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Athletics Maths

Athletics personal bests maths challenge

A child-friendly sports challenge using personal bests to practise subtraction with real examples.

Quick answer

You can use subtraction to find how much better your personal best is than a previous time or distance in athletics, like comparing your 100m race time to your last best.

Learning outcome

By the end of this page, you will be able to find the difference between two athletics times or distances using subtraction to see how much you have improved. Success signs:
  • You can subtract two numbers to find how much faster or further you went
  • You can use a number line or written method to solve subtraction problems
  • You can compare your own athletics personal best to a past time or distance
  • You can explain how much you improved using subtraction

Why this matters

In athletics, knowing how much you've improved helps you stay motivated and track your progress. Whether it's running faster, jumping higher, or throwing further, subtraction helps you see your personal bests. This maths is used by athletes, coaches, and sports scientists to measure success. It's also useful in everyday life – like checking how much time you saved on your journey or how much more you grew this year.

How it works

To find how much better your personal best is, you subtract your old time or distance from your new one. If your new time is faster, the answer will be a positive number showing how much faster you are. If your new distance is longer, the answer will also be positive. For example:
  1. Find your old time or distance
  2. Find your new time or distance
  3. Subtract the old from the new
  4. Read the difference to see how much you improved

Examples you can see

Let’s look at some real-life athletics examples where subtraction helps us see improvement. Example 1: Running 100m
  • Your old 100m time: 15 seconds
  • Your new 100m time: 13 seconds
  • Subtract: 15 - 13 = 2 seconds
  • You ran 2 seconds faster!
Example 2: Long Jump
  • Your old long jump: 2.5 metres
  • Your new long jump: 3.1 metres
  • Subtract: 3.1 - 2.5 = 0.6 metres
  • You jumped 0.6 metres further!
Example 3: Shot Put
  • Your old shot put distance: 8.2 metres
  • Your new shot put distance: 9.7 metres
  • Subtract: 9.7 - 8.2 = 1.5 metres
  • You threw 1.5 metres further!
These examples show how subtraction helps us measure progress in athletics.

Try it as a mini adventure

Adventure: The Personal Best Challenge You are a young athlete who wants to track your improvement in the school athletics competition. You have a list of your old and new personal bests for different events. Your goal is to find how much better you are now than before. Here's your challenge:
  • 100m race: Old time = 18 seconds, New time = 16 seconds
  • High Jump: Old height = 1.1 metres, New height = 1.3 metres
  • 400m race: Old time = 65 seconds, New time = 60 seconds
  • Discus Throw: Old distance = 12.5 metres, New distance = 14.2 metres
Step-by-step challenge:
  1. Find how much faster you are in 100m: 18 - 16 = ?
  2. Find how much higher you jumped in High Jump: 1.3 - 1.1 = ?
  3. Find how much faster you are in 400m: 65 - 60 = ?
  4. Find how much further you threw in Discus: 14.2 - 12.5 = ?
Now, imagine you're a coach giving feedback to your friend – explain how much better you are in each event using subtraction.

Common mistakes

  • Mistake: Subtracting the new number from the old number instead of the old from the new.
    Why it happens: Confusion about which number is better.
    Fix: Always subtract the old time/distance from the new one to see improvement.
  • Mistake: Forgetting to line up decimal points when subtracting decimals.
    Why it happens: Not paying attention to place value.
    Fix: Write numbers in columns with decimal points aligned.
  • Mistake: Thinking that a smaller number means better performance.
    Why it happens: Confusion with time and distance.
    Fix: Remember, for time, a smaller number is better; for distance, a larger number is better.

Parent and carer guide

Parents and carers can support their child by:
  • Using real-life examples from family sports or games
  • Practising subtraction with decimal numbers in a fun way
  • Encouraging the child to explain their subtraction steps
  • Using a number line or visual aids to help with subtraction
  • Checking that subtraction makes sense (e.g., if you're faster, the answer should be positive)
What to say:
  • "How much faster did you get?"
  • "What number shows how much you improved?"
  • "Can you draw a number line to show the difference?"
What not to worry about:
  • Not knowing all the athletics events – focus on simple examples
  • Perfect answers – mistakes are part of learning
  • Speed – take time to check each calculation

Practice questions

  1. Old 200m time: 40 seconds. New time: 37 seconds. How much faster?
  2. Old high jump: 1.2 metres. New jump: 1.5 metres. How much higher?
  3. Old long jump: 2.8 metres. New jump: 3.3 metres. How much further?
  4. Old shot put: 10.4 metres. New shot put: 11.9 metres. How much further?
  5. Old 400m time: 70 seconds. New time: 68 seconds. How much faster?
Answers:
  1. 40 - 37 = 3 seconds faster
  2. 1.5 - 1.2 = 0.3 metres higher
  3. 3.3 - 2.8 = 0.5 metres further
  4. 11.9 - 10.4 = 1.5 metres further
  5. 70 - 68 = 2 seconds faster

FAQ

What is a personal best in athletics?

A personal best is your best performance in a specific athletics event. It's the fastest time, highest jump, or farthest throw you've ever achieved.

Why do we use subtraction to find improvement?

Subtraction helps us see the exact difference between your old performance and your new one. It shows how much you've improved.

How can I track my personal bests?

You can write them down in a notebook or use a simple chart. Each time you try an event, record your new time or distance and compare it to your old best.

Can I use this maths for other sports?

Yes! This subtraction method works for any sport where you track time, distance, or score. It's useful in swimming, cycling, basketball, and more.

What if my performance gets worse?

If your new time is slower or your distance is shorter, the subtraction will give a negative number. This shows you need to practice more or that you had a bad day!