Lesson video

Hello there, my name is Mr. Tazzyman, and today we're gonna be learning together.

I'm looking forward to it and I hope you are too.

So if you're ready, we can get started.

Here's the outcome for the lesson, then.

By the end, I want you to be able to say, "I can solve problems involving comparing and ordering unit fractions." These are the key words that you might hear and you'll need to understand them.

I'll say them and you can 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 back.

Ready? My turn, whole.

Your turn.

My turn, part.

Your turn.

My turn, denominator.

Your turn.

My turn, unit fraction.

Your turn.

Okay, let's make sure that we understand what each of those mean.

The whole is all of a group or number.

A part is a section of the whole.

And the bar model at the bottom there shows that relationship between the whole and part.

A denominator is the bottom number in a fraction.

It shows how many parts a whole has been divided into.

A unit fraction is a fraction where the numerator is one.

Here's the outline then for this lesson on solving problems involving comparing unit fractions.

To begin with, we're gonna look at comparing and ordering in different contexts, and in the second part we're gonna look at something called fraction grids.

Let's get started with the first part.

Today you are gonna meet Izzy and Jun.

They are maths friends who are gonna help us because they're gonna discuss some of the prompts on screen, give us their thoughts, and they're also gonna lead us through some of the different problems that you are gonna face.

Okay then, let's see what they start with.

Jun and Izzy discuss the fraction wall.

We can use this to help us compare and order unit fractions.

Yes, we can.

As long as the whole stays the same.

Shall we show the unit fractions on their own to make it easier to compare? Sounds like a good idea.

Jun and Izzy choose two fractions each to order.

I'll choose 1/2 and 1/3.

Okay, I'll choose 1/5 and 1/4.

Let's order these using the fraction wall.

Yes, from smallest to largest.

Really important point now from Izzy.

You've got to know which direction you are gonna be ordering them in.

On the fraction wall, I can see that 1/5 is smallest.

There it goes.

I can see that 1/2 is largest.

Izzy places that with a gap in-between for the other two fractions.

1/4 is smaller than 1/3.

So we've got 1/5, 1/4, 1/3, 1/2.

Let's place the wall parts next to them to check.

1/5, 1/4, 1/3, and 1/2.

You can see the fractions increasing in size as you go from left to right.

Jun and Izzy use inequality symbols to show the relationship between the unit fractions.

We need to put an inequality symbol between each.

I agree.

They get greater as you go from left to right.

I can see that 1/5 is less than 1/4.

So they put a less than symbol in-between 1/5 and 1/4.

1/4 is less than 1/3.

There's that symbol again.

Finally 1/2 is greater than 1/3, so the less than symbol is put in-between them, given the order they're in.

Izzy, Jun and Sam race around a track.

There's the track.

You can see the start point labelled.

They are given 30 seconds to get as far around the track as they can.

The results are shown in a table using unit fractions.

You can see the table there.

We've got the name for the left hand column, and then in the right hand column we've got nit fraction of the track run.

Who finished first, second, and third? Jun works out first, second and third place.

We've got a podium there ready for some of the children to stand on.

Jun says, "The greater the denominator, the smaller the fraction." Well remember, Jun, a really key piece of learning.

The greatest denominator was six, which means that's the smallest fraction.

So Sam was slowest and finished third.

1/3 is smaller than 1/2, so Izzy was second.

I was first because I ran 1/2 of the track.

Well done, Jun.

Good running and good calculating.

Excellent.

Okay, let's check your understanding.

What is the mistake on the podium below? Pause the video here and have a go at that.

Welcome back.

Did you manage to spot the mistake? Well, let's reveal it.

1/3 is the greatest, so Sofia won.

You can see there that Alex got 1/5 and 1/5 is actually the smallest fraction of those three.

Sofia was the winner.

In science, Jun and Izzy are making musical instrument using identical glasses filled with different fractions of the whole.

"If we tap the glasses with a spoon, they make a ringing sound," says John.

The full of the glass, the lower the pitch of sound.

Each glass has a unit fraction of water as part of the whole.

Can you estimate the unit fractions? So look at those glasses and look at how much water is in them.

What fraction could you use to describe how full they are with water? Well, the first one was 1/2, the second was 1/4, the third one was 1/3, and the last one was 1/6.

Jun and Izzy need to order the glasses from lowest pitch to highest pitch to complete their instrument.

"The lowest pitch is the fullest," said Jun.

That's 1/2, so that's in the right place.

You can see the glass that's 1/2 full is on the left hand side already.

The smaller the denominator, the greater the fraction.

Well remember, Jun, greater fractions mean a fuller glass and lower pitch.

Three is the lowest denominator, so the next fullest glass.

Then it's 1/4 because four is less than six.

Let's use inequality symbols too.

So I wonder what symbol would go between these.

It's the greater than symbol between them all.

1/2 is greater than 1/3, which is greater than 1/4, which is greater than 1/6.

Their instrument is sorted.

I wonder what tunes they'll be able to play.

It's time to check your understanding now.

Izzy has ordered the glasses below from highest pitch to lowest pitch.

Can you spot a mistake? Okay, pause the video and see if you can spot it.

Welcome back.

Did you manage to spot a mistake? Jun's gonna explain it to us.

1/3 is greater than 1/4.

They need to swap round.

Jun and Izzy are playing a computer game with two friends.

They battle robots.

Each robot has six equal tokens for their life force.

Every time the robot takes a hit, it loses one equal part.

There are the four robots.

There's their life force.

After one minute, the game stops and the robot with the largest fraction of life force remaining is the winner.

There are the results.

What unit fraction of the whole remains for each robot and can they be ordered? What a great problem.

Izzy says, "I'll use my knowledge of multiplication facts associated with six here.

The first robot has two tokens left.

Two tokens could fit into the total of six three times.

So this robot has 1/3 of its life force remaining." 1/3 is labelled next to the life force.

"The second robot has three tokens remaining.

Three is half of six.

so this robot has 1/2 of its life force remaining." There's the fraction notation next to the life force.

"The third robot has only one token left out of six.

It's 1/6.

The last robot has nothing left.

The numerator can't be one, so there's no unit fraction to describe it." Poor robot.

Jun says, "I'll order them from smallest to largest.

1/6 has the greatest denominator, so that's the smallest.

1/2 has the smallest denominator, so that's the greatest." There they are ordered.

1/6 is less than 1/3 which is less than 1/2.

"The flying robot is the winner!" Not really a surprise that, is it? Okay, it's time for your first practise task.

For number one, you need to order the fractions written in notation below from greatest to smallest.

Use the fraction wall to help.

Write the correct inequality symbol between them.

For number two, the children in the table run around a track for 30 seconds.

The unit fraction shows what fraction of the track they completed.

Who was first, second, and third? Izzy ran 1/5, Sophia ran 1/4 and Sam ran 1/7.

For number three, in teams, children complete a water relay race.

They fill a bucket of water by sprinting with a cup full of water across the playground.

Estimate the unit fraction filled with water for each bucket and then order them using fraction notation.

Okay, pause the video here and have a go at those problems. I'll be back in a little while for some feedback.

Welcome back.

This is the correct order and inequality symbols for the first question.

1/2 is greater than 1/3, which is greater than 1/5, which is greater than 1/6.

Let's move on and look at number two.

For number two, Sam was third, Izzy was second, and Sofia was first.

And that's because 1/7 is less than 1/5 which is less than 1/4.

For number three, the relay race, we had Team A getting 1/2, Team B getting 1/5 and Team C getting 1/3.

If you put those in order, going from the smallest to the greatest, we had Team B, then Team C, and then Team A.

How did you get on? Did they make sense? Okay, let's move on to the next part of the lesson.

Here we are gonna be looking at fraction grids.

Jun orders some unit fractions.

The greater the denominator, the smaller the fraction.

1/10 is less than 1/9, which is less than 1/8, which is less than 1/7, which is less than 1/6, which is less than 1/5, which is less than 1/4, which is less than 1/3, which is less than 1/2.

Well done, Jun.

Then, Jun arranges them in a three by three fraction grid.

What do you notice? Look at those fractions, compare them, think about their size.

Jun says, "I've arranged them so that each column and row are ordered from smallest to largest." Izzy has a go at solving a fraction grid.

She starts by ordering those fractions from smallest to largest.

Now that I've ordered them using inequalities, I can sort them into the grid.

I will place 1/20 top left because that's the smallest.

There it is.

I'll put one half bottom right as that's the greatest.

There it is.

Now I will work my way along the inequalities.

So you can see there that the top row goes from the smallest to the greatest, and so does the first column.

She puts 1/7 in the middle and then she says, "It doesn't make a difference which way I place 1/5 or 1/3." So if you look at that grid, you can see that all the rows are sets of three fractions which are ordered from smallest to greatest, and it's the same with the columns.

Okay, let's check your understanding of that.

Can you spot a mistake in the fraction grid below? Pause the video and see if you can find it.

Welcome back.

Did you manage to find it? Well, let's see what Jun thinks.

These two fractions need to be swapped.

1/10 is greater than 1/20.

Okay then, I hope you found that.

Let's move on.

Jun solves the same fraction grid as Izzy.

What do you notice? So look at those two fraction grids.

What do you notice? Jun says, "We have different solutions here." Izzy says, "Both still work though." There's more than one solution.

All right, let's check your understanding again.

Can you swap two unit fractions, but make sure that the fraction grid still works? Pause the video and have a go.

Welcome back.

Here's what Izzy did.

She swapped around 1/3 and 1/4 and it still worked.

You might have made some other choices.

"You might have done it differently," says Izzy.

Jun and Izzy decide to turn their fraction grids into a puzzle race.

Here's how they do it.

Let's write our grids onto coloured paper or card.

Now we can cut each fraction out individually.

They're all cut out.

Then we can shuffle them up and put them in a pile.

There's their piles.

Time to race! Let's give our decks to one another.

Now we can see who arranges them in the grid first.

"Ah, you win! Only just, though," says Izzy.

She'd nearly done it.

She was just missing that 1/3 in the correct place.

Okay then, it's time for your practise task, Task B.

Use the fractions below to complete the fraction grid.

Find two different solutions.

And for number two, it's gonna be the same thing, but we've got some slightly different unit fractions.

For number three, you're gonna take one of your sets of solutions and turn it into a puzzle to race someone with, and you can see the three steps there.

First of all, write them on a piece of card.

Next, cut them out, and step three, pile them up and shuffle them.

Okay, pause the video here and enjoy those tasks.

I'll be back shortly for some feedback.

Welcome back.

Let's look at the first one.

Here are two different solutions that you might have got.

Pause the video here so you can mark them carefully.

Welcome back.

Here are two solutions that Izzy came up with for number one.

You might have had some other solutions.

Pause the video so you can mark yours accurately here.

Okay, let's move on to number two.

Same again.

These were Jun's two solutions, but you might have had others.

Pause the video so you can mark them carefully.

Okay, number three.

Now, you might have really enjoyed playing some races with other people in this.

Izzy says she managed to win this time.

And Jun asks you, "Did you win against somebody?" Okay, let's summarise what we've learned today.

Problems involve reasoning in different ways.

Worded problems require you to fully understand the context and apply your understanding.

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

Similarly, reasoning is needed to justify choices made while solving puzzles like fraction grids, which require the understanding and ordering of unit fractions.

I hope you enjoyed those tasks today.

I think some of them were quite good fun, and I hope that I'll see you again in future in some more maths lessons.

My name is Mr. Tazzyman.

Bye-bye for now.