Lesson video

Hi there.

My name is Mr. Tilstone.

It's great to see you today.

I hope you're having a good day.

I hope you're having a successful day.

Let's make it even more successful by developing your knowledge of parts and wholes.

So if you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can construct a whole when given a part, and the number of parts.

Our key words.

I'll say it first and you say it back.

Are you ready? My turn, whole.

Your turn.

My turn, part.

Your turn.

And my turn, construct.

Your turn.

Now I think two of those words are going to be very familiar to you, and I think you've probably been using two of those words quite recently, which is whole and part, maybe construct is a bit more unfamiliar.

Let's have a look what those words mean.

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

A part is some but not all of the whole.

So it can be a small part or a large part.

And constructing something involves making something by joining parts together.

That's what constructing is, and that's what you're going to do today.

Our lesson is split into two parts.

So we could think of our lesson as a whole and it's got two parts.

The first will be constructing a whole, and the second constructing a whole within a context.

So if you are ready, let's start by concentrating on constructing a whole.

In this lesson, you're going to meet Izzy and Jun.

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

Jun is thinking of a shape and he's given a clue.

This is one part of my whole.

Okay, so that's not the whole, that's a part of it.

Hmm, so I think we probably need some more information, don't you? Can you draw the whole shape that this part is from? Hmm, you might want to have a guess now.

You might want to have a go if you've got a whiteboard or something like that.

You might want to sketch what you think Jun's shape could be.

You might be right.

Izzy says, "Your whole could be any of these.

They all make use of your part." Yes, they do.

So let's have a look at some of these.

So the first shape we can see is that triangle that he drew with a square attached to it.

The next shape is that triangle that he drew with a larger triangle attached to it.

And the neck shape is that triangle with a rectangle attached to it and a triangle attached to that.

And the final shape is that triangle with a parallelogram attached to it, and then another triangle attached to it.

So there's all sorts of different things that it could be hundreds really.

She says, "Maybe you thought of some more," but Jun says, "My shape is not any of those." Hmm, Izzy says, "Can you give us a clue? What information do we need to help us to draw Jun's shape? 'Cause we do need some more, don't we, than that.

Otherwise, it could be almost endless possibilities.

He says, "My whole is made from parts that are all the same shape and size as this part." Ha! Okay, so in other words, they've got equal parts.

I wonder if that's what you drew and you had a guess.

If not, why do you have another go now? What could his shape be? He's saying that they are the same shape and size, the other parts.

Izzy says, "Your whole could be any of these." Did you draw any of these shapes? Maybe you did, maybe you didn't.

All of the parts are the same size and shape.

Yes, indeed they are.

So these are possibilities.

I still think there's something else that we need to know from Jun, don't you? Just to narrow it down a bit more.

And Izzy says, "Maybe you thought of some more." Jun says, "My shape is not any of those." Hmm.

Izzy says, "Can you give us another clue?" What would you like to know? If you could ask Jun for a little clue, what kind of thing would you ask him? So we know that that is a part of the shape.

We know that it's got other equal parts.

Hmm, I think there's one crucial bit of information still missing.

What could we ask? What could we say? What could Jun say to us? Ha! Here we go.

He says, "My whole has been divided into three equal parts." That's what we needed to know, isn't it? We know what one of the parts is.

We know they're equal parts.

We just didn't know how many equal parts, but now we do: three.

Do you want to maybe have another go, have another go at sketching out what you think his shape could be? I think there's more than one possibility.

Have a guess.

Izzy says, "Your whole must be this." And Jun says, "That's correct." Is that what you got? Is there another way that that shape could have been composed? To construct a whole from a known part, we need to know the number of parts, and whether the parts are of equal size and shape.

This rhombus is one part of a whole made outta three equal parts.

Look at the wholes that have been constructed.

And before you do that, you might want to visualise.

So picture some possibilities.

You might want to sketch a few possibilities.

We know that's one part of the whole made of three equal parts.

So there'll be three of those rhombus'.

And here are some possibilities, some different shapes that could be constructed from that rhombus if we've got three of them.

So what's the same about these shapes and what's different? What can you notice? Be a good mathematician and notice something.

Well, each whole is made of three equal parts.

So that is what's the same about them.

Each whole has a different number of sides.

That's what's different about them, and so it's a different polygon.

And I wonder if you could even name what these polygons are.

This shape is a parallelogram.

It's got two pairs of parallel equal sides.

This shape is an octagon and, in fact, an irregular octagon.

It's got eight sides.

And this one is a hexagon, an irregular hexagon.

It's got six sides.

Let's have a check for understanding.

Look at this part of a shape.

This is one part of a whole made of three equal parts.

So let's make sure you've understood that.

That's one of three equal parts.

Which is the correct shape? Is it A, is it B, is it C or is it D? Take your time with that.

Talk it over with a partner, swap ideas, pause the video, and I will give you the answer shortly.

Well, if there are three equal parts, we're looking for a shape that's got three parts and that will be the whole.

And there's two possibilities.

This is one.

That shape is constructed from three of those shapes.

But so is that one.

So well done if you said B and C.

A had too many parts that had four parts, we only needed three equal parts.

It's time for some practise.

Number one, construct the whole.

This square is one part of a whole made of four equal parts.

So one of four equal parts.

Construct at least three different wholes.

You might want to do even more than that, but three is a minimum.

And what is the same about your shapes and what is different? Can you explain that? Lots of possibilities for this.

Number two, this shape is one of five equal parts of a whole shape.

Jun has constructed the whole shape or has he? Explain why Jun cannot be correct.

Right here, pause the video.

Off you go.

Welcome back.

Let's give you some answers.

Let's see how you got them.

So number one, you might have constructed some wholes that look a little bit like this.

These are just some possibilities.

You might have noted that each whole was divided into four equal parts, but that the wholes were different polygons and maybe you even named them.

This is a square, this is a rectangle, this is an octagon.

Number two, Jun has constructed the whole shape.

Explain why Jun cannot be correct.

You might have explained that Jun can't be correct because his whole shape has been divided into six equal parts, not five.

There we go.

The given part needs to be included in the total number of parts, but Jun just drew another five parts onto the given part.

The whole shape could have looked like this.

How many pieces will it have? How many squares? How many parts? Five.

Five equal parts, five squares.

You're doing very, very well and I think you are ready for the next cycle, which is constructing a whole within a context.

So let's put some different context onto this.

So Jun is doing some sewing and cuts a ribbon into five equal parts.

Five equal parts.

This is one part of my ribbon.

So that's not the whole, that's one part of the whole.

Remember he is going to cut a ribbon into five equal parts.

That's one of them.

How can we determine how long Jun's ribbon was to start with? Now remember once again, that is a part, that's one of five parts.

So what could we do? To determine the whole, we can recombine the five parts.

So here we go.

So that was that one part with the other four parts with it now.

So this is the whole ribbon, the length of the whole ribbon.

Now let's look at a different context.

Izzy is preparing fruit bags to give out at her party.

Very healthy.

I like that.

Izzy needs to make four bags with equal numbers of strawberries.

Here are the strawberries that she puts into one bag.

So can you count those or sabotage those? That is five strawberries so five strawberries in one bag.

How many strawberries will she use in total? So what will be the whole? So one part is five strawberries.

So when she puts those five strawberries into a bag, that's one part.

The whole is made from four equal parts.

So that's one of them.

So how many more will there need to be? We can represent this as a drawing and as a bar model.

Here we go so we could draw some strawberries, four equal parts.

Each part is composed of five strawberries so you can see all four of those parts.

And here's a bar model which is quicker to draw and more efficient.

So we've got the whole for the top of the bar model and the four equal parts on the bottom.

So that number five represents the number of strawberries, and there are four groups of five.

Four equal parts of five.

That's 4 x 5, 4 multiplied by 5 equals 20.

Izzy will need 20 strawberries and that's the whole amount.

So 20 strawberries is the whole, five strawberries is one part.

Let's have a check for understanding.

Let's see how you're doing.

Izzy has bought three equal packs of colouring pencils and this is one pack.

So you might want to sabotage and see how many is in one pack.

But the question is how many colouring pencils has she bought in total? So pause the video and have a think.

So that pack of colouring pencils is one part, one of three equal parts.

So we could draw that and we could draw that as a bond model as well.

So there are three equal parts of five.

So that's 3 x 5, which equals 15.

So Izzy has bought 15 colouring pencils, and that's the whole amount.

So five pencils was one part, 15 pencils was the whole.

It's time for some more practise.

Number one, solve these problems. Jun has cut a ribbon into three equal parts.

This is one part of his ribbon.

Use this part to help you draw how long the ribbon was to start with.

So remember that's not the whole, that's a part.

B, Izzy has divided some flowers that she bought into four equal bunches, each with three flowers.

Here is one of the bunches.

How many flowers did she buy? Number two, using the given information, construct the whole lines and determine the length of the whole line.

So A, draw a line segment of five centimetres.

So nice and accurate, please.

Remember all the rules about drawing accurate lines.

This is one of three equal parts of the whole.

So that five centimetre line segment is one of three equal parts so that's a whole line look like.

Draw a line segment of three centimetres.

This is one of four equal parts of the whole, one of four.

And then C, draw a line segment of two centimetres.

This is one of five equal parts of the whole.

Right, well good luck with that, and I will see you shortly for some answers.

Welcome back.

Let's see how we got on.

So number one, you might have drawn another two parts to form the whole ribbon like this.

So we had one part that was one of three equal parts so you need to draw two more like that.

So yours should have three equal parts and that's the length of the whole ribbon.

And then Izzy's divided some flowers that she brought into four equal bunches, each with three flowers.

Here's one of the bunches.

So three flowers equals one bunch, and that's one of four equal bunches.

So you might have drawn a representation of this or represented it as a bar model.

So you might have drawn some flowers and you needed to draw four altogether bunches of flowers.

And you could also show that as a bar model.

So the each three represents a bunch of flowers and we've got four of them, and that means a total number of flowers bought is 12 because 4 multiplied by 3 equals 12.

Izzy bought 12 flowers, and that's the whole amount.

So three flowers was a part, 12 flowers is the whole.

And then using the given information, construct the whole lines and determine the length of the whole line.

So the first thing you were asked to do is draw a line segment of five centimetres and that was one of three equal parts.

So you needed to draw three, five centimetre lines together like that.

And then that made one whole line so that's a whole.

Five centimetres was a part, and 15 centimetres was the whole.

Whole line is 15 centimetres long.

For B, you were drawing a line segment of three centimetres, which was one of four equal parts of the whole.

So you needed to draw altogether four, three centimetre lines together, and there are four equal parts of three.

That's 4 multiplied by 3, which equals 12.

So the whole line is 12 centimetres long.

Three centimetres was one part, 12 centimetres was the whole.

And finally you were drawing a line segment of two centimetres, which was one of five equal parts.

So here we go.

So you needed to draw five two centimetre lines together, five equal parts of two.

That's 5 multiplied by 2, which equals 10.

So the whole line was 10 centimetres long and two centimetres was a part.

We've come to the end of the lesson.

You've done incredibly well today.

In today's lesson we've been reviewing, constructing a whole when given a part and the number of parts.

So when constructing a whole, you can start with a part as we have done today.

To construct a whole, you need to know how many parts make it up, and whether those parts are equal.

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

So we've covered lots of ground today, and I feel like we've really developed your knowledge of parts and wholes.

So very well done.

I think you need to do two things.

Number one, I think you need to breathe a sigh of relief.

(exhales sharply) And number two, I think you need to give yourself a very well deserved pat on the shoulder.

Hmm, I've really enjoyed spending this math lesson with you, and I hope I get the chance to spend another maths lesson with you in the near future.

But until then, take care.

Goodbye.