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I can explain how finding half of a number relates to halving and doubling.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

To find half of a number you split it into 2 equal parts
Use knowledge of doubles and halves to find half of a number
If you double the half you will end up with the whole number

Common misconception

Children may find it difficult to find the whole when they are told the size of the half and may try to find half of the half.

Use a bar model representation to help children see the structure of double and half. Use gesture, colour and/or circling when discussing what each part of the bar model represents.

Keywords

Double - To become twice as many.
Half - To divide into 2 equal parts.

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Hello there.

My name is Mr. Tilstone.

It's really lovely to see you today.

I hope you're having a nice day.

Let's see if we can make that date even better with this lesson, which is all about fractions.

And I know you're getting really good at fractions.

So if you're ready for the lesson, will you help me by counting down from five.

Five, four, three, two, one.

Let's begin.

The outcome of today's lesson is I can explain how finding half of a number relates to halving and doubling.

And we've got some keywords.

If I say them, will you say them back, please? My turn, one half.

Your turn.

My turn, half.

Your turn.

My turn, double.

Your turn.

These are words that I'm sure you've met before, lots of times and they're going to come up a lot in today's lesson.

Our lesson is split into two cycles, two different parts.

The first will be use known facts to find one-half and the second relate halving and doubling to finding one-half.

Let's start by using known facts, things that you already know and have hopefully memorised to find one-half.

And in this lesson you're going to meet Lucas and Aisha.

Have you met them before.

They're here today to give us a helping hand with the maths.

Lucas and Aisha want to share these pencils so that they have one-half each.

How could they do that? Hmm? What strategies have you got? What would you do? \"If we share them into two equal groups,\" says Aisha, \"We will each have one-half.\" And Lucas says, \"Let's keep taking one each, until all the pencils have been shared.\" That's a good strategy.

That would work.

Have you done that before? \"Wait, I think I might know a more efficient way to find one-half,\" says Aisha.

Hmm.

I wonder what that is.

She says, \"The whole is 10 because there are 10 pencils in the pot.\" And what Aisha is doing here is drawing a bar model.

And that's going to be really helpful.

\"To find half of 10, we need to divide the whole into two equal parts.\" That's how we find half of something.

You knew that, didn't you? So that's our two equal parts.

So that's our bar model.

\"I already know that five plus five is equal to 10.\" So we can complete our bar model.

\"I can use this fact to work out that half of 10 equals five.\" Wow.

Aisha, that was quick.

That was much quicker than sharing them out.

And that was using your known facts, something you already knew.

Now Lucas is going to try and use a bar model to represent the known facts that can help him to find one-half.

So let's have a look.

What's our whole, this time.

\"The whole is eight because there are eight strawberries in the bag.\" So let's make that bar model.

So we've got eight for the whole.

\"To find half of eight, we need to divide the whole into two equal parts.\" And that's what we've done here.

That's what we're showing on the bar model.

The whole divided into two equal parts.

Now, let's think about our known facts.

Lucas knows that four plus four is equal to eight.

He knows that off by heart.

It's a known fact.

So, \"I can use this fact to work out that one-half of eight equals four.\" Wow, well done, Lucas.

That really was quick and efficient.

\"Spot on,\" says Aisha.

\"Well done, Lucas.\" And well done to you, Aisha, as well.

Let's have a little check.

Let's see if you can use this strategy.

We've got a bar model here already.

Just missing the numbers.

Complete the bar model to show the known fact that would help find one-half of these sweets.

So find the whole and see if you can use known facts to find the half.

Pause the video.

Well, the whole in this case was six.

There were six sweets in the bag.

So we can add that to our bar model.

That's the whole.

And then we're looking to find one-half and we don't need to share the sweets out to find one-half because we can use known facts.

I know that three plus three is equal to six, so therefore we can say that one-half of six equals three.

How quick was that? Now Aisha is going to try and use a bar model to represent the known fact that can help her find one-half of 16.

So a bigger number this time.

She says, \"I think I can do this without any objects.\" Okay, I like the confidence.

Let's see.

\"I want to find one-half of 16 so I know the whole is 16.\" So we could write that in our bar model.

\"I can remember that eight plus eight is equal to 16.\" So a number plus the same number eight plus eight equals 16.

And because those numbers are the same and they total 16, we can say that one-half of 16 equals eight.

Lucas has remembered a fact that he learned in maths last week.

\"I learned that 12 plus 12 is equal to 24.\" Well done for remembering that fact, Lucas.

I wonder how many known facts you've got.

He says, \"I can represent this using a bar model.\" Okay, can you picture how that might look? It might look like this.

24 is the whole and half of that is 12.

So half of 24 equals 12.

Lucas and Aisha want to find one-half of 20.

Whose bar model is the most helpful and how do you know? Hmm? Have a look at both of them and decide.

Pause the video.

What did you notice there? What did you notice about Aisha's? Hmm? The two parts were different, weren't they? They were unequal.

The two parts of Lucas's were the same, they were equal.

Aisha's bar model does not help her to find one-half of 20 because she has not divided the whole into two equal parts.

But Lucas's bar model does help him to find one-half of 20 because he has divided the whole into two equal parts, and his bar model is showing that one-half of 20 equals 10.

So well done, Lucas, and well done you if you spotted that.

I think you're ready for some practise.

You're doing very, very well.

Number one, complete the bar models using your knowledge of facts that you've learned before.

Now if you are thinking to yourself, there's some facts that I don't know, don't worry, we've got a strategy for you.

If there are any facts you can't remember, you could use counters on ten frames to help you, just like this.

And then number two, write two equations to show one-half of the whole and A's already been done for you.

So for A, you can see half of four equals two and two equals half of four.

Can you do that for the other ones? Right, yeah.

Pause the video and a way you go.

Welcome back.

How are you getting on? Are you feeling confident about finding half without using objects using your known facts? So number one, complete the bar models using your knowledge of facts that you have learned before.

So hopefully for A, you knew that four plus four equals eight.

And for B, you know that one plus one equals two.

For C, three plus three equals six.

For D, hmm? Andeep found that it tricky.

So he used the tens frames to help.

So he had seven on the top, seven on the bottom, and seven plus seven, you could see from that tens frame equals 14.

So that wasn't a known fact for Andeep, but he was able to find it out.

For E, eight plus eight equals 16.

And for F, nine plus nine equals 18.

So those are our known facts.

Number two, write two equations to show one-half of the whole.

A, has already been done for you.

So for A, one-half of four equals two or two equals one-half of four.

What about the others? For B, one-half of 12 equals six or six equals one-half of 12.

For C, one-half of 10 equals five or five equals one-half of 10.

For D, one-half of 20 equals 10 or 10 equals one-half of 20.

For E, one-half of 22 equals 11 or 11 equals one-half of 22.

And for F, one-half of 24 equals 12 or 12 equals one-half of 24.

You're doing ever so well.

I think you're ready for the next part of the lesson and that's relating halving and doubling to finding one-half.

Lucas and Aisha are looking at one of their bar models, again, and this is it.

Aisha says, \"I know that one-half of 16 equals eight.\" Hmm, true? True.

And Lucas says, \"I know another way to describe this fact.\" Hmm? I wonder what Lucas is going to say.

\"What would you say, Lucas? He says, \"I would say that double eight is 16.\" Oh, yes it is, isn't it? And you can see that from the bar model.

Double eight is equal to 16.

So that bar model is showing two different related facts.

First one, double eight is 16 and the second half of 16 is eight.

Lucas and Aisha have a look at another of their bar models.

Hmm, I wonder if you can see two different related facts here.

Aisha says, \"I would say one-half of 10 is five.\" What do you think Lucas is going to say? He likes talking about doubles, doesn't he? Can you see a doubles fact? He says, \"I would say double five is 10.\" Hmm.

Double five is 10 and half of 10 is five.

Two related facts and both of them can be seen from that bar model.

Let's check to see if you've got this too.

Can you complete the sentences? So remember Aisha likes talking about halves.

Lucas likes talking about doubles.

Let's see if you can fill in their stem sentences.

Aisha says, \"I would say one-half of mm is mm.\" And Lucas says, \"I would say double mm is mm.\" So look at that bar model and fill in those stem sentences.

Pause the video.

Let's see.

\"I would say one-half of 20 is 10.\" And yes, I can see that from the bar model.

And Lucas says, \"I would say double 10 is 20.\" And yes, I can see that from the bar model too.

Those bar models are so helpful, aren't they? Double 10 is 20, half of 20 is 10.

And very well done if you manage to fill those incorrectly, you're on tracking the lesson.

You're ready for the next part of the learning.

Lucas and Aisha have another look at this bar model.

Aisha says, \"I can use my knowledge of doubles to find one-half of a number.\" Lucas says, \"Me too, I've noticed that if you double the half, you end up with the whole.\" Yeah, so double five is 10, half of 10 is five.

Lucas and Aisha are going to use their knowledge of doubles to find one-half of different numbers.

Lucas says, \"I will ask you a question.

You need to think about doubles to answer it.\" And Aisha says, \"Okay, I'm ready for the first question.\" Are you ready? He says, \"What is one-half of 14?\" And Aisha's going to think about doubles to answer it.

What is one-half of 14? So Aisha's going to think, well, what do I double to get 14.

She says, \"I know that double seven is 14, so half of 14 equals seven.\" Double seven is 14, half of 14 is seven.

\"Well done, Aisha, you are right.

Seven is equal to half of 14.\" Lucas has another question for Aisha.

Are you ready for it? He says, \"What is one-half of 24?\" Remember Aisha's going to think about doubles to answer this.

What's one-half of 24? What do you double to get 24? Is there a known fact? She says, \"I know that double 12 is 24.\" Good known fact there.

\"So half of 24 equals 12.\" Double 12 is 24, half of 24 is 12.

This is working really well, isn't it? They're being really quick and efficient.

\"Well done, Aisha, you are right.

12 is equal to one-half of 24.\" Let's have a check.

Now Lucas has a question for you.

And he says, \"What is one-half of 18? And you're going to think about doubles to answer it.

Here we go.

What's one half of 18? And we've got a stem sentence.

\"I know double mm is 18, so half of 18 equals mm.\" Use the bar model to help and fill in the gaps on the stem sentences.

Pause the video.

Good luck.

Let's see.

\"I know double nine is 18.\" Well done if that was a known fact for you and you didn't have to use resources to find that out.

Double nine is 18, so half of 18 equals nine.

And we can see that from the bar model.

Double nine is 18, half of 18 is nine.

Well done if you got that.

It's time for some final practise and I think you're ready.

In fact, I know you're ready.

Number one, use the bar model to help you solve each problem.

A, Lucas bought 16 dog biscuits for his two dogs.

He wants to give each dog the same amount of biscuits.

How many biscuits will each dog get? And we've got that stem sentence.

Double mm is mm.

Half of mm is mm.

Each dog will get mm.

And then B, Aisha has saved up 20 pounds.

Ooh, look at Aisha.

She wants to spend half of her money.

How much will she have left? And again, we've got that stem sentence to help.

Number two, complete the bar models and solve the problems using your knowledge of doubling and halving.

You could draw a picture to help too.

So A, this morning, there were six birds on the wall.

Now there are half that number.

How many birds are on the wall now? We've got that stem sentence to help.

We've got the bar model to help.

And B, Aisha has 12 stickers.

She gives Lucas half of her stickers.

How many stickers does she have left? And once again, complete the bar model.

Complete the stem sentences.

They're both there to help.

C, Lucas had some sweets.

He ate half of them and he has seven sweets left.

How many sweets did he have to start with? Think about your knowledge of doubles.

D, a car has four tyres, half the tyres have a puncture.

How many tyres need to be repaired? Hmm.

Good luck with that.

If you can work with a partner, I always recommend that, that you can help each other out and share some ideas and share your known facts.

Pause the video and I'll see you soon.

Welcome back.

How did you get on? Let's give you some answers.

Number one, a dog biscuit question.

So 16 dog biscuits.

He wanted to give each dog the same amount of biscuits.

He's got two dogs.

So we've got our whole, that's 16.

And half of 16 is eight.

So double eight is 16 and half of 16 is eight.

We can say it both ways.

Each dog will get eight biscuits.

And then B, Aisha with her 20 pounds, she wants to spend half of her money.

How much will she have left? Well, half of 20 is 10 because double 10 is 20 and half of 20 is 10.

Aisha will have 10 pounds left.

A, this morning, there were six birds on the wall.

Now there are half that number.

How many birds are on the wall now? Hmm.

While using our bar model and our stem sentences.

There's our six birds.

There's our whole.

Half of that is three.

So double three is six and half of six is three.

Now, there are three birds on the wall.

That bar model was so helpful there to see the doubles and the halves.

Aisha has 12 stickers.

She gives Lucas half of her stickers.

How many stickers does she have left? So here's some stickers.

That's 12 stickers.

That's our whole.

That's half of it.

And using my knowledge of doubles, I know that double six is 12, so therefore half of 12 is six.

Aisha has six stickers left.

And C, Lucas had some sweets.

He ate half of them and he has seven sweets left.

How many sweets did he have to start with? Hmm.

That's slightly different to before, isn't it? Where would we put seven this time? Hmm, that's the half that we know this time.

So we can fill that in as the part as one of the two equal parts.

Therefore, the other equal part is also seven.

And then we can say double seven is 14 and half of 14 is seven.

Lucas had 14 sweets to start with.

And D, a car has four tyres.

Half the tyres have a puncture.

How many tyres need to be repaired? These are four tyres.

That's our whole.

That's half of them.

What do we double to get four? We double two to get four.

Double two is four and half of four is two.

Two tyres need to be repaired.

We've come to the end of the lesson.

I've had lots and lots of fun and I hope you have too.

You're making so much progress here.

Very well done.

Today, we've been relating finding half of a number to halving and doubling and they're very closely linked, aren't they? You can use known facts to find one-half of a number and the more known facts you've got, the better, and the easier, and the quicker that will be.

If you double the half, you end up with the whole number.

It can be helpful to represent a known fact as a bar model.

I find that very, very helpful.

Because in the bar model, you can see the halves and the doubles, and to use stem sentences to describe the relationship between double and half.

So let's see an example here.

You can see from this bar model that double three is six and half of six is three.

Well, you've just been amazing today and it's been a great pleasure working with you.

I can't wait to spend another math lesson with you.

But until then, take care.

Have a great day and I'll see you soon.

Goodbye.

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\\frac{1}{2}

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\\frac{1}{2}

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\\frac{1}{4}

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\\frac{1}{3}

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\\frac{1}{2}

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\\frac{1}{3}

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\\frac{1}{4}

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\\frac{1}{4}

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\\frac{1}{2}

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\\frac{1}{3}

" } } ], "id": "cb2821f1-6e9a-59b1-5252-00e8cf2c240e", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" }, { "type": "Question", "question": { "text": "Which picture shows

\\frac{1}{2}

of the whole amount is circled?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1715686682%2Fncdnx2qaedmpqnd54wan.png&w=640&q=75", "imageKey": "4aa6428c-7c5c-0404-9910-00f4caad89e0/question/fc361ccceefc3f013b9d5e652704293a.png" }, "questionType": "Multiple choice", "correct": [ { "text": "b" } ], "choices": [ { "text": "a" }, { "text": "b" }, { "text": "c" } ], "id": "47b1b4e8-f13c-d401-b192-9f7050ff6cae", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" }, { "type": "Question", "question": { "text": "Match the equation to the correct answer." }, "questionType": "Matching", "pairs": [ { "left": { "text": "

\\frac{1}{2}

of 6 =" }, "right": { "text": "3" } }, { "left": { "text": "

\\frac{1}{2}

of 12 =" }, "right": { "text": "6" } }, { "left": { "text": "

\\frac{1}{2}

of 16 =" }, "right": { "text": "8" } }, { "left": { "text": "

\\frac{1}{2}

of 14 =" }, "right": { "text": "7" } }, { "left": { "text": "

\\frac{1}{2}

of 8 =" }, "right": { "text": "4" } } ], "id": "3c0b3896-49ef-845e-0a55-cc062061de93", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" } ], "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666", "meta": { "gradeStageId": "ks1", "subject": "Maths", "grade": "Year 2", "topic": null, "unit": "Fractions: identify equal parts and be familiar with halves, thirds and quarters", "lessonCount": "10", "age": [ 6, 7 ], "gradeId": "age_6_7", "gradeStage": "Key Stage 1", "lesson": "Relate finding half of a number to halving and doubling" } }, { "id": "9890af80-f422-db8b-b095-c09d9cd974b3", "type": "Resource", "resourceType": "Quiz", "title": "Relate finding half of a number to halving and doubling", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "Match the double fact to its answer." }, "questionType": "Matching", "pairs": [ { "left": { "text": "Double 10 is" }, "right": { "text": "20" } }, { "left": { "text": "Double 6 is" }, "right": { "text": "12" } }, { "left": { "text": "Double 7 is" }, "right": { "text": "14" } }, { "left": { "text": "Double 8 is" }, "right": { "text": "16" } }, { "left": { "text": "Double 9 is" }, "right": { "text": "18" } } ], "id": "40d94b88-a907-b5e3-a26c-1b8d9b4c6b0d", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" }, { "type": "Question", "question": { "text": "Each missing part on this bar model represents one-half of the whole number of pencils. What numbers are missing?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1716378449%2Fbqsn4c8zlsfvxzqaejj4.png&w=640&q=75", "imageKey": "9890af80-f422-db8b-b095-c09d9cd974b3/question/6cc4e58f5b3b69898d95c0daaad57e0d.png" }, "questionType": "Multiple choice", "correct": [ { "text": "5 and 5" } ], "choices": [ { "text": "6 and 4" }, { "text": "5 and 5" }, { "text": "3 and 7" }, { "text": "8 and 2" } ], "id": "da71915f-de64-d72c-749e-5866e08491cd", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" }, { "type": "Question", "question": { "text": "Which equations are true for this bar model?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1716378449%2Fqfq5sptqft1rf5vilps0.png&w=640&q=75", "imageKey": "9890af80-f422-db8b-b095-c09d9cd974b3/question/c9fdb3f3c28fa765c205b652db3e0cd6.png" }, "questionType": "Multiple choice", "correct": [ { "text": "

\\frac{1}{2}

of 20 = 10" }, { "text": "10 =

\\frac{1}{2}

of 20" } ], "choices": [ { "text": "

\\frac{1}{2}

of 20 = 10" }, { "text": "20 =

\\frac{1}{2}

of 10" }, { "text": "10 =

\\frac{1}{2}

of 20" }, { "text": "

\\frac{1}{2}

of 10 = 20" } ], "id": "2e74b605-9c40-76e4-722f-87822905b841", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" }, { "type": "Question", "question": { "text": "What facts does this bar model show?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1716378449%2Fidnxikh8qqq8ayczcoh2.png&w=640&q=75", "imageKey": "9890af80-f422-db8b-b095-c09d9cd974b3/question/e2036fd465879ea8792961ea27a42d35.png" }, "questionType": "Multiple choice", "correct": [ { "text": "Double 7 is 14" }, { "text": "One-half of 14 is 7" } ], "choices": [ { "text": "Double 7 is 14" }, { "text": "One-half of 7 is 14" }, { "text": "Double 14 is 7" }, { "text": "One-half of 14 is 7" } ], "id": "86651c04-d9c1-1876-4922-7a3ea7071141", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" }, { "type": "Question", "question": { "text": "Match the statements that link doubling and halving facts." }, "questionType": "Matching", "pairs": [ { "left": { "text": "Double 3 is 6" }, "right": { "text": "Half of 6 is 3" } }, { "left": { "text": "Double 6 is 12" }, "right": { "text": "Half of 12 is 6" } }, { "left": { "text": "Double 5 is 10" }, "right": { "text": "Half of 10 is 5" } }, { "left": { "text": "Double 10 is 20" }, "right": { "text": "Half of 20 is 10" } } ], "id": "1efdb1e3-e3e1-0430-aff0-86d71e64e8cb", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" }, { "type": "Question", "question": { "text": "Lucas has 16 new coloured pens.\nHe gave half of them to Aisha to use.\nHow many pens do they now each have?" }, "questionType": "Short answer", "correct": [ { "text": "8" } ], "id": "82af5fa6-5237-98bb-a780-dfa161b98d20", "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666" } ], "lessonId": "ad5c2b79-e95d-f451-bfbb-814a995f0666", "meta": { "gradeStageId": "ks1", "subject": "Maths", "grade": "Year 2", "topic": null, "unit": "Fractions: identify equal parts and be familiar with halves, thirds and quarters", "lessonCount": "10", "age": [ 6, 7 ], "gradeId": "age_6_7", "gradeStage": "Key Stage 1", "lesson": "Relate finding half of a number to halving and doubling" } } ] }