Lesson video

Hi there, my name's Miss Darwish, and for our maths lesson today, we are going to be looking at how to calculate the mean, or the average, for a set of numbers.

But before we get started, if I could just ask you to take yourself to a nice, quiet place, just so you're ready for the lesson.

Okay, so for our session today, we're going to start off just by looking at some representations, and then we'll be having a look at mean, an average, of a set of numbers and seeing what does the mean mean, and then we'll be looking at some word problems, and then at the end of the session, there will be, of course, a quiz for you to complete on today's learning.

So, before we start, if I could just ask you to grab yourself a pencil, a sheet of paper or a notebook, and a ruler, just so you're ready for the lesson.

Okay, here's a question for you.

How many different ways can we represent the number 15? And you've got some rods next to you.

I'm going to give you 10 seconds to write down, jot down, as many different ways as you can come up with.

I'm going to do the same.

You ready? Go.

And three, two, one.

Pencils down.

How did you do? There are lots of different ways.

Okay, so one way that I came up with was just a simple rod of five and a rod of 10.

10 out of five is equal to 15.

Or we could have had six and nine, which is equal to 15 of course.

What did you come up with? So I also came up with five and five and five.

So three lots of rods of five, which is 15, or we could have had an eight and a seven, or a four and a three and an eight.

There are lots of different options.

Okay.

So here is a word problem.

A teacher has a reward system where her pupils earn cubes, and at the end of the week, the table with the most amount of cubes gets extra playtime.

Does your teacher do something similar? Maybe you have different rewards at school, raffle tickets, amarbles, Dojos, credits, merits.

Okay, so this teacher, what she does is each child gets a cube.

So if they produce some outstanding or brilliant homework or a piece of work in class, then they might get a cube or two cubes.

If they offer to help or if they show a lot of kindness, then maybe they get some cubes as well.

And then at the end of the week, what she does is she doesn't look up and see which child got the most.

No, it's the table.

So the tables sort of have to work together to get the most number of cubes, and that winning table gets the extra playtime.

Cool.

So this is Table A.

Meet Table A.

How many children are sat at Table A? Six children are sat at Table A.

Okay, now, can you see the child, can you point to the child in Table A that got the most number of cubes? And tell me how many cubes did she get? I counted 10 cubes.

Did you count 10 cubes? And what about the child with the least number of cubes? There's two of them.

Two of the children on table six only got four cubes, okay? What is the total number of cubes that Table A received? Or earned, they earned those cubes.

What's the total that Table A received? How many, how many cubes did they earn in Table A? Okay, I counted a total of 42.

What about you? So all together, all together Table A received 42 cubes.

Well done, Table A, that's very good.

Okay, now this is Table B.

How many children are sat at table B? Four children are sat at Table B, well done.

Now, can you point or find me the child that received the most number of cubes? And tell me how many cubes did this child receive? 10, 10 as well.

Well done if you said 10.

So the child on Table A that received the most number of cubes had 10, and on Table B, also 10.

Now, my next question is how many cubes did Table B receive all together? Can you count them all for me, please? I've counted them.

Let's see if we got the same to check each other's answers.

Okay, ready? I counted 32.

Did you get that? So a total of 32.

Now, Table A had a total of 42.

Table B had a total of 32.

Remember what the teacher said? The table with the most number of cubes get the extra play.

Which table got the extra play, A or B? Table A, well done Table A.

Now, it does seem a bit fair to be honest, not fair.

It doesn't seem fair.

Do you think it seems fair? There are children sat on Table A that only received four cubes and they get extra play, and everyone on Table B got more than four cubes and they did not get extra play.

How is that fair? Also, there are six children sat at Table A and there are only four tables sat at, four children sat at Table B.

What if we had a table that had 20 children sat on it? That table would probably win because there is more, there are more children sat at that table.

This just definitely does not seem fair.

Do you think it sounds fair? No.

I think we need to have a word with this teacher, and I think we need to change how the reward system works.

I love the fact that she's used cubes, okay, and that the table at the end get the extra playtime.

This is a great incentive, but maybe it needs to be calculated different.

Maybe we shouldn't be focusing on the total number of cubes, because on one table you might have six children, on another table you might have eight children, on another table you have might have five children.

What's it like at your school? You have different children, a number of children, sat on different tables.

It just doesn't seem fair.

Okay, so, now, Group A we said received a total of 42 cubes all together in total, right? Now, what if we shared these cubes between the children? How many would they receive? So six children on Table A.

if I shared these 42 cubes, it's like saying each child received, how many? Can you count them for me? Seven.

So it has an average of seven.

There is an average of seven.

It's like saying each child received seven cubes, okay, because we got 42, the total number of cubes, and we shared them between six.

So it's like saying A had a table average of six cubes.

Okay, let's have a look at B, Table B.

32 cubes in total, and we're sharing it amongst the four children.

And that's like saying each child got how many cubes? Can you count them for me? Eight cubes.

It's like saying they average, they had an average, sorry, of eight.

Table A had an average of seven.

Table B had an average of eight.

I think table B should have won and got the extra playtime.

What do you think? I don't think it's right for the teacher to look at the total number of cubes.

Like we said, if there are different children sat on the table, it just doesn't seem fair.

Then actually what they should have done, what the teacher should have done, is that the teacher should have looked at the average, or the mean, and that's where we get the total number of cubes in this example and divided it by the number of children sat at the table.

So let's say a table, a table with five children had 25 cubes in total, we would do 25 divided by five, and that table would have an average of five, okay? So if we go back, we're going to change something a bit here now.

A teacher has a reward system where her pupils earn cubes, and at the end of the week, the table with the most cubes gets extra playtime.

We're going to change that.

What that should be is that the table with the highest average gets extra playtime.

Now that seems fair, don't you think? Okay.

Right, the average, or the mean, is really important to look at if we're making a comparison.

Let's have a look at a new word problem.

Layla shoots hoops each day after school.

Below are the number of baskets that she got each day.

So on Monday she got 12.

Tuesday, how many did she get in? Eight.

What about Wednesday? 15.

What about Thursday? Nine.

And then Friday? 11.

So she had a very, very good day on Wednesday, didn't she, 'cause she got 15 in.

Well done, Layla.

So, can you guess what I'm going to ask you now? Okay.

Well, so the mean, then what is the mean number of hoops per day? Or the average.

We can say mean or the average number of hoops per day.

So we've got here over the course of five days, okay, and we want to know what's that roughly the same as like saying she got in one day.

So first of all, what's the first thing we're going to do? We want to find out the total number of hoops that she got on Monday, Tuesday, Wednesday, Thursday, and Friday.

So 12 add 8 add 15 add 9 add 11.

We're finding the total number of hoops that she got that week.

Can you add them up for me? What answer did you get? What's her total for the week.

Okay, let's see if you got it right.

55, did you get 55? Okay, now, so that's the total number of hoops.

Now what have we got to do? That's 55 hoops over the course of five days, over five days.

We just want to know one day.

So 55 divided by five.

And that would give us the average, or the mean, and what's 55 divided by five equal to? 11.

So she scored an average of 11.

It's like saying she scored 11 each day, 'cause 11 times five is equal to 55, the total that she got for that week.

Well done, Layla.

Okay, let's have a look at another word problem.

So this is Billy, and Billy has been very good.

He's been saving some of his pocket money each week.

Do you save your pocket money? So, in week one, he received two pounds.

In week two, how much did he receive? Three pounds.

What about in week three? One pound 50.

And in week four? Two pound 50.

So in week two, he was very good.

He did not spend a lot of money.

He managed to save three pounds.

But in week three, he spent a bit of money then.

So he only saved one pound 50.

Can you guess what I'm going to ask you now? What is the mean amount of money that he saved each day? Each week, sorry, that should be each week.

So the mean amount that he saved each week, not each day.

Okay, so in week one, two pounds.

Week two, three pounds.

Week three, one pound 50.

Week four, two pound 50.

So we've got the total amount of money that he saved was two pounds add three pounds add one pound 50 add two pound 50.

So how much money did he save in total? Nine pounds.

Well done, Billy.

Now, to find the mean, I need to do nine divided by four, which is equal to 2.

25, or two and a quarter.

We can say two and a quarter or 2.

25.

But as we're talking about money, we're saying two pounds 25.

So two pounds 25 was the mean amount he managed to save.

Okay, well done.

Now it's time for you to pause the video to complete your task.

Once you've had a go and you finished, then come back and we will check the answers together.

Okay, welcome back.

Hope you found that okay.

Let's have a look at the answers.

So first of all, we had a table, and we were looking at each table.

So we've got Table One.

We had a table of tables, if that makes sense.

The table, the grid, and it had each different table, and it showed the reward system which each child won.

Now, which group, which table group, had the highest mean? So if you look at Table A, Maria had six, Ava had 10, and Hassan had five.

So six add 10 add five is equal to 21, and there are three children sat at the table, so 21 divided by three is equal to seven.

So the mean for Table A, or the average for Table A, was seven.

Okay.

Next table then, Table B.

Toby had two, Stanley had eight, Aliyah had one, and Maria had one.

So the total for that table is two add eight add one add one, which is equal to 12, and there are four children sat at that table, so 12 divided by four is equal to three.

And then let's have a look at Table C.

So Sonia had two rewards, Devak had eight rewards, and Omar had eight, and if we add them up, two add eight add eight is equal to 16.

So Table C received 16 as a total, but there are three children sat at that table, sorry, Table A, table.

Let's start again.

Table C received two add eight add eight, which is equal to 18, 18 rewards as a total for Table C, and there are three children sat on Table C, so 18 divided by three is equal to six.

So Table C had a mean of six.

And then let's look at Table D.

Tia received four rewards, Brody four, Ali nine, and Dalia seven.

So you got four add four add nine add seven, which is equal to 24.

So the total for Table D was 24, but we want to know the average so it's fair.

And there are four children sat on that table, so 24 divided by four is equal to six.

Well done if you said six.

Table E, Rhean scored five, Evie seven, Maya five, and Caleb 11, whew, Caleb scored 11.

And the total for Table E was 28, and there are four children sat on that table, so 28 divided by four is equal to seven.

So Table E's mean, or average, score was seven.

Okay.

So Table A had a mean score of seven, Table B had a mean, or an average, score of three.

What was the mean, or average, for Table C? Six.

What about Table D? Six.

And Table E? Seven.

So it says which group had the highest mean, or the highest average? A and E.

So if it was extra play time, it will be tables A and tables E going outside.

So well done, Table A and well done Table E.

Table B's got a lot of catching up to do.

Okay, well done.

If you would like to share your work with us here at Oak National, then please do ask your parent or carer to share your work for you on Twitter, tagging @OakNational and to use the hashtag LearnwithOak.

Well done on all the brilliant learning that you have completed today in our session.

Now I'm just going to ask you to go and complete the quiz based on today's learning.

Good luck.