Tens and ones

Each digit has its own place

Why is 34 written just like that? Because each digit has its own place and its own job.

The digits at the back are ones — single pieces. The digits in front of them are tens — finished packs of ten.

34 means: 3 packs of ten and 4 extra pieces. Thirty and four. Thirty-four.

Picture eggs. Boxes of ten and loose eggs beside them. 3 boxes and 4 eggs = 34 eggs. You do not have to count them one by one. You just count the boxes and the pieces.

Try saying it out loud: thirty-four. Do you hear both parts? Thirty — those are the tens. Four — those are the ones. English tells you by itself. You just have to listen to what you say, and write it in order. Today you will learn to take numbers apart and put them back together.

This is one of the biggest tricks in maths. Two digits can tell you a big number. You just have to know which is which.

Adam helps dad in the cellar, packing bottles into crates. Exactly ten bottles fit in one crate. They fill 2 crates and 6 bottles are left on the floor. “How many bottles do we have?” asks dad. Adam starts counting one by one, then stops. “Two crates… that is twenty. And six on the floor. Twenty-six!” Dad writes 26 on a slip of paper. “The two is the crates, the six is the floor,” Adam laughs. From then on he sees crates and bottles in every number. Even in maths class: 53? Five crates, three bottles on the floor.

How to take a number apart and put it together

Taking a number apart. Take 52. The back digit 2 = ones, 2 pieces. The front digit 5 = tens, 5 packs of ten, so fifty. In all: 50 and 2, fifty-two.

Putting a number together. I have 7 tens and 3 ones. The tens make 70. With the three ones: 73.

The method is always the same:

1. Find the back digit — those are the ones.
2. Find the front digit — those are the tens.
3. Read: tens times ten, and the ones on top.

Watch the order. 26 and 62 have the same digits, but they are completely different numbers. 26 = 2 crates and 6 bottles. 62 = 6 crates and 2 bottles. Six crates is much more!

And zero? The number 40: 4 tens and 0 ones. Zero says: there are no pieces, only full packs. Without zero, 40 would be 4 — zero holds the place so the four stays in the tens place.

Try it with money: 10 Kč coins are tens, 1 Kč coins are ones. 3 coins of 10 Kč and 5 coins of 1 Kč = 35 Kč.

Take apart the number 48

Back digit: 8. That is 8 ones — eight pieces.

Front digit: 4. That is 4 tens — four packs of ten, so forty.

48 = 40 + 8. I read: forty-eight.

Check with eggs: 4 full boxes of ten and 8 loose eggs. Boxes: 10, 20, 30, 40. And eight on top: 48. It matches.

Put together a number from 6 tens and 0 ones

Six tens: 10, 20, 30, 40, 50, 60. Sixty.

Ones: none. Zero.

I write: 60. The zero must be there. If I left it out, 6 would be left — and six is something completely different from sixty.

Zero in the ones place says: only full boxes, no loose egg.

Compare 39 and 41

Which is bigger? Do not look at the big digits first. Compare the tens first.

39 has 3 tens. 41 has 4 tens. Four crates are more than three.

So 41 > 39. Even though 39 has a big nine at the back!

Tens decide first. Ones only come in when the tens are the same: with 45 and 42, 5 against 2 decides at last.

Practice: now you do it 🎲

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

How many tens does the number have, and how many ones?

Practise the questions

On paper

Paper, a pencil, and ideally a few 10 Kč and 1 Kč coins to play with.

1. Take apart the numbers 25, 60, 84 and 19: write how many tens and how many ones they have.

2. Put numbers together: 3 tens and 7 ones, 5 tens and 0 ones, 9 tens and 9 ones.

3. Make the amount 46 Kč from 10 Kč and 1 Kč coins. How many coins of each kind do you need?

4. Compare 58 and 63: tens first, then write the comparison with a sign.

Now you 💪

1. For every two-digit number I can say how many tens and ones it has.
2. I can put a number together from tens and ones, even with zero.
3. When I compare, I look at the tens first.

What to take from this lesson

• Back digit = ones, pieces. Front = tens, packs of ten.
• 34 = 30 + 4. Three tens and four ones.
• The order of the digits decides: 26 is not 62.
• Zero holds the place: 40 without zero would be only 4.
• When comparing, tens decide first.

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