Lesson video

Hello, my name's Mrs. Hopper and I'm excited to be working with you in this lesson from the unit on comparing fractions using equivalents and decimals.

I love fractions and I hope you do too.

And I hope during this lesson you'll be able to see and understand a little bit more about them and how they link to decimals.

So if you're ready, let's make a start.

So in this lesson, we're going to be recalling common fraction-decimal equivalents and using them in games and in some other mathematical activities as well.

So, let's make a start.

We've only got one keyword and that's equivalent.

So my turn, equivalent.

Your turn.

I'm sure you know what it means, but just let's remind ourselves.

Numbers are equivalent when they have exactly the same value and it's important to remember that.

They can look quite different.

They could be a fraction, they could be a decimal, they could be two different fractions that look different, but have the equivalent value.

They are exactly the same.

Two parts to our lesson.

In the first part, we're going to be recalling fraction and decimal equivalents and in the second part, we're going to be recalling and comparing them.

So let's make a start with part one.

And we've got Lucas and Sam helping us today.

So you can work out fraction and decimal equivalents, but it is really useful to know them off by heart.

They're a bit like an extension of our times table facts and other number facts.

Really useful to know them because it can help us to be more efficient when we're calculating and working our answers to problems. So let's have a look at completing this table.

You might want to have a little look and think what you could fill in straight away and what you might have to do a bit of thinking about.

Let's see what Sam and Lucas have come up with.

Lucas says, "I know that 1 half is equivalent to 5 tenths, which is 0.

5." Yep, really good one to remember.

Well done Lucas.

Sam says, "I know that 1 fifth is equivalent to 2 tenths, which is 0.

2." Well done Sam.

That's a really good one to remember.

Sometimes one that we might overlook a little bit, but a really useful one to know.

Okay, over to you.

If you know that 1 fifth is 0.

2, can you work out these missing values here? So use what Sam knew and see if you can work out those missing values there.

Pause the video, have a go and then we'll look at the answers together.

What did you reckon then? Sam says, "1 fifth is 0.

2.

So 2 fifths must be 0.

4." Lucas says, "0.

6 must be equivalent then to 3 fifths and 0.

8 to 4 fifths 'cause we're adding a fifth each time, 3 fifths and then 4 fifths." I hope that's what you've got too.

Is that the thinking you used as well? "1 fifth is 0.

2, so 2 fifths is equal to 0.

4.

There's an extra 0.

2 for every 1 fifth you add," says Sam.

So which other equivalents can you remember? Oh, Sam's remembering the interesting one.

"I remember that 1 third is equivalent to 0.

33333." Well it's almost equivalent Sam.

It's not exact, but it goes on forever.

So there's 0.

333.

"Oh," says Lucas, "then 0.

6666666, going on forever and ever and possibly rounded up to 7, must be equivalent to 2 thirds." So we can add in that fraction as well.

Okay, which of the remaining gaps can you work out by knowing about tenths and hundredths as decimals and fractions? So have a think about tenths and hundredths and see which ones you can work out.

Pause the video, have a go, and we'll come back together for some answers.

How did you get on? Sam says, "Well 0.

1 is 1 tenth.

So the fraction equivalent must be 1 tenth written as a fraction." So there we go.

So there's our 0.

1 as 1 tenth.

And Lucas says, "0.

01 is 1 hundredth.

So the fraction equivalent must be 1 one-hundredth." Okay.

"There's another 0.

2, which is 2 tenths, which is 2 tenths as a fraction." Ah, that's interesting, isn't it? So there's another 0.

2 in our chart, which is 2 tenths is equal to 1 fifth.

They are equivalent.

And there it is.

Okay, so what do you know about quarters and eighths to help you fill in the final gaps? So that's all we are left with.

Pause the video, have a go, and we'll get back together for the answers.

How did you get on? Sam says she remembers, that, "0.

25 is equivalent to 1 quarter, so 3 quarters must be equivalent to 0.

75." Well done, Sam.

We could have worked through 25 one-hundredths and then simplified, but it's a really useful one to know and this is about remembering, recalling those fraction and decimal equivalents.

Okay, Lucas, it's over to you for the remaining gaps.

Ah, he says, "0.

125 is half of 25, so it must be equivalent to 1 eighth.

So 3 eighths then must be equal to 0.

375.

1 eighth is 0.

125, 3 eighths is 0.

375." And Sam says, "We did it.

Now we need to remember them all." It is useful to remember them all.

You can work them out and it's always useful to know where they've come from and how they've been worked out, but if you can remember them, it will save you time when you are working with fractions and decimals in the future.

Right? Lucas says, "We can play 'Snap' with these cards to test our knowledge." "We each turn over a card and if they are equivalent, the first person to say 'Snap' keeps them." I'm sure you've all played "Snap" before, but I wonder if you've played them with fractions and decimals? Okay, let's see.

Can you beat Sam and Lucas? Let's have a look.

Nobody's saying anything.

Well done.

Nobody's saying anything.

Oh, well done.

Oh, Lucas, I think you were just there first.

"You just beat me to it," says Sam, "well done." Lucas says, "I remember that 1 third is equivalent to 0.

333333.

So 2 thirds is equal to 0.

66666." Well done Lucas, and he gets to keep the cards.

Okay, so time for you to do some practise and you are going to play "Snap." So you've got the set of cards that Lucas and Sam were using.

If you don't make a pair, challenge yourselves to write down the equivalent fractional decimal as quickly as you can.

So we are really looking for those equivalences.

But if you want an extra challenge, you could write down the equivalent fraction or decimal if they aren't equivalent in your pair.

So pause the video, have a go at playing "Snap," and we'll come back and look at some of the ones that we chose.

They probably won't be the same as the ones you chose.

Pause the video and we'll see you later.

So did you have fun playing "Snap?" I hope you did.

Here was one that we turned over.

So we turned over 0.

4 and 1 quarter.

Is it a snap? No, it's not a snap is it? But I wonder if we can challenge ourselves to write down the equivalences.

Oh, Lucas says, "Oh no it isn't snap is it?" There's a 4 there, but they aren't representing the same thing.

Sam says, "A quarter is equal to 0.

25 as a decimal, so it's not a snap." And 0.

4 is equivalent to 4 tenths as a fraction.

So they're not equivalent, are they? Okay.

And on into the second part of our lesson.

We're going to recall and compare fraction and decimal equivalents.

So we're going to do some comparison in this one as well, but also work on recalling them as quickly as we can.

So how would we solve this problem? We've got 0.

75 plus 1 quarter is equal to something.

Well, Sam says, "I can write the fraction 1 quarter as 25 one-hundredths or 0.

25." So we could rewrite the fraction as a decimal.

And then we could rewrite our equation.

So this time we've got 0.

75 plus 0.

25.

But Lucas says, "I know the equivalent fraction for 0.

75 is 3 quarters." So we could rewrite the equation using fractions.

3 quarters plus 1 quarter is equal to.

Now I wonder which one of those you feel most confident with or most comfortable with? Or Sam says, "0.

75 plus 0.

25 is equal to 1." And Lucas says, "3 quarters plus 1 quarter is equal to 1." It's entirely up to you.

And you may feel more confident with one of those than the other.

One of them might just sit in your mind more easily than the others.

I think 3 quarters plus 1 quarter to me makes sense, And look at 0.

75 and 0.

25.

And I sort of think about, oh, exchanging and there's lots of stuff going on there.

3 quarters and another quarter is equal to 1 whole.

But it is entirely up to you which way you see it as the way that works best for you.

Whichever way worked for you though, the answer to all of those calculations or equations is 1.

Knowing the fraction and decimal equivalence means that you can rewrite one of the add-ins to solve the calculation and you can rewrite it the way that works best for you.

Time to check your understanding.

Can you use fraction and decimal equivalences to solve this problem? Pause the video, have a go, and then we'll look at the possible answers.

How did you get on? Of course, there's only one answer to the calculation, but there's different ways we might have got there.

Sam says, "I can write the fraction 3 tenths as 0.

3." So she's really written the equation as 0.

4 plus 0.

3.

Lucas says, "I know that the equivalent fraction for 0.

4 is 4 tenths." 4 tenths plus 3 tenths is equal to.

I wonder which way appeals to you most as the way to solve the problem? This time, I think, I don't mind which way round it is because I know about 4 plus 3.

And so I know that 4 tenths plus 3 tenths is equal to 7 tenths, whether that's a decimal or a fraction.

So Lucas has solved it using the fractions and Sam solved it using the decimals.

But however we've solved it, we know that the answer is 0.

7 or 7 tenths.

So now we're going to use our knowledge of those fraction and decimal equivalents and the fact that we can convert between them to order some numbers from the smallest to the largest.

So can you use your knowledge of equivalence to convert between fractions and decimals in order to do this? You might want to stop and have a little look before we go through it together.

But here we've got a mixed group of fractions and decimals.

Ah, Lucas says, "I know that two thirds is 0.

66666." He's just put the 3 sixes there.

So we can rewrite the fraction 2 thirds as 0.

66666.

So there we go.

Are there any others that you know? Oh, he says, "I also know that 1 half is 0.

5." So Lucas is working to change the fractions into decimals.

"Okay," says Sam, "I know that 3 quarters is 0.

75 and place value said that 5 one-hundredths must be 0.

05." She's thinking of the place value chart.

So now we've got all our numbers expressed as decimals.

Now that Sam and Lucas have found the decimal equivalents, they can order the decimals.

So they can order that mixed set, but now they've got them all expressed as decimals, they'll be able to order them easily.

So 0.

04 is the smallest, then 0.

05, then 0.

4, 0.

5, 0.

6666, 0.

7, and 0.

75.

So there are our decimals ordered from smallest to largest.

Now this time Sam and Lucas have found the fraction equivalents and ordered them.

Have they done it correctly? Time to check your understanding.

Can you pause the video and check to see whether they've ordered the fractions correctly, having converted the decimals into fractions? So pause the video, have a go, and we'll look at the answers together.

What did you think? Well, Sam and Lucas have correctly found the fraction equivalents, but they have not ordered the fractions correctly.

Can you see what they've done? They've made a mistake, haven't they? They have assumed that the smallest number denominator is the smallest fraction and the largest denominator is the largest fraction, and we know that's not how things work with fractions.

The larger the denominator, the more pieces there are in the whole.

Okay, so over to you.

Can you order the fractions correctly? Pause the video, have a go, and then we'll look at the order together.

How did you get on? So this is the correct order.

Hundredths are much smaller than tenths and we've only got 4 and 5 of those hundredths, so they're both much smaller than 4 tenths.

And we know that 4 one-hundredths is smaller than 5 one-hundredths.

And you can now compare the fractions to 1 half.

So 2 thirds, 7 tenths and 3 quarters are all greater than a half.

3 quarters is greater than 7 tenths.

Do we know that 3 quarters is greater than 7 tenths? Well, a quarter of 10 we know is 0.

25.

So 3 quarters of 10 must be 0.

75 outta 10.

So 7 outta 10 must be smaller than 3 quarters.

And we might think of our decimals to know that 2 thirds is smaller than 7 tenths, 0.

6666 is smaller than 0.

7.

So you might go back to thinking about decimals to compare some of them, or you might think about those common divisions of 10 in order to help you.

Time for you to do some practise.

You are going to use your knowledge of fraction and decimal equivalents to solve these equations.

Remember, if we can find the fraction that's equivalent to a decimal or the decimal that's equivalent to a fraction, we can substitute it, we can use it to replace that part of the equation.

And for question two, you're going to order these numbers from the largest to the smallest, or we've changed the order this time.

So from the largest to the smallest.

And remember, you can convert the fractions into decimals or the decimals into fractions, whichever way you find is best.

So pause the video, have a go at your two tasks, and we'll get together for some answers and some feedback.

How did you get on? So here are the first ones of our equations.

So you could convert the fractions into decimals for A, B, C, and D.

So 3 tenths is equal to 0.

3.

So the calculation will become 0.

6 plus 0.

3 is equal to 0.

9.

0.

05 subtract 1 one-hundredth becomes subtract 0.

01 and gives us an answer of 0.

04.

0.

75 plus 1 quarter becomes 0.

75 plus 0.

25.

And we know that that is equal to 1.

75 plus 25 hundredths are equal to 100 hundredths, which is equal to 1.

And finally we had 0.

8 subtract 5 one-hundredths.

So 0.

8 subtract 0.

05, which gives us 0.

75.

You could convert different ways for E, F, G, and H.

So you might have decided to do some in one way and some in another way.

This is how we did it.

So for E, you could have converted the 0.

333 into 1 third or the 0.

666 into 2 thirds.

But whichever way, we've got 2 thirds subtract 1 third, which equals 1 third or 0.

3333 carrying on forever, whichever way you did it.

So for F, we could have converted 1 tenth into 0.

1, and then we've got 0.

1 plus 0.

01, which gives us 0.

11.

For G, we could have converted the 0.

6666 into 2 thirds or the 2 thirds into 0.

666, but whichever way, we end up with 2 thirds subtract 2 thirds or 0.

666 subtract 0.

666, both of which are equal to 0.

We're subtracting the same thing from itself.

And for H, we could have converted 9 tenths into 0.

9 or 0.

5 into 5 tenths.

But whichever way, we end up with 9 tenths subtract 5 tenths, which is equal to 4 tenths, and we can express that as a fraction or a decimal.

For part two, you had to order the numbers from the largest to the smallest.

So you could convert the decimals into fractions.

So we'd have had 3 tenths, 5 tenths or 1 half and 5 hundredths or 1 twentieth.

Or, you could have converted the fractions into decimals.

So we'd have had 1 fifth is equal to 0.

2, 1 third is equal to 0.

333 and 1 quarter is equal to 0.

25.

So you could now decide to order the decimals or the fractions.

Whichever way you chose to order it, the correct order was the largest was 1 half, everything else was less than a half.

Then 1 third, 0.

333.

0.

3, which is smaller than a third.

1 quarter, which is smaller than a third and smaller than 0.

3 'cause its decimal is 0.

25.

1 fifth, which has a decimal of 0.

2.

And the smallest was our 0.

05 or 5 one-hundredths or 1 twentieth.

I hope you were successful.

I wonder if you went for the decimal option or for the fraction option? And we've come to the end of our lesson.

We've been recalling common fraction and decimal equivalents, and we've been using them to help us to solve inequalities and to solve equations.

What have we learned? We've learned that it is useful to know common fraction decimal equivalents by heart so that we don't have to work them out each time, but that converting between fractions and decimal equivalents can help to calculate and order fractions and decimals.

If we have forgotten those equivalences, then thinking of fractions as equivalent fractions with 10 or a hundred as the denominator can help you to convert fractions into their decimal equivalents.

Thank you for all your hard work and your mathematical thinking today, and I hope I get to work with you again soon.

Bye-Bye.