Lesson video

Hey everybody, great to see you again here on Oak National Academy.

Thank you for joining me, Mr. Ward for another lesson in our unit on multiplication and division.

Wherever you are in the country I hope you are in a nice quiet spot right now and you're ready for your mathematical learning.

I have just been busy keeping myself entertained with my new favourite toy which is fantastic for scratching my itch, especially if I'm trying to teach with my video lessons.

I can also pick my nose but I'm not going to do that 'cause that would just be revolting, wouldn't it? So, to stop me messing around with my new favourite toy I think it's time to make a start in our learning.

So let me ask you one question.

Are you in a quiet space? Are you free of distraction and are you ready to learn? Yeah.

So am I.

Absolutely.

Let's make a start.

We're just about to make a start from the main learning but before that there is, of course, always time for a mathematical joke which is one of the customs of a Mr. Ward lesson.

This one's a belter, it must be 'cause I've been chuckling for like three minutes to myself which I know is a little bit sad but it is a quite funny joke so I hope you enjoy it.

They say there are three kinds of people in this world.

Those that can count and those that can't.

If you think you've got enough out of the joke which is even better than mine and how could it be any better than that absolute belter and I will be sharing details at the end of the lesson on how your parent or carer can send in your work or mathematical joke to us here at Oak National Academy so please keep watching the video until the very last slide.

So, a little overview of today's lesson we're going to be recapping on some of our prime knowledge.

So, if you haven't watched any of the previous lessons in the unit on multiplications and divisions it might be worth doing so.

Lesson one is on multiples of factors, lesson two is on factor blocks, and lesson three is on prime numbers and that's all going to be useful information to today's lesson.

Then you're going to have a talk task in which I introduce the concept of a factor and multiple chains and how we can create long chains by using factors and multiples.

Then we're going to develop our learning a bit further by looking a alternative chains.

How we can change and adapt the rule slightly to find different source of chains still connecting with factors and multiples.

And then I'm going to hand over the reigns to you and you're going to have a go at the independent task in which you try and create the longest alternative chains that you can and then, as always, at Oak National Academy, we ask you to end the lesson by having a go a the quiz to see how much of that learning from the lesson has been embedded and how confident and familiar you are with some of the key terminology and key concepts taught.

It's important to have all he right equipment as we always ask before the lesson.

So, please make sure you've got a pencil or something to write down, paper or a book that you might have been provided to by your school.

Now, it doesn't have to be green paper it can be lined or just plain paper or even the back of a cereal box.

Anything you can do your jottings on.

And you might find it useful to have a ruler because rulers are useful for presentation but they are also great as some sort of mental arithmetic, almost a calculator 'cause you can count, you can divide, you can add.

You can do all sorts with a ruler.

So, all of that equipment.

If you've got none of it, you need to go and find it.

Please pause the video, go and get exactly what you need.

Get yourself in the right mind frame and then when you're ready to resume the lesson, press play and you can continue enjoying this.

See you in a few moments if you need to go and get what you need now.

Before we start introducing the new concept for today we're able to get warmed up.

So, I'd like us to have a go at some more speedy tables.

There are two tables on your desk with missing values.

Can you time yourself and try and complete those tables? I think a good amount of time is about three minutes per table.

But if you don't feel like you have to challenge yourself with time you can take as long as you need to complete those tables.

'so it's a mixture of multiplication but you might have to use some inverse to try and identify the missing tables.

So pause the video, complete the tables as quick as you can and then come back and check your answers with mine.

See you in a few moments.

Right, let's just have a quick look a your answers.

I wonder how long it did it take you.

This is a great one to keep going back to and back to and back to and then you can try and beat your score each time to try and sharpen your mental arithmetic in the speed in which you can recall your numbers and your multiplication and division.

I said earlier on that we're going to review so I'll keep covering again if you're not that familiar with the terms multiples and factors you might want to go all the way back to lesson one in the unit.

Hopefully, it's smooth where it's not too unfamiliar to you.

Can you define the term and there's a good way to check So, I've got on your board 24 is a multiple of and 24 is a factor of.

Can you define the words multiples and factors and then give some examples using the two words and the number 24.

Spend a couple of minutes on that and then go on to the next slide.

A multiple is the result of multiplying a number by an integer.

So, for instance 24 is a multiple of 6 because 6 can be multiplied by 4.

24 is a multiple of 12 because 12 can be multiplied by 2.

24 is a multiple of 4 'cause 4 can be multiplied by 6 and so on and so forth.

A factor on the other hand is a whole number that when multiplied by another factor or factors makes a given number.

So, 24 is a factor of 72 because it can be multiplied by 3.

24 is a factor of 240 'cause it can be multiplied by 10 which is just an example of being multiplied by factors the yes in the bracket I can multiple 24 by 5 to give a 120 then multiply it by 2 to give 240 because 2 is also a factor of 240.

With that knowledge of factors and multiples we're going to be able to create what we call factors and multiples chains.

A factor and a multiple ain is a chain of numbers which is made of connecting factors and multiples.

So, the first chains we're going to make is going to be a chain of numbers that either have factors or multiples in the chain.

It can be played as a one player game or a two player game.

So, depending on where you're working and who you're working with you can play this on your own or in a group with somebody else.

Now, I would like you to watch very carefully 'cause I'm going to model how this game is played for the talk task and then you can do that independently.

So, number one you need to pick an even number from the grid opposite.

You can see I've got the 1-50 grid.

Pick an even number from the grid and then cross it out.

So, I'm going to choose 26 and that's the start of my chain.

Now that 26 is the start of my chain, the next number must be a factor or multiple of that first number, of the previous number.

So 26 is my first number so I must pick a multiple or a factor of 26.

So, I've gone for a factor 'cause I know two is a factor I know that 2 is a factor of 26 because 26 is an even number and therefore it must be a multiple of two.

Then we're going to continue to build the chain by choosing a factor or a multiple from the grid that has not yet been chosen and it has to be a factor or multiple of the previous number until there are no longer any possibilities.

So, now I must pick a factor or a multiple of two to continue the chain, and so on and so forth.

But here's an example of my chain.

So, I went for 26, then I went for 2, then I went for a multiple of 2 which was 18.

Then I decided to go for a factor of 18 which was 9.

Then I decided to go for a multiple of 9 which was 27.

Then I decided to go for a factor of 27 which was 3.

Then I went for a multiple of 3 which was 30.

Then I went for a factor of 30 of 30 which was 15.

Then I decided to go for a factor of 15 which was 5 and I ended that.

I could've continued.

So, I could've continued by finding 10 which was a multiple of 5.

Interestingly I could only have gone for 1 as a factor of 5, couldn't I? Because a prime number means that there are only two factors.

Five is a prime number because it's only got five and one as a factor.

So, I ended my chain now but it could've continued.

It could've gotten bigger and bigger.

So, I could've gone 5 to 10.

And then I could've gone 10, I could've gone a multiple of 10 is 40 and so on, so forth.

So, my chain could actually have expanded and gotten bigger and bigger and bigger.

So, your chains don't have a limit.

You can use as many as you can 'til all possible possibilities, all possible factors and multiples for the previous number have been exhausted and you can no longer continue that chain.

Why don't you have a go a one now before the talk task on your own.

Remember the rules.

Pick an even number from the group, cross it out, then that is the start of your chain and then you must continue the chain by picking a factor or multiple of the previous number.

How many numbers can you make in your chain? Have a go now on your own.

Pause the video, have go.

Cross out the numbers every time you use them then see how big your chain can be.

See you in a few moments.

Right, now that you've had a go at that on your own, I wonder how many numbers you did come up with your chain.

Apparently people have been known to create chains that are in a 1 to 50 grid.

Up to 42 numbers.

And in a 1 to 100 grid, they've managed to produced chains of over 74 or more.

Over 70 numbers I should say.

So, that's a lot of numbers in the grid, okay.

And depending on which numbers you choose.

So, now that you've had a go and you've practised and you've followed my model example, you're going to have a go on your own or with a partner at creating your own factors and multiples chain.

So if you want to play on your own.

This will be the screen that you can use or that you can write down on our page or print off.

I wonder how big your chain can be.

So, there's a 1 to 50 grid, pick an even number and then decide whether to do your factor or multiple.

You don't have to go alternately, you can go factor, factor, factor, you can go multiple, multiple multiple or you can go factor, multiple, factor, multiple.

It's up to you.

Okay.

Try and create the biggest chain that you can.

If you have a partner, this is how it might look.

You'll both have a grid and you can pick a number from your grid but make sure you cross off the grid both sides as you go, okay, and see how big the chain that you can make with a partner.

So, for instance, you can see that we've began by starting on 26 then player one in red went for 2 then player 2 went for 18, 9, 27, back and forth, back and forth, okay.

Because you're playing with two partners and there are two 50 grids, you'll find that actually the chain will be very long and there are lots and lots of options there.

So take your time and make sure you're following the rules every time.

Remember those rules.

And it is good that you might want a print off which will allow you to play.

If you have no printer you could write this down on your paper or book and follow it and then just cross off the numbers as you go.

Okay, I'd like to know what your longest chain was.

Obviously, we can't share them right now so perhaps you can speak to your parent or carer about sharing your work, details of which I will give at the end of today's lesson.

But there are some questions for you to consider and I hope you were talking about this while you were doing your multiple and factor chains.

What was your longest chain? Did you find the number two was used a lot? Did you find any numbers stop your chain from developing? Are there any numbers to avoid? Now, of course, chains can get very, very long but you might find that two is an even number and it's a multiple of half the numbers on that grid, isn't it? So actually, two is always, ever present and will probably be involved in a the chains.

Whereas one, there are of course multiples of one.

But as a factor it's also involved in all the other numbers as well.

So, a factor, one is a factor of all the other numbers but it doesn't really go anywhere else after that.

There are other numbers like prime numbers that you might find kind of reduce dramatically the length of your chain because there's actually very few options you can go afterwards with only few places you can go with it.

Now that you've had a go in the talk task, and you shared your work with each other and discussed it, and hopefully created some nice, long chains.

We're going to look at alternatives or alternating chains.

So, alternative chains using 100 square.

So, we're going to expand it now we're going to double the amount of numbers that you've got from 50 to 100.

There are alternative chains we can make changing the rules and using 100 square grits that we're now going to have double the amount of numbers which in theory should give us double the amount of options and therefore our chain should be even longer.

So hear are the different options that you could use.

There are chains which alternate between a multiple or a factor each time.

So whereas before you had a choice between a multiple or a factor you'd go multiple, multiple or factor, factor.

This time you must go multiple factor, multiple factor.

It has to alternate each time.

You cannot have two multiples together, you cannot have two factors together.

So using an alternating chain, what's the longest that you can make? You can see my example there was 40, a factor of 40 is 10, a multiple of 10 is 100, a factor of 100 is 25, a multiple of 25 is 50, a factor of 50 is 5, a multiple of 5 is 45, a factor of 45 is 9 and so on and so forth.

You can continue that chain.

A second chain, is a chain that is made up only of multiples of the first numbers.

You select an even number.

You probably want to star with a low number and then all you can do is, the longest chain you can make, only using multiples of that number.

So, for instance, I've got four there.

So, he next multiple I chose was 12 and then I decided to do 24, and then I did 48 and 96.

I can't go any further with 100 square of 96.

The next multiple of 96 would be 192 if I was to double it.

So, you see that that chain is quite small.

But I wonder what is the longest multiple chain you can create only using multiples and starting off on an even number.

Chains which are made up of factors of the first number only.

So, this is the third option, the third alternative chain that you can make.

You start with a number and then you can only use factors of that first number, or the previous number.

So, I started with 100 and then my first factor was 50 and then 25 is a factor of 50 and then the next factor is 5 and then 1.

I can't go any further than 1, so actually that chain is ended.

A five number chain.

I wonder how long you can make your chains that have multiples and how long you can make a factor chain.

So, now that I've explained the rules, its over to you to have a go at making alternative chains.

The three options there, the three possible alternative chains you can create.

How may different chains can you create for the three different types of alternative chains? Use 100 square.

Either print it off or write it yourself.

And how many different chains, and how long can you make them trying out the three alternative chains.

So, that's just a reminder of number one, you can make a chain which alternates between a multiple and a factor each time.

You can, number two, you can make a chain that's only made up of multiples.

And number three is a chain which are made up of factors of the first number only.

So, all those factors must be related to the number.

If you're doing this, here's a grid that you can use.

You can print this off or you can replicate that or you can see there's not a big space there for a chain.

You may need more space that because, actually, you might find out that your chain goes on and on and on.

You can create a really big chain.

Like I said, some chains have been known to be more than 60 numbers long within 100 square.

So, you have gotten your work cut out to see what goes on, 'till you've exhausted all the possible options.

And alternatively, if you want to play against somebody and make it a litt;e bit more competitive you can do that.

You can try and make the longest chain as opposed to somebody else, so the winner might be the person with the longest chain.

The winner might be the person that makes the smallest chain, he shortest chain, depending on how you adapt the rules to suite the game that you want to play.

So, as long as you follow the rules of each alternative chain then you will be exploring your math, so there's a bit of flexibility there in the task that you complete.

So, pause the video now.

Try and make, maybe, a chain for each of the alternative chains, or, you might decide to make two or three or one of the types.

You might be on your own, or you might be working with a partner.

Either way just have fun exploring numbers, try and spot some visible patterns.

While you're doing that, discuss what's making it bigger, what factors are behind the chains being small.

Which chains generally create larger chains? Is there a number that is difficult to continue a chain from? And just explore as you're doing your work.

Let's look, I hope you enjoy the tasks and I'll see you, hopefully in about 10-15 minutes.

See you soon.

Okay, now we can't share our chains today with very much an open task in which you create your multiple or factor chains and your alternative chains.

However, if you would like to share with us your work and show us what you've created, especially if you've come up with a really, really long chain.

Or, you've spotted some patterns that you just definitely have to share with us 'cause you think that it'll make our knowledge better id love to hear from you.

I'm going to show you some information in a few moments time in which, how your parent or carer can share your work with us here at Oak National Academy.

So, please keep a hold of anything you produce and if you happen to keep hold of it, maybe show your teacher next time you see your teacher.

Or, show your friends next time you get an opportunity to show them what you've created and see who's come up with the biggest chains.

Now, those who are not quite ready to finish, and don't want to put away their ruler and pencil, I'm really enjoying the lesson on multiple and factor chains I've got an extension challenge for you so please pause the video and have a go by reading the instructions carefully on your page.

Now, I really enjoyed that lesson.

Again, it was a very open lesson.

There's no real wrong answers really, just exploration of the numbers and of multiples and factors.

So, I really hope you enjoyed it and I hope you took away the very fact that maths can be fun and it can be open and then it can be creative.

I really enjoyed doing my own multiple and factor chains in my own space here at home.

Now it's time just to make sure that that information that we taught to day has been embedded and you feel confident with the concepts.

Not only on multiple and factor chains but also about key recovery of prime numbers are factor slogs of factors and multiples.

So, please find the quiz have a go at it and then when you've completed it, come back and finish the video off.

See you in few minutes.

Best of luck with the quiz.

As I mentioned previously you may have created some fantastic factor and multiple chains.

You probably created really long ones or you may have spotted some interesting patterns or have some of the numbers seem to create different results.

You may be so proud of your work you want to share it with us here and we would love to see it.

So if you've got a mathematical joke or some work that you're really proud of, you can ask your parent and carer to share that work with us here on Oak National Academy at Twitter, tagging @OakNationalAcademy and #LearnwithOak.

Okay everybody.

Unfortunately, we've run out of time now so that means the end of the lesson.

I think you all deserve a we earned break for all that hard work that you did there today with factors and multiples chains.

Give yourself a high five.

Or a pat on the back for a job well done.

I look forward to seeing some of you here on Oak National Academy as we continue our unit on multiplication and division.

So, until I see you again, have a great rest of day.

Bye from me, Mr. Ward.

See you soon.

Bye-bye for now.