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K02 • Lesson 14 of 105

Hundreds and Regrouping: Building Bigger Numbers

Students extend place value understanding to three-digit numbers by discovering the hundreds place. Using base-10 blocks, they see that 10 tens make 1 hundred, compose and decompose numbers like 365 into 3 hundreds, 6 tens, and 5 ones, and practice regrouping — trading 10 ones for 1 ten or 10 tens for 1 hundred.

K-2 Foundations • K-2

Prerequisites: E01, K01

Key Concepts

  • hundreds place
  • regrouping ones as tens
  • regrouping tens as hundreds
  • composing and decomposing three-digit numbers

Hundreds and Regrouping: Building Bigger Numbers

You already know about tens and ones. Now we go bigger! When we collect 10 tens, we can trade them for 1 hundred. This lets us write three-digit numbers like 365.

Big Idea

Our number system is built on groups of ten: 10 ones make 1 ten, and 10 tens make 1 hundred. This pattern goes on forever!

The Hundreds Place

Three-digit numbers have three places:

HundredsTensOnes
365
365 = 300 + 60 + 5

The base-10 blocks for hundreds look like a flat square made of 100 tiny cubes (10 rows of 10).

BlockShapeValue
Ones cubeTiny cube1
Tens rodLong stick10
Hundreds flatBig square100

Worked Example 1: Reading a Three-Digit Number

What number is shown by 2 hundreds flats, 4 tens rods, and 7 ones cubes?

  1. 2 hundreds = 200
  2. 4 tens = 40
  3. 7 ones = 7
  4. 200 + 40 + 7 = 247

Composing and Decomposing Numbers

Composing means putting parts together to make a number. Decomposing means breaking a number into parts.

Worked Example 2: Decomposing 528

  1. The 5 is in the hundreds place: value is 500
  2. The 2 is in the tens place: value is 20
  3. The 8 is in the ones place: value is 8
528 = 500 + 20 + 8

Regrouping

Sometimes we need to trade smaller pieces for bigger ones (or bigger ones for smaller):

Regrouping Up

10 ones = 1 ten

10 tens = 1 hundred

We do this when adding!

Regrouping Down

1 ten = 10 ones

1 hundred = 10 tens

We do this when subtracting!

Worked Example 3: Regrouping Ones into Tens

You have 3 hundreds, 2 tens, and 15 ones. Regroup to write the correct number.

  1. 15 ones is too many for the ones place (only 0-9 fit). Trade 10 ones for 1 ten.
  2. Now: 3 hundreds, 3 tens (2+1), and 5 ones.
  3. The number is 335.

Watch Out!

Each place can only hold one digit (0 through 9). If you count 12 tens, you must trade 10 of them for 1 hundred. 12 tens = 1 hundred and 2 tens.

Real-World Connection

Think about dollars, dimes, and pennies. 10 pennies = 1 dime. 10 dimes = 1 dollar. A dollar is like a hundred, a dime is like a ten, and a penny is like a one!

Practice Problems

1. Write 473 in expanded form.

Show Answer

473 = 400 + 70 + 3

2. What number has 6 hundreds, 0 tens, and 9 ones?

Show Answer

609. When there are 0 tens, we write a 0 in the tens place.

3. You have 2 hundreds, 14 tens, and 3 ones. Regroup and write the number.

Show Answer

14 tens = 1 hundred + 4 tens. So 2+1 = 3 hundreds, 4 tens, 3 ones = 343.

4. How many tens are in the number 850?

Show Answer

The tens digit is 5, so there are 5 tens in the tens place. But the total number of tens in 850 is 85 (since 850 divided by 10 is 85).

5. Decompose 700 into hundreds, tens, and ones.

Show Answer

700 = 7 hundreds + 0 tens + 0 ones. In expanded form: 700 + 0 + 0.

Lesson Summary

Overview