Lesson video

Hello, my name is Suzie Robertson.

In this lesson we are going to be looking at doubling and then looking at the inverse of half.

When we've done that, we're going to do a bit of an investigation to find out what numbers can't be halfed and what numbers can.

For this lesson, you will need 10 things and a pothole model.

If you like you just draw your pothole model on a piece of paper.

Pause the video now to collect the resources if you need to.

And when you're finished, press play.

First, we're going to think about doubling.

When you double something, it means that you have the same amount again.

So for example, in the picture, there are two dogs.

There is a big daddy dog and there's a little baby dog.

The baby dog just has one can of dog food.

Whereas the daddy dog has two cans of dog food.

The dad is double the amount of his son.

So one can for the son, and two for dad.

Every time his son eats one can, the dad eats two cans.

So he is eating the same again.

So if I have here, the amount that dad eats.

Here I have the amount of daddy it's one, two, and here I have the amount that the son eats, which is just one.

In order for them to be the same, I'd have to add the same amount again to the sons for them to be equal.

So the son eats one can every time the dad eats two.

So if the son ate two cans, the dad would have to eat double that so double that would be two and two again.

So if the son ate two cans, the dad would eat four.

Double two is four.

When we think about doubling we quite often use a ladybirds to help us because they have two different sides to their back.

And normally in nature, if you see a ladybird, they have the same amount of spots on one side as they do on the other, so they have double the spots.

If they have two spots on one side and two spots on the other side, altogether, they will have four spots.

So we quite often use them to help us working out doubles.

And we can draw on them, we can draw two spots on one side and two on the other and all together, there will be four spots.

So double two is four.

I'm going to draw on my whiteboard a ladybird and I'm going to add my cubes to demonstrate some different doubles.

I'm going to need your help too to figure out what some of the doubles are.

So you're going to have to get your counting finger ready.

Here is my ladybird.

I'm going to use some cubes as her spots, and I'm going to pop them on either side to make double making sure that each side is the same.

Double is always adding the same again.

So if I put two on this side, I will have to put two on this side.

So one, two.

Two and two is equal to four.

Double two is four.

Can you join in with that sentence? Double two is four.

Fantastic.

Let's try another number.

Now I'm going to double one.

One there and one there.

One and one.

So remember, they have to be the same on each side.

Double one is two.

Can you join in? Double one is two.

Fantastic.

Let's try one more.

So I've got three and three.

Have account using your finger to point at the screen if that helps you how many there are all together what is double three? Can you say it as a full sentence? Three and three is equal to six.

Double three is six.

Let's try one more.

Is this one a double number? No, they're not the same size.

I've got one on this side and three over here, that's not a double number.

Double needs to be the same again.

So this time, I'm going to try and put four and four.

There we go.

Now they're te same on each side, four and four.

Using your finger to count if you need to, how many are there all together? Using the sentence double four is? Double four is eight.

Four plus four is equal to eight.

Now that we thought about doubling, we're going to think about halfing.

When you have something, you need to find two equal parts.

So two parts that are exactly the same.

Below on the screen, you can see a pothole model.

It has a hole.

So I might put four cubes in the hole.

And to half that, I have to share them out to make sure that each part is the same.

Here I have four.

And I want to share it into two parts.

And these two parts will have to be the same size.

Every time I share, say, One for you one for you.

Would you like to help me with that you can join in Ready? One for you, one for you.

One for you, one for you.

Here are two here are two this is equal.

They have been shared into two equal parts.

Let's try the number three.

Let's try and share three.

One for you, one for you.

One for you, Oh, aah, two here and one here.

These are not equal.

And maybe if I move that one there.

No, they're still not equal.

Because I still have one and two, they're different numbers different amounts.

I can compare them by popping them next to each other.

But I can see that this one has one more.

So they are not equal.

If you think about it as being sweets, or maybe oranges, and this is one child's lunch and another child's lunch, this is not fair.

It's not equal for one child to have.

Sorry, it's not fair for one child to have one.

And for the other child to have two.

We'd like things to be even so when we shared four you were able to give two to this child and two to this child.

That means that both children are having the same amount.

So that's fair.

That's what we call a fair share.

And finding half we always have to find two equal parts.

So this number four can be halfed equally.

Two and two make four and half of four is two.

That's checking by using the inverse equation.

Let metry one more.

And when I'm finished sharing, I'd like you to tell me whether you think it's equal or not equal.

Whether it's fair or not.

So, here I have six cubes.

2, 4, 6.

I'm going to go One for you, one for you.

Can you join in? One for you, one for you.

One for you, one for you.

Could we half this? Could we find two equal groups? Are these groups equal? Yes, they are.

We can half three and three.

I can check by putting them into towers and putting them side by side.

And I can see that they are the same size three and three.

That's the same quantity in each half.

So yes, we can half the number six.

Your task today is to investigate what numbers ithin 10 can be halfed and what numbers cannot be halfed.

A number can be halfed if you can share it into two equal groups.

A number cannot be halfed, if you cannot share it into two groups.

So if you share and you end up with different amounts in each group.

To do this, you're going to need a pothole model.

And you're going to need at least 10 things because you're going to use those to share, to figure out what the two different groups would be.

I'm going to show you using my cubes, me sharing a few to demonstrate and then it'll be your turn to investigate.

You might like to make a little list of can share and cannot share, or can half and cannot half.

So that afterwards, you can check and see if there's any patterns in the numbers that can be halfed, and the numbers that can't.

So I'm going to have 1234 to start with I'm going to have four and then all I need to do is share into my two parts.

And at the end, I have to check that both parts are equal.

So I'm going to go one for you, one for you.

One for you, one for you.

I had fours in my whole and I've shared it into two equal parts.

Because I can see there are two here and two here.

two and two are equal because they are the same size.

I can check that by holding them next to each other too by this and they are the same.

And I've shared that equally now into two parts.

So this number can be shared.

So four would be added to my list of things that I can share equally.

Then I'm going to try the next number.

I'm going to try the number five.

Here's five and I'm going to share.

One for you, one for you.

One for you, one for you, one for you.

Hmm, there are three in this part and two in this part.

Three and two.

They are not equal.

Not equal.

I can check that by putting them together.

So by popping into their towers and put them side by side, I can see that this one is bigger, this one has one more cube.

If I tried sharing this one into this group instead, there's still three and two.

So this one is not equal.

These cannot be shared equally.

Which means that I cannot half this because remember halfing is sharing into two equal groups.

So this number cannot be halfed.

Five, I would write under my cannot half list.

Pause the video now to complete your investigation.

You're going to try and find groups of things that can be halfed and things that cannot be halfed.

And recording them in those two lists might help you later when you come to explain it to somebody else.

Pause the video now to complete your task.

When you're finished, press play.

Here is the table that I made while I was doing the task of trying to see what numbers I could share into two groups and what numbers I couldn't.

So what numbers could I half and what numbers could I not half? Now, the ones that I couldn't share, I just couldn't share equally.

It's not that I couldn't share them out, but the groups weren't equal.

So it wasn't half.

Half needs to have both parts be exactly the same.

So in my can share, I have the number two.

Half of two was one, half of four was two, half of six was three, half of eight was four, and half of 10 was five.

So I could share all of those.

And actually, it really helped me to remember what half of those numbers were.

Can you see a pattern in those numbers? I spotted a pattern.

They are numbers that we use when we count in twos.

So it goes 2, 4, 6, 8, 10, ,12 14, 16 18, 20, I wonder if I kept counting in twos, I wonder if all of those numbers would also be able to be shared equally into two parts.

If we're if I can have those numbers too.

It's because they're all equal numbers.

Equal numbers are the numbers that we can share evenly into two groups.

So I think that if I kept going, if I kept investigating, I'm sure that if I kept counting in twos, all of those numbers will be able to be shared into two groups.

And I cannot share I have unequal numbers.

Then if you look at my cannot share column, they're all uneven numbers.

It's every second number, and it's still a bit like I'm counting in twos, but instead I'm starting at the number one.

So 1 , 3, 5, 7, 9.

Now, I couldn't share any of these equally.

I could share them if I didn't mind what size the different groups were that I ended up with, but because I'm halfing and to half both groups need to be the same size none of these numbers work.

So one, I'd have to cut this into pieces and I can't do that.

Three, I could have two and one or one and two, but they are not equal, they're not the same size, this one's always going to have more.

So that didn't work out.

Five, and seven, and nine were all the same.

None of the groups could be the same size, not what I'm sharing just into two groups.

And halfing remember is two groups.

Have a quick look at the answers that you came up with? Are they similar to the ones that I've come up with? I worked systematically today.

That's one of my favourite ways of working when I'm doing some maths.

That meant that I started with the number one, and then I shared the number two and then I shared the number three, and I worked in an order.

So I made sure I shared all the numbers to 10.

But it also meant when I recorded my results in the table that you can see on the screen, that it was quite easy for me to see patterns too because I've made sure that I've got organised my thinking.

If you are looking at your answers, see if you've got the same answers as me.

And if you work systematically, see if you spot the same patterns that I can spot.

You might even find some different patterns or notice any things that I haven't talked about.

If you find something in your investigation that you think is really interesting, you can always find a talk partner, a parent or carer and you could share whatever it is that you found with them.

I'm sure they'd be really interested to find out about your investigation.

Thank you for joining me for this lesson on doubling and halving.

I hope you've had as much fun as I have.

You've done some fantastic learning.

If you'd like to share your work with us, please ask your parent or carer to share your work on Twitter by tagging at Oak national and using the hashtag learn with oak.

We'd love to see what you've been up to.

Thanks again for joining me.

See you next time.