Lesson video

This lesson is called Marathon Training.

A marathon is a really long way to run, over 26 miles.

Now, I don't know that from experience.

The furthest I've ever run was three miles.

I did receive this medal for it.

Have you run before and received any medals or certificates? I wonder how far do you run? Let's get ourselves ready for the Maths lesson where we'll be learning more about marathons and how hard it is, how much hard work is needed to train for one.

Check that you are distraction-free in a quiet space, ready to focus on your learning.

And if you're not yet there, press pause.

Take yourself off somewhere where you will be able to focus for about 20 minutes on this Maths lesson.

Press pause and come back when you're ready to start.

In this lesson, we will be developing strategies for planning and solving problems. We'll start off with a quick activity looking at sequences, before we spend some time exploring the problem, responding to the problem, and then I will you to complete the problem independently.

All you need for this lesson is something to write on, something to write with, and a ruler if you have one.

Press pause, collect the items that you need and come back and we'll start.

Let's kick start the lesson with some sequences.

I'd like you to complete them.

Fill in the gaps.

Press pause, have a go at this, come back and we'll look at the solutions.

Should we take a look? So, first sequence, look at what's the same, look at what's different between the numbers, and what that difference is.

Have you noticed there's a change between the numbers of two hundredths? An increase of two hundredths between each number.

So these should be the numbers that you have filled in to complete that sequence.

Second one, again, what's the same, what's different.

What's changing.

How is it changing it? A decrease of 100th between 12 and 11 hundredths.

Apply that difference and you should have these numbers.

Third one.

What did you notice was changing, increase or decrease? Increase, of how much? Five hundredths.

If you apply that to the other three numbers, you will have those three.

Hmm, the fourth one, I'm having to change my approach.

I had been looking at the first two or three numbers, but I've only got one number at the start of this sequence.

Let's look at the end.

9.

4, 9.

45, what's the change? An increase of how much? Good, five hundredths.

So then go back to 9.

2 and apply that change increasing by five hundredths each time.

Last one, we haven't got any numbers on the left to help us.

So we're looking to the right.

What's changing? And how is it changing? So a decrease each time of one-tenth.

So, we could work from 3.

2 and increase by one-tenth.

Increase again and increase a third time.

So that then when we work from the left backwards, the decrease of one-tenth between each number is working.

Hold up your have your paper, let me see how you got on.

Good, and if there are any errors, it's okay.

So long as you can spot where you went wrong, how you went wrong, and there'll be some learning that comes from that as a result.

Let's have a look at the problem for this session, Marathon Training.

Tacita is training to run a marathon.

Her first session, so her first training session, lasts 30 minutes.

Each training session afterwards increases by eight minutes each time.

There are three questions that you're going to have answered by the end of the session.

We're not going to answer them now.

Let's slow things down, but for your independent task, you'll be answering those three and we'll check the solutions at the end.

So, breaking it down, some questions for you.

How long did Tacita to run for during her first training session? Let me give you a moment to find that solution.

Got it? Was it there? Her first session lasts 30 minutes.

Second question.

How much longer will her second training session be, compared to her first training session? I'll give you a moment to find it in those first two sentences, three sentences even.

Got it? Was it there in the third? Good, and the solution? The second training session will be eight minutes longer than the first.

Third question.

Okay, so then how long will her second training session be? Good, 30 minutes plus add eight minutes, 38 minutes.

It's the length of her first session plus another eight.

Next, how much longer will her third training session be, compared to her second training session? Got it? Look back at the paragraph if you need to.

Each session afterwards increases by eight minutes each time.

So, it will be eight minutes longer.

How long will her third training session be? So we know that is going to be eight minutes longer.

Previously we'd worked out the second session would be 38 minutes, add another eight and we've got this sessions' length.

Session three, 46 minutes.

It might help you to write that down on some paper if you haven't already.

Session one, 30 minutes.

Write it down.

Grab a pencil, write it down.

Session one, one, 30 minutes, two, 38 minutes, three, 46 minutes.

Maybe you could just write M for minutes or maybe not.

That might confuse us and make us think we're working with metres.

Maybe write down M-I-N for short to stand for minutes, good.

Are you ready? Read them back to me.

One, 30 minutes.

Two, 38 minutes.

Three, 46 minutes.

Okay, six and seven.

I'd like you to pause and have a go at independently.

Use what you've recorded about the first, second and third training sessions to answer the questions about the fourth and the fifth.

Press pause, come back when you've got some solutions.

Should we take a look? Okay, so we know each training session increases by eight minutes each time.

So, session one, 30 minutes.

Session two, 38 minutes.

Session three, 46 minutes.

Add eight minutes on and you should have 54 minutes for session four.

What did you get for session five? Good, another eight minutes on from 54 minutes.

62 minutes for training session five.

Now, we're going to be, as we solve this problem, looking at sessions up to number 10 and beyond.

I wonder, looking at what you've just calculated for session five.

Maybe make a quick prediction for how long session 10 might be.

Record it on your paper.

Ready for you to check against as you work independently in a few moments.

So, a quick prediction.

Session 10, how many minutes might it be? Call out your prediction to me.

That is a lot of minutes.

We will see.

We will find out for sure.

Based on what you've been recording so far, just hold it up to me so I can see how you've been laying out your findings.

Okay, so I'm wondering now, if we're going to be working up to session 10, 11, 12, and onwards, how could we organise our maths and organise our thinking? I've got a suggestion for you and it's a table like this.

Do you see session first, second, third, fourth, fifth, and so on, and a space underneath for the number of minutes spent training.

We're ready almost to have a go at solving those first three questions from the beginning of the session.

The ones I said you would work on independently.

How long will her 12th training session be? What will be the total amount of hours, she has spent training after six sessions? You need to think about all six sessions and the total amount spent training.

Then third, Tacita is aiming to run two and a half hours in a session, wow! Running for two and a half hours, ah! Which will be the first session when she runs more than this time? Here's the table again.

There's a copy of it for you to use or to copy down onto your own paper, so that you're able to find out the lengths of the training sessions, the number of minutes for all of these to help you then answer those three questions.

Press pause, go and have a go at solving the problem.

Come back and share with me what you found out.

How did you get on? I don't know about you, but just looking at the number of minutes she spent running has left me feeling tired.

Shall we see if we've got the same number of minutes? This is what I found out.

Are you ready? So I've recorded it in my table.

I knew the first five, we'd worked on them together.

And I know that for each next session, the number must increase by eight.

So, I increased my numbers by eight each time.

Just check that up to 10, this is what you got.

And just on number 10, how did that compare to your prediction? How many minutes did you think she would spend running in session 10? And was that prediction more or less than the amount that it ended up being, 102 minutes? Okay, I'm filling in the rest up to session 16.

These are the minutes that you should have found.

I wonder if anyone noticed any patterns between those numbers of minutes.

We know they're increasing by eight each time, but did you notice any patterns, particularly in the ones place.

Did you notice? Zero, eight, six, four, two, zero, eight, six, four, two.

That was really helpful for preventing any little slips.

If you made a little bit of an error in adding on your eight.

If you'd been noticing that pattern, you would know if you were right or wrong or when an error had happened.

So as for those actual questions then.

So number one, how long will her 12th training session be? 118 minutes.

Number two, the total amount of hours she spent training after six sessions.

Now, did you answer 70 minutes.

If you did, that's the amount of time from session six.

If you didn't, did you include the first, second, third, fourth, and fifth, as well as the sixth.

And did you then find the total? That's what the question is asking you to do? Do you see the number of minutes from each of those sessions? Six, five, four, three, two, and one.

If you then totaled them, you should have had 300 minutes.

But, if you've left the answer as 300 minutes, you've missed part of the question.

Which parts of the question have you missed? The total amount of hours.

Five hours, 60 minutes, and one hour.

300 minutes in five hours.

Number three, Tacita is aiming to run two and a half hours in a session, which will be the first session when she runs more than this time? I thought about what two and a half hours is in minutes.

So two hours is 120 minutes.

Half hour is 30 minutes.

That's 150 minutes in total.

And I can see session 16 is 150 minutes.

Is session 16 the answer then? Which will be the first session when she runs more than this time? So definitely in session 17, eight minutes more.

That will be the first time she runs more than two and a half hours.

I hope you enjoyed this session, Marathon Training.

We are so lucky that all we had to do, was sit back and work with some numbers today.

Can you imagine running for as long as Tacita did in some of those sessions? I am tired just looking at those numbers.

If you would like to share any of your findings from this problem with Oak National, please ask a parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Has this lesson left you feeling inspired to run a marathon one day.

Now you've seen just how much training Tacita has needed.

I wonder if that has spurred you on or made you a little bit more cautious.

Hopefully one day you will manage some running, and you will receive some certificates or medals.

I look back on my three-mile run and think, I could probably give that a better shots now, and maybe run a longer distance.

But looking at Tacita's training records, I don't think it will be easy.

Some work will be needed.

Thanks for joining me for this Maths lesson.

I hope you've enjoyed it.

And with any more learning that you've got lined up for the day, I hope you enjoy that too.

See you again soon for some more Maths learning.

Bye.