Lesson video

Hello, my name is Mr. Taziman, and I'm really looking forward to learning with you today.

I hope you sat comfortably because we're ready to start! Here's the outcome for today's lesson.

We want you to be able to say, by the end of this, "I can identify the number of equal "or unequal parts in a whole." Here are the key words that we are going to be using.

Whole.

part, equal and unequal.

I'm gonna 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.

Your turn.

My turn, unequal.

Your turn.

Now let's look at what those words mean.

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

A part is some of the whole.

You can see a bar model at the bottom of the page there, illustrating these concepts.

We say that two or more things are equal if they have the same quantity or value.

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.

And to start with, we're going to look at equal and unequal parts.

Then we're gonna move on and think about how we might categorise and count the parts in a whole.

Let's do the first part.

Here's two maths friends that we are gonna meet, Izzy and Jun.

They're gonna really help us today by discussing some of the prompts on screen and revealing some of the answers.

They'll also give us some really good hints and tips along the way.

Jun and Alex are looking at flags.

Chile, Columbia, Peru, Jamaica, France, Germany.

Jun says, "There are so many different designs! "They're all split into different parts." Izzy says, "All the different coloured shaped parts "join together to make the whole flag." "Which flag am I describing? "It has black, yellow, and green parts." Which do you think, hmm? I'm gonna look at all those flags and see which of those matches the colours that Jun has said.

"Jamaica.

"It has those different coloured parts making the whole.

"How about this one? "This flag has black, red, and yellow parts." Which do you think that is? Have a look.

"Germany, I think! "It's the only flag "with that combination of parts making the whole." Well done, Jun.

Okay, let's check your understanding so far.

True or false? A whole is made of many parts.

Pause the video here and think about whether you believe that to be true or false.

Welcome back! What did you think? Well, that was true.

Here's two justifications.

A, parts are always smaller and they join together to make the whole, or B, wholes and parts are the same, so they each make each other.

Which of those two do you think is the correct justification? Pause the video and have a think.

Okay, which did you think, A or B? The answer was A.

Parts are always smaller and they join together to make the whole Jun and Izzy compare the parts of their chosen flags.

We've got the Jamaica flag on the left and the Germany flag on the right.

Jun says, "I will split my flag "into the different coloured shapes, which are the parts." There they go.

"I'll do the same," says Izzy.

"Then," says Jen, "we can group the parts by colour." You can see all the parts moving into a group which has the same colour.

Izzy concludes, "So the German and Jamaican flag both have parts "that are yellow and black." "Yes," says Jun, "but the Jamaica flag has a green part, "whereas the German flag has a red part." Jun describes another flag using colour.

"Which flag am I describing? "It has blue, white, and red parts." Which do you think? Have a look at those flags, which has blue, white, and red parts.

Izzy says, "Erm, there's two options here! "It's either France or Chile." "Ah, yes," says Jun.

"You'll need more clues.

"The flag I've chosen is divided into equal parts." "What does that mean," asks Izzy? "Like we did before, "we can split both flags up into parts." Izzy says, "But if you group the parts by colour, "that won't give me a clue!" "I know," says Jun, "but look at the parts in the French flag.

"They are the same size.

"They are equal parts." "Oh, I see," says Izzy! "The parts of the Chile flag are unequal.

"They are unequal parts." Jun says, "So my flag had equal parts "of blue, white, and red." "That must be the French flag as that has equal parts." Okay, your turn.

Let's check your understanding.

Below are the flags of Canada and Peru, which of the flags are Jun and Izzy describing and who gave the best clue? Jun says, "If the flag is the whole, "it has red and white parts." Izzy says, "If the flag is the whole, "it has equal sized parts." Okay, pause the video, have a go and I'll be back in a little while.

Welcome back.

How did you get on? Let's see.

The correct flag was Peru, being described from those clues, but who gave the best clue? Here's an explanation and an answer.

Izzy's clue is best because Jun's clue is true of both flags.

Izzy's clue is only true of the Peruvian flag, which is made of equal sized parts.

Jun and Izzy each take a paper square.

"Let's spit them into four parts and compare," says Jun.

"Okay, but no peaking whilst we do it!" There's Jun's and there's Izzy's.

"Interesting," says Jun.

"Shall we do some more shapes?" Jun and Alex, repeat the task with more shapes.

"Let's try an equilateral triangle." So you can see the equilateral triangles there for Jun and one for Izzy.

"What about a circle," says Izzy? She does hers and Jun does his.

"Okay, now a rhombus," says Jun.

He splits his up and Izzy does hers.

They decide to sort the shapes into a table.

You can see the two headings there, equal parts and unequal parts.

"Equal and unequal parts," says Jun.

"Yes, I start with equal parts," says Izzy.

She starts to move them across.

"The rest must be unequal then" says Jun.

"I think something is wrong here," says Izzy! "One of these is incorrect." What do you think? Have a look through all those shapes and think, do they have equal size? Are they the same area? Is each of the parts the same area, hmm? Let's see what they thought.

Jun says, "I think it's the rhombus at the bottom!" They decide to look more closely at the rhombus.

"The parts look equal," says Izzy.

"That's because the height of each part is equal! "But the area is different." You can see an arrow there showing the height of each of the parts.

They're all the same height.

Izzy, still a bit suspicious, says, "Let's cut it up to see.

"Wow," she says! "They're definitely not equal." They return to the table to correct it.

"So the rhombus needs to move over," says Jun.

"I agree," says Izzy! Let's check your understanding.

Which of these two shapes has been split into equal parts? Chat with somebody near you about it to explain your thinking and I'll be back in a little while to reveal the answer.

Okay, welcome back! Which of these has been split into equal parts? Well, it's the one on the left.

Okay, Jun and Izzy continue to think about splitting shapes into equal and unequal parts.

Izzy says, "So far we have only used straight lines "to split shapes." Jun says, "I don't think you can divide a whole shape "into equal parts without using straight lines!" "I think you can," says Izzy! "Let's investigate." Who do you agree with? Do you agree with Jun and think that you can only use straight lines or do you agree with Izzy and think you might be able to use some different types of lines? "Let's try a circle," says Izzy.

"You have to use straight lines here.

"See," says Jun.

Izzy says, "What if we try curving each line "in the same way?" "Ah, I see.

"The lines from the centre are all identical, "so the parts will be equal." Okay, let's check your understanding which shape has been split into equal parts? Same task as last time.

Pause the video and have a go.

Welcome back.

Which did you think? Here's the answer.

Even though the line on the left is curvy, it's still showing this square's been split up into two equal parts, whereas the line on the right isn't splitting the shape into two equal parts.

Those parts are unequal.

Jun and Izzy consider equal and unequal parts in a new context.

"In dance lessons, our teacher often asks us "to get into groups." Izzy says, "I think they mean "that each group should have the same number of people." Jun replies, "So if the class of children is the whole, "then the groups are the parts." "Yes," says Izzy, "and the teacher normally wants equal parts." "If they wanted us to split into two equal groups, "we might do this." "Yeah.

"Or if they wanted us in four equal groups, "we might do this." "I don't think we could split "into three equal groups," says Jun.

What do you think? Have a look at the number of children there.

Could you split them into three equal groups? "No, you're right," says Izzy.

"It would have to be three unequal groups like this." You can see on screen there we've got three groups.

Two of them have three children in, but one of them only has a pair.

"This feels very different to our shapes," says Jun.

"You can count the parts in this context." "I agree.

"The shapes were about the area of the parts." Time to check your understanding, true or false? With nine children, you can make equal groups.

Pause the video here and choose true or false.

Welcome back.

What did you think? True or false? It was true! Okay, now it's time to look at some justifications for that answer.

A, nine can be divided into equal groups.

There would be three children in each group, or B, any number can be divided into anything, so you can make equal groups.

Which of those two justifications do you think is best? Pause the video and have a think.

Welcome back.

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

Nine can be divided into equal groups.

There would be three children in each group.

Okay, it's time for your first practise task.

For each of the following statements, say true or false and explain your answer.

Really important to explain what you are thinking.

A, only shapes can be split into parts.

B, a whole is made up of many parts.

C, you have to use straight lines to split a shape into equal parts.

D, a whole is always bigger than a part.

For number two, we want you for each of these contexts to state whether the whole has been split into equal or unequal parts.

A, the whole is all the children standing in groups.

B, the whole is a circle.

Okay, number three, this is where you get to be a bit creative.

Choose two or three colours and colour in the block for each flag design, which features equal parts and one that features unequal parts.

So, you can see there you've got an equal parts and an unequal parts and you've got a grid with some blocks in.

You've got to create some flags on those.

The first one has to be in equal parts and the next one has to be in unequal parts.

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

Good luck! Welcome back! Let's give you some feedback.

Here's number one.

A, only shapes can be split into parts.

That's false.

"You can split any whole into parts," says Izzy.

B, a whole is made up of many parts.

True, any whole has lots of parts in it.

C, you have to use straight lines to split a shape into equal parts.

That's false.

You can use curved lines as well.

And D, a whole is always bigger than a part.

True.

Otherwise the part would be the whole.

Okay, pause the video here if you need to keep marking and I'll be back in a moment to do the rest of the questions.

Here's number two.

A, the whole is all the children standing in groups.

You can see from the labelling of the numbers there that these are unequal parts, because the children are stood in groups of three, then two and then three.

This one though, has been split into equal parts because each of the parts is the same shape and so it must have the same area.

And here's the designs of Izzy, for number three.

She, on the first one split her flag into horizontal strips that were equal.

For the second part, she had some different shapes with different colours.

You might have had some different designs to that.

Pause the video here and maybe share a few of those designs.

Okay, it's time to move on to the second part of today's lesson.

Count and categorise the parts in a whole.

Are you ready? Let's go! Jun and Izzy plan to share a pizza.

"Okay," says Jun, I'll cut it into parts for us, "so that we can each have some." There he goes.

He's cut it.

Izzy says, "But you've cut it into six equal parts.

"There's only us two." "True," says Jun.

"I'll give you your part then." How do you think Izzy feels about that? "There we go.

"Now we both have some," says Jun.

"But that's not equal," says Izzy! "The parts are equal! "They're the same size." "But you have five equal parts and I only have one! "That's not fair." "Oh, I see! "So now we are counting parts rather "than thinking about them as area." "Exactly.

"We each need three equal parts.

"So give me the rest of my slices," says Izzy! There they go.

So in the end, if the pizza was the whole, it was divided into six equal slices.

Jun and Izzy consider equal and unequal parts.

in a different context.

"Let's fold some strips of paper "in different ways," says Jun.

And there they are, three strips folded in different ways.

"Here are mine," says Izzy.

"I think we can describe these." So, you can see she's also folded three strips.

Jun says, "Then we can work out "which one the other person has said." "Okay.

"Try this, the whole has been divided "into three equal parts." Which one do you think it is? Have a look at each of those strips.

We're looking for three equal parts.

"I'll start by labelling the number of parts "for each whole," says Jun.

"Now," says Jun, "I'll remove all of those that don't have three parts." Okay, and he has a look at these last two strips and he says, "One of these has equal parts "and the other doesn't." "Well done! "You've got it right," says Izzy! Jun and Izzy use lines instead of paper strips.

They want to split them up into parts.

"Let's split these lines into different parts "and play the same game," says Jun.

"This might be tough.

"I think I'll use a ruler for making equal parts." "Great thinking! "I'll measure the length of the lines." Puts the ruler across, looks at the start and the finish.

"So each line is six centimetres.

"That helps me! "Okay, let's turn the wholes into parts." Here goes Jun, and now is Izzy.

"Okay, the line I'm looking at is divided "into three equal parts." Which line do you think it is? Have a look at all of them.

Which one's been divided into three equal parts? "Alright," says Izzy.

"I'll start like you did "by counting the parts in each line." Here she goes.

Two, one, five.

"Hang on," says Jun! "I don't think that's right." "You're right," says Izzy.

"I was counting the pen marks not the parts.

"I'll start again." "Three, two, six, three, four, five.

"Now I'll remove all the lines "that aren't split into three parts." There they go.

"Then I'll remove the line that had unequal parts.

"Was it this line?" "Yes! "Well done, Izzy." Okay, time to check your understanding.

Match the descriptions with the lines.

The first description says the line has been split into six equal parts.

The second description says the line has been split into two equal parts, and the third description says the line has been split into two unequal parts.

Pause the video here and match the lines with their descriptions.

Welcome back! Let's see how you got on.

The top one matched with the bottom line.

The middle one matched with the middle line, and the bottom one matched with the top line.

Did you get them? I hope so.

Let's move on.

Jun and Izzy look at a sorting diagram.

You can see the headings there.

We've got equal parts and unequal parts.

They're the headings for the columns.

Then we've got two parts and more than two parts.

Those are the headings for the rows.

Jun says, "Let's use a shape split "into parts to complete it." "Okay," says Izzy, "I'll go first.

"I'll use a square to start with and I'll split it up." There we go.

What do you think? Where do you think this should go? "I'll count the parts," says Jun.

"One, two, three, four.

"There are four parts.

"That means it needs to go on the bottom row "because four is more than or greater than two." Izzy follows that up with, "They are unequal parts "because they have different sized areas." So, she highlights the unequal parts heading.

"I'll put it into the box where those two conditions meet!" There it goes.

Jun says, "Let's do the rest of the table.

"Try this circle as a whole split into parts." What do you think? Where should that go? "The shape has been split "into two equal parts," says is Izzy.

"So it is in the top row because it has two parts." "Yes, and it is in the equal parts column." There it goes.

"Okay.

"What about this Rebus as a whole?" What do you think? Where would you place that rhombus split into parts? "Well again, it's been split into two parts "so it's in the top row" "Yes, and they're unequal "so it goes in the second column." "So it goes in this box," says Jun.

"Okay, I'll try and draw a last one to fit in the box." "Why don't you try using a triangle this time?" Good challenge, Izzy.

How might you split the triangle? "Okay, it must have more than two equal parts.

"How about this?" "Well," says Izzy, "it has four equal parts, "which is more than two.

"Well done! "It works, so I'll put it in." There it goes.

Alright, time to check your understanding again.

Match the shape to the description.

The first one says the square has been split into four unequal parts and the second one says the square has been split into four equal parts.

Pause the video, have a go! Welcome back! Let's check that you have understood.

The top one matched with the bottom shape and the bottom one matched with the top.

Did you get it? Hopefully.

Okay, here's the practise task for the second part of the lesson.

Number one, circle the two folded strips of paper described by Jun and Izzy.

Jun says, "This folded strip of paper "has been split into eight equal parts." So, which one of the strips is that do you think? And then Izzy says, "This folded strip of paper "has been split into four unequal parts." So, that will be a different strip.

Which one do you think that is? Number two, you've got to tick the two divided lines described by Jun and Izzy.

So, it's the same kind of task.

Jun says, "This line has been split into six equal parts." Izzy says, "This line has been split "into five unequal parts." Number three, again, a bit of a creative challenge, you have to colour in the blocks to design a flag that fits the conditions in this sorting diagram.

The columns are equal parts and unequal parts.

That's quite similar to the number three task in the first part of the lesson.

But you've also got the rows, three parts and more than three parts.

Okay, have a good go at these tasks and I'll be back in a little while to give you some feedback, so pause the video here.

Welcome back! Let's reveal some of these answers.

So, be ready to mark.

You can see there that that was the strip of paper folded into eight equal parts.

They've been counted out.

And there's Izzy's because there are four parts and they are unequal.

Okay, let's move on to number two.

Here are the lines.

Through the counting we can see that this one has six parts and that they're equal.

That was Jun's line.

And there's Izzy's.

That was five parts but they were unequal.

Alright, let's look at number three.

This is what you might have tried.

Equal parts and three of them, unequal parts and three of them.

This one was tricky.

In order to make sure that you had more than three parts and they were equal, you had to use nine different colours because each block was a part, and then there was more than three parts, but unequal.

That gave you a bit more freedom.

Here's a summary of the learning that we've enjoyed today.

A whole is made up of many parts.

Parts can be equal or unequal.

This is true in different contexts such as the size of the area, counting objects or people and splitting up lines.

And we can describe a whole by counting the number of parts it has and stating whether they are equal or unequal.

Hopefully, you are able to identify the number of equal or unequal parts in a whole.

I've really enjoyed learning with you today.

My name's Mr. Taziman, and I hope to see you again in the future in some more math lessons, bye!.