join us when you've finished.

Well how was that? I have to say when I did it, I took several attempts at getting it right.

I was finding it rather tricky.

So, I'm sure you did a better job than me.

Shall we take a look at which ones go together? I've represented them slightly differently I have not done them in size order this time on the answers.

Cheeky me I know.

So you'll just have to check it all off.

Here we go.

And I think there were a couple that were quite clear.

If we look down the twos column, really clear that these two lines must mean two right? This looks like a number two and so does this.

I also found a few of the hundreds quite easy 'cause look, the most recognisable thing about the number 100 is there's two zeros at the end well here, here and here, really quite similar, okay? Others, not quite as easy.

The 13 here I thought was quite simple 'cause that was clearly a three at the end, and that then made me realise that this must be worth 10.

So then the 25 makes sense.

Look, two tens and the five.

See what I mean there? Does that make sense the way I just explained that? I looked at what was similar so I could see if this is 10, this must be two tens, well the only number that had two tens in it was 25.

So this then must represent five.

So that then helped me find 58 'cause there's my five at the beginning.

Okay? Others were just really clear.

Really clear really clear, super obvious.

This one however, stumped me so many times I kept thinking right okay here's 24, oh wait no, there is no 24, and that was tricking me a lot.

And then I kept thinking oh, 93, Oh hang on there is no 93 mate this is 83.

So was tricky but then I realised that this must represent one because it's at the beginning of my 100.

Yeah? So lots of detective work was going on there.

So, now that you've done the detective work, let's get creative.

Using what you've just done.

Can you figure out how to write these numbers in each of those scripts? So can you write 23 in all of these different ways? We know what 20 is, we know what three is, so that will help.

Can you write 51? And can you write 12 in all of those ways? And now be patient, it took me several attempts until I was happy.

But, I know you can do it.

So you're looking to write 23, 51 and 12 in all of those scripts.

Best of luck guys, off you go and come back when you're ready.

You're amazing.

Tough going right? Well, I'm going to show you how I drew them.

Now, it doesn't have to be spot on and perfect, you're going to get the idea, I'm sure.

And then I wonder what skills you use to help you work them out, and as a final challenge, I'm going to say to you, can you find out who might use each of these scripts? I've purposely not told you 'cause I want you to go away and find out.

Well, here are the answers that I came up with right here.

Now I'm hoping that you started to spot how you could use those little clues to help you and if you did, amazing work guys, I've really enjoyed this session.

And I'd love to explore a little bit more about various number scripts and I think I might even go away and do that.

And I'd encourage you to do the same 'cause it's very very interesting.

Some of the number script systems are just beautiful.

Really pretty when you look at them.

So give it a go, do a bit of investigating.

Very well done on that.

I'm going to ask you now to pop away and take our final knowledge quiz, and then when you're done, just come on back so that we're ready.

Welcome back everyone.

This has not been an easy session.

There's been a lot of tricky stuff in there so you have done a phenomenal job seeing it through to the end.

I'm really proud of you and you should get really proud of yourselves, so, until we see each other again, from me Mr. C that's it, have a great rest of the day and I'll see you very soon.

Bye bye.