Lesson video

Hi, my name is Mr. Tazman and I'm very excited to be learning with you today.

If you are ready, then we can get started.

Let's think about the outcome for this lesson.

By the end, we want you to be able to say, "I can identify equal parts when they do not look the same." Here are the key words that you are going to come across: whole, part, and equal or unequal.

I'm going to say them and I want you to repeat them back to me.

So I'll say my turn, say the word, and then I'll say your turn and you can repeat it back.

My turn, whole.

Your turn.

My turn, part.

Your turn.

My turn, equal or unequal.

Your turn.

Okay, let's see what each of those means so that we can think about them when we discuss the maths in this lesson.

The whole is all the parts or everything, the total amount.

A part is some of the whole.

There's a bar model on the page there to illustrate these concepts.

You can see that there are two parts making the whole.

We say that two or more things are equal if they have the same quantity or value, and we say that two or more things are unequal if they do not have the same quantity or value.

Here's the outline of today's lesson.

Identify the number of equal or unequal parts in a whole.

We're gonna start by looking at the fact that equal parts can look different and then we're going to identify equal parts that look different.

Let's get started with the first part.

Here are two people that you are going to meet during this lesson.

We've got Aisha and Sofia.

They're going to help us by discussing some of the maths prompts on screen, answering some of the questions, and then giving us some hints and tips.

Aisha and Sofia are looking at some 2D shapes.

Aisha says, "I can see some 2D shapes that are the same." "Let's group them," says Sofia.

"Some of these aren't the same." "Are you sure? I think they are." What do you think? Have a look at these pairs of shapes.

Are they the same or are any of them different to their pair? "But they don't look the same," says Aisha.

They're tilted." "Let's rotate them so that one side is horizontal," says Sofia.

"These two shapes are the same.

They are the same size," says Aisha.

"I agree.

They were just rotated differently before.

The two shapes are equal." "These two are unequal," says Aisha.

"Agreed, they are both squares but are not the same size." Okay, let's check your understanding so far.

Tick the pair of 2D shapes that are the same size and shape.

So we're looking for a pair that's of the same size and shape.

Pause the video, have a good look and find them, and I'll be back in a moment to reveal where they are.

Welcome back.

Did you find them? Let's see.

There they are.

Sofia says some of these have a pair that is the same shape, but their size is unequal.

Aisha and Sofia are splitting shapes into parts.

Aisha says, "Let's split a square into four equal parts and compare them.

No peeking." "Okay, sounds good.

I wonder what will be similar and what will be different." "My turn first," says Aisha.

She takes a square.

She splits it.

Now is Sofia's turn.

She splits it as well.

Aisha says, "I said equal parts.

Your parts are unequal because they're not the same shape." I wonder if she's right or not.

Sofia says, "I think they are equal parts." Who do you agree with? Do you think Aisha's right? They aren't the same shape.

Do you think Sofia's right? They're still equal parts.

Hmm.

Sofia sets out to prove that the parts are equal.

Let's see what she does.

"First of all, I'm going to separate the whole into the four parts," she says.

There they go, she's cut them up.

"I've got to prove that the oblongs are the same size as the squares." And she's labelled it to help us.

We've got two squares and two oblongs.

You can see them there.

"I'll cut the oblongs in half horizontally." And she does that.

I wonder what she's up to.

"Then I'll place them over the top of the squares to show they are the same size." And she does that, too.

"It worked.

They are the same size so they're equal parts." "So equal parts can look different as long as they take up the same amount of space," says Aisha.

Sofia and Aisha look again at the squares split into differently sized equal parts.

Aisha says, "I'm going to change one of your lines into a diagonal to see if it works." And she does just that.

You can see it there.

"Hmm, two triangles.

Last time you proved it with rectangles not triangles.

Will it work?" Really good question to ask, Aisha.

But what do you think? Do you think that the triangular parts will have the same size as the square parts? Hmm.

"I think this works," says Sofia confidently.

"Let's spit it up into parts to help us to think about it." She cuts it up again.

"We need to show that the triangle is the same size as the square so I'll focus on those." She moves two of them away and keeps two of them to work on.

"Now I'll draw a dotted line from the top of the square part across the triangle part." She draws it there.

"Then I'll cut that little part off." Snip, off it comes.

"Now I'll rotate the part I've cut to fit into the part that I cut from." "It makes a square the same size, so the triangle and square are equal parts." Sofia and Aisha investigate differently sized equal parts further.

"Shall we try a different starting shape this time?" "Okay then, how about a triangle?" "I'll try and create differently sized equal parts." "Okay, I think they're still equal." What do you think? Look at those triangular parts.

They've got different shapes, but are they the same size, I wonder? Hmm.

"There are two pairs of different parts," says Sofia.

"I have called them A and B." We've got small triangle A, small triangle A, small triangle B, and small triangle B.

"I'll start my proof by splitting the whole into the parts," says Aisha.

"Then, I'll concentrate on two different triangles." So she's moved two of them to the side.

She doesn't need those to prove that they are the same size.

"Next, I'll draw a dotted line through this triangle.

Then I'll cut along the line.

Next I'll rotate the cut off part.

These can go over the top so they are equal parts." "So the shape of the whole doesn't matter.

Equal parts can be differently shaped." Time to check your understanding.

True or false.

Equal parts can look different.

Pause the video here and think about whether you want to put true or false.

Welcome back.

What did you think? True or false? The answer was true.

Equal parts can look different.

There's two justifications below.

A says it doesn't matter what shape or size the parts are if the lines are straight.

B says they can look different but have to take up the same amount of space.

Which of those justifications do you think proves that that statement is true the best? Pause the video here and have a think about that.

Welcome back.

Which did you think, A or B? Well, B was the best justification.

They can look different but they have to take up the same amount of space.

Here's your first practise task.

What I'd like you to do is to cut and rearrange the templates below to prove that equal parts can be differently shaped.

What you've just seen Aisha and Sofia do, you are going to do yourself.

Cutting, and rearranging to make sure that you can see that those differently shaped parts can indeed be equal.

Pause the video here and I'll be back in a little while with some feedback.

Enjoy the cutting.

Welcome back.

Sofia says, "Did you cut and rotate like I did? Are you happy the parts are equal?" Did you cut the shape to show the parts are equal? And here's the example from one of the shapes.

You can see the grey bits are where two of the parts that are differently shaped have been cut out and the line across the triangular part shows where you might have made a cut to rotate the little triangle and show that in fact they have the same space within them.

There you go.

Okay, that's the end of the first part of the lesson and it's time to move on now to identifying equal parts that look different.

Are you ready? Okay, let's go.

Aisha and Sofia split up squares into four equal parts that are the same shape.

There they are.

Aisha says, "We know that each of the parts in each square are equal size." "Yes, but they're differently shaped," says Sofia.

"So let's look at each part individually." They've taken each individual part and they've shown only that.

Sofia says, "We could use these to make squares split into differently shaped equal parts." Good thinking.

Aisha uses combinations of these parts to create squares split into equal parts with different sizes.

"Let's build some squares with differently shaped equal parts," she says.

There's her first one.

There's the second.

There's the third.

And there's her fourth.

What do you notice? Have a look at all of those.

Sofia says, "That last part can't be used in combination with the others." So you can see, the square at the end has been made up of four equally sized, yes, but also the same shaped parts.

Aisha and Sofia make some more squares split into parts.

Aisha suggests, "Let's sort them into groups if we can." "Okay, we can make use of a sorting diagram." They use a sorting diagram.

You can see the headings there.

Same shape parts, different shape parts.

The row titles are equal parts and unequal parts.

"Let's sort them one at a time." Good thinking, Sofia.

It's always best to be systematic in this sort of situation.

"Okay, what about this one?" "Well the parts are different shapes." "But they're not equal.

One part is too small." You can see the smallest triangular part is smaller than the others in the top right of the square.

"I agree.

There's a small triangle," says Sofia.

They sort the rest of the squares one at a time.

Aisha says, "I think there's a mistake somewhere in this." What do you think? Look at each of those squares split into parts and ask yourself, "Do they match the column title and do they match the row title? Are they in the right box?" Sofia says, "I think it's this one.

The shapes are different but so is their size." "It's deceptive," says Aisha, "because the lines are evenly spaced." So she means it's hard to spot that.

"It has unequal parts so it needs to move," says Sofia.

And there it goes.

Okay, check your understanding now.

Can you spot the two mistakes in this sorting diagram? Have a good look.

Maybe discuss it with somebody else.

Pause the video and I'll be back in a moment to reveal the answers.

Welcome back.

Did you manage to find the mistakes? Well, here's the first one.

Aisha says, "The shapes are the same for each part." And here's the second.

"This has equal parts even though they are differently shaped." Did you get them? Alright, ready to go? Let's do it.

Aisha creates a puzzle for Sofia to solve.

She uses two 3 x 3 grids.

And you can see them there.

"These are my wholes.

There are two wholes.

The aim of this puzzle will be to piece together two wholes.

I'll start by splitting the first whole into equal parts of the same shape." She's used three oblongs.

"Next, I will split the second whole up.

But this time, I will use equal parts differently shaped." She started with an oblong, but now she's changed the shape.

"Then I'll cut the parts out for both of the wholes." There they go.

"Now to muddle them up, Sofia will have to rearrange them so that she creates two wholes, both with equal parts." There they go.

She's muddled them.

She's even rotated a few just to add a little bit of extra confusion and difficulty.

Sofia solves the puzzle.

"Challenge accepted," she says.

"I'll have a go.

I'll start by grouping them by shape of the part." There they go.

They've been grouped into those four oblongs and then those two hexagons, irregular hexagons.

"Then I'll use three of the same shaped parts to make a whole." There she goes.

She puts three of the oblongs together and then she rotates them so that it matches what she started with.

"Lastly, I'll piece together the other parts that are differently shaped.

That's the next whole.

It's completed," she says.

Sofia wants to make it harder.

She uses the same wholes but makes a third.

"I'm going to include a third whole with unequal parts," she says.

"I'll use more than three parts as well." Here she goes.

How many parts has she's used? She's used four, but they're not equal.

They're not the same shape and they don't have the same size.

"This whole has been split into four unequal parts," she says.

"Here they are all muddled up." That's a lot of parts there.

"Well, I'll try," says Aisha.

"I'll sort them by size and shape first." There they go.

"I can definitely make a whole from equal parts with the same shape.

She does that.

"So the next whole definitely won't have the same shaped parts." And she completes that one.

"Now to combine these parts of different shapes." There they go.

"Amazing," says Sofia.

Here's the final task.

Number one, there are three squares in the table below.

Split them into parts so that they fit the criteria of the table.

You can see you've got headings for this sorting diagram.

We've got same shape parts and different shape parts for the columns and equal parts and unequal parts for the rows.

And Sofia also asks a further question, "Why isn't there a square in one of the cells?" The cells are the boxes.

Number two, I'd like you to create your own version of the puzzle for someone else to solve.

And they've been helpful here, Sofia and Aisha.

Sofia said, "Here are my three to remind you." You can see them at the bottom.

And Aisha says, "You could try a 4 x 4 grid if you wanted." If you feel like a challenge.

Okay, pause the video, and then I'll be back in a little while with some feedback.

Enjoy.

Welcome back.

Are you ready for some answers? Here's what Aisha did.

She split up the first square into the same shape parts that were equal.

The second square, she put different shape parts but they were still equal.

And in the third one, she put different shapes and different sizes so they were unequal parts.

Sofia had asked, "Why isn't there a square in one of the cells?" Aisha had said, "One cell is empty because you can't have unequal parts the same shape." Okay, did you manage to create your own version for somebody else to solve? Hopefully you enjoyed it.

Here's what Aisha came up with.

That was hers.

What was yours like? Might well have been different.

Okay, that brings us to the end of this lesson on identifying equal parts when they do not look the same.

Here's a summary of the things that we've learned, discussed, and talked about.

A whole is made up of many parts.

Parts can be equal or unequal.

Equal parts can look different but still be equal.

A whole can be made from equal parts that look different.

I've really enjoyed learning with you today.

Thank you very much.

My name is Mr. Tazman, and I can't wait to see you again in future maths lessons.

Goodbye.