Lesson video

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

If you're 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 solve problems involving identifying equal parts and the whole." Here are the keywords that you might hear during this lesson.

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

I'll say, "My turn," say the word, and then I'll say, "Your turn," and you can say it.

Ready? My turn, whole.

Your turn.

My turn, part.

Your turn.

My turn, equal or unequal? Your turn.

My turn, fraction.

Your turn.

Okay, here's what those words mean.

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

A part is some of the whole.

The bar model at the bottom there shows us this.

The whole stretches across both of those parts.

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.

A fraction describes the relationship between a part and a whole.

Here's the outline for the lesson today.

We're gonna start by looking at problems with sorting diagrams. Then we're gonna think about using something called odd one out.

I'm sure you've come across that before.

Are you ready to start? Let's go for it.

These are the two friends who are gonna help us today, Izzy, and Jun.

They'll be discussing some of the maths problems that we see, and through looking at what they say, we're hoping that that will help to unlock problem solving for you.

Izzy and Jun are looking at a sorting diagram.

Jun says, "The table has rows which are horizontal." Izzy says, "Yes and columns that are vertical." "The row headings are different criteria." We've got fruit and veg as our row headings, "And so are the column headings," says Izzy.

Green and red.

In the top left box we need a green fruit.

There's a pear.

In the top right, we need a red fruit.

We've got a red apple.

Bottom left needs to be a green vegetable.

There's a lettuce.

And bottom right needs to be a red vegetable.

That's a beetroot.

That's the sorting diagram complete.

Let's check your understanding of sorting diagrams. What's the mistake in this sorting diagram? The headings for the column are purple, and green.

And for the rows, circle, and square.

Pause the video and see if you can spot the mistake.

Welcome back.

Did you spot the mistake? Here it is.

"This should be a square, not a circle," says Izzy.

If you look at where the box meets, it's got the heading, green, but it's got the row heading, square.

All right, let's keep going with these sorting diagrams. Izzy he looks at a different sorting diagram with representations next to it.

The column headings are line and shape, but the row headings are equal parts, and unequal parts.

"This time I have to sort these representations," says Izzy, "I'll start top left.

A line divided into equal parts." In it goes.

"Then I'll do bottom left, a line divided into unequal parts." There it goes.

She's completed the first column.

They're both lines.

One has been separated into equal parts, and the other into unequal parts.

"Now to look at the shapes.

Which has equal parts?" And she moves it into the correct box.

Lastly, this shape has been divided into unequal parts.

Jun looks at another sorting diagram.

The headings are different here.

For the columns we've got 1/3 and 1/4.

We've got fractions.

And for the row headings we've got notation, which is where you've written numerals down as a denominator and a numerator, and used the division bar to separate them.

And then the bottom row heading is shape.

Let's see how Jun does.

"I'll start top left.

Notation showing 1/3.

Then I'll do top right.

1/4 in notation." So Jun has decided to complete the rows first, rather than doing it by column, which is how Izzy did it before.

He moves on.

"Now to look at the shape.

Which has one 1/3 shaded?" And he pops that in.

"Lastly, this shape is showing 1/4." Well done Jun.

Izzy and Jun look at another sorting diagram, and Jun says, "It's different this time.

The headings are missing." "We will need to work them out," says Izzy.

Have a look there.

What do you think the column headings would be? And what do you think the row headings might be? Hmm.

Well, Jun says, "What is different between the rows?" "The top row are shape, and the bottom are counters," says Izzy.

That makes sense.

How about the columns? What's different here? The first column is showing 1/5.

In the top left box you can see a cross shape that's been separated into five equal parts with one shaded.

That's 1/5.

And in the bottom left you've got five counters, one of them is yellow, which is 1/5.

The second column is showing 1/2.

Izzy and Jun look at a last sorting diagram.

"We've no representations to sort here," says Jun.

"I think we need to create some then," says Izzy.

What do you think? What would you put in each of these boxes to make sure that they match the headings? "I'll do the first column," says Izzy.

She's got shape.

She draws a shape with equal parts, and a shape with unequal parts.

"I'll do the second column," says Jun.

This is line, so he draws a line with equal parts, and then a line with unequal parts.

And they've done it.

Here's your practise task.

You're gonna be facing a series of very similar problems to the one that Jun and Izzy have just completed.

Number one, you have to complete the sorting diagram by placing the representations in the correct place.

Your column headings are 1/4 and 1/5, and your row headings are notation and shape.

For number two, you've got to write in the column, and row headings they're missing.

Izzy gives you a little tip here, "Start with the difference between the columns and then do rows." For number three, you've got to complete the sorting diagram by drawing inside the empty cells.

Cell is just the name for the boxes.

Jun gives you a tip.

"Remember that it's easier to start with the part." And then make the whole.

Okay, pause the video here, and have a go at those tasks.

Enjoy.

Welcome back.

Let's mark these to see whether you've understood.

Here's number one.

1/4 should have gone top left as notation.

Then you should have put the triangular whole in the bottom left because it was showing 1/4.

It had been split into four equal parts, and one of them was shaded.

1/5 as notation went in the top right, and then this whole went in the bottom right.

Okay then here's number two.

This time you had to complete the headings.

We had shape in the first column heading, and line in the second column heading.

Then it was 1/2 in the first row heading, and 1/3 in the second row heading.

If you look at the shapes, you can see that clearly.

The shape in the top left has been split into two equal parts with one shaded.

That's 1/2.

The shape in the bottom left has been split into three equal parts with one shaded.

That's 1/3.

Here's number three.

This is what Jun created.

You might have created something different here though.

We've got counters here.

He's drawn in five of them with one yellow, and the other four red.

He's done similar for the bottom row except he's drawn six counters this time.

Next we've got the shape.

Here's his shape for 1/5, and here's his shape for 1/6.

He's clearly started with a part to help him out.

Now you might have done something differently here, so pause the video, and maybe have a chat with people near you to compare, what's the same, what's different? Okay, we've come to the end of the first part of the lesson, so now it's time to move on to odd one out.

Are you ready? Let's go for it.

Jun and Izzy play a game of odd one out with three things.

They have to choose the odd one out, and explain their choice.

We've gone back to our fruit and veg here.

We've got pear, an apple and a beetroot.

What do you think? Which would you select as the odd one out and why? Jun says, "I think it's the pear because the others are both red." Izzy says, "I think it's the beetroot because it's the only vegetable." "Could the apple be the odd one out?" says Jun, because neither of them selected that.

"I suppose it could because it's the only one that's a red fruit." Jun and Izzy play again.

This time they look at three folded paper strips showing parts and wholes.

They try to find an explanation for each being the odd one out.

What do you think? Look at each of those folded strips of paper.

How could you create an explanation for each one being the odd one out? Jun says, "The top one has been divided into four parts." "So have the middle and bottom one," says Izzy.

That's not gonna be distinctive enough.

"Ah you're right," says Jun, "but the middle one is made up of unequal parts." So that is what makes the middle one the odd one out.

The top and bottom both have equal parts, but unequal length.

"I agree," says Izzy, "So the bottom is the odd one out because the whole is shortest." "The top is the odd one out because it is the longest strip with equal parts." Okay, let's check your understanding.

Why is the middle strip the odd one out? Pause the video and have a go at explaining that.

Izzy has said it's because, "It has unequal parts." Did you get that? I hope so.

All right, ready to move on? Let's see if they continue playing odd one out with a different context.

Jun and Izzy play again.

This time they look at squares divided into parts.

What do you think? Which of these would you select as the odd one out, and could you explain why? Jun says, "The first one has been divided into four equal parts." Izzy says, "The second one has been divided into four unequal parts." "The third one has been divided into unequal parts too." "Yes, but it has five unequal parts." Jun and Izzy play odd one out with fractions.

They start by writing the fraction notation for each shape.

So here's a quick recap for something you might have learned previously.

What do you think? The first triangle has been divided into four equal parts, so the denominator is 4.

One part has been shaded, so the numerator is 1, the fraction is 1/4.

The cross in the middle has been divided into 4 parts.

It has a denominator of 4 with one part shaded, so a numerator of 1.

It's also 1/4.

The last one has one half shaded, so it's 1/2.

How can we make the two the same each be the odd one out? Jun says, "Let's use the shape.

The first has triangular parts whereas the second has square parts." Jun and Izzy put their thoughts into a table.

On that left hand column you can see they've drawn in the representation.

And then in the second column they written in why it's the odd one out.

The first one it represents 1/4, and has triangular parts.

The next one, the whole is not a triangle, and the third one it represents 1/2.

Okay, let's check your understanding.

Spot the mistake in the table below.

We've got representations on the left, and then we've got why it's the odd one out on the right.

For the first row, it represents 1/4, and has square parts.

In the second row it represents 1/5 and has square parts, and in the last row we've got it represents 1/5.

Pause the video and have a go at finding the mistake.

Welcome back.

Did you spot the mistake? Well, here it is.

You can see that the fraction notation is incorrect on the bottom row.

Izzy says, "The whole has been divided into 4 equal parts.

The denominator should be 4." Jun and Izzy look at a new table.

Representation but they're all blank.

Why it's the odd one out, we've got it represents 1/6.

Second row, it represents 1/4, and has oblong parts.

And in the last row it represents 1/4, and has square parts.

"This time we have to draw in the representations," says Jun.

"I'll draw in a shape divided into six equal parts," says Izzy.

"Then I'll shade in one of those parts to make 1/6." Jun says, great piece of advice, "I'll start with a part." He draws an oblong part because that matches the description.

"Then I'll draw three more identical oblongs to create four equal parts in total.

Then I'll shade one part into match the numerator." He's created that representation for the second row.

"I'll do the same, but start with a square part," says Izzy.

She puts in the other square parts to make four in total matching the denominator.

Then she shades in one of them to match the numerator.

And they've done it.

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

For number one, you've got to complete the table writing why each representation might be considered the odd one out? So you're gonna need to compare them all.

In number two, you've got to draw in a representation to match the description for each being the odd one out.

Jun gives us a good tip here.

"Remember that it's easier to start with the part." Pause the video here, have a good go at those, and I'll be back in a little while with some feedback.

Welcome back.

Firstly, you were asked to complete the table writing why each representation might be considered the odd one out? Jun points out there could be some different answers that you've got here.

I'll show you what Jun came up with.

He said it represents 1/4 and it has rectangular parts, for the first representation.

It represents 1/4 and it has triangular parts for the second representation.

And it represents 1/5 for the last representation.

Pause it here, and have a discussion in case you've got any different answers that could still be valid.

Here's number two.

These are the representations that Jun came up with to match the descriptions, but as he points out, you might have had lots of different designs here.

I suggest that you pause the video, and do some comparison between yours, and anybody else's who might have had a go at the practise task, and you can discuss whether you think they're correct or not.

We've come to the end of the lesson, so here's a summary of what we might have learned, or thought about.

Problems involve reasoning in different ways.

Sorting diagrams require you to look at differences between individual columns and rows, and sort things into boxes.

This sort of reasoning can be applied to your understanding of fractions and wholes and parts.

Similarly, reasoning is needed to justify choices when playing odd one out.

This can be applied to your understanding of fractions, wholes and parts as well.

My name's Mr. Tasman, and I've enjoyed learning with you today.

Thank you very much.

I hope that I'll be able to see you again soon in another maths lesson.

Bye-bye.