Lesson video

Hi, my name is Mr. Whitehead, and I am here ready for your Maths lesson.

I'm hoping that you are ready for that lesson to start.

You'll know if you're ready if you are sat in a quiet space, free of distractions, where you are able to give me your full attention for the next 20 minutes.

If you're looking around you and thinking, perhaps there are a few distractions ready and waiting for you, please press pause now, take yourself off somewhere quieter or switch those distractions off.

Press play again as soon as you're ready to start the lesson.

In this lesson, we will be converting between mixed numbers and improper fractions.

We're going to start off with a skip counting activity.

Then we will focus on identifying value when looking at representations of fractions.

From there, we will look at those relationships and how we can convert between mixed numbers and improper fractions.

That will leave you ready for your independent task at the end of the lesson.

Things that you're going to need, a pen or pencil, some paper or pad or book from school, and a ruler.

Pause while you go and collect those items, come back as soon as you've got them and we will start.

Take a look at the number stick and notice the number of divisions.

How many are there? 10.

What is the length of the stick? Good.

One tenth or 10 hundredths is the distance between one tenth and two tenths, 10 hundredths and 20 hundredths.

Let's count in hundredths back from 20 hundredths.

My turn, your turn.

20 hundredths, 18 hundredths, 16 hundredths, 14 hundredths, 12 hundredths, 10 hundredths.

Fantastic.

If we were to continue counting back from 10 hundredths, what would the next number be? And the one after that? Good, eight hundredths.

Well done.

Okay.

Mixed numbers, improper fractions and converting between them.

Let's start by looking at these rods.

The white rod is worth one half.

I want to know what the other rods are worth, just in words.

If you want to pause and make your list of them in words, do that now.

Otherwise, play along and say as we go.

If the white rod is worth one half, then the red rod is worth? One, good.

The green? The pink? The yellow? Now look carefully for the black.

Fantastic.

Why is it an increase of one and not an increase of half? Good.

The difference between yellow and black is one red, not one white.

So the last one, the blue, same again, there's an increase of two halves.

An increase of one red, two white, black and red, black and two white make blue, make dark blue.

So that in words, the value? Good, four and a half.

Do the same, but as decimal numbers now.

So if the white rod is worth zero point.

Thank you, 0.

5, then the red rod is worth? Good, keep going.

Green? Pink? Yellow? Black? Good work, 3.

5.

Blue? 4.

5.

Notice the increase of one instead of one half for the final two rods.

Same again, but now as mixed numbers, really nice link to how we say the values in words.

If the white road is worth half, then the red rod is worth? One.

Green? One and a half, one and a half, we record as a one and a fraction half.

There's your mixed number.

Pink? Yellow? Well done.

Black? Oops, sorry, I missed that for the yellow, yellow? Two and a half.

Thank you for spotting that missed part of the mixed number.

Black? Yes, three and a half.

Blue? Four and a half.

Well done.

They are your mixed numbers.

Finally for this set of rods where white represents half, let's represent these now, please.

The values of the rods as improper fractions.

Just tell me the number of halves that each rod is equal to.

What? One half? Red? Two halves.

Good.

How many for green? Yeah, pink? Yellow? Black? Yes, an increase of two halves.

Blue? Super.

Now watch.

Notice how many halves make each rod? How many halves each rod is equal to.

That's what we can record as improper fractions.

The number of halves.

What do you notice about the numerators on these fractions? Good.

They are all larger numbers than the denominator as a number normally.

Well, not normally, if the fraction is not improper, if it's proper, then the numerator will be smaller than the number that is the denominator.

If the white rod is worth one quarter, I'd like you to count in quarters with me, just in representing the number of quarters that there are.

So one quarter, let's count together.

Two quarters, three quarters, four quarters.

Uh, four quarters equal to? One.

Continue in quarters.

Five quarters, six quarters, seven quarters, eight quarters equal to two.

Continue.

Nine quarters, 10 quarters, 11 quarters, 12 quarters equal to? Three.

Continue.

13 quarters, 14 quarters, 15 quarters equal to? 15 quarters equal to three.

One, two, three, and three quarters.

Can you see it? I'm showing you here, the improper fraction, the number of quarters, 15 of them and the mixed number three and three quarters.

They're equivalent values.

15 quarters, three and three quarters.

A really nice way to visualise the link between improper fractions and mixed numbers.

How many individual quarters in this case, and then as those quarters are arranged, how many wholes are we making from them? Four quarters, one whole.

Another four quarters? Another whole.

And in this case, a third whole from our third set of four quarters.

Let's have a look at another one.

This time one white rod is worth one fifth, can we count in fifths? Ready? One fifth, two fifths, join in.

Three fifths, louder.

Four fifths, five fifths or one.

Continue in as an improper, telling me the number of fifths.

Continue.

Six fifths, seven fifths, eight fifths, nine fifths, 10 fifths, or two 10 fifths, or two, keep going.

11 fifths.

11 fifths is where we stop.

As a improper fraction, it's the number of fifths that there are.

11 fifths as a mixed number what would it be? Two and one fifth.

If we just go back, when we got to here, we'd had five fifths and we said one.

I'd like you to now carry on, but as mixed numbers.

So our next one is one and one fifth.

Next? One and two fifths.

Keep going.

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

And that's where we stop.

We had 11 fifths.

We've created two and one fifth from that.

If the white rod is worth one quarter, you ready? Two quarters, three quarters, four quarters.

I'm going to count in improper fractions.

I want you to count as mixed number.

So right now when I say four quarters and you say? Four.

So do as a my turn, your turn, five quarters? One and one quarter, good.

Six quarters? One and two quarters, or you might say one and a half.

Seven quarters? Good, one and three quarters.

I say eight quarters, you say? Super, two.

Oh, nine quarters? 10 quarters? 11 quarters? What did you say? Two and three quarters, yeah.

12 quarters? It's challenging this.

I'm thinking about what you're saying and what I'm saying.

I say 13 quarters, you say? Good, three and one quarter.

14 quarters? 15 quarters? What did you say? Three and three quarters, good.

And I say 16 quarters, you say? You say four.

I say 16 quarters, you say four.

The improper fraction? 16 quarters.

Why is the mixed number just a four? 16 quarters we've made four lots of one whole, four lots of one whole using 16 of the quarters.

Four lots of four to create our four lots of one whole.

Right.

I've got some mixed number and improper fractions for you.

I'd like you to draw an image to represent them.

An image to represent two and two thirds, and an image to represent eight thirds, then an image for 15 quarters, and an image for three and three quarters.

With those images, you'll be able to compare the two fractions.

Are they equal in value? Is one greater than the other? Is one less than the other? Pause, really think carefully about those images you're drawing.

For the ones I used, it was always based around that one white square and that one white square representing seven.

So it represented quarters.

It can represent fifths.

And in your case, it can represent thirds.

Just think carefully about how many of them you need, and how many of them would create a whole.

Come back when you're ready.

How did you get on? Hold your paper up, please.

Let me look.

Oh, now I know this is not an art lesson.

It is a Maths lesson, but wow, have you worked hard to keep these drawings neat? Mathematically neat, really important from a Maths point of view, that what you have drawn is representing the maths.

I'm really glad that those squares are looking equal in size.

Well done.

Compared to what I've got here.

So, first of all, I'm representing two and two thirds.

I'm going to represent eight thirds above it.

What did we find out about the mixed number and the improper fraction? They're equal, eight thirds and two and two thirds are equal.

The next one, I drew 15 quarters.

So now my squares are not representing thirds.

Each square is a quarter.

I've got 15 of them and underneath I'm representing three and three quarters.

Now one is four quarters.

Another one, so two, that's eight of my quarters.

My third whole is 12 of my quarters, four, eight, 12 quarters, and three quarters, 15 quarters, three and three quarters.

What have we discovered about these two, the improper fraction and the mixed number? They are equivalent as well.

They are worth the same value.

True or false now.

Are these two also equal in value? Press pause, use your drawings again, a little bit of a challenge in how I've represented that decimal, but I know you've got some connections you can make from decimals to fractions.

Use some drawings to prove whether or not this is true or false.

Come back when you're ready.

How did you get on? Hold your paper up, I want to see, keep it steady.

Oh, you are blowing me away again.

Look at this, fantastic.

The drawings, it's not art.

It's Maths, but it could be art.

They are just so neat.

Mathematically neat, and representing what they need to represent.

Well done.

Can I show you mine? Well, first of all, hands up if you thought that this was true, and you're drawing proves it's true.

Who thinks it's false? And does your drawing prove it's false? Yeah, let's see.

So I thought about 5.

25 was five and something point two five, 0.

25.

I know that's a quarter, it's five and a quarter.

So I'm comparing five and a quarter with 21 quarters, five and a quarter just fits on my screen and 21 quarters.

21 quarters also fits on my screen.

Four quarters is one whole.

Four, eight, 12, 16, 20 quarters is five, one quarter more, five and a quarter.

So the drawing has proved that it is indeed true.

It is definitely time for you to have a go at this independently now.

Some similar tasks for you to the ones we've just looked at.

Use drawings, use your visualisation skills.

Do you agree with the statements or not? Come back when you're ready to have a look at it together.

Okay.

Hold up your paper I want to see.

Fantastic.

Look at this.

Look at these drawings everyone, you've worked so hard.

You're really showing how deep your understanding is through the drawings that you've been choosing there.

And I'm really, really pleased with it.

Paper down, let's check off and compare.

So true or false for the first one? 4.

2 comparing to 20 fifths.

I'm making some connections, 4.

2, two in the tenths place, four and two tenths, four and two tenths compared to 20 fifths.

Well I know that four and two tenths is the same as four and one fifth.

Okay, four and one fifth compared to 20 fifths.

Four and one fifth, 20 fifths, 20 fifths would be the same as four, five, 10, 15, 20.

I would use twenty fifth to create four.

So four and one fifth is actually greater than four, only just by one fifth.

So I think this is false, it needs to be a greater than symbol.

I haven't shown a drawing here, but I know that you have on your paper and that's what's led you to your solution.

So I'm just talking you through at this point my thinking, the changes I've made that have led all the way to the solution.

Next one, who thought this was true? Okay, false? 33 sixths compared to five and a half.

I need to make some changes, 33 sixths.

Well, that's equal to five.

Well, sorry, we're finding out if it's equal.

Five and a half is equal to five and three sixths.

If I make a change to my half and give an equivalent fraction in sixths, I can then start to compare more easily.

So 33 sixths, is that equal to five and three sixths? Well 33 sixths, What's that as a mixed number? Six, 12, 18, 24, 30.

I can create five wholes using 36.

I would have three sixths remaining, five and three sixths, that's equal to five and a half.

It's equal to five and three sixths.

Now I chose to work this way.

I chose to represent my improper fraction as a mixed number.

I could have kept 33 sixths and converted five and three sixths into an improper fraction as well.

I would then have had another set of 33 sixths.

I still have the same solution.

It's a different way to approach it.

I wonder if you approached it this way or in a different way.

Give me a thumbs up if you thought true, and a thumbs down if you thought false.

Okay, so this time three and three fifths compared to 36 tenths.

I made a change three and three fifths, I changed to three and six tenths because now I can compare tenths.

Three and six tenths and 36 tenths.

Well, 36 tenths, how many can I represent that as a mixed number using the number of tenths that I need to create a whole? 10 20, 30, a three.

So I can create three wholes and I'll have six tenths remaining.

Three and six tenths is equal to three and six tenths.

It's the correct symbol.

This is true.

Last one, 2.

75 is equal to 20 eighths.

Whoa, they're some changes to make.

Two and 0.

75, two and three quarters.

Quarters compared to eighths? Two and three quarters, that's two and six eighths.

Two and six eighths compared to 20 eighths.

Okay, 20 eighths.

How many as a mixed number? What is that? 20 eighths, a 16.

I can make two wholes using 16 eighths.

I've got four eighths remaining.

Two and six eighths is greater than two and four eighths.

2.

75 is greater than 20 eighths.

This statement is false, it should be the greater than symbol.

I didn't show you my drawings, but I would love to see yours.

So please, if you would like to share your learning from this session, please ask your parents or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

That was a fantastic lesson.

Thank you so much for joining me.

Once again, I am feeling really proud of all of your contributions and your fantastic learning.

You should be feeling really pleased and proud of yourselves as well.

If you've got any more learning lined up for the day, take a well earned break first.

That's exactly what I'm going to do.

I look forward to seeing you again soon for some more maths.

Until then, look after yourselves and I will see you soon.

Bye.