Crossing ten · 마틴과 코딩하기

First fill the ten, then go on

8 + 5. You can do it on fingers, but you do not have enough fingers. There comes a moment when the ones spill over ten. That is called crossing ten.

The trick is lovely. Ten is like a full egg box. First you fill the box to the top. Only then do you carry on.

8 + 5? Eight needs 2 to reach ten. So from the five you give it two: 8 + 2 = 10. Three are left from the five. And 10 + 3 = 13. Done: 8 + 5 = 13.

Why through ten? Because counting from ten is the easiest in the world. Ten and three you see at once — thirteen. So it pays to make a stop at ten. A small detour, a big saving.

You split the five into 2 and 3. Exactly as much as was needed to reach ten. This is the most important trick of the whole first year. Anyone who can do it counts fast and without fingers.

Ema helps mum put eggs away. The box has ten holes, eight are full. Mum hands Ema five eggs. Where do they go? Ema fills two holes — the box is full, ten. Three eggs are left in her hand. “Mum, we have thirteen eggs! A full box and three extra.” Mum is surprised: “You counted that in your head?” Ema shrugs: “Not in my head. From the box.” In the evening she teaches Adam: first fill the box, then count the leftover. Adam tries it with bricks instead of eggs. Eight bricks in a row, he fills two, three are left. Thirteen! The box works even without eggs.

💡

Always ask: how many does the first number need to reach ten? Take exactly that many from the second number.

Fill up to ten and add the leftover

Example: 7 + 6. Three steps:

1. How many does seven need to reach ten? Three. (Here the pairs to ten help: 7 + 3 = 10.)

2. Split the six. I need 3 from it to reach ten. 6 is 3 and 3. The first three fill: 7 + 3 = 10. The second three wait.

3. Add the leftover to ten. 10 + 3 = 13. That is already easy — ten and three is thirteen.

So 7 + 6 = 13.

The whole method on paper you can write like this:

7 + 6 = 7 + 3 + 3 = 10 + 3 = 13

For this trick you need two things you already know. Pairs to ten (9 + 1, 8 + 2, 7 + 3, 6 + 4, 5 + 5) — they tell you how many is missing. And splitting numbers — being able to split six into 3 and 3. We will look at splitting on its own too. It is an important helper.

At the start, help yourself with bricks: make a row of ten holes like an egg box and fill them. Hands will teach the head.

9 + 4 = ?

How many does nine need to reach ten? One.

I split the four: 4 is 1 and 3.

I fill: 9 + 1 = 10. I add the leftover: 10 + 3 = 13.

Writing the method: 9 + 4 = 9 + 1 + 3 = 10 + 3 = 13.

With nine it is the easiest: it always takes only one. The result is almost the same as the second number, just one smaller and with a ten at the front.

6 + 8 = ?

I start with the bigger number: 8 + 6.

How many does eight need to reach ten? Two.

I split the six: 6 is 2 and 4.

I fill: 8 + 2 = 10. I add the leftover: 10 + 4 = 14.

8 + 6 = 14. So 6 + 8 = 14 too.

Check on fingers or bricks: fourteen comes out again.

5 + 7 = ?

I swap: 7 + 5.

Seven needs 3 to reach ten. I split the five into 3 and 2.

7 + 3 = 10. Then 10 + 2 = 12.

Writing: 7 + 5 = 7 + 3 + 2 = 10 + 2 = 12.

Write the whole method until it goes by itself. In a few weeks you will write 7 + 5 = 12 straight away and the method will run only in your head.

⚠️

A common mistake: you split the second number wrong and a bit gets lost. 8 + 5: you take 2 to reach ten, but you forget that 3 were left. Always check that both bits make the original number together.

Practice: now you do it 🎲

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

First a warm-up: fill in what is missing to make the number.

Practise the questions

On paper

Paper, a pencil and ten bricks as an egg box.

Calculate with the whole method written down: 8 + 4, 9 + 6, 7 + 7. Pattern: 8 + 4 = 8 + 2 + 2 = 10 + 2 = 12.
Make a row of ten holes from bottle caps, or draw an egg box. Solve 6 + 7 by filling.
Write all the pairs to ten by heart: 9 + 1, 8 + 2… You need them for this trick.
Make up one question of your own with crossing ten and solve it with the method.

Now you 💪

I can say how many each number needs to reach ten.
I can split the number I add into two bits and not lose any.
I can write the whole method: fill to 10, add the leftover.

✅

Done when: You solve 8 + 5, 9 + 7 and 6 + 6 with the method written down and all of them match.

What to take from this lesson

Crossing ten: the ones spill over ten.
The trick: fill the first number to ten, then add the leftover.
Split the second number exactly into what is missing, and the leftover.
Pairs to ten are the key. Learn them by heart.
Write the whole method until the trick runs by itself in your head.