Adding to 100

Tens to tens, ones to ones

34 + 25. A big question? Not at all. They are two small questions in disguise.

34 is 3 tens and 4 ones. 25 is 2 tens and 5 ones.

Add the packs on their own: 30 + 20 = 50. Add the pieces on their own: 4 + 5 = 9. And put it together: 50 + 9 = 59.

Crates to crates, bottles to bottles. Never mix them.

This idea is bigger than it looks. Split big work into two small jobs — and you already know both. That is how almost all maths works: hard things get cut into easy bits. Adding to a hundred is your first big cutting. And you can see it nicely on bricks: piles of ten to piles, single bricks to bricks.

Today we start with questions where the ones do not spill over ten. Then we add spilling too — but do not worry, you already know the trick of filling to ten.

Tereza and Adam count a shared collection of chestnuts. Tereza has 42, Adam 36. “That is a terrible lot of counting,” Adam worries. Tereza makes piles of ten. Her chestnuts: 4 piles and 2 chestnuts. Adam’s: 3 piles and 6 chestnuts. “Piles together: seven, that is seventy. Chestnuts: two and six is eight.” Adam finishes: “Seventy-eight!” Then they count them all one by one. 78. It takes ten times longer and comes out the same. “Next time I will not count one by one,” Adam promises. They leave the piles of ten on the windowsill as an autumn trophy.

Add in parts

Method for 34 + 25:

1. Split: 34 = 30 + 4 and 25 = 20 + 5.
2. Tens: 30 + 20 = 50. (Small question 3 + 2.)
3. Ones: 4 + 5 = 9.
4. Put together: 50 + 9 = 59.

Writing the method: 34 + 25 = 30 + 20 + 4 + 5 = 50 + 9 = 59.

And when the ones spill over? 47 + 25: tens 40 + 20 = 60, ones 7 + 5 = 12. Put together: 60 + 12 = 72. The ones made more than ten — no problem, you just add twelve: 60 + 12 is 60 + 10 + 2.

Another path: in bits. Some people like adding on, step by step. 34 + 25: first add the tens — 34 + 20 = 54. Then the ones — 54 + 5 = 59. You jump on the line: first two big jumps of ten, then five small ones.

Both paths are right. Try both and keep the one you count better with. The main rule is always the same: tens belong with tens, ones with ones.

52 + 34 = ?

I split: 52 = 50 + 2, 34 = 30 + 4.

Tens: 50 + 30 = 80.

Ones: 2 + 4 = 6.

I put together: 80 + 6 = 86.

Writing: 52 + 34 = 50 + 30 + 2 + 4 = 80 + 6 = 86.

Check in bits: 52 + 30 = 82, then 82 + 4 = 86. It matches.

38 + 6 = ?

I am only adding ones, but they spill over: 8 + 6 is more than ten.

I use the good old trick: fill to ten. Thirty-eight needs 2 to reach forty.

I split the six: 6 = 2 + 4.

38 + 2 = 40. Then 40 + 4 = 44.

38 + 6 = 44. Filling to ten works with big numbers just the same as with small ones.

46 + 27 = ?

Tens: 40 + 20 = 60.

Ones: 6 + 7 = 13. It spilled over ten — that is fine.

I put together: 60 + 13 = 60 + 10 + 3 = 73.

46 + 27 = 73.

That thirteen hides a new ten. That is why the result is 73, not 63. Watch this the most.

Practice: now you do it 🎲

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

Add to 100. Tens on their own, ones on their own.

Practise the questions

On paper

Paper and a pencil. Write the whole methods, not just the results.

1. Calculate with the method: 23 + 45, 61 + 28, 34 + 52.

2. Calculate with ones spilling over: 27 + 36, 48 + 25. Watch the new ten!

3. Solve 43 + 32 in bits: first + 30, then + 2.

4. Make up a question about two friends’ chestnuts and solve it.

Now you 💪

1. I split numbers into tens and ones and add them on their own.
2. When the ones spill over, I do not forget the new ten.
3. I can add in bits too: first the tens, then the ones.

What to take from this lesson

• Tens to tens, ones to ones.
• 34 + 25: tens 50, ones 9, together 59.
• Spilled-over ones carry a new ten. Do not lose it.
• Path in bits: first add the tens, then the ones.
• Filling to ten works with big numbers too.

© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款