Lesson video

Hello, everyone.

Welcome back to another maths lesson with me, Mrs. Pochciol.

I can't wait for us to have lots of fun together and hopefully learn lots of new things.

So let's get started.

This lesson is called explain how a division equation with two as a divisor is related to halving.

And it comes from the unit; doubling, halving, quotative and partitive division.

By the end of this lesson, you should be able to explain how a division equation with two as a divisor is related to halving.

Let's have a look at our keywords; divisor, half and halving.

Let's practise them.

My turn, divisor.

Your turn.

My turn, half.

Your turn.

My turn, halving.

Your turn.

Fantastic.

You should be really confident at these words but let's see how they're going to help us today.

Here is today's lesson outline.

In the first part of our learning, we're going to be looking when two is the number of groups.

And in the second part of our learning, we're going to be looking at when two is the number in each group.

So let's get started with the first part of our learning when two is the number of groups.

Jacob and Sofia are back to help us with our learning again today.

Are you ready, guys? Let's get started.

Jacob and Sofia are splitting 20 litres of water into smaller buckets.

If they have two buckets, how many litres of water do they need to pour in each bucket? Hmm, Sofia seems to think that we are splitting our whole into two equal parts.

Jacob thinks that we are dividing by two.

Hmm, who is correct? Have a think.

Who do you agree with? Jacob notices that two times 10 is equal to 20.

So 20 litres divided into two groups will be equal to 10.

And he records the equation, 20 divided by two is equal to 10.

Sofia thinks that we're dividing the whole between two equal parts, which is halving.

So half of 20 litres is equal to 10 litres in each, and she records it as half of 20 is equal to 10.

Hmm, do you notice anything? What do you notice? Jacob noticed that he divided by two, but Sofia halved, but they both got the same results, so they did.

20 divided by two is equal to 10 and half of 20 is equal to 10.

I wonder why that is.

Jacob explores the problem a little bit further.

20 is our whole, two is the divisor, that's the number of groups we are sharing the whole between.

And 10 is the size of each share, so when we split it into those two equal groups, there will be 10 in each.

So when we divide between two equal groups, we are also halving.

Jacob represents this problem with counters.

Each counter represents one litre, so he has his 20 litres in his larger bucket and he splits it between the two smaller buckets and there is 10 in each.

Jacob notices that if the divisors is two, the number in each group is half of the whole.

So can we see our whole is 20, we divide it by two and 10 is our answer.

It is half of the whole.

So when we're dividing between two equal groups, we are actually halving.

So you can use your halving knowledge.

Wow, well done Jacob and Sofia, that's a really useful thing for you to notice because that's really going to help us with our learning.

Jacob and Sofia now explore some other possibilities when they're sharing the water between the two buckets.

Their wholes will be the total number of litres and the amount in each bucket will be their answer.

If there are 10 litres in total and we divide it by two, it will be equal to half of 10, which is five litres.

So 10 divided by two is equal to five.

If we have eight litres as the whole and we divide it by two, it would be equal to half of eight in each bucket, which is four.

Eight divided by two is equal to four.

And finally, if there were six litres divided by two is equal to three litres in each bucket because half of six is equal to three.

Wow, that's an even more efficient way than using my two times tables because I'm so confident with my halves.

How do you feel about your halves? I think you're gonna do a great job with this learning.

Are we ready? Over to you then.

If there were 18 litres in the larger bucket, how many litres will be in each bucket when they split equally between the two buckets? 18 divided by two.

So have a think at what Jacob has just realised.

How could you work out how many litres will be in each of the two buckets? Come on back once you found a solution and make sure you've explained how you worked it out.

Welcome back.

Let's have a look then.

The divisor is two, so we can see the number in each bucket will be half of the whole.

We know that half of 18 is equal to nine, so 18 divided by two is equal to nine.

There will be nine litres in each of the two buckets when it's split equally.

Wow, well done, Jacob, I'm really impressed at your half as well, you knew straight away that half of 18 was nine.

And well done to you if you got that one correct using the same knowledge as Jacob did.

With the water, the children fill 64 water balloons.

Half of 64 is equal to 32, so how many balloons can be filled using just one of the smaller buckets? When we divide the hole into two buckets, there will be half in each.

We know that half of 64 is equal to 32.

So 64 divided by two is equal to 32.

So that means that there will be 32 water balloons in each bucket.

Wow, Jacob used that halving fact there to help him to solve this division.

Well done to you.

Do you think you could have a go at this? Are you ready? Half of 36 is equal to 18, so what would be the missing part of this division? 36 divided by two is equal to something.

Pause this video, have a think and make sure you explain how you worked it out and come on back when you are ready to continue.

Welcome back.

Let's have a look then.

We know that the divisor is two, so the number in each group will be half of the whole.

We can see from the top that half of 36 is equal to 18.

So 36 divided by two is equal to 18.

Using that halving knowledge to solve the division, well done to you and well done to Jacob for completing that check.

Let's continue to practise this skill through task A.

Task A is to fill in the missing numbers.

So A and B, you can see that you've been given the halving fact, so can you use that to then help you to solve the division.

And C and D, you've been given the division but can you use your knowledge to help complete the halving fact? Once you've completed task A, you might like to create your own problem for somebody else to solve.

So pause this video, have a go at A, B, C, and D and come on back when you are ready to find out how you got on.

Welcome back.

Let's have a look then at how we got on.

When we divide by two, the number in each group is half of the whole.

So if half of 56 is equal to 28, then 56 divided by two must be equal to 28 because that is half of the whole.

B, half of 82 is equal to 41, so 82 divided by two must be equal to 41 because that is half of the whole.

Let's have a look at C then.

Dividing a whole into two equal groups is the same as halving so if 94 divided by two is equal to 47, that means that half of 94 is equal to 47 because 47 is half of the whole.

And D, 76 divided by two is equal to 38.

When we divide by two, it's the same as halving.

So we know that half of 76 is equal to 38.

Well done if you completed A, B, C and D.

I wonder if you managed to create your own problem for somebody else to solve.

I wish I could hear all your great ideas but let's continue our learning.

The second part of our learning is to look at when two is the number in each group.

So we've already looked at two as the number of groups, we are now looking when two is the number in each group.

So let's get started.

Jacob and Sofia are tidying up, there are 16 shoes in the cloak room, if they pair them up, how many pairs of shoes will there be? Sofia has noticed that dividing by two is the same as halving, so the number of pairs will be half of 16.

Will that still be correct? We aren't dividing into equal groups this time, we are putting them into groups of two.

Jacob is not sure if that strategy will still work for grouping rather than sharing.

So they decide to explore the problem.

We have 16 shoes and we are putting them in pairs or groups of two.

So that 16 divided by two, 16 is our whole two is the divisor, which in this case is the number in each group, so our answer will be the number of groups that we are dividing the whole into.

Jacob and Sofia aren't sure if halving will help them here, so Sofia decides to use her two times tables to help because that's another strategy that she's learned to divide by two.

Eight twos are equal to 16, so 16 divided into groups of two should be equal to eight.

Let's have a look.

16 divided into groups of two is equal to eight.

Look, we have eight pairs of shoes, how neat and tidy do they look now? We can see that the number of pairs made was half of the whole, so that means that we can use this strategy whether we're grouping or sharing.

When two is our divisor, the number of groups that we can make when we make groups of two will be half of the whole.

So let's use this knowledge to help you to solve this problem.

There are 14 shoes in the cloak room, if they pair them up, how many pairs of shoes will there be? Record this as an equation before you find your answer.

Pause this video and come on back once you've recorded your equation and found out how many pairs we can make.

Welcome back.

Let's have a look then.

When the divisor is two, the number of groups is half of the whole.

So we can record this as 14 divided by two because we have 14 as our whole and we are dividing it into groups of two or pairs.

The number of groups will be half of the whole and half of 14 is equal to seven, so we should be able to make seven pairs of shoes.

Should we have a look? One, two, three, four, five, six, seven, so 14 shoes will pair up to make seven pairs of shoes.

Well done to you if you've got this correct.

So now Sofia and Jacob have explored both sharing and grouping, they can confidently say that whether it's sharing or grouping, whenever the divisors is two, the whole is halved.

So if the divisor is two, whether we are finding the number of groups or the number in each group, we know that it will be half of the whole.

So 12 divided by two, what would that be? We know that 12 is our whole, two is a divisor, half of 12 is equal to six.

So 12 divided by two is the same as half of 12, which is six.

Let's check that this is correct in sharing and grouping.

We can see this as 12 divided between two equal groups and there will be six in each group.

Or we might see this as 12 divided into groups of two which is equal to six groups.

So either way, it is correct.

So when our divisor is two, we can see this as half of the whole.

Well done to Jacob and Sofia and I really like those bar models there to visualise what you're explaining.

Well done.

So let's practise this a little bit further.

Over to you.

Which of these problems could we use halving to solve the problem? A, Jacob places 24 pencils equally into two pots.

How many pencils will be in each pot? B, Sofia has 15 suites, she puts them into bags of five, how many bags of sweets can she make? And C, Lucas has eight socks, he puts them into pairs, how many pairs of socks will Lucas have? So explore each of those problems there and have a think which of those could we use halving to solve the problem.

Pause this video and come on back once you've had a go and you've decided which ones we could use halving for.

Welcome back.

Let's have a look then.

Jacob, what did you think? Ooh, so Jacob thought that A and C we could use our halving facts.

Why is that Jacob? We can see that in A, we are dividing 24 between two parts.

So that's 24 divided by two, which can be solved using our halving knowledge.

In B, we are dividing 15 into groups of five, which isn't dividing by two, so we wouldn't be able to use halving there because remember we can only use halving when we are dividing by two.

And in C, we are dividing eight into pairs and we know pairs are groups of two.

So that means that eight divided by two, which can be solved using our halving knowledge.

Thank you for that, Jacob, and well done to you if you've got that correct.

Let's continue to practise this skill in task B.

So task B is to record each problem as an equation and solve.

A, Jacob puts 22 pencils away in some pots, he puts two pencils in each pot.

How many pots will he need to put all 22 pencils away? B, Sofia has 24 suites for her birthday party, she puts two sweets in each party bag.

How many party bags will Sofia be able to put sweets in? And C, Lucas has 20 socks, he puts them into pairs.

How many pairs of socks will Lucas have? So for each of these problems, record the equation and then solve.

Come on back when you are ready to see how you've got on.

Welcome back.

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

A, Jacob puts 22 pencils away in some pots, he puts two pencils in each pot.

How many parts will he need to put all 22 pencils away? We can see this as 22 divided by two.

When we divide into groups of two, the number of groups will be half of the whole.

Half of 22 is equal to 11.

So 11 pots will be needed to put away all of the pencils.

B, Sofia has 24 suites for her birthday party, she puts two sweets in each party bag.

How many party bags will Sofia be able to put sweets in? We can see this as 24 divided by two because she's putting them into groups of two.

When we divide into groups of two, the number of groups will be half of the whole.

Half of 24 is equal to 12, so we will be able to put sweets in 12 party bags.

Well done if you said this.

And finally, Lucas has 20 socks, he puts them into pairs.

How many pairs of socks can Lucas make? We can see this as 20 divided by two.

A pair is a group of two, so when we divide into groups of two, the number of groups will be half of the whole.

Half of 20 is equal to 10, so he can bake 10 pairs of socks from his 20 socks.

Well done to Sofia for solving those problems, and well done to you if you got them correct.

Welcome for completing task B and completing the lesson.

Let's see what we've covered today.

Halving is dividing into two equal parts.

Halving is the same as dividing by two.

Halving can be used for a division equation where two is the divisor.

We can use halving facts when the divisor is two.

I love how we've made so many connections between our learning today, it's really helped me to feel really confident with dividing by two, I don't about you.

Thank you for joining me today and thank you for all of your hard work as always.

I can't wait to see you all again soon for some more learning.

Goodbye.