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I can use a bar model to represent the different ways of partitioning a number into two parts.

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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

Partitioning can be represented using the bar model.
There are ___ objects. ___ is the whole.
There are ___ and ___. ___ is a part. ___ is a part.
Combine the bars to form the full bar model, and compare this with the part-part-whole model.

Common misconception

Children may not see the bar model as proportional, so may think that the parts are equal.

Encourage children to see that the bars are proportional to help them get a sense of the size of the parts and whole.

Keywords

Partition - To split a whole up into parts.
Combine - To put parts together to make a whole.
Bar model - A bar model is a pictorial representation of a problem where bars are used to represent the known and unknown quantities.

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Hello, I'm Mrs. Kaylee and I'm going to help you with your learning today.

So today we're going to use a bar model to represent a whole partitioned into two parts.

Here's the outcome of today's lesson.

I can use a bar model to represent the different ways of partitioning a number into two parts.

Here are keywords for today's lesson.

Can you repeat them after me? My turn partition, your turn.

My turn combine, your turn.

My turn bar model, your turn.

So you might have seen these words before.

Partition means that we're going to split a whole into parts and combine means we're going to put the parts together to make the whole.

A bar model is a representation used to show the whole and the parts using bars.

Here's the lesson outline.

We're going to use a bar model to represent a whole partitioned into two parts.

We start off by partitioning and then we'll look at combining the parts.

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

We've got Alex and Sam.

Alex and Sam are counting birds.

Can you see how many birds there are? Can you count them with me? Let's point at them when we count.

One bird, two birds, three birds, four birds, five birds.

There are five birds.

Alex is counting them.

One bird, two birds, three birds, four birds, five birds.

Sam said there are five birds altogether.

There are five birds.

So five is the whole.

Each bird can be represented as a cube.

So we've got five birds and we've got five cubes.

Alex is asking what do the cubes represent? Sam said the cubes represent the five birds.

So we've got five birds in the whole and we've got five cubes in the whole.

We can represent each cube and each bird as a bar on the bar model.

Each bird can be represented as a part of a bar model.

There are five birds.

There are five parts on the bar model and there are five in the whole.

What do the bars represent? The bars together represent the five birds.

The whole and its parts can be represented as a bar model.

There are five birds.

Each part has been represented on the bar model and the whole is shown on the bar model.

This time we've got some different coloured birds.

Five is the whole, three birds are red and two birds are white.

Each bird can be represented as a cube.

There are five birds in the whole and there are five cubes.

What do the cubes represent? The cubes represent the red and the white birds.

We can represent it as a bar model.

What do the bars represent? The bars represent the three red birds and the two white birds.

So can you see the two parts on the bar model? We've got three and two and that makes five in the whole.

The birds can be represented as a bar model, five is the whole.

This time two birds are red and three birds are white.

The birds can be represented as a bar model.

So we've got five birds in the whole and we've got five cubes and we've got five on the bar model.

It's been partitioned into two and three.

What do the cubes represent? The cubes represent the red and the white birds.

We've got two red birds and three white birds.

What do the bars represent? The bars represent the two red birds and the three white birds.

We've got a different number of red birds this time.

Five is the whole, one bird is red and four birds are white.

The birds can be represented as a bar model.

There are five birds, there are five cubes and there are five in the whole.

The bar model shows we've got one part and four part.

The bar model shows that five has been partitioned into one and four.

What do the cubes represent? The cubes represent the red and white birds.

What do the bars represent? The bars represent the one red bird and the four white birds.

This time we've got a different number of red birds.

Five is the whole.

Four birds are red and one bird is white.

There are five birds in the whole and there are five cubes and there are two parts on the bar model.

We've got four and one, five has been partitioned into four and one.

The birds can be represented as a bar model.

What do the cubes represent? The cubes represent the red and the white birds.

What do the bars represent? The bars represent the four red birds and the one white bird.

This time all of the birds are red, five is the whole, five birds are red and zero birds are white.

We can see there are five birds in the whole and there are five red cubes and there are five in the whole on the bar model.

The birds can be represented as a bar model.

What do the cubes represent? The cubes represent the red and white birds.

What does the bar represent? The bar represents the five red birds and zero white birds.

Let's focus on the bar model.

Here we can see we've got one red cube and four white cubes, and on the bar model you can see five is the whole, one is apart and four is apart.

So five has been partitioned into one and four.

Alex is asking what can we see? Sam said, we can see the whole is five, one red cube is apart and four white cubes is apart.

Here's the part-part whole model.

What is the same? Sam said, the bar model shows the same as the part-part whole model we have looked at.

Both models show five being partitioned into one and four.

This time, five is the whole and two cubes are red, three cubes are white.

Can you see it on the bar model and the part-part whole model? Alex is asking what is the same? Sam said they both show five being partitioned into two and three.

The whole is five, two is apart and three is apart.

We've got five cubes in the whole again, this time three cubes are red and two cubes are white.

You can see it on the bar model and the part-part whole model.

Five has been partitioned into three and two.

Alex is asking what is the same? Sam said they both show five being partitioned into three and two.

So we can see the whole is five, three is apart and two is apart.

We've got five cubes in the whole again this time four cubes are red and one cube is white.

We can see that on the bar model and the part-part whole model.

Alex is asking what is the same? Sam said they both show five being partitioned into four and one.

The whole is five, four is a part and one is a part.

We can represent partitioning as a part-part whole model or a bar model.

So you can see from the two different representations that the whole is shown and the parts are shown as well.

What is the same and what is different? They both show the whole and the parts even though they look different.

With the bar model, we can make the parts look bigger if they're bigger and smaller if they're smaller.

But they combine to make the whole.

Let's check your understanding, which bar model matches the picture? So look at the picture of the cubes and think about which bar model goes with this picture.

Pause the video and think about it.

That's right, it was the middle one.

I can see five is the whole, three is apart and two is apart.

So five has been partitioned into three and two.

Let's check your understanding again.

Which bar model matches the part-part whole model? Pause the video and think about this one.

That's right, it was the first one.

I can see they've both got four as the whole and three as a part and one as apart.

So four as being partitioned into three and one.

What's the same and what's different here? Have a look at the bar models and the part-part home models that go with them.

Think about what is the same and what's different.

Well, I can see that we've always got five as the whole and we've got four as a part and one as a part.

So Alex said the whole is the same and the parts have been swapped round.

Did you notice that they've been swap round but it's still four and one.

Let's check your understanding, what's the same and what's different here.

Pause the video and think about this one.

That's right, the parts have been swapped round again.

The whole is the same but the parts have been swapped round.

The whole is still the same.

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

Can you use the part-part whole models and bar models to partition four cubes in different ways and record your thinking.

I filled out some of the numbers on the bar models and the part-part whole models for you.

So we can see the whole is four and we can see one of the parts.

See if you can work out what the other part is.

You can colour the cubes to show your thinking.

You can use real cubes to help you or you can draw your own or colour them in there.

So pause the video and have a go at your task.

How did you get on with your task? Did you use the part-part whole models and bar models to partition four cubes in different ways.

So we always had four as the whole and I can see it's being partitioned into three and one, two and two and one and three and I've coloured the cubes to show those different parts and wholes.

Is that what you found? Let's move on to the second part of the lesson.

We'll be combining the parts.

Alex and Sam are counting birds again.

Wonder how many birds there are here.

Alex said, I can see two red birds.

Sam said, I can see three white birds.

I wonder what those two parts combine to make.

Alex said we can combine the parts to make the whole.

Sam said two is a part and three is a part.

So five is the whole.

There are five birds in the whole group.

If we know the parts, we can combine the parts to make the whole, I wonder what the whole is here.

You could look at the cubes or the bar model or the part-part whole model to work out the whole from the parts.

Two is a part and three is a part.

So the whole is five.

We can write that on the bar model and the part-part whole model.

If we know the parts, we can combine the parts to make the whole, I wonder what the whole's going to be this time.

Four is a part and one is a part.

What do you think the whole will be? What do you think they combine to make? The whole is five.

So we can put that on the bar model and the part-part whole model.

I can see there are five cubes in total.

If we know the parts, we can combine the parts to make the whole.

I wonder what the whole is going to be this time.

Three is a part and two is a part.

What do they combine to make? They make five, the whole is five.

So we can put that on the part-part whole model and the bar model.

Have a look at the two bar models here.

They're representing the red and the white cubes.

What's the same and what's different? Sam said the whole is five, three is apart and two is apart.

But can you see that sometimes the whole is at the top of the bar model and sometimes it's at the bottom of the bar model.

It's still showing the whole in the parts.

Let's check your understanding.

What is the whole here? Look at the cubes and the bar model to work out what the whole is.

Is it two, three, or five? Pause the video and think about this one.

That's right, the whole is five.

I can see three is apart and two is apart.

So the whole is five.

Let's check your understanding again.

What is the whole this time? Pause the video and think about whether it's two, three, or five.

That's right, the whole is five.

I can see two is apart and three is apart.

So five is the whole.

Let's check your understanding again.

What is the whole for each of these? I can see a bar model and a part part-whole model to represent the cubes.

Pause the video and think about what the whole is, for each of these examples.

I can see on the first one we've got two as a part and one as a part.

These can be combined to make three.

Three is the whole.

In the middle one we've got three as a part and one as a part.

These can be combined to make four.

So four is the whole.

And on the last one we've got four as a part and one is a part.

These can be combined to make five.

So five is the whole.

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

Can you work out the whole from these parts? You could check with cubes.

So can you fill out the whole on the bar models and the part-part whole models? Pause the video and have a go at your task.

How did you get on with your task? Did you work out the whole from these parts? So the first one, we had three as a part and two as a part, and they can combine to make five.

In the middle one we had two as apart and two as a part.

And these can combine to make four.

And in the final one we had one as a part and four as a part.

These combine to make five as the whole.

How do you get on with those ones? We've got to the end of our lesson, well done everyone.

Today we were using a bar model to represent a whole partitioned into two parts.

Partitioning can be represented using the bar model.

The bar model can be used to represent the parts and the whole, the parts can be combined to make the whole.

And there we've got a picture of the bar model.

You can see the whole and you can see the parts it's been partitioned into.

Well done everyone, see you next time.

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", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703074761%2Fcvxnagb6ljqbh5ejan28.png&w=1200&q=75", "imageKey": "ca942acb-9b65-98d8-8c38-8b603b2003c7/question/6623f96ba824666e938ca02282b7eab4.png" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703074760%2Fxeaergwrikbukzdvlpgf.png&w=384&q=75", "imageKey": "ca942acb-9b65-98d8-8c38-8b603b2003c7/question/fbd47d3faf5df25e1b0aa17f0a99f32e.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703074760%2Fxeaergwrikbukzdvlpgf.png&w=384&q=75", "imageKey": "ca942acb-9b65-98d8-8c38-8b603b2003c7/question/fbd47d3faf5df25e1b0aa17f0a99f32e.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703074760%2Fx9dc0tao0jga77wwa01n.png&w=640&q=75", "imageKey": "ca942acb-9b65-98d8-8c38-8b603b2003c7/question/a61f82a19a72b44d6167b388a017f829.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703074761%2Floljxzsmqgzsacu6gbhb.png&w=640&q=75", "imageKey": "ca942acb-9b65-98d8-8c38-8b603b2003c7/question/e42476b4dc6c4fab96ed1a55da1336f4.png" } ], "id": "9028f3b4-dea9-c23f-a635-7284e8e278a0", "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763" } ], "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763", "meta": { "gradeStageId": "ks1", "subject": "Maths", "grade": "Year 1", "topic": null, "unit": "Composition of numbers 0 to 5", "lessonCount": "10", "age": [ 5, 6 ], "gradeId": "age_5_6", "gradeStage": "Key Stage 1", "lesson": "Use a bar model to represent a whole partitioned into two parts" } }, { "id": "49ac82b8-55e9-51d7-f608-7b615107686e", "type": "Resource", "resourceType": "Quiz", "title": "Use a bar model to represent a whole partitioned into two parts", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "Match each word to its definition. " }, "questionType": "Matching", "pairs": [ { "left": { "text": "Partition" }, "right": { "text": "to split a whole up into parts. " } }, { "left": { "text": "Combine" }, "right": { "text": "to put the parts together to make the whole. " } } ], "id": "0783dde8-4f11-2bf9-e1ee-83ca13834aaa", "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763" }, { "type": "Question", "question": { "text": "Which bar model is showing these cubes partitioned correctly? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075512%2Ffjofqy952aca3qarlf7c.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/047add843853fd60a24fd5d967d658dc.png" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075511%2Fojstpowbazwrsts8xw18.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/ee45b7a60a6f72e1172c0593f3071c33.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075511%2Fmjkwdwdpqk8xbrovdkql.png&w=750&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/55348c0ddfed440daf3e3b2379ef3d39.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075511%2Frzrvwrw9qkiqw4d7gt78.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/aa92bf0636d09bba11bee6c0d338d97c.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075511%2Fojstpowbazwrsts8xw18.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/ee45b7a60a6f72e1172c0593f3071c33.png" } ], "id": "98b94136-d682-6443-1c58-2ce3f6ccd95f", "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763" }, { "type": "Question", "question": { "text": "Which bar model matches the part-part-whole model? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075514%2Fwnernwm0q3l4lnxli8bt.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/03f4d5d178a25e9a1d945fe907a0e0a6.png" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075512%2Fhzd9glmeaedmpz0f91db.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/144bf58df3e7cc3f805fc2d35a71f2fc.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075512%2Fiwyjugdont11rpfemhom.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/df7a0dcf35af1122b8f192b4c47a8d4d.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075512%2Fhzd9glmeaedmpz0f91db.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/144bf58df3e7cc3f805fc2d35a71f2fc.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075514%2Ft5zpdcwa1utopq1ncf8b.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/07b29fd3199a2dd155229e62c494eb14.png" } ], "id": "44f3d3a7-d531-d911-6e6a-77678f84e6d3", "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763" }, { "type": "Question", "question": { "text": "Jacob has 2 cubes and Izzy has 1 cube. Which bar model is correctly showing their cubes? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075517%2Fcr1wz54jrn9atpjaxmzw.png&w=1080&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/f9efd166b292ba582ed4aa75e0ab0e1c.png" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075515%2Flm9omqrusaedn21glifa.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/0af83f840ce4a24a1e69903e81434397.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075515%2Fzi3ns7vpmjk5vekskdzq.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/21b8dce3ef8d2d3872f2a614935b0d92.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075515%2Flm9omqrusaedn21glifa.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/0af83f840ce4a24a1e69903e81434397.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075516%2Fqjg8ixkm456glsstxvlw.png&w=640&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/08011da9ff506c8203263bb56ee31add.png" } ], "id": "0a2dd02e-588f-da9c-bdb3-ce2426e4057a", "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763" }, { "type": "Question", "question": { "text": "Jacob thinks the missing part will be the same for all of these. Is he correct? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075517%2Farozmspjzwipvr4hcgvg.png&w=1920&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/043a6a6690817f1423d42719c47d3750.png" }, "questionType": "Multiple choice", "correct": [ { "text": "No" } ], "choices": [ { "text": "Yes" }, { "text": "No" } ], "id": "8dd4ba48-043a-40b8-764f-445090a5f2f3", "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763" }, { "type": "Question", "question": { "text": "Izzy thinks the missing part will be the same for all of these. Is she correct? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703075517%2Fqqrnv9cmjmsrmbf1hcd2.png&w=1920&q=75", "imageKey": "49ac82b8-55e9-51d7-f608-7b615107686e/question/e2c36666e3083ffc927b7c16ab5213b7.png" }, "questionType": "Multiple choice", "correct": [ { "text": "Yes" } ], "choices": [ { "text": "Yes" }, { "text": "No " } ], "id": "93f83808-9284-9ff7-6efd-2eb29d16036f", "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763" } ], "lessonId": "057246ad-b5b2-91ad-aeef-0afe37902763", "meta": { "gradeStageId": "ks1", "subject": "Maths", "grade": "Year 1", "topic": null, "unit": "Composition of numbers 0 to 5", "lessonCount": "10", "age": [ 5, 6 ], "gradeId": "age_5_6", "gradeStage": "Key Stage 1", "lesson": "Use a bar model to represent a whole partitioned into two parts" } } ] }