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I can construct a whole when given a part and the number of 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

If you know one part and how many parts there are we can construct the whole.
If you know that the part is one out of 4 equal parts we can draw the whole.
The whole can be one shape or a group of objects.

Common misconception

Children might think that any shape they draw around or use is a whole and the new shapes they create represent lots of wholes joined together.

Ensure the children understand that a whole can be anything and can change as you add parts to it. A piggy bank is a good analogy for this as you are constantly adding money to the whole and it is made up of many parts.

Keywords

Whole - The whole is all the parts or everything, the total amount.
Part - A part is some of the whole.
Construct - Constructing something involves making something by joining parts together.

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

If you are ready, then we can get started.

Here's the outcome for today's lesson.

By the end, we want you to be able to say, I can construct a whole when given a part, and the number of parts.

Here are the key words that we are going to come across.

I'm gonna get you to repeat them back to me.

I'll 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, construct, your turn.

But what do those words mean? Well, here are some of the definitions.

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

A part is some of the whole and you can see that expressed here in the bar model towards the bottom of the screen.

We've got the whole split into two unequal parts.

Constructing something involves making something by joining parts together.

Here's the outline of the lesson today.

We're gonna start by looking at the fact that we need to start with the part, not the whole when we are constructing, and then we're gonna think about this in different contexts.

Are you ready to start? Let's meet some friends, first.

We've got Andeep and Sam.

They're gonna help us by discussing some of the maths that we are going to come across.

They'll give us some helpful hints and clues and they'll also discuss some of the answers so that we can fully understand them.

Right, let's get going.

Andeep and Sam are asked to show an oblong divided into three equal parts.

Sam says, I'll start with the whole, measure it and divide it into three equal parts.

There's the oblong to start with, there's a ruler to measure it.

You can see that Sam has realised it's nine centimetres long, so they've divided that into three equal parts of three centimetres each.

Andeep has a different method.

He says I'll start with the part and then use it to draw the whole, I don't need to measure.

There's one part, there's two parts, there's three parts, he started with the part.

Whose method is correct? What do you think? Is there one that you would prefer to use? Is there one that you've not really thought about using? Well, Sam says both our methods had the same whole.

I agree, says Andeep, there was no correct way, starting with the part isn't used as often.

I wonder if you've used starting with the part before.

Sam sets a puzzle for Andeep.

Some paper strips are folded into equal parts and partially concealed.

You can see strip A and strip B and there's a piece of paper over the end of them so you can't see how long they are.

Sam says I folded strip A into four equal parts, I folded strip B into three equal parts, which is longer and how do you know? If you look on the strips, you can see the fold lines as dotted lines there.

What do you think the answer might be? Which of these strips is longer? Andeep says, I like a challenge, good attitude, Andeep.

Both strips have equal parts that are the same size.

But strip A has more parts making up the whole, so it must be longer.

Let's reveal the paper to see.

There we go, well done, Andeep? Yes, I was right, the parts were equal size, but the whole of strip A was longer.

Is that what you managed to get? Okay, let's check your understanding.

Which is the longest strip of paper? We've got strip A and B and they've been concealed by another piece of paper.

Sam gives a clue.

I folded strip A into five equal parts.

I folded strip B into four equal parts, which do you think is longest then? Pause the video, have a think, and I'll give you the answer in a moment.

Welcome back, which strip did you think was longest? Well, it was strip A.

Andeep says strip A is longer because the parts are the same size and it has more parts making the whole.

Andeep challenges Sam to make two wholes using a triangular part.

Connect triangles like this as parts to make two different wholes.

Okay, that sounds fun, says Sam.

Here are a few different wholes that I can make.

No, they're not correct, says Andeep.

I wonder what he means.

The first one has a triangle that's the same shape but a different size.

The second one has a rectangular part.

Can you spot those things in the parts that been connected together by Sam? You didn't tell me something important then, says, Sam.

You are right, I should have said, use this triangle as an equal part to make two different wholes.

Now I understand, says Sam, here are some more completed.

I missed something else says, Andeep.

What now, says Sam.

I should have said use this triangle as an equal part to make two different wholes made of three parts.

So now, he's given the number of parts that make up the whole.

All right, last try, says Sam.

This is the best I can do.

Andeep says, they're the same whole but one is rotated.

You can probably see that on the screen that actually these two wholes that have been constructed by equal-sized parts are actually the same.

It's just that one has been rotated more than the other.

It's impossible, says Andeep.

What a mean challenge, says Sam.

This time Sam sets the challenge, I should think so.

Create two different wholes made up of three equal parts by connecting rhombuses as equal parts.

Okay, here you go, says Andeep.

What's the same and what's different about these two constructions that Andeep has created? Well, they're both wholes that are divided into three equal parts of the same shape.

The parts have been connected differently and rotated so the wholes are different shapes.

They look a bit strange, I think.

Would you agree with Sam? I'm used to wholes looking as though they're complete.

Yes, I agree, but they are still wholes, they don't have to look perfect.

Sam and Andeep set a similar problem for their classmates.

Create a whole made up of three equal parts by connecting this shape as the equal part.

There's Jun's, there's Sofia's, there's Aisha's, and there's Lucas's.

Andeep says, I think that two are correct and two are incorrect.

What do you think? Can you spot the correct ones and the incorrect ones? Jun has a whole made up of three equal parts of the same shape.

He's got it right, says Andeep.

Sofia hasn't shown any parts but we could draw them in.

There they go.

That's a whole made up of four equal parts of the same shape.

So she's incorrect, says Andeep.

Aisha has a whole made up of three equal parts of the same shape.

Her whole works then, says Andeep.

Lucas has a whole made up of three equal parts of the same shape, but they're not the shape we chose.

His whole is incorrect then, says Andeep.

Let's check your understanding, which of the following wholes are correct? Sam asked her classmates this, she extracted them, create a whole made up of three equal parts by connecting this shape as the equal part.

So what do you think? Who's got it correct and who's got it incorrect? Pause the video here, have a think, maybe a chat with someone else about it and I'll be back in a moment to reveal who was incorrect and who was correct.

Welcome back.

Let's see which of these classmates got it correct.

Jun was correct.

Sofia was incorrect, that's because her shape wasn't the same and was a smaller size.

Aisha was incorrect, that's because she's used four equal parts.

And Lucas was correct even though it didn't look the same as Jun's, it was still a whole made up of three equal parts and the parts were the ones that Sam had chosen.

Okay, Andy and Sam have some Sticky Notes.

Andeep says, use these as equal parts, how many different wholes can you make with three? There's the three Sticky Notes.

And Sam says, that sounds fun, let me try.

I'll be systematic and record them as I go by drawing them.

Great, that's a really important thing to do in maths, to be systematic and record observations as you go.

There's her first one, there's the second, there's her third.

But Andeep says, I think last two are the same whole.

What do you think to that? Why do you think Andeep might think they're the same? If we rotate the whole, you can see it's the same.

It's been rotated.

You can match it now with the other drawing.

Okay, let's have a go at that first practise task.

Use the shape below to create a whole featuring six equal parts.

Can you make a whole that no one else will make? Compare your whole with a friend, what's the same? What's different? Number two, have a go at the Sticky Note challenge.

Use four Sticky Notes as the parts.

How many different shaped wholes can you find? Watch out for rotations.

Pause the video here and have a go at those practise tasks.

Good luck.

Welcome back, let's start with number one.

You were asked to make a whole featuring six equal parts and you needed to use that shape.

Here's Sandeep's effort.

He's connected together six equal parts.

You might have then compared it with a friend and said, what's the same and what's different? Here we've got Sam's effort and we've got Andeep's effort.

Sam says, this was mine.

She says, yours is symmetrical.

Andeep says yes, and I didn't leave a hole in the middle of the whole.

That's funny, hole and whole.

But both are made of six equal parts, says Sam.

Okay, let's move on to number two.

Here are some examples.

Some are reflections of one another but not the same, says Andeep.

If you look at the last two shapes that were revealed, you can see that if you put a mirror between them, they'd be creating the mirror image of one another.

They're highlighted there.

Okay, let's move on to the second part of the lesson.

Here, we are going to look at what we've learned so far, but in different contexts.

Sam draws round a hexagon to construct a whole from equal parts.

She makes a numeral.

Now take care here because the hexagon part that she's using is not a regular hexagon, but it still has six sides.

I've made the numeral two says, Sam, how many equal parts have I used? Let's label and count them to check says Andeep.

One, two, three, four, five equal parts.

I've used five equal parts, says Sam, I'll try and make another numeral using five equal parts, says Andeep.

One, two, three, four, five.

I've made the numeral three, says Andeep.

Sam has the idea to make all of them outta five equal parts, to make all the numerals.

Here's the numeral four says Andeep.

Sam looks and says, I don't think that's five parts.

Let's count and see, says Andeep.

One, two, three, four, it's only four parts.

It looks like the numerals can't all be made from five equal parts.

Let's check your understanding.

These numerals have been constructed from equal parts, which numerals have the same number of equal parts? Okay, pause the video, have a look, and I'll be back in a moment to reveal the answer.

Welcome back.

Let's have a look.

Let's label them and count 'em to check, says Andeep.

There we can see, they've done that with the numeral six and there are six parts.

They've done it with eight and there are seven parts.

They've done it with nine and there are six parts, so the two numerals with the same number of parts constructed to make the whole are six and nine.

Six and nine numerals are the same.

Sam and Andeep are creating racing circuits using track parts to make a whole.

They use curved and straight parts of equal length.

You can see at the bottom of the screen there that the straight part is 20 centimetres and so is the curved part.

There's Sam's circuit.

There's Andeep's circuit.

Ours look different, says Sam.

Are they equal length? Asks Sandeep.

Let's count the parts, good idea Sam.

Sam has used eight parts to make her circuit Andeep has also used eight parts, eight in each, so they're the same length.

They are eight lots of 20, which is 160 centimetres.

Okay, let's check your understanding of that.

Which circuit is a bigger whole? Pause the video here and see if you can work it out.

Welcome back, let's count and label these.

There are 10 parts in that first circuit and only eight parts in the second circuit.

So the first circuit is the bigger whole because it has a greater number of equal parts.

Sam says the first one has more parts of equal length, so it's longer.

Sam and Andeep are sorting out the PE shed, well done, Sam and Andeep, good volunteering.

Their teacher has divided up the tennis balls into equal groups and given them five buckets to fill equally.

You can see the five buckets on the screen there.

Here's the first group, says Sam, there are the tennis balls.

That group has to go in one of the buckets.

Andeep says there are 10 balls in this group and Sam asks, so how many balls are there all together? There must be 50, says Andeep.

There are five equal parts of 10.

He's right.

If you imagine each of those buckets filled with 10 tennis balls, then you can see that there would be 50 balls in total.

Okay, here's the second practise task.

What I'd like you to do is to create the numerals zero through to nine using the same shape.

You can use the template if you wish.

Then complete the table below by putting the numerals next to the number of equal parts they're made from.

One has already been done.

So you can see in the table there in the left hand column we've got the number of equal parts, and then in the right hand column we've got numeral.

The numeral two has been put next to five equal parts and you can see from the image on the right but that's because there are equal parts used to construct that numeral.

Okay, pause the video here, have a go at that task and I'll be back in a little while with some feedback.

Welcome back, let's see which numerals went into which particular boxes.

When you had two equal parts, you could construct numeral one.

With three equal parts, you could construct numeral seven.

With four equal parts, you could construct numeral four.

With five equal parts, you could construct numeral two as we already knew, numeral three and numeral five.

With six equal parts, you could construct numeral zero, six and nine.

And finally, you needed seven equal parts to construct the numeral eight.

Okay, let's summarise all of our learning today.

When constructing a whole, you can start with the part.

Different shaped wholes can be constructed using the same shaped equal parts.

My name's Mr. Tasman, I've really enjoyed today's lesson and I hope you have.

I hope you've all learned something new.

I hope to see you again as well on the next maths lesson.

Goodbye.

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