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Hello there.
How are you today? I hope you're having a really good day.
My name is Ms. Coe.
I am really, really excited to be learning with you today in this maths lesson where we're thinking about doubling and halving.
Now, you may have had some recent experience looking at the two-times table, and if you can recall or remember any of those two-times tables facts, that's gonna be really helpful in your learning today.
So if you're ready, let's get started.
In this lesson today, we're continuing to think about doubling and halving, and you may have some recent experience of doubling and halving.
By the end of this lesson, you will be able to say that you can halve even, two-digit numbers from 12 to 28 and unitize and apply known facts to halve even multiples of 10.
We have some keywords in this lesson today.
I'm going to say them and I'd like you to say them back to me.
Are you ready? My turn.
Double.
Your turn.
My turn.
Doubling.
Your turn.
My turn.
Half.
Your turn.
My turn.
Halving.
Your turn.
My turn.
Partition.
Your turn.
Now hopefully you are familiar with some of these words.
Keep an eye out for them in our lesson today and see if you can use them in your own explanations.
In our lesson today, we're halving even, two digit numbers and multiples of 10, and we have two cycles to our learning.
In the first cycle, we're going to be halving to find two equal parts, and in the second cycle, we're going to be focusing on halving even, two-digit numbers.
If you're ready, let's get started with the first cycle of our learning.
In our lesson today, we're going to meet Aisha and Alex, and they're going to be helping us with our maths along the way.
So let's start here.
Aisha and Alex are exploring this bar model and they're talking about what they already know.
Now before they start chattering, I wonder if you can spot anything that you notice about this bar model.
Have you seen something similar before? Can you talk about any of the bits of the bar model? Let's see what they say.
Alex has noticed that the bar model has two equal parts that make the whole.
We can see that the whole is six and we can see underneath the whole, there are two equal-sized parts, and we don't know what they are.
Can you say what they are? That's right, Aisha.
"I know that double three is equal to six, so three must be the value of the missing parts." Remember, we can use our doubling facts to find a half fact.
Double three is equal to six, so if we know that double three is equal to six, what else do we know? Can you say anything else? Well that's right, Aisha, we can also see that half of six is equal to three.
Alex and Aisha take a look at a different bar model.
What is the value of the missing parts now? Hmm, I wonder.
Well, Alex says that he can see that 12 is the whole, so each part will be half of 12.
I wonder what half of 12 is.
Alex uses 10 frames to halve 12, so we can see that he's shown 12 on his 10 frames and he says that he knows 10 and two is equal to 12, so he has partitioned 12 into 10 and two, and shown that on different 10 frames, so now he can halve each of the parts.
Half of 10 is five, half of two is one, and remember to find half of 12, we can add those together.
Five plus one is equal to six, so half of 12 is equal to six.
Time to check your understanding.
Use your 10 frames and the stem sentences to half 14, so think about how 14 can be partitioned and then remember we can halve the partitioned parts and recombine those to find half of 14.
Pause the video here and have a go.
Welcome back.
How did you get on? Well, Alex showed 14 on his 10 frame and he partitioned 14 into 10 and four, because 10 and four is equal to 14.
He then halved each of the parts, so half of 10 is five and half of four is two, and remember, he can combine those parts back together to find half of 14.
Five plus two is equal to seven, so half of 14 is equal to seven.
Well done if you said that.
When we find a half, we split the whole into two equal parts and you may remember this from earlier learning.
Alex remembers that he's thought about halves and wholes before, so if we think about the pizza as the whole, we can split it into two equal parts and each part is a half of the whole.
So when we find half of anything, we split the whole into two equal parts.
This time, 14 is our whole, so we split that into two equal groups and we can think about it like splitting it down the middle.
Seven is one half and seven is another half.
We've split it into two equal groups.
Seven is one half of 14, so half of 14 is equal to seven.
Alex and Aisha move on to exploring the idea of halving multiples of 10.
Aisha's going to use 10-pence coins to represent tens, so we have two 10-pence coins in front of us.
Here we have two tens which is the same as 20, so we have 20 pence.
We can split those coins into two equal groups.
Half of two tens is one 10, so half of 20 is 10.
So what would happen if she halved four tens? So we have four groups of 10 here, we have four tens or 40.
Can you imagine splitting them into two equal groups? Can you imagine what that would look like? Well, that's right, if we split it into two equal groups like so, we have two tens in each group, so we can say that half of four tens is two tens, and what's the value of that group? That's right, it's 20, so we can say that half of 40 is 20.
Time to check your understanding.
Now, can you halve six tens? If you have 10-pence coins in front of you, great.
If not, you could use six counters to represent the 10-pence coins.
Remember, think about how you might split them into two equal groups.
Pause the video here and have a go.
Welcome back.
How did you get on? Well, we had six tens or 60, and if we split them into two equal groups like so, we can see that each group has three tens in it, so we can say that half of six tens is three tens.
We had 60 and we now have 30 in each group, so we can say that half of 60 is 30.
Well done if you halved six tens and extra well done.
If you said it in those two different ways, Aisha used her known factor.
She said, "I knew that half of six is three", so therefore she can use that to help her.
If half of six is three, then half of six tens is three tens.
Let's explore Aisha's idea a little bit more using if I know mm, then I know mm.
So if I know that half of two is equal to one, then I know that half of 20 is equal to 10 because half of two tens is equal to one 10.
If I know that half of four is equal to two, then I know that half of 40 is equal to 20 because half of four tens is equal to two tens.
What's about this one? Well that's right.
If I know half of six is equal to three, what am I going to say next? That's right.
Then I know that half of 60 is equal to 30 because half of six tens is equal to three tens.
Can you see a pattern emerging there? Time for your first practise task.
Use the digit cards to complete the statements.
So you have some cards here with 20, six, 40, seven, eight, and 12 on, and you have six spaces.
Each card fits into one of those spaces.
See if you can put them in the right places.
So for A, half of 14 is equal to mm.
Which of those digit cards goes in that spot? Remember you can use 10 frames to help you if you need to.
For question two, complete the statements.
So A, half of 20 is equal to mm.
Can you use your known facts there? B, if I know that half of eight is equal to four, then I know half of mm is equal to 40.
For C, if I know that half of something is equal to something, then I know that half of 60 is equal to 30.
What known fact can help you there? And then for D, you have a picture to think about.
What fact has been shown there? Can you complete the missing numbers? Good luck with those two tasks.
Pause the video here and I'll see you shortly for some feedback.
Welcome back.
How did you get on with those two tasks? So for question one, did you manage to find where all the digit cards went? For A, half of 14 is equal to mm.
Well 14 can be partitioned into 10 and four.
Half of 10 is five.
Half of four is two.
Five plus two is equal to seven, so seven goes in that space.
B, half of something is equal to four.
Well if I know that half of something is equal to four, then I know that double four is equal to the missing number.
Double four is equal to eight, so eight goes in that space.
For C, half of something is equal to something.
Oh, and D is the same as well.
Well that's tricky.
Well this time I can use what I know about the numbers.
So I have 20, 40, six, and 12.
Well I can say that half of 20 is equal to 10, but I don't have a 10, so I needed to find pairs of numbers that worked in C and D.
Remember, C and D could have gone either way round, so half of 12 is equal to six and half of 40 is equal to 20.
As long as you have the numbers in the right order in the statements, it doesn't matter if you put 40 and 20 in for C, and 12 and six in for D.
For question two, I asked you to complete the statements.
Half of 20 is equal to mm.
Well, if I know that half of two is equal to one, then I know that half of 20 is equal to 10.
For B, if I know that half of eight is equal to four, then I know that half of 80 is equal to four because 80 is eight tens.
I know that half of eight tens is equal to four tens, so half of 80 is equal to 40.
Well done if you reasoned about that.
For C, I know half of something is equal to something then I know half of 60 is equal to 30.
Hmm, how did you work this one out? Well, if I think about 60 as six tens, I can say that half of six tens is equal to three tens.
That means that I knew that half of six is equal to three, and finally what factors have been shown here? Well, the whole is 40 or four tens, and half of it is two tens or 20, so I could have written half of 40 is equal to 20.
Well done if you've got all of those.
I know you've worked really hard doubling and halving with some larger numbers, so let's focus on the second cycle of our learning where we're halving even, two-digit numbers.
Alex and Aisha are now going to apply their halving knowledge to help them halve the number 26.
Alex thinks we can use the same partitioning strategy to halve 26, and Aisha has remembered from earlier learning where she used Base 10 equipment for doubling, and so she's going to use Base 10 to represent the number 26.
You might have used Base 10 equipment before when you were doubling.
If you've got some Base 10 blocks lying around, you might want to use them in the next part of this lesson.
So what is half of 26? Well we can see 26 as two tens and six ones, and we can use our Base 10 equipment to show that.
We have two tens and six ones, which is 26.
We can think about half of 26 as the same as half of 20 and half of six.
Aisha knows that half of 20 is 10 because we can divide it into two equal parts, and half of six is three, and so therefore, we can add those two parts together to find half of 26.
10 plus three is equal to half of 26.
10 plus three is equal to 13, which means that half of 26 is 13.
Time to check your understanding.
Use your Base 10 blocks and the stem sentences to halve 22.
So think about half of 22.
Think about what you could partition 22 into and recombine those parts to find half of 22.
Pause the video here and have a go.
Welcome back.
How did you get on? Well, we can think of 22 as two tens and two ones, so we can partition it into 20 and two, and we can halve those parts to find half of 22.
Half of 20 is equal to 10 because it is 20 divided into two equal parts.
Half of two is equal to one.
We can add those parts, 10 and one, together, to make 11, so we know that half of 22 is 11.
Well done if you said half of 22 is 11 and you used your Base 10 blocks to work that out.
Alex and Aisha move on to thinking about half of 30 and they've shown 30 using coins.
Now Aisha says that 30 is an odd number of tens, but she has an idea.
"Let's try partitioning like we did earlier." So she realises that we can't just split those three 10-pence coins into two equal groups, because we can't break the coins in half.
Alex tries to think about it as three tens and he says that half of three is, hmm, wait.
Three is an odd number, so half of three wouldn't be a whole number, so how can we find half of 30? Well, Aisha uses Base 10 to represent 30, 3 tens.
Three tens can be partitioned into 20 and 10.
Now, they're not two equal groups yet, so I don't think we've quite found half of 30, but we can use that partitioning method to find half of 30.
We can think about half of 20 plus half of 10 and that's the same as half of 30, so half of two is one, so half of 20 is 10, that's the first bit done.
What about half of 10? Well I know that half of 10 is equal to five and I can partition it like so, 10 divided into two equal groups is five, so I now know half of 20 and I know half of 10, and I can use that to find half of 30.
10 plus five is equal to 15, so half of 30 is 15.
Time to check your understanding.
What is half of 70? Aisha is reminding you that 70 is an odd number of tens, so you need to think about how you're going to partition in order to halve it.
Pause the video and have a go.
Welcome back.
How did you get on? Well, if we partition 70 to 60 and 10, we can use that to find half of 70.
Half of 60 plus half of 10 is equal to half of 70.
So half of 60 is 30 because half of six tens is three tens.
Half of 10, remember, we can divide it into two equal parts, half of 10 is equal to five.
Now we just need to add those bits together.
30 plus five is equal to 35, so half of 70 is 35.
Well done if you got that.
Time for your second practise task.
I would like you to practise halving two-digit numbers.
So you're going to turn over a number card.
Aisha turns over the number 28.
Then you're going to use Base 10, or counters, or your known halving facts to 10, halve your number.
So if you need to use Base 10 or counters on 10 frames to do it, that's absolutely fine.
So Aisha is going to halve 28.
Remember you can use your halving facts up to 10 to help you halve tens digits.
Once you've had a go with one number, try a few different combinations.
See how confident you can become at halving two-digit numbers.
Pause the video here and have a go.
Welcome back.
Now remember, there are a few different two-digit numbers that you could have halved, so let's see what Alex and Aisha did.
Let's see how Aisha halved 28.
She partitioned 28 into 20 and eight.
She knew that half of two is one, so half of 20 is 10, and half of eight is four.
Now we need to recombine those parts.
Half of 20 plus half of eight is the same as half of 28, so we can add 10 and four together to make 14, so we can say that half of 28 is 14.
Alex is really impressed because Aisha didn't need to use any resources and she used the halving facts that she already knew.
Remember, it's absolutely fine if you used Base 10 or 10 frames to help you.
We've come to the end of this lesson where we've been halving even, two-digit numbers and multiples of 10.
Let's summarise our learning.
Halving facts to 10 can help you halve two-digit numbers.
To halve two-digit numbers, you can partition the two-digit number, halve the tens, and then the ones, and then recombine those halved tens and ones to find half of the two-digit number.
When you are halving an odd number of tens, you can partition it into an even multiple of 10 and 10 more.
You can half that even number of tens and then halve 10, and then you can recombine those halved tens and ones.
Thank you so much for all of your hard work in this lesson today, and I hope to see you in another maths lesson soon.
