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I can explore, discuss and compare tetrominoes and pentominoes.

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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

Four connected squares make a tetromino, and five connected squares make a pentomino.
The five possible tetrominoes can be explored, discussed and compared.
The 12 possible pentominoes can be explored, discussed and compared.
Tetrominoes and pentominoes can be rotated and flipped.
A particular tetromino or pentomino can be transformed into another by moving some of the squares.

Common misconception

Might not recognise that the arrangement is still the same when it has been rotated or flipped.

Allow plenty of opportunity to explore practically and model rotating, flipping and comparing arrangements.

Keywords

Arrangement - The way something is organised.
Tetromino - An arrangement of four connected squares.
Pentomino - An arrangement of four connected squares.
Rotate - To spin around.
Flip - To reflect in a mirror line.

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Hello, everybody.

My name is Mrs. Johnson.

I am really excited to be here today to help you with some of your maths learning.

I hope that you are ready to do some hard work and have lots of fun.

Let's have a look at what we are going to be learning today.

Today's lesson is called Tetrominoes and Pentominoes and it comes from the unit to recognise, compose, decompose, and manipulate 2D and 3D shapes.

By the end of this lesson, you will be able to explore, discuss, and compare tetrominoes and pentominoes.

Don't worry if you don't know what those are at the moment because we're going to learn all about them together and we're going to be brilliant.

Have you ever learned about making patterns before? If you have, that might help you in today's lesson.

Let's have a look at our keywords.

We have got five keywords today.

Some of them might be words that you haven't said before, so we're going to practise saying them a couple of times.

Our first word is arrangement.

Can you say arrangement? Can you whisper arrangement? Well done.

The second word is probably a word that you haven't heard before.

It is tetromino.

Can you say tetromino? And whisper tetromino.

Well done.

Then we have pentomino.

Say pentomino.

Whisper pentomino.

Nice job.

Then we have the next key word, rotate.

Can you say rotate? And whisper rotate.

Well done.

And our last keyword is flip.

Can you say flip? Can you whisper flip? Good job.

Look out for those keywords in this lesson, because they are really going to help you with what we are learning.

We have two parts to this lesson today.

In the first part, we are going to learn all about tetrominoes, and then later on we are going to learn about pentominoes.

So let's get started and see if we can find out what tetrominoes might be.

Look out for these two friends today, Lucas and Sam.

They are going to help us with our learning too.

Lucas has been playing with some square stickers and he's been arranging them.

Look carefully at how he has arranged his square stickers.

What do you notice about them? If you have a friend or a partner or a grownup there who you can talk to, pause the video, and tell them what you notice.

Well done.

Did you see that each one of his arrangements has four squares in it? Good job if you noticed that.

If Lucas was using four squares each time, do you think there's anything else that he could have made? Let's have a look.

Arrangements of four squares are called tetrominoes.

Lucas was making tetrominoes with his square stickers.

Lucas thinks that the word tetromino sounds a little bit like the word domino.

They do sound very similar, don't they? I wonder if there's a reason why they sound similar.

Sam says that dominoes are arrangements of two squares, and we know that tetrominoes are arrangements of four squares, so perhaps those words sound similar, because they are both things that are made out of squares.

How many different tetrominoes do you think there might be? How many different ways could you arrange four squares? If you want to pause it and go and have a try, you can do before we carry on.

Did you find this out? There are five possible tetrominoes.

Let's count them.

One, two, three, four, five.

Those are the five different tetrominoes that you can make.

Each one has four squares in it, in a different arrangement, and each one shows the squares connected.

The squares are always connected in a tetromino.

That means they are touching together.

Lucas has made some more arrangements with his squares, but this time they are not all tetrominoes.

Which arrangement do you think is a tetromino and why? Let's have a look at them.

Do you think A is a tetromino? Do you think B is a tetromino? Do you think C is a tetromino? Pause the video to tell somebody why you think one of them is a tetromino.

Well done if you chose A.

A is the tetromino.

B is not a tetromino, because it only has three squares.

And C is not a tetromino.

It does have four squares, but they are not all connected.

So A is the tetromino.

Now I'd like you to see if you can match the photo to the tetromino.

So if you look at this photo here, do you think it matches A, B or C? This one matches B.

Good job if you said B.

What about this photo? Does this tetromino arrangement match A, B or C? This one matches C.

Good job for noticing that.

What about this photo? Does this tetromino arrangement match with A, or B, or C? This one matches A.

Well done.

Lucas has made two arrangements with his squares.

Have a careful look at them.

Can you see something that is the same and something that is different about his two arrangements? Pause the video to tell somebody what you notice.

Well done for looking carefully.

You might have said something similar to what Lucas has noticed.

One arrangement has four squares in a row.

The other only has three squares in a row, and it has one square on top.

So they both have some squares in a row, but one has four in a row, and one only has three.

If we moved one square, we could make a new arrangement.

Watch the yellow squares to see what happens.

We moved one square, and now we have made it the same arrangement as the first one.

By moving one square, we can make a new tetromino arrangement.

You are going to have a think.

If you started with this arrangement and you moved only one square, which tetrominoes could you make? Could you make A? Could you make B? Could you make C? If you would like to pause the video and try this out with your own squares, you could go and do that now.

Let's have a look.

If we move one square, we could make this arrangement, which is the same as B.

Or if we move a different square to a different place, we could make this arrangement, which is the same as C.

But we cannot move one square to make A.

Now have a think about this one.

Again, if you want to use your own squares first, you can do.

Let's have a look at our three choices.

If we move one square, could we make A? Could we make B? Could we make C? What do you think? Let's have a look.

Watch the orange squares.

If we move one square, we could make this arrangement, which is the same as A, or if we move the square to a different place, we could make this arrangement, which is B.

But we couldn't only move one square to make C.

Now Lucas has made three more arrangements with his squares.

Have a look at these.

What do you notice this time? What is the same? What is different? If you have somebody to talk to, pause it and tell them your ideas now.

Lucas says they all have lines of two squares.

The squares are in lines of two.

Did you notice that some of them are pointing sideways, and some of them are pointing up and down? That's a useful thing to notice, because what you are going to find out here is that sometimes tetromino arrangements might look different, because they've been rotated or flipped.

But the arrangement is still the same.

What Lucas said is true.

Each one has rows of two squares.

The arrangement has not changed.

It's just been rotated.

It's been spun around or it's been flipped over.

But the arrangement is the same.

Let's have a look at that a little bit more.

You can rotate the tetromino like this, but the arrangement is still the same.

Let's watch it rotate again.

And again.

It's rotating.

It's spinning around.

But the arrangement is the same.

Look at how Lucas describes the arrangement.

They all have a row of three squares with one square at the end.

We haven't moved any squares, so the arrangement is the same.

It has been rotated.

And then we're going to have a look at flipping.

You can flip a tetromino, but the arrangement will stay the same, because again, we are not moving any squares.

We are just flipping them over.

Watch what flipping looks like.

We could flip across, to the left or to the right, and we can also flip up or down.

Can you look carefully at these tetromino arrangements and see if you can match them together? This time they have been rotated or flipped, so look carefully and see which ones you think match.

The first photo matches the blue tetromino.

The yellow tetromino matches the third photo.

And the photo in the middle matches the purple tetromino.

Now you are going to go and do some practise with tetrominoes.

You are going to use some squares of your own to have a go at making different tetrominoes.

If you don't have any squares, ask an adult to help you cut some out.

Once you've made a tetromino, can you have a look at the ones on your sheet and say which one have you made? Can you copy all of the tetromino arrangements? Can you rotate them? Can you flip them after you've made each arrangement? When you do that, what is the same and what is different? Go and use your squares to make your tetrominoes.

Off you go.

Well done, everybody.

You might have used your squares to make some tetrominoes that look a bit like this.

You might have done what Lucas has done.

Lucas said, \"I made some tetrominoes that were rotated and flipped, but the arrangement was still the same.\" Do you think you made any like that? Well done if you were able to rotate and flip your tetrominoes.

Good job.

Now that we've learned all about tetrominoes, we are going to move on to learn about pentominoes.

What do you notice about Sam's arrangements? Can you think of anything else that Sam could have made? Pause the video to have a little think or to tell a partner about your ideas.

Did you notice that Sam has used five squares in each arrangement? Arrangements of five squares are called pentominoes.

I wonder how many pentominoes there are.

When we learned about tetrominoes, we found out there were five different arrangements.

Maybe you could use your squares to try and find out.

Pause this video and have a go.

How many different arrangements can you make with five squares? I wonder if you found this out.

There are 12 different possible pentominoes.

Each one uses five squares in a different arrangement.

Look at all of these.

These are all the different pentominoes that you could make.

Can you have a look carefully at this pentomino and see if you can match which arrangement it goes with? Do you think it's the same as A, or B, or C? This one matches C.

Well done if you said C.

How about this photo? Do you think this photo matches A, or B, or C? This one matches A.

Good job if you said A.

How about this photo? Look at this pentomino arrangement.

Do you think it matches A, or B, or C? This one matches C.

Well done.

Sam has made two more arrangements.

Can you have a look carefully and see what is the same and what is different? And if you have a partner nearby, pause the video to tell them about your thinking.

Sam has noticed that one arrangement has two rows of two squares, and then one more at the bottom, but then they think that the other one is a cross shape, and it doesn't have any rows of two squares.

Did you notice that as well? You can move a square to a different place to make a new arrangement.

Watch the squares carefully on the screen.

If we move one square, we can change it into a new arrangement.

I'll let you watch that one more time.

Watch the grey squares.

If I move one square, it makes a new pentomino arrangement.

How could you move one square to change the first arrangement into the second arrangement? So you've got to move one square to make the red one the same as the yellow one.

Which square could you move? If you'd like to get your squares and try this out first, pause the video now to go and get them.

You could move this square, and now we've got two arrangements that are the same.

What about this one? Again, how could you move one square to change the first arrangement into the second arrangement? So look at the brown squares.

You can only move one, and you've got to make it look the same as the grey squares.

Which square would you move? You could move this one underneath, and now they are the same pentomino arrangements.

Now we're going to have another look at rotating and flipping.

Watch this pentomino carefully.

You can rotate it like this, or you can flip.

So watch again.

You can rotate or you can flip.

The arrangement is still the same, because no squares have been moved into a new place.

We've spun it around, we've rotated it, and we've flipped it over, but we haven't moved any squares.

So all of these are the same pentomino arrangement.

They all have a row of three squares with one at the end, and one in the middle.

You are going to have a go at matching the pentominoes to the photos at the bottom.

Sam says, \"I tried to rotate and flip the pentominoes.

Which ones do you think I rotated? Which ones did I flip?\" See if you can match the pentominoes to the photos at the bottom, and then think about whether Sam has rotated or flipped the arrangement.

Pause the video if you need a little bit longer.

Let's have a look.

The first pentomino matches the third photo, and it has been rotated.

The pentomino in the middle matches the first photo, and it could be flipped or rotated.

The third pentomino matches the photo in the middle, and it has been flipped.

Well done if you were able to match those up, and start thinking about whether they've been rotated, or flipped, or both.

Now, in your next bit of practise, you are going to go and use your own squares to go and make pentominoes.

I would like you to try and make all the pentominoes on this sheet.

There are 12 different ones to make.

You are going to see if you can make them all, and then you are going to see if you can rotate and flip the pentominoes that you have made.

Get your squares ready.

Off you go.

Well done, everybody.

You've tried really hard to make those pentominoes with your five squares.

You might have found that your squares could have looked like this.

Some of them are the same arrangement, and they've been rotated.

Some of them are different arrangements.

Sam says, \"I moved the squares to different positions to make a new arrangement.\" Did you move your squares like Sam to make a new arrangement? Lucas says, \"I rotated and flipped the squares to show the same pentomino arrangement in different ways.\" Did you rotate and flip your arrangements like Lucas? Now that we're at the end of this lesson, you have found out that you can make different arrangements with four squares to make tetrominoes, and with five squares to make pentominoes.

We can see one tetromino and one pentomino on our screen.

You have learned that you can move the squares to make a different arrangement like this, and you've also learned that sometimes you can match arrangements together, and that they might look different, but it's just because they might have been rotated, or they might have been flipped.

You have worked really hard learning all about tetrominoes and pentominoes today.

Well, done everybody.

I hope you'll be ready to learn about some more maths soon.

Goodbye.

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"https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698420339%2Fmpdfocrkgsls1ol0jkcy.png&w=256&q=75", "text": "C", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/69f2e0a0961c14a08ba54f9d7592f2ea.png" } ], "id": "b0fdb07f-448a-2a06-bb0c-ad4a6c9d0f82", "lessonId": "ce59fa7e-a3ca-8821-d2bf-01de4ae99484" }, { "type": "Question", "question": { "text": "Which images represent 5?" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698220355%2Fhrzyj3ntcsmeptnk01dg.jpg&w=384&q=75", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/53463164dffd3c2762eb4651b8ab861b.jpeg" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244745%2Fsmu3j6oughpxp6za8xdj.png&w=750&q=75", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/e5148a6d1e84c3f475c063ea727df9b8.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1696413034%2Fgeotabqkgflci5oah1ux.png&w=750&q=75", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/6883b58d4f975d0c0409a8e4e688b386.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698220363%2Fjpnlkctqlf10ihmkmcwh.jpg&w=1920&q=75", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/b1172168a1a7c4869cabb7126ba498de.jpeg" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698220355%2Fhrzyj3ntcsmeptnk01dg.jpg&w=384&q=75", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/53463164dffd3c2762eb4651b8ab861b.jpeg" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244745%2Fsmu3j6oughpxp6za8xdj.png&w=750&q=75", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/e5148a6d1e84c3f475c063ea727df9b8.png" } ], "id": "ec416643-f2f5-43a8-6035-1d95df990fd3", "lessonId": "ce59fa7e-a3ca-8821-d2bf-01de4ae99484" }, { "type": "Question", "question": { "text": "Which pattern blocks are connected?" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698220434%2Fnnyvuh2qsfyorvbkxpxk.png&w=750&q=75", "text": "B", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/ee2fcacd8ad146c4ba40fc29330f3912.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698220431%2Ff4e5neuekyrdtqkt1hqb.png&w=1080&q=75", "text": "A", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/9c417a145e9f9fa7c52c7f661fc83669.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698220434%2Fnnyvuh2qsfyorvbkxpxk.png&w=750&q=75", "text": "B", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/ee2fcacd8ad146c4ba40fc29330f3912.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698220438%2Frm0yrpnyu98yfvlvpf2m.png&w=640&q=75", "text": "C", "imageKey": "e1b5be2b-a44c-9954-83dd-7876e3d68bbc/question/50f8493c528a28214b83dc2b07ba1f2c.png" } ], "id": "5ec69a97-7664-bdc8-c95d-887e82e84308", "lessonId": "ce59fa7e-a3ca-8821-d2bf-01de4ae99484" } ], "lessonId": 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"https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244740%2Fnpzflhz45escavzqrizr.png&w=640&q=75", "text": "A", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/b3e6b2ecb4ad094ee8676c4a54aeab4b.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244740%2Fiyifyegru4azxuo03wzn.png&w=256&q=75", "text": "B", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/e190abc08b02703f52f2ae8b811ec259.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244741%2Fvcrtkekbprpnst7ftn3j.png&w=384&q=75", "text": "C", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/bcb01b009da32e06f08b4acd9f600b42.png" } ], "id": "b908d271-cce6-1fee-3cd3-f538f68c1ff9", "lessonId": "ce59fa7e-a3ca-8821-d2bf-01de4ae99484" }, { "type": "Question", 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"fbd0a363-983f-2575-a3c0-d6e34407b6ea", "lessonId": "ce59fa7e-a3ca-8821-d2bf-01de4ae99484" }, { "type": "Question", "question": { "text": "Which two images show the same tetromino arrangement?" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244742%2Filhwfrxhescqdv5tjhxn.png&w=384&q=75", "text": "B", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/ec43ba83bb6691d5b1804a900c277cbb.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244742%2Fldggelgx0vuhmxfbgoea.png&w=640&q=75", "text": "D", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/f79b7d832af411f152326c6cfef35d3a.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244743%2Fbqlilnw3ncqohzudxiwv.png&w=640&q=75", "text": "A", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/1b004115494e91f055ecf12d4c4e0b34.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244742%2Filhwfrxhescqdv5tjhxn.png&w=384&q=75", "text": "B", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/ec43ba83bb6691d5b1804a900c277cbb.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244742%2Fwfx6rvlws9noky1fpiih.png&w=384&q=75", "text": "C", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/e1f73c5162ccf34478f3e93295932d44.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244742%2Fldggelgx0vuhmxfbgoea.png&w=640&q=75", "text": "D", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/f79b7d832af411f152326c6cfef35d3a.png" } ], "id": "1c972f64-c7a2-245c-826b-eb51870c8e55", "lessonId": "ce59fa7e-a3ca-8821-d2bf-01de4ae99484" }, { "type": "Question", "question": { "text": "Which two images show the same pentomino arrangement?" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244743%2Fjhtpohtaxluemjid1epd.png&w=640&q=75", "text": "A", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/8117c6ec0f79fc97c16892811fb551bd.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244744%2Fzllhuw8k3w9cevd1cjgr.png&w=640&q=75", "text": "D", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/57b1338d5b2fe41a616f4c828c973768.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244743%2Fjhtpohtaxluemjid1epd.png&w=640&q=75", "text": "A", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/8117c6ec0f79fc97c16892811fb551bd.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1698244743%2Funb8641jnalfdmjuzqgi.png&w=640&q=75", "text": "B", "imageKey": "f927dc25-0e7d-2ca2-8f02-28eedd882eec/question/55a0dfb9562e1c858cedaaab719551b5.png" }, { "image": 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