Counting, place value foundation, number sense
Elementary Foundations • K-5
Numbers are everywhere! When you count your toys, tell someone your age, or read a clock, you are using numbers. In this lesson, we will explore what numbers really mean and how our number system works.
Counting means saying numbers in order while matching each number to one object. This is called one-to-one correspondence -- every object gets exactly one number, and every number gets exactly one object.
Imagine five stars in a row:
Touch each star as you count: 1, 2, 3, 4, 5. There are 5 stars. The last number you say tells you how many there are in all.
Here are the key counting rules:
Our number system uses only ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We call these digits. But we can make numbers as big as we want by using place value -- the position of a digit tells you its value.
| Place | Value | Example in 352 |
|---|---|---|
| Hundreds | 100 | 3 means 300 |
| Tens | 10 | 5 means 50 |
| Ones | 1 | 2 means 2 |
So the number 352 means 300 + 50 + 2. Each place is worth ten times more than the place to its right.
The number 74 has two digits:
The 7 is in the tens place, so it means 7 tens, or 70.
The 4 is in the ones place, so it means 4 ones, or 4.
Zero is a very special number. It means "none" or "nothing," but it is also a placeholder. In the number 105, the zero holds the tens place. Without it, 105 would look like 15 -- a very different number!
Students sometimes skip numbers when counting or count the same object twice. Fix: Line up objects in a row and move each one aside as you count it. This makes sure every object is counted exactly once.
You can count by groups to go faster! Counting by 2s (2, 4, 6, 8...), by 5s (5, 10, 15, 20...), or by 10s (10, 20, 30, 40...) helps you count large groups quickly.
1. How many shapes are here?
♦ ♦ ♦ ♦ ♦ ♦ ♦
Count each diamond: 1, 2, 3, 4, 5, 6, 7. There are 7 shapes.
2. In the number 486, what does the digit 8 mean?
The 8 is in the tens place, so it means 80 (eight tens).
3. Write the number that means 200 + 30 + 7.
237. The 2 goes in the hundreds place, the 3 in the tens place, and the 7 in the ones place.
4. What number comes right after 99?
100. After 99, we need a new place -- the hundreds place. 100 means 1 hundred, 0 tens, and 0 ones.
5. Break apart the number 560 into hundreds, tens, and ones.
560 = 500 + 60 + 0. That is 5 hundreds, 6 tens, and 0 ones.
Summary: Numbers are built from the digits 0 through 9. Counting means matching one number to each object. Place value tells us what each digit is worth based on its position -- ones, tens, hundreds, and beyond. Understanding place value is the foundation for all of math.