Lesson video

Hello everyone.

I am Mrs. Crane and today's session is part of the unit multiplication and division, and our objective today is to look at division facts for the multiplication table of three.

For this lesson, you will need a pencil and some paper.

Please pause the video now to go and get these things if you haven't got them already.

I thought I'd start today with a cat fact.

Did you know that a cat can jump up to five times its own height? This cat here isn't my cat but he is a very cute kitten who has obviously climbed quite high up a tree.

Let's have a look at today's agenda.

So, today, as I said, we're going to be learning the division facts for the multiplication table of three.

I'm going to start with a quiz to test your knowledge, then we're going to look at our star words for today.

We'll look at part-whole models and how we can use arrays to help us to solve division equations.

Then there'll be time for us to do today's talk task.

We're then going to develop our understanding of the different ways that an array can be arranged and the different division equations that this can produce.

That was quite complicated, but don't worry, we'll go through it really carefully and slowly together to make it, what I mean by that.

Then we'll do today's independent task and review the answers together.

And last but not least, there'll be a quiz to see what you've remembered.

Please pause the video now to complete your starter quiz.

Okay, welcome back.

Let's have look then at today's star words.

So, we're going to do my turn, your turn, with the star words.

Share, divide, equal, part, whole, groups.

Okay then, let's have a look at our new learning.

So, we have got some information here, it says, every plane needs three pilots.

So, we've got our plane here and we've got all of our pilots here.

How many planes can take off if there are 15 pilots? So, how many planes can take off if there are 15 of these pilots? We need to think about what we know about the parts and what we know about the whole.

So, we need to have a think.

What do you know about the parts and what do you know about the whole? Five seconds thinking time.

Okay, well, I know that in total we have 15 pilots, so, that's my whole, and I know that the value of each part is three, but I don't know how many of those parts there are at the moment.

So, let's see if we can work out a way to find out our answer.

So, here we have our 15 pilots in this whole box here, 'cause we know that's the total of pilots that we have.

We know that each part has a value of three because each plane needs three pilots to be able to take off.

We don't know how many of those boxes we need so that we have enough, so we have all 15 pilots on all of our planes.

So, we're going to use this part-part-whole model to help us.

So, here we have our 15 pilots again.

This time we have lots of different boxes here and we're going to count those boxes.

But this box contains three pilots.

We have one, two, three, four, five boxes, each containing three.

So, let's count up in our threes to double check that our pilots are the right amount.

So, they have 15.

So together count with me, we're going to speak out our threes.

Three, six, nine, 12, 15.

Fantastic.

We have 15 pilots here, ready to go.

We know we had to group them into five groups of three, they're all equal.

Now, I want you to have a think.

Can you think of an equation that you could write for this? Have a think.

Let's have a look then.

So, I could write three times by five is equal to 15 because I've got three in each box and I've times them, I've counted them up 'cause we did a minute ago and our fives, didn't we? To get to 15.

Now, we're going to be looking more at the division equations today.

So, I have that 15 here, the 15, and I wanted to split them equally.

So, what I did, was I did 15, and I wanted to divide them into threes, and then I had one, two, three, four, five.

So, it could be 15 divided by three is equal to five.

Or I could say 15 divided by five because I've split them into five groups is equal to three because in each group there was three people.

So, there's two ways of writing our divisions.

So, have a look then at another example.

This time we've got 12 eggs and three nests.

Each nest has an equal amount of eggs.

How many eggs are in each nest? So, here are three nests, and here are our 12 eggs.

What do we know about the parts and the whole this time? I'm going to give you five seconds to think about that question.

Okay, we know that in total, so that our whole, we have 12 eggs and we know that one of the parts, there's three parts, sorry, because we know there's three nests.

Now, we need to work out the value.

So, how many go in each of our nests? So, order to do that, we need to split our whole equally into our three nests.

Let's do that.

Okay.

So, we have 12 eggs, we can now equally split them into three nests.

Let's count how many eggs are in each nest.

One, two, three, four.

One, two, three, four.

One, two, three, four.

Okay.

So, there's now four eggs in each nest.

So, I could say, "Three, so, I have one, two, three nests, times by four, because I have four in each nest, is equal to 12 because I had 12 eggs and I've equally shared them out between my nests." So, I could have, as I said, three times by four is equal to 12.

Now, let's think about their division equation for this.

I have 12 and I split them into three.

Each part was therefore worth four because I had four eggs in it.

So, it could be 12 divided by three is equal to four.

Or like I said, a moment ago, I could split it.

So, I had 12 eggs and each group of eggs is grouped into four.

So, I have four groups of, I had four, I divided my 12, sorry, into four, and I had one, two, three groups of that four.

So, I could have 12 divided by four is equal to three.

So, can you see the link here? Our product, our answer to our multiplication question became the number that was our whole, that we were dividing into groups.

So, when we divided 12 into three groups, three nests, we had four eggs each.

When we divided our 12, the 12 eggs, into groups of four, we had three groups of four because we had three nests with four eggs in them.

Right then, it's time to have a look at today's talk task.

Today's talk task, you have got two questions, here and here.

You've got a part-part-whole model here, and you've got your say it out loud.

What I'd like you to do today is using your paper, I would like you to draw out the part-part-whole model and draw out how you would divide these pictures, of, this time they're bottles, into your three equal groups, and then have a go at writing the division equation or any other equations you can for the first one, and then do the same for the second one when there's the lemons.

So, look at the question really carefully.

Look at how you're going to divide it, where's the whole and how it's split for you and draw them in and have a got a writing the equations.

Don't forget, you can use the say it out loud.

I have divided, into parts, with a value of, there are parts in the whole, each part has a value of, divided by, is equal to.

Please pause the video now to have a go at today's talk task.

Okay, welcome back, let's have a look then.

We're going to look at one example from the talk task together, before we move on to the develop learning.

So, there are 15 bottles, divide them into three equal groups.

What division equations can you say? What other equations can you say? So, what do I already know? Well, I know that there's 15 bottles here, so that becomes my whole, so, I need to put that into this box here.

Over there.

Now, I need to divide them into three equal groups.

So, I've got 15 and I want to divide them into three equal groups and say what happens.

So, I've split them, as you can see, into three equal groups of five.

So, let's add our fives to just double check that we get to 15.

Five, 10, 15.

Yeah, we did.

So, we know that they have been split equally into our three groups, and we know that each group has a value of five because there are five bottles in each group.

Okay then, we're going to develop our learning now.

So, let's have a look at this question, it's very similar to the first question, but there's a slight difference, and we'll look at the difference in a moment.

Every jumbo jet needs five pilots, how many planes can take off if there are 15 pilots? So, again, what do we know about the parts and what do we know about the whole? Well done to those of you who've said, "The whole is all of our pilots, the whole is 15, and the parts or each part is worth five pilots because each plane is worth five pilots, you can't fly it without the five." So, here we go, is our part-part-whole model.

We've got our 15 pilots here, we've started to split them, we know that each plane, each part has a value of five.

We need to know how many boxes we can use.

So, we're counting our fives, we've got five, 10, 15.

How many boxes did we use? Well done, we used three boxes.

So, if I need to think about the equation, I would have 15 divided by five, because we've divided them by five, is equal to one, two, three.

So, have a look then about what is the same and what is different about the two equations that we've looked at.

So, we looked, firstly, where every plane needed three pilots.

And then we looked second, at where every plane needed five pilots.

We have the same amount of pilots both times, we have 15 pilots.

So, have a think, what's the same and what is different? Well done to those of you that have said, "Well, the whole is the same because we had 15 pilots each time." The difference is that in our first question, each plane could only hold three pilots.

So, we needed to do three times by something to give us 15.

So, we did 15 divided by three, which gave us five.

So, we had the five part here for the value of three each.

The second time, it changed.

Each plane this time was able to carry and it needed five pilots, the whole stayed the same, but the difference was five pilots were about to be sent onto each plane.

So, we had to work out 15 divided by something was going to give us the five.

So, I knew then, once I put five people, five pilots, sorry, here, 10, 15, I knew then, that it needed three parts each with a value of five.

So, there's similarities and differences between these two.

Let's have a look at the ways in which we could arrange this group as an array.

So, imagine each of these purple dots is one of the pilots, okay? We have three, here, and five across here.

If I do three times five, I know that is equal to 15.

So, I know this represents 15 pilots.

There's two ways though that I can show this array.

I can show it like this, or I could show it like this.

Just like the two different ways I could show my pilots.

I could show them in groups of three, ready to go on their jets here, or I could show them as groups of five, ready to go on their jets here.

So, there's two different ways we could show that group.

Now, let's have a look at them when we can put them side by side.

So, as I said, we could show our 15 pilots in our groups of three like this, and we imagine here is our 15 pilots again here, and this time our groups of three are here, like we just looked up.

Or I could show them as my 15 pilots.

Again, the same array, it just looks different, it's just the different ways that has been highlighted that make it different.

And again, this time my jumbo jet was allowed to take five.

So, this time I'm looking across, at our five pilots each time and I still have 15.

So, I can write them either way and they give me the same number.

So, you can see here, we looked at them as if there was three groups of five, you can see that in the orange.

And if we looked at them as if there was five groups of three in the blue, you could see them going down the columns, these go across the rows, these go down the columns.

The same amount of pilots, we've just arranged them in two different ways.

Let's have a look then at today's independent task.

So, I would like you to complete the equations that each array represents.

You've been given an array each time and you've been given an equation.

The first three, you need to work out the missing numbers.

The last one, you need to work out the two different division equations, just like you've been given here, that this array matches with.

Please pause the video now to complete your task.

Welcome back, let's have a look then at our answers.

So, we have the first array here.

We have 18 divided by three.

So, we can see three, here, and we have to count how many across here.

We can see one, two, three, four, five, six.

If I was to divide by 18 by three, I would have six.

This time, if I was to divide 18 by six, I would have one, two, three.

So, my answer would be three.

Now, I have 12 here and I want to divide it by something to give me four.

Well, I can see here one, two, three, four.

So, I need to count how many are in each group.

One, two, three.

So, if I divide 12 by three, I know there's four groups of it.

So, this time I know that if I do 12 divided by four, I can see there's one, two, three in each.

So, our missing number must be four.

Something divided by three is equal to 10.

Here is my three, and then I know this must be my 10.

So, if I do three times by 10, that gives me 30, because I know this is three and this is 10, three times by 10 is equal to 30.

Then, I know something divided by 10 is equal to three, I know that 30 divided by 10 is equal to three because my array shows me 30.

Lastly then, I've got two empty equations, but I know three is going to be one of the numbers.

I know that one, two, three, four, five, six, seven, eight.

So, I could say eight times three is equal to 24, but we're looking at the division equations.

So, we're going to be looking at 24, divided by eight is going to be equal to three, or I could say 24 divided by three is equal to eight.

Well done, everybody for working so hard today, I've been really, really impressed.

Hopefully, we'll see you again soon.

Pause the video now to have a go at the final quiz.

Thank you very much and goodbye.