# Lesson video

In progress...

Hello, everybody, thank you for joining me Mr. Ward here on oak National Academy once again.

Today I'm quite excited 'cause I'm going to start brand new unit on multiplication and division.

There'll be 15 lessons across this unit, all the lessons, of course can be found on Oak National Academy.

Now today's lesson, we'll be starting the unit by focusing on multiples and factors, discussing what they are and how we find them.

Now I need to be free of distraction, and ready to focus throughout the duration of this lesson.

So pause the video while you get everything you need.

Or find a nice quiet space and then resume when you're ready to go, see you in a few moments.

In case it's the first time you've come across a Mr. Ward lesson here on Oak National Academy.

I just like to explain that before the main learning.

I like to start with a mathematical joke to hopefully make smile it definitely makes me crack up, so it puts me in a good mood for my learning, it always gets is using a bit of mathematical vocabulary and gets in the mindset for our mathematical work for the day.

So today's absolute belting joke is this.

Why do plants hate maths? Because it gives them square roots.

Some of you must have been way ahead of me there and knew what was coming 'cause I could hear the grown miles and miles away.

But I'm in a good mood now and I'm ready to go.

So let's make a stop.

The unit lessons only follows the same pattern.

Ultimately, it will change today's schedule for the lesson starts with a new learning we introduce factors and multiples and kind of identify some of our prior knowledge.

And then we're going to do a talk task which can be paused you can do on your own you can do in groups or pairs.

And that's when we will look at finding factors and strategies we might need to do that.

Then we're going to take our learning a bit further and expand it by looking at how we can use our knowledge of facts and multiples to identify mystery numbers.

And now once we did a couple of examples of that, and we've worked through systematically, that's going to be one of our big words they systematic.

Once we work systematically through and identify some of those mystery numbers, then I'm going to give the reins to you and you're going to have a go independently trying to find some further mystery number puzzles, but on your own without any assistance from me.

And then of course, as is a custom here, at Oak National Academy at the end of the lesson, we ask you to go and find the quiz and have a go and try and see how much of that information has been embedded in you from today's learning.

As always, it's important to have the right equipment so we can get the most out of our lessons.

You going to need somewhere to write something down with pencils hopefully the ideal because you don't rub it out.

And it is lightweight and you're good to use.

You need a ruler and you need some paper, ideally grid paper but any sort of paper will do or the book that you may provided for your school.

A rubber in a Mr. Ward lesson is optional because I think robbers spent far too much time rubbers take too much time.

I prefer see somebody put a line in the work.

And then they can say, "I put line through it "because I realised it was a mistake, "I spotted mistake, and this is my correct answer, "which means that I've learned "from my misconceptions".

And that is a fantastic demonstration of how mathematical learning should go.

So don't spend forever rubbing out your work.

It's not an art lesson.

What I want to see if mathematical thinking people identifying where they went wrong, and how they're going to fix that.

I should just explain that every time you see that handsome face in the top right hand corner of that icon with a question mark, that generally indicates that there's a question or two or a task that I require you to have a go at on the screen.

So wherever you are home in the classroom, have a go, you can do it on your own, you can reflect on it, you can talk with somebody else's maybe there are groups of people there's always something for you to do.

You see that icon look out for it.

Have a go whatever is on the screen.

Now today's warm up is connected to your timetables, because the unit is going to be on multiplication divisions.

And it's fundamental that we know on timetables, it's so important.

So, if you're still struggling with some of your timetables, I implore you to go home and practise, do a little bit daily each time.

It's so important that you can go between your multiplication and division tables and are confident and familiar, and you can go quite speedily through it makes it so much easier.

So your first activity is a warm up.

You can see that there are 100 Square for multiples of seven and 100 Square for multiples of six.

Can you correctly identify the multiples of seven on your hundred square? And can you correctly identify the multiples of six on your hundred square? Pause the video now spend as long as you need and then resume when you're ready to check your answers.

Best of luck.

Would you very quickly check our answers, you'll see that the multiples of seven I've circled all the way and they've got two in blue.

And the reason I've circled those two in blues, is that for some reason people seem to think that once they've finished at 12, lots of seven to 12 timetable, they.

that's it that's the end of multiples that is the multiples of seven doesn't go on but of course it goes on inventively, multiples of seven go off forever.

And you can use your timetable.

In fact, you can use your 10 times seven to help you work at any multiple seven, because 91 here is actually 13 lots of seven.

How do I know that? But I know 10 lots of seven is 70 and three lots of seven is 21 so I team them together to makes 91.

13 lots of seven.

Likewise 98 at 14 lots of seven.

How do that Mr. Ward? Well, because I know 10 lots seven is 70 and four lots of seven is 28, add them together, I've got 98.

So with that mindset, lets look multiples of six.

And just check that you've got all the correct multiples of six up to 12, lots of six.

You would have noticed that they're all even numbers as well.

However, you notice that I've also got four multiples of six within the hundred square, which are beyond our 12 timetable.

12 times six, but that's okay, because 96 for instance, is 16 lots of six.

How do I know that Mr. Ward? We don't have a 16 times table? No, you don't.

But what you do have is 10 lots of six, and six, lots of six, for 10 lots of six is 60 and six, is 36 add them together, I get 96 and that shows me 16 lots of six.

So just to reiterate, multiples are beyond the 12 times table they go on and on.

But you can use all your knowledge that you've acquired from your one to 10 times tables to work out the multiples of any number.

So, we introduced the concept of multiples and factors.

Now what are we asking you to do, as part of the unit is to bring in prior knowledge.

So you should also already be familiar with multiples of factors, having used them in your timetables, for instance, but it doesn't matter if you're not comfortable.

It doesn't matter if you haven't done it before, or you've missed out on that, 'cause we are going to revisit it now.

But any prior knowledge you already have will be a bonus.

And if you find that you already know this, you can move forward through the lesson at a quicker pace than if you just need a bit of revisiting of this concept.

So three questions for you to think of, first of all, as you can see on the board, I've given an example of eight is a multiple of and eight is a factor of.

What do know about factors and multiples? Can you define these terms, can you explain and define what those words mean, Multiple and factor? And then can you give me some example using eight as an example, multiples of eight and eight is a factor of what? So three things for you to do.

Pause the video if you need a little bit extra time.

And I'll speak to you in a few moments.

Probably just spend a few minutes writing down some examples and you've written down your definitions or at least you've been verbally discussing them.

You don't have that exactly same terminology as long as you understand what multiple and a factor are and how they are different and how you can identify and find them.

So these are my definitions a multiple is the result of multiplying a number by an integer.

So, sound more complicated than it is, basically eight is a multiple of four because four can be multiplied by two to make eight.

And a factor on the other hand is a whole that when multiplied by another factor or factors makes a given number, so eight is a factor of 80, because I can multiply eight by 10 to give me 80.

I can also multiply eight by five, and then by two to give me 80, as well, so I can multiply multiple folk factors.

And examples here just to reiterate again, using some terminology that we like to use when we're looking at multiples and factors, eight is a multiple of four, because eight is equal to four multiplied by two.

Eight is a factor of 16.

Because eight multiplied by two is equal to 16.

And 16 is a multiple of eight because 16 divided by two is equal to eight.

Now there are other ways that we can represent our multiple factors.

And I'm going to use counters to show a raise to try and reaffirm 24 is a multiple and also a factor.

And just as a top tip, it's great to have things to use as counters at home.

So if you've got coins, if you actually counters fantastic if you've got coins, or lots of objects that look very similar, you can use them.

You can cut out circles or just cut out squires and use square counters.

Anything you've got that you can make multiple copies of and then you can use to kind of reiterate your math because sometimes it's difficult to think of math multiples and factors abstractly as a digit.

We like to see them in a kind of pictorial way.

So this makes it a lot easier for some people to show 24 in just three different ways.

So we've got two rows of 12, or 12 rows, or two, we've got four of the six or six rows of four, and we've got three rows of eight or eight rows of three.

Now 24 is a multiple of 12.

I know that because I can multiply two by 12 to give me 24.

24 is a multiple of six, because I know I can multiply six by four to make 24 and 24 is a multiple of eight 'cause I know I can multiply three by eight to make 24.

On the same way that 24 is also a factor of 48.

Because I could do 24 times , 24 is a factor of 240.

Because I could have 24, multiply by 10.

24 is a multiple of 72.

Because I could have 24 multiplied by three.

And again, just to reiterate there some examples, again, 24 is multiple six, four and 12 as the array showed, but then I can multiply those arrays to make bigger factors.

So rather to make bigger multiples, so 24, I can prove is a factor of 72 times it by three, I could prove it was a factor of 240, 'cause I multiply by 10.

And to double it to make 48.

So just to remind you, a multiple is a result of multiplying a number by an integer.

A factor is a whole number that When multiplied by another factor or factors makes a given number.

We're now going to look at the top task element of today's lesson.

And just to reiterate that top tasks are often done in the classroom, in a pair or group or your whole class basis.

However, many of you may be working on your own at home and thinking, well, I can't do that who I'm I going to talk to, that's perfectly fine.

You can pause the video you still haven't got the task, you just work independently reflect on the information in front of you.

However, if there's somebody nearby, parent carer, your pet dog, grab them, get them near, show them what you're learning about and see if they'll get involved in a brief math discussion with you about what you see on your screen.

I'm going to model a toll for you but before this just trying to mind you, it will be really good if you've got some counters or something that you can create a raise with today, doesn't have to be round counters just the same colour.

You can cut some squares out of paper, you can grab 10 apples or 15 apple, 20 apples or you can grab coins, anything You've got that you can use as a substitute for counters to help create these arrays.

And what I'm going to do is I'm going to use my counters to make an array to match the number on my screen.

And then I'm going to use the information within that array to be able to say and write down the four sentences that give me facts about multiples and factors.

So my example is 10.

I'm going to use arrays to make 10 counters.

I'm going to make or rather I'm going to use 10 counters to make an array that shows 10.

But I can also identify factors and multiples within that array.

So, I have decided to go for five rows of four or two rows of five depending on how you look at it.

And from that array, I can now say confidently the statements these are the mathematical facts, that this array shows us all.

First of all that five is a factor of 10.

I know that five of the factor of 10 because two lots of five is equal to 10.

I also know that 10 is a multiple of five, because five lots of two, is equal to 10.

I know that two is a factor of 10, because 10 divided by five is equal to two.

And finally, I know that 10 is a multiple of two, because 10 divided by five is equal to two.

So now that I'm giving you an example, you're going to have a go again, with the counters that you've got.

If you have to create them, that's fair enough.

You don't have to have to count if you haven't got the counters you just probably go with this.

But it will be a little bit harder.

You can draw them on your sheet, you can draw the arrays in your book, so you don't have to physically have the counters if you don't have the right equipment.

What I want you to do is produce those arrays, so the numbers that you see on your board, and then once you have that array, use the mathematical facts within the array to say or Write down those four sentences that you saw.

Again, if you need to go over the example of this bit, go back on the video to watch we do that example again, if not pick one, two, three or four or all of them as long as you want to create different arrays, and then to say those sentences, the facts that are in there, pause the video, spend as long as you need on this and then resume the video when you're ready to share some of your knowledge and learning speak to you very soon.

Okay, it be quite open tasks, I think quite a long time to be have spent a lot of time on that, fantastic.

I'm sure you've come up with some great arrays.

I did another one here.

Just an example.

I won't go through all the numbers, but I'll give you an example of what I did with 18.

I decided that six and three are both factors.

'Cause I know that, "cause I know my timetable.

So I six and three were how I'm going to set my rail, six rows of three or three rows of six.

And these are what I could come up with three the factor of 18, because three multiplied by six is equal to 18.

18 is a multiple of three because three, lots of six is equal to 18.

Six is also a factor of 18.

Because 18 divided by three is equal to six, and 18 is a multiple of six, because 18 divided by three is equal to six.

Now work systematically there by going through step by step and going through the clues that are there and statement and completing those sentences.

Your rail could look different ways, you could have done two, lots of nine, two rows of nine to show 18.

You could have done one row of 18 to show 18.

So, the different ways that you could have created your arrays to show the same number.

So, I've spent lots of time now familiarising ourselves with multiple factors and being able to define what they are, and to be able to identify them.

We're going to use those skills in an activity now called mystery number.

Now I'm going to ask you to work systematically through this puzzle.

And you hear me use the word systematically a lot.

The word systematically simply means to work in an orderly and efficient way.

So, you will use a step by step method to try and get to your answers.

To be orderly, calm, and step by step is an efficient way of using our mathematical knowledge to get to our answers.

As you can see on your screen, you've got 100 square, and I'm thinking of a number that is less than 100.

So at the moment, there's 99 possible options and I need to really identify that number by, narrowing down my options.

So I'm going to use a series of clues that are provided to you.

The clues are based on multiple factors knowledge, and so you go out to work methodically, step by step to narrow down the options till you find the right puzzle.

It's essentially a mathematical version of guess who.

I'm thinking of number less than 100, first clue is that it's a multiple six, circle highlighter, put a line through all the multiples of six.

As you see I've narrowed down my board by about a third there, about a quarter.

But there's still a lot of options there.

So I need my second clue, which is five is a factor of this number.

Now I know that five is a is a factor of multiples of five or 10.

So factor is a multiple is a factor of five and 10, therefore multiples of 10.

But there are no fives highlighted in this column.

So I'm thinking it's got to be somewhere in this column 'cause there are multiples of 10 and five is a factor of 10.

I've narrowed down now to three possible answers 30.

60 or 90.

A third clue is also a multiple of 20.

Now again, this is where my knowledge comes in.

So two lots of three makes six, so therefore, three lots of 20 must make 60.

So the only possible answer there is 60.

So I can put a line through that and clarify I have simplified the missing mystery number as being 60.

Because it's a multiple of six.

It's got a factor, of five for one of the factors is five check, And it is a multiple of 20, check.

Because I also know that three and 20 are also factors of 60.

'cause three lots of 20 makes 60.

So my missing number is 60.

Got the hang of it.

Let's have a go one more time.

This time, I'm thinking of a number less than 100.

And my first clue is a multiple of 15.

So I'm going to highlight all of the multiples of 15.

15, 30, 45, 60, 75, 90.

Okay, I've got six options now.

So, I really helped us out with that first clue, but I'm still going to narrow it down to just one out of the six.

So my second clue is that in nine is a factor.

Well Nine, 18 so that eradicate 15 straightaway.

If I times nine by 10, I know 90 so 90 is one of the options, so I just go through methodically, I cross off the ones that are rather circle ones that have got nine as a factor 45 and 90.

'Cause five lots of nine, 45.

10 lots of nine is 90.

So I know there's two answers there.

So now it's 50/50.

But again, I'm not guessing I'm using my methodical systematic way of identifying the correct answer in mathematical facts.

So now, the last clue is it's a multiple of 10.

So one of the factors of this number is 10.

So 10, lots of nine makes 90, 10 does not go into 45 because 45 is an odd number.

90 is the only even number.

So therefore, my mystery number has to be 90.

Okay, I hope you follow those examples, as you work systematically yourself, you are going to be able to complete the independent task without too much of a concern,zzzzzzz and hopefully will give you the confidence to even create your own mystery number puzzles or there be an extension once you've found three answers.

But now that you've spent some time in the developmental stage of our lesson, having a go with how to identify mystery number and how to work through the clues.

I'm now going to ask you to have a go independently and see if you can do that on your own.

You're going to use your knowledge of multiple factors to identify the mystery number.

There are three different puzzles.

I need you to work through the clues that are presented to you working systematically to identify the mystery number.

As you can see on your screen here is puzzle number one.

Here is puzzle number two.

And here is puzzle number three.

As always, when we do independent task, you pause the video, spend as long as you need there is no time limit.

And when you are ready to resume the video and check your answers, come back, press play, and I'll speak to you very soon.

Everybody, let's just see how you got on in identifying those mystery numbers in the task today.

Hopefully you work systematically as we explained earlier in the lesson to get I went through the clue's one by one and found the ideal number.

So, puzzle number one, the mystery number was 72.

Puzzle number two and mystery number was 84.

And puzzle number three, the mystery number was puzzle number 56.

Now for those that like spotting patterns, you will notice that all of those numbers are both a multiple of four, and they're even number.

I didn't plan it that way that just how the numbers have come up in the answers.

But looking at it now I can clearly see that there are multiples two, multiples of four.

And they're all even numbers.

Strange how numbers work out sometimes.

Well there's always those that not quite ready to put away their ruler and their pencil and want to just continue with their mathematical learning, which I love to hear.

Fantastic.

You can pause this slide and you can read through the clues.

See if you can come up with some clues to go alongside the mystery numbers you see on your screen you see there's a mystery number that's been presented.

What clues would you write to help somebody get to that point and to find that mystery number? And we're almost At the end of our lesson, okay thank you again for your work today and your hard work.

And obviously, you have to bring a lot of prior knowledge into this lesson about multiple factors which really helped.

If you're still struggling a little bit with your multiples and factors, timetables.

Practise your timetable daily, if you can, because all multiples under 100 can be easily identified by knowing your timetables.

So please start on the ones that you're sure about 10s, fives, twos and then build up from there.

It's really, key fundamental to your mathematics that you are able to do your timetables.

If you are ready to go on to the quiz, as we always have at the end of our Oak National Academy lessons, please find the quiz.

And let's see how that information has been embedded within you today.

Best of luck.

Finally, just to remind you that we try and Is your work to be shared, and we would love to hear from you and see some of the work you've been producing and hear some of your wonderful jokes, which are clearly better than mine.

Even though I do chuckle, my own sense of humour.

Nobody else does, but I do.