Lesson video

Welcome to Oak National Academy.

Thank you for joining me Mr. Ward, as we begin a new unit on securing multiplication facts.

Today's lesson is focusing on multiplication patterns.

Now wherever you are in the country, I hope you're well, and I hope you're looking forward to your mathematical journey with me, Mr.Ward.

However, before we make a start it's important that you are free of distraction.

I'll ask you to try and find a nice quiet space in which you can focus on your learning.

When you feel ready to begin, continue the video and we can get started because I'm quite excited, I hope you are too.

See in a few moments.

Before we make a start on our main lesson, I like to introduce a mathematical joke into my lessons to get a smile on your face and hopefully get you enthusiastic about the lesson ahead.

Today's mathematical joke, I think is an absolute go-to, but of course you can be the judge of that.

Why were the school pupils found doing their arithmetic questions on the floor? They did not want to get in trouble, their math teacher had told them not to use their tables.

Now, if you think you can do much better than me, and let's be honest, that's not very high bar to set, I'll be sharing details at the end of today's lesson on how your parent and carer can share your work and your mathematical jokes with us here at Oak National Academy.

So please keep watching until the end of the lesson.

If unbelievably didn't find that mathematical joke absolutely hilarious, and you're here of your mathematical learning, don't worry, there are no more terrible jokes coming your way.

Just lots of detailed concepts in which we'll share together.

Here's a quick overview of what the lesson looks like today.

I'll introduce the idea of multiplying using a counting stick and sharing all derived knowledge.

Then we're going to have a Talk Task in which we're going to explore some multiplication patterns, and we're going to take our learning a bit further by discussing those patterns and seeing if we can spot some of the trends that came from the multiplication grids.

Then I'm going to pass it over to you.

And you're going to have a go at an Independent Task in which you need to identify further patterns using different multiplication facts.

And then as always here at Oak National Academy, we ask you to end the lesson by having to go with the quiz to see how much of today's learning has been embedded and how confident you will be working on these concepts in the future.

Maximise our session, it's important we have the right equipment if possible.

So I'll ask you to have a pencil or a pen, something to jot down your ideas, a ruler, some paper, doesn't have to be good paper or that's idea when we use our math learning, but plain paper, line paper, or even the back of cereal boxes or cardboard.

Something to jot down ideas if you have nothing else would be fine.

But if you have got a notebook from your school, that would be great as well.

You'll also see there's a picture of a rubber there.

Now a rubber is optional and actually in a Mr. Ward lesson, I like to encourage pupils not to rub out, but to just put a line, a neat line through their mistakes.

And say, look I've just made a mistake.

I noticed it was a mistake.

We've learned that it was a mistake and to show the right answers and the correct maths.

'Cause that's a really good way of demonstrating your mathematical learning.

Now if you haven't got any of this material or equipment right now, pause the video, go and get exactly what you need.

And then when you're ready to begin the main lesson, resume the video and you can join us.

Speak to you on a few minutes.

Okay, we need to get our brains firing on all cylinders and try and get some of those multiplication facts back into our kind of consciousness.

So today's warm up which you should only spend about three or four minutes on this.

So you need to pause the video, complete the calculations below.

Can you find the missing values of what will make these number sentences complete? When you're ready to share your answers and check you've got right, resume the video, and we can see how you've got on.

Speak to you a few minutes.

Welcome back everybody.

The answers are on your screen.

Just check that you got them correct.

These are all parked.

These are all derived facts or facts within the multiplication tables.

Some of which we'll come across today during our learning.

If you have made any mistakes, just check where your misconception is.

Did you get the wrong product? Did you just misread the question? And try and identify and self-correct yourself.

Okay we're going to make a start from the New Learning.

We use a counting stick to show time tables.

Now you may have seen this in your classroom, your teacher or adult that you worked with on your maths may have demonstrated this in the past.

And if they have that's fantastic, this is a really good way to do it.

You may also recognise that long line.

I've got a few in my classrooms. They are useful.

They're metre sticks basically, but we use them also because of the section we can demonstrate bar modelling, we can demonstrate multiplication, we can do the inverse and show division.

There's all sorts of things we can use these for.

Today, I'm going to demonstrate how we would use a counting stick to show times tables.

I wonder how confident you are with your six times tables.

And if you are very confident, what advice could we give to someone who doesn't know them by memory? So this activity is really great on two folds.

If you're not very secure with your six times tables, then I'm going to demonstrate some of the ideas that I would suggest to help you consolidate that information.

And if you do, then you can think about what you would do it, and whether you would follow the advice I'm giving or whether you would give different advice to somebody that needed some support with their multiplication tables.

First of all, I'm going to start with the multiplication fact I know securely.

I know zero lots of six is zero, because if I were to multiply anything by zero.

There's nothing there.

I also know that one lot of six, is six.

And now look, if one lot of six is six, and I multiple about 10, that will give me the product that it's 10 times greater.

So 10 lots of six will be 60.

And also because I know one lot of six, I can double that by adding it together or multiplying by two, to give me 12.

So two lots of six is 12.

Now that I know and lots of six, I can half that by dividing by two to give me five lots of six which is 30.

The fact that I need to know there is it two lots of three makes six or six divided by two makes three.

And that allows me to do it on a factor of 10.

Because I know two lots of six is 12, I can also pull that by finding that by two and give me four lots of six, which is 24.

I can have either added 12 together or just 12 times two.

I can then also multiply four by two, or two lots of six by four to get me eight lots of six which is 48.

Again, I could have added 24 and 24 together to do two lots of four, or I could have done 12 times four.

Now, because I know five lots of six.

And I know one lot of six, I can work out that six lots of six is 36.

Then I'm about to find three lots of six or I could have done two lots of six, which is 12 and added it to one lots of six, which is six.

12 plus six is 18.

So that allows me to work out the three and six times eight.

And because I know the nine times table, I could either add five lots of six which is 30 and 4 lots of six which is 24.

I could take one lots of six away from 10 lots of six.

So six take away six, or I could multiply three lots of six which is 18, three times to give me the answer of 54.

Seven times table, I could done my knowledge of five lots of six being 30, plus two lots of six being 12 to make 42, or I could have taken one six away from eight lots of six.

So one six away from 48 or added one lots of six with 36 to get 42.

So I have various different ways in which I can identify some of my multiplication facts.

Just take a moment and pause the video if you need a bit longer to look at all of our multiples within this six times table.

From one lots of six all the way up to 10 lots of six.

Do you see any patterns? Do you see any trends? What stands out for you? Hopefully, you can have identified that all the numbers are even.

This is because the multiples of six are all multiples of two and two is an even number.

You might also have seen a recurring pattern of the ones digits.

If we look that goes two, eight, four, zero, six, two, eight.

And that allows us to predict.

So the next one will have a four.

We presume in the units column, which would be 54.

The next one would have a zero which is 60, the next one would have a six, which is 66 and so on and so forth.

Now I'd like you to spend a few moments shading in all the multiples of six that you created and the rest within the hundred square.

Now there is a blank 10 by 10 grid you can see here.

Which represents a hundred square, which is without the numbers shown.

So you could find one, two, three, four, five, six, and identify that as the first of multiple six.

One, two, three, four, five, six, that would be 12.

So that would be multiple of six.

I'd like you to spend a few moments.

Again, you're up.

You will have to pause the video, I think to shade in the 10 by 10 grid.

And if you're not comfortable using a blank grid, why don't you circle all the multiples that you can find on that hundred square that you see on your screen.

Just to be clear I'd like you to shade all multiples of six in your grid.

And I want you to continue beyond 10 lots of six being 60.

For instance, 10 lots of six is 60.

And five lots of six is 30.

That would suggest that 15 lots of six will create 90.

What patterns do you notice as you shade your grid? Here's an example of what I mean and just in case you're still a little bit confused.

Pause the video now, for as long as you need to complete shading your grids and then resume the video, when you want the feedback.

I'm interested in what patterns emerge from our shaded grid.

Here's our completed grid.

And let's just for a very brief moment, discuss any patterns that seem to be emerging.

Well, I think to notice that on every third.

Every third line there appears to be one multiple.

So one.

We've every four no, every four, my mistake, every four or five.

So the first line is one, two, two, one multiple, two, two, one multiple, two, two, one multiple.

There's an interval of obviously five blind squares between each multiple, because it's going up in six.

There these beautiful lines in the fact are amaze.

Isn't it? I can imagine these in a Roman Villa somewhere, with all these beautiful colours.

There were no multiples in the three column.

So this is where three, 13, 23.

There are no multiples in the five columns.

So that means that a number where the digit, the ones this five are no multiples of six.

There are no multiples in the seventh column.

So every number ends with a seven.

So 17, 27, 37.

And there are no multiples of six in the column there where the ones end in nine, interesting.

I wonder what pattern you found and what you think about this multiplication grid.

Now let's add a bit of colour to it makes it look a little bit different, doesn't it? Can presents it in a slight different way.

We're now going to do counting stick again, with our 12 times table.

And you might notice something come out of six and 12.

I'm going to say right now, but hopefully you've spotted it.

And we going to go through the counting stick again.

Again, if you are not very confident with the 12 times table, this might be a really useful piece of advice that I'm giving you and a useful exercise to do.

If you are confident with using 12 times table, think about what order you will present the information.

And which of the multiplication facts you would probably advise they work on.

Okay, and we start with the fact that we know.

We know that zero lots of 12 is zero because there's no product there.

One lot of 12 creates 12, the product of 10 lots of 12 is 120, because 10 is 10 times greater than one, and therefore 120 is 10 times greater than 12.

Because I know one lot of 12, I can double on that.

Make two lots of 12.

Because I know that we have 10 lots of 12 makes 120.

I can half that because 12 is a multiple two, so I can divide it by two to give me six.

Therefore, half of 120 is 60.

I can then work two lots of 12 we get 24 to make 48, or I can take one lot of 12 away from 60 to make 48.

I could all then add one lot of 12 to five lots of 12 to create 72.

Now that I know what six lots of 12 is, I can half that by dividing by two, or I could add one lot of 12 to two lots of 12, which will be 12 plus 24 to create 36.

That also allows me to work out six lots of 12 if I haven't already done so, because I could double three lots of 12.

Because I know four lots of 12 is 48.

I could double that by two or multiply by two to create eight lots of 12 and 96.

Or I could take the five lots of 12 which is 60 and add three lots of 12 which is 36.

36 plus 60 would create 96 as well.

Finally, I could work out my seven lots of 12 by adding five lots of 12 and two lots of 12 together.

Or I could take one lot of 12 away from 96, or I could add one lot of 12 to 72.

I have multiple options to help you here.

The same with nine lots of 12, I could subtract one lot of 12 from 10 lots of to 12.

I could add one lot of 12 to eight lots of 12, or I could add five lots of 12 to 60 and four lots of 12 which is 48 together to create 108.

Hopefully what I've demonstrated is that we can focus on our core and secure number facts and multiplication facts, and then we can use a variety of different flexible ways to find the rest.

Look at the two counting sticks and the multiples.

For the multiples of six and the 12 times table.

What's the same? And what's different? What's the same and what's different? Well hopefully you identified that all the multiples of 12 or so appear in the multiples of six.

However not all the multiples of six appear in the multiples of 12.

18, 30, 42 to name but a few are no longer there.

We can see that there seems to be.

Because two lots of six is 12, the distance doubles each time.

So if I look at two lots of six is 12 and two lots of 12 is 24.

And the difference between 12 and 24 is one.

And we double it becomes two.

The difference between 24 and 60 down here, is one, two, three.

The difference here is six.

One, two, three, four, five.

Two, three, four.

So you see the difference is doubling every time.

Well again, I'd like you to take this grid.

This time we've got a 10 times 12 grid to allow us to get all the multiples on the counting stick shaded.

I'd like you to shape your grid with all the multiples of 12, which we have discovered using our counting stick.

And again, let me ask you what patterns do you notice within the grid.

If you don't want to use the grid, and you'd rather use a hundred square that you may have, circle all the multiples of 12 that exist within that hundred square.

But be mindful that a hundred square will only go to a hundred.

And therefore, you will will be missing of a couple of the multiples which we'll identified.

So take as long as you need, and then resume the video, when you want to share.

In order to best see the similarities and differences between the two shaded grids, we can lay them side by side.

On the left, you will notice it's in 12 times table grid.

On the right, it is the six times table grid.

The first thing that sticks out for me is that there are twice as many multiples in the six times table grid, than there are in the 12 times square grid.

And that's not really surprising when we consider that six times two or two lots of six is equivalent to 12.

Therefore, it shouldn't really be a surprise that there are twice as many multiples.

It's also clear that in terms of similarities, neither multiples of 12 or multiple six exist within the columns that would end with one, at one in a unit or three or end with a five, or end with seven, or end with a nine.

What's also different is that whereas there's a multiple on every line of the six times table and the grid, on the grid for the 12 times table, there are some lines or some rows should I say rather that have no multiples in its all.

Look at the top and half way along.

Now, this is of course not as surprised when we consider that 12 is obviously greater than 10.

And as all grades only go to 10, then of course there are going to be occasions when we needed to start a new line in which to put that multiple down.

So that's not a surprise.

Therefore, that also suggest that the interval is going to be different.

Whereas the interval between multiples is five blank squares, here the differences is 11 blank squares.

However we do get that lovely pattern.

I think I prefer my six times table in my Roman villa just because of that more blue.

But we will see the same kind of diagonal pattern on both sides.

And we know that because we identified a few minutes ago that all multiples of 12 exist within the six times table.

Now we're going to move on to a Talk Task.

I want to let you know that Talk Tasks within schools are usually done in small pairs, or small groups, or whole class settings.

And of course, I understand that some of you will be working on your own and that won't be possible, but that doesn't mean that you can't complete the Talk Task.

You can do it independently.

And you can either reflect on the information that you see or write down some ideas and jottings.

Or if you've got somebody nearby, an adult, a carer, your pet, a sibling, get them over, and try encourage them to have a go at this task with you.

And talk about the maths that you're seeing.

So there's no excuse for nobody not doing this task.

And it's a really good opportunity to use some of the mathematical vocabulary during the activity.

Here's your Talk Task for today.

I'd like to explore multiplication patterns.

We've just looked at the six and the 12 times table grids.

I'd now like you to do 10 by 10 grids for the two times table, the four times table, and the eight times tables.

Once you've shaded all the multiples of two, four, and eight within the 10 by 10 grid, I'd like to reflect on the following questions.

By either jotting down some ideas or talking with people that you have been working with.

What do you notice about the grids? What's the same? what's different? And what patterns exist within our grids? Pause the video now, spend as long as you need on the task.

And then when you're happy to share what you've got and have a look at some of the ideas I've jotted down, you can resume the video.

Complete your task and I'll speak to you all in a few moments time.

Bye for now.

Okay, welcome back.

And we're going to move straight into our Developing our Learning because half of this learning is about looking at some of the patterns and similarities within the groups that you've just done.

So we can feed back on our completed tables.

I'd love to be sitting in a big, big room right now with all of you discussing our maths, but that's not quite possible.

So you're going to have your ideas in front of you.

I'm going to share what I saw and I hope that there are some similarities.

If you found things that I didn't find that absolutely fantastic.

And that's great to see.

And of course, that's the beauty of maths.

We will always sometimes find things that other people don't see.

Here are the three multiplication grids that have been shaded.

We can see, there are far more multiples in the two times table.

But that's not a surprise is there because two lots of two makes four and two lots of four makes eight.

So therefore, there's going to be, we should imagine four times as many multiples in the two times than they are the eight and twice as many multiples in the two times table, than they're on the four.

Here's a list of what I found.

No numbers in the three tables end in three, five, seven, or nine.

No numbers end in a one either, I should have said that.

I didn't see that.

I've just seen it right now.

But in the ones column, where it would be one, 11, 21, 31, there are no multiples of two, four, or eight.

That's not surprising when I consider that all the numbers are even, aren't they? All numbers in the four and eight, are in the two times table.

The two times they table include all numbers in the 10 times table.

Some of the 10 times table exist in the four and eight times table, but not all of the numbers.

And every other number in the four times table exists in the eight times table.

We're now going to move over to the Independent Task.

And this is an opportunity for you to have a go at the task without support.

Although if you are a little bit unsure, you can go back over the previous slides and the parts of the video to try and check some of the information that you weren't quite sure about.

Now your task is this.

We'd like you to identify multiplication patterns.

You're going to continue doing a very similar to what we've done previously, but looking at new time cycles.

So I would like you to look at the three, seven, 11 and the 12 times table again.

Once you've shaded all those grids and you may already have the 12th time table shaded from earlier, I'd like you to compare the different multiplication tables and consider these questions that we've already asked in the lesson.

What do you notice about the grids that have been shaded? What's the same? what's different? And what if any, patterns exist within these multiplication tables? If you need to have your hundred square with you to help with the multiples, feel free to do so.

It goes on the grid.

And if you haven't been working in groups or with someone nearby, take the opportunity to once again, discuss your maths and share some of the patterns that you're spotting.

Pause the video now, take as long as you need through the task and try to use a rich variety of vocabulary, which we've introduced during today's lesson.

I hope you enjoy the task.

And I look forward to speaking to you all very, very soon when we share our results.

Bye for now.

Okay, we'll quickly reflect on some of the ideas and feedback.

These are the grids I shaded in my time.

So I hope yours look very similar.

They should.

There correct multiples.

I would be interested to hear what you found the same again.

I think I've got a lot of three times table.

That's definitely something I'd like to have a my Roman Villa.

I will love the colours as well.

The 11 times table looks past that he's perfectly diagonal.

Isn't it? Whereas the 12 times table again we can see those rows where they're missing multiples.

The same as the Eleven's actually there are two rows here that don't have any multiples as is the same case for the 12 times table.

And that's not surprising.

We consider again 11 and 12 are both greater than 10, whereas seven and three are less than 10.

And therefore, each row has at least one multiple on.

The seventh is interesting in terms of you've got one, one, two, one, two, one, two, one, one, two.

So there seems to be a recurring theme there.

Okay, for those that are not quite ready to end the lesson and you want to continue with your mathematical learning, that's a fantastic to hear, and it makes me beam with a big toothy smiles.

You can do this Challenge Slide.

I miss the whole lesson.

We'll always have a Challenge Slide at the end of the video.

How many different ways can you complete the multiplications shown below? How many different ways can you complete the different multiplications shown below? Have you enjoyed this task? Take as long as you need on it and then resume the video when you want to finish today's lesson.

So it almost, and I mean almost at the end of the lesson, but not quite because it is now time for the quiz.

At the end of every Oak National Academy lesson, we asked you to try and demonstrate how much of the learning has been embedded by having a go at the quiz, which you can find.

Once you finish the quiz, and read the question questions very carefully, please come back for the final few messages from me on today's lesson.

The one key reflection I'd like you to take away from today's lesson is knowing the intervals between multiples will help us be more efficient with our times tables.

Okay, a little quiz everybody.

I mentioned it at the start of the lesson.

We here at Oak National Academy would love to see some of the work we have produced while you were at home.

If you would like to share your work or your mathematical jokes, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

We're looking forward to seeing some of the fantastic work that you're proud to have produced.

All right everybody that does bring us to the end of today's lesson.

Thank you for your whole working and your focus.

You did a really good job, and I hope you found it interesting to look at multiplication tables from a new perspective.

And see that how our new knowledge of multiples and the patterns that exist within our mathematics can allow us to work with our confidence with larger numbers or to predict future multiples.

Now, I hope to see you again here on Oak National Academy, along with some better jokes, fingers crossed I can't promise, but for now have a great rest of the day.

I'll look forward to seeing you again.

My name's Mr. Ward.

You've been great.

Thank you for now.