# Lesson video

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Hello, everybody.

My name's Mr. Ward.

And welcome to this session in the unit of securing multiplication facts, in which we review and consolidate the key concepts taught across the unit.

Now, before we make a start on the session, it's important that you've got all the correct equipment, that you are free of distraction, and if possible, you've got a quiet space in which you can focus on the lesson.

If those things are all in place, then I think we should make a start on the learning, so see you in a few moments.

But before we make it start on the main lesson, for the final time in the unit, I'd like to share with you one of my cracking mathematical jokes for the day taken from my rich archive of comedic material.

I think this is one of the better jokes I have, but then I say that most sessions.

I hope you agree.

Fingers crossed you do.

What would I have if I had 12 apples in one hand and 12 oranges in the other hand, what would I have? Enormous hands, of course.

Well, it's made me laugh, it's put me in a good mood, and you do really want to have a maths teacher in a good mood.

So hopefully, fingers crossed, you're chuckling, too.

Jokes aside, this is how the lesson will look today.

A little bit different to some of the other sessions in the unit because we're going to be revisiting and returning to some of the concepts already taught, and we're going to deliver the concepts through a series of small questions and tasks for you to complete at each stage.

So we'll start by looking at how we can represent calculations.

The next section is based on true and false statements you have to prove.

Then we're going to return to the idea of multiples and what would happen to multiples if they move, you know, how would that look with number sequences changed? Could you identify the different multiples? And then the final section is the mystery number, which is a problem in which you need to use your knowledge of factors and multiples to help identify a mystery number.

As always, we conclude our lesson with a challenge slide if you wanted a bit of an extension and an end of lesson quiz, which is a custom here at every Oak National Academy lesson.

To maximise our learning, it's important we have all the equipment that we need.

So I'm going to ask you to have, if possible, the following equipment.

A pencil is ideal, but something to jot down your ideas with a pen or a pencil or colouring pencils.

A ruler is always useful in maths lessons.

Paper, ideally grid paper, but if you haven't got that and you've just got lined paper, blank paper, cardboard, anything to jot down ideas, that's absolutely fine.

You'll also see a 100 square there.

That's been a piece of equipment that we've used throughout the unit in every lesson.

However, you can create your own 100 square, or you could just follow the questions on the screen and make your notes as you go.

If you haven't got any of the equipment that you need and you know where it is, pause the video, go and get what you need, and then press play to resume the video when you are ready to start your learning.

I like to begin every session with a quick warmup to get ourselves thinking mathematically from the very first moment.

How many multiples of four and three can you place correctly onto the Venn diagram? You will see I've given four example numbers.

One is a multiple of four, one is a multiple of three, and two of the numbers are multiples of four and three.

Pause the video.

Spend a minute or two thinking of how many examples you could come up with and where you would place them on the Venn diagram.

Speak to you in a few minutes.

Welcome back.

You can see I've put a few more examples on there.

I wonder what you came up with.

I wondered, by the way, if anybody came up with a multiple or a number that was neither a multiple of four or three.

Could've been a prime number, for instance, 17.

I could place that outside of the Venn diagram.

I really wish I should've have done that now.

I hope you have done that, too.

You can see some of the other examples that had both multiples of four and three in the middle.

Whatever you came up with, you can double check to make sure it's correct by dividing that whole by the multiple to see if you've got the answer.

So for instance, I can divide 90 by three to give me 30.

So I know that 90 is a multiple of three.

I'm going to move on to the first section of our lesson today, and we're going to review and return to the idea of how we can represent multiplication.

Lesson four of the unit focused on the seven times table, and we demonstrated how we can show a number of different multiplications equations from the seven times table using different pictorial and concrete representations.

Can you identify the equation based on the representation? Below are four examples.

You can see that the array is being used to show seven rows of six columns to create a product of 42.

The bar model is being used to show seven groups of eight, seven equal parts, both, each part representing eight gives us 56.

The empty number line is seven lots of seven.

And the Cuisenaire rods we used, each rod was worth nine and there were seven rods in total.

So I represented seven times nine to create the product of 63.

So can you identify the equation based on the representation shown? Pause the video now and write down the equation you think is shown by the representation.

Did you get the correct answers? Five lots of five is 25.

It's also a squared number, 25.

Five equal parts with each part worth six would give us the product of 30.

And five lots of nine is 45, which is also half of 10 lots of nine, which is 90, if you wanted to use some of your inverse and to use some of your knowledge of division to help.

Three more representations of multiplications.

Again, pause the video if you need a little bit more time, or just very quickly jot down the equations you think these representations show us.

So in the area model, we were missing the value.

I had to use my inverse knowledge 36 divided by three equals 12.

Therefore the two factors of 36 are 12 and three.

The empty number line showed me nine steps, nine jumps, and each jump was worth three.

Three lots of nine equals 27.

Finally, I used the knowledge on the law of distributive law to break 22 times three equals 66.

Now, I broke 22, partitioned, if you will, into 20 and two, and then I partitioned the 20 into two lots of 10.

10 lots of threes, 30, plus 10 lots of three, which is another 30, and that gave me 60, and then I added the two lots of three to make six.

That's an example of distributive law.

We can also represent it in different ways.

Again, my knowledge distributive law can be used for the first one.

Here are two examples.

Seven times four is equal to two lots of four added to five lots of four using the cubes, because that gives me two products, eight and 20, when added together to create 28.

I can also show seven lots of four is equal to 10 lots of four subtract three lots of four, because 10 lots of four shown by using the deans.

There were four 10-deans there.

10 lots of four is 40, but then I'm going to subtract three lots of four, which is 12.

40 take away 12 is equal to 28.

Now I would like you to look at the cubes in front of you that use distributive law.

What is the multiplication shown by the representation on your screen? The modification was four times six equals 24, and it was shown in two equal groups of 12, four rows of three columns twice, both added up to 12, and when added together, they created 24.

What is the multiplication shown now on your screen? Again, distributive law has been used.

If you feel I'm going too fast, feel free to the pause video at any stage that you need to either discuss the sum of the equation in front of you or spend a little bit longer trying to find the answer.

The multiplication was five lots of eight equals 40.

We broke that in and partitioned eight into five and three.

Five multiplied by five gives you the product of 25 and five multiplied by three gives us a product of 15.

I can then add the two products together to create 40.

So we can say with confidence five times five added to five times three is equal to five lots of eights.

Now we're going to use the representation using the deans.

What is the multiplication shown below? The multiplication was six times eight equals 48.

We know this because there was six rods of 10, which was worth 60, but then we subtracted six multiplied by two, which is 12.

So 60 subtracted, so 60 subtract 12 equals 48.

But you be counting up our knowledge of the deans and the rods.

There were four lots of 10, and on each row of 10, six has been removed.

So we have 40, because four tens, and we're going to subtract four rows of six, so 24.

40 take away 24 equal to 16, and that is equal to four multiplied by four.

Now we're going to work on our second section today.

Well done so far.

We are covering lots of key concepts.

If you're unfamiliar with anything that I revisit today, feel free to go to an earlier lesson within the unit to become more familiar as we teach those concepts in detail.

Today, we're going to look at true or false statements.

You need to discuss your reasoning.

Now, this is a good opportunity to work with a partner or small group or even a whole class if you happen to be working with others.

If, however, you are working on your own independently, that's absolutely fine.

You can jot down some of your reasoning ideas and reflect on the maths that's being delivered and complete the questions.

Your task is do you agree or disagree with the following statements made by Joe? Can you explain your reasoning for why he's right or wrong? You can use a 100 square to help if you would like.

Here is Joe's first statement.

There is only one number that is a multiple of seven and nine, and that's 63.

I know this because seven times nine equals 63.

Is Joe right or wrong? Is that statement true or false? Do you agree or disagree? And can you explain why you agree or disagree? Pause the video now, reflect on that statement, and think if you can come up with the evidence to support your answer.

Speak to you in a few minutes.

Welcome back.

Hope you identified, like I have, that Joe is incorrect.

It's a false statement.

And the reason it's false is because he seems to be using the incorrect vocabulary.

63 is the only product of seven multiplied by nine.

So seven times nine creates 63.

However, seven and nine are not the only multiples within the 100 square.

So he's used the incorrect language.

I can see this because 14 is also a multiple of seven.

21 is a multiple of seven.

18 is a multiple of nine.

27 and so on, for instance.

That's my evidence to support the fact that Joe was wrong.

He used incorrect language.

Okay, let's see how Joe got with this statement.

Again, is this statement Joe is making true or false, and can you think of evidence to support your opinion or whether you think it's a true statement or a false statement? All multiples of eight and four are even.

All multiples of eight and four are even.

Well, the statement is true.

We know that all multiples of eight and four are even because they are all multiples of two and two is an even number.

I've circled some of my examples.

And I can demonstrate by showing you six examples of multiples of eight and four, and they are all even.

I know this can't be odd because they are multiples of two.

I've therefore proved that this statement is true.

Statement number three.

Joe says there is only one multiple of nine on each row of a 10 by 10 grid.

There was only one multiple of nine on each row of a 10 by 10 grid.

Is Joe correct? Is this statement true or is this statement false? Spend as long as you need collecting the evidence to support your answer and be able to explain it verbally or with some written down ideas.

The statement is false.

There is only one multiple of nine on each row of a 10 by 10 grid apart from the row that starts with 81, the ninth row of the grid.

There are two multiples within that row, 81 and 90.

Now, we know a 10 by 10 grid goes across in intervals of 10.

Well, we know also that nine is one less than 10.

So of course there is always going to be a few examples when there is going to be two multiples.

So by circling my examples and identifying a row, I can prove that that statement is false.

The final true and false statement for this section is the following.

The product 39 can only be created by the multiplication one times 39 or 39 times one.

That's the only way the product 39 can be created, with only the factors one and 39.

Is that statement made by Joe true or false, and have you got evidence to support your answer? Joe unfortunately is wrong.

His statement is false.

I hope that you were able to identify why it was false.

I've come up with an example that actually three and 13 are also factors of 39, and when multiplied together, they produce a product of 39.

Therefore one and 39 are not the only multiple factors that can create 39.

So I've proven that statement false.

I hope you identified that, as well.

Thank you, everybody, for your work and focus so far.

We're now moving onto a new section called moving multiples.

I'd like you to say hello to Mike the Machine, who's going to be featuring heavily within this section.

Mike is a very cheeky machine and likes to play around with multiples, and that's going to be the basis for these questions.

I will read the instructions out for the first question, and then you can complete the questions.

Should we make a start? I think we should.

Here are the first 10 multiples of seven.

Mike the Machine, being mischievous as he is, has increased each multiple by the same value.

What do you notice about the digits in the one's place in the new pattern? Will the number 73 and 88 be in this new pattern? And can you identify a three-digit number within this new pattern? If you happen to be working in a pair or small group, feel free to continue solving these questions together, talking about it and explaining your reasoning.

But if you're working independently on your own, not to worry, that's absolutely fine.

Pause the video now, and then when you're ready to complete the section, press play and resume the video so we can share your answers.

Speak to you in a few minutes.

Welcome back.

Hopefully you identified that Mike had changed each multiple by increasing it by four.

There was two ways of looking at it, actually.

You could either look at it as each multiple of seven has increased by four.

So seven became 11, 14 became 18, 21 became 25, et cetera, et cetera.

But a little further down.

I noticed when I started at 21 that when I removed 10, I got to 11.

28, I removed 10, I got to 18.

35, take away 10, 25.

And that would allow me to predict future multiples within the new pattern if I was secure with my knowledge of existing multiples of seven.

What do you notice about the ones digits, or the digits in the ones place, within the new sequence of numbers? Well, first of all, I noticed that they went odd, even, odd, even, odd.

So after 46, which is an even number, the next number would be odd, and I know the next number would be 53.

I also noticed that the ones digits seemed to be going down intervals of three.

So eight, five, two.

And if that two, for instance, was 12, for instance, three less than 12 is nine, six, three, and so on and so forth.

Will the numbers 73 and 88 be in the new pattern? 73 would not be in the new pattern, but 88 would be.

And there were two ways to find the answer.

Now, I knew, having identified earlier on that each new multiple within this new sequence was 10 less than an actual existing multiple of seven.

So if I know that 98 is a multiple of seven, which is 10 lots of seven plus four lots of seven for 14 lots of seven, I could remove 10, subtract 10, and I would get 88.

So yes, I knew it was in the new pattern.

I also know that Mike had increased the multiples of seven by four, and 84 is a multiple of seven because 84 is 12 lots of seven.

So I could add four to that to make 88.

So there's two ways of getting the answer.

And finally, can you identify a three-digit number in the new pattern? Again, knowing that I subtract 10 from an existing multiple, I know that two lots of seven is 14, therefore 20 lots of seven is 140.

If I subtracted 10 from that, I would get 130.

If I subtract 10 from 147, which is 21 lots of seven, I would get 137.

And if I subtract 10 from 154, which is 22 lots of seven, I would get 144.

And so on and so forth.

I hope that you have identified a new three-digit number within the pattern.

Okay, so here's the section question in the section.

This time I'm not going to read the instructions.

I'd like you to read each sentence and all the instructions and questions that you need to do.

So read the instructions carefully, pause the video, spend as long as you need.

We will share our answers in a couple of minutes.

Press play when you're ready to resume.

Welcome back.

As we can see, our multiples provided were the original multiples of nine, then Mike increased each multiple and this time increased it by six.

So each multiple went up by six.

What do you notice about the digits in the ones place this time? I had noticed, I hope you did too, that they were reducing, or they were one less each time, five, four, three, two, one.

And that allows me to predict.

So the next one would be 69 from 10 to nine.

And the next one after that would probably be 78, and then 87, and so on and so forth.

Will the number 87 and 114 be in the new pattern? Yes, they both will be.

I could see that not only was each multiple increased by six, and I know that 81 is a multiple of nine, nine lots of nine.

So I know that 87 would be.

I also noticed that each multiple seem to be three less.

So 18 take away three is 15.

27 take away three is 24.

36 take away three is 33, and so forth.

So if I know that nine lots of 10 is 90, I then can take three away from that to get me a new multiple, which is 87.

The same with 114.

I know that nine lots of 12 is 108.

And therefore I know that 13 lots of nine is 117.

I can then remove three, and that gave me 114.

And three examples of three-digit numbers that I came up with, 132, 177, 267.

And an easy way to check is if you were to divide that by nine and then add three, you would get, by using my inverse, divide by nine and then add three, you should get an original multiple of nine.

I hope you enjoyed that challenge using your knowledge of multiples.

And we're going to move on to our final section today, which is called a mystery number challenge.

Once again, you're going to need your prior knowledge of multiples, and perhaps it will be also useful if you were comfortable with the idea of factors so that you can use inverse to check your answers and to be sure about the number you think you've identified.

This game is called mystery number.

I'm going to read the clues carefully.

Eliminate the possible answers until you are left with one.

Double-check the clues again.

You may use your 100 square to help.

I will read out the clues for the first question, and then I'm going to ask you to read the clues yourself for the second question.

So here is question number one for the mystery number.

I am thinking of a number.

It is a multiple of seven.

So you need to identify all of the multiples of seven within the 100 square.

Number greater than 30, but less than 100.

It is not a multiple of nine or six.

Let me repeat that.

It is not a multiple of nine or six.

It is an even number where one digit has a value less than six.

The final clue is the sum of the digits is 11.

What is the number? Pause the video if you need a little bit of time to read through all the clues and to check off the numbers it can't possibly be to leave you with the number you are pretty sure it is.

So read the clues through again.

One by one, eliminate each number that you believe the number cannot be, and hopefully you will be left with one option.

The number I was thinking of was 56.

It is a multiple of seven.

The number is greater than 30, but less than 100.

So that would've got rid of all the multiples before of seven.

So seven, 14, 21, 28.

It is not a multiple of nine or six.

It is an even number where one digit has a value less than six.

So the tens column, the digit in the tens column was five.

That's one less than six.

And finally, the sum of the digits when those digits are added together gives us 11.

The number was 56.

How did you do? Did you identify that number correctly, or did you perhaps eliminate it by accident? Perhaps you had more than one option left and you weren't quite sure which one.

It's absolutely fine if you didn't get that number, but it is a very good way of working systematically.

So listen and read the clues carefully and then eliminate as you go.

Remember, you can pause the video at any stage to take your time to find the correct answer.

This is a second question on the mystery number.

I won't read the clues out to you.

All right, did you identify the mystery number I was thinking of? It's 35.

It's a multiple of five.

I know that because five lots of seven make 35.

The number is greater than five, but less than 50.

So you could have eradicated all the multiples of five from 50, 55, 60 onwards.

You could also have eliminated five.

It's not a multiple of eight, four, or three.

So that allowed you to eradicate options such as 20 and 40 and 30.

It is an odd number one where one digit has a value greater than two.

We can see both of the digits are greater than two.

And it is an odd number.

And finally, the sum of the digits is eight.

Three plus five is eight.

How'd you get on? Did you identify that number? I hope you did well.

If you're not quite sure, you can always go back through the clues again and try and spot where you made your misconception.

Did you take off the incorrect number? Did you eliminate the wrong one? Or have you got multiple options left because you haven't quite identified which one needs to be eliminated? Great work today reflecting and reviewing the key concepts.

Almost there, but it is of course, quiz time, which is a custom here at Oak National Academy.

The key reflection I'd like you to take away from today's session and into the quiz is knowing your multiplication facts from one to 10 will allow you to calculate very large numbers.

So think back to the counting stick in which we've used in other lessons within the unit or the different ways that we represent our multiplication facts.

Knowing those facts and knowing our times tables gives us so much confidence and security to calculate with very, very large numbers.

So find the quiz, take your time, read the questions very carefully.

I've got my fingers crossed for you, but I know you do not need luck because you've got this.

You've got the mathematical knowledge inside you already.

Once you finish the quiz, hopefully full of confidence and happy and smiling, come back to the final few messages for today's lesson.

I would just like to take a moment to remind you that there is an opportunity to share your work and mathematical jokes with us here at Oak National Academy.

We're looking forward to seeing some of the fabulous mathematical learning that's been taking place across the country.

And that, ladies and gentlemen, brings us to not only the end of today's lesson, but the end of the unit as a whole.

You've done a really good job.

Thank you for sticking with me.

I've really enjoyed teaching this unit and I hope you leave feeling more confident and familiar with some of the key strategies and concepts that really help underpin our multiplication knowledge.

It's been a fantastic opportunity to teach you.

I hope you got out of it as much as I have.

And I hope to see you again in other units here on Oak National Academy.

So thank you for joining me and thank you for your hard work.

You've made it an absolute joy to be your teacher for today and for this unit.

From me, Mr. Ward, bye-bye for now.