Lesson video

Hello, everybody is me, Mr.C.

Ready for our maths lesson today, continuing to reason about patterns and sequences and looking at identifying patterns.

Welcome back! Great to have you.

Well, welcome back.

Shall we get cracking?Eeeeh.

I think we should.

So let's start off with a little math riddle for you.

Here is and pay close attention.

Remember, in previous math riddles, I may have put little trick questions to try and catch you out.

This could be one of them.

Have a look here, it says a grandfather, two fathers and two sons went to the cinema together and bought everyone one move it to movie tickets each.

How many tickets did they buy in total? Okay, so we've got let's work this out.

We've got I'm going to do G for grandfather, F for father and S for son.

So we've got a grandfather, two fathers and two sons.

Hmm.

Hmmm.

Hmmm.

They bought a ticket each.

How many tickets did they buy in total? Five seconds.

See what you can do four-three-two-one and time is up guys.

The answer is.

This, I'm really sorry.

The answer is not five.

Sorry.

I've tricked you again.

It's another trick question.

Let me try and explain this to you.

Okay.

A grandfather here he is.

Two fathers and two sons.

Okay, well, this is clearly a father and this is clearly a son.

But they only actually bought three tickets.

Shall I explain why? Oop!The grandfather, is his grandfather, but he's actually this guy's father.

So, the grandfather is one of those two fathers remember we had grandfather, father, father, son, son.

So, grandfather, yeah, check.

You've got him, but he's also the father of this guy.

So, there we are, one ticket.

That's the same person, grandfather and also father to him.

Father, to him, but son to him.

So Father to him, son to him, and one son left.

So we've in fact got one-two-three tickets.

Sorry, that was a really cheeky little tricky one.

So remember, you can be two different things.

If you're someone's Father, you can also be someone's son.

So, this was a tricky little one there with a much simpler solution, but people always seem to think it's harder than it is to work it out.

It's just one of those cheeky trick questions.

Guilty of throwing one of those at you again, sorry.

You got it? Well done! Brilliant! All right.

You're going to need your equipment, your pencil, your ruler, something to work on, whether it's paper book or printouts and somewhere quiet with no distractions.

Our agenda then key vocab and learning is coming up in a moment with a number fit warmup.

Recapping our prior learning from the last few sessions, Roman numerals and in sequence activities and a function machine challenge.

I'm going to talk very little today, because I just want you to go and explore and put together all the skills you've developed and smash these activities.

So, key learning then, to identify a pattern.

And our key vocab pattern, sequence, digit, increase, decrease, term, and rule.

Brilliant.

Another word for increase we know is? Ascend, another word for decreases is? Brilliant!Descend.

You guys are experts, brilliant work.

So you know how this works.

However, I've given you a trickier one today.

Look at it, we've got to fit these numbers into our grid.

Now I've said to you, in other times when we've looked at these, look for the number that has the least options, and we've always had one with just one option left.

Usually our six digit number has got one six digit number left to put in there.

And it's an obvious start.

But look, ooh, five digits, we've got one-two-three-four-five-six of them left.

This is going to be trickier.

I am going to say though, start with your five digits.

And look at this one and this one, they will help you.

So this five digit number and this five digit number.

What do you already have, that will help you work this out? Aaahmmm! And Aaahmmm! Hopefully, that very, very subtle clue will help.

All right.

See how well you do fit in those numbers.

It's time to do your number fit.

Starter, off you go.

And welcome back.

Here we are, then, hopefully, you did what I had suggested.

And you started with those two that I pointed out, shall we just take a look at how they could have helped? Well, we know that both five digit numbers, so here's our five digit number column.

But we don't have any clues apart from the final digit.

So the final digit in this five digit number is three, the final digit and this one is five.

So I'm going to scan down my five digit column and look for one that ends in three, and one that ends in five.

And what do you know? There's one ending in three-two-four-one-seven-three.

Are there any others? No! So, two-four-one-seven-three, and let's cross that out so we don't we reuse it and make sure that completely crossed as well.

So same here, a five digit number that ends in five.

But all I know I would have used that one.

Here it is, four-one-three-eight-five, four-one-three-eight-five.

Brilliant.

And then I can start to look at the rest.

I can fill in this three digit number, because I've got my first digit and there's only one that starts with eight-eight-four-two.

And then hopefully if you've gone through the rest of those numbers in the same way, you should have some answers that look like you're ready.

Drumroll.

Brrrrrrrr! Well it was terrible.

This, scan over them check your answers.

I'm sure you did a brilliant job.

Proud of you.

Very well done.

Okay, well with that in mind, let's move on so that I talk less and you explore more.

All right, just to recap on Roman numerals, in Roman numerals, we're going to use letters to represent numbers.

If the larger number symbol is followed by a smaller number symbol, we add them together.

And also if they're the same, so X is bigger than I, so we would add the X and the I together to make 11.

Because X is 10, I is one.

Same with this one, V is bigger than I and I five and two, that's seven, and so on.

If the smaller number symbol is followed by the larger one, then we take it away.

So if it's I, which is smaller than X, it's 10 takeaway one.

So one less than 10.

Nine.

Okay, 10 less than the L is 50, so 10 less than 50 is, 40 and so on.

So just to recap, can you fill in these numbers.

Okay, got it? I'm going to do it at the same time.

Let's see if we can pace ourselves.

Ready? On your marks, get set, go! Just the orange box.

We'll worry about the sums in a moment.

Okay, so four.

One less than five.

Great, five, six is five, and one more.

Seven, five and two more.

Eight is five, and three more and nine is one less than 10.

Did you see what I was doing there? Did you see how my saying out loud helped.

So four is one less than five, six is five and one more.

I just find that quite useful.

So now we've done that.

Can we work out the answers here? Well, V plus V, V is five.

So five plus five is 10.

So, my answer would be X.

I plus I plus V, one plus one plus one plus one plus five.

Five and two more that's seven.

So, VII.

X and V.

10 and five that's 15.

Brilliant! X takeaway IV, IV is one less than five that's four.

10 takeaway four is six.

Six is.

Brilliant! X takeaway III? Well, III, X takeaway three that's seven.

So that's five and two more.

And X takeaway five and two more, so X takeaway seven is three.

Aiiit.

Aiiit.

Aiiit.

Yeah, got it.

Brilliant work, guys.

Okay, that's going to help you for something coming up.

Have a look here though.

First, I've circled for you one-two-three-four numbers on that hundred square that's in Roman numerals.

Remember, we have one here, and we have 100 down here, so it goes one-two-three-four-five-six-seven eight-nine-10-11 down here.

So let me write that in 21-31-41-51 and so on.

That should really be helpful.

So take a look.

Can you work out what those circled numbers are? Give it a go.

And remember, use knowledge that you already have to help you.

You all know really well.

How a number square 100 Square works.

You know where those numbers are positioned.

So use that to help you work out what those circled numbers are.

Go for it! Five seconds left.

And Your time's up folks.

So let's start with this one here.

If X is 10, XX must be 10 and 10 which is.

Yaaah.

20.

Okay, so XXI is 31.

So, the XXX must be 30 and one and five IV one less than five.

Yeah, 34.

Brilliant.

Okay, let's try this L is 50.

So 51-52 and so on.

So VIII we know is five and three more five-six-seven-eight.

So 58.

Okay, X-C-I-I hmm? Well, XC is 10 less than 100 that's 90.

So this must be 91 and by process of elimination, this must be 92.

Great.

So, use that to help you with what's coming up.

Here, you've got some more calculations, all in Roman numerals.

I want the answer in Roman numerals too.

Now when I give you the answers on here, I'm only going to show you the calculations in our number script that we would use on a daily basis.

I'm not going to give you the Roman numeral answers you're going to have to use your brain power and detective work to figure those out.

So just remind you I is one, V is five, X is 10, L is 50, C is 100, D is 500 and M is 1000.

Can you work out the answers to those calculations, and probably do it in regular digits first, and then convert your answer into Roman numerals.

Off you go and try your hardest.

I know you'll do brilliantly.

Good luck, guys.

Welcome back.

All right.

I'm going to show you the answers but not the full answers.

The final Roman numeral numeral answer was a bit of a mouthful.

You need to work out yourselves.

So take a look.

These are the calculations you were doing.

The answers are at the end.

Can you figure out what they would be in Roman numerals? I'm going to give you one of them for free.

Ooooh!Sorry, I gave you the easiest one as well.

Didn't I? XXX that's 30.

All right.

Give it a go.

If you haven't already done so.

And let's move on.

So, really quickly thinking about number sequences again, take a look at the one below.

Always ask yourself these three questions.

Is it increasing or decreasing? How do we get from one term to the next or what's the rule? And what are the missing terms? Well, what have I done to get from 13 to 26? What have I done to get from 26 to 39? Hopefully, it's the same thing.

If I wanted to just do a real quick and I do 26 takeaway 13 and see what my answer was, real quick in your heads.

So this time to get from 13 to 26.

I've added 13.

What about that? If I get from 26 to 39? What have I done then? Just spend a second, is it the same? Just add 13 on 26 and see if it is the same.

Give it a go take a look It is, isn't it? 26 add 13 is 39.

So our rule must be adding 13 so what would our next number be after 39? And then after that, and then after that? Yeah, you go it 52.

I'm going to go slow so you can keep up 65, 78, 91.

All right, you got it? Okay, the first number and the last number.

That will help you to work out whether it's increasing or decreasing.

Just to top tip.

Remember, if the last number is bigger than the first number, then it must have been an increasing pattern.

If the last number is smaller than the first number, then it must have been a decreasing pattern.

So take a look.

You are absolutely right.

If you have said that this is in fact, an increasing pattern.

It's getting bigger.

Isn't it? The sequence is bigger, 91 is bigger than 13.

The sequences ascending, increasing.

Great! Glad you spotted that.

So have a look at this.

You're going to be for each of these writing six numbers, the rule, but each one is different.

And the starting number is different.

So what I would do first to make sure I don't make any mistakes here.

Looking at my number sequence, I'm going to write down the first number in each sequence and it says to me here, the start point is 11.

So I'm going to write 11 down.

Here, the start point is what? Yeah, I'm here our start point is nine.

This one is brilliant.

And this one is.

Whoooo! So what we then need to do is work out the first six terms in each so you need to find the next five numbers for each one.

Because we've already got the first one.

So on this one, we're adding 10 each time.

Here we're adding five.

Here the rule is subtract 13.

Here, the rule is subtract nine.

And here the rule is add 100 but be careful.

Okay? When you're looking at negative numbers, if you are adding to a negative number, it almost looks like the numbers are going backwards.

So for example, minus two add one isn't minus three, it goes backwards, it would be minus one.

It's tricky to get your head around, but it does make sense okay? So just really be careful and think about that when you're adding to negative numbers.

It goes the opposite way to what your gut instinct tells you.

So have a go, working up the next numbers in each sequence, working out the missing terms. Good luck! So let's check out those answers.

Here they come ladies and gents.

Now hopefully, the one that I thought was going to be the trickiest one, the sneaky one at the end hopefully the majority didn't fall into the trap.

So well done if you remembered that minus 394 add 100 wouldn't have been minus 494.

That's a mistake that a lot of people would make.

If you didn't make that mistake.

Amazing.

If you did make that mistake, don't worry, because loads of people would have done the same.

I still have to think very carefully about it when I'm adding and subtracting with decimal with negative numbers which tricks me too Okay, Ready? So I have a challenge for you.

This is the final thing I'm going to be setting for you today.

Okay, no final knowledge quiz because we've been really working our brains to the limit today.

So take a look at our challenge.

Here it is right now.

So we've got two sets of function machines.

When I put a number in here, it goes through this machine spits out into this one and out at the end.

So for example, if I'm putting the number four in here, four would go in, I'd add four to it, spit the answer into that.

And whatever the answer was, I'd multiply by five to get me this answer.

So let me give an example if I was putting three in, three goes in.

Three plus four is, yeah, seven.

Seven times five is.

Okay.

So this goes in, that comes out.

The rule is, add four, and then multiply by five.

On this one, we've got the number coming out.

So we've got to imagine it's in reverse.

So we're going to be using and I'm just going to pop this here the inverse because we're going backwards.

So instead of starting at this side, we're starting here.

So instead of multiply by three, we'll do the inverse will be 45.

Hmmm!Three, and then whatever the answer is, will be, hmmm, five, we're using the inverse.

I'm just going to do the aggressive hermeto again, so it'd be 45 hmm three, and then whatever that answer is, hmm five.

Makes sense? I hope so.

Because I'm just making strange noises at you otherwise.

Okay.

Give it a real good go.

Remember, check check, check as you go along to make sure what is going in and what is coming out links and make some sense.

Good luck with that challenge, folks.

Here it is.

Pause and come back when you're ready.

Hello, hello, hello, welcome back.

Okay, let's take a look at those answers and see how you did with them.

I'm sure you did a fantastic job, here they are checking them out.

If you've got them, and you smashed them then I'm really proud of every single one of you, and if you didn't, but you just kept going.

I'm equally proud because being resilient is a wonderful personality trait.

Good job, guys.

Okay, So we've heard quite a session again today.

Lots things to work through.

Don't forget if you didn't quite get the Roman numeral answers.

Go back now and see if you can figure them out use that hundred square with the Roman numerals to help you.

And I very much look forward to seeing you in our next session.

So have a wonderful rest of the day.

Look after yourselves.

Be kind to people around you and take care.

So for me, Mr.C.