Counting in tens up to a hundred
Here are 9 groups of ten. Count them in tens: 10, 20, 30, 40, 50, 60, 70, 80, 90. That is 90 ones in all.
Now add 1 more group of ten. The count goes on to 100, so 10 tens make 100.
9 groups of ten: 90.
One more group of ten makes 10 groups of ten.
Ten tens push together
Push the 10 groups of ten side by side and they make one square. The square has 10 rows, and each row has 10 small squares, so it holds 100 small squares. This square is one hundred.
Nothing was added and nothing was taken away. The 100 small squares are still all there; they are packed into one square instead of 10 separate groups.
You have seen this move before: 10 ones make 1 ten. Now 10 tens make 1 hundred. Each time, ten of one size make one of the next size up.
The 10 groups of ten joined into one square of a hundred: 10 tens = 100.
7 tens = 70
Add rods until ten tens make a hundred
Each rod is ten. The tenth rod closes the rods into one square of a hundred, and a rod after that starts the next group of tens.
Hundreds, tens and ones
Every 3-digit number is made of hundreds, tens and ones. 234 is 2 hundreds, 3 tens and 4 ones. The 2 on the left counts the hundred squares, the 3 in the middle counts the groups of ten, and the 4 on the right counts the ones.
Each digit tells you what it is worth by its place. The 2 is worth 200, the 3 is worth 30, and the 4 is worth 4, so 234 = 200 + 30 + 4.
2 hundreds, 3 tens and 4 ones: 200 + 30 + 4 = 234.
Keep each part in its place
A place with nothing in it still gets a digit. 2 hundreds and 6 ones, with no tens, is written 206. The 0 in the middle says there are no tens, and it keeps the 2 in the hundreds place. Leave it out and the number becomes 26.
Swapping the tens and the ones is the other slip. 2 hundreds, 3 tens and 4 ones is 234, not 243. Count each kind of block on its own and write its count in its own place.
2 hundreds, no tens and 6 ones: 206.
More than nine tens
Each place holds one digit, from 0 to 9. So when you have 10 or more tens, 10 of them become 1 more hundred. 2 hundreds and 15 tens is too many tens for one place: swap 10 of the tens for 1 hundred, and you have 3 hundreds and 5 tens.
Worked example: Blocks with More Than Nine Tens
Question Mei has 2 hundreds blocks, 15 tens blocks and 4 ones blocks. She swaps 10 of the tens blocks for 1 hundreds block. (a) How many hundreds blocks and how many tens blocks does she have now? (b) What number do her blocks show?
1.Put the blocks in three columns: 2 hundreds, 15 tens and 4 ones. A place holds only one digit, and 15 is too many tens for one place.
There are 2 hundreds, 15 tens and 4 ones. A place holds only one digit, and 15 is too many tens. 2.Ring 10 of the tens blocks. Ten tens are 100, which is the same as 1 hundreds block.
Ring 10 of the tens blocks. Ten tens are 100, the same as 1 hundreds block. 3.(a) Swap the ringed tens for 1 hundreds block. The hundreds are 2 + 1 = 3 and the tens are 15 − 10 = 5. Mei has 3 hundreds blocks and 5 tens blocks.
(a) The ringed tens are swapped for 1 hundreds block. Now there are 3 hundreds blocks and 5 tens blocks. 4.(b) 3 hundreds, 5 tens and 4 ones is 300 + 50 + 4 = 354. Check: 200 + 150 + 4 = 354.
(b) 3 hundreds, 5 tens and 4 ones is 300 + 50 + 4 = 354.
Answer: (a) 3 hundreds blocks and 5 tens blocks; (b) 354
Common mistakes
- Writing the three counts side by side as 2154. Each place holds one digit, so the 15 tens must first be exchanged: 10 of them become 1 more hundred.
- Dropping the extra tens and writing 254. The 10 tens that were swapped are still there as 1 more hundred, so the hundreds digit goes up to 3.