🏗️ Place Value: Ones, Tens, Hundreds
What Is Place Value?
Place value is one of the most important concepts in all of elementary math, and the good news is that it is very hands-on and very learnable. Here is the big idea: the value of a digit depends on its position in the number.
In the number 352: - The 2 is in the ones place. It is worth 2. - The 5 is in the tens place. It is worth 50. - The 3 is in the hundreds place. It is worth 300.
Same digits can mean very different things depending on where they sit. That is place value!
Beans and Cups: Build It Physically
This is my favorite way to teach place value, and it costs almost nothing. Here is what to do:
Ones = individual beans Tens = a cup (or small bag) with exactly 10 beans inside Hundreds = a group of 10 cups banded together (100 beans total)
Start by having your child count out beans and make cups of ten.
Activity 1: Making Tens Pour a pile of beans on the table. Have your child count beans one by one and put them in cups, 10 per cup. When a cup has 10, it becomes a "ten." Leftover beans that do not fill a cup are "ones."
If they count out 34 beans, they should end up with 3 cups of ten and 4 loose beans. Three tens and four ones equals 34!
Activity 2: Build My Number Call out a number and have your child build it. "Show me 57!" They grab 5 cups of ten and 7 loose beans. "Show me 123!" They grab 1 group of ten cups (hundreds), 2 single cups of ten, and 3 loose beans.
Activity 3: What Number Did I Build? You build a number with cups and beans, and your child figures out what number it is. Put down 2 cups of ten and 6 beans. "What number is this?" 26!
The Place Value Chart
Once your child is comfortable building numbers, introduce a written place value chart. Draw three columns on paper:
| Hundreds | Tens | Ones |
|---|---|---|
Practice writing numbers in the chart. For 185:
| Hundreds | Tens | Ones |
|---|---|---|
| 1 | 8 | 5 |
That means 100 + 80 + 5 = 185. This is called expanded form, and it helps kids see what each digit really means.
Practice Problems
Build these with beans and cups, then write them in expanded form:
- 46 = ___ tens + ___ ones = 40 + 6
- 83 = ___ tens + ___ ones = 80 + 3
- 127 = ___ hundred + ___ tens + ___ ones = 100 + 20 + 7
- 305 = ___ hundreds + ___ tens + ___ ones = 300 + 0 + 5
- 210 = ___ hundreds + ___ ten + ___ ones = 200 + 10 + 0
The tricky ones are numbers with zeros (like 305 or 210) because there are no beans in one of the places. That zero is a placeholder - it holds the spot even though there is nothing there.
Fun Extension: Trading Game
Play this game with your child: 1. Take turns rolling a die. 2. Take that many beans (ones). 3. When you get 10 ones, trade them for a cup (one ten). 4. When you get 10 tens, trade them for a hundred. 5. First person to reach a target number (like 100) wins!
This game naturally teaches regrouping, which is the foundation for carrying in addition and borrowing in subtraction.
Tips for Parents
Do not rush past place value. If your child does not understand that the 5 in 50 means fifty and not five, then multi-digit addition and subtraction will be confusing later. Spend as many days as you need building, trading, and talking about numbers. The beans and cups are simple, but they build a rock-solid foundation.