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Athletics Maths

Maths in athletics: race rankings

Use first, second, third and places.

Quick answer

Maths in athletics: race rankings helps you understand how to order runners by who came first, second, third, and so on. You use counting, comparing, and ordering numbers to figure out who wins.

Learning outcome

By the end of this page, you will be able to rank runners in a race by their finishing times or positions. You will know how to compare times, place runners in order, and understand what first, second, third, and other positions mean in a race. Success signs:
  • You can say who came first, second, third, etc. in a race
  • You can order race times from fastest to slowest
  • You can explain why a runner is in a certain position
  • You can use race positions to solve simple problems

Why this matters

Maths in athletics helps you understand how races work and who wins. Whether you're watching a football match, a swimming race, or a running competition, knowing how to rank runners helps you follow along and understand what's happening. It's also useful in real life when you're comparing scores, times, or results. You might use this when you're playing a board game, making a chart for a school project, or even when you're timing yourself to see if you're getting faster!

How it works

To rank runners in a race, you need to:
  1. Look at each runner's time or position
  2. Compare the times or positions
  3. Order them from fastest to slowest (or first to last)
  4. Give each runner a place: first, second, third, and so on
Let's imagine a race with 5 runners. Each runner has a time in seconds:
  • Runner A: 12 seconds
  • Runner B: 15 seconds
  • Runner C: 10 seconds
  • Runner D: 18 seconds
  • Runner E: 14 seconds
Now, you compare all the times. The fastest time is 10 seconds, so Runner C comes first. Then 12 seconds (Runner A), then 14 seconds (Runner E), then 15 seconds (Runner B), and finally 18 seconds (Runner D). So the ranking is:
  1. Runner C (10 seconds)
  2. Runner A (12 seconds)
  3. Runner E (14 seconds)
  4. Runner B (15 seconds)
  5. Runner D (18 seconds)

Examples you can see

Let's look at some real-life examples to understand race rankings better. Example 1: School Sports Day At your school, there are 4 races. In the 100-metre race, the times are:
  • Emma: 16 seconds
  • Jack: 19 seconds
  • Lily: 14 seconds
  • Tom: 20 seconds
To find the ranking:
  1. Lily: 14 seconds (fastest)
  2. Emma: 16 seconds
  3. Jack: 19 seconds
  4. Tom: 20 seconds (slowest)
So Lily comes first, Emma second, Jack third, and Tom last. Example 2: Swimming Competition In a swimming pool, 6 swimmers race. Their times are:
  • Sam: 42 seconds
  • Jess: 45 seconds
  • Maya: 39 seconds
  • Riley: 47 seconds
  • Leo: 41 seconds
  • Sienna: 48 seconds
Ranking them from fastest to slowest:
  1. Maya: 39 seconds
  2. Leo: 41 seconds
  3. Sam: 42 seconds
  4. Jess: 45 seconds
  5. Riley: 47 seconds
  6. Sienna: 48 seconds
Example 3: Running Challenge You and your friends are racing to see who can run 50 metres the fastest. Here are the times:
  • You: 11 seconds
  • Ben: 13 seconds
  • Anna: 10 seconds
  • Max: 15 seconds
Ranking them:
  1. Anna: 10 seconds
  2. You: 11 seconds
  3. Ben: 13 seconds
  4. Max: 15 seconds

Try it as a mini adventure

Adventure: The Great Race Challenge You are the race official for a fun race in the park. There are 6 kids racing to see who can run 20 metres the fastest. You have to write down their times and then rank them from first to last. Here are the times:
  • Alex: 8 seconds
  • Sophie: 10 seconds
  • Oliver: 12 seconds
  • Grace: 9 seconds
  • Harry: 14 seconds
  • Isabella: 11 seconds
Your mission:
  1. Write the times in order from fastest to slowest
  2. Give each runner a position
  3. Find out who came first, second, third, fourth, fifth, and sixth
Here's your work:
  1. Grace: 9 seconds (1st)
  2. Alex: 8 seconds (2nd)
  3. Isabella: 11 seconds (3rd)
  4. Sophie: 10 seconds (4th)
  5. Oliver: 12 seconds (5th)
  6. Harry: 14 seconds (6th)
Great job! You've ranked the race perfectly.

Common mistakes

  • Mistake: Thinking the slowest time comes first
    Why it happens: It's easy to get confused when you're used to seeing "fastest" and "slowest" in different contexts.
    Fix: Remember, in race rankings, the fastest time comes first, not the slowest.
  • Mistake: Mixing up second and third place
    Why it happens: The words "second" and "third" are similar and can be easy to swap.
    Fix: Count your positions carefully. First, second, third, fourth, fifth, sixth.
  • Mistake: Not comparing all times
    Why it happens: When there are many runners, it's easy to miss one or two times.
    Fix: Go through each runner one by one and compare all times carefully.
  • Mistake: Writing times in the wrong order
    Why it happens: Sometimes kids write times in the order they hear them, not in the correct ranking order.
    Fix: Always sort times from fastest to slowest, or slowest to fastest, and then assign positions.

Parent and carer guide

As a parent or carer, you can help your child understand race rankings by:
  • Playing a game where you race with your child or others and time each run
  • Looking at real races together, like on TV or online, and asking who came first, second, etc.
  • Using a chart or table to record race times and then ranking them
  • Practising with simple races at home, like a race to the kitchen or to the front door
  • Encouraging your child to explain how they ranked the runners
  • Using simple language and real-life examples to make it fun and clear
Remember, it's okay if your child makes mistakes. They are learning how to compare and order numbers, which is a key skill in maths. Be patient, encouraging, and always check that your child understands the process, not just the answer.

Practice questions

  1. Five runners finish a race with these times: 13 seconds, 17 seconds, 11 seconds, 19 seconds, 15 seconds. What is the order from first to last?
  2. Which runner came first in a race with times: 22 seconds, 18 seconds, 25 seconds, 20 seconds?
  3. Four runners have times: 10 seconds, 14 seconds, 12 seconds, 16 seconds. Who came second?
  4. In a race, the times are 15 seconds, 12 seconds, 18 seconds, 14 seconds. Who came third?
  5. If the race times are 9 seconds, 11 seconds, 13 seconds, 10 seconds, who came first?
Answers:
  1. 11 seconds (1st), 13 seconds (2nd), 15 seconds (3rd), 17 seconds (4th), 19 seconds (5th)
  2. Runner with 18 seconds came first
  3. Runner with 12 seconds came second
  4. Runner with 15 seconds came third
  5. Runner with 9 seconds came first

FAQ

What does "ranking" mean in athletics?

Ranking means putting runners in order based on their performance. The fastest runner comes first, and the slowest comes last.

How do you know who came first in a race?

The person with the fastest time (the lowest number of seconds) comes first.

Can two runners have the same time?

Yes, two runners can have the same time. When this happens, they are tied for the same position.

Why is it important to learn about race rankings?

Learning race rankings helps you understand how races work, compare results, and solve problems involving time and order.

How can I practice race rankings at home?

You can time yourself or others doing simple races, write down the times, and then rank them. You can also look at race results online or on TV and practice ranking the runners.