Lesson video

Hello everybody.

My name's Mr. Ward, and wherever you are in the country, welcome once again to Oak National Academy.

We're going to continue our unit on securing multiplication facts by looking specifically at the seven times table today and the different ways in which we can represent our knowledge of the seven times table.

Now, as always, I ask that you're free of distraction, that you have everything that you need for the lesson, and that you're able to focus on the next half an hour or so as we work our way through our mathematical lesson today.

If you're ready to begin, I am.

I'm excited about this lesson and all the different representations I'm going to show you, so let's make a start.

Before we make a start on the main lesson, it is, of course, time for the mathematical joke of the day.

If you are new to Oak National Academy or a Mr. Ward lesson, I should pre-warn you that I like to start every session with a mathematical joke to put a smile on your face and to share my comedic value.

Now, this one has been making me chuckle several times in the last half an hour, so I hope you enjoy it too.

What piece of equipment in a toolbox is actually great for solving maths? Multi-pliers, of course.

I'll put these away back in my mathematical tool box and we can make a start in our lesson.

If you think you can do better than me, I'll be sharing information at the end of the lesson on how your parent or carer can send in your work or mathematical jokes to us here at Oak National Academy, so please keep watching.

That was a good one, I think.

Come on, you got to give me some credit.

If mathematical jokes aren't for you but your mathematical learning is the reason you're here, then this is still the place to be.

No more jokes, but just lots of great content.

I'm going to introduce in our new learning section how we represent the seven times table in a number of different ways.

And then we are talk tasking, in which you can independently try and match the different representations with the different calculations.

We're going to take our learning a little bit further and develop it by looking at more representations.

And then I'm going to hand over responsibility to you and ask you to have a go at the independent task, in which you will represent multiplications in a variety of different strategies that I've shown.

And then of course, as is common practise here at Oak National Academy, we ask you to end the lesson by having a go with the quiz.

It's important we can maximise our session that we have the right equipment, if possible.

So I asked you to have a pencil or pen, something to jot down and write down your ideas; some paper, it can, ideally grid paper's great in maths, but if you haven't got that, you've just got plain paper, lined paper, or even just cardboard, or short boarders, anything to jot down ideas, that will be absolutely fine.

A ruler's always useful for presentation, but also to help with some mental arithmetic.

And finally, a hundred square, which has been used on every session within this unit.

So you may already have a hundred square to you or one that you've used previously.

If you don't have one, absolutely fine.

You can either print it out of the downloaded resource, draw your own, or just look at the square that you see on your screen to help.

If you haven't got any of the equipment and you know you can go and get it, please pause the video, get what you need, get yourself ready, and then press play and resume the video when you're ready to make a start on the learning.

Right, everybody, the very first task for us to do today is to get warmed up and get operating and firing on all cylinders.

So your warmup today's called "Multiple Mystery." Can you use your knowledge of the four times multiplication table to identify all of the multiples of four that exist within the numbers present on your screen? Pause the video.

Spend as long as you need and try to use your derived facts that you know from the four time table to help you identify multiples of four beyond 40.

Speak to you in a few minutes.

Welcome back, everybody.

Let's quickly share our answers.

There were only four multiples of four, believe it or not, although some of them may have been there to trick you or to get you to second guess yourself, especially those that ended eight or four, which are normal multiple of four.

But doesn't it make it a multiple of four just because a number ended four and eight, that's worth knowing.

So the four that were there, 64, which you could have partitioned between 40 and 24; at 452, which again you could partition between 12 and 440; 12; and 940, which I partitioned between 800 and 140, knowing that 200 fours made 800 and that 35 lots of four make 140.

I hope you did okay.

Don't worry if you didn't get all of them right.

or you made a few errors.

That's okay as long as you can identify where you went wrong and your misconception.

Okay, we're going to introduce a new learning element today by representing the seven times multiplication table in a variety of different ways.

But before that, let's see how confident you are with your seven times tables.

As I have done in previous lessons you may have watched, I've introduced the counting stick.

I have one of these in my classroom.

They're a fantastic resource to use.

Essentially a metre stick, so I use it for measurements, but they allow me to do all sorts of mathematical tricks, and one of them is to represent the multiplication tables by showing the different stages.

Now, let me ask you, if you are confident with your seven times table, I want you to still watch the next few slides and I want you to consider what advice you would give to someone who wasn't as confident or didn't know their seven times table by memory.

Would you go the same way that I did? Would you give the same advice? Or would you offer different advice? If you're not so confident in your seven times table, I think you can appreciate this trick, so please watch closely.

We start off with our knowledge that we already know, our simple derived fact.

I know zero lots of seven is zero because I'm multiplying one of my factors with zero, with nothing.

So if I multiply by nothing, I can't have anything as a product.

One lot of seven is seven, and therefore 10 lots of seven is 70 because it's 10 times greater.

Now that I know one lot, I can double that to make you lots of seven, to be 14.

I then can double again to make four lots of seven, which is 28, or 14 twice, so two times twice, two tubes of four.

I can then add my four times table and my two times.

I've go four lots of seven and two lots of seven.

28 and 14 together to make six lots of seven, which is 42.

I also know 10 lots of seven is 70, so I could halve that to make 35.

I could also add four lots of seven and one lot of seven, 28 and seven, to make 35.

So I've got various different ways I can go.

Because I know 10 lots of seven I can subtract one lot of seven, one group of seven to make 63 for nine lots of seven.

Because I know five lots of seven and four lots of seven, I could have added them together to make nine lots of seven.

So that's two different ways I could have got to nine lots of seven being 63.

I know five lots of seven is 35.

And I know one lot of seven is seven.

So seven and 35 together make 42, and that gave me the answer for six lots of seven.

I could then halve six lots of seven by dividing by two to make three lots of seven, 21.

Alternatively, I could have added two lots of seven and one lot of seven, 14 and seven respectively, to create 21, and to give me three lots of seven.

That leaves two left within our multiplication table.

Well, I know four lots of seven is 28, I came by that earlier, but I could double that to make 56.

I could add six lots of seven and two lots of seven, 42 and 14, to create 56.

Or I could subtract a further group of seven from nine lots of seven to create 56.

And finally for my seven times table, there's lots of different ways, but I favoured the method of knowing five lots of seven and two lots of seven and adding them together to make seven lots of seven 49.

You may know that eight lots of seven are 56, so you could take away one lot of seven if you're good with your subtraction.

Or you may decide that you're going to double three lots of seven to make 42, and then add another lot of seven.

Like I said, there's lots of different ways.

I hope that was useful in sharing the different ways that we can use our derived facts to build up our other multiplications that we're not quite so secure on or confident with.

So there are all the multiples between zero lots of seven and 10 lots of seven.

Did you spot any patterns? Is there anything emerging when we look at these multiples? I would like to pause the video now and spend a couple of minutes shading in all the multiples on your blank hundred square or circling all the sevens or the multiples of seven on your numbered hundred square, if you're more confident using that resource.

So spend a little time shading, identifying all the multiples and then looking to see if there are any patterns that help us predict what might happen in the future multiples, or just nice, aesthetically pleasing patterns with our multiples.

Pause now and I'll speak to you in a few minutes.

Okay, let's see what we would have come up with.

On our side with our blank number square you will see it's quite a pretty pattern, I think.

Actually a nice little green that I've chosen for my shading.

I don't know what colour you would have chosen.

And then obviously on the given a hundred square with all the numbers, you can see the same patterns emerging.

One thing that I did notice, hopefully you did too, that all the multiples are going in a sequence of odd, even, odd, even.

So we're up to 70, which is an even number, so the next one will be 77, odd.

The next one will be 84, even.

So there is that kind of one in, one out, odd, even, odd, even sequence.

I also notice that is it's not really a pattern switch, but there's a line that there's one multiple, one multiple, two multiples, one multiples, two multiples, one multiple, two multiples, one multiples, one multiples, two multiples, which is quite interesting.

So that would mean that the next line afterwards would be, if I drew it on here, would be one multiple, and the next line would be two multiples, and then so on and so forth.

That allows me to predict.

I also know that every third multiple is exactly 21 greater or 21 higher value.

So we started off with seven, so the third multiple in, so seven, 14, 21, 28, is two tens and one across.

28, the third multiple across is going to be two tens, 48 plus one 49.

The third multiple, again, from that will be two tens plus one, 21.

So there's a gap of 21 on the third multiple.

Well that's because, obviously, we're looking at multiples of seven, and 21 divided by three is seven.

Okay, little bit different now.

I'd like to know when we're exploring how we represent the seven times table.

All of these different ways of representing these multiples, what's this same, what's different, and can you group them together? Would you be able to put them into two categories? What's the same about these multiples and these representations, and what's different? Look at these representations using Geoboards and Cuisenaire rods.

What's the same? And what's different? All right, I wonder how you did.

Now, a lot of the representations did, of course, look the same.

And the main similarity was that involve the numbers seven and five, which would give us a product of 35.

However, depending on the question, the context of the question, there may be different ways of sorting out the multiplication.

But also, the way that it's represented will differ.

And I separated my calculations into two groups to look at the sum of seven groups of five or to look at the calculations five groups of seven.

As you can see, my bar model here represents seven groups of five clearly 'cause there was seven equal parts and each part represents the value of five.

Same with my array here.

My array has seven rows of five to give me 35.

My number sentence down here has seven lots of five, so seven lots of five with repeated addition.

That looks slightly different to five groups of seven because my number line here, which is similar to a bar model, I suppose, has five jumps with each jump representing seven.

So with my array, this time I have five rows of seven columns, or my repeated addition being five lots of seven added together.

So it's a subtle change, but it is a difference.

Again, how did I separate my Cuisenaire rods and my Geoboards? Well, I've separated it into seven groups of five and five groups of seven.

Some of the Geoboards represented by one pin, so we would have had seven rows of five.

And sometimes there's four pins that kind of represent the square, so you can see that all the four pins would be one.

Again, I would have seven blocks by five blocks.

My Cuisenaire rods could have been different values.

Each rod here is worthy of seven, five lots of seven.

Whereas the yellow rods will, a value with five, so add seven lots of five.

Now in mathematics we use the commutative law to look at multiplication, and we can represent multiplication in different orders.

So we can have seven lots of five is equal to five lots of seven because it gives us the same product.

35 is the product for both seven lots of five and five lots of seven.

However, it's important that we realise that commutative law worked only when the problem is appropriate.

And the word problem itself might not be the appropriate use of this law.

We might only be able to calculate one way or to see the answer in one way.

So for instance, if the word problem says multipacks of crisps have seven individual bags per pack, Sita buys five multipacks when shopping, how many crisps has she bought? I want to look at that question from the context of knowing that each multipack has seven packs in it.

So I'm looking for five groups of seven.

We'll give then the answer, hopefully, of 35.

And you can see I'm representing the way that I could, the appropriate representation to this.

I'm looking at five groups of seven, or I'm going to add five groups of seven in repeated addition with my number line, and in my array, five rows of seven columns.

With that in mind then and the way that we can identify different calculations and they can be represented using different ways and strategies, you're going to have a go yourself.

Your talk task today, you're called to match the representations.

Can you match the multiplications with the representations? Now a talk task is generally done in pairs, or small groups, or whole-class discussion based.

But if you happen to be working on your own, not to worry, please complete the task independently and jot down some of the ideas that you would have shared verbally with partners.

If you are lucky enough to work with somebody, fantastic.

Make the most of it and try and use some of the rich vocabulary that we've been introducing during the lesson.

So look at the representations and match them with the correct multiplications and equations.

Pause the video now as long as you need for the task, and when you're ready to continue, press play.

I hope you enjoy this short task.

And remember, try to use some of the key vocabulary in your verbal communication.

Welcome back.

I wonder how you got on and how you grouped those representations.

I've set them out using the arrays, actually.

There was four arrays and I thought that they looked slightly different, so I used the arrays to match the rest of my representations.

So we had three groups of seven, we had seven groups of four, I had four groups of seven, and I had seven lots or seven groups of three.

And we can see how those represents equally match up.

Yep, I hope you enjoy that, and I hope that makes sense to you that actually, for instance, when we're looking at three lots of seven, in repeated addition, I've got seven three times as opposed to seven lots of three, when I had seven lots of three, so three seven times I could add together.

Yes, of course the product comes to 21.

Product is 21 on both of these.

And the product for seven groups of seven and seven lots of four is both 28.

But of course, just remember, because the product is the same doesn't mean the representations will automatically match.

It's about specifically the appropriateness of the question.

So let's continue to look at different representations to show and demonstrate equations.

I wonder how else could we represent seven lots of four? I could write it as an abstract number sentence, seven times four.

How else could I represent it in a pictorial, pictorially, concretely, or abstractly? Well, I could write and say in a word question seven groups of four.

I could say seven lots of four.

I could flip it and say four multiplied by seven.

I could use repeated addition, have seven lots of four added together.

I could use a blank number line and show on that number line seven steps of four, seven lots of four being added together.

I can show a bar model with the bar having seven equal parts, and each part representing four.

So therefore we could, and you can see actually like a bar model and a number line do look quite similar.

We moved the bar, but the steps can be shown the same.

So although I've only shown you four in one of my equal parts here, that actually shows me that every part, because it's equal, is the same as four.

So therefore, it would have seven lots of four.

I could use an array to show seven rows of four columns.

I could use an area model which shows that seven times four would give me my answer in here.

And I could have Cuisenaire rods to show that each of the rods represent four, so we're four, and there's seven of them, so seven lots of four.

Obviously, the answer all together would be 28, the product will be 28.

Using commutative law, seven lots of four equals 28 is equal to four lots of seven.

But of course, the representations may not necessarily allow us to go between the two, depending on the appropriateness of the question.

The time has now come to hand over responsibility for you to see if you can use some of the strategies and representations that we have demonstrated throughout today's lesson.

You may continue to represent multiplications within the seven times table.

I'd like you to find different ways to represent the following equations on your screen using different abstract equations, drawings, equipment, and jottings.

Some of the representation you could use include using bar models, area models, physically using Cuisenaire rods, or jotting down in drawing what those rods look like, arrays, writing number sentences, and again, using Geoboards either physically or jotting down and drawing how they would look if you were to have them in front of you.

I think it would be good for you to come up with three different, a minimum of three different representations to demonstrate each of the calculations that you see on your screen.

Pause the video now as long as you you need.

Remember, it's not an art lesson, so your jottings don't have to be exact, but they do have to look like the representations that you are showing.

If you're a little bit unsure again about some of the examples, feel free to go back to earlier slides in the video to remind yourself of what those representations look like.

Hope you find the task okay, you enjoy the task.

And then when you're happy to finish the lesson off and share some of your answers, please press the play button and resume the lesson.

Speak to you very soon.

Okay, we obviously cannot share all of our examples, but I've given just a few on the board that I could have done and I would have done.

I would have used an array, for instance, to demonstrate seven lots of six.

You can see the seven rows of six columns to show 42.

I used a bar model to demonstrate seven lots of eight.

You can see seven equal parts.

Each part is worth eight.

That would give me a total or product of 56.

I used a number line, an unmarked number line to demonstrate seven lots of seven.

You see seven jumps of seven would give me the product of 49.

And then for seven lots of nine, I've drawn Cuisenaire rods, how it would look.

Each of my rods would be worth nine, and I would draw seven of those rods to show seven lots of nine, creating the product of 63.

I was not quite ready to put away the equipment.

I have got an additional challenge slide, as usual on a Mr. Ward lesson.

Here is your challenge.

Can you use inverse to show these equations? And how many different ways can you do so? So for instance, the first one, something divided by something equals 32.

Well how could you turn that into a multiplication sum? And how many different ways can you do it? This may be something you can work independently on your own with, or you might choose to work with a partner or a group to share different ideas and to discuss the maths taking place.

Pause the video.

Spend as long as you need on the challenge slide, but I do hope you enjoy it.

It's a good way of stretching our thinking and keeping us busy till the very, very last minute.

We're almost at the end of today's lesson, but not quite because, of course, it is the mandatory quiz time.

As always at Oak National Academy, we asked you to have a go at the quiz to see how much of the learning from today's lesson has been embedded and how confident you will be using those concepts moving forward into the future.

The key reflection I'd like you to take away from today's lesson is knowing that a wide range of representations can be used to show our multiplication facts.

Hopefully you're confident, whether it's bar models, arrays, Cuisenaire rods, or showing it using an empty number line.

They are all good ways of demonstrating the facts that you know about your multiplications.

Read the questions very carefully on the quiz.

Take your time.

And then when you finish, please come back for the end-of-lesson messages.

Good luck, everybody.

Speak to you soon.

Finally, I just want to remind you that we love to receive work and mathematical jokes here at Oak National Academy.

I'm sure today would be a great lesson to demonstrate the work that you've produced because you've got some great jottings, and drawings, and diagrams that demonstrate the multiplication facts that you know.

So if you would like to do so, please ask your parent or carer to share your work and jokes on Twitter, tagging @OakNational and #LearnwithOak.

All right, everybody, thank you once again for your hard work, but that is officially the end of today's lesson.

It's been another fantastic lesson here on Oak National Academy.

I think you've done a really, really good job again, and I hope that you will take away from this lesson the knowledge that those different representations can be used to show your multiplications, and that you can choose and be flexible on the representation that you feel most confident about.

I've been very impressed with your focus.

We have one final lesson in the unit to come which will be consolidating all of the different concepts we've delivered across the unit.

So I look forward to seeing you then, but for the meantime, from me, Mr. Ward, have a great rest of the day and I look forward to seeing you again soon.

Bye for now.