Lesson video

Hi, I'm Mrs. Wheelhouse.

And welcome to today's lesson that's from the unit Maths in the workplace.

In this series of lessons, we're exploring how maths is used in different careers.

So let's get started.

In today's lesson, we're going to be looking at some of the ways that maths is used by emergency response workers.

Let's get started.

In our lesson today, we're going to be using a couple of key words.

Now these words should be familiar to you, but if they're not, feel free to pause the video now while you have a read through their definitions.

Our lesson is broken into two parts today.

And we're gonna begin by looking at uses of formulas.

Formulas are everywhere in our world.

We see them in maths.

We see them in science.

We use them in cooking.

And some people believe you can even write a formula for love.

Now emergency responders use formulas on a daily basis.

This is the gauge of a firefighter's breathing apparatus.

When a firefighter connects this to their oxygen tank, the gauge tells them how many bar of pressure are left.

In the UK, a firefighter must have a minimum 240 bar of pressure in their oxygen tank before they can enter a building.

Let's do a quick check then.

In the UK, a firefighter must have a minimum 240 bar of pressure in order to enter a building.

Which of these tanks can be safely used by the firefighter? Pause the video and make your choice now.

Welcome back.

What did you go for? Well, it's definitely not A, that's nowhere near enough.

B on the other hand, we can see easily that's in excess of 250 bar of pressure, so that's definitely safe.

Now C is technically safe, but this is the very minimum.

I'd want to be very careful if I was using that oxygen tank.

Now firefighters might enter the building to fight a blaze.

They might be entering a large building which has lots of people in it in order to perform a search and rescue during a fire.

Before entering, they each have to use a key formula.

And that's this formula here.

Let's explore what this means.

The t stands for the estimated turn-around pressure.

B is the number of bar of pressure they enter the building with.

This formula helps them calculate when each firefighter must turn around and exit the burning building.

For example, a firefighter entering with 240 bar of pressure, so we'll substitute that into the formula, has a turn-around pressure of 150.

In other words, they have to turn around and exit the building when their pressure gauge reads 150 bar.

150 bar might sound like a lot of remaining pressure, but the firefighter might be deep inside the building and may use a lot of air making their way out.

They might even be carrying someone.

So let's do a quick check.

At what bar will a firefighter entering with 290 bar of pressure turn around? Pause the video and work this out now.

Welcome back.

Well, if you substitute the 290 correctly into the formula, you should have calculated that they'll turn around when their pressure gauge reads 175 bar.

Well done if you got that right.

Lucas is calculating the estimated turn-around point of a firefighter entering a building with 260 bar.

Lucas says, 260 plus 30 equals 290.

Half of that is 145.

So they will turn around after 145 minutes.

Now Lucas has made at least one error here.

Could you please spot his errors and then explain how he should correct them.

Pause the video and do this now.

Welcome back.

How did you get on? Well, the first thing we should have done is pointed out that Lucas has failed to apply the priority of operations.

The 260 bar should be multiplied by 1/2 before the plus 30 is applied.

You might also have said Lucas has used incorrect units in his answer.

The turn around is in units of pressure, so bar, it is not a unit of time spent inside the building.

Now firefighting is not the only emergency response career to use formulas.

Accident investigators in the police force can use a formula at the scene of an accident to calculate the speed at which a vehicle was travelling.

They use this formula here.

S is the speed of the car and it's the speed that it was travelling at in miles per hour.

D is the distance the car skidded in feet.

And f is the coefficient of friction.

Now the coefficient of friction is the friction between the tyres and the road.

And this number will vary depending on the condition and the type of surface.

For example, on a dry concrete surface, the coefficient of friction is 0.

8, whereas on a wet concrete surface, the coefficient of friction is 0.

4.

In other words, the coefficient of friction is higher where there's like to be more friction and it's lower if there's less friction.

A police officer measures these skid marks at the scene of an accident on a concrete road on a dry day.

We can see here that the distance of the skid marks is 120 feet.

By substituting into the formula, they can calculate how fast that car was travelling at the point they applied their brakes.

So let's see how fast they were travelling.

D is 120 and f is 0.

8.

So we put that into our formula and we calculate that s is equal to 53 point, well, you can see the calculator display.

There's quite a lot of digits there.

So we're gonna round to one decimal place.

In other words, the car is travelling at 53.

7 miles per hour.

It's now time for a quick check.

A police officer measures these skid marks at the scene of an accident on a concrete road on a wet day.

Was the car exceeding the 30 mile per hour speed limit? And I'm going to let you know that the coefficient of friction on a wet concrete surface is 0.

4.

So, pause the video now and calculate was the car exceeding that 30 mile per hour speed limit? Pause and do this now.

Welcome back.

What did you work out? Well by substituting in d is 97 and f is 0.

4, we get that, ah, look, even to one decimal place, our speed is 34.

1 miles per hour, which is definitely in excess of that 30 mile per hour speed limit.

In other words, the car was speeding.

It's now time for first task.

In question 1 part A, I'd like you to calculate at what bar the firefighter should turn around and start exiting the building? And in part B, the firefighter has an estimated turn-around pressure of 160 bar, so how many bar of pressure did they have when they entered? Pause and work this out now.

Welcome back.

Now carrying on part C, what's the difference in turn-around pressures between entering with 240 bar and entering with 300 bar? And then part D, why do you think the formula includes a plus 30 instead of just being your turnaround is equal to 1/2 of the pressure you walked in with? Hmm, why might that be? Pause while you work these out now.

Welcome back.

Question 2 A, you are a police officer investigating an accident.

Use the formula to calculate the speed of this car on a dry concrete surface.

And then in part B, if a car were travelling 70 miles per hour on a wet concrete surface, how long would you expect the skid mark to be? Pause while you work these out now.

Right, in part C, Lucas has used the formula incorrectly to calculate the speed of a car with a skid mark of 60 feet on a dry concrete surface.

Please explain his error to him and correct his work.

Pause and do this now.

Welcome back.

Final part here.

A police officer investigating an accident in a 20 mile per hour zone with a dry concrete surface declares, the length of the skid marks were 20 feet to the nearest 10 feet.

Explain why they cannot round like this when investigating this accident.

Pause and work this out now.

Time to go through our answers.

So of question 1, part A, the firefighters should turn around when their pressure gauge shows 210 bar of pressure.

In part B, how many bar of pressure did they have when they entered the building? Well, 160 was the result, so we'll need to substitute that into the formula and rearrange.

So by subtracting 30 from both sides and then multiplying both sides by 2, we know that the firefighter entered with 260 bar of pressure.

In part C, we want to know the difference in turn-around pressures here.

So let's calculate for both situations.

So we can see that there's a difference here, a 30 bar of pressure.

In part D, why do we have this plus 30? Well, you might have said, if the formula were t equals 1/2 b firefighters would turn around after using exactly half their air.

Now if they exerted more effort exiting, because for example they were carrying someone, they would not have sufficient air to get out safely.

So the plus 30 is there to give them a small safety barrier.

So question 2, part A, I asked you to use the formula to calculate the speed of this car.

So by substituting in d is 197 and f is 0.

8, you should have calculated the speed to be 68.

8 miles per hour to one decimal place.

In part B, I wanted to know how long you'd expect the skid mark to be.

So we substituting the information we know and we're going to need to rearrange.

So the first thing I did was I simplified what was under the square root sign.

So I did 30 multiply by 0.

4 to get 12.

Then I squared both sides.

And then divided by 12 to give me that d is equal to 408.

3 feet to one decimal place.

Now Lucas has made an error here.

I'm not entirely sure, Lucas, you would have a car travelling at 262.

9 miles per hour.

So I think Lucas should have realised he'd made a mistake.

But did you spot where? Well, you might have said the vinculum should group the 30df.

In other words, he should be square rooting the entire expression there, not just the 30.

The car was actually travelling at 37.

9 miles per hour, a far more reasonable speed.

In part D then, why can our police officer not round to the nearest 10 feet when investigating an accident? Well, you might have said, by rounding to the nearest 10, the actual length falls in the region of 15 to 25 feet, which makes the bounds for the speed.

Well, let's have a look.

So bear in mind, the length of the marks were 20 feet to nearest 10 feet.

Well, that means it could have been 15 feet and we've rounded up to 20, or it could have been just under 25 feet and we rounded down.

Hmm, so what speed could I have been travelling at? Well, it means that my car could have been going at as little as 19 miles per hour, but as much as just under 24.

5 miles per hour.

So I could have been speeding but also might not have been speeding.

We can't tell if our measurement's been given to the nearest 10 feet.

So we can't prove whether this driver was obeying the speed limit or not.

And that's no use.

It's now time for the second part of our lesson on uses of data.

Now, data forms an essential part of operating successfully for emergency service workers.

Data enables emergency services to adequately plan to meet the needs of the public.

So an ambulance station records data on the reason for call-outs for its paramedics for a quarter.

This data tells them that they need to stock their ambulances with larger amounts of medical supplies to treat, injury, in particular trauma, abdominal pain, and respiratory distress.

Let's go a quick check to see that you understand that.

A different ambulance station in a city centre records data.

To what illnesses should they dedicate the most training time for their emergency responders? Pause the video while you write this down now.

Welcome back.

Let's see what you put.

Well, psychiatric disorder and chest pain would definitely be there.

I mean, look at that, that's almost 50%.

Now if you ever call for an ambulance, you get through to an emergency responder whose job it is to assess and prioritise your need.

For illnesses which have an immediate threat to life, the emergency services set target response times An ambulance station records the average time it takes for them to reach every single call for cardiac arrest over two years.

The target response time is seven minutes or less.

What patterns do you see in these response times? Pause the video while you have a discussion with the person next to you or you have a think.

So what patterns do you see? Well, I see that they hit their target response time in the mid to late winter and early spring months.

But they seem to miss their target response time in the summer months and in November, December.

This sort of analysis might lead to changes in practise, staff numbers or shift patterns in order to ensure seven minutes is more consistently hit.

Let's do a quick check.

An ambulance station records this data on the average time it takes them to attend call-outs for strokes, which is a category two threat to life.

The target response time is 18 minutes.

What can you conclude from this data? Pause the video and work this out now.

What did you conclude? While this station is not yet meeting its target, but the trend is improving.

If the trend continues, we can expect them to hit 18 minutes next year.

It's time now for your final task.

An ambulance station records their average response times to emergency calls for one year.

What patterns did you see in this data? Pause the video while you work this out now.

Question 2, a regional fire service records the reasons for house fires over a year and produces this chart.

What advice would you give this fire service? Write at least three sentences.

So think about what you might suggest that they do with their practise, what they might or how they might use this information.

Pause the video while you do this now.

Welcome back.

Let's go through the answers.

So the ambulance station records their average response times to emergency calls for a year.

What patterns do you see in this data? Well, you might have said, response times to life-threatening calls, so that was the shorter blue bars, are improving.

Whereas non-life threatening response times are getting worse.

And that's the red bars that you can see slowly increasing as we move through the year.

Now for question 2, I asked what advice you'd give this fire service and that you had to write at least three sentences.

Well, you might have said, the fire engines need to be adequately stopped with the correct gear to tackle cooking appliance fires as these account for more than half of house fires.

In other words, we want to stock the fire engines appropriately so we have the right equipment when we arrive.

You might have also said that appliances, both cooking and domestic, account for around three quarters of fires.

This fire service might consider extra training for firefighters on these types of fires.

Additionally, they might consider a public campaign to help raise awareness of what causes these fires and what can be done to prevent them.

It's time to sum up what we've learned today.

Maths is used in different ways by emergency response workers.

Firefighters use a formula to calculate their turn-around time before entering a burning building.

Police officers use a formula to calculate the speed of cars that were involved in accidents.

All emergency services use data to track their performance over time and to make sure they are prepared to meet the demands placed upon them by the general public.

Well done today.

I hope you've enjoyed learning just some of the ways maths is used by emergency response workers.

And we didn't just look at one type of emergency response worker, we considered firefighters, we considered the police, and we considered the ambulance service.

I really hope that you found this useful and informative.

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

Bye for now.