Lesson video

Hi, I'm Mrs. Wheelhouse, and welcome to today's lesson, which is from the unit, "Maths in the workplace." In this series of lessons, we're exploring how maths is used in different careers.

Let's get started.

By the end of today's lesson, you're going to have looked at some of the ways that maths is used by sports coaches.

Now on the screen, you'll see some keywords.

If you need to, feel free to pause so you can have a read through these words and the definitions if they're unfamiliar to you.

Feel free to do this now.

Our lesson today is broken into two parts, and we're going to begin by looking at recording and using data.

Now sports coaches use a lot of mathematics in their work.

One thing they do an awful lot of is measuring.

"Well done, Sophia," says Coach Lucas, "you did that 800 in 2:16." The 800 is a measure of distance, and the 2:16 is a measure of time.

In fact, sports coaches and athletes are so familiar with their measures, they automatically know what units are being used.

Did you spot that Lucas hadn't given the units? What units do you think Coach Lucas is using here? Pause the video and have a quick chat.

Welcome back.

So what units do you think Lucas is using? Well, the 800 is actually 800 metres, and the 2:16 is two minutes and 16 seconds.

Let's do a quick check.

What units is Coach Lucas talking about here? "Well done, Sophia, that long jump was 3.

95." Hmm, what units could Coach Lucas be referring to? And then, to Aisha, he says, "Well done, Aisha.

You ran that half marathon in 1:57.

That is an average speed of seven," what? Pause the video while you work this out now.

Welcome back.

Let's go through our answers.

So, the 3.

95 that Sophia jumped, that's 3.

95 metres.

Could you imagine if it was centimetres, she'd only jumped that far? It's not really a long jump now, is it? But what about Aisha? She ran that half marathon in 1:57, and that's an average speed of what? Well, the 1:57 refers to one hour and 57 minutes.

Now marathons normally have their distance stated in miles.

So this would mean that her average speed is likely to be seven miles per hour.

Well done if you worked that out.

Traditionally, coaches have used devices like stopwatches to record performances.

These devices gave us limited information, and it all had to be written down.

Modern technology does a lot of the recording now.

The technology records a variety of data which coaches and athletes can use to monitor performance.

Which of these things do you think smart tech can record for athletes and coaches? So you can see, there are eight things listed on the screen.

We have time taken, speed, heart rate, calories burnt, distance covered, average speed, average heart rate, and total hours trained.

Pause the video and have a discussion about which of these you think smart tech can record for us.

Do that now.

Welcome back.

So which ones did you pick? Well, you should have chosen, that's right, all of them.

All of these things can be recorded for us.

Smartwatches or smartphones are smart.

They give athletes and coaches a lot of varied data to enable the analysis and improvement of performance.

Now, in sports, we encounter some units we might not have seen before.

Kcal is short for kilocalories.

A calorie is a unit of energy that we get from food and drink.

Teenagers burn roughly between 1,600 and 2,400 calories every day.

Now, Sophia trains at high intensity three or more times a week, and factors these extra calories that she needs into her diet.

Bpm stands for beats per minute.

This is the number of times your heart beats in one minute.

Teenagers and adults will have a resting bpm of between 60 to a hundred.

During exercise, your bpm increases, as your heart works hard to get oxygen to your muscles.

Let's do a quick check.

Coach Lucas is using an app which has recorded in graphs Sophia's heart rate during a training session.

When do you think Sophia was working at a high intensity, so she was working hard, and when do you think she was stretching? Pause the video while you work this out now.

Welcome back.

So what did you put? Well, I think, as the heart rate is starting to increase, Sophia's warming up.

I think that high intensity was there, when her heart rate went above 160 beats per minute.

I think when her heart rate slowed all the way down to 60 beats per minute, she's likely to have been stretching, and then she builds back up to a high intensity there at the end.

Now Sophia's heart rate was as low as 60 beats per minute and as high as 165 beats per minute during her training session.

Let's see if that's normal.

Now teenagers and adults have a resting heart rate of between 60 to a hundred bpm.

Athletes do tend to be at the lower end of that scale and have a lower heart rate when resting.

During exercise, your heart rate will rise, but what should we be aiming for? To maintain a healthy heart, it is important to raise your heart rate frequently through exercise.

There is a calculation for your target heart rate.

Now your maximum heart rate is 220 beats per minute minus your age.

The target heart rate for moderate exercise is 50 to 70% of the maximum.

The target heart rate for high intensity is 70 to 85% of the maximum.

Sophia is 14 and was operating at high intensity.

So was 165 beats per minute the right heart rate for her? Well, let's check.

Her max heart rate is 206.

70% of that is 144 beats per minute, and 85% is 175.

Well, at 165 beats per minute, Sophia was in the correct zone for intense exercise.

Brilliant, she was working at the intensity she needed to be.

Let's do a quick check.

Jacob is just taking up regular exercise.

He wants to do moderate exercise three times a week, and he wants to count his heart rate.

So I've put some information up to help you with your calculations.

Jacob is 13.

What range for heart rate should Jacob be aiming for? Pause the video while you work this out now.

Welcome back.

Have you got a range for Jacob? Well, let's check the maths.

First of all, we need to calculate his maximum heart rate.

So that's 220 minus Jacob's age of 13 gives us 207.

Now he wants to be aiming, remember, for moderate exercise.

So, 50% of his maximum is 104 beats per minute.

You can see, we've got 103.

5 on our calculator, and we've rounded up here.

Then the higher bound will be, well, from 144.

9, we've rounded up to 145.

So Jacob should aim for a heart rate between 104 to 145 beats per minute for moderate exercise.

Now there are other less technical ways to measure effort for people just taking up regular exercise.

Lucas says, "Coaches like me will use an RPE chart to plan your training sessions, Jacob." On the screen you can see an RPE chart.

RPE stands for rate of perceived exertion.

In other words, you could ask your client, or in this case, Lucas could ask Jacob, how he's feeling or how much effort he thinks he's putting in, and Jacob could give a score.

This allows coaches to assess how hard someone is working.

Feel free to pause at this point if you wanna have a proper read through that chart.

So let's see how the chart is used.

Jacob says, "Is skateboarding a good exercise? I fancy taking that up," and Lucas points out, "That's great exercise! Now, how you're feeling when you're skateboarding will vary.

It's likely that it will probably start off as light and probably build to moderate if you're going quite fast." Let's do a quick check.

Where do you think these activities would be on the chart for someone just taking up exercise? So we've got walking on a treadmill, walking up a steep hill, 10 minutes cycling to a friend's house, two minutes intense trampolining, and gaming.

Pause the video while you assign each of these activities a score.

Welcome back.

Let's see what score you gave.

So, I said walking on a treadmill, that's very likely to be light exercise.

For just walking on a treadmill, it should be easy to maintain that for quite a while, and conversation should come easily.

Walking up a steep hill is likely to be moderate.

We could continue to do this, but our breathing is likely to be a bit heavier, and conversations are likely to be quite short.

10 minutes cycling, well, if we're just going quite lightly, it's down here because we could talk while we're cycling, and we can maintain that.

Remember, we didn't say we were gonna cycle really hard.

Two minutes intense trampolining is likely to be vigorous.

In other words, we're gonna start to get quite short of breath and maybe only shout single sentences out.

You might have even said it's hard or very hard, and you might have given it a nine or pushed it towards the eight/nine boundary.

Gaming, very light.

We're just sitting down, playing on a computer game, or we're sitting at home, playing a board game.

That's very, very light activity.

Now Lucas says, "If you're just starting, I don't want to see a nine or a 10 just yet." So he's saying, "Okay, look, you might, with your intense trampolining, be pushing towards a nine, but you've just started to exercise, and you're not used to it, so do be careful, and don't push yourself too hard at the start." Good advice, Coach Lucas.

Now Coach Lucas calculates averages to monitor Sophia's performances in the 800 metres.

He points out he can calculate the averages for her times.

If he wants to calculate the mode, he can see it's 132 seconds.

The median's 132 as well, and the mean is 132.

8.

Gosh, Sophia's really consistent.

So she points out, "I'm most likely to run 132 seconds as my time, but I might run 138.

Oh, that's not enough to beat my competitors!" She's not happy about this.

Coach Lucas, though, says, "Relax, I know you're improving.

You ever heard of three-point moving averages?" What's that? Well, let's graph Sophia's times.

Now that line is erratic.

Is it gonna go back up next? Will it go down? Is she improving? Quite hard to tell from this.

Let's consider this three-point average, though, that Lucas was talking about.

By doing that, we should see a trend.

If there is one, should be a lot easier to spot.

So what we do is we take the average of three points.

So let's consider the first three times.

W average them, and get a time of 135.

3.

Now I'm gonna round this to the nearest second, so we'll go with 135.

We then plot that point.

We'll then move to the next three averages, so we only shift one along.

Now we find the average of these three-points, and that's 134, and then we plot that.

We now do the next three and plot that point, and this continues.

So after populating the whole table and plotting all three-point moving averages, we see a far smoother line with a clear trend moving downwards.

Sophia is improving over time.

No wonder she looks happy.

Quick check now.

Find the remaining three-point moving averages and continue Sophia's trendline to check that she has continued to improve.

Pause and do this now.

Welcome back.

So let's just check your averages, first of all.

We should have 129, another 129, and then 128.

So we plot these to continue the graph.

Sophia has indeed continued to improve.

Her rate of improvement has slowed, but that is not unusual for high performers as they near their maximum potential.

It's time now for your first task.

For question one, part a, Jacob goes skateboarding, and his watch to records his bpm.

Write at least three sentences to describe Jacob's skating session.

Use words like moderate intensity and high intensity.

You could even refer to the RPE chart if you wish.

Pause and do this now.

Welcome back.

Part b, rank these three moments with a numerical value from the trainer's RPE chart.

So if you didn't do this part in part a, now's a great time to do it, and you might even wanna go back and improve your sentences to part a.

Pause the video and do this now.

Question two, sporty Sophia is filling in a target heart rate chart for older members of her family to use while they exercise.

She's got some information there to help her calculate this.

Using that information, please fill in the blanks in the table.

Pause and do this now.

Question three, Aisha is trying to improve her 400 metre time.

Here are her best times over 10 weeks of training.

Part a, please calculate the mean, mode, and median of her times, and then in part b, write a sentence explaining why these three averages alone do not inform you as to whether Aisha is improving or not.

Pause the video and work this out now.

Part c, populate the table of three-point moving averages to the nearest whole number.

The first one's been done for you.

In part d, graph Aisha's three-point moving averages and write a comment as to whether she's improving or not, and then in part e, use your three-point moving averages to make a prediction as to when Aisha might break the 60-second barrier.

Pause and do this now.

Welcome back.

Time to go through our answers.

So, I asked you to write at least three sentences to describe Jacob's skating session.

So you might have written, "Jacob spent the first 20 minutes skating at a moderate intensity.

He then had a period of rest and finished with a period of high intensity, where his heart rate looked like it was at its max." In part b, I asked you to rank these moments.

So, anywhere between a four to a six would be appropriate for the first moment.

Second moment's likely to be a one, down that resting heart rate, and then that high intensity is likely to be a seven or an eight.

Now, for sporty Sophia, I asked you to fill in the heart rate chart.

These are the values you should have got.

Feel free to pause the video now while you check my answers against your own.

Question three, you need to calculate the mean, the mode, and the median of Aisha's times.

Well, the mode is 70 seconds, the median is 68 seconds, and the mean is 67.

9 seconds.

Now why do those averages alone not inform you as to whether Aisha's improving? Well, you might have said, "These averages are calculated over the whole 10 weeks.

They give us important information but show nothing about progress over time." Part c, you need to populate the table with three-point moving averages.

These are the values you should have got.

Do feel free to pause the video if you need to check these.

And then part d, I asked you to graph it, and now write a comment as to whether she's improving.

So you might have said, "Aisha's three-point moving averages are trending downwards, therefore she is improving." Well done, Aisha.

And then for e, use these averages to make a prediction as to when Aisha might break the 60-second barrier.

Well, you might have said, "Aisha's three-point moving averages are improving by approximately half a second per week.

If this trend continues, she should break the 60-second barrier in another 10 weeks." Good luck with that, Aisha.

We're now on to the second part of our lesson, and that's using data to plan training sessions.

Sports coaches use data to plan training sessions which fit the training needs of the athlete.

Researchers told us that different types of athletes have different training needs, so should be training differently.

The training plan needs to meet the performance targets of the athlete.

This table tells you how three different types of athletes should train.

Rep is short for repetition.

That is a single repetition of an exercise.

For example, one press-up could be one rep.

A set is a collection of reps.

For example, 10 press-ups could be called one set.

The rest period is the time spent recovering between the sets.

An intensity is how hard your body is working during an exercise.

1RM is an abbreviation of one rep max, i.

e.

, it is the maximum that can be achieved in one repetition of an exercise by an athlete.

A long distance runner might have a training goal of endurance.

They need to keep going for a long time after all.

A decathlete might be training for muscle leanness because they need to perform a variety of athletic challenges, and a weightlifter might be training for muscle strength.

Let's do a quick check that you've got that.

What I'd like to do, please, is read through the sentences and fill in the gaps.

Pause and do this now.

Welcome back.

Let's go through this.

So someone with the training goal muscle strength will typically do the fewest reps.

You can see that in the muscle strength row, reps is under six.

Someone with the training goal endurance will typically do the fewest sets, and you can see in the sets column, endurance is only three to four, where muscle leanness is three to six, and muscle strength is four to six.

And then, finally, someone training at 70% of 1RM is training towards muscle leanness, and we got that from our intensity column.

Well done.

Lucas is putting together a training plan for his older sister who is trying to get into competitive power lifting.

Lucas' sister is over 18, so her body is fully developed, so therefore she can train suggested above for muscle strength.

Lucas says, "We're gonna start with an easier plan for a month and then build up.

Her current 1RM is 120 kilos," so in other words, that's the maximum that she can lift.

So, this is her starter plan.

We're gonna start off at the lower end of the intensity, in other words, she's gonna be lifting 105 kilos.

She's going to do four sets of four reps, so in other words, the smallest number of sets, and she's doing quite a low number of repetitions.

The rest period's gonna be high.

Remember, she's just starting out here, so she needs to be able to recover between her sets.

Lucas says, "Right, it's now been a month, and she's training well.

We're stepping up the training plan." So this is her plan.

The intensity is going to stay the same, but look at what's changed now.

Instead of doing four sets of four, she's now doing six sets of four.

And the rest period has come down a little bit, but not by much.

Remember, we want her to improve, so what we're doing is we're upping what she's doing towards the higher end of the sets and the reps.

Now let's consider an expert plan.

What do you think that might look like for muscle strength development with someone who has 1RM of 120 kilos? Think about what I changed and what I kept the same.

Have a go at this now.

Welcome back.

Now this is an example of what you could have put.

You could have said, "Right, we're on to the expert now, let's increase that weight," so now she's gonna be lifting 108 kilos.

We're at the point now where she's worked quite hard, and we've built up to this slowly, so she's gonna do six sets and of five reps, and the rest period has dropped down, so she's really working a lot harder now and should have built up to this gradually over the weeks.

Now this is not the only solution, but your solution should have included an increase in intensity, sets, or reps, so it didn't have to be all of them, could have just been one, and that's fine too, and we're looking for a reduction of the rest time.

Well done if you did something like this.

Let's consider this one.

What do you think is wrong with this plan for muscle strength development? So imagine that we'd come up with this instead for Lucas' sister.

Can you spot what's wrong with it? Pause the video and work this out now.

Welcome back.

Did you spot the mistakes? Well, the first one is, we can't be working at 110% of our maximum.

That's not possible, and those reps, they're way too high.

Reps should be less than six, not equal to six, and did you spot the rest time? The minimum resting period is two minutes, and we've said 90 seconds.

So there's a lot wrong with this plan.

It's time for your final task.

Question one, Sophia's older brother is training for a heptathlon, therefore needs to develop muscle leanness.

He's working on his bench press, and has a 1RM of 80 kilos.

Create for him a starter plan, an improver plan, and an expert plan.

Pause the video while you work out the plans now.

Question two, part a, someone with a 1RM of 125 kilos in deadlifting is doing reps of 76 kilos.

So what's their training goal? And then part b, someone tells you they did 60 repetitions across all of their sets.

What could their training goal be? And then in part c, someone tells you they are intensely training for muscle leanness and are deadlifting 136 kilos.

What is their 1RM? Pause the video while you work this out now.

Welcome back.

Let's go through our answers.

So, we need to create a starter plan, improver plan, and expert plan.

Now, remember, these are just examples.

For the starter plan, I said, "Well, let's start low." So we're gonna do 70% of the 80 that we're doing, which means 56 kilos is what we need to be using.

And the sets and reps, while I've said three sets, so the lower end of the sets, six repetitions, lower end of that as well, and the rest period is the maximum it can be, so 90 seconds.

When we move to improving, I said, "Okay, I'm gonna increase the weight, but I've kept the sets and the reps low." So as I've built up, I maybe done more reps or more sets in my starter plan.

When I'm ready to move to improver, I move up the weight, and look how the rest period didn't change either.

Then for the expert plan, this time, I didn't change the weight, but I've increased the sets and the reps to pretty much maximum, and I've reduced that rest period.

If you've done something similar, well done, but you should see a gradual build here.

What we don't wanna do is make everything jump up every time.

Well done if you followed those guidelines.

Question two, part a, someone with a 1RM of 125 kilos in deadlifting is doing reps of 76 kilos.

So what's their training goal? Well, if they're lifting 76 kilos, that's 60.

8% of 1RM.

Well, that means they're training for endurance.

Now, someone tells you they did 60 repetitions across all of their sets in part b.

So what could their training goal be? Well, if they did four sets of 15 reps, then they're training for endurance.

If they did three sets of 20 reps, they're also training for endurance.

If they did six sets of 10 reps, then they'd be training for muscle leanness.

They could also do five sets of 12 reps, and again, be training for muscle leanness.

Now if they did 60 repetitions, there's no way they're training for muscle strength because if I do the maximum number of sets, which is six, and the maximum number of reps, which is five, that gives me 30, so there's no way I got to 60.

So we cannot be training for muscle strength.

In part c, someone tells you they're intensely training for muscle leanness and are deadlifting 136 kilos.

So what is their 1RM? Well, the most intense level for muscle leanness is 85% of their 1RM.

So if we assume that's what the 136 kilos is, this tells us that their 1RM must be 160 kilos.

It's now time to sum up what we've looked at today.

Sports coaches use data to track performance of an athlete and demonstrate improvements.

They also use data to plan the training needs of an athlete to help their athletes improve.

Well done.

I hope you've enjoyed learning about some of the ways that maths is used by sports coaches.

I look forward to seeing you for more math in the future.

Goodbye for now.