Adding whole tens · البرمجة مع مارتن

Count packs, not pieces

30 + 20. It looks like a big question. But it is tiny.

30 is 3 crates of ten. 20 is 2 crates. Together 5 crates. And 5 crates is 50.

See it? 30 + 20 you count like 3 + 2. Only at the end you say the result in tens: not five, but fifty.

Whole tens add as easily as numbers to ten. You do not count pieces, you count packs. The same trick works for subtracting too: 50 − 20 is like 5 − 2, so 30.

Where does it help? With money, almost all the time. 10 Kč coins are whole tens: three 10 Kč coins and two 10 Kč coins is five 10 Kč coins, so fifty Kč. Anyone who can add tens counts change like a shopkeeper. And a shopkeeper does not slip.

Today you will practise this fast trick. You will need it in the next lesson, where all numbers to a hundred get added.

Filip sells gingerbread at the school fair, ten in a bag. In the morning he sold 4 bags, in the afternoon 3 bags. “How many gingerbreads did you sell?” asks the teacher. Filip starts counting one gingerbread in his head and gets lost. Ema whispers beside him: “Count the bags! Four and three is seven bags.” Filip lights up: “Seven bags of ten… seventy gingerbreads!” The teacher praises him. Ema grins: “Packs count faster than pieces.” In the afternoon Filip sells two more bags. Ninety gingerbreads in all — counted before anyone could even ask. Bag maths wins.

💡

Add whole tens like small numbers: 40 + 30 → 4 + 3 = 7 → 70. Just do not forget to put the zero back at the end.

A small question hidden in a big one

Every question with whole tens has a small question hidden inside.

Method for 40 + 30:

Cross out the zeros in your head: 4 + 3 is left.
Calculate the small question: 4 + 3 = 7.
Put the zero back: 70.

Method for 60 − 40:

Cross out the zeros: 6 − 4.
Calculate: 2.
Put the zero back: 20.

Why does it work? Because you are counting packs of ten. 6 packs without 4 packs = 2 packs = 20 pieces.

Crossing a hundred works with adding too: 70 + 30 → 7 + 3 = 10 → 100. Ten packs is a round hundred.

You can also help yourself with a number line in tens: 0, 10, 20… 100. The question 40 + 30 is three jumps right in tens: 50, 60, 70.

One trap: the trick works only for whole tens. With the number 42 you must not cross out zeros — that is not a full pack. Mixed numbers come in the next lesson.

50 + 20 = ?

I cross out the zeros: 5 + 2.

Small question: 5 + 2 = 7.

I put the zero back: 70.

50 + 20 = 70.

Check with crates: 5 crates and 2 crates is 7 crates. Seven crates of ten bottles is 70 bottles. It matches.

90 − 60 = ?

I cross out the zeros: 9 − 6.

Small question: 9 − 6 = 3.

I put the zero back: 30.

90 − 60 = 30.

Check by adding: 30 + 60 = 90? Small questions: 3 + 6 = 9. Yes, it matches.

80 + 20 = ?

I cross out the zeros: 8 + 2.

That is a ten pair! 8 + 2 = 10.

I put the zero back: 10 with a zero is 100.

80 + 20 = 100. Exactly a hundred — ten full packs.

All the ten pairs work big too: 90 + 10 = 100, 70 + 30 = 100, 60 + 40 = 100, 50 + 50 = 100.

⚠️

The trick of crossing out zeros only holds for whole tens. 42 + 30 cannot be counted this way — forty-two is not a full pack. The zero at the end is said to hold the place: do not cross it out where you must not.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. البداية with ten. If it goes well, add more.

Add to 100. Count whole tens through a small question.

Practise the questions

On paper

Paper, a pencil. If you have them, you can take 10 Kč coins.

Calculate: 20 + 30, 40 + 50, 60 − 30, 100 − 70.
For each question write its small question too. Pattern: 20 + 30 → 2 + 3 = 5 → 50.
Write all the pairs of tens that make 100 together. البداية: 90 + 10…
Make 40 + 30 from 10 Kč coins and count the coins.

Now you 💪

I see the small question in the big one: 30 + 20 is like 3 + 2.
I do not forget to put the zero back at the end.
I know the trick only holds for whole tens.

✅

Done when: You calculate six questions with whole tens quickly and without counting one by one.

What to take from this lesson

Whole tens = packs of ten. Count the packs.
30 + 20: cross out the zeros, calculate 3 + 2, put the zero back.
It works for plus and minus.
Pairs to 100: 90 + 10, 80 + 20, 70 + 30, 60 + 40, 50 + 50.
With mixed numbers like 42 you must not cross out zeros.