Lesson video

Hi here.

My name's Ms. Lambo.

Really pleased that you've decided to join me today to do some maths.

Come on, let's get started.

Welcome to today's lesson.

The title of today's lesson is Problem Solving with Fractions and Decimals.

And this is within our unit, comparing and ordering fractions and decimals, including positives and negatives.

By the end of this lesson, you'll be able to use your knowledge of fractions and decimals to solve problems. So this lesson might be a little bit different to ones you may have seen previously.

A reminder of some words or key phrases.

An improper fraction is a fraction where the numerator is greater or equal to the denominator, and proportion is a part to whole, sometimes part to part comparison.

So we are using that word proportion later on.

Today's lesson, I've split into three separate learning cycles.

In the first one, we'll just concentrate on solving problems with fractions.

Then we'll move on to looking at problems with decimals.

And then once we've done that, we'll be confident to be able to mix those two things together and solve some nice complicated problems. Let's start with the first one, solving problems with fractions.

Laura and Jacob are going to help us work through this.

We've got to arrange five different digits into this inequality.

So here are our boxes and we need to place five different digits into the boxes so that the one on the left is greater than the one on the middle, and that's greater than the one on the left signified by our inequality symbols.

Laura puts these digits into the inequality and asks Jacob to check if she's right.

Let's see what Laura did.

So she decides to put in, she decides to use to do one, two, three, four, five and she puts them in like this.

How could Jacob check if she's right? Well, Jacob has said already that can't be right because you have two improper fractions and said they are less than one.

Ah, yeah, oh yes, Laura spotted her mistake.

Improper fractions are greater than or equal to one, so therefore that can't be right.

Jacob wants to have a go now, let's see whether Jacob can solve this problem.

He decides to put his digits in in this arrangement.

He's used the same digits one to five, but he's arranged them differently.

How can Laura, so it's down to Laura to check now.

How can she check he's right? She says, I can change them all into decimals to check if you are right.

By this point, we are super confident with converting from fractions to decimals.

That's how we do it.

And remember, three quarters is one of our important ones that often we can just remember.

Two fifths again, there's how we get to 0.

4, but lots of you will remember that 0.

4 is one of our common fraction and decimal equivalents that we use.

Is it right then? So if I rewrite what Jacob has done using the decimals, it does make it easier to compare.

Well, I think so anyway.

One is greater than 0.

75.

0.

75 is greater than 0.

4.

Yes, that's right, isn't it? So Laura says, yes, well done, you're right.

Or she even says, "You were right, well done." Here we're still looking at how Jacob arranged the numbers into the inequality and he's suggesting that we could have converted the fractions.

So they all had a common denominator.

Yes, we could, let's check that.

So let's check what's the lowest core multiple of four and five.

That's 20, so we convert them so they're into twentieths.

And again, I'm not gonna go through all of those steps because you are super confident with this now and then we can rewrite our inequality and we can see that it's correct.

Laura has now just realised that there was a much easier way to check than this.

Jacob says, me too.

We know that three quarters is more than a half and we know that two fifths is less than a half, so it must be right.

So remember, please don't just jump into converting to decimals, convert into fractions with a common denominator.

I want you to use your number sense.

Number sense is the first thing I want you to check when looking at any question.

Now your turn, true or false, two thirds is less than three fifths.

Pause the video, decide, make sure that you've got your justification ready because I'll be revealing those in a moment.

Is it true or false? And remember, I don't want any guesses.

Pause the video now what did you decide? False, the correct answer was false.

Now you need to impress me with your justification.

Here are justifications.

Two thirds is equal to 10 over 15 and three fifths is equal to nine over 15.

Is that the correct justification, or is it that 2.

3 is less than 3.

5? And you've said A.

Two thirds is 10 fifteenths, that's correct.

Three fifths is nine fifteenths, that's correct.

So we can now see that it's false because 10 is greater than nine and because the denominator's the same, we can just compare the numerators.

Well done.

Now we're gonna move on to looking at another problem.

Now we have Asia, Jun and Sofia, and they each have a tub suites lucky them, which I had some sweets here with me.

Now they can't, what fraction of their tubs are red sweets? Asia says a third of hers are red.

Jun says three tenths of mine are red.

And let's see what fraction of Sophia's are red.

Sophia's says two fifth of mine.

I want to know who has the greatest proportion of red sweets.

So it's very similar to something that you will have done in a previous lesson when we were comparing the scores with shooting penalties or shooting basketballs or scores in a competition.

It's very hard to compare because we do not have a common denominator or a common decimal form.

Would we use a common decimal form here? And I know you've just said no because three is not a factor of 10, a hundred or a thousand.

So we do need to use that common denominator approach.

What is the lowest common multiple of three, 10 and five? The lowest core, multiple of three, 10 and five is 30.

I'm converting them.

And again, I'm just gonna show you those and give you a moment to look through.

'Cause this is super familiar to you now.

Now it's very easy to see who has the greatest proportion of red sweets.

We're now going to order them from smallest to largest proportion.

So we start with Jun, followed by Asia, followed by Sofia.

Here we can consider the numerator because we've converted them so that they all have a common denominator of 30.

So nine is the lowest followed by 10, followed by 12.

Now it's your turn.

To compare four ninths, five sixths, one half, and two thirds, you would use which common denominator? And the correct answer is 18.

Nine is a factor of 18, six is a factor of 18, two is a factor of 18, and three is a factor of 18.

If we look at six, nine is not a factor of six.

If we look at 12, nine is not a factor of 12.

If we look at 27, 9 is a factor, but six is not a factor of 27.

So therefore it's 18.

Now you are ready to have a go at your task.

Now you'll see this looks very similar to the task that you did in the examples, but please don't use the same numbers because otherwise you could just rewind the video and put the same numbers in.

I have added an extra question where I've rearranged the boxes in a slightly different way.

You can pause the video now and come back when you're ready.

Well done.

A little bit harder now, so we've got more digits, but this time specifically there are nine boxes and I'd like you to use the digits one to nine and each of them only once.

This is really challenging, but you've got all of the skills remember, to be successful.

So really stick with it, pause the video and come back when you're ready.

Great work on that.

Now let's look at a third question.

So Izzy, Andeep, Lucas, Alex and Sam record their scores for a spelling competition.

I'd like you please to rank them from worst to best.

So who didn't do so well to who did the best? Pause the video now, good luck.

Come back and remember, no calculators.

Well done.

Now we can go through our answers.

So one, so again, these are just examples.

You could use your calculator to check these.

You could type them into the calculator, change into decimals.

That will make it easier to check.

Question two, again, these are some examples of correct answers.

And then question three here, there is only one correct order and the order is Andeep, Lucas, Sam, Alex, and Izzy.

Well done if you've got that right, I'm hoping that you've got all of your equivalent fractions there to back up why you've ranked them the way you have.

Now we are going to move on to our second learning cycle, which is solving problems with decimals.

Here we've got some items. We've got cupcake, apple, ice cream, banana.

I'm gonna call that limeade, a sandwich and a chocolate milkshake.

We're gonna write them in order from the cheapest to the most expensive.

So we can see the apple is the cheapest at 56 pence followed by the banana at 75 pence.

Then the cupcake 1.

24 pounds then the limeade 1.

26 pounds, then a chocolate milkshake, 1.

84 pounds, the ice cream at 2.

19 pound and finishing up with the sandwich at 2.

75 pound.

So you'll be familiar with ordering decimals and particularly if it's in money, that seems to make things a lot easier for us, doesn't it? What can you buy that would be closest to spending five pounds? Pause the video, have a think.

What could you buy that would be the closest to spending five pounds? Come back when you've got an answer.

Let's see if you've got the same answer as me.

I came up with the sandwich and an ice cream.

A sandwich was 2.

75 pounds and an ice cream was 2.

19 pounds, meaning I've spent 4.

94 pounds.

I don't think there was any way of getting closer.

Your turn now.

I'd like you to decide for me if you can buy an apple, a cupcake and a sandwich if you've got five pounds only.

You can pause the video now and come back when you've got your answer.

Remember, I don't just want a yes or no.

I want the calculations to back up, to justify your decision, good luck.

Let's take a look then.

So an apple is 56 pence, a cupcake 1.

24 pounds, and a sandwich 2.

75 pounds.

If we add all of those up, we get total cost of 4.

55 pounds.

So the answer to the question is yes, you can.

If you've got five pounds, you can certainly buy all three of those items. We're now ready, it was very quick, wasn't it for task B? So you've got lots of questions here.

You've got the same items, but I've changed the cost of each item.

So you're now ready to pause the video, have a go at these questions and then come back when you're ready.

Gosh, that was fast.

Let's check our answers.

So A, we are writing 'em in order from smallest or cheapest to most expensive.

So we have banana, apple, limeade, cupcake, ice cream, chocolate milkshake and sandwich.

B, a sandwich and a milkshake total cost 2.

95 pounds, add 1.

98 is 4.

93 pounds and C would be an apple, a banana, a juice, and a cupcake.

77 pence, 76 pence, 1.

54 pound, 1.

58 pounds is 4.

65 pounds.

Now we're gonna move on to combining fractions with decimals.

So we've just done solving problems with fractions and we've done decimals.

Now we can combine the two.

Here we have Laura and Laura is buying some ribbon to go around the edge of a cushion.

She gets to the shop and she realises she must have written a measurement down incorrectly.

Let's see what she's written down on her piece of paper.

Which measurement do you think she has recorded incorrectly? Now I know you've said 12 and two fifth metres.

Can you imagine a cushion 12 and two fifth metres long? That's roughly the height of the Statue of Zeus.

I don't think we'd have a cushion that long.

She texted mum to get the correct measurement and her mum says it's 0.

85 metres.

So she corrects it on a sheet of paper.

She wants to know how many metres of ribbon she needs.

So here we need to do a conversion.

We know that three quarters is equal to 0.

75.

And remember she was finding the ribbon to go around the edge of the cushion.

So she needs two lots of 0.

75, add 0.

85.

So here I've decided to add together the length and the width and then double it because there's two of each side.

Alternatively, you could add together the four sides separately.

It makes no difference.

You could also double the length, double the width, and add them all together.

Either way, you will end up with an answer of 3.

2 metres of ribbon.

So Laura now knows how much she needs to buy and when she gets home, she can put that ribbon around her cushion.

Here's a question that I would like you to answer.

How many metres of ribbon will Laura need for this cushion? I'd like you to pause the video, work out your answer, and then come back to me when you're ready.

Well done, let's take a look.

Four fifths is 0.

8 metres.

So notice here I've decided to change it into decimals.

I think that's the most efficient way of doing this.

The length of ribbon needed.

And again, I've decided to add together the length and the width and double it because there's two of each side and I get an answer of 4.

08 metres.

It doesn't matter.

Remember if you've used one of the other methods for finding the distance around the edge of a cushion, which you'll remember would be the perimeter of the cushion as long as you get 4.

08 metres.

Now you are ready to finish up with task C.

Here I have given you some different widths and lengths of cushions.

All of the dimensions are in metres.

What I would like you to do is to convert the length or width so that they are both in the same format.

I would strongly suggest you do decimals, but you may choose to do fractions.

That would just make your life a little bit harder in my opinion.

So I would change the fractions to decimals.

Then I've got a column there for the calculation.

You don't necessarily need this table printed off, you could just write it onto a piece of paper.

It doesn't even need to be a table.

And then finally, I'd like you to calculate for each cushion the length of ribbon that is needed.

You can pause the video now and then you can come back when you're ready.

Good luck with these.

Question number two.

Now this is a little bit more challenging, okay? And you need to think really, really carefully about this and about time and what you know about units of time.

I don't wanna say any more than that because I don't want to give anything away.

We've got stopwatch measures, time in minutes and seconds.

So that's important, it's minutes and seconds.

And I would like you please to answer the questions using the two times that we can see on those digital displays.

20:50 and 20:30.

Now, like I said, these questions are a lot more challenging, but I have every confidence that you'll be able to do them.

But don't worry if you do get stuck 'cause you can join me back again when we go through the answers and I may say something that helps you to understand where you went wrong or how you could be successful at that question in the future.

Good luck with these.

I look forward to seeing you when you come back.

You can pause the video now.

Brilliant, well done for persevering with that, right? I'm now going to take you through the answers.

Question number one, let's start with the top row.

The converted length was 0.

45.

Remember, that's an example of a calculation.

The main thing is that you get 2.

18 metres, the total length needed.

The second row, 0.

6, we need 3.

96 metres.

Third row, 0.

12, we need 0.

54 metres, fourth row, 0.

35, and we need 2.

84 metres and then the final row, 0.

875 and we need 3.

69 metres.

Well done if you've got those right, if you didn't, see if you can spot where your errors were.

Now moving on to question two, which like I said I think was really challenging.

So well done if you've got these answers right, some of them right or well done, if you've just managed to persevere with them and you've joined me to see what the answers are to see if you can work out how to be successful in the future.

A, it is 20 seconds more than 20.

5 minutes.

B, it is 12 seconds more than 20.

3 minutes.

C, 20:30 is exactly equal to 20 and five 10th minutes, and D 20:30 is closer to 20 and a third minutes as this would be 20:20.

The most important thing to remember here is that there are not a hundred seconds in a minute.

There are only 60 seconds in a minute.

So we need to be really careful with that decimal conversion.

Here is the answer to E.

I'm not going to read all of that out because it got quite confusing.

So I'm gonna suggest you pause the video, read through it in your own time and check your own answer.

Now we can summarise the learning from today's lesson.

Fractions can be compared and ordered by converting them into decimals.

Remember, we are going to use that method when the denominator is a factor of 10, a hundred or a thousand.

Fractions can be compared and ordered by converting them to have a common denominator.

So if the denominators are not factors of 10, a hundred and a thousand, then we need to use that common denominator method.

Decimals are ordered and compared using place value.

So we can use the place value grid if we need to.

When comparing fractions and decimals, they must be in the same form.

So they must all be decimals or all be fractions before we can think about making comparisons with them.

Well done on today's lesson.

There was some really challenging stuff in there today, but you did fantastically.

Thank you for joining me, bye.