Lesson video

Hello everyone, I'm Miss Brinkworth and I'm going to be doing this lesson with you today, which is about multiplying two digit numbers by eight, and we'll be using a partitioning method to do that.

So I hope you're all ready for some maths.

Let's look at today's lesson then.

Well firstly, I've got a little bit of maths fun for you.

I wonder if you've ever heard of square numbers.

This is a square number.

It is four.

It is made of two times two.

Two times two is four, and so four is a square number.

What do you think is the next square number? Two times two is four.

The next square number is three times three, so the next square number is nine.

Pause the video here.

What do you think the next number that's going to appear is going to be? Did you manage to work it out? We did two times two and we got four, we then did three times three and got nine, so the next grand number is four times four, which is 16.

If you went to challenge yourself, you can carry on and try and find as many square numbers as possible.

Just a little maths teaser to get us started there today.

So, let's just make sure you've got everything you need, pen or pencil, and something to write on.

And if you can find some online Dienes, so Google Dienes.

They're the little blocks that you've used in school.

There are some really good online tools.

If you can find those, they may be useful, but you don't have to.

If you can't find them, please don't worry about it.

Pen and paper will be fine.

Okay, let's get started then with our key words.

Our star words for today are all about multiplication.

So I'll say them, and if you could repeat them at home, it'd be really useful.

So we have multiplication, regroup, partition, factor, times, commutative, equal parts, column addition.

So this is vocabulary that we're going to be using during our lesson today.

Okay, here's another little warm up for you.

Which of these numbers are multiples of six? There are four of them, which are multiples of six.

And if you managed to work that out, have a think about how you know.

How do you know which ones are multiples of six, or how do you know ones aren't multiples of six? Have a go.

How did you get on? Let's have a look.

Multiples of six, then.

There are four.

Let's see how you got them.

These are the four numbers here, which are multiples of six.

I'm pleased if you didn't get caught out by numbers like 16 or 601.

We know that just because a number has six in it like 16 or 601, it's not necessarily in the six times table.

But how did you know then that 330 was in the six times table or 186? I'm sure 12 was maybe the easiest one to find.

We know that two times six is 12, and 66, well, 11 times six is 66.

But the other two, we have to do a little bit more investigating.

So, maybe you were able to see that 330 is 300 and 30.

300 is definitely in the six times table, because 30's in the six times table.

So 300 will also be in the six times table.

And for 186, well, 18 and 180 is 18 times 10.

And we know that 18 is in the six times table, and then we just added another six on, so must be a multiple of six.

Well done if you could see all of those.

Again, I mentioned sometimes when you see a question like this, you could work out which ones aren't multiples of six.

So you could dismiss 16 quite quickly when you know that 18 is a multiple of six, so 16 can't be.

And then when we come on to 73 and 601.

Those are odd numbers.

Odd numbers don't appear in the six times table.

So we could dismiss those quite quickly as well.

Well done if you were able to get all of those right.

Okay, moving on to today's lesson then.

It's going to be really important that we know how to multiply by 10.

Now this should be a quick bit of revision for you.

If you look at that example there, we can see that 21, when we multiply by 10 would make it 10 times bigger.

Each digit moves one decimal place to the left.

So the two from the tens moves into the hundreds, and the one, which is in the ones column, moves into the tens.

And then we can put that zero in its place holder if we need it.

So 21 times by 10 is 210.

Pause the video here, and have a go at timesing those other five numbers by 10.

Let's have a look at how you got on.

Like I said, this should be quite simple for you, but it is a really good skill to have at your disposal really quickly, and it's going to be super crucial for today's learning.

So, 12 times by 10 is 120.

10 times by 10 is 100.

83 times by 10 is 830.

Notice that the eight and three are still right next to each other.

Sometimes a zero creeps in and people make a mistake.

And the zero's only ever used right at the end as a place holder.

The eight and the three stay next to each other.

So 83 becomes 830.

140 becomes 1,400, and 210 becomes 2,100.

Well done if you got all of those right.

So that's a really good start to today's lesson.

So let's have a look at that learning objective in a bit more detail.

We are going to multiply two digit numbers by eight using partitioning.

Two digit numbers, we looked at these already a little bit.

These are numbers, which have two digits, so they have a dig in the ones and a digit in the tens as well.

So all of these numbers here are two digit numbers.

And we're going to be multiplying by eight.

Hopefully, your eight times table is one that you're quite confident with now, but remember that you can use your four times table and double it to make you eight times table if that's one that you feel a little bit happier using.

And then I'll find thing on our learning objective today is we're going to be using partitioning method.

And this is what we mean by partitioning.

16, for example, partition splits into 10 and six.

So, this alert these three things, so two digit numbers multiplying by eight, partitioning two digit numbers, and timesing by 10 that we just looked at are our main skills we're going to be utilising to achieve this learning objective today.

So, let's have a look at what this looks like.

So, for an example, a question like 14 times eight, the first thing we're going to do is partition that two digit number.

So our two digit number in that question is 14.

So, 14 partitions into 10 and four.

We then multiply each of those by eight, 10 times by eight, four times by eight.

And if you've got some online Dienes, you can use those to help you.

We've got eight lots of 10 there.

And you can use eight lots of four as well.

So what are the answers to these questions? So, 14 times eight, we're going to do 10 times eight, and then we're going to do four times eight.

10 times eight is 80, and four times eight is 32.

We haven't got the answer to our question just yet though.

So the final step is to add those two numbers together using column addition.

So 80 and 32, lining them up beautifully with our with our column addition means that we get the answer 112.

Let's look at that in a little bit more detail.

Here's the method you're going to be using today.

And here's your success criteria.

So three simple steps.

If you follow them each time, you should get your accurate answers.

So the first thing is to partition the two digit number.

And you can see from this example here, I've done that for you already.

I partitioned 48 into 40 and eight, and then I've put them on this grid.

Now you might have seen a grid where they're the other way around, so maybe eight at the side, and then 40 and eight, and then it's split down the middle vertically.

It doesn't make any difference which order we do our multiplication in.

And if you prefer to set it out that way, that's fine.

I'm going to set it out like this for this lesson.

So, we've partitioned 48 into 40 and eight.

Next thing, multiply by eight.

So 40 times by eight.

Hmm, I don't know my eight times table all the way up to 40, but I do know four times eight, and I can use that to help me.

So four times eight is 32, and then I can make 10 times bigger.

Multiply it by 10 to get 320.

I've then done 40 times eight.

I then just need to do eight times eight, which is 64, and then my final step of my success criteria there is to add the answers using column addition, so 320 at 64 gives me that final full correct answer, 384.

So let me just go through that one more time with you what I've done there.

I have partitioned the two digit number.

I've then put it in this grid, so that I can see I'm going to multiply 40 by eight, and I'm going to multiply eight by eight.

I've done both those multiplications separately, and with a question with a multiple of 10, like 40, I've used four times eight, and then I timesed it by 10.

And then finally I've added them both together with column addition.

Do you take care with your column addition.

That can be a part of the question where people make silly mistakes, and that can be the part where actually they ended up getting the question wrong.

So don't rush your column addition.

Line them up in those place value columns correctly, and just check your answer that's reasonable.

We're doing 48 times eight.

I would expect my answer definitely to be in the hundreds, not into the thousands.

And that's where my answer has sat.

So it looks like a reasonable answer to me.

Let's try another one.

I've done the first part of your success criteria for you here.

I have partitioned 52 into 50 and two.

Pause the video here and see if you can follow the success criteria and get that question answered.

How did you get on? So we need to do 50 times eight.

I don't know my eight times table all the way up to 50, but I'm really confident with five times eight, 'cause I love my five times table, and I know that five times is 40, so 50 times eight, I just need to make it 10 times bigger, gives me 400.

Well done if you got that bit.

Really, really well done.

You got one of the really key skills needed to get all of these answers right.

Good work.

And then it's just two times eight.

And again, I feel really confident with my two times tables.

And two times eight is 16.

Not finished, though.

Don't forget that last step.

Got to add these two together, and column addition is really useful.

So 400 add 16 gives us 416.

Well done if you got the right answer there.

And let's try one more.

This time, it's your go to draw out the grid as you'd like to and to partition that two digit number.

Pause the video here and have a go.

How did you get on? Let's have a look.

Did you get this far? Have you got something on your page that looks like this? You've positioned 33 into 30 and three.

And you can see that you're going to times them both by eight as well.

That's all that that grid is there for, just to split that number up and keep those two multiplication sums separate while we work out our multiplication, and then we can put them back together at the end.

Then it's 30 times eight.

Were you able to see that you could use three times eight and multiply it by 10? And then get an answer 240.

And then it's three times eight again, and I already worked out that that's 24.

So it's 24 in that one as well.

I then just need to add those two together with column addition and well done if you were able to get all of those right, all of that sequence right.

Well done.

We're just going to look at a word problem now.

So we've got exactly the same success criteria.

We just need to work out what the question's asking us.

So it says the eight children each buy 47 sweets.

How many did they buy in total? With a word problem, I really like to get a picture in my head.

I like to see the story.

I like to picture these eight children that they go rushing into a sweet shop, they fill it up.

And they're buying 47 sweets each.

That's a lot of sweets.

Maybe it's a special occasion.

Maybe it's somebody's birthday.

And I really do like to get that image in my face in my head.

I like to go see them with a big bag of sweets each.

Eight children, 47 sweets each.

That's a lot of sweets.

We are working out eight times 47, or 47 times eight.

It doesn't matter which order you do it in.

We can then do our grid and partition are two digit number, working out four times eight is 32, making it 10 times bigger, 320.

And seven times eight, one of my favourite facts, seven times eight is 56.

I remember that one, because 56 is seven times eight, five, six, seven, eight.

Am I done? Not quite.

Just need to use my column addition to add those two together.

Well done.

So, just before you get on to your independent work, I just want to recap your success criteria, because if you follow it clearly, you will get each answer right.

Partition each number into tens and ones.

So if you'd like, you can use this part-whole model.

So, 35 goes into 30 and five.

Then multiply each by eight.

30 times by eight.

I can use what I know three times eight is 24.

So 30 times eight is 240, and then don't forget to do five times eight is 40, and use your column addition to add them together.

Follow these three steps on your independent task and you'll do really well.

So it's time now to pause the video.

I'd just like to say that for the C section, it is a bit of a challenge.

Just try different combinations.

Try a little bit of trial and error, and see how you get on with C.

Okay, let's see how you did.

So we've got some missing numbers here.

Some of them are the answer.

Sometimes we need to put in the question.

So for question one, 45 times eight, 360.

83 times eight, well, we would definitely expect it to be a much bigger answer than the one we got before, because 83 is so much bigger than 45.

So we have got that much bigger answer there, 664.

Okay, what times eight gives us 560? Well, I know that seven times eight is 56.

So 70 times eight must be 560.

And eight times what gives me 800? Well, eight times 10 is 80, so eight times 100 is 800.

Now do you think this person's got this answer right or not, multiplying 22 by eight and getting the answer 1,616? Now, when I look at the answer, to me, it looks too big.

And if you were able to say that he got that wrong, you're right.

He did get it wrong.

He I don't think added the numbers up correctly.

He should have had 160 at 16 for 20 times eight and two times eight.

And I think maybe he added those two numbers incorrectly.

I think it was in the column addition he made the mistake there.

Part B.

Hopefully you can see this nice pattern here at eight times four, eight times 40, eight times 400.

And well done if you had a go at doing that with another set of numbers as well.

It's really good to see those connections.

And which of these numbers is a multiple of eight, and how do you know? We should be feeling really confident with your multiples of eight now.

And these ones are your multiples of eight.

Well done if you were able to see those.

And there's just some information there about how you could work out that those are multiples of eight, 16, is sorry, 160 is 16 times 10.

So if 16 is in the eight times table, timesing it by 10 will also be, sorry, in the eight times table.

Then 160 would also be in the eight times table.

Same with 240.

24 is in the eight times table.

So 240 is in the eight times table.

With 4,000, well 40 is in the eight times table.

So 400 and 4,000 would also be in the eight times table.

And for 96, it's just a continuation of your eight times table there.

Well done.

Okay, and for C, how did you get on? Now to work this out, I had to write out all of my eight times table and all of my five times table, and then see which combination of my eight times table and my five times table would add up to give me 73.

And this is where I got to.

I worked out that I could do six lots of eight are 48, and five lots of five are 25.

Adding those together, get me 73.

It really did take me a long time to work that one out.

So if you got that far, well done.

And if you got another combination, then well done to you as well.

Really, really good work.

Okay, time for your final knowledge quiz.

Well done, everyone.

Lots of new learning there.

Lots of different steps to getting those answers correct, so well done for all your hard work.

Bye bye.