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Athletics Maths

Maths in athletics: personal bests

Find the difference between old and new records.

Quick answer

Maths in athletics: personal bests helps you find how much better your new time or distance is than your old one by calculating the difference between them.

Learning outcome

By the end of this page, you will be able to find the difference between your old and new athletics times or distances to see how much you have improved. Success signs:
  • You can subtract two numbers to find the difference
  • You can measure and compare your own athletics times or distances
  • You can understand how much you have improved
  • You can use a number line or counting to check your subtraction

Why this matters

Maths helps you understand how good you are at athletics and how much you are improving. When you run faster or jump further, you can use subtraction to find out how much better you are now than before. This helps you set goals, track your progress, and feel proud of your achievements. Whether you're running a race, jumping high, or throwing a ball, knowing how to find the difference helps you celebrate your improvements.

How it works

To find how much better your new athletics result is than your old one, follow these simple steps:
  1. Write down your old result
  2. Write down your new result
  3. Subtract the old result from the new result
  4. If the new result is bigger, the answer shows how much you improved

Examples you can see

Let’s imagine you are learning to run a 100-metre race. Example 1: You ran the race in 25 seconds last week. This week, you ran it in 22 seconds. How much faster are you now? To find out, subtract the old time from the new time: 25 seconds – 22 seconds = 3 seconds You are 3 seconds faster this week. Example 2: You jumped 1.2 metres in the long jump last month. This month, you jumped 1.5 metres. How much further did you jump? 1.5 metres – 1.2 metres = 0.3 metres You jumped 0.3 metres further. Example 3: You threw a javelin 15.7 metres last year. This year, you threw it 18.2 metres. How much further did you throw? 18.2 metres – 15.7 metres = 2.5 metres You threw 2.5 metres further this year.

Try it as a mini adventure

Adventure: The Athletic Challenge You are going to be an athlete for a day! You have a challenge to improve your personal best in different sports. Here’s how to play: Step 1: Choose a sport you like – maybe running, jumping, or throwing. Step 2: Record your old best time or distance. Step 3: Try the same activity again and record your new result. Step 4: Subtract your old result from your new result to see how much you improved. Step 5: Write down your improvement in a journal or on a chart. Step 6: Share your results with a parent or friend. Example: You are trying to beat your 50-metre sprint time.
  • Old time: 12.5 seconds
  • New time: 11.2 seconds
  • Improvement: 12.5 – 11.2 = 1.3 seconds
You are 1.3 seconds faster! You can even draw a chart to show how much faster you are.

Common mistakes

  • Mistake: Subtracting the new result from the old result instead of the other way around.
    Why it happens: Confusing which number is bigger.
    Fix: Always subtract the smaller number from the bigger number to find how much you improved.
  • Mistake: Forgetting to use the same units (like seconds and metres).
    Why it happens: Not paying attention to what you are measuring.
    Fix: Make sure both numbers are in the same unit before subtracting.
  • Mistake: Thinking that a smaller time or distance means you did better.
    Why it happens: Not understanding what the numbers mean.
    Fix: Remember: in running, a smaller time is better. In jumping or throwing, a bigger distance is better.

Parent and carer guide

As a parent or carer, you can help your child understand personal bests in athletics by:
  • Encouraging your child to record their old and new times or distances
  • Helping them use subtraction to find the difference
  • Using a number line or counting on to check their answer
  • Letting them create a chart or graph to show their progress
  • Practising with real-life examples like running, jumping, or throwing
If your child is struggling, try using physical objects like blocks or counters to help them see the difference. You can also make it fun by turning it into a game or challenge.

Practice questions

  1. Old time: 20 seconds. New time: 18 seconds. How much faster?
  2. Old jump: 1.4 metres. New jump: 1.7 metres. How much further?
  3. Old throw: 12.3 metres. New throw: 14.1 metres. How much further?
  4. Old time: 15.8 seconds. New time: 14.2 seconds. How much faster?
  5. Old distance: 2.1 metres. New distance: 2.5 metres. How much further?
Answers:
  1. 20 – 18 = 2 seconds
  2. 1.7 – 1.4 = 0.3 metres
  3. 14.1 – 12.3 = 1.8 metres
  4. 15.8 – 14.2 = 1.6 seconds
  5. 2.5 – 2.1 = 0.4 metres

FAQ

What does personal best mean?

Your personal best is the best time or distance you have ever achieved in a sport. It’s your own record that you try to beat.

Why is it important to track personal bests?

Tracking personal bests helps you see how much you are improving. It makes you feel proud and gives you goals to work towards.

How do I find the difference in athletics times?

Subtract your old time from your new time. If the new time is smaller, you improved.

Can I use this for jumping or throwing?

Yes! You can use the same method for any athletics activity. Just subtract the old distance from the new distance.

How can I make this fun for my child?

You can turn it into a game or challenge. Use a stopwatch, measuring tape, or even a chart to track progress. Celebrate every improvement!