Lesson video

Hello there, my name is Mr. Tilstone.

If I've met you before, it's lovely to see you again, And if I haven't met you before, it's nice to meet you.

I hope you're ready for today's maths challenge.

If you are, let's begin.

The outcome of today's lesson is this, "I can explain the relationship between the mean average and sharing equally." Our keywords, we've got 2 sets.

If I say them, will you say them back? Ready? My turn, mean average.

Your turn.

And my turn, set of data.

Your turn.

What do these phrases mean? Let's have a look.

Well, the mean average is a single number expressing the typical value in a set of data, and we're going to be exploring that today.

It's calculated by finding the total of the set of data and dividing by how many values there are.

Don't worry if that doesn't mean much to you now, it will do by the end of the lesson, I promise.

And a set of data is a collection of facts such as numbers, words, measurements, observations, or even just descriptions of things.

Our lesson today is split into two cycles.

The first will be identifying equal sharing, and the second, what is the mean average? Let's start by identifying equal sharing.

In this lesson, you're going to meet Laura and Lucas.

Have you met them before? They're here today to give us a helping hand with the maths.

The Oak children have been collecting superhero cards.

They want to play a game.

So let's have a look at the table.

What's the table showing? We've got a column that's got the names in the left hand column and the number of cards in the right.

Laura says, to play the game, we will need to have the same number of cards.

Okay? And Lucas says, perhaps we could organise ourselves and share the cards equally.

Hmm, good idea.

Because you might notice that some have got more than others.

So Lucas has got the fewest, Laura's got the most, et cetera, et cetera, but they could share them equally.

"How could we do that though?" said Laura, "How many would we each get?" What would you do? Well, they represent the cards in a different way.

They've got this sort of bar graph.

The cards are not shared equally at the moment.

How could we do that? Hmm? And if you had cards, you could organise them just like this, couldn't you? "So if Jacob gives a card to me," says Lucas.

Let's see.

Right.

Well, they've got the same number.

Now Lucas, Jacob, and Sam have all got the same number, but Laura hasn't.

So they haven't been shared equally yet.

But she says, "And I give one to you, Jacob and Sam." Oh, that would work.

Look.

Yep.

Ah! "We will all have the same number of cards." Yes, they have.

They've got an equal number now.

They've been shared equally.

Let's have a little check what is the same and what's different.

Have a good look at that.

What could you say is the same and what's different? Pause the video.

What do you think? What's the same? What's different? Well, Laura says, "I have fewer cards than I had before." Have a look at that.

So yes, she had 8.

She's got 5 now.

That's different.

Lucas says, "Sam and I have more cards than we had before." Yes, they do.

Lucas did have 3, now he's got 5.

Sam did have 4, now he's got 5.

And Jacob has the same number of cards as he did before.

His number's not changed.

It was 5, and it's now 5.

But the cards are now shared equally.

That's what's the same now.

What about the total number of cards? Hmm? Do we still have the same number of cards in total? How could you find out? Well, we can add.

So remember, you can add in any order.

So you might find a nice efficient way to do this, but when you add 8, 3, 5, and 4, it's equal to 20.

And when you have 5, 5, 5 and 5, it's also equal to 20.

So what can we say? We can say that yes, they do still have the same number of cards in total.

There's been no more cards added or taken away.

They've just been shared equally.

They think about what's happened to the cards and they record the cards in a bar model.

So have a look at this bar model.

So that was before the sharing the top row of the bar model, the 8, 3, 5, and 4.

And then after the sharing, the 5, 5, 5 and 5, both of those are equal to 20 each.

Laura says if we had started with 20 cards and shared them equally, we would've got 5 each.

Yes, we started with 20, but they were shared on equally.

They were shared on equally.

A week later, they have 24 cards altogether.

How many will they each get if they share them equally? Hmm.

Pause the video.

So this time the whole has changed.

The total has changed.

It's 24 now.

Still the same number that's being shared by equally.

So this time we're doing 24 divided by 4.

And Laura says, "I can use my 4 times table." 24 divided by 4 is equal to 6.

That was an instant fact for her.

She'd memorised that.

And then Lucas says 24 shared equally between 4 is the same as 24 divided by 4.

And that gives us 6.

So well done, if you said they each got 6 cards after sharing them equally, They will each have 6 cards.

Let's do another little check.

How many cards will the children have each if they share them equally? So we've got different numbers of cards this time.

Same number of children, how many cards after sharing equally, what is your first step going to be? And then what will you do after that? Pause the video.

How did you start? Did you start by adding the number of cards? Well, whatever way you did that, and you might have done that in a different order.

You'll get 28.

So there's 28 cards altogether.

Then that's being shared or divided equally between 4 people.

So the equation there is 28 divided by 4, and that's equal to 7.

And hopefully, if you know your times tables off by heart, which I hope you do, you'd have known that instantly.

So that's 7.

7 cards after sharing, if you got that, well done.

You're on track for the next part of the learning.

And the next part of the learning is some practise.

So number one, how many cards will each child get if they are shared equally? And how did you calculate this? Number two, Six children have 24 superhero cards that have been shared equally.

Questions.

A, how many cards does each child get when they have been shared equally? And B, how many cards could Sam and Alex have had before they were shared equally? If you can work with somebody else, if your teacher is okay with that, I always recommend that because then you can share ideas with each other, bounce ideas off each other, help each other out if things are starting to go a little bit wrong.

Pause the video and away you go.

Welcome back.

How are you feeling? How are you getting on? Are you feeling confident? Let's see.

Let's give you some answers.

So number one, to calculate the equal share, find the total number of cards and then divide by the total number of children.

And for B, you had a bit more arithmetic to do here.

Perhaps you use written methods.

If you add all of those cards together and divide by how many there are, which in this case is 7, that's 25 each.

And number two, 6 children have 24 superhero cards that have been shared equally.

How many cards does each child get when they've been shared equally? Well, there are 6 children.

So 24 divided by 6 is equal to 4.

How many cards could Sam and Alex have had before they were shared equally? Well, there are 24 cards.

So Sam and Alex's cards must have a total of 6.

As the known cards have a total of 18.

So for example, if Sam's got one card, Alex has got 5.

If Sam's got 2, Alex has got 4.

If Sam's got 3, Alex has got 3.

If Sam's got 4, Alex has got 2.

And if Sam's got 5, Alex has got 1.

Lots of possibilities there.

It is time for the next cycle.

That's, what is the mean average? We shared the cards equally to play the game, but 5 is a good number to represent a typical number of cards we each have.

Yes, some have more and some have fewer, but 5 is sort of in the middle.

So yeah, Laura had more than 5 and Lucas had less than 5.

But 5 is a good middle point.

The children have calculated the mean average number of cards of the four children.

We found the total number of the four sets of cards and shared them equally between the four children.

So they added 8, 3, 5, and 4 and divided by 4.

So 8 plus 3 plus 5 plus 4 is equal to 20.

And again, you might have done that in different order, but that's 20.

And then 20 divided by 4 is equal to 5.

The mean average is calculated by finding the total of the set of data and dividing by how many values there are.

So let's put that into practise.

Let's see what those values are.

The mean average is calculated by finding the total of the set of data.

So in this case, that's 8 plus 3 plus 5 plus 4, and dividing by how many values there are.

In this case, that's 4.

So add those numbers together and you've got 20, 20 cards.

And then 20 cards divided by 4, the 4 people, is equal to 5.

Our set of data is a number of cards each person has.

There are four values.

So the set of data is equal to 20.

There are four values.

So that's four people in this case, and 5 represents the mean average number of cards we have.

So that's what we call the mean average.

Okay, what is the mean average of Alex, John, Sophia, and Aisha's cards? So let's have a look, so we know Alex has got 8, John's got 5, Sophia's got 6, Ashia's got 9.

What's the total value and what's the mean average? Well, let's start by finding that total value.

So when we add those numbers together, that gives us 28.

So they've got 28 cards altogether in the group.

Now, how many people are there in the group? And there's four, so we divide the total by how many values there are.

So that's 28 divided by 4, and that's equal to 7.

So when they're shared out equally, 7 is a number of cards that each person has.

So we can say that 7, is the mean average.

The mean average is 7.

Let's do a little check.

Let's see if you've got that.

So which shape represents the set of data? Which shape represents the number of values and which shape represents the mean average? Pause the video.

Let's have a look.

So the set of data, that's this.

So the 8, the 5, the 6, and the 9, that's the cards that they've got.

That's the set of data.

The number of values, that's 4.

So in this case is 4 people, 4 children.

And then the mean average, when we divide that set of data by 4, that gives us 7.

That's a mean average.

So well done if you matched those up properly, you're ready for the next part of the learning.

Let's do another check.

Calculate the mean average of this set of data.

So the mean average is calculated by finding the total of the set of data and dividing by how many values there are.

Pause the video and give that a go.

So we're starting with an addition.

I can see some number bonds to 10 there.

You might want to start with those.

But either way, whatever order you do that in that is equal to 36.

So the total of the set of data is 36.

They've got 36 cards altogether.

Now you divide the total of the set of data by the number of values in the set.

There aren't 4 children here this time.

There are 6 children, so that's 36.

That's a set of data divided by 6.

That's the number of values in the set, and that's equal to 6.

So there are 6 values in the set of data.

The mean average of this set of data is 6.

So each child will have 6 cards.

Let's do some practise, some final practise.

Number one, what is the mean average of the spelling test scores for each of these groups? So let's have a look at each.

Each got 6, 10, 7, 9, and 8.

You are going to work out the mean average.

Think about how many children there are in the Beech group.

Chestnut, a different group.

They've got 8, 5, 7, 9, 5, 8, and 7.

Now you might notice there's a different number of children in that group, so be careful of that.

And then for Pine, they got 5, 4, 7, 9, 5 and 9.

And once again, a different number of children in that group.

But what's the mean average? Number two, the mean average of the spelling test scores for Ash group is one mark higher than Beech.

What could the scores be? So let's have look at Beech.

So in Beech we've got five children, they've got 6, 10, 7, 9, and 8.

So we need to look at the mean average of that.

And then the mean average for Ash is one more higher than that.

But notice how many children there are in the Ash group.

What could the scores be? There are many possibilities there.

So see if you can find more than one.

If you come up with somebody else, please do.

Pause the video and away you go.

Welcome back.

How are you getting on with that? How are you feeling? Let's give you some answers and you can compare.

So number one, the total score is equal to 40.

So when we add 6, 10, 7, 9, and 8, it gives us 40, and there's five children in that group.

So 40 divided by 5 is equal to 8.

So the mean average there is 8.

Some got less than that, some got more than that.

It's a good middle point, 8.

So for the Chestnut group, well when you add together 8, 5, 7, 9, 5, 8 and 7, that gives us 49.

There are 7 children in that group.

So 49 divided by 7 is equal to 7.

And maybe for you, that was an instantaneous fact because you know your times tables off by heart.

I hope it was.

So mean average, 7.

So their mean average is slightly lower than Beech.

And then for Pine, when we had together 5, 4, 7, 9, 5, and 9, it gives us 39.

Now there are 6 children in that group.

6 isn't a factor of 39.

So it's going to give us an answer with a decimal number.

So that's 6.

5.

So the mean average there is 6.

5.

Some got less than that, some got more than that, but that's a good middle point.

And number two, the mean average of the spelling test scores for Ash group is one mark higher than Beech.

What could the scores be? So let's have a look at Beech.

So they've got 6, 10, 7, 9, and 8.

When you add those numbers together and divide by 5, it gives you 8.

That must mean the mean average score for Ash, which is one higher, is 9.

Now there are 6 in the group.

So the total score must be what? So 9 multiplied by 6 is equal to 54.

So the individual scores must total 54.

So there's lots and lots and lots of possibilities here, but when you add those numbers together, they've got to equal 54.

So here's just one of many possible examples.

10 plus 8 plus nine plus 7 plus 10 plus 10 is equal to 54.

And when you divide 54 by 6, it's equal to 9.

That's just one possibility.

We've come to the end of the lesson, and my goodness, you've been amazing today.

Very well done.

Today, we've been explaining the relationship between the mean average and sharing equally, and hopefully that word mean average means a lot more to you now.

The mean average of a set of data is the size of each part when a quantity is shared equally.

So the mean average is calculated by finding the total of the set of data.

So that's your first step.

You're adding those numbers together and then dividing by how many values there are in the set.

So it goes addition first, division second.

The mean average provides a typical value for a set of data.

It's a sort of middle point.

Well done on your accomplishments and your achievements today.

Give yourself a pat on the back and say, "Well done, me." I hope to spend another math lesson with you at some point in the near future.

But until then, have a fabulous day, whatever you've got in store.

And whatever you do, be the best version of you that you can possibly be.

You can't ask for more.

Take care and goodbye.