Maths History
Why ten became a special number
Explain base 10 through fingers, place value, money and everyday counting systems.
Quick answer
The number ten became special because humans have ten fingers, and our counting system developed around this natural way of counting. This is why we use a base-10 system, where each place value is ten times bigger than the one before it.Learning outcome
By the end of this page, you will understand why the number ten is special in maths and how it helps us count, group, and share things more easily. Success signs:- You can explain that our number system uses groups of ten
- You can show how numbers like 23 are made of 2 tens and 3 ones
- You can count using groups of ten, like 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
- You can use your fingers to show numbers up to 100
Why this matters
Understanding why ten is special helps us learn how to count, add, subtract, and solve problems more easily. It's the foundation for everything we learn in maths after we start counting. From money to time to how many cookies we eat, we use the base-10 system every day. Knowing this helps us understand bigger numbers and how they work.How it works
The base-10 system means we group things into tens. This is like having a box that holds exactly 10 items. When we have more than 10, we put 10 in the first box and count the rest separately. This helps us count large numbers quickly. Let's look at how this works step by step:- Start with one finger on your hand
- Count all your fingers – you have 10 fingers
- When you have more than 10 things, you group them into tens
- Each group of 10 is one "ten"
- Then you count how many groups of 10 you have, and how many are left over
Examples you can see
Let's use real examples to show how base-10 works. Example 1: Counting with fingers You have 10 fingers. That's one group of ten. If you use both hands, you have 20 fingers – that's 2 groups of ten. Example 2: Money A ten-pound note is worth ten one-pound coins. If you have 3 ten-pound notes, that's 3 groups of ten pounds, or 30 pounds total. Example 3: Building blocks If you stack blocks in towers of 10, and you make 4 towers, you have 40 blocks total. This is 4 groups of 10 blocks. Example 4: Counting in school When you count from 1 to 100, you're counting in groups of ten. You say 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.Try it as a mini adventure
Adventure: The Treasure Hunt You are on a treasure hunt. You have found a chest with 127 gold coins. Your mission is to organize them into groups of ten. 1st time: You put 10 coins in a bag. That's 1 group of ten. 2nd time: You put another 10 coins in a bag. That's 2 groups of ten. 3rd time: You put another 10 coins in a bag. That's 3 groups of ten. 4th time: You put another 10 coins in a bag. That's 4 groups of ten. 5th time: You put another 10 coins in a bag. That's 5 groups of ten. 6th time: You put another 10 coins in a bag. That's 6 groups of ten. 7th time: You put another 10 coins in a bag. That's 7 groups of ten. 8th time: You put another 10 coins in a bag. That's 8 groups of ten. 9th time: You put another 10 coins in a bag. That's 9 groups of ten. 10th time: You put another 10 coins in a bag. That's 10 groups of ten. 11th time: You put another 10 coins in a bag. That's 11 groups of ten. 12th time: You put another 10 coins in a bag. That's 12 groups of ten. 13th time: You have 7 coins left over. That's 12 groups of ten, and 7 more coins. So 127 coins = 12 groups of ten + 7 ones Now, you can write this as 127 = 12 tens + 7 ones.Common mistakes
- Mistake: Thinking 100 is 10 groups of 10, not 10 groups of 10.
Why it happens: Confusing how many tens there are with how many ones there are.
Fix: Use objects or drawings to show that 100 is 10 groups of 10, not 10 tens and 10 ones. - Mistake: Counting 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 by ones instead of tens.
Why it happens: Not understanding that each step is 10 more.
Fix: Practice counting by tens with fingers or objects, and use a number line to show the jumps. - Mistake: Writing 23 as 2 tens and 3 tens instead of 2 tens and 3 ones.
Why it happens: Mixing up the place values.
Fix: Use base-10 blocks or drawings to show that 23 = 2 tens + 3 ones.
Parent and carer guide
Parents and carers can help by:- Using fingers to show how 10 is special – count your fingers and show 10, then 20, then 30
- Practicing counting in tens using everyday objects like buttons, coins, or toys
- Using base-10 blocks or drawings to show how numbers are made up of tens and ones
- Playing games where you count in tens, like "Count to 100 by tens"
- Looking for examples of tens in daily life – like 10 eggs in a carton, 10 coins in your pocket, or 10 steps to the door
Practice questions
- How many tens are in 45?
- How many ones are in 45?
- Write 67 as tens and ones.
- Count by tens to 100. What number comes after 80?
- How many groups of ten can you make from 90 objects?
- 4 tens
- 5 ones
- 6 tens and 7 ones
- 90
- 9 groups
FAQ
Why do we use base-10?
We use base-10 because humans have 10 fingers, and it's easy to count and group things in tens.
Can we use other numbers instead of 10?
Yes! Some cultures used base-5 or base-20. But base-10 became popular because it matches our fingers and is easy to learn.
How does base-10 help us in maths?
Base-10 helps us understand place value, which makes it easier to add, subtract, multiply, and divide big numbers.
What is place value?
Place value means that the position of a digit in a number tells you how much it's worth. For example, in 23, the 2 is worth 20 because it's in the tens place.
Why is 10 special in maths?
10 is special because it's the base of our number system. It's the number we use to group things, and it makes counting and maths easier.