Too many to count one by one

Liri tried to count the stars in a bright star cluster. By twenty she had already lost track.

Liri: “There are so many! I keep counting wrong.”
Erklärus: “Then you’re counting the wrong way. From now on we bundle. Ten stars become one bundle. And then you count the bundles.”
Liri: “A bundle of ten?”
Erklärus: “Exactly. That is the most important trick in all of mathematics: ten of something become one new thing.”

📦 Tens and ones – how numbers are built

Every number up to 100 is made of tens (T) and ones (O). The number 47, for example, is 4 tens and 7 ones.

4 tens rods
7 ones cubes

4 tens + 7 ones = 47

How many tens and ones are there in 63?
tens ones

✏️ Secret code – lines and dots

A quick trick for drawing numbers: one line for every ten, one dot for every one.

| | |   • • • •
= 3 tens, 4 ones = 34

Which number is this: | | | | |   • • ?

🧩 Hundred-square puzzle

This is how you find the missing number from its neighbours: look at one of the four neighbouring numbers and work back from there to the gap.

Neighbour on the right: work out −1  ·  neighbour on the left: work out +1
Neighbour above: work out +10  ·  neighbour below: work out −10

Fill in the missing number:

55
56
57
65
67
75
76
77

🗣️ A peculiarity of German

In German, numbers are spoken backwards: first the ones, then the tens. 47 is not “forty-seven” but “siebenundvierzig” – “seven-and-forty” – the 7 comes first! English used to do this too: think of “four-and-twenty blackbirds”.

Liri: “That’s confusing. Is that why some children accidentally write 74 instead of 47?”
Erklärus: “That happens a lot. When you write, what counts is the order of the digits – not the order in which we say them.”
🌌 Numbers up to 100 in the universe

The Ariane 5 launch rocket is about 50 metres tall.
Before an astronaut is allowed to fly into space for the first time, they often train for 24 months.
A full-moon cycle – from one full moon to the next – lasts about 29 days.

❌ Common mistake

Because German says “siebenundvierzig”, some children accidentally write the 7 first and then the 4 – that is 74 instead of 47.

Tip: always think first about how many bundles of ten there are – the tens digit always comes first when writing, even if it comes last when speaking!

🔢 Exercise 1
A star catalogue shows: 5 tens and 8 ones. Which number is that?
🧩 Exercise 2 – Neighbouring number
On the number line stands 80. Which number is exactly 10 more?
🗣️ Exercise 3 – Number word
Erklärus says “einundsechzig” (“one-and-sixty”). Which digit do you write down first – the tens digit or the ones digit?
The tens digit (6)
The ones digit (1)

Bundle by bundle

Liri counted the star cluster once more – this time in bundles of ten. Six bundles, three single stars. 63.

Liri: “I didn’t count any more. I bundled.”
Erklärus: “That is the whole trick behind big numbers. You never really count everything one by one – you bundle, and bundle again.”

Liri wrote the star cluster with its 63 stars onto her star map – another bundled piece of memory on the way home.

“Numbers up to 100 are made of tens and ones. When writing, the tens digit comes first, even if in German we say the ones first. On the hundred square: from the right-hand neighbour work out −1, from the neighbour below work out −10.”
What you learned today
47 = 4 tens + 7 ones
Write the tens digit first  ·  Hundred square: right-hand neighbour −1, neighbour below −10
🌟

Chapter 7 mastered!

From counting one by one to bundling in tens – Liri now thinks in bundles.

Erklärus’s notebook – page 7:
“Numbers up to 100: tens (T) and ones (O). 47 = 4T + 7O. When writing, the order of the digits counts, not the order of speaking. On the hundred square: right-hand neighbour −1, left-hand neighbour +1, neighbour below −10, neighbour above +10.”
← Back to overview 7 – Numbers up to 100