Decompose 3-digit numbers worksheet with examples and practice problems.

Let's solve the worksheet step by step.

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Understanding the Task

The goal is to decompose each 3-digit number in two different ways using base-ten blocks. This means breaking the number into hundreds, tens, and ones — but not necessarily just the standard form (e.g., 500 + 90 + 3). You can regroup the tens or hundreds as long as the total value stays the same.

For example:
- Standard: $ 200 + 70 + 8 = 278 $
- Regrouped: $ 100 + 170 + 8 = 278 $ (we took 100 from the hundreds and added it to the tens)

So we can exchange one hundred for ten tens, or one ten for ten ones, etc.

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Problem 1: 593

We want two different decompositions of 593.

#### First way (standard):
Break into hundreds, tens, and ones:
- 500 (hundreds)
- 90 (tens)
- 3 (ones)

So:
$$
500 + 90 + 3 = 593
$$

#### Second way (regrouping):
Let’s take one hundred and convert it into ten tens.
- Reduce hundreds: $ 500 - 100 = 400 $
- Add 10 tens to the existing 90 tens → $ 90 + 100 = 190 $

Now:
$$
400 + 190 + 3 = 593
$$

✔ Valid decomposition.

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Problem 2: 362

#### First way (standard):
- 300
- 60
- 2

$$
300 + 60 + 2 = 362
$$

#### Second way (regrouping):
Take one hundred and turn it into 10 tens.
- Hundreds: $ 300 - 100 = 200 $
- Tens: $ 60 + 100 = 160 $
- Ones: 2

$$
200 + 160 + 2 = 362
$$

✔ Valid.

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Problem 3: 745

#### First way (standard):
- 700
- 40
- 5

$$
700 + 40 + 5 = 745
$$

#### Second way (regrouping):
Take one hundred → convert to 10 tens.
- Hundreds: $ 700 - 100 = 600 $
- Tens: $ 40 + 100 = 140 $
- Ones: 5

$$
600 + 140 + 5 = 745
$$

✔ Valid.

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✔ Final Answers:

#### 1. 593
- $ 500 + 90 + 3 = 593 $
- $ 400 + 190 + 3 = 593 $

#### 2. 362
- $ 300 + 60 + 2 = 362 $
- $ 200 + 160 + 2 = 362 $

#### 3. 745
- $ 700 + 40 + 5 = 745 $
- $ 600 + 140 + 5 = 745 $

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📝 Explanation:

- We used place value understanding.
- The key idea is that 1 hundred = 10 tens, so we can exchange them.
- This helps students understand flexibility in number representation and regrouping (which is useful for addition/subtraction).

You can also do other variations (like taking 1 ten and turning it into 10 ones), but since the problem asks for three addends (hundreds, tens, ones), keeping the structure consistent makes sense.

Let me know if you'd like a visual version using base-ten blocks!