Lesson video

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Hello, and welcome to this lesson.

My name is Mrs. Behan, and I'm going to be our teacher.

For this lesson we are going to learn to use dienes of base 10 equipment to multiply a two digit number by a one digit number.

Let's get started by checking out our lesson agenda.

First of all, we're going to take a look at regrouping.

We're going to see what this means and find out what it looks like.

We're then going to use dienes to multiply, focusing on two digit numbers multiplied by a one digit number.

We will then have a practise activity, and then you will be prepared for your independent task.

So you'll have a go at some questions by yourself.

I know that you will be keen to find out how you got on.

So I will make sure that I go through the answers with you.

You will just need two things, something to write with, so a pencil or a pen, and something to write on.

If you don't have those things to hand, just pause the video whilst you go and get them.

Try to put yourself in a quiet place where you won't be disturbed during the lesson.

So like I said earlier, we're going to learn how to multiply a two digit number by a one digit number.

We're going to put this in the context of a school play.

So it could be any school play in the year, Christmas, Easter, harvest, which one's your favourite? Is at the end of year production.

Well, the audience needs to have somewhere to sit.

So we're going to do some calculating to figure out how many chairs we need, but how many chairs multiplied by the number of rows, okay? Before we start though, there's a couple of words or a few words that are need to share with you to make sure that we can access the lesson.

The first word is partition, and you can see that I'm doing this action.

It looks like I'm pulling something apart.

The word part is actually hiding down in that word at the beginning of it.

So when we partition a number, we break it down into different pieces, different parts, could be 10s and ones usually, okay? So the number 32 would be partitioned into 30 and two.

So three 10s and two ones.

When we put those parts back together, we recombine them.

Try the action with me, recombine.

So that basically means our parts are coming back together to make the whole.

Another word that I need to share with you today is regroup.

So in this lesson we are going to be regrouping ones into 10s.

So once we've got 10 ones, we're going to, instead of have them a single one blocks, we're going to put them into a 10 stick or one of the dienes, okay? We may have 10 10s.

So instead of using 10 10s, what could we use instead? A 100, okay? So that's what we mean when we say regroup.

So we've got partition, recombine and regroup.

So we're going to start by laying out two rows of chairs, each row having 34 chairs.

So I'd like to know how many chairs we have altogether.

So instead of counting in 10s using the picture or twos or ones, we're going to use multiplication.

So to represent 34.

So one row has 34 chairs.

I'm going to dienes.

So here I've represented 34 using dienes.

34 partition into 10s and one is 30 plus four.

But I have two rows, so I'm going to show 34 twice.

34 multiplied by two is equal to 30 times two plus four times two.

So here in this calculation, here is my 10s or here are my 10s, and I've multiplied them by two.

And here are my ones, and I've multiplied them by two, one for each row.

So you can see how many ones there are altogether and how many 10s there are altogether.

So we're going to gather them up there.

Okay, so here they are gathered up.

We have six 10s and we have eight ones.

So 30 multiplied by two is equal to 60, and four multiply by two is equal to eight.

So I'm going to recombine 60 plus eight, and now I have 68.

So I would have 68 chairs in total.

I'd now like to know how many chairs altogether if I have three rows each with 24 chairs.

So what did these dienes represent? Well, 24 represents one row of chairs.

Another 24 represents two rows of chairs.

And this last 24 here represents the third row of chairs.

So I need to gather them all up to find out how many chairs all together.

So 24 multiplied by three is going to be equal to 20 multiplied by three because we've got 20 three times plus four multiplied by three.

We have four ones three times.

So let's get ready to gather them up.

So we've gathered the ones, there are now 12 ones.

We've gathered the 10s, there are now six 10s.

Let's have a good look at those ones.

I think we can regroup.

Let's regroup 10 ones for a 10.

Now we have seven ones, sorry, we now have seven 10s and two ones.

So 60 plus 12 ones or 70 plus two, because we changed 10 of the ones into a 10, gives us the total of 72.

So three rows, each of the 24 chairs, how many chairs are together? There are 72 chairs.

It is very important for us to remember to regroup.

Say the words on the screen with me.

If there are 10 or more ones, we must regroup the ones into 10s and ones.

Say it again with me.

If there are 10 or more ones, we must regroup the ones into 10s and ones.

Because our performance is going to be so popular, we're going to need more chairs.

So let's try four rows each with 32 chairs.

So I've represented 32 four times, because we've got 32 multiplied by four is equal to 30 or three 10s multiplied by four plus two multiplied by four, or two one's multiplied by four.

Two ones multiply by four is equal to eight, three 10s multiplied by four is equal to 12 10s.

Let's group them together.

So I've got our eight ones, and well let's gather them up, so we've got our 12 10s.

We're going to regroup the 10s into hundreds and 10s.

12 10s is equal to 100 and two 10s.

12 10s is equal to 100 plus two 10s.

So what did we regroup this time? That's right, we have regrouped the 10s into hundreds and 10s.

So to finish our calculation, we know that 32 two multiplied by four is equal to 120 plus eight, which when recombined is 128.

So we know how important to is to regroup ones into 10s.

We've now seen the importance of regrouping 10s into one hundreds.

So we now know if there are 10 or more 10s, we must regroup the 10s into hundreds and 10s.

Say the words on the screen with me.

If there are 10 or more 10s, we must regroup the 10s into hundreds and 10s.

Do you think you've got the hang of regrouping now? Let's check.

I'm going to show you four different sets of dienes, and I'd like you to say which ones need regrouping.

Option one, option two, option three, option four.

Pause the video here whilst you have a think whether the sets need regrouping, and if they do, how do they need regrouping? Come back to me as soon as you finished.

How did you get on? Did you manage to find out which sets need regrouping? Let's look at each option in turn.

So let's take option one.

Do we have any ones that need regrouping into 10s? No.

Do we have 10 10s that we can regroup into one hundreds? No.

So does this need regrouping? Eh eh, no, it doesn't.

Let's look option two.

Do we have any ones that need regrouping into 10s? No, we only have eight ones.

Do we have 10 10s that need regrouping into one hundreds? Yes, we do.

We've got more than 10 10s.

So that one will need regrouping so that we have 100 and 10s and ones.

If we look at option three, do we have 10 ones that will need regrouping into 10s? Yes, we do.

We have 12 ones, so we're going to need to regroup into 10 and two ones.

Do we have 10 10s to regroup into one hundreds? Yes, oh, no.

No, we don't, we only have eight 10s.

So we don't have to regroup the 10s into 100s.

But we do have to regroup the ones in the 10s.

So that one still gets a thumbs up.

Let's look at option four.

Do we have more than 10 ones that need regrouping into 10s and ones? Yes, we do.

Let's look at the 10s.

Do we have more than 10 10s that need to regroup in into 100? Yes, and this one we do, I make sure I get it right this time.

This time we have more than 10 10s, so we need to regroup into hundreds and 10s.

So that one, all needs regrouping.

So that one gets another thumbs up.

We don't always have dienes available to us to move around and play around with regrouping 10s on ones, we don't always have pictures to look at either.

So I've done a calculation here, and I've shown you how you can draw 10s on ones or hundreds to help you multiply if you don't have dienes available.

So you can say I have represented ones, 10s and hundreds using drawings.

They're just jottings, they don't need to be the neatest, they just have to be really, really clear.

So I always had to think, "Do I need to regroup any ones into 10s? And do I need to regroup any 10s into hundreds? And that's the key to this lesson.

Are you ready for a challenge? Do you think you can represent your multiplication by drawing dienes? Well, here's my example again, just to remind you, and this is what I would like you to multiply.

45 multiplied by three equals blank, what's the product? Draw out your 10s and ones just like I did, and don't forget, you may need to do some regrouping.

Pause the video here was to have a go, and when you're ready, come back to me.

So what did you come up with? Let's have a look together.

45 multiplied by three, I got the product of 135.

I'm hoping that that's what you got too.

So the first step was to draw out 45 three times, okay? So that's what you can see here.

Four 10s and five ones three times.

Then I had to think, can I regroup any ones into 10s? Oh, yes, I could.

So I put a pink ring around them or a pink box around 10 ones, and I've drawn my other 10 over here.

So then I had to draw them out again, and I thought right, I lay out all of my 10s together first.

So I actually had 12 10s, and then I had my one 10 from when I regrouped my ones.

So I actually have 13 10s and five ones.

So then I had to check.

Can I regroup any 10s into 100? Yes, I could.

I can regroup 10 10s into 100, and I would have three 10s over here.

So now I have drawn one 100, three 10s and five ones.

You are ready now with all of the skills and the knowledge to try the independent task.

Find the product of each equation, draw the dienes to show you working out.

When you've done it, sort the equations into the table.

So here are the equations I'd like you to solve.

And then I want you to put the calculations of these equations into the table depending on whether you had to regroup or whether it did not require regrouping.

So for each of the calculations really, you should be drawing out the dienes and then using the arrows like I showed you earlier to regroup any 10s or any ones, then you sort them into the table.

Does the calculation require you to regroup or does it not require you to regroup? Pause the video here to have a go at the task.

Once you finished, come back to me, and we will go through the answers together.

How did you get on? I can't wait to find out.

So I had a look at 26 multiplied by two, and I found that the product is 52.

So I drew out 26 two times, and I thought right, do I have to regroup any ones into 10s? Yes, I could.

So I did that.

Then do I have to regroup any 10s into hundreds? No, I don't.

So I could stop there.

So the product of 26 multiplied by two is 52.

I then moved to 34 multiply by two.

And I found out that the product was 68.

I drew 34 two times and realise actually I don't need to regroup any ones because there were only eight of them, and I don't need to regroup any 10s because there are only six of them.

So that was lovely and easy.

22 multiplied by three.

Did that need regrouping? No, no regrouping required.

22 laid out three times was equal to 66.

No regrouping of the ones, no regrouping of the 10s.

This one though, oh my, there's lots to regroup here.

36 multiplied by five gave a product of 180.

Let's take a look.

So in grey, you can see where I started, three 10s and six ones, and I did this five times.

So I've drawn them out there.

What I realised then when I was checking, do I need to regroup any ones into 10s? I could regroup three 10s, there were 30 ones, so I regrouped it into three 10s, so I've drawn them here in pink.

I then put all of my hands together, and I realised I actually had 18 10s in total.

So 18 10s can be regrouped into 100 and eight 10s.

So my product is 180.

There are zero ones.

So I've made zero there as a placeholder.

I then moved to 41 multiplied by three, and the product was 123.

I calculated or I've drawn out 41 three times, and then I thought there's no regrouping required there, there's only three ones, but do I have to regroup any 10s into hundreds? And I did, because there were 12 10s.

So 12 10s can be regrouped into one 100 and two 10s.

And I already had three ones, so the product of 31, sorry, the product of 41 and three is 123.

The next part of the test asked you to sort out the calculations into the table.

So let's quickly go through the calculations again without the dienes drawings.

26 multiplied by two is equal to 52.

22 multiplied by three is equal to 66.

34 multiplied by two is equal to 68.

36 multiplied by five is equal to 180.

41 multiplied by three is equal to 123.

So now we need to put them into the table.

26 multiplied by two did need some regrouping.

So we've put that in the does require regrouping colour.

22 multiply by three however did not, we didn't have to regroup any ones or 10s.

We didn't have to regroup any ones or 10s in 34 multiply by two either, so that's going into that column of does not require regrouping.

36 multiply by five needed a lot of regrouping if you remember, we had to regroup the 10s and the ones.

41 multiplied by three is equal to 123, that one needed some regrouping as well.

We didn't need to regroup any ones but we did need to regroup the 10s into one hundreds.