Lesson video

Hello everybody.

Nice to see you again.

Thank you for joining me.

Mr. Ward here on Oak National Academy.

We going to continue the unit on multiplication and division by looking specifically at prime numbers today.

I have one question before we make a start.

Are you ready for your learning? Yes? Fantastic.

Let's get going then.

Before we make a start on the main learning today, there's of course time for the mathematical joke of the day to put a smile on your face, that will crack me up and it will get me in the mood for teaching.

Did you hear about the maths teacher who was terrified of negative numbers? Is that he'll stop at nothing to avoid them.

Isn't a great one, all about negative numbers.

Now if you've got your own joke to add to the collection, I'd love to hear them hear out at Oak National Academy.

Details of how to share your jokes and your work will be shown at the end of today's lesson, so please keep watching the video slides until the end.

Quick overview of today's lesson, we'll be having our new learning element.

As we discussed today's idea is about factor slugs.

Then you'll have a go at talk task using arrays.

Then we're going to take our learning further by introducing the prime number aspect of the lesson today.

And then it'll be over to you to try and find prime numbers independently in the task, before having a go at the end of lesson quiz, which hopefully you'll be able to demonstrate how much confidence you have in the concept of prime numbers.

The equipment you'll need today.

A pencil of course as always, with some paper to write down on.

It could be squared, line, blank, or that notebook that you've been provided by your school.

And I'm going to ask you to try and find some counters.

And now you might not have round counters, so you can use anything really to replace those counters.

You can cut out some squares or cut out some circles to act as counters.

You can use coins.

Like I say, you can be quite creative what you use in order to create counters.

We're going to use them to look at arrays.

So have a look around, see what you can find.

If you've got none of that equipment now, you need a bit of time to go and prepare some counters, pause the video, go get exactly what you need and then when you're ready to resume the video press play and you can continue with it today's lesson.

So the first thing I would like you to do today to get yourself warmed up, is to complete the speedy tables you can see on your screen.

It is a number of different timetables that you need to know.

So it's a mixture of your mathematical knowledge.

How many can you do in three minutes? So you don't have to time yourself.

You can just do as many as you want, but if you'd like an extra challenge see how many you can do in three minutes.

Pause the video, complete the task and we'll quickly share the answers in a few minutes.

Welcome back.

Very quickly then, all of the answers to your speedy tables grid, is in front of you.

Like we say, it's a range of activities.

A top tip for completing task and challenges like this, is to go with the ones that you are more familiar with to start with.

So you can start with your tens, for instance and then you could have halved it to your fives.

You could've done your one time table then double it to do two.

And then double that to do four, and so on and so forth.

So using your doubling and halving ability is a really good way of going quickly and efficiently through your timetables challenges.

Should we carry on and do our main learning today? Yep, you ready to go? Excellent, so am I.

Starting out with the question obviously you can see in the top right hand corner, is can you make some factor bugs for these numbers? Now, if you're not familiar with factor bugs, we introduce these into lesson two of the unit and it is when you create a bug in the sense you show antennas and legs, that show the number of factors and factor pairs within a number.

So, can you create factor bugs for these two numbers, seven and 11? How many different factor pairs can you find for seven and 11? Now, what did you find when creating those factor bugs? What was so special about those numbers? I added an extra one, 13 'cause that's also has the same circumstances as seven and 11.

It has a lot in common.

What did you notice about the factor bugs that you tried to create for seven, 11 and 13? That's right, they only had two factors.

There was no main body and no legs.

They only had factors of itself and one, and you can see the three examples are exactly the same.

So the only two factors, they have one pair of factors was one and 11 or one and 13, one and seven.

And we know that because one multiplied by seven will give you seven.

So when that happens, we like to call them, factor slugs.

We create factor slugs, because there are no legs are there? And there are no additional limbs to our bugs.

So they're not really bugs, they're slugs.

Nice long body with no additional details.

So in front of you, you see a factor slug.

I'm sure you can do better than me and be a little bit more creative but what do we call these numbers? These special numbers that only have two factors? No more, no less, only have two factors.

What do we call these numbers? They are called prime numbers.

It's a whole number that has exactly two factors, one and itself.

How many different rectangular arrays can I make with seven counters? How many different rectangular arrays can you make with seven counters? Like I said, at the start of the lesson, it will be useful if you had something today to use as counters, but if you haven't, you could draw the circles out in your book and you could create arrays just by jotting.

So either physically or writing it on your page will do, but I'd like you to look at the different arrays, rectangular arrays that you can make with the seven counters.

Pause the video, spend a couple of minutes coming up with different suggestions for how you could turn those seven counters into rectangular arrays.

Right, so this is my first example.

Check if you've got this.

There is one row of seven or seven rows of one, depending how you look at it.

So one row of seven is one way of doing a rectangular array.

I could have done it the other way.

Again, I think it's influenced, gives you the same thing one row of seven, but I present it in a slightly different way.

It still has one in seven.

It still gives me a total of seven.

Now because the title said rectangular arrays, it means we're looking for equal rows and columns.

So I couldn't do it this way.

Four and three, because that's not a rectangular array.

I couldn't do it this way, four and three or rather you know, two different columns.

I couldn't do this, because it's not equal.

It's not a rectangular array.

So we're going to move onto the talk task element of the lesson now.

Just a reminder that talk tasks generally happen in pairs, small groups and whole class situations, but you can do this on your own.

Not to worry.

You can pause the video and you can do the task and write down some of your reasoning and ideas and help them to share, next time you have the opportunity but if there's anyone in the room or nearby, sibling, parent, carer, pet, your fluffy teddy bear, get them over and try getting them engaged in the mathematics, show them what you're learning and try have a discussion about what you can see on the screen.

We're going to explore with numbers.

You've exploring them with creating arrays.

So you can either use resources you might have so number cards, counters, or you could draw the arrays and the counters and you could either cut out number cards, make your own, or just select numbers and investigate those numbers on your soon.

So there variety of options that you could have.

So you're going to place the number cards down and then you select a number.

And then when you look at that number, you take the number of counters that equates that number.

So for instance, I picked seven as an example, I'm going to take seven counters.

And then you going to try and make as many arrays as you can.

Now you get one point for making it an unequal array.

So for instance on your screen, you can see I've got one row of four, one row of three.

That's not very good array.

It's unequal.

I get one point for it 'cause I've tried to make it, but you can see there's an odd one at the end.

And if you happen to make a even array a rectangular array, that has even number of columns and rows, you get two points.

Okay? So you'll get one point for an unequal array and two points for a equal rectangular array.

What I want you to look at when you're investigating and exploring these numbers, is what do you notice about the numbers that earn you lots and lots of points and the numbers that don't earn as many points? Okay, so you might want to make a little record of the number of points that you build up.

So you get two points for a rectangular equal array.

You get only one point for creating an unequal array.

But what you got exploring and you're doing these arrays I always want you to use a bit of a cavalry, either on your own, you can write these down or talk to yourself, something I do all the time.

Or you can have a discussion with people in your room or in your group, or in your partners.

And I want you to say this, so you might pick out for instance, six.

I'll pick the number six, I have six counters and what I selected number six, I can make two arrays, so two rectangular arrays could be made.

You can make two by three, or one by six.

So you would get four points for making two rectangular arrays there.

Pupil B, I have selected the number 13.

You can make one array which has one lot of 13 and that's it.

So you would only get one point, sorry you would only get two points for number 13, whereas you would have earned four points for number six.

So already, this you know, I wonder what's different about the number six and the number 13 that might suggest you get more points for number six than you do for number 13.

Pause the video, you'll need probably a bit of time here.

You can do all the numbers, as many of these as you like.

A few of the numbers, but make sure you're trying to compare the number of arrays and compare the numbers and see if you start spotting some trends and patterns.

I'll see you, when you're finished resume the video and we can feed back on what we found out.

See you in a few minutes.

Okay let's just quickly share what we've discovered.

Hopefully you've got lots of information then and lots of evidence of arrays you either made them or you drew them, and you've got a collection of your tallies for your points, so you know, which numbers collected the most amount of points.

I wonder if you notice the same as I did, that you didn't tend to earn many points when you use the numbers three, five, seven, 11, 13, 17, and 19.

They didn't seem to earn many points.

It's very hard to make a rectangular array.

In fact, when I use those numbers I can only ever make one rectangular array.

One lot of 19, for instance, or one lot of 17.

So a bit like our factor slugs earlier on, these would be factor slugs because they only had two factors.

They had themselves, and one.

That was it.

No other factors involved in those numbers.

They are factor slugs.

They're also odd numbers.

And I wonder if that is a reoccurring theme in the idea of factor slugs.

So they all are odd numbers, and the even numbers allowed us to generate a greater amount of variation in equal rectangular arrays and therefore they earned us a lot more points.

With that idea of some numbers especially odd numbers, only having two factors, we're going to develop that a bit further and look at it in a bit more detail.

A numbers that only have two factors, as we reminded earlier in the lesson are called prime numbers.

They only have themselves and one, as factors.

So we're going to look at finding all the prime numbers that are less than a hundred.

You can see there's a hundred square on your page.

We're going to try and find all the prime numbers in there, by working systematically.

First question for you to ponder, is one, the number one, is it a prime number? Hmm.

It's a factor, yes and it's a factor in other prime numbers as we discovered, so for instance, 11 is a prime number and it has one and 11.

So one is a factor, but is it a prime number as well? The answer is no.

One is not a prime number because it does not have two factors.

It only has one factor, itself.

So that's a good way of consolidating that knowledge about factors.

To be a factor, you must have two, or you must have two other, to be a prime.

Sorry, I'll start again.

You to be a prime number, you must have two factors.

One can be a factor, but it cannot be a prime number 'cause it only has one as a factor and needs to have two.

Which means the very first prime number, is what? Hmm.

Where would you start? How can we find all the prime numbers less than a hundred? Well, we know that a multiple of a prime number cannot be a prime number because it will have more than two factors.

So a multiple of a prime number cannot be a prime number because it will have more than two factors.

So for instance, we know that 11 is a prime number 'cause we talked about that in our talk task, but as a multiple of 11 it's 22.

So 22 cannot be a prime number.

We're going to start with two, believe it or not.

Now we did day in the talk task that there are all of those numbers seem to be odd numbers that were primed.

Two, is an even number, isn't it? And that starts as our first prime.

Why is two a prime number, I hear you ask? Well, because two has two factors.

It has one and it has two.

It has no more factors.

So by the very letter of the definition a two is a prime number.

But four is not a prime number nor is six, nor is eight because they are multiples of two and they have more than two factors.

Four has one, two and four.

Six has one, two, three and six.

Eight has one, two, four and eight.

So you see that if you find the multiple of a prime number it cannot be a prime itself.

Next one is three, again the factors of three are one and three.

However, a multiple of three is six and nine.

So nine cannot be a prime number 'cause it is a multiple of three.

Having spent some time I can find what prime numbers are and how we can start to identify them within a hundred square.

That's exactly the task that you are now going to do.

You're to continue the identification of prime numbers using a hundred square.

The task is called Prime Time.

As we were modelling briefly, on our developing our learning section, we started off by identifying that two was a prime number but then any multiple of two, could not be a prime number as it had more than two factors.

Your job is to follow the clues for systematically on the screen, to try and identify all of the prime numbers between one and a hundred.

Now remember one is not a prime number because? That's right.

It only has one factor not two.

So pause the video, spend as long as you need on this task.

Remember to keep reviewing the clues that you've got there and the facts about what we know about prime numbers and what we know about factors.

And I'm hoping that you are going to be identify all of the prime numbers that exist within that hundred square.

Spend as long as you need.

If you're waiting with somebody, working with somebody, talk about it, discuss your ideas.

You may disagree on some of those questions or some of the numbers and that's perfectly fine.

Make sure you can always explain why you disagree and why you believe a certain number is a prime number.

Pause the video now, take as long as you need and I look forward to seeing some of your work in the next few minutes.

See you soon.

Okay, let's share our answers.

I'm sure you've been beavering very hard on your work.

You've done a really good job.

Remembering that one is not a prime number so already we got rid of that.

On your screen I've circled all of the prime numbers.

See if that matches your hundred square.

Did you miss any out? Did you have any by accident? Did you add any more? If you have, you've obviously included ones that are not prime numbers, that actually have more than two factors.

Interestingly though, here's a question for you.

What do you notice about those numbers? And you can see them on your screen circled.

Is there anything you notice about the prime numbers and how they're distributed on a hundred square? Well hopefully the first thing you notice that other than two, which is an even number, no other prime number is an even number and that's because all multiples of two cannot be prime numbers because they've got more than two factors.

And as we know, all even numbers are multiples of two.

So once two has been identified, there were no other even prime numbers.

You might also notice that there's some columns that are not, have no prime numbers at all.

So all multiples of four, of course that's an even number or multiples of six, and all multiples of eight and all multiples of 10.

Again, they are all even numbers.

So that's no surprise there.

However, here I found this interesting, that there's only one in the column of five.

Five itself because of one and five, but then of course, all multiples of five, 10, 15, 20, 25, 35, have more than two factors.

But then, so I suppose, it's not surprising that there are no other multiples of five that are prime number, okay.

And it's also interesting to note that actually although some columns have a lot of prime numbers in them, so the threes, for instance, three, 13, 23, not all of the numbers are prime numbers.

And that's important to note because they are multiples.

So for instance, 33 is a multiple of 11.

63 is a multiple of 21 and of seven.

93 is a multiple of 31 for instance.

There are some patterns then and there are some similarities that I wondered if you noticed any of that, when you were looking at our prime numbers in the hundred square.

Well done now if you've managed to identify nearly all of them or exactly all of the prime numbers, you did a fantastic job and hopefully I got you talking and discussing and reasoning with your mathematical learning.

If you're not quite ready to put away your ruler and pencil just yet, you can continue with this challenge side called the Prime Time Hundred Club.

Pause the video, read the instructions very carefully and then you can continue investigations into prime numbers as part of the Prime Time Hundred Club.

Well a fantastic lesson everyone.

You can give yourself a big pat on the back.

Hopefully you leave today feeling a lot more confident understanding what prime numbers are and how you can identify them.

But now it's time as always, to put your learning interactions to demonstrate what you have taken on board by doing the end of lesson quiz.

So return back to the video and once you've completed the quiz hopefully fingers crossed, you've done really, really well.

Take your time, read the questions carefully.

Try to remember all of the great vocabulary that we were discussing today throughout the lesson on factor slugs and prime numbers.

And it's just time for me to share with you the information about how you can share your work or mathematical joke with us here at Oak National Academy.

Please ask your parent or carer to share your work on Twitter, tagging at Oak National and hashtag learn with Oak.

It's very important you speak to your parent and carers and get them to do that.

But we would love to see some of the work that you produce over the course of this unit and all the rest of the mathematical lessons that you are doing on Oak National Academy.

So everybody that brings us to the end of another lesson.

I just want to say, well done again.

You have done a fantastic job today.

And I think you're going to leave today feeling far more confident in identifying prime numbers.

Now we talked about factor slugs today, and also talked about factor bugs.

Now, have you not been used to factor bugs, you might want to come back into a previous lesson in this unit which is lesson two in which we explore factor bugs in a little bit more detail.

So feel free to go and find that lesson on Oak National Academy if you need to.

However, for today's lesson, you've done a really super job and I'm really happy with the focus that you've shown.

So I'm going to go enjoy the rest of my day.

I hope you've got something nice planned, but I do look forward to seeing some of you again very soon here on Oak National Academy.

So from me, Mr. Ward, have a great rest of the day and I'll see you soon.

Bye for now guys, bye-bye.