# Lesson video

In progress...

Hello, everybody.

My name is Mr. Kelsall, and welcome to today's lesson about adding and subtracting fractions fluently.

Before we start, you are going to need a pen and a piece of paper.

Also, please try and find somewhere quiet, somewhere you're not going be disturbed.

And don't forget to remove any source of distractions.

For example, put your mobile phone on silent or move it away completely.

Pause the video, and then when you are ready, let's begin.

Today's lesson is learning to add and subtract fractions fluently.

By this I mean accurately, efficiently and flexibly.

We are going to start by counting fluently in fractions.

We'll then look at how to convert mentally and then we will look at how to convert fluently.

After that, it's quiz time.

I mentioned that you'll need a pen and a piece of paper.

Our star words for today are fraction, denominator, numerator and vinculum.

We are going to be talking about proper fractions, improper fractions and mixed number fractions.

We will be talking about equivalent fractions and simplifying a fraction.

And to do this, you'll need to find a common denominator.

A quick reminder of what you will need for today: you'll need to understand a fraction is a part of a whole, the denominator is the number of parts the whole is split into, while the numerator is the number of parts of the whole selected.

The vinculum is the line between the numerator and the denominator.

A proper fraction is where the numerator is less than the denominator.

An improper fraction is where the numerator is greater than the denominator.

A mixed number fraction is where you've got a whole and a fraction together.

An equivalent fraction is a fraction that represents the same number.

And to simplify a fraction, you need to reduce the numerator and the denominator at the same time.

If you've got a fraction with the same denominator, you can just add the numerator.

If you've got a fraction with a common denominator, you need to find equivalent fractions and then just add the numerator.

We also need to think about crossing a barrier and think how you are going to achieve this.

So, let's start with some new learning.

We're going to count forwards, backwards, as a fraction, decimal, mixed number, improper fraction.

So, we are going to start in tenths.

I will start.

Can you count along with me, please? We're going to start at 0.

6, 0.

7, 0.

8, 0.

9, 1.

0, 1.

1, 1.

2, 1.

3.

Let's stop and let's go backwards.

1.

3, 1.

2, 1.

1, 1.

0, 0.

9, 0.

8, 0.

7.

Probably do the same scale in fractions, in tenths.

Six tenths, seven tenths, eight tenths, nine tenths, one whole one, one and one tenth, one and two tenths, one and three tenths.

And backwards, one and three tenths, one and two tenths, one and one tenth, one.

Nine tenths, eight tenths, seven tenths.

Okay, this time we're going to do a similar thing, but I'm going to give you the starting point and I'd like you to carry on counting on your own.

We're starting with hundredths.

97 hundredths.

You should have said 98 hundredths, 99 hundredths, a hundred hundredths, which is one whole one, one and one hundredth, one and two hundredths, one and three hundredths.

If we count backwards, one and three hundredths, one and two hundredths, one and one hundredth, one, 99 hundredths, 98 hundredths, 97 hundredths.

Okay, you get the idea of this now.

Let's carry on and let's count in halves.

Three and a half, four, four and a half, five.

Five, four and a half, four, three and a half, three, two and a half, two.

Same scale in thirds.

Let's start at two.

Two, two and one third, two and two thirds, three, three and one third, three and two thirds, four, four and one third, four and two thirds, five.

Let's count backwards.

Five, four and two thirds, four and one third, four, three and two thirds, three and one third, three, two and two thirds, two and one third, two.

And let's repeat this in quarters.

This time I'm going to start at six.

Six and one quarter, six and two quarters, six and three quarters, seven, seven and one quarter, seven and two quarters, seven and three quarters, eight.

Let's count backwards.

Eight, seven and three quarters, seven and two quarters, seven and one quarter, seven, six and three quarters, six and two quarters, six on one quarter, six.

Let's start at fifths.

Four fifths, one, one and one fifth, one and two fifths, one and three fifths, one and four fifths, two, two and one fifth, two and two fifths.

Let's count backwards.

Two and two fifths, two and one fifth, two, one and four fifths, one and three fifths, one and two fifths, one and one fifth, one, four fifths, three fifths.

Okay.

What I'd like you to do, is if you feel confident with this, move to the next slide.

If you feel you need a bit more practise, rewind the video, go back and practise these again.

You can also practise writing in mixed number fractions, improper fractions, decimals.

If you struggle, maybe write it down to begin with, and then read out, count it fluently forwards, fluently backwards.

This is a skill you really need to practise before you can truly truly understand fractions.

So pause the video, practise what you need, and then when you're ready press play to continue.

Well, for our first skill, we need to be able to mentally add and subtract fractions.

And to do this, you need to first of all, find the lowest common denominator.

You then need to convert mentally and then add and subtract.

So, if we start by writing it down and then we're going to move from writing it down to doing it, in our heads.

So, to begin with, first move one half add one quarter.

I'm trying to make this a common denominator of four.

So I'm converting one half, to quarters.

And I know one half is two quarters.

Two quarters add one quarter is three quarters.

I need to do that process mentally.

I need to mentally say, "A half is the same as two quarters.

Two quarters add one quarter is three quarters." So I'm going to do that on the next example.

Two thirds add on one sixth.

Converting thirds to sixthses.

Two thirds is the same as four sixthses.

Four sixthses one add one sixthses is five sixthses.

I think maybe the most difficult parts of that is identifying how to convert thirds to sixthses.

And if I need to do, I can imagine a picture of two thirds and I can split it to get my four sixthses.

We need to move away from these pictures eventually, so just use those as a backup.

Okay? Let's try again.

This time we've got three quarters takeaway two eighths.

I'm looking at quarters and eighths, and I need to convert them to eighths.

Three quarters is the same as six eighths.

Six eighths take two eighths gives me four eighths.

I also know that this isn't in its simplest form.

So I can simplify it as two quarters, and ultimately simplify it to become one half.

My next question is four fifths takeaway one tenth.

Again, I need to convert fifths to tenths.

I double it.

Four fifths is the same as eight tenths.

Eight tenths take one tenth is seven tenths.

So we're now moving to multi step questions.

With this question, five sixthses take six twelfths, add one third.

I can, first of all, find the lowest common denominator or I can just find a common denominator.

The lowest common denominator is sixthses, whereas a common denominator would be twelfths.

I'll show you how to do it both ways, and you'd decide which is fastest.

Method one, five sixthses is the same as 10 twelfths.

I'm going to take away six twelfths and I'm going to add one third.

One third is the same as, four, eight twelfths, three, six, nine twelfths.

That's the same as four twelfths.

So, 10 twelfths takes six twelfths is four twelfths.

Add another four twelfths, gives me eight twelfths.

And I can simplify that if I need.

That's the same as four sixthses, which is two thirds.

I'll show you method number two.

This time I'm converting to sixthses.

So five sixthses remains the same.

Six twelfths, I can simplify that to become three sixthses.

And, one third, I can find an equivalent fraction.

That becomes two sixthses.

I've now got five sixthses take away three sixthses is two sixthses.

Add another two sixthses is four sixthses.

I know that four sixthses is equivalent to two thirds.

Now, the second method we found the lowest common denominator, sixthses, whereas the first method, we just found a common denominator.

You decide which you think is the quickest way to solve this.

Now it's time to develop our learning.

Add these fractions: the sum of the two bricks is equal to the brick above.

So if I look an example from the first one, if I add one half and one quarter, that will give me the sum of this brick.

I know that one half and one quarter.

A half is the same as two quarters.

Add one quarter is three quarters.

Have a look at the other side.

Now, if I start with one and one fifth, I need to take away 11 twentieths to give me this missing box here.

Okay, I've give you the starting point.

Pause the video, have a go and press play when you're ready.

I know one quarter add one eighth.

A quarter is the same as two eighths.

Two eighths add one eight is three eighths.

Three eight add three quarters.

Three quarters is the same as six eighths.

Six eighths add three eighths is nine eighths.

If I want to write as a mixed number fraction, it's one and one eighth.

The question two, I started and I converted one and one fifth as one and four twentieths, and then took away 11 twentieths.

I have to count it down.

So I said four twentieths, three twentieths, two twentieths, one twentieth, zero twentieths.

And then add another seven to go.

So, 19 twentieths, 18 twentieths, 17 twentieths, 16 twentieths, 15 twentieths, 14 twentieths, 13 twentieths.

So, one and four twentieths taken away 11 twentieths gave me 13 twentieths.

I then tried to solve blocks at the bottom.

I did 11 twentieths to take away three tenths.

Three tenths is the same as six twentieths.

So 11 twentieths take away six twentieths gave me five twentieths.

I could simplify this to give me one quarter.

I then did 13 twentieths take away five twentieths to give me eight twentieths.

And again, I can simplify my eight twentieths.

I can simplify as four tenths, or I simplify it further as two fifths.

Now it's time for your independent task.

Luca pole vaults at a height of four and a quarter metres and Marcus pole vaults three quarters of the metre less.

How high does Marcus jump? Pause the video, and when you're ready press play for the answer.

Marcus' jump is three and a half metres.