Lesson video

Hello everybody, my name is Mr. Ward, and welcome to Oak National Academy.

We're going to continue today with our unit on securing multiplication facts by looking at the quirky and unique world of the nine times table.

I'm looking forward to sharing you the trick to the tray when multiplying world of the nine times table.

Before we make a start for the lesson, we need to make sure that we are free of distraction, that you have a quiet spot that you can focus on your learning and that you have everything that you need.

If you feel ready to begin the lesson, I'm excited and enthusiastic about it.

So I think we should make a start, shouldn't we? Let's get going.

See you in a few moments.

But before we make a start on the main learning for today's lesson, there is a course time for the mathematical joke of the day to crack a smile on your face and get you in the mood for the session.

Today's is an absolute better one of my favourites, I've told it in other units because I think it's such a good joke.

Which famous irritable King absolutely love fractions? Henry the 1/8, of course.

Hope you really like the bar model I've presented demonstrates that Henry the 1/8 could be shown as one part of eight in a whole.

If you haven't used bone models before, or you haven't studied Henry the 1/8 either way, this jokes will be wasted on you.

But I hope folks at home appreciated it.

Of course, if you believe you can do better than my mathematical jokes and you probably could, I'll be sharing information on how your parents and carers can share your work on mathematical jokes with us hear on Oak National Academy, details of which I will be sharing at the end of today's lessons.

So please keep watching the video slides until the very end.

An overview of today's lesson is on front of you on the screen, you will see that our new learning will consist of me introducing nine time to table and showing you a few tricks and facts about the table then we'll to a task in which I ask you a couple of statements that are always sometimes or never true.

Then we'll get it developed our learning a bit further by introducing more tricks for the nine times table, and then I'm going to hand over responsibility to you and ask you to have a go at an independent task called multiplication mischief before you finished the lesson as is custom here at Oak National Academy with the end of lesson quiz.

Important we are equipped in the most out of our lessons, so please try and get the correct equipment if you can, definitely should have a pencil or pen or something to jot down your ideas with a ruler, some paper and ideally is good paper or notebook given by your school but if you haven't got that you've got blank paper, lined paper, you've only got a chalkboard board or the back of a pizza box or anything, that's absolutely fine.

Anything that jot your ideas down and you can do sort of you're working out and Oh, there's a hundred square, we haven't had this resource.

That's fantastic.

You may have used it for other lessons.

If you haven't got these, you can either create your own hundred square resource print off the downloadable worksheet or write and draw your own hundred square.

A rubber as always to remind you is optional in a Mr. Ward lesson and actually I encourage people not to rub their work but instead join neat line through it to show that they've made a mistake.

They understand where the mistake is and that they've corrected their misconception.

If you haven't got any of the equipment that you need right now, please pause the video, get what you need so you're ready to make a start on your learning and you won't be distracted.

When you have got everything and you want to make a start, press a play button and resume the video and then you can get onto the main content of the lesson.

A warm up is a good idea I think to get our brain firing on all cylinders, so today's is called multiple mystery.

Look at all the numbers on your screen.

Can you use your knowledge of that three times multiplication table to identify all the multiples of three.

Pause the video spend as long as you need on this task and then when you're ready to share your answers and see if you've identified all of the multiples of three, press play.

Speak to you soon in a few minutes.

Very quickly then let's see if you've noticed them all.

You need to use your knowledge of the three types tables, so for instance, if you know 10 time three 30, you will then know that a hundred lots of threes is 300 for instance.

If you know for instance, that five lots of the three is 15 and 10 lots of three is 30, you will then know 15 lots of three must be 45 and therefore it must be in the three times table.

So you can see that the numbers circled are all in the three times table.

The numbers that are not circle, are not multiples of three, even though some of them have either got three in the ones column or they feel like they should be, they just feel right, but they're not.

So for instance, at 452, well, we kind of know that three lots of four is 12, but if we took 12 away from 52 we'd have found 40, which is not a multiple of three.

Anyway, I hope you did well on that task if you got them all right, congratulations, well done! Have you got a few of them right, that's okay you're on the right lines and if you did get some mistakes, don't worry about it these things happen, but just try and remember those key facts from one to 10 times three will allow you to work at any multiple of three.

Well, we're going to start today's learning by introducing the nine times table.

Now, if you've done lesson one, lesson two you will be familiar with the representation of accounts and stick on your screen.

If this is a new lesson in the unit for you not to worry I wonder if you do recognise what you see in front of you.

In my classroom, I use this as a counting stick.

It's also a meta states on use it for measuring the length, et cetera.

However, I also liked to demonstrate multiplication using the sticks are really good practical tool.

How confident are you with your nine times multiplication tables? Now, if you're not, I hope you find the following exercise very useful to you and please focus and stay, pay attention to in order in which I give the facts I know to build on other facts that I'm not so secure with.

If you are very comfortable and secure with your nine times table, think about what advice you would give to someone who isn't as confident, would you go the same order that I do or would you do it a different way? And we're going to start with the derive knowledge and facts I do know I'm secure with.

I know that nine times zero or zero lots of nine is zero because I'm multiplying by nothing.

And therefore I can't have nothing to my total.

My product would be nothing.

I know that one loss of nine is nine.

So once I have nine is nine and therefore I know that 10 lots of nine is 90 because I've multiplied by 10 is 10 times greater.

This allows me to do, one lots of nine make you lots of nine to make eighteen.

So I can double that.

I can also work at nine lots of nine because I'm going to subtract nine away from 90 to give me 81.

Now that I know my two times nine, I can double that again give me four lots of nine.

So it would be for lots of nine is 36 or two lots of 18, because two lots of nine is 18.

I can also work out my eight lots of nine.

Now, if you do this two ways because I know nine lots of nine is 81.

I could subtract another nine away or because I know that four lots of nine is 36, I could double that to give me a lots of nine being 72.

So I know do lots of nine and one lot of nine I can add those together to give me three lots of nine which is 27, or I could remove nine away from 36 to give me 27.

I could also work out five lots of nine because I know 10 lots of nine is 90, I can have this, or I could have added four lots of nine which I knew was 36 to one lot of nine which was nine, then 36 plus nine also equal to 45.

Now because I know five lots of nine is 45 and two lots of nine is 18, I could add those two totals together to make 63 or I could remove one lot of nine from eight lots of nine to give me 63.

And finally, there's different ways I can get six lots of nine being 54, I can do that by adding one lot of nine to five lots of nine, or I could add two lots of nine 18 to four lots of nine 36 or I could remove one lot of nine from seven lots of nine to give me 54.

So now that we've got our complete nine times table.

What do you notice about noise tape? I would say so.

Timestamp, I'm losing my words there.

What do you notice about the multiples within the nine times table? Look specifically at both the columns the tens, in the units.

Do you spot any patterns? I wonder.

Maybe this will help.

You have a blank a hundred square, which you can see represents a hundred square from one to a hundred.

Can you spend a few minutes now? You need to pause the video to fill in your blank square with all the multiples of nine that you identified within the counting stick strategy.

If you have got a hundred square not blank one, circle all the multiples are nine on the hundred squares.

In a few minutes now doing that and once you've done it, look closely, do you spot any patterns? Is there anything unusual about the answers that you see? I speak to you in a few minutes.

Pause with them now.

So you've got a few minutes.

Hopefully you've not passed.

So you either use both or one or the other and you will see, this is what we've got.

What do you notice about the shaded in blank hundred square or the circled hundred square with all the multiples of nine? Well, I notice that there's one line in particular that stuck out to me and there is one line where there are two multiples.

So every row has a one multiple with nine in, apart from this row here.

The ninth row which has two multiples of nine.

I also notice that not each row underneath that the unit was one less.

So you notice it is 18, then it's 27, then it's 36, then it's 45.

Hope you notice that as well.

when we lay of power products here, you will see actually it's quite clear, isn't it? And I can say this with confidence, each time I add a nine, my 10th did you increase it by one and the ones digit decreases by one.

Now this is because when I add nine, it's the same as adding 10 and then subtracting one.

You need to see that in our blank square.

So let's start here with nine.

If I added 10, I would have 19, subtract one, I get 280.

That's correct.

If I've got 18 and add 10 we get 28, subtract one, that'd be 27.

If I've 27 I added 10, I would be at 37, subtract one, I'm at 36.

So that's absolutely right.

And we can see here, the ones column, the digit is increasing by one each time and the ones column is decreasing by one each time.

It's quite a quirky trick I think.

You should know that there's a time to table finger trick to help emphasise that fact about the tens column going up, the digit going up by one and the digit in the ones column going down by one, you may be shown this in your classroom and if you have.

fantastic! I hope you use it when you need it.

If you haven't been shown it, I'm going to spend a couple of minutes now showing you.

I think you'll find it pretty cool.

I do.

It's really interesting and quirky concept.

Let's be clear that this tricky is very unique to the nine times table and one of the reasons why it's such a quirky member of the multiplication family.

Let's start with our fingers out.

First of all, I'm going to multiply on my first finger here.

So one lot of nine.

So lot of nine, remove that finger, I'm left with nine.

This time, I'm going to multiply my second finger.

So my second finger here, so two lots of nine makes 18.

One 10 and eight units.

Third fingure here is going to be three lots of nine or three lots of nine creates two tens, 20 and seven units.

So I have three lots of nine is 27.

Four lots of nine creates three tens, 30 and six units, six.

So I have 36.

Five lots of nine becomes four tens and five units.

So five lots of nine makes 45.

Six lots of nine makes five tens and four units, 54.

Seven lots of nine makes six 10, 60 and three units, 63.

Eight lots of nine make seven tens, and two units, 72.

Nine lots of nine, make eight tens and one little unit there, 81.

And finally 10 lots of nine creates nine tens, and zero units which creates 90.

So there you have it with your fingers hopefully they're not as big as mine I'm struggling to get them into my visualise it, but I hope you could see that by multiplying by nine we can use our fingers to demonstrate how the multiples of nine go up each time.

And that's because each time our tens are just going up by one and our unit digits, were going down by one.

A pretty nifty trick, I hope you agree.

We're now going to move on to our Talk Task element of the lesson.

A reminder that Talk Task generally take place in pairs, small groups, or even in a whole class discussion when we're in school.

If you happen to be working on your own, independently, that's absolutely fine, there's still a task for you to complete.

And it's just a case of recording some of your ideas and jotting down your verbal reasoning if you haven't got anyone that you can verbally discuss it with in person.

We're going to look at exploring the patterns of the nine times table and using those facts to help us identify whether the statements given are always, sometimes or never true.

Greg has got some statements that he thinks he would like to share with the class and he's pretty confident they're correct.

So we need to work out whether his statements are always, sometimes, or never true.

His first statement is this, nine, 18, 27.

If a number is a multiple of nine, all the digits will add together to make nine.

For instance, I think is one and eight, and that makes nine.

27, three lots of nine is two and seven and that makes nine, 36.

If you fall off the nine, three and six makes nine.

So if a number is a multiple of nine, all the digits will add together to make nine.

Is Greg correct? Is that statement always true? Sometimes true or never true.

I'd like to pause the video for some time, think some reasoning and some evidence to support your answer.

And then when you're happy with what you've discussed and what you found out, press play to resume the video.

Good luck with your investigation.

Welcome back.

We're going to go into developing and learning by looking at the results of that Talk Task and whether the information presented was accurate or not.

Whether Greg was or wrong.

And we knew straight away that it must be always or sometimes because there was evidence that one plus eight was nine, and two plus seven was nine, and 3 plus six was nine.

So he was correct on the first three examples.

So therefore we can rule out the never staying obviously is sometimes true or always true.

Then we looked at some of the other examples.

Nine times nine is 81, so eight plus one is nine.

Nine lots of five is 45, four plus five is nine.

Then I looked and I hope you did the same.

Then what happens if I go beyond 10 lots of nine? Why was if I do a bigger number 17 lots of nine.

Well, that gave me 153.

One plus five plus three that was nine always.

Also, so let me ask you, did you think that Greg was always right or do you think Greg statement was sometimes right still? And the evidence we've looked at so far and examples on the screen would suggest he's always right.

However, how about when you multiply by 11? Nine lots of 11.

What answer does that give us? It gives us 99, doesn't it? And nine plus nine equals 18.

So I tried that again, nine lots of 22 gave me 198.

When I added one and nine and eight that gave me 18 as well.

And when I multiplied nine lots of 33 that gave me 297, two plus nine plus seven, that also gave me 18.

I found that very, very interesting but it did prove that the statement that Greg had made was only sometimes true.

It's interesting that when you looked at the numbers that created that anomaly 11,22 and 33 they were twice one of the active wasn't it? So nine lots of nine, two lots of nine makes 18.

So two is a factor 18, but then when we doubled that or repeated that 20, 22 it then suddenly became two lots of nine made 18, not nine.

When we did nine lots of three 27 that did add up to nine digits.

But when we repeated that, is suddenly had two lots of three, and then it became nine, nine and 18.

I find that very interesting.

While exploring the nine times table, Greg had another statement that he wished to share with the class and he was confident it was correct.

He says another way to multiply by nine is to multiply by 10 and then subtract one of the groups.

The example is given, he said, he knows that two lots of nine is 18, so you could multiply two lots of 10 and then subtract one of the groups of two to give you 18.

He presented the calculation in written form as well.

Two groups of 10 is equal to 20, I've got one too many groups of two, so therefore 20 minus two is equal to 18, the equivalent of two lots of nine.

Is Greg right this time? Is this statement always true, sometimes true or never true? I want you to pause the video and use a few examples to try and support your answer and your reasoning.

Don't forget to go beyond 10 times nine and look at what might happen if you times by 20 for instance or turns one number in the 30s.

For a few minutes and then resume the video when you want to check if we're on the same wavelength and whether you agree with Greg or not.

I looked at some examples, such as seven lots of nine, 14 lots of nine, 12 lots of nine and 28 lots of nine.

So remember that I could multiply by 10 and then subtract one of the groups.

So, seven lots of nine, is 63.

So if I multiply seven by 10 to make 70 then subtracting one of the groups of seven, I would have 63.

That is true.

12 lots of nine 108, If I multiply the 12 by 10, I would have another 20, then I'm subtract one of the groups, 12, I would have 109.

That is true.

I'm pretty sure.

Hopefully you're the same that this is always true, this statement, but let's just double check with a few of the other examples as we go beyond 10 lots of nine.

So 14 lots of nine, 126, so if I'm multiplied 14 by 10, get 140 then subtracted one of the groups 14 I would have 126.

And finally then 28 lots of nine is 252.

If I multiply 28 by 10 to give you 280, then I subtracted on the groups of 28, I would have 252.

Now like you, I'm sure, I am pretty confident that this statement that Greg has made is actually always true and I haven't found any examples that would go against that.

So I'm confident and assured that it's always true that method.

Haven't shared a range of different strategies and tricks that you could use to secure your multiplication facts for the nine times table, it's now time to put that into practise.

You're going to have a go and independent ask multiplication mischief, swap the digits.

Let's read the instructions together.

Each equation is incorrect because two digits it's a swap position.

Identify which two digits need to be swapped to create a correct multiplication equation.

Use one of the different tricks and strategies shown to check your answer is right.

The example you can see is six lots of nine equals 73.

Well, that's not right because I know 10 lots of 6 is 60, therefore nine lots of six is 54.

Well, clearly the two digits incorrect.

However, I do know that seven lots of nine makes 63.

So if I swap the six and the seven over, I've got seven times nine equals 63 that I've created a correct equation that involves the nine times table.

I'm very happy with that.

So you can see there's a range of questions, swap the digits incorrect or the incorrect digits into the right places to create the correct equations.

You may need use a nine times table or a hundred square with all the multiple shown if you're not overly familiar or confident about your knowledge of nine times table.

Pause the video now, spend as long as you need on the task, do not rush and when you're ready to check your answers, please press play and resume the video for the rest of the lesson.

Enjoy the task, speak to you in a few minutes.

Bye for now.

Welcome back.

Briefly on your screen you'll see all the correct answers, incorrect calculations, how they were written and how the calculation should look by swapping the correct digits over.

Just check that you got the right answers and if you went wrong anywhere, any misconceptions, just double check now and try and spot where you went wrong.

Sometimes you've just misplaced it, sometimes you just got really confused and sometimes you just use unsecured multiplication or division facts, and that's led to a little errors.

But it's not sorry if you don't get them all right, as long as you're on the right path and you were able to get some of those correct it means that you are able to understand the instructions.

Was it not yet ready to where that pencil, ruler and I want to continue.

We've got a challenge slide for you, generally put the nine times table in order, in a line.

What do you notice about this line of digits and discuss this with someone.

There are two patterns that I've noticed when I looked at this challenge, can you spot the same two patterns I noticed, I'm intrigued.

If you are happy to work with somebody else or somebody in the room, please get them out because this is a really good task to do verbally with somebody else and you can really see if you can both spot the patterns.

Hope you enjoy this task.

Almost at the end of today's lesson but not quite because it of course is quiz time in which you are going to have a chance to see how much of that learning for today's lesson you were confident about and has been embedded.

The key reflection I want you to take away from the session is different strategies that you can use next time you need to work at in out of table.

It could be the magic fingers, it could be the counting stake in the order of derived facts that you know, it could just be a case of multiplying by 10 and then taking away one of the groups.

Best of luck with a quiz, read the questions very carefully, and then once you finish come back for the front a few matches from today's lesson.

Bye for now.

To reminder to you all that we love to see work being created across the country here at Oak National Academy, if you would like to share your work or your multiplication jokes with us here at Oak National Academy, please ask your parent or carer to share on Twitter, tagging @OakNational and #LearnwithOak.

All right everybody, that is now officially the end of today's lesson and what another fantastic session we've had here on Oak national Academy, thank you for joining me today.

And I hope if nothing else you take away from today's session that fantastic and quite quirky trick with our fingers for multiplying by times tables.

I hope you have a great rest of the day wherever you are in the country and I look forward to seeing you again soon here on Oak National Academy as we continue our journey into securing multiplication facts.

But for me, Mr. Ward for now, have a great rest of the day.

Thank you for your hard work.

Bye-bye.