Lesson video

Hello, my name is Mr. Tilstone.

I'm a teacher and I just love maths.

It's my favourite subject.

So it's a real pleasure to be here with you today to teach you this maths lesson.

If you are ready to start, will you help me by counting down from five? Are you ready? Five, four, three, two, one, let's begin.

The Outcome of today's lesson is this, "I can order and arrange objects in patterns and I can talk about the patterns that I have made." We've got some Keywords.

If I say them, will you say them back? Are you ready? My turn, pattern.

Your turn.

My turn, unit of repeat.

Your turn.

My turn, rotate.

Your turn.

And my turn, rotation.

Your turn.

Now, I'll bet that some of those words are familiar to you, and I'll bet that some of those words are not familiar to you, but don't worry, by the end, we're going to practise them lots and you'll be an expert.

Our lesson is split into two cycles or two parts today.

The first will be describing a pattern and the second extending a pattern.

So if you're ready, let's begin by describing a pattern.

In this lesson, you'll meet Jacob and Sam.

Have you met Jacob and Sam before? They're here today to give us a helping hand with the maths.

Jacob is making patterns by printing with shapes.

What do you notice? Have a look at those patterns.

What can you see? Well, it goes circle, triangle, circle, triangle, circle, triangle.

The unit of repeat, that's one of our keywords for today, for this pattern is circle, triangle.

So we can think of circle, triangle as one part, and that part is repeated.

This is a unit of repeat.

Jacob makes another pattern by printing with his shapes.

Have a look yourself first, and see what you notice this time.

Hmm, I wonder if you could identify a unit of repeat? This time is going pentagon, triangle, circle, pentagon, triangle, circle and it carries on.

The unit of repeat for this pattern is pentagon, triangle, circle.

So well done if you spotted that as a unit of repeat.

We could think of that as one part that keeps getting repeated.

So let's have a little check.

What is the unit of repeat for these patterns? Have a good look.

See what you can notice.

That's what good mathematicians do, they notice things.

What's the unit of repeat? Pause the video.

Did you spot the unit of repeat? Well, it went triangle, pentagon, pentagon, triangle, pentagon, pentagon.

So the unit of repeat is this, triangle, pentagon, pentagon.

Then that keeps coming up, triangle, pentagon, pentagon, triangle, pentagon, pentagon.

So that unit is repeated.

And what about this one? It went circle, hexagon, triangle, circle, hexagon, triangle.

So what was the unit of repeat? What's being repeated? This is a unit of repeat, circle, hexagon, triangle.

Jacob makes another pattern by printing with his shapes.

What do you notice this time about Jacob's pattern? It's different isn't it? Goes square, square, circle, square, square, circle.

Hmm, did you spot the unit of repeat? The unit of repeat for this pattern could be square, square, circle.

There we go.

What was different though? It's harder to see where this pattern starts, because it goes all the way round in a circle, so it doesn't really have a start point.

So that's why it was a bit harder to find that unit of repeat.

The unit of repeat for this pattern could be something else.

It could be square, circle, square.

And that's repeated, square, circle, square, square, circle, square.

Let's have a check.

You've got another circular arrangement.

What could the unit of repeat be for this pattern? Hmm, see what you can notice.

Pause the video.

What did you come up with here? Let's have a look.

Well, it could be this for the unit of repeat, triangle, circle, circle.

It could be this for the unit of repeat, circle, circle, triangle.

It could be this for the unit of repeat, circle, triangle, circle.

So it all really depends on where you start in the circle.

Sam wants to make a pattern by printing with her shapes.

She says, "I only have a triangle.

How can I make a pattern?" Hmm, any ideas? Well, Sam can use rotation to make a pattern.

How about that? The triangle makes a half turn each time.

And I bet you would know lots about half turns.

I bet you've got lots of experience with that.

Sam says, "I've noticed that the third triangle looks the same as the first triangle." Have you spotted that? Hmm, so what could the unit of repeat be? When the shape returns to its starting position, it helps you to find the unit of repeat.

So it's back to its start, so that means that's a unit of repeat.

Sam uses printing to make another pattern using rotation.

She only uses a hexagon this time.

Have a little look at it, see what you can notice.

See at what point the hexagon goes back to its starting point.

That will help you to find the unit of repeat.

The hexagon this time makes a quarter turn clockwise each time.

You could also say that the hexagon makes a three-quarter turn anti-clockwise each time.

But what's the unit of repeat? Here's where the shape has returned to its starting position.

So we could say that this is a unit of repeat.

Let's have a little check.

What rotation can you see in this pattern? Here's one kind of rotation and here's another.

How can you describe that? Pause the video.

Did you give one or even both of those kinds of rotations? Well, you could say the triangle's making a quarter turn anti-clockwise each time.

Or you could say it's making a three-quarter turn clockwise each time.

And this is our unit of repeat.

After that, it goes back to the original starting point and we do it all again.

It's time for some practise.

Let's see if you can put those skills into action.

So number one, match the patterns to the descriptions.

So look carefully at those patterns.

One of them is the pentagon makes a half turn each time.

One of them is the pentagon makes a quarter turn clockwise each time.

One of them is the pentagon makes a quarter turn anti-clockwise each time.

Can you match them up? And can you think of any other ways to describe each pattern? Number two, choose one shape and make your own pattern using rotation.

And Jacob says, "Look for when your shape returns to its starting position to help you find the unit of repeat." So lots and lots of possibilities there.

And when you've done one, have a go at another one and keep going.

"How could you describe your pattern? Is there more than one way," asks Sam.

And number three, Sam is describing her pattern.

Can you draw it? She says, "I've only used triangles in my pattern.

The triangle makes a half turn each time." Can you draw that? And Jacob says, "Compare your pattern with your partners.

What do you notice? Could this have looked any different?" Hmm, lots of possibilities I think.

Okay, pause the video and away you go.

Welcome back, how did you get on? Let's have a look.

Number one, match the patterns to their description.

So the pentagon makes a half turn each time, is this one, the middle one.

The pentagon makes a quarter turn clockwise each time, that's describing this pattern.

And finally, the pentagon makes a quarter turn anti-clockwise each time, is describing the first pattern.

And you could have said instead, it could be making a three-quarter turn anti-clockwise, rather than a quarter turn clockwise.

You could say it could be making a three-quarter turn clockwise each time, rather than a quarter turn anti-clockwise.

And number two, choose one shape.

Make your own pattern using rotation.

This is one of many possible examples.

You might have chosen a different shape, a different kind of pattern.

You might have had a longer unit of repeat, a different unit of repeat, lots and lots of possibilities.

So the rectangle makes a quarter turn each time.

It could be clockwise or anti-clockwise rotation.

And in this one the quadrilateral makes a quarter turn clockwise each time.

It could also be making a three-quarter turn anticlockwise each time.

And number three, you could have drawn Sam's pattern like this.

That's one possibility.

The triangle's making a half turn each time.

Jacob says, "I think Sam's pattern could look different." Did yours? It depends on what type of triangle you draw and which way the triangle's facing at the start of the pattern.

That's true.

So maybe you did more than one example of that pattern.

Here's a different one.

And here's a different one again.

Okay, are you ready for the next cycle that is extending a pattern? Jacob is looking again at the patterns he made earlier.

So he has established his unit of repeat, that's it, goes pentagon, triangle, circle.

And he says, "If I know the unit of repeat, I can extend the pattern." And it goes pentagon, triangle, circle.

Then we can see pentagon, triangle, circle, and then once again, pentagon, triangle circle.

Could he keep going? Yes, pentagon, triangle, circle.

Jacob has extended the pattern by following the rule to make the pattern longer.

Could you keep going, do another pentagon, triangle, circle? Absolutely, you could do 1,000 of them if you liked.

Jacob is going to extend another pattern.

Have a look at this.

He says, "I notice that the first two shapes are in the same position.

Is this a unit of repeat?" What do you think? Do we see that unit repeated again and again? No, the unit of repeat should show the part of the pattern that is repeated.

Jacob is not correct, because there is a shape in his pattern that is not included in the unit of repeat.

So let's change that unit of repeat.

He has another go at finding it.

What do you think? What would you circle? Is that the unit of repeat? Yes it is.

"I can check if my unit to repeat is correct by describing the pattern." There are two rectangles that look the same, then one rectangle that's made a quarter turn.

And you could say that again for the next part.

There are two rectangles that look the same, then one rectangle that's made a quarter turn.

The next part of the pattern is the same as a unit of repeat.

This shows that Jacob has found the unit of repeat correctly now.

Could he keep going? Yes, he could.

"Now that I know the unit of repeat, I can extend the pattern." So two rectangles that look the same, then one rectangle that's made a quarter turn.

And let's finish with two rectangles that look the same.

We could carry on.

Let's have a check.

Extend these patterns.

Which shape should be next? Hmm, two possibilities.

Which one should be next each time? Have a good look.

Pause the video.

Did you spot it? Well, that's our unit of repeat.

So the triangles in this pattern are in pairs.

Did you notice? Each pair of triangles has made a half turn.

So the next one would be this one.

And here's our unit of repeat for the next pattern.

There's one quadrilateral in the starting position and then two of the same.

So that's our unit of repeat.

They've made a half turn.

So the one we're looking for is this one.

Well done if you said that.

It's time for some final practise.

And I think you're ready.

In fact, I know you are.

Number one, draw around the unit of repeat in each pattern and then extend the pattern by drawing more shapes.

And you can extend it this as far as you like.

So we've got three different examples there.

So remember to find that unit of repeat first.

Number two, look at these patterns that have been made by rotating a domino.

Can you draw more dominoes to extend the pattern? Again, you can find a unit of repeat there.

Sam says, "Maybe you could choose a domino of your own and rotate it to create your own pattern to extend?" Have you got dominoes in your class? That will be good.

Right here, we'll pause the video and away you go.

Welcome back, how did you get on? Are you getting good at finding those units of repeat and extending your pattern? Let's have a look.

So draw around the unit of repeat in each pattern.

There's a unit of repeat and then you can extend it.

You might have gone even further than that.

And here's a unit of repeat.

And you can see it one more time, but you could extend it.

You could do it one more time, two more times, one and a bit more time as in this case.

And what about this? That's our unit of repeat.

And that's extending that unit of repeat.

And number two, look at the patterns that have been created by rotating a domino.

So we could draw this one next.

So the one and the four, that was where our pattern started.

And then four, one and that was our unit of repeat.

You could keep going.

Let's do that.

In this pattern, the domino is making a half turn each time.

And for B, we could extend it like so.

That's our unit of repeat and we could keep going.

And in this pattern, the domino is making a quarter turn anti-clockwise each time.

So there are four dominoes in that unit of repeat.

And for C, that's our unit to repeat those three dominoes.

And we could extend that by repeating those three dominoes in the same order.

And then we could keep going.

In this pattern, the domino is making a quarter turn clockwise each time.

And maybe your pattern was shorter than that, or maybe your pattern was longer than that.

We've come to the end of the lesson.

I think it's been such a fun lesson and I hope you've found it fun too.

And I hope you've learned lots.

Today, we've been ordering and arranging objects in patterns and explaining the pattern.

A pattern is an arrangement of shapes or objects according to a rule.

And you've been looking at lots of different examples of those rules.

You can make a pattern by rotating shapes, for example.

These rotations can be described using mathematical language such as clockwise, anti-clockwise, half turn, quarter turn, and three-quarter turn.

A pattern can be extended by finding the unit of repeat and then following the rule.

And I think you got really good at finding those units of repeat and extending.

Well done on your achievements and your accomplishments today.

You might like to give yourself a little pat on the back and say, "Well done, me." You've been fantastic, and I really hope I get the chance to spend another math lesson with you at some point in the near future.

But until then, have an amazing day and be successful and work really hard.

Take care and goodbye.