Lesson video

Hi there.

My name is Mr. (indistinct) and I'm gonna be teaching you a lesson today from the unit about statistics.

It's a really important unit and one that will help you to understand things around you through number.

Sit comfortably 'cause we're ready to start.

Here's the outcome for the lesson then.

By the end, we want you to be able to say, I can solve problems using line graphs and pie charts.

These are the key words that you might expect to hear during the lesson, line graph, pie chart and sector.

I'm gonna say them and I want you to repeat them back to me.

So I'll say my turn, say the word or phrase and then I'll say your turn and it will be your turn.

My turn, line graph.

Your turn.

My turn pie chart.

Your turn.

My turn, sector, your turn.

Here's what each of those key words or phrases means.

A line graph is a graph where the points are connected by lines.

It shows how something changes in value, usually over time.

A pie chart is a circular graph where sectors represent different groups in proportion to each other, and a sector is a part or pie slice part of a pie chart, and in the image at the bottom there we can see a pie chart and it's been divided into two sectors of unequal value.

This is the outline for today's lesson then.

We're gonna start by solving problems using line graphs then we're gonna do some solving problems using pie charts.

Sofia, Izzy and Jacob are going to join us for the lesson today.

They're gonna be discussing some of the maths on screen.

They'll also be doing some of the prompts and giving us some hints and tips.

Hi Sofia, hi Izzy, hi Jacob.

I hope you're ready.

Are you ready? Let's go for it.

"It's Sports Day, says Sofia." The children in year six take part in a long distance race.

Anybody who wanted to could run 800 metres.

This line graph shows my long distance race.

You can see a title there.

Line graph showing Jacob's 800 metre race.

Jacob got off to a good start but then slowed down.

The x axis shows the time in minutes.

There are 60 seconds in a minute.

Halfway between one and two minutes is one minute 30 seconds.

This line represents two minutes, 30 seconds and you can see the line has been drawn halfway between two and three on the x axis, which is of course minutes.

Let's estimate how long it took Jacob to complete his race.

"It took me over five minutes to complete the race." Can you see the dotted line that's been drawn there right down to the x axis to help this estimate? But not quite long as five minutes and 30 seconds.

Five minutes and 30 seconds is halfway between five and six on the x axis.

A good estimate would be five minutes and 20 seconds.

Let's estimate how far Jacob had run in three minutes.

There's the point that we are looking for.

If you look at three on the x axis and then move your eyes up along the vertical line, you can see the dot above.

"I travelled over 600 metres after three minutes of running," they've drawn a horizontal dotted line to see where that dot meets the y axis.

The Y axis is the distance completed in metres.

Jacob wasn't quite halfway between 600 metres and 700 metres.

A good estimate here would be 630 metres.

"I really wish I'd paced myself more." How many of you have ever burst out of the traps really fast and found yourself tiring towards the end of a long distance race? Sofia also took part in the long distance race.

Let's estimate Sofia's finishing time.

Sofia took more than four minutes to complete the race.

A good estimate here would be four minutes, 15 seconds.

Let's estimate how far Sofia had run in three minutes.

Sofia had run almost 600 metres in three minutes.

Can you see they've looked up from three minutes along the vertical line to see where the point was plotted for three minutes.

Then they've looked across to see where this point met the y axis.

It was somewhere between 500 and 600 metres.

A good estimate here would be 575 metres.

Sofia did a brilliant job of pacing herself.

Okay, your turn.

Let's check your understanding so far.

Izzy wants to compare the two races.

When did Sofia catch up with Jacob? How much time had passed? How far had we both run? Okay, pause the video here and have a go at answering those questions.

Welcome back.

Well, "Sofia," so Jacob says, "Caught me up three minutes, 30 seconds into the race." Can you see where the two different lines for each character crosses? "We both run about 675 metres" and you can see that by looking at where those two cross lines meet the y axis.

The children in year six take part in an obstacle race, line graph showing Izzy's obstacle race.

"We had to run 80 metres and complete challenges on the way." That sounds great fun.

"We had to complete each challenge before we could run again." "First we ran, then we did five skips before running to the next obstacle." "Next we put it on an extra T-shirt, then ran to the last obstacle." "Finally, we put on a hat and ran to the finish line." Let's estimate the time that Izzy reached the second obstacle, the shirt.

Hmm.

Have a look at that graph.

When do you think Izzy reached the second obstacle? Well, the time is between 20 and 25 seconds, but nearer 20.

Can you see where the line graph has gone flat for a second time? That meant that Izzy wasn't travelling any distance.

In fact, she was stood up trying to put this T-shirt on.

A good estimate for Izzy reaching the shirt is 22 seconds.

Okay, your turn.

You need to estimate how long it took Izzy to put on the shirt.

Pause the video here and I'll be back in a moment to reveal the answer.

Welcome back.

Izzy says I started putting the shirt on 22 seconds into the race.

Izzy started running again at 35 seconds, so she had to put it on by then.

35 Subtract 22 is equal to 13, so Izzy took about 13 seconds to put the shirt on.

"It was a very difficult shirt to put on." Okay, it's time for your first practise task.

Izzy and Jun competed in the 800 metre race.

"The line graph shows how Jun and I completed the race." Look carefully at the times and distances on the line graph.

And here are some different questions to answer.

A, estimate how far Izzy had run in three minutes.

B, estimate how long it took Jun to run 400 metres of the race.

C.

Estimate how much faster Izzy completed the race than Jun.

And D, Estimate the distance between Izzy and Jun two minutes into the race.

For number two, Jacob competed in the obstacle race.

"The line graph represents my obstacle race," he says.

Look carefully at the times and distances on the line graph.

And we've got some more questions to answer about that line graph.

A, estimate how far Jacob had run in the first 30 seconds.

B, how long did it take Jacob to complete the first obstacle? And C, what do you think happened to Jacob when he had completed 70 metres of the race? Jacob tells us that skipping was the first challenge.

Okay, pause the video and use the line graph to answer those questions.

Good luck.

Welcome back.

Here are the answers then.

First we had to estimate how far Izzy had run in three minutes.

The point is about halfway between 550 metres and 600 metres.

In three minutes Izzy had completed about 575 metres of the race.

B.

Estimate how long it took Jun to run 400 metres of the race.

Jun completed 400 metres, somewhere between two minutes, 30 seconds and three minutes.

The answer is closer to three minutes.

It took Jun about two minutes, 50 seconds to complete 400 metres of the race.

C.

Estimate how much faster Izzy completed the race than Jun.

Izzy completed the race in about four minutes, 50 seconds.

Jun completed the race in about five minutes, 50 seconds.

Izzy completed the race about one minute faster than Jun.

D, estimate the distance between Izzy and Jun two minutes into the race.

Two minutes into the race, Izzy had completed about 460 metres of the distance.

Two minutes into the race Jun had completed about 280 metres of the distance.

460 subtract 280 is equal to 180.

Two minutes into the race Izzy was about 180 metres ahead of Jun.

Okay, here's number two then.

A, estimate how far Jacob had run in the first 30 seconds.

In the first 30 seconds, Jacob had run about 46 metres and you can see there if you trace up from 30 on the X axis to where it meets the line and then go across to see where that point meets the Y axis.

It's about 46 metres.

B, how long did it take Jacob to complete the first obstacle? Jacob started skipping about eight seconds into the race.

He stops skipping about 14 seconds into the race.

Jacob skipped for approximately six seconds.

C, what do you think happened to Jacob when he had completed 70 metres of the race? At 70 metres, Jacob changes direction, runs back and stops for a couple of seconds.

He then carries on running to the finish line.

Jacob ran back for some reason.

Your answer may have been something like Jacob's hat fell off and he had to go back and put it on again.

Sounds likely.

Okay, let's go to the second part of this lesson then.

We're now gonna look at solving problems using pie charts.

The children take part in a beanbag challenge, pie chart showing scores in the beanbag challenge.

We've got Izzy, Jacob, Sofia, and June.

"We had to throw beanbags at a target," says Izzy.

"We scored points depending on where each beanbag landed.

We scored 240 points all together." "Let's work out how many points each of us scored using the pie chart." I can see right angles in Jun's and Jacob's sectors.

That means that JU and I each scored one quarter of the total points.

One quarter is half of one half.

One half of 240 is equal to 120.

One quarter of 240 is equal to 60.

Jacob and Jun both scored 60 points each.

Okay, let's check your understanding then of what we've looked at so far.

How many points did Sofia and Izzy score? Our team scored 240 points altogether.

Sofia scored twice as many points as Izzy.

A vital clue there from Jacob.

Pause the video here and have a go at finding out how many points Sofia and Izzy scored.

Welcome back.

"Jun and I scored 120 points" says Jacob, so Izzy and Sofia also scored half the total points.

Izzy and Sofia scored 120 points between them.

You could have divided 120 by three to get 40.

Sofia scored 40 at 40 points, which is equal to 80.

Izzy scored 40 points, "But it was a team game and the individual scores don't matter." Quite right, Jacob.

Okay, let's look at this part then.

This time we've got Izzy's team competing in a skipping challenge.

We've got a table there with points scored and percentage of the points scored and there's a pie chart showing scores in the skipping challenge.

"We had to skip as many times as we could in one minute.

We scored 60 points altogether."0 How many points did Jun score? There are 360 degrees in a circle.

Jun's sector measures 36 degrees, which is equal to one 10th or 10% of 360 degrees, so we are using angles here to work out the proportions.

10% of 60 points is equal to six points.

Jun scored six points.

How many points did Sofia score? Hmm, well, Sofia scored 20% of the total points.

10% of 60 is equal to six.

Ah, so that means 10% multiplied by two is equal to 20%, so six points multiplied by two equals 12 points.

"Sofia scored 12 points." Great multiplicative reasoning is Izzy, well done.

Okay, let's check your understanding then.

Your task is to complete the table.

"Jacob and I scored the same number of points as each other." A very useful clue.

Thank you, Izzy.

Pause the video here and see if you can complete the table.

Welcome back.

"Jun and Sofia scored 30% of the points between them.

So Jacob and I scored 70% of the points." 70% divided by two is equal to 35%.

Remember, Jacob and Izzy both scored the same number of points.

We each scored 35% of the total points.

10% of 60 points is equal to six points.

Seven multiplied by 10% equals 70%, seven times six equals 42 points.

We scored 42 points between us.

42 divided by two or halved is equal to 21.

We each scored 21 points.

It's time for your second practise task now.

You're gonna put into practise those skills of being able to answer questions based on pie charts.

And the pie chart shown here is about Izzy's team who compete in a football challenge.

The title is pie chart showing scores in the football challenge.

We've got Jun, Jacob, Sofia, and Izzy, and there are some other bits on the pie chart that are really useful too.

"We each had to kick a ball at some targets.

We scored 160 points altogether." Work out the number of points and the percentage of the total that we each scored.

There's the table ready to fill in.

"Complete the table says Izzy." Pause the video here and have a go at that practise task.

Good luck.

Welcome back.

Here are the answers then.

We've got the table with the blanks.

Let's fill them in.

Jun's sector has a right angle, so he scored one quarter or 25% of the points.

25% of 160 points is equal to 40 points.

Sofia's sector has a 72 degrees angle.

72 degrees is one fifth or 20% of 360 degrees.

10% of 160 equals 16.

20% of 160 is equal to 32.

45% is equal to 25%, add 20.

40 plus 32 is equal to 72.

"I scored 72 points." 45% plus 25% plus 20% equals 90%.

Jacob scored 10% of the total points.

10% of 160 is equal to 16.

The table is finished.

I'm gonna check the points add to the correct total, which is 160.

Really good thing to do to make sure that you've got an accurate answer.

I'm gonna use some quick mental edition thinking about numbers that add easily.

Can you see which numbers would add easily in that table? Well, 72 plus 32 is equal to 104.

104 plus 16 is equal to 120.

120 plus 40 is equal to 160.

Fantastic.

The four scores add together to equal 160.

Okay, let's summarise today's learning then.

A pie chart represents parts of a whole.

A line graph represents the relationship between two variables.

Place value helps you to interpret partially marked scales and axis.

My name's Mr. (indistinct) hope you enjoyed that lesson.

I did.

I hope you have a good Sports Day this year too.

Maybe I'll see you again soon.

Bye for now.