Lesson video

Hello, welcome to your Maths lesson with me Miss Jones.

Are you ready to get started? Let's have a look at what we're going to be doing.

In today's lesson, we're going to be calculating non-unit fractions of quantities.

And non-unit fraction is a fraction which has a numerator greater than one, for example, two thirds or three quarters.

So, we're going to think about how we find a fraction of an amount or a quantity.

Then you're going to have a go to talk task, and then a main task, and then the lesson quiz.

You'll need today a pencil or pen, something to write with and something to write on so a piece of paper.

And I'm going to be using counters today in my examples.

If you have counters or something similar, such as coins or countable objects or cubes at home, you can be using those.

If you don't, the best thing to do would be to draw dots to represent your counters on your piece of paper.

If you haven't got what you need, take a moment now to go and get it and then come back to the video.

Okay, hopefully you've got what you need, and you're raring to go.

Okay, here, I've got 18 counters.

I know there's 18 because I've got three in each column.

Let's count in threes, three, six, nine, 12, 15, 18.

If you're drawing counters today, you might want to draw 18 dots.

My question asks me, what is one third of 18? Let's think about what one third means.

Now, I know my numerator tells me that we need to find out what one part is.

And my denominator, the number three here tells me, how many equal parts we need to split 18 into three equal parts.

How can we do that? Well, we need to divide these into three equal groups.

So we could share them out one by one.

But we've already arranged them here in a nice array.

So they're quite easy to separate into groups, I can see that I've got three rows.

If I draw a line here, I should end up with three equal groups.

I need to know what is one third? So I need to find out how many counters are in one of my equal groups? Can you quickly count how many? That's right, there are six.

One, two, three, four, five, six.

One third of 18 is equal to six.

However, what we've done here is we've found out a unit fraction of 18, one third.

What would happen if I wanted to find out what two thirds were? What can we do? Well, instead of just looking at one part, we need to find out how many would be in two parts.

But we're still using three equal parts.

So we can still use the same diagram here, split into three equal parts.

If one third was six, two thirds would be two lots of six.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, or six times two.

So two thirds of 18 would be equal to 12.

Here, I've got the same amount of counters 18 again, but it's asking me to find one sixth.

I might arrange my counter slightly differently this time.

I know that I had six counters in each row here going across.

So if I draw lines down my columns, I can create six equal groups.

Have I got six equal groups? I did, great.

Okay, so it's asking for one sixth, I've got my six equal groups.

And I need to find out first of all, how many is in one of those groups, or how many are in one of those groups.

So in one of my equal groups, I can see there are one, two, three.

One sixth of 18 is equal to three.

Now we found out the unit fraction.

So what happens if we want to find out what five sixths are? What could we do then? Well, same again, what we'll need to do is not only look at one of those parts, let's look at our numerator, we need to look at how many are in five of those parts.

So there are three in one of those parts.

How many will there be in five of those parts? Let's count in threes, three, six, nine, 12,15.

I don't need to count the sixth part.

What I've done there is I've taken what one sixth was, and I've multiplied it by five.

Five sixth of 18 is equal to 15.

Okay, hope you enjoyed exploring 24 counters in your talk task.

We're going to stick with 24 counters here, but we're going to look at something slightly different.

We're going to think about instead of writing two thirds of a fraction, how I could write the same value, the denominator of 24.

Let me try and explain.

So if we're looking at two thirds, I know I split my 24 counters into three equal parts.

So out of 24 counters, what would two thirds look like? Well, they would look like eight, it could be one third.

So 16 would be two thirds.

Two thirds is the same value as 16 24th.

Okay, let's have a look at the next one.

Got five sixths.

So imagine we were thinking about six equal parts, and I'll just show that by splitting our three equal parts again.

Okay, so five sixths, we'd be thinking about five of these groups.

Now, if we were to write that as a fraction out of 24, what would our numerator be? Well, one sixth, we know would be one, two, three, four, counters.

Five sixth will be five lots of four.

So five sixth is the same as 20 24ths, or 20 counters out of 24.

These fractions are equivalent.

What about 12ths? Well, we had six equal parts.

If I split those into two should end up with 12 equal parts.

We can see that one 12th would be two.

So 11 12ths would be two lots of 11, and it would be 22 24ths.

These fractions are equivalent as well.

Okay, what if we were looking at a different denominator, quarter's? We're going to split these into quarters like this, this time.

We can see that one quarter has a value of six.

So three quarters, what would that look like with a denominator of 24? Well, if one part here is six, three parts would be sixth, 12th, 18th.

We could write three quarters as 18 24ths.

What about eighths? How could I split this in half again? I could add two more segments there to make eight.

So you can see one eighth has three parts.

So seven, eighths must have seven lots of three parts.

We could write that as 21,24ths.

Seven eighths is equivalent to 21 24ths.

In your task today, you're going to be using counters to represent non-unit fractions.

And using the same set of counters to represent more than one non-unit fraction.

For example, we could represent three quarters with 24 counters, by splitting them into equal groups of four and identifying three of them.

We could split it up.

We could represent it using eight counters by splitting our eight counters into equal groups of four, and then identifying three of them.

Now with each representation, we could write more than one fraction that it's equivalent to.

But this one, we could say this is representing three quarters, or it's representing 18 over 24.

For this representation, we could say it's representing three quarters, or we could say it's representing six, eighths.

Notice that the amount of counters I'm using is a multiple of four.

That means that I can split it into four equal groups.

So bear that in mind in your task today.

Would there be any other amount of counters I could use to represent three quarters? However think, perhaps I could use 12 counters because I could easily split those into four equal groups and identify three of them.

I wonder if I could have identified any other equivalent fractions, perhaps with a denominator of 12, or something else.

Here's some sentence stems that might help you with today's task.

What you need to do is create a set of counters that represent more than one fraction and write down your equivalents with it.

Okay, it's time to pause the video and go into your task.

Enjoy.

How'd you get on with your task today? Hope you had fun exploring those equivalent fractions.

If you have any drawings or objects today that you might have taken a photo of, you need to ask your parents or carer if you want to share them with us.

You can share them on Instagram, Facebook or Twitter tagging OakNational and #LearnwithOak.

Once you're all done, make sure you go and complete your quiz.

Thanks everyone for a great lesson.

Bye bye.