Lesson video

Hi everybody, it's me Mr C.

How are you? Hope you're well, hope you're ready to learn cause I'm certainly ready to do some learning with you.

Alright, we are continuing with our reasoning with patterns and sequences and today we're going to be looking at identifying and completing number sequences.

So, let's take a little look at what's.

Before we look at our agenda, I've got a little brain teaser for you and here it is.

Now, this one's called Crazy Eights.

You've got eight number eights, so eight, eight, eight, eight, eight, eight, eight, eight number eights.

Now, you can arrange those any way you like and you're going to try make a total of a thousand but you're only using addition.

So for example, you could use two of the eights and put them together to make 88.

You could use four of the eights to make 8,888 but you'd have gone too far there because you can only use addition, you can't use subtraction.

Now, you have to use them all to get to the answer.

Can you use eight eights to make a thousand? Have a go, I'm going to give you a minute.

Okay, so now might be a good time for you to pause if you need to.

Okay folks, how did you do? Did you get there? Okay, I'll show you how I did it.

Shall I put you out of your misery? This is what I did.

I started with 888 and I added 88, 8, 8 and 8 because 888 add to 88 gives us 976.

I've got three eights left over, three times eight is 24 976 add 24 gives us a grand total of 1000.

So if you got it, brilliant! If you got a different way of doing it, I'd love to know.

So, I think we are, we've oiled our brains a little there, we're ready to go.

Shall we move on.

So, you're going to need, your pencil, your ruler, your usual thing you write on, if it's the sheets that you've printed, brilliant, if a book you're working in, amazing.

And you're also going to need somewhere with no distractions.

Now, our agenda for today.

Key learning and vocab is coming in a moment, speedy tables then, and then a recap on Roman numerals, then we're going to look at how do you spot number sequences, filling in some terms in a number sequence, a number sequence challenge, and then a final knowledge quiz.

So it's quite a busy agenda today but they're all short, sharp activities and that we'll zoom through.

Okay, so our key learning is to identify and complete number sequences.

And our key vocabulary are sequence, increase, decrease, ascend, descend, rule and term.

Now, you'll notice I did a bit of pointing for some of those there's a reason behind that.

If a sequence increases or ascends, it means it goes up or gets bigger.

If it decreases or descends, it means it gets smaller, remember that.

Okay, here's your speedy times tables challenge.

I'm not going to talk you through this, you know how it works.

Pencils on the ready, and go! Think you're ready? Showing the answers, let's take a look.

Here they come.

I'll zoom in on those so you can just check them out.

Alright, how did you do, got them all? Hope so, let's move ahead.

So let's just recap then on our Roman numerals.

This is the first thing I want you to do, I have given you the Roman numeral hundred square over there to help you.

You've got your Arabic numerals down one side, so 100, 54 and 48 and then also 25, 36, and 13.

Can you write the Roman numeral equivalent for each of those? Now remember, that hundred square is there to help you but don't rely on it, try and make sure that you can figure them out for yourselves.

Now, I'm simply going to give you a countdown.

I'm not even going to give you time to pause it, I'm going to count down from 20 and then reveal the answers.

So, are you ready? Pens good to go? Go! 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, nine, eight, seven, six, five, four, three, two, one and here come the answers.

You get them? If you did, mega style well done.

Great job, okay.

So let's move on then and talk a little bit about number sequences.

So, have a look at the sequence below, okay? We're going to think about what kind of sequence it is and how we know.

And there's three questions I want you to think about.

Question number one is, is it increasing or decreasing? So increasing, getting bigger, decreasing, getting smaller.

What do you think? And then, what are we doing to get from one term, each number in a sequence we call, the term, so from this term to that one.

What step do we follow to get from this term to the next one? So what's the rule to get us there? Three, six, nine, and so on.

And then we need to think about what are the missing terms, okay? So let's just break it down, shall we? Well, I can understand what the rule is because I know I'm counting basically in threes, three, six, nine.

I'm adding three on each term.

So if these first two I'm adding three on, I must be doing it for all the rest of them.

So I might just write that in to remind me.

So the rule here so far is add three to get to the next term.

So after nine if I'm adding three my next term would be, yeah, 12, and so on.

So, we can agree that these would be the next terms in our sequence.

So, does it increase, get bigger in value, or decrease, get smaller in value? So look at the first and the last.

Is three bigger or smaller than 21? It's smaller.

So the number we started with is smaller than the number we ended with.

So it's gone small, getting bigger, bigger, bigger, biggest.

So it's gotten bigger in value, it's increased, yeah? All making sense so far, right? None of this, is anything that you don't know.

This is all pretty straightforward.

So the information we've got so far.

Our rule is that we're adding three and that this is an increasing number sequence.

And we now know that the missing terms, remember terms are what we said are the numbers in a sequence, are 12, 15, 18 and 21.

Pretty straightforward, isn't it? Makes sense.

So now try these.

Go through the same thought process, is it getting bigger or smaller? What's happening to get from one term to the next, so what's the rule? And what are the missing values? What are the missing terms in our sequence? Give that a go, think of all the things we just talked about, key words to remember, term, rule, sequence.

Have a go and see if we can fill them in, perfect.

And I'm going to talk through it slowly as you're doing it.

I can see here that actually what's happening is, the number in front hasn't changed for these first three terms but have gone two, four, six at the end.

So 3.

2 to 3.

4 that must mean that I've, okay, it's getting bigger so I'm adding something.

So it's increasing, I've added nothing at the front, so nothing for the whole number.

Point, what's our difference two to four, 0.

2.

So I'm adding 0.

2 each time.

So if I add 0.

2 to this one I have to do the same.

And so on.

3.

6 add 0.

2 would be 3.

8.

0.

2 would be four, 4.

2, 4.

4.

Let's take a look at this one.

My first term is 75, my next term is 70.

The term after that is 65, so I can see that these numbers are getting smaller, so another way of saying getting smaller is to say that those numbers are decreasing, so this is a decreasing sequence.

It's getting smaller.

What have I taken from 75 to get to 70? Okay simple, I've taken five away.

So the rule is, subtract five.

So now I need to work out my next term.

75, 70, 65 oh, 60, 55, 50, 45, okay? This one is increasing, this one is decreasing.

Really straightforward, hey? Okay so, let's think about this.

Something else you need to remember are negative numbers.

Remember a negative number is when you put the minus sign in front of the number.

So anything below zero, anything lower than zero.

I often think of a thermometer, that's an easy way of doing it, thinking of temperature.

In number sequences, sometimes people forget that zero itself does still count as a number.

People think because it's zero, if you have nothing in front of you, you have zero items in front of you, there's nothing there and that's fair to say when you're looking at physical objects but zero in itself does have a value in a number sequence.

So if I was counting back in twos from four, I'd go, four, two and then I wouldn't go minus two, look, one two, one two, I've landed on zero.

So zero can have a value in a number sequence.

So from zero going this way your numbers would increase, going backwards they would decrease.

And we represent a negative number by having a minus sign in front of it, okay? This number is a lower number than this one.

Think of it in temperature.

Would you rather be minus one in a freezer or minus 10? I think neither, but minus one would be the least horrible.

Okay, makes sense? Hopefully I'm not just waffling at you.

So, have a look here now.

Try these sequences using negative numbers.

Now remember, those key things we need to think about, what's the rule that's happening? What terms do I already have? And what are the missing terms? Can I give you a headstart and then I'm going to go through it, talking through my thinking as well.

If you need to, use the number line.

Okay so in this one, I'm starting on three and I'm going back to one.

Three.

So I've done two bounces and so I must have taken two away.

Let's check it.

Yeah, okay so in this one I'm taking two each time.

So now one two add, minus three, minus five, minus seven, minus nine.

And here, 20, 10, zero.

It's getting smaller, let me just remind myself that's decreasing, that's decreasing.

What have I taken.

Okay, that works, so taken 10.

So them I would go from zero, take away 10, what would that be? Oh okay, yeah brilliant, minus 10.

Oh I think I've got this now.

There you go! Negative numbers, not something to feel negative about.

They're actually really simple.

Okay so, if you got those, brilliant.

Alright so, take a look here, here is your main task.

I'd like you to work out the rule for each of these sequences and fill in the missing terms, okay? So just think to yourself, what have I done from this first number to get to the next? Now on this one here, this is trickier because I don't have the first number.

So I'll work out what's happening between these numbers and if I'm adding something to go this way, to go the opposite direction or to do the opposite of that, which is the inverse which is subtract.

So, if you have to work backwards on a pattern, you do the inverse of what you've done for all the rest of it.

That's the only rule you need to remember, the rest of the rules you need to work out for each sequence.

Give it a go and I'll see you when you're ready.

Okay, hopefully you managed to work your way through those sequences really nicely and you've been pretty accurate.

So let's take a look at the answers.

Check them over, pause the video here if you need to, just to check them.

Alright, how did you do? Did you work out the rules? So for example, did you know that on this one it was a decreasing sequence? And did you know that you were taking two away each time? Well, amazing! Okay so, have a go now at this.

So here, you can see that you've got sets of numbers in different colours.

You've got some purple, some blue, some green, some red and some black.

Now all the black numbers go together to make one sequence, all the red to make another, all the purple to make another, and so on.

What you need to do is arrange each of those so that they create an increasing sequence.

A sequence where the numbers are getting bigger.

So, to remind you, you going to go from smallest to largest.

Can you now arrange those into five different sequences? A pink sequence, a blue sequence, a green sequence, a red sequence and a black sequence.

Have a go and I'll see you soon.

Excellent, I'm sure you did an amazing job.

Let's just check over then on those sequences, shall we? Wonder if you could describe what's happening.

Let's have a look at that first sequence, what's happening in the black number sequence? Yeah, we're adding three each time.

What about in the blue? Yeah we're adding two each time.

And here? Adding 10.

And here? Yeah good, well done you're adding seven.

And what about here? Yeah, adding 0.

2.

So, go ahead and write those rules next to it to remind you.

Very well done with that, if you go those all right, you really are blowing me away.

Now, if you haven't already done so, that's it for today.

See how quickly we whizzed through that? Take the final knowledge quiz and come back as soon as you're ready.

See you in a moment.

Okay, welcome back everyone.

Great job, you've worked extremely hard again today.

Make sure you're always looking out for number patterns, they're everywhere, sequences and number patterns are everywhere.

And if you're anything like me, every time you see numbers grouped together, you'll start trying to think, I wonder if there's a pattern here, I wonder if there's a sequence.

It's not a bad thing, in fact probably quite a good thing to think about the order of the world around you.

Oh well, enough of me talking away.

Enjoy the rest of your day, I really look forward to seeing you in our next session.

I will see you very soon, so from me, Mr C, bye bye.