Lesson video

Hi there.

My name is Mr. Tazzyman, and I'm really looking forward to teaching you this lesson today from the unit all about the composition of non-unit fractions.

Some people can find fractions a bit tricky sometimes, but I hope with what I'm about to show you, I can make sure that you finish this lesson feeling really confident, and ready to tackle any fractions that come your way.

Okay, we're gonna get started.

The outcome for today's lesson then is for you to be able to say, "I can subtract fractions with the same denominator." These are the key words that you will expect to see in these slides.

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 say it back, ready? My turn, minuend, your turn.

My turn, subtrahend, your turn.

My turn, numerator, your turn.

My turn, denominator, your turn.

Okay, let's see what those words actually mean if we don't know already.

The minuend is the number being subtracted from.

A subtrahend is a number subtracted from another.

There can be more than one.

You can see an equation written at the bottom there.

Seven subtract three is equal to four, and in that equation, seven is the minuend, and three is the subtrahend.

A numerator is the top number in a fraction.

It shows how many parts we have.

A denominator is the bottom number in a fraction, It shows how many parts a whole has been divided into.

Okay, here's the structure of the lesson.

We're gonna start by thinking about subtracting fractions in a partitioning structure.

Then, we're gonna move on to subtracting fractions in a reduction structure.

All of this is gonna help us to subtract fractions with the same denominator.

We'll start with the first part then.

We've got some friends who are gonna help us out.

This is Aisha and Alex, and these guys are gonna be chatting about some of the maths that we are gonna come across.

They'll give us some hints and some tips and help our understanding along the way.

Hi Aisha.

Hi Alex.

Okay, there are five bananas in a bunch.

Two of them have been eaten.

How many have not been eaten? "This is a subtraction question," says Aisha.

One part of the whole amount has been partitioned from the whole group.

This is a type of subtraction.

Alex decides to represent the same question as a bar model to understand the structure.

"First I will draw bars around the parts.

Then I will draw a bar for the whole.

The whole is five bananas.

The parts are three bananas and two bananas." There are five birds in a flock.

Two of them are blue.

How many are not blue? This time, Aisha represents this problem in a bar model.

"First, I will draw bars around the parts.

Then I will draw a bar for the whole.

The whole is five birds.

The parts are three birds and two birds.

Three birds are not blue." There are five pens in a pile.

Two of them are highlighters.

We all love highlighters.

How many are not highlighters? Alex represents this problem in a bar model.

"First I will draw bars around the parts.

Then I will draw a bar for the whole.

The whole is five pens.

The parts are three pens and two pens.

Three pens are not highlighters." Alex looks at all the bar models they've created.

We've got our bananas bar model, our birds bar model, and our pens bar model.

What's the same and what's different.

So look at all three of those.

Look for similarities and look for differences.

"They all have the same structure.

They use the known fact, three added to two equals five.

They all have different units.

Bananas, birds and pens are all different." Aisha and Alex use counters to show the structure for the problems they've solved.

"Let's use counters to represent any unit." "Okay, the whole was always five, so here are five counters in a row.

The parts were always three and two." "This represents all of those problems then." "Yes, with the counters being any unit.

Okay, your turn to check your understanding so far.

Represent and solve this problem using a bar model.

There are five apples in a bowl.

Two of them are red.

How many are not red? Okay, pause the video and represent away.

Welcome back.

Here's what your bar model may have looked like.

We had five apples as our whole, three apples and two apples as our parts.

Two of them were red, so you might have coloured two of them red or perhaps you just labelled it.

Alex tells us three aren't red.

Are you ready to move on? Okay, Aisha represents each as a subtraction equation.

Five bananas subtract three bananas is equal to two bananas.

Five birds subtract three birds is equal to two birds.

Five pens subtract three pens is equal to two pens.

What's the same? What's different? Have a look again, compare them.

Can you see any similarities or any differences? "Like the bar model, they all have the same structure but different units." A snail needs to creep 5/10 of a metre to reach a tasty lettuce leaf.

It creeps 2/10 of a metre.

How much further does it have to go? What do you notice? Hmm.

The numerator we already know are two and five.

So it is the same structure as the other questions.

There's that structure that they've drawn as a bar model.

The unit is different though.

Each counter is 1/10 of a metre.

They're labelled.

"So the snail will need to go three 1/10 of a metre.

There it is five 1/10 is 5/10.

So they've replaced those counters with 5/10 of a metre.

"Two 1/10 is 2/10." They've done the same thing again, that just leaves this last part.

Three 1/10 is 3/10.

There it is.

"The snail has 3/10 of a metre to go." Aisha transforms the bar model into an equation.

This was a subtraction equation.

5/10 of a metre was partitioned.

So 5/10 was the minuend.

There it is.

The snail travelled 2/10 of a metre.

So 2/10 was the subtrahend.

So that's been subtracted.

That meant there were 3/10 still to go.

So 3/10 was the difference.

5/10 of a metre subtract 2/10 of a metre is equal to 3/10 of a metre.

There's our equation.

Aisha and Alex share a pizza.

Alex eats 3/8, how much does Aisha eat? "I'll represent this as a bar model and an equation.

The whole was a pizza.

I know that it had been cut into slices of 1/8.

This is because of the denominator of eight.

So 1/8 is my unit." There it is sliced up.

"So I can start with eight 1/8 as my whole and minuend." So he's drawn the whole at the top of a bar model and he's written down 8/8 as his minuend.

"I know that Aisha ate three 1/8, because she had three slices.

Subtract 3/8.

"I know that eight subtract three is equal to five.

So I know that 8/8 subtract 3/8 is 5/8." And he's completed the bar model with those five pizza slices representing 5/8 of the pizza and the equation reads 8/8 subtract 3/8 is equal to 5/8.

Aisha compares the fraction equations they've used so far.

5/10 of a metre subtract 2/10 of a metre is equal to 3/10 of a metre.

8/8 subtract 3/8 is equal to 5/8.

What's the same and what's different? Compare these two again.

Look within the equation.

What stays the same and what changes and look across the equations.

What do you notice that's similar? What can you generalise? Both of these involve fractions.

Well that's definitely true, isn't it? The denominators stay the same.

It is the numerator that change.

When subtracting fractions with the same denominator.

The denominator stays the same, and the numerator change.

Spot the mistake below to check your understanding.

5/10 subtract 2/10 equals 3/20.

Pause the video, have a go at that.

Welcome back, did you spot the mistake? Well, it was the 1/20.

When subtracting fractions with the same denominator, the denominator stays the same and the numerator change.

The denominator has been changed.

They have added together 10 and 10, which is equal to 20.

To make this correct, it should have read 5/10 take away 2/10 is equal to 3/10, because the denominator is the unit.

It doesn't change.

All right, then let's move on.

Alex solves some missing fraction problems represented on a bar model.

We've got a bar model drawn out there.

The hole is 6/7 and one part is 4/7.

Let's see what Alex says.

"6/7 is six lots of 1/7.

4/7 is four lots of 1/7.

I know that six subtract four is equal to two, so I know that 6/7 subtract 4/7 is equal to 2/7, and he fills in the bar model.

Well done Alex.

Okay, here's your first practise task.

For number one, I want you to match the bar models with the fraction subtraction equations and solve them.

You can see all the question marks there.

You've got to make sure that you filled those in carefully.

But remember, the representations show the equations so match them up first.

For number two, you are gonna complete the stem sentences to solve the equation.

7/9 subtract 3/9 is equal to we don't know yet, and you've got some blank spaces in those sentences to fill in.

Number three, solve these worded problems. Write them as an equation first.

A snail needs to crawl 8/10 of a metre to get to some tasty green leaves.

It travels 3/10 of a metre.

How much further does it have to go? And B, Aisha eats 1/6 of a pizza.

How much is left for Alex to eat? Okay, pause the video here, and when you finish those, I'll be back to give you some feedback.

Welcome back.

Let's look at number one first.

So be ready to mark.

The top one was represented by the middle representation.

7/10 subtract 5/10 is equal to 2/10.

You can see on the bar model that we had a whole at the top, which was seven.

Each of those counters was worth 1/10.

We had a part that was five and the missing part there four would've been 2/10.

But the second equation, this is what we had as a solution, 3/7.

That's because 7/7 subtract 4/7 was equal to 3/7, even though our final results switched round there, it doesn't matter.

As long as those two expressions are equal.

You can write it in whatever order you prefer.

But do remember that subtraction isn't commutative.

You can't swap round the minuend and the subtrahend like you can when you're using add-ins and addition, it matched that bottom bar model, and that's because the whole was 7/7, and we had 4/7 of one part, which is what we subtracted.

So the missing part was 3/7, and finally the bottom equation, 5/8 subtract 3/8 is equal to 2/8.

Again, the denominators are staying the same, and we could simply use a known fact of five subtract three is equal to two.

You can see that in the bar model at the top there.

Doesn't that look like a familiar structure? That was the one that we started off with when we were looking at our bananas, and our birds, and our pens.

Okay, ready to move on to look at number two.

Here we go.

For number two, we had to complete the stem sentences and solve the equation.

7/9 is seven lots of 1/9, 3/8 is three lots of 1/9.

I know that seven subtract three is equal to four, so I know that 7/9 subtract 3/9 is equal to 4/9, and then it's been written in fraction notation at the top to complete that equation.

Okay, let's move on to number three.

We had to solve the worded problems here.

It was about recognising the equation within the context to help.

So on the first one we had 8/10 of a metre subtract 3/10 of a metre.

So the answer was 5/10 of a metre, and for B, we had 6/6 subtracts 1/6 is equal to 5/6.

Did you get those? Is it making sense? I do hope so, because now it's time for us to move on to the second part of the lesson.

Here we're gonna look at a change in structure.

We are thinking no longer about partitioning, but now about reduction.

A full box of eggs contains 12 eggs.

First there were nine eggs in the box.

Then four eggs were used to make pancake batter.

Mm, pancakes.

Now there are five eggs left over in the box.

"This is another kind of subtraction question." The whole has been reduced to create a new amount.

This type of subtraction is called reduction.

Aisha represents the reduction on a number line "12 eggs in a full box, so I will draw my intervals from zero to 12." There they are.

Don't forget that interval means the gap between the marks on the number line.

Just be careful of that.

First, there were nine eggs in the box, then four eggs were used to make pancake batter.

Now there are five eggs left over in the box.

Alex reconsiders the reduction using fractions.

Always good to reconsider things that we know to be true in different ways.

If there are 12 eggs in a box of eggs, then each egg is 1/12.

So I will change the intervals to 1/12.

There they go.

First there were nine eggs in the box.

That's 9/12.

Then four eggs were used to make pancake batter.

So we subtract 4/12.

Remember, each egg is worth 1/12.

Now there are five eggs left over in the box.

That's 5/12.

Aisha uses a fraction equation.

First there were nine eggs in the box.

This is the minuend.

It is the fraction we began with 9/12.

Then four eggs we use to make pancake butter.

This is the subtrahend.

It's the fraction we subtract.

Take away 4/12.

Now there are five eggs left over in the box.

That's the difference.

It's what's left over.

So now our equation reads 9/12 subtract 4/12 is equal to 5/12, and it compares the reduction in partitioning equations and representations using the eggs and pizza questions.

Lots of comparison here is a great way to be able to learn in maths.

What do you notice? So look at these, and consider what's the same and what's different between them.

I noticed that the equations have the same structure.

I also noticed that in both of them, the denominator stays the same.

It is the numerator that gives the minuend and subtrahend.

Okay, let's check your understanding with a true or false.

When subtracting fractions with the same denominator, the denominator should be different.

Is this true or is it false? Pause the video, and think about this, and I'll be back with the answer in a moment.

Welcome back.

That was false.

So let's think about a justification for why it might have been false.

Here's two, and I want you to select the best one.

Is it A, the denominators are just a way of showing that it's a fraction so you can ignore them or is it B, the denominators are the unit you are calculating with, so they must stay the same.

Pause the video again whilst you have a think.

Okay, then which one did you think was best? Well, it was B.

The denominators aren't just a way of showing that it's a fraction.

You can't ignore them.

Denominators are actually the unit that we are dealing with, so we need to make sure that they stay the same.

Aisha and Alex look at another reduction problem.

First there were nine eggs in the box.

This sounds familiar.

Then four eggs were used to make pancake batter.

Then three eggs were used to make an omelette.

Obviously they like using eggs here.

What fraction of the eggs are left in the box now? What do you notice? "This time, There are two subtrahends to subtract." Alex uses a number line.

I'll use one 12th intervals again like I did last time.

Remember the intervals are the gaps between the marks.

He labels them carefully.

First, there were nine eggs in the box, so he starts on 9/12.

Then four eggs we use to make pancake butter.

So he takes away 4/12 to land on 5/12.

Then three eggs we use to make an omelette, and this is the extra bit.

He takes away 3/12 more, what fraction of the eggs are left in the box now? We can see that it's ended up on 2/12.

There are 2/12 of the eggs in the box remaining.

Aisha uses a fraction equation.

First there were nine eggs in the box.

"This is the minuend.

It is the fraction we began with," 9/12.

Then four eggs were used to make pancake batter.

This is the first subtrahend, the first fraction we subtract, take away four twelfths.

Then three eggs were used to make an omelette.

This is the second subtrahend.

We subtract this as well.

Take away 3/12.

What fraction of the eggs are left in the box now? I know that nine take away four, take away three is equal to two, so I know that 9/12 subtract 4/12 subtract 3/12 is 2/12.

There's the full equation written down.

Okay, let's check your understanding then.

What mistake has been made here.

Pause the video and have a look.

Welcome back.

We've got 10/11 subtract 3/11 subtract 4/11 is equal to 3/4.

I wonder what mistake they've made.

They have subtracted seven in total from the numerator, which is correct.

10 take away three, take away four is equal to three, but they have also subtracted seven from the denominator as well, which shouldn't change.

So it should be 3/11.

That's correct now.

All right, it's time for your second practise task.

You are gonna match the number lines with the fraction subtractions and solve them, similar to what you did last time, except the representations are now number lines instead of using bar models.

For number two, you're gonna draw this problem as a number line, write it out as an equation, and then solve it.

A box of chocolates can hold 15 altogether.

First, they were 12 chocolates in the box.

Then four chocolates were eaten by Aisha.

Then seven chocolates were eaten by Alex.

What fraction of the chocolates are left in the box now? Then we've got number three, and here you've got to find the missing numbers in the equations below.

Remember our generalisation, and the fact that the denominator will always remain the same, because it's the unit that we are using.

Okay, good luck, pause the video, and I will be back for some feedback shortly.

Here we go then.

Number one, are you ready to mark? Well, the top one match the top one on the other side, 6/7 subtract 2/7 subtract 3/7 is equal to 1/7.

The second one, 3/7 is equal to 7/7 subtract 4/7 match the bottom one.

And the bottom equation matched the middle number line.

Now you'll note that the only equation that features two subtrahends is the number line that has two jumps.

Okay, pause the video here if you want to discuss any of that, and I'll be back with number two feedback in a minute.

Okay, here's number two then.

You needed to draw it as a number line.

Here's the number line, zero and one at either end, and the intervals needed to be 1/15.

You needed to start on 12/15 because there were 12 chocolates in the box.

Then you were gonna subtract 4/15 from that.

You can see the equation forming here as well.

Then you needed to subtract 7/15 and you finished with 1/15.

12/15 subtract 4/15 subtract 7/15 is equal to 1/15.

Okay, here are the missing numbers then.

For A, it was 2/9.

Note the denominator stayed the same and that will be true for all of these.

For B, it was 5/8.

Now the difference was in a different place, wasn't it? The difference was at the start, but that doesn't matter.

As long as both expressions are equal value, then you can put them in any order you like.

For C, 13/16 subtract 5/16 subtract 3/16, that was equal to 5/16.

The denominator didn't change, and I know that 13 take away five take away three is equal to five.

Let's look at D then.

Here we started to have missing numerators and denominators.

Well, we know that the denominator's gonna stay the same, and then we've got a known fact of six subtract two is equal to four, so the numerator was four, and the denominator was seven.

Let's look at E.

We had 3/4 subtract 2/4 is equal to 1/4.

The way to work out that missing en numerator there was to use the inverse.

We had something take away two was equal to one, so if we did one, add two, we would've got three, and of course we know that the denominator is always four.

Let's look at F then.

12/20 subtract 4/20 subtract 5/20 was equal to 3/20.

The denominators are still all the same.

Okay, if you need a bit of time to finish marking those off carefully, then take it now by pausing the video.

Okay, that brings us to the end of the lesson then.

Here's a summary about the things that we've learned.

Subtraction has different contexts and structures such as partitioning and reduction.

When subtracting fractions with the same denominator, the denominator tells us the unit and the numerator denotes the minuend and subtrahends.

When subtracting fractions with the same denominator, the denominator stays the same and the numerator changes.

We can use known subtraction facts to support calculations involving subtracting numerators.

My name is Mr. Tazzyman.

I've really enjoyed today's lesson, and I hope you did too.

I'll see you again soon, bye-Bye.