Lesson video

Hello, I'm Mrs. Cayley and I'm really excited to be learning with you today.

So in today's lesson, we're going to double the numbers six to nine and halve the result.

So let's have a look at today's lesson outcome.

Here's the outcome of today's lesson.

I can double the numbers six to nine and halve the result explaining what doubling and halving is.

So by the end of the lesson, you'll be able to do this.

Here are our keywords for today's lesson.

Can you say them after me? My turn.

Double.

Your turn.

My turn.

Halve.

Your turn.

You might have seen these words before, so look out for them in today's lesson.

Here's today's lesson outline.

We're going to double the numbers six to nine and halve the result.

We'll start off with doubling and then we'll move on to halving.

Let's start on the learning.

Here are some children that are going to help us today.

We've got Alex and Aisha.

Doubling means we have two of something, so look out for two of these things.

Here we've got one counter and another counter.

So one has been doubled.

One and another one is equal to two.

So one plus one is equal to two.

That's double one.

Here it is on a part-part-whole model.

Can you see double one makes two.

Now we've got two counters.

Two plus another two is equal to four.

So double two is four.

Two plus two is equal to four.

Can you see it on the part-part-whole model? Now we've got three counters.

Three plus another three is equal to six.

So three and three is equal to six.

This is double three, and there it is on the part-part-whole model.

Four counters plus another four counters.

That makes eight counters.

So four plus four is equal to eight, and you can see it on the part-part-whole model there.

Now we've got five counters plus another five counters.

This makes 10 counters.

So five plus five is equal to 10.

That's double five.

So you can see it on the part-part-whole model.

Alex said, "The sum of each doubling equation is even." Can you see the sums there? So the total amount when we double, can you see the sum each time is an even number? Two, four, six, eight, and 10.

They're all even numbers.

Alex said, "I can see that this is because each counter has a counter to pair up with." Even numbers come in pairs, don't they? Alex said, "All doubles are made from groups of two so they must be even." Can you see the groups of two here? I'm going to put a purple box around them.

Here's the groups of two.

Doubling a whole number always gives an even number.

Let's check your understanding.

Which representations are showing a double? Remember a double means we've got two of something.

So pause the video and think about which of these are showing a double.

Which ones do you think show a double? The first one is showing a double.

I can see we've got five and another five, so that's showing a double.

This part-part-whole model is showing a double as well, three and another three.

Double three is six.

The other representations aren't showing a double, are they? It's nearly a double but not quite.

Alex and Aisha are collecting up the pencils.

Can you see how many pencils they've got? They've both got the same amount, haven't they? Alex said, "We have collected the same amount." Aisha said, "We have collected five and one more." How many is that in total? Aisha said, "Let's put them together." Alex and Aisha have put their pencils together.

Alex said, "We both collected six pencils." Aisha said, "We have the same so we can double." I wonder what double six is.

Alex said, "We have two groups of five and two groups of one." So we can double the parts, can't we? Double five is 10.

So there we've got the groups of five pencils.

Double five is equal to 10 and double one is equal to two.

So double six is 10 and two.

Double six is 12.

Six can be partitioned into five and one.

Can you see it there on the 10 frames? To double six, we can double five and then double one.

So if we double five, we get 10.

Double five is 10.

If we double one, we get two, so double one is two.

So I wonder what double six is.

Double six is 12.

So we've got the 10 and the two put together to make 12.

Alex and Aisha are collecting up more pencils.

Can you see how many pencils they've got this time? Have they got the same each? Alex said, "We have collected the same amount." Aisha said, "We have both collected five and two more." How many is that in total? Aisha said, "Let's put them together." Alex and Aisha have put their pencils together.

Can you see all their pencils there? Alex said, "We both collected seven pencils." Aisha said, "We have the same so we can double." Alex said, "We have two groups of five and two groups of two." Aisha thinks double five is 10.

Do you agree with her? So double five is 10.

Alex thinks double two is four.

Yes, double two is four.

So I wonder what double seven is.

So double seven is 10 and four.

Double seven is 14.

Here we can show it on the 10 frames.

Seven can be partitioned into five and two.

To double seven, we can double five and double two.

Seven is the same as five and two.

So we can double the five.

Double five is 10, and then we can double the two.

Double two is four.

So double seven is 14.

I can see that on the 10 frames.

10 and four is 14.

What do you notice here? We've got the numbers six, seven, and eight.

Alex and Aisha are going to double those numbers.

So double six is 12, double seven is 14, and double eight is 16.

Alex has noticed that the answers are even numbers.

Aisha said, "I wonder if this is always true." What do you think? Let's check your understanding.

To double eight, we can double five and double three, because eight is five and three.

Use 10 frames to double eight.

So if you've got some 10 frames, you could try doubling the number eight, or you could draw it on a piece of paper.

Pause the video while you think about this one.

So what did you think about this one? What's double eight? Can you double it on the 10 frames? So eight was made of five and three.

Double five is 10, and double three is six.

So double eight is 16.

Is that what you thought? Here's a task for you to have a go at.

Look at the representations here.

Which doubles can you see here? Circle the doubles.

So we've got some dominoes, some part-part-whole models, and some fingers.

Some of them are showing doubles.

Can you put a circle around the ones that are showing a double, and then can you draw some more doubles of your own? Here's the second part of your task.

Can you use the 10 frames to double these numbers? So we're going to try to double the number eight and nine.

On the 10 frame, you can see that eight can be partitioned into five and something else, and then can you double those two parts to find out what double eight is? Then have a go at nine.

Nine is made of five and a bit more.

So can you double those parts and see what double nine is? So pause the video while you have a go at your tasks.

How did you get on with your tasks? Did you circle the doubles? So I can see here that we've got some dominoes that are showing doubles.

We've got double five and we've got double six.

Then we've got some hands that are showing double five.

That makes 10.

And we've got a part-part-whole model that's showing double seven.

That's 14.

The other ones aren't quite showing a double, are they? They're a near double.

It's nearly a double.

Did you draw some more doubles of your own? So you may have drawn some part-part-whole models showing doubles, or you might have shown counters on a 10 frame, or you might have found some objects like pencils.

These are all showing a double, aren't they? The part-part-whole model is showing double six, the 10 frames are showing double eight, and the pencils are showing double seven.

What did you draw? How did you get on with the second part of your task? Did you use the 10 frames to double these numbers? So we had the number eight, which is made of five and three.

If you double five, you get 10, and if you double three, you get six, so double eight is 16.

That's made of 10 and six.

Then moving on to the number nine.

Nine is made of five and four, so double five is 10, and double four is eight, and if you put those together, 10 and eight, that makes 18, so double nine is 18.

Let's move on to the second part of the lesson.

We'll be halving.

Halving means showing something as two equal parts.

We can use what we know about doubling to find half.

So here on the part-part-whole model, you can see that double two is four.

So half of four is two.

I know that double two is four, so half of four is two.

This part-part-whole model is showing double three.

I know that double three is six, so half of six is three.

Alex and Aisha have 12 pencils.

Can you see, we've got a pack of 10 and two more.

They are splitting their pencils into two equal groups, so they're going to split them in half.

How many will be in each group? So Alex said, "We need to find half.

What is half of 12?" Aisha said, "We can use what we know about doubles." Alex said, "We can partition to help.

12 is made of 10 and two." "What can be doubled to make 10?" Alex said, "I know half of 10 is five, because double five is 10." So we can split the 10 pencils into two groups of five.

Now we've got two pencils left in the middle.

"I know half of two is one because double one is two." So we can put one in each group.

So now we've got five and one in each group.

There will be six in each group.

Half of 12 is six.

So remember, you can do half of 10 and half of two to find out half of 12.

Alex and Aisha show this using counters.

Can you see we've got 12 counters? We've got 10 and two more.

To halve 12, we can partition it into 10 and two.

Aisha said, "I know double five is 10 so half of 10 is five." Can you see 10 counters on the 10 frame? Now we've halved them.

Half of 10 is five.

Alex said, "I know double one is two, so half of two is one." So we're going to half the two, and we're left with one.

Can you see how many counts are left? Aisha said, "I know double six is 12 so half of 12 is six." Alex and Aisha have 16 pencils.

They are splitting their pencils into two equal groups.

How many will be in each group? Alex said, "Halving is the opposite of doubling." Aisha said, "Even numbers can be split in half." Alex said, "16 is made of 10 and six." So we can halve 10 and halve six.

Alex said, "I know half of 10 is five because double five is 10." So we can split the group of 10 into two groups of five.

Now we've got six pencils left in the middle.

Aisha said, "I know half of six is three because double three is six." So we're going to split those six pencils in half, three and another three.

So now we've got two equal groups, and the groups have got five and three more pencils.

I wonder how many we've got in each group.

There will be eight in each group.

Half of 16 is eight.

Alex and Aisha show this using counters.

Can you see we've got 16 counters here? 16 is made of 10 and six more.

To halve 16, we can partition it into 10 and six.

Aisha said, "I know that double five is 10 so half of 10 is five." So we can halve the 10 counters.

That makes five counters.

Alex said, "I know that double three is six, so half of six is three." So here we've got three counters.

So I wonder what half of 16 is.

Half of 16 is eight.

Aisha said, "I know that double eight is 16 so half of 16 is eight." Can an odd number of counters be split exactly in half? So have a look at these 10 frames.

They're showing an odd number because we haven't got groups of two.

I wonder if an odd number of counters can be split exactly in half.

What do you think? Alex said, "Halving means showing something as two equal groups." Can we make two equal groups out of these counters? I can see that we've got 17 counters here.

We've got 10 counters on the bottom 10 frame and seven counters on the top 10 frame.

Aisha said, "Double five is 10 so half of 10 is five." So we can halve the bottom 10 frame.

Can we halve the counters on the top 10 frame? Alex said, "Seven cannot be split into two equal whole parts." Aisha said, "You could have three and four, but they aren't equal." So an odd number can't be split exactly in half to make two equal whole parts.

Let's check your understanding.

Who is correct, and how do you know? Look at the part-part-whole model here.

Alex said, "This is showing double six." Aisha said, "This is showing half of 12." Who do you think is correct, and how do you know? Pause the video while you think about this one.

What did you think about this one? They were both correct, weren't they? This is showing double six is equal to 12, and it's also showing half of 12 is equal to six.

I know that double six is 12, so half of 12 is six.

So if you know a doubling fact, you can work out a halving fact as well.

Here's a task for you to have a go at.

Can you pick a number, six, seven, eight, or nine and use 10 frames to show what double the number is? So here's an example.

We've got seven blue counters on the 10 frames, and we've doubled it by having another group the same with the red counters.

So double seven is 14.

I can see now we've got 10 and four counters.

That makes 14.

So try this with some other numbers.

Then ask a friend to find half of your number, and use the sentence, "I know that double (hums) is (hums), so half of (hums) is (hums)." Pause video while you have a go at your task.

How did you find the task? You might have tried, here we've got seven counters, and we've doubled it to make 14 counters.

Seven and seven makes 14.

Here's the stem sentence to help.

I know that double seven is 14, so half of 14 is seven.

I know that double five is 10, so half of 10 is five, and I know that double two is four, so half of four is two.

What other numbers did you try? We've come to the end of our lesson.

Today we were doubling the numbers six to nine and halving the result, and this is what we found out.

Doubling means to have two of something.

Halving means to split into two equal groups.

Doubling the number six to nine gives an even number, and it's an even teen number.

Halving an even teen number gives a number from six to nine.

Well done, everyone.

See you soon.