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subtraction

Subtraction as counting up

Find the difference by counting up from the smaller number.

Quick answer

Subtraction as counting up means finding the difference between two numbers by starting at the smaller number and counting up to the larger number. It’s a helpful way to solve subtraction problems, especially when the numbers are far apart.

Learning outcome

By the end of this page, you will be able to find the difference between two numbers by counting up from the smaller number to the bigger number. Success signs:
  • You can solve subtraction problems by counting up instead of counting back
  • You can explain why counting up works
  • You can use counting up to solve real-life problems
  • You can check your subtraction answers using counting up

Why this matters

Counting up helps you solve subtraction problems more easily, especially when the numbers are far apart. It’s useful for:
  • Shopping – how much more money do you need?
  • Time – how much time is left until your next activity?
  • Games – how many more points do you need to win?
  • Measuring – how much longer is one object than another?
This method helps you think about subtraction as "how much more" or "how much difference" there is between two numbers.

How it works

To subtract using counting up, follow these steps:
  1. Look at the two numbers you are subtracting.
  2. Start at the smaller number.
  3. Count up to the larger number.
  4. Count how many numbers you counted – that’s your answer!
Let’s try this with a simple example: 15 – 8. 1. Start at 8 (the smaller number). 2. Count up: 9, 10, 11, 12, 13, 14, 15. 3. You counted 7 numbers. 4. So, 15 – 8 = 7.

Examples you can see

Here are some clear examples to help you understand counting up. Example 1: Small numbers Problem: 9 – 4 = ? Start at 4 and count up to 9: 4 → 5, 6, 7, 8, 9. You counted 5 numbers. So, 9 – 4 = 5. Example 2: Bigger numbers Problem: 27 – 13 = ? Start at 13 and count up to 27: 13 → 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27. You counted 14 numbers. So, 27 – 13 = 14. Example 3: Real-world example – money You have £10 and want to buy a toy that costs £6. How much more money do you need? Start at £6 and count up to £10: 6 → 7, 8, 9, 10. You counted 4 numbers. So, you need £4 more. Example 4: Time example Your football game starts at 3 o’clock and it’s now 1 o’clock. How many hours until the game? Start at 1 and count up to 3: 1 → 2, 3. You counted 2 hours. So, the game starts in 2 hours.

Try it as a mini adventure

The Treasure Hunt Challenge You are on a treasure hunt! You have a map that says: “Start at the big tree, walk 8 steps forward, then turn and walk 13 steps to the right.” You are at the big tree, and you’ve walked 8 steps forward. How many more steps do you need to walk to reach the treasure? Start at 8 and count up to 13: 8 → 9, 10, 11, 12, 13. You counted 5 steps. So, you need 5 more steps to reach the treasure! Try this challenge again: You are at the big tree, and you’ve walked 12 steps forward. You need to walk 19 steps forward to reach the treasure. Start at 12 and count up to 19: 12 → 13, 14, 15, 16, 17, 18, 19. You counted 7 steps. So, you need 7 more steps.

Common mistakes

  • Mistake: Forgetting to count the starting number. Why it happens: You start counting from the next number. Fix: Always include the starting number in your count. If you start at 5, count: 5, 6, 7, 8. That’s 4 numbers, not 3.
  • Mistake: Counting backwards instead of forwards. Why it happens: You’re used to counting down. Fix: Remember: always count up from the smaller number to the bigger number.
  • Mistake: Adding the starting number to the difference. Why it happens: You think you need to add the two numbers. Fix: Counting up means counting the gap between the numbers, not adding them.

Parent and carer guide

Parents and carers can help children by:
  • Using objects like counters or blocks to show counting up
  • Practising with real-life examples like money, time, or distances
  • Encouraging children to say the numbers out loud as they count
  • Checking if the child understands that counting up finds the difference
  • Reinforcing that the starting number is part of the count
It’s okay if children get confused at first – counting up is a new way of thinking. Be patient and keep practising with simple examples.

Practice questions

  1. 10 – 3 = ?
  2. 17 – 9 = ?
  3. 25 – 16 = ?
  4. 30 – 22 = ?
  5. 12 – 5 = ?
  6. 18 – 11 = ?
  7. 21 – 14 = ?
  8. 28 – 20 = ?
  9. 15 – 8 = ?
  10. 23 – 17 = ?
Answers:
  1. 7
  2. 8
  3. 9
  4. 8
  5. 7
  6. 7
  7. 7
  8. 8
  9. 7
  10. 6

FAQ

What is subtraction as counting up?

Subtraction as counting up means finding the difference between two numbers by starting at the smaller number and counting up to the bigger number.

Why is counting up useful?

Counting up is useful because it helps you solve subtraction problems more easily, especially when the numbers are far apart. It’s also helpful for real-life situations like checking how much more money you need.

Can I use counting up for any subtraction problem?

Yes, you can use counting up for any subtraction problem. It works the same way whether the numbers are small or big.

How can I practice counting up?

You can practice by using objects like counters or blocks, or by thinking of real-life situations like time, money, or distances. Try counting up from small numbers to bigger ones.

Is counting up the same as counting backwards?

No, counting up means going forward from the smaller number to the bigger number, while counting backwards means going from the bigger number to the smaller number.