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I can identify different 2D nets which will create the same 3D shape.

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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

A net is a 2D shape that can be folded and joined to create a 3D shape.
There can be more than one way to create a net for a given 3D shape.
Not all arrangements of shapes will form the net of a 3D shape.

Common misconception

It is perfectly possible for pupils to be highly numerate but struggle with the spatial awareness needed to visualise / imagine whether a 2D net will fold together to form a 2D shape.

As part of the lesson design process you may wish to incorporate manipulatives such as construction materials for those pupils whose learning needs scaffolding. As with all scaffolding, aim to move pupils away from this when you can.

Keywords

Net - A net is a 2D representation of the faces of a 3D shape, that can be folded up into the 3D object.

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Hi there, my name is Mr. Tilstone.

I'm a primary school teacher and I teach all of the different subjects, but my favourite has to be maths, I love it.

It's a real pleasure then, and a real delight and a real honour to be with you today teaching you this lesson, which is all about nets of 3D shapes.

So if you are ready, I'm ready, let's begin.

The outcome of today's lesson is I can identify 2D nets, which will create the same 3D shape.

Now you might have had some very recent experience of learning about what nets are and the fact that a net can make a 3D shape.

Today we're going to focus on the idea that a 3D shape can be made from different nets.

And our keywords, we've just got the one, my turn, net, your turn.

What is a net, could you explain it in your own words? How about this? A net is a 2D representation of the faces of a 3D shape that can be folded up into the 3D object.

So for example, a cube is a 3D shape and it's got a net, that's 2D that folds up to make the cube.

Our lesson is split into two cycles.

The first will be same 3D shape, different 2D nets, and the second, solving problems with nets of cubes.

But if you are ready, let's focus on same 3D shape, different 2D nets.

In this lesson, you're going to meet Andeep, Jun, Sofia, and Sam.

Have you met them before? They're here today to give us a helping hand with our maths.

Jun uses construction shapes to make a triangular prism.

Have you got some construction shapes in your classroom? Because if you have, they're a great way for you to explore today's lesson.

He unfolds it to show the net.

So on the left you can see the net, and on the right you can see the 3D shape, the triangular prism that the net folds to make.

Is it the only possible net though? Is there another way that we can do it? Let's have a look.

A net can be composed in different ways.

So for example, the triangles could be repositioned.

Let's have a look.

So the rectangles in this case have stayed in the same position, but the triangles are moving about, so that would work.

And so would this, they're in different positions, but it would still fold together.

And I can picture that in my mind, that shape, that net folding together to make the triangular prism.

That would work, but what about this one? That wouldn't work, but why? So the shapes just can't go anywhere.

They will work in certain positions, but not in others.

Why wouldn't they work where they are now, what's wrong? Well, the triangles in this case need to be opposite of each other or they will overlap.

Now we repositioned the triangles there.

What about the rectangles? They could be repositioned too.

Have a look at this.

So one of those rectangles has been moved to a different position, but that would still fold together to make that triangular prism, it works.

And another one, this time the rectangles aren't even touching at all, but it would still fold together to make the triangular prism, it works.

There are other possibilities.

So there are lots of different ways that a net can be composed and still fold together to make the same 3D shape.

How about this one? Look at this shape, this is a 3D shape.

Can't see all the faces this time, but they're there.

I can imagine them, I can visualise them.

It's a different triangular prism, a different shape.

This is a possible net that would fold together.

Is it the only net? It's not the only net, but what about this one? Is that a different possible net for that shape? Would that work, or is there something that you've noticed? Hmm, how about that? That's a clue.

No, that wouldn't work.

That wouldn't fold together to make that triangular prism.

The side lengths here do not match.

There would be gaps in the 3D shape, so that wouldn't form an edge.

So not all arrangements will fold to make the 3D shape.

That one, however, would work.

A net has been drawn for this pentagonal prism.

Sketch at least one alternative net.

So it could look like that, what else could it look like? Can you think of a different way? Pause the video and explore.

What did you come up with? There are lots and lots of possibilities.

I'm just going to give you one.

You may have repositioned one of the pentagons, for example, this, or this, or this or this.

They would all fold together to make that pentagonal prism.

It's time for some practise.

Add one more shape onto each of these nets to form the 3D shape.

How many other nets can you sketch to make the same 3D shape? Remember, you can reposition those shapes.

So have a look at A, needs one more shape add-in, what is the shape, where could you put it? Same for B.

And number two, a net has been given for each 3D shape.

Sketch at least one alternative net for each.

So how else could those shapes be positioned and still fold together to make the 3D shape? Have fun exploring that and I'll see you shortly for some feedback.

Welcome back, how did you get on with that? Let's have a look at some possible answers, there are many.

So for A, here are a few possible sketches you might have made.

So you needed one more triangle, but they could have been repositioned in lots of different ways.

And that's just three of them.

Did you get any of those three? Did you manage to get some other ones? Did you check with a partner to see if they agree that it would fold together to make that square based pyramid? What about B? Let's have a look at B.

So you needed to add one more shape onto that.

And here are some possible sketches that you might have made.

All of those would work, have you got any of those? Have you got some different ones? And have you checked with somebody else that they agree? Number two, a net's been given for each 3D shape, sketch at least one alternative net.

Again, many, many, many possibilities.

Wouldn't have time to give all of them here, but here's just some.

Well done if you've got any of those or anything like those.

Are you ready for the next cycle, that solving problems with nets of cubes? So we looked at some different 3D shapes.

Now we're going to focus specifically on cubes.

So this is a cube, cubes are very common 3D objects.

You'll see them every day.

The Oak pupils are sketching nets for the cube.

They know a cube has six square faces.

So their nets need to have six connected squares connected on the sides.

So here are two of the nets that have been sketched for this cube.

Here's one, do you think that would work, hmm? Gonna investigate in a second, what do you think there? Can you visualise it? And here is another, same again, try and visualise it folding together, would it work? And then we'll prove it in a second.

It was Andeep and Jun that sketched them and now they're going to fold their nets to check if they form cubes.

So if they cut them out, they're going to fold them up.

Let's have a look.

Well done, Andeep, that worked.

What about Jun, let's see? And well done, Jun, that worked.

So can you see they're different nets, but they both folded together to form the exact same shape? Would this net fold to make a cube? Thumbs up if you think it would, and thumbs down if you think it wouldn't.

What about this? This is a clue.

No, it wouldn't.

These two faces would overlap and would end up in the same position.

So once again, we can't just put the shapes anywhere in a net, they have to go in specific positions.

One of them would need to the opposite side.

We've got a couple of choices here, but as long as it's on the opposite side, we could do something like that.

And now it works, now we've got the net for a cube.

Sam says, \"I've made a different net to Jun, but mine also forms a cube.\" Is she right? Pause a video and explore.

What do you think, is she right or not? Can you explain yourself? Let's have a look.

It will form a cube, but it's the same net as Jun's.

It's just been rotated, so they weren't different at all.

They were exactly the same net, just in different orientations.

Did you spot that? Well done if you did.

Here we go, look, that proves it, they are the same net.

Dice are cube shaped and I'm sure you've got some dice in your classroom, they're cube shaped.

Did you know, you might have known this, that spots on opposite faces of a dice sum to seven? So for example, if one is on one side, six is on the other, did you know that? Here we go, look, so here's six.

If six is there, one just couldn't go anywhere, it would need to go on the face that's opposite.

Which one would it be, can you visualise it? If it was folded together, which one would be opposite? It would be there, so that six and one makes seven.

Let's have a look at another pair.

What about the two? If two was here, what goes with two to make seven? Five, so where could the five be? There's three positions, but only one of them could be where the five goes.

And it's got to be opposite the two.

And that is exactly where it would be.

And then we've got the three.

So if three's there, then opposite three will be four.

It's time for a check, where would three be on this dice? So there's four, where would three be, in position A, B, C, D, or E? Have a think about that, try and visualise it.

See if your partner agrees.

And I'll give you the answer in a second, pause the video.

What do you think needs to be opposite? So what's the opposite face to that? Opposite faces total seven.

When the net is folded to make a cube, the four will be opposite face C.

So that is where three would be, just there.

Well done if you got that.

It's time for some more practise.

There are 11 different nets for a cube.

Can you sketch them all, find all 11? You may wish to check by using construction materials or by cutting out and folding your sketches.

Remember, don't make the mistake of thinking that your nets are different if they're just rotated.

They've got to be different.

Choose one of your cube net sketches and add dice dots to it.

Remember that the dots on opposite faces sum to seven.

Number three, draw some dots on the correct blank faces of this dice.

So three of those numbers are in already.

Think about opposite faces and that they total seven.

Righty-ho, pause the video, off you go.

Let's have a look, so these are the 11 nets of a cube.

Now remember, you may have orientated them differently, so they might not be in this exact position, but as long as they're composed the same, these are all 11.

Have a look at those, well done if you've got all of them.

And number two, choose one of your cube net sketches.

This one might be a different one.

And add dice dots to it.

So here's an example and the opposite faces here total seven.

So we've got one and six on opposite faces, two and five are, and four and three are.

And draw dots on the correct blank faces of this dice.

So visualise those opposite faces when it's folded together.

So six will be there because that when folded together will be opposite the one.

And that four would be there 'cause when folded together it will be opposite the three, and the two would be there, again, when folded together, it will be opposite the five.

So all of those pairs total seven.

We've come to the end of the lesson.

Today's lesson has been about the fact that the same 3D shapes can be composed from different 2D nets.

There are multiple possibilities each time.

So a net is a 2D representation of a 3D shape.

It is composed of the faces of the 3D shape, so it's got to have the exact same faces.

Each 3D shape has many possible nets, which can be found by rearranging the shapes.

However, not all arrangements will produce a net that folds into a 3D shape.

So the shapes have got to be in particular positions.

They can't just go anywhere.

And I'm sure you've found that out yourself today.

Very well done on your achievements and accomplishments and learning successes today.

You've been fantastic.

Hope you're proud of yourself.

I'm proud of you and I'm sure your teacher is too.

Hope you've enjoyed this math lesson.

I also hope you have an amazing day, whatever it is that you've got coming up next.

Take care, see you soon and goodbye.

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It would need two pentagons in its net. How many rectangles would it need?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589888%2Fnona54qyyiud8v63bbpi.png&w=640&q=75", "imageKey": "3cbd0d17-7a31-3619-7d89-755537cd6d69/question/a71d47ddf5b3b3b33a6136b396c02343.png" }, "questionType": "Short answer", "correct": [ { "text": "5" }, { "text": "five" } ], "id": "5bd1f999-b5cf-86c0-f4cf-9c000f96c2c6", "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597" }, { "type": "Question", "question": { "text": "What needs to happen to this net to make it the net of a triangular prism?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589883%2Fvew9ies3pwaflin50duf.png&w=640&q=75", "imageKey": "3cbd0d17-7a31-3619-7d89-755537cd6d69/question/3620b09a9fed9e17e5090c33df260e7b.png" }, "questionType": "Multiple choice", "correct": [ { "text": "Add another rectangle." } ], "choices": [ { "text": "Nothing. It is already the net of a triangular prism. " }, { "text": "Add another rectangle." }, { "text": "Add another triangle. " }, { "text": "Remove a rectangle." } ], "id": "629bf64d-3ac1-fe46-7aee-4a1d127ab586", "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597" } ], "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 6", "topic": null, "unit": "Draw, compose and decompose shapes", "lessonCount": "10", "age": [ 10, 11 ], "gradeId": "age_10_11", "gradeStage": "Key Stage 2", "lesson": "The same 3D shapes can be composed from different 2D nets" } }, { "id": "8a636089-3585-cee8-93ab-d287f136162e", "type": "Resource", "resourceType": "Quiz", "title": "The same 3D shapes can be composed from different 2D nets", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "Which of these statements is true?" }, "questionType": "Multiple choice", "correct": [ { "text": "All 3D shapes have a net." }, { "text": "It is possible for a 3D shape to have more than one net." } ], "choices": [ { "text": "All 3D shapes have a net." }, { "text": "All 3D shapes have exactly one net. " }, { "text": "It is possible for a 3D shape to have more than one net." } ], "id": "6a199a9d-5812-7452-21b4-c68d479c4eea", "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597" }, { "type": "Question", "question": { "text": "Which of these statements is true?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589884%2Fbaeibfj5irn8re5tfwsi.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/1944de30549058203cf3f3b19fe1451c.png" }, "questionType": "Multiple choice", "correct": [ { "text": "Both nets would form a triangular prism. " } ], "choices": [ { "text": "Net a would form a triangular prism but net b would not. " }, { "text": "Net b would form a triangular prism but net a would not." }, { "text": "Both nets would form a triangular prism. " } ], "id": "30597bef-7831-fb55-70cb-e875582ba345", "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597" }, { "type": "Question", "question": { "text": "Which of these are nets for a triangular prism?" }, "questionType": "Multiple choice", "correct": [ { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589884%2Fmv1qqha0vcafldsmb99e.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/448931dde68d0cda5d31a0a2ce8270f7.png" }, { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589883%2Ffusuujrcpn8sxcmeao7b.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/2d680d2d533ad6161f85f17f74cdf076.png" } ], "choices": [ { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589884%2Fmv1qqha0vcafldsmb99e.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/448931dde68d0cda5d31a0a2ce8270f7.png" }, { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589883%2Ffusuujrcpn8sxcmeao7b.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/2d680d2d533ad6161f85f17f74cdf076.png" }, { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589884%2Ff2qlmuemvdihp0zzzsr9.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/423e3007df524c0e76133edd51623bd6.png" }, { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589884%2Fbdjku1thoz1bhxqas5os.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/3cecd880a457633b322dd01183eaa8a6.png" } ], "id": "0911e210-76c1-2b98-01fb-e16e053e133e", "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597" }, { "type": "Question", "question": { "text": "Look carefully at the net of the cube. Match the letters so that opposite faces of the cube are together.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589884%2Fmjfkwcdybg0zzhyihvlj.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/94e3faf0ae53aeaa832521df674a35f3.png" }, "questionType": "Matching", "pairs": [ { "left": { "text": "a" }, "right": { "text": "d" } }, { "left": { "text": "b" }, "right": { "text": "e" } }, { "left": { "text": "c" }, "right": { "text": "f" } } ], "id": "005867c0-2f9c-9d62-313e-278ec1470471", "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597" }, { "type": "Question", "question": { "text": "This is a net for a dice. Which face would have 2 spots?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589885%2Fum17dkvscoejev0quj8q.png&w=640&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/5ef75d9fec2fd20604b4c27914eb4671.png" }, "questionType": "Multiple choice", "correct": [ { "text": "Face c" } ], "choices": [ { "text": "Face a" }, { "text": "Face b" }, { "text": "Face c" }, { "text": "Face d" }, { "text": "Face e" } ], "id": "49bdcfc0-b193-66b9-1022-f228148dfdba", "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597" }, { "type": "Question", "question": { "text": "Which of these are nets of a cube?" }, "questionType": "Multiple choice", "correct": [ { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589885%2Fn7x1v8iiyef1gxvuw7d5.png&w=384&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/2660e83befc216a1bb40062940748ee8.png" }, { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589887%2Fgbejj0i07i1tjj7cdebs.png&w=384&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/27ba66d8531db113f32104f31163ab34.png" } ], "choices": [ { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589885%2Foxtz5cnxjcjhw3hxokbs.png&w=384&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/a758579f9f3715a02f733d7785720269.png" }, { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589885%2Fn7x1v8iiyef1gxvuw7d5.png&w=384&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/2660e83befc216a1bb40062940748ee8.png" }, { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589887%2Fgbejj0i07i1tjj7cdebs.png&w=384&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/27ba66d8531db113f32104f31163ab34.png" }, { "text": "", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1719589886%2Fuakhaeo3gqtk7grb2kwr.png&w=384&q=75", "imageKey": "8a636089-3585-cee8-93ab-d287f136162e/question/6be52e72bfb85aa491a56a0bafdcf5e8.png" } ], "id": "e8f1988e-10e9-d27c-35ca-9d59f9ac0df9", "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597" } ], "lessonId": "bb8494fe-a932-37d3-55cc-3668cdf48597", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 6", "topic": null, "unit": "Draw, compose and decompose shapes", "lessonCount": "10", "age": [ 10, 11 ], "gradeId": "age_10_11", "gradeStage": "Key Stage 2", "lesson": "The same 3D shapes can be composed from different 2D nets" } } ] }