Compose & Decompose Three-Digit Numbers | Grade 2 Math

Compose and Decompose Three-Digit Numbers - Grade 2 Math
Grade 2 Math  ›  Numbers & Place Value  ›  Lesson 2
Grade 2 Math - Numbers and Place Value

Compose & Decompose Three-Digit Numbers

Learn how to build three-digit numbers from hundreds, tens, and ones and how to rename the same number in more than one place-value way.

Students trade 1 hundred for 10 tens and 1 ten for 10 ones, use concrete place-value reasoning, and explain why different decompositions can still represent exactly the same total.

Compose numbers Decompose numbers Hundreds, tens & ones Equivalent representations 2nd Grade Math

๐ŸŽฏ What You Will Learn

Compose a three-digit number
Combine hundreds, tens, and ones to build one total.
Decompose a number
Break one number into hundreds, tens, and ones.
Trade equal place-value units
Rename 1 hundred as 10 tens or 1 ten as 10 ones.
Make equivalent representations
Show the same number in more than one correct place-value way.
For parents & teachers — standards alignment: The standard hundreds-tens-ones work in this lesson directly reinforces CCSS 2.NBT.A.1, including the idea that 10 tens make 1 hundred. The alternate decompositions provide conceptual preparation for CCSS 2.NBT.B.7, where students sometimes compose or decompose tens or hundreds while adding and subtracting within 1,000. Texas Grade 2 TEKS 2.2(A) explicitly expects students to use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way. MathLattice keeps the main examples here within three-digit numbers and reserves the broader Texas number range for the later state-extension lesson.

๐Ÿง  Key Vocabulary

compose — put place-value parts together to make a number.
decompose — break a number into place-value parts.
equivalent — having the same total value even when written in a different way.
trade / regroup — rename one place-value unit as an equal amount of another unit without changing the total.
hundred — a group equal to 10 tens or 100 ones.
ten — a group equal to 10 ones.

๐Ÿงฉ Compose: Put the Parts Together

To compose a number, combine its place-value parts. For example, 3 hundreds, 5 tens, and 2 ones make 352.

300 + 50 + 2 = 352

๐Ÿงฑ Decompose: Break the Number Apart

The standard place-value decomposition of 352 is 3 hundreds + 5 tens + 2 ones. But that is not the only correct way to show 352.

352
3 hundreds + 5 tens + 2 ones
352
2 hundreds + 15 tens + 2 ones
352
3 hundreds + 4 tens + 12 ones
Big idea: different decompositions can be equivalent. The number of hundreds, tens, or ones may change, but the total value stays the same.
Standard form versus an alternate decomposition: in the usual hundreds-tens-ones form, each place is represented by one digit from 0 to 9. After a trade, an equivalent decomposition may correctly contain 10 or more tens or ones, such as 2 hundreds + 15 tens + 2 ones.

๐Ÿ”„ Trade Equal Place-Value Units

A trade does not change the amount. It changes only the way the amount is grouped. This flexible place-value thinking will become very useful when students add and subtract larger numbers.

Common mistake: after trading 1 hundred for 10 tens, remember to remove that hundred. For example, 3 hundreds + 5 tens does not become 3 hundreds + 15 tens. It becomes 2 hundreds + 15 tens.

๐Ÿง  One Number, Many Correct Forms

Start with 641 = 6 hundreds + 4 tens + 1 one. If we trade 1 hundred for 10 tens, we get another correct representation: 5 hundreds + 14 tens + 1 one.

6 H + 4 T + 1 O = 5 H + 14 T + 1 O = 641
Check your decomposition: turn each group back into its value and add. If the total is the original number, the decomposition is equivalent.

๐ŸŒŸ 25 Worked Examples

Try each problem first. Then open “Show solution” to check the place-value reasoning.
1 Compose a standard place-value model
A model has 3 hundreds, 5 tens, and 2 ones. What number does it represent?
Show solution Hide solution

Three hundreds make 300, five tens make 50, and two ones make 2. Together, 300 + 50 + 2 = 352.

2 Decompose a number in the standard way
Write 684 as hundreds, tens, and ones.
Show solution Hide solution

The digits show the standard place-value decomposition: 6 hundreds, 8 tens, and 4 ones.

3 Compose when one place has zero
What number is 4 hundreds, 0 tens, and 7 ones?
Show solution Hide solution

Four hundreds make 400, there are no tens, and there are 7 ones. The number is 407.

4 Decompose with a zero in the ones place
Write 530 as hundreds, tens, and ones.
Show solution Hide solution

530 has 5 hundreds, 3 tens, and 0 ones.

5 Trade one hundred for ten tens
Start with 352 = 3 hundreds + 5 tens + 2 ones. Trade 1 hundred for 10 tens. What new decomposition do you get?
Show solution Hide solution

Trading 1 hundred removes one hundred and adds 10 tens. So 3 hundreds become 2 hundreds, and 5 tens become 15 tens. The value stays the same: 352 = 2 hundreds + 15 tens + 2 ones.

6 Trade one ten for ten ones
Start with 352 = 3 hundreds + 5 tens + 2 ones. Trade 1 ten for 10 ones. What new decomposition do you get?
Show solution Hide solution

Trading 1 ten leaves 4 tens and adds 10 ones to the 2 ones. So 352 = 3 hundreds + 4 tens + 12 ones.

7 Make two trades
Rewrite 352 after trading 1 hundred for 10 tens and then trading 1 ten for 10 ones.
Show solution Hide solution

First, 352 = 2 hundreds + 15 tens + 2 ones. Then trade 1 of those tens for 10 ones: 352 = 2 hundreds + 14 tens + 12 ones.

8 Compose an equivalent nonstandard model
What number is 2 hundreds, 15 tens, and 2 ones?
Show solution Hide solution

2 hundreds = 200, 15 tens = 150, and 2 ones = 2. Then 200 + 150 + 2 = 352.

9 Decompose 420 in another way
Write 420 with one fewer hundred than its standard decomposition.
Show solution Hide solution

The standard form is 4 hundreds + 2 tens + 0 ones. Trade 1 hundred for 10 tens: 420 = 3 hundreds + 12 tens + 0 ones.

10 Trade a ten in 420
Write 420 with one fewer ten than its standard decomposition.
Show solution Hide solution

Start with 4 hundreds + 2 tens + 0 ones. Trade 1 ten for 10 ones: 420 = 4 hundreds + 1 ten + 10 ones.

11 Decompose 305 with extra tens
Write 305 using 2 hundreds instead of 3 hundreds.
Show solution Hide solution

Trade 1 hundred for 10 tens. Then 305 = 2 hundreds + 10 tens + 5 ones.

12 Decompose a whole hundred
Write 700 using 6 hundreds and some tens.
Show solution Hide solution

Trade 1 hundred for 10 tens. So 700 = 6 hundreds + 10 tens + 0 ones.

13 Use tens instead of hundreds
Write 246 using no hundreds, only tens and ones.
Show solution Hide solution

Two hundreds are 20 tens. Add the original 4 tens to get 24 tens. So 246 = 24 tens + 6 ones.

14 Use hundreds and extra ones
Rewrite 246 using 2 hundreds and no tens.
Show solution Hide solution

Four tens are 40 ones. Add the original 6 ones: 40 + 6 = 46 ones. So 246 = 2 hundreds + 0 tens + 46 ones.

15 Turn a number into tens
Write 390 using only tens and ones.
Show solution Hide solution

3 hundreds = 30 tens. Add the original 9 tens to get 39 tens. There are 0 ones, so 390 = 39 tens + 0 ones.

16 Choose an equivalent representation
Which representation equals 572: A) 4 hundreds + 17 tens + 2 ones or B) 5 hundreds + 6 tens + 2 ones?
Show solution Hide solution

A is correct: 400 + 170 + 2 = 572. Choice B is 500 + 60 + 2 = 562, so it is not equivalent.

17 Spot a decomposition mistake
A student says 432 = 4 hundreds + 13 tens + 2 ones. Is the student correct?
Show solution Hide solution

No. 4 hundreds + 13 tens + 2 ones = 400 + 130 + 2 = 532. For 432 with 13 tens, one correct form is 3 hundreds + 13 tens + 2 ones.

18 Compose from extra tens
What number is 1 hundred, 18 tens, and 4 ones?
Show solution Hide solution

1 hundred = 100, 18 tens = 180, and 4 ones = 4. The total is 100 + 180 + 4 = 284.

19 Compose from extra tens again
What number is 2 hundreds, 13 tens, and 7 ones?
Show solution Hide solution

2 hundreds = 200, 13 tens = 130, and 7 ones = 7. The total is 337.

20 Give two decompositions
Write 641 in two different hundreds-tens-ones ways.
Show solution Hide solution

One way is 6 hundreds + 4 tens + 1 one. Trade 1 hundred for 10 tens for another way: 5 hundreds + 14 tens + 1 one.

21 Give three decompositions
Write 508 in three different place-value ways.
Show solution Hide solution

Examples: 5 hundreds + 0 tens + 8 ones; 4 hundreds + 10 tens + 8 ones; and after trading 1 of those tens, 4 hundreds + 9 tens + 18 ones.

22 Compare two decompositions
Do 2 hundreds + 17 tens + 3 ones and 3 hundreds + 7 tens + 3 ones represent the same number?
Show solution Hide solution

Yes. The first is 200 + 170 + 3 = 373. The second is 300 + 70 + 3 = 373. Both represent 373.

23 Use one fewer hundred
Rewrite 650 using 5 hundreds.
Show solution Hide solution

650 is 6 hundreds + 5 tens. Trade 1 hundred for 10 tens: 650 = 5 hundreds + 15 tens + 0 ones.

24 Explain why a trade keeps the value
Why does replacing 1 hundred with 10 tens not change the number?
Show solution Hide solution

Because 1 hundred and 10 tens have the same value: 1 hundred = 10 tens = 100. The units are renamed, but the total amount stays the same.

25 Challenge: use only tens and ones
Write 460 using no hundreds.
Show solution Hide solution

Four hundreds are 40 tens. Add the original 6 tens: 40 tens + 6 tens = 46 tens. So 460 = 46 tens + 0 ones.

๐ŸŽฎ Independent Practice — 30 Problems

  1. Write 371 as hundreds, tens, and ones.
  2. Write 609 as hundreds, tens, and ones.
  3. What number is 4 hundreds, 2 tens, and 8 ones?
  4. What number is 7 hundreds, 0 tens, and 5 ones?
  5. Rewrite 352 using 2 hundreds.
  6. Rewrite 352 using 4 tens.
  7. Rewrite 481 using 3 hundreds.
  8. Rewrite 481 using 7 tens.
  9. Rewrite 620 using 5 hundreds.
  10. Rewrite 620 using 1 ten.
  11. Rewrite 305 using 2 hundreds.
  12. Rewrite 700 using 6 hundreds.
  13. Write 246 using no hundreds.
  14. Write 390 using no hundreds.
  15. Write 215 using no tens.
  16. What number is 3 hundreds, 14 tens, and 2 ones?
  17. What number is 1 hundred, 25 tens, and 6 ones?
  18. What number is 5 hundreds, 3 tens, and 14 ones?
  19. True or false: 4 hundreds + 12 tens + 3 ones = 523.
  20. True or false: 6 hundreds + 15 tens + 2 ones = 652.
  21. Which equals 468: 3 hundreds + 16 tens + 8 ones, or 4 hundreds + 5 tens + 8 ones?
  22. Which equals 730: 6 hundreds + 13 tens, or 7 hundreds + 13 tens?
  23. Give two different decompositions of 542.
  24. Give two different decompositions of 306.
  25. Give three different decompositions of 430.
  26. Explain why 2 hundreds + 15 tens + 2 ones equals 352.
  27. A student says 527 = 5 hundreds + 12 tens + 7 ones. Is the student correct?
  28. Fix the mistake: 384 = 2 hundreds + 8 tens + 4 ones.
  29. Rewrite 900 using exactly 8 hundreds and some tens.
  30. Challenge: write 674 using no hundreds.

๐Ÿ† Lesson Test — 15 Questions

  1. Write 482 as hundreds, tens, and ones.
  2. What number is 6 hundreds, 3 tens, and 5 ones?
  3. Rewrite 482 using 3 hundreds.
  4. Rewrite 482 using 7 tens.
  5. Rewrite 710 using 6 hundreds.
  6. Write 328 using no hundreds.
  7. What number is 2 hundreds, 16 tens, and 4 ones?
  8. True or false: 5 hundreds + 14 tens + 3 ones = 643.
  9. True or false: 3 hundreds + 15 tens + 8 ones = 458.
  10. Which equals 592: 4 hundreds + 19 tens + 2 ones, or 5 hundreds + 8 tens + 2 ones?
  11. Give two different decompositions of 604.
  12. Rewrite 450 using no hundreds.
  13. Explain why 1 hundred and 10 tens are equivalent.
  14. A student says 372 = 2 hundreds + 7 tens + 2 ones. Explain the mistake.
  15. Challenge: write 508 in three different place-value ways.

๐Ÿ” Complete Answer Key

Show practice answer key Hide practice answer key

Practice Answers

Answer-key note: For prompts that ask for a decomposition in a particular way, other equivalent representations that satisfy the stated condition are also correct.

1. 3 hundreds, 7 tens, 1 one.
2. 6 hundreds, 0 tens, 9 ones.
3. 428
4. 705
5. Possible answer: 2 hundreds, 15 tens, 2 ones.
6. Possible answer: 3 hundreds, 4 tens, 12 ones.
7. Possible answer: 3 hundreds, 18 tens, 1 one.
8. Possible answer: 4 hundreds, 7 tens, 11 ones.
9. Possible answer: 5 hundreds, 12 tens, 0 ones.
10. Possible answer: 6 hundreds, 1 ten, 10 ones.
11. Possible answer: 2 hundreds, 10 tens, 5 ones.
12. Possible answer: 6 hundreds, 10 tens, 0 ones.
13. Possible answer: 24 tens, 6 ones.
14. Possible answer: 39 tens, 0 ones.
15. Possible answer: 2 hundreds, 0 tens, 15 ones.
16. 442
17. 356
18. 544
19. True.
20. False. It equals 752.
21. 3 hundreds + 16 tens + 8 ones.
22. 6 hundreds + 13 tens.
23. Possible answer: 5 hundreds + 4 tens + 2 ones; 4 hundreds + 14 tens + 2 ones.
24. Possible answer: 3 hundreds + 0 tens + 6 ones; 2 hundreds + 10 tens + 6 ones.
25. Possible answer: 4 hundreds + 3 tens + 0 ones; 3 hundreds + 13 tens + 0 ones; 3 hundreds + 12 tens + 10 ones.
26. Because 200 + 150 + 2 = 352.
27. No. That representation equals 627.
28. A correct form using 2 hundreds is 2 hundreds + 18 tens + 4 ones.
29. Possible answer: 8 hundreds + 10 tens + 0 ones.
30. Possible answer: 67 tens + 4 ones.
Show test answer key Hide test answer key

Test Answers

Answer-key note: For decomposition prompts, other equivalent representations that satisfy the stated condition are also correct.

1. 4 hundreds, 8 tens, 2 ones.
2. 635
3. Possible answer: 3 hundreds, 18 tens, 2 ones.
4. Possible answer: 4 hundreds, 7 tens, 12 ones.
5. Possible answer: 6 hundreds, 11 tens, 0 ones.
6. Possible answer: 32 tens, 8 ones.
7. 364
8. True.
9. True.
10. 4 hundreds + 19 tens + 2 ones.
11. Possible answer: 6 hundreds + 0 tens + 4 ones; 5 hundreds + 10 tens + 4 ones.
12. Possible answer: 45 tens + 0 ones.
13. They are both worth 100.
14. 2 hundreds + 7 tens + 2 ones is 272. Using 2 hundreds, 372 needs 17 tens and 2 ones.
15. Possible answer: 5 hundreds + 0 tens + 8 ones; 4 hundreds + 10 tens + 8 ones; 4 hundreds + 9 tens + 18 ones.

๐Ÿ’ก Common Mistakes to Watch For

Trading without removing the old unit
If 1 hundred becomes 10 tens, the original hundred is no longer counted.
Changing the total
A correct trade changes the grouping, not the value of the number.
Mixing tens and ones
12 tens means 120, while 12 ones means only 12.
Rejecting a nonstandard decomposition
A number can have more than 9 tens or more than 9 ones in a correct alternate decomposition.
What comes next: Lesson 3 connects these place-value ideas to standard form, word form, and expanded form for numbers to 1,000.

๐Ÿ”— Related Lessons

Lesson 1 — Numbers to 1,000: Hundreds, Tens & Ones Review the meaning of each place before renaming the same number in different ways. Grade 1 — Tens and Ones: Understanding Place Value Review the ten-ones-equals-one-ten relationship that this lesson extends to hundreds.

๐Ÿ–จ️ Printable Companion

A future Compose & Decompose Three-Digit Numbers Practice Pack can include base-ten trades, equivalent-decomposition cards, place-value puzzles, error-analysis tasks, mixed review, and a complete answer key.

← Lesson 1: Numbers to 1,000 Grade 2 Math Hub Next: Read, Write & Expand Numbers to 1,000 →

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