Maths in sports day: relay order

Quick answer

When planning a sports day relay race, you need to think about how to arrange your team members so that the race is fair, fun, and fast. The order of runners can make a big difference to how well your team does. You can use maths to work out the best way to line up your runners, considering their speeds, strengths, and how the race works.

Learning outcome

By the end of this page, you will be able to decide the best order for runners in a relay race using simple maths ideas like speed, teamwork, and fair play.

• I can think about who should run first, second, third, and fourth in a relay race.
• I can use simple maths to compare runner speeds and plan a good team order.
• I can explain why a certain order might be better than another.
• I can help plan a relay race with my friends or family.

Why this matters

Maths helps us make smart decisions in sports. When planning a relay race, you use maths to decide who runs which part of the race. This helps your team do better and makes the race more exciting for everyone. Whether you're at school or playing with friends, thinking about order and speed is a great way to use maths in real life.

How it works

Planning the order of runners in a relay race is like solving a puzzle. You need to think about:

1. How fast each runner is
2. What part of the race they are best at
3. How the race is set up (how long each leg is)
4. How to make sure the whole team works well together

For example, if you have a very fast runner, they might be best for the first leg so they can start the race quickly. A strong runner might be better for the last leg to finish strong. Sometimes, you might want to put your fastest runner in the middle to keep the race close.

Examples you can see

Imagine you are planning a 4-person relay race with these runners:

• Runner A: 10 seconds for 50 metres
• Runner B: 12 seconds for 50 metres
• Runner C: 11 seconds for 50 metres
• Runner D: 13 seconds for 50 metres

Who should run first? The fastest runner is A, so they should probably go first to get a good start. Who should go last? Runner D is the slowest, so they might be best for the last leg to make sure they still finish strong.

Here’s how you might plan it:

This order makes the race fair and fast. It uses the fastest runners early and keeps the team strong to the end.

Try it as a mini adventure

Let’s go on a fun adventure! Imagine you are the coach of a school sports day team. You have 4 runners, and you need to decide who runs which part of the relay race.

Your team members are:

• Emma – runs 50 metres in 10 seconds
• Leo – runs 50 metres in 11 seconds
• Maya – runs 50 metres in 12 seconds
• Sam – runs 50 metres in 13 seconds

Here’s your challenge:

1. Who should run first?
2. Who should run second?
3. Who should run third?
4. Who should run fourth?

Draw a picture of your team with the runners in the order you think is best. Explain why you chose this order.

Common mistakes

• Mistake: Putting the fastest runner in the last leg. Why it happens: Kids might think that the best runner should always go last to finish strong. Fix: The fastest runner should go first to get a good start, not last.
• Mistake: Not thinking about the race distance or how long each leg is. Why it happens: Some children focus only on speed and forget that longer legs might need stronger runners. Fix: Think about how the race is set up and what each runner can do best.
• Mistake: Trying to match runners by speed only. Why it happens: It’s easy to think that the fastest runner should always go first. Fix: Think about strategy – sometimes it’s better to put a slower but strong runner in the middle to keep the race close.

Parent and carer guide

Helping your child plan a relay race order is a fun way to use maths at home. Here’s how to support them in 5–10 minutes:

• Ask questions: "Who do you think should go first? Why?"
• Use real examples: Think about a race you’ve watched or played in together.
• Draw it out: Use paper or a whiteboard to show the runners and their order.
• Encourage thinking: Let them explain their thinking, even if it’s not perfect.
• Keep it fun: This is a chance to play and think like a coach!

Remember, it’s not about getting the "right" answer – it’s about thinking about how maths helps us solve problems in sports and real life.

Practice questions

1. Which runner should go first in a relay if their times are: A – 10 seconds, B – 12 seconds, C – 11 seconds? Answer: Runner A
2. Which runner should go last if their times are: A – 10 seconds, B – 12 seconds, C – 11 seconds? Answer: Runner B
3. Which runner should go second if their times are: A – 10 seconds, B – 12 seconds, C – 11 seconds? Answer: Runner C
4. If a relay race has 4 legs and each leg is 50 metres, and your fastest runner is 10 seconds, how long does the first leg take? Answer: 10 seconds
5. Which runner should go in the middle of a 4-leg race if their times are: A – 10 seconds, B – 12 seconds, C – 11 seconds, D – 13 seconds? Answer: Runner C

FAQ

Why do we need to think about the order of runners in a relay race?

Because the right order can make your team faster and more successful. It helps you use each runner's strengths to the best of their ability.

Can we change the order if someone gets tired?

Yes! Sometimes, you might change the order during a race if someone gets tired or if the race changes. This is part of using maths to solve problems.

What if all runners are about the same speed?

If everyone runs at about the same speed, you might choose the order based on who is most confident or who works best with the team.

Is it better to have the fastest runner go first or last?

It’s usually better to have the fastest runner go first so they can get a good start. But sometimes, a strong runner in the middle can help keep the race close.

Can we use maths to plan other parts of sports day?

Yes! Maths helps with timing, scoring, setting up games, and even choosing which games to play. It’s a useful tool for planning and making sports day fun for everyone.