Add Within 1,000: Compose Tens & Hundreds | Grade 2 Math

Grade 2 Math ›  Addition & Subtraction Within 1,000  ›  Lesson 16

Grade 2 Math — Three-Digit Addition with Regrouping

Add Within 1,000: Compose Tens & Hundreds

Learn to add three-digit numbers by trading 10 ones for 1 ten and 10 tens for 1 hundred. Follow colorful base-ten block models, a hundreds–tens–ones chart, expanded form, and an open number line to understand why regrouping works.

Start with one trade and move to two trades in the same addition problem. Learn to explain every new unit you make, check that your sum is reasonable, and practice with 25 fully solved examples, 30 exercises, and a 15-question test.

10 ones = 1 ten10 tens = 1 hundredAdd within 1,000Base-ten blocksRegroup and explain

🎯 What You Will Learn

Compose a new ten
Trade ten single ones for one ten rod without changing the value.

Compose a new hundred
Trade ten ten rods for one hundred flat and keep any leftover tens.

Regroup twice
Include each newly composed unit when adding the next place.

Show and check your thinking
Use models, place-value charts, written methods, and number-line jumps to explain a sum.

For parents & teachers — standards alignment: This lesson focuses on CCSS 2.NBT.B.7: add within 1,000 with concrete or pictorial place-value models and explain when ones form tens and tens form hundreds. It reinforces 2.NBT.A.1(a) (ten tens make one hundred) and 2.NBT.B.9 (explain why a strategy works). Texas Grade 2 materials also develop composing tens and hundreds when adding within 1,000. This lesson is an addition lesson; the corresponding subtraction exchanges come in Lessons 17–18.

🧠 Key Vocabulary

compose
To make a larger place-value unit from smaller equal units, such as 10 ones becoming 1 ten.

regroup / trade
Rename an amount with equal-value units; the total stays exactly the same.

one / unit cube
One single unit with a value of 1.

ten rod
A group of 10 unit cubes worth 10.

hundred flat
A 10-by-10 square model with 100 unit squares.

addend and sum
An addend is a number being added; the sum is the total.

place-value chart
A chart that organizes the hundreds, tens, and ones.

expanded form
Writing a number by value of its places, such as 348 = 300 + 40 + 8.

🟡 First: Ten Ones Make One Ten

Suppose you add 7 ones + 6 ones. Together there are 13 ones. Trade exactly ten ones for a ten rod. Three ones remain. Nothing was added or taken away—the pieces were renamed.

Before composing

13 ones

After composing

1 ten + 3 ones = 13

13 ones = 1 ten + 3 ones   ·   10 ones = 1 ten

Important: We trade ten ones for a ten; we do not keep those ten ones and add another ten. That would count them twice.

🟩 Next: Ten Tens Make One Hundred

When adding 6 tens + 7 tens, we get 13 tens. Ten of those tens make a hundred flat, leaving three ten rods. So 60 + 70 = 130.

Before composing

13 tens = 130

After composing

1 hundred + 3 tens = 130

13 tens = 1 hundred + 3 tens   ·   10 tens = 1 hundred

🟦 Add 348 + 276: Compose a Ten and a Hundred

Let us add 348 + 276. Combine hundreds with hundreds, tens with tens, and ones with ones. The block model below shows what changes each time we make a larger unit.

1. Compose ones8 ones + 6 ones = 14 ones. Trade 10 ones for 1 new ten; 4 ones remain.

2. Compose tens4 tens + 7 tens + 1 new ten = 12 tens. Trade 10 tens for 1 new hundred; 2 tens remain.

3. Combine hundreds3 hundreds + 2 hundreds + 1 new hundred = 6 hundreds. The sum is 624.

Base-ten blocks: follow both trades

Swipe sideways to inspect all columns, or focus the model and use the arrow keys.

Step

Hundreds

Tens

Ones

348

3 hundreds

4 tens

8 ones

+ 276

2 hundreds

7 tens

6 ones

Before trades

5 hundreds

11 tens

14 ones

Trade ones

5 hundreds

12 tens

4 ones

Trade tens: 624

6 hundreds

2 tens

4 ones

Read the changes: first we have 5 hundreds, 11 tens, and 14 ones. After trading the ones, we have 5 hundreds, 12 tens, and 4 ones. After trading the tens, we have 6 hundreds, 2 tens, and 4 ones.

348 + 276 = 624

📊 Record the Same Trades in a Place-Value Chart

Swipe sideways to see the Tens and Ones columns, or focus the table area and use the arrow keys.

Step	Hundreds	Tens	Ones
348	3	4	8
+ 276	2	7	6
Before trades	5	11	14
After trading ones	5	12	4
After trading tens	6	2	4

A temporary count of 14 in the ones column or 12 in the tens column is useful while regrouping. When we finish, each of the tens and ones places has a single digit from 0 to 9.

➕ Expanded Form Shows Why the Written Method Works

Use the value of each part rather than treating the digits as separate numbers. In expanded form:

(300 + 40 + 8) + (200 + 70 + 6)
= 500 + 110 + 14
= 500 + 100 + 10 + 10 + 4
= 624

The same result can be written in columns. Start at the ones, trade 10 ones for one ten, then include that new ten when adding tens. After trading 10 tens for a hundred, include the new hundred when adding hundreds. The written steps record the same trades shown by the blocks.

Remember: It is not enough to write only the last digit of 14 or 12. Every traded group must be included in the next place-value column.

➡️ Check with an Open Number Line

An open number line gives another way to see the same total. Start at 348 and add 276 in helpful parts: 200, then 70, then 6. The final +6 jump crosses the next ten, 620, even though that point is not marked. Number-line jumps and block trading are different representations of the same addition.

348 → 548 (+200) → 618 (+70) → 624 (+6). This open number line is not drawn to scale.

🧭 Which Kind of Trade Does the Problem Need?

Only a new ten

124 + 137 = 261

4 + 7 makes 11 ones, but 2 + 3 + 1 makes only 6 tens.

Only a new hundred

270 + 360 = 630

7 + 6 makes 13 tens, while the ones do not need a trade.

Compose both units

348 + 276 = 624

14 ones first make a new ten, then 12 tens make a new hundred.

Make exactly 1,000 (extension)

575 + 425 = 1,000

First make a new ten, then a new hundred; 10 hundreds together are 1,000.

Think → Combine → Trade → Check. For each place, ask: “How many of this kind of unit do we have now? Are there ten or more? What equal-value trade can we make?”

🌟 25 Worked Examples

Try each problem before opening Show solution. We start with one trade, then compose hundreds, then combine both trades. The final examples include a story, a missing digit, error analysis, and a challenge that reaches exactly 1,000.

1Compose one ten

Find 124 + 137 using place value.

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Add the ones: 4 ones + 7 ones = 11 ones. Trade 10 of them for 1 new ten, leaving 1 one.

Add the tens, including the new ten if there is one: 2 tens + 3 tens + 1 new ten = 6 tens. Keep those tens.

Add the hundreds: 1 hundred + 1 hundred = 2 hundreds. The final places are 2 hundreds, 6 tens, and 1 one.

Answer: 124 + 137 = 261.

Check: the hundreds, tens, and ones shown at the end represent the same total as the original two addends.

2Compose one ten

Find 216 + 145 using place value.

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Add the ones: 6 ones + 5 ones = 11 ones. Trade 10 of them for 1 new ten, leaving 1 one.

Add the tens, including the new ten if there is one: 1 ten + 4 tens + 1 new ten = 6 tens. Keep those tens.

Add the hundreds: 2 hundreds + 1 hundred = 3 hundreds. The final places are 3 hundreds, 6 tens, and 1 one.

Answer: 216 + 145 = 361.

3Compose one ten

Find 328 + 154 using place value.

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Add the ones: 8 ones + 4 ones = 12 ones. Trade 10 of them for 1 new ten, leaving 2 ones.

Add the tens, including the new ten if there is one: 2 tens + 5 tens + 1 new ten = 8 tens. Keep those tens.

Add the hundreds: 3 hundreds + 1 hundred = 4 hundreds. The final places are 4 hundreds, 8 tens, and 2 ones.

Answer: 328 + 154 = 482.

4Compose one ten in a three-digit sum

Find 235 + 416 using place value.

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Add the ones: 5 ones + 6 ones = 11 ones. Trade 10 of them for 1 new ten, leaving 1 one.

Add the tens, including the new ten if there is one: 3 tens + 1 ten + 1 new ten = 5 tens. Keep those tens.

Add the hundreds: 2 hundreds + 4 hundreds = 6 hundreds. The final places are 6 hundreds, 5 tens, and 1 one.

Answer: 235 + 416 = 651.

5Compose one hundred

Find 270 + 360 using place value.

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Add the ones: 0 ones + 0 ones = 0 ones. No trade is needed in the ones place.

Add the tens, including the new ten if there is one: 7 tens + 6 tens = 13 tens. Trade 10 tens for 1 new hundred, leaving 3 tens.

Add the hundreds: 2 hundreds + 3 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 3 tens, and 0 ones.

Answer: 270 + 360 = 630.

Check: the hundreds, tens, and ones shown at the end represent the same total as the original two addends.

6Compose a hundred from tens

Find 451 + 290 using place value.

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Add the ones: 1 one + 0 ones = 1 one. No trade is needed in the ones place.

Add the tens, including the new ten if there is one: 5 tens + 9 tens = 14 tens. Trade 10 tens for 1 new hundred, leaving 4 tens.

Add the hundreds: 4 hundreds + 2 hundreds + 1 new hundred = 7 hundreds. The final places are 7 hundreds, 4 tens, and 1 one.

Answer: 451 + 290 = 741.

7Trade ten tens for one hundred

Find 364 + 280 using place value.

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Add the ones: 4 ones + 0 ones = 4 ones. No trade is needed in the ones place.

Add the tens, including the new ten if there is one: 6 tens + 8 tens = 14 tens. Trade 10 tens for 1 new hundred, leaving 4 tens.

Add the hundreds: 3 hundreds + 2 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 4 tens, and 4 ones.

Answer: 364 + 280 = 644.

8Add multiples of ten and compose a hundred

Find 570 + 250 using place value.

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Add the ones: 0 ones + 0 ones = 0 ones. No trade is needed in the ones place.

Add the tens, including the new ten if there is one: 7 tens + 5 tens = 12 tens. Trade 10 tens for 1 new hundred, leaving 2 tens.

Add the hundreds: 5 hundreds + 2 hundreds + 1 new hundred = 8 hundreds. The final places are 8 hundreds, 2 tens, and 0 ones.

Answer: 570 + 250 = 820.

9Compose a ten AND a hundred

Find 348 + 276 using place value.

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Add the ones: 8 ones + 6 ones = 14 ones. Trade 10 of them for 1 new ten, leaving 4 ones.

Add the tens, including the new ten if there is one: 4 tens + 7 tens + 1 new ten = 12 tens. Trade 10 tens for 1 new hundred, leaving 2 tens.

Add the hundreds: 3 hundreds + 2 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 2 tens, and 4 ones.

Answer: 348 + 276 = 624.

Check: the hundreds, tens, and ones shown at the end represent the same total as the original two addends.

10Compose two new place-value units

Find 157 + 468 using place value.

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Add the ones: 7 ones + 8 ones = 15 ones. Trade 10 of them for 1 new ten, leaving 5 ones.

Add the tens, including the new ten if there is one: 5 tens + 6 tens + 1 new ten = 12 tens. Trade 10 tens for 1 new hundred, leaving 2 tens.

Add the hundreds: 1 hundred + 4 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 2 tens, and 5 ones.

Answer: 157 + 468 = 625.

11Two-step regrouping with a larger tens total

Find 286 + 347 using place value.

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Add the ones: 6 ones + 7 ones = 13 ones. Trade 10 of them for 1 new ten, leaving 3 ones.

Add the tens, including the new ten if there is one: 8 tens + 4 tens + 1 new ten = 13 tens. Trade 10 tens for 1 new hundred, leaving 3 tens.

Add the hundreds: 2 hundreds + 3 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 3 tens, and 3 ones.

Answer: 286 + 347 = 633.

12Compose twice and keep the leftover ones

Find 479 + 154 using place value.

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Add the ones: 9 ones + 4 ones = 13 ones. Trade 10 of them for 1 new ten, leaving 3 ones.

Add the tens, including the new ten if there is one: 7 tens + 5 tens + 1 new ten = 13 tens. Trade 10 tens for 1 new hundred, leaving 3 tens.

Add the hundreds: 4 hundreds + 1 hundred + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 3 tens, and 3 ones.

Answer: 479 + 154 = 633.

13Regroup when the first number has zero tens

Find 306 + 187 using place value.

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Add the ones: 6 ones + 7 ones = 13 ones. Trade 10 of them for 1 new ten, leaving 3 ones.

Add the tens, including the new ten if there is one: 0 tens + 8 tens + 1 new ten = 9 tens. Keep those tens.

Add the hundreds: 3 hundreds + 1 hundred = 4 hundreds. The final places are 4 hundreds, 9 tens, and 3 ones.

Answer: 306 + 187 = 493.

Check: the hundreds, tens, and ones shown at the end represent the same total as the original two addends.

14Regroup across a zero tens place

Find 608 + 175 using place value.

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Add the ones: 8 ones + 5 ones = 13 ones. Trade 10 of them for 1 new ten, leaving 3 ones.

Add the tens, including the new ten if there is one: 0 tens + 7 tens + 1 new ten = 8 tens. Keep those tens.

Add the hundreds: 6 hundreds + 1 hundred = 7 hundreds. The final places are 7 hundreds, 8 tens, and 3 ones.

Answer: 608 + 175 = 783.

15Compose a hundred without a ones trade

Find 480 + 345 using place value.

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Add the ones: 0 ones + 5 ones = 5 ones. No trade is needed in the ones place.

Add the tens, including the new ten if there is one: 8 tens + 4 tens = 12 tens. Trade 10 tens for 1 new hundred, leaving 2 tens.

Add the hundreds: 4 hundreds + 3 hundreds + 1 new hundred = 8 hundreds. The final places are 8 hundreds, 2 tens, and 5 ones.

Answer: 480 + 345 = 825.

16Compose one ten with a zero-free result

Find 129 + 358 using place value.

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Add the ones: 9 ones + 8 ones = 17 ones. Trade 10 of them for 1 new ten, leaving 7 ones.

Add the tens, including the new ten if there is one: 2 tens + 5 tens + 1 new ten = 8 tens. Keep those tens.

Add the hundreds: 1 hundred + 3 hundreds = 4 hundreds. The final places are 4 hundreds, 8 tens, and 7 ones.

Answer: 129 + 358 = 487.

Check: the hundreds, tens, and ones shown at the end represent the same total as the original two addends.

17Compose a ten and a hundred

Find 268 + 195 using place value.

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Add the ones: 8 ones + 5 ones = 13 ones. Trade 10 of them for 1 new ten, leaving 3 ones.

Add the tens, including the new ten if there is one: 6 tens + 9 tens + 1 new ten = 16 tens. Trade 10 tens for 1 new hundred, leaving 6 tens.

Add the hundreds: 2 hundreds + 1 hundred + 1 new hundred = 4 hundreds. The final places are 4 hundreds, 6 tens, and 3 ones.

Answer: 268 + 195 = 463.

18When the tens place has nine

Find 496 + 287 using place value.

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Add the ones: 6 ones + 7 ones = 13 ones. Trade 10 of them for 1 new ten, leaving 3 ones.

Add the tens, including the new ten if there is one: 9 tens + 8 tens + 1 new ten = 18 tens. Trade 10 tens for 1 new hundred, leaving 8 tens.

Add the hundreds: 4 hundreds + 2 hundreds + 1 new hundred = 7 hundreds. The final places are 7 hundreds, 8 tens, and 3 ones.

Answer: 496 + 287 = 783.

19Connect expanded form to regrouping

Use expanded form to add 378 + 249.

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Add the ones: 8 ones + 9 ones = 17 ones. Trade 10 of them for 1 new ten, leaving 7 ones.

Add the tens, including the new ten if there is one: 7 tens + 4 tens + 1 new ten = 12 tens. Trade 10 tens for 1 new hundred, leaving 2 tens.

Add the hundreds: 3 hundreds + 2 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 2 tens, and 7 ones.

Answer: 378 + 249 = 627.

Expanded form confirms the same trades: (300 + 70 + 8) + (200 + 40 + 9) = 500 + 110 + 17 = 627.

20Use place value and a number line

Find 367 + 258 with a number line or a place-value model.

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Add the ones: 7 ones + 8 ones = 15 ones. Trade 10 of them for 1 new ten, leaving 5 ones.

Add the tens, including the new ten if there is one: 6 tens + 5 tens + 1 new ten = 12 tens. Trade 10 tens for 1 new hundred, leaving 2 tens.

Add the hundreds: 3 hundreds + 2 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 2 tens, and 5 ones.

Answer: 367 + 258 = 625.

Check on a number line: 367 → 567 (+200) → 617 (+50) → 625 (+8). Both methods give 625.

21Solve a two-group collection story

A class collected 268 blue bottle caps and 175 red bottle caps. How many bottle caps did the class collect altogether?

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Add the ones: 8 ones + 5 ones = 13 ones. Trade 10 of them for 1 new ten, leaving 3 ones.

Add the tens, including the new ten if there is one: 6 tens + 7 tens + 1 new ten = 14 tens. Trade 10 tens for 1 new hundred, leaving 4 tens.

Add the hundreds: 2 hundreds + 1 hundred + 1 new hundred = 4 hundreds. The final places are 4 hundreds, 4 tens, and 3 ones.

Answer: 268 + 175 = 443.

The story asks for all the caps, so addition is appropriate. The class collected 443 bottle caps.

22Find a missing tens digit

Find the missing tens digit: 4□8 + 176 = 624.

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Start with the known ones: 8 ones + 6 ones = 14 ones. Write 4 ones and compose 1 new ten.

The result 624 has 2 tens. Because the hundreds column must gain a new hundred, the tens must total 12. The unknown tens digit must satisfy □ + 7 + 1 = 12, so □ = 4.

Check the hundreds: 4 hundreds + 1 hundred + 1 new hundred = 6 hundreds. The completed equation is 448 + 176 = 624.

23Explain why two trades are needed

Find 254 + 388 and explain why two trades are needed.

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Add the ones: 4 ones + 8 ones = 12 ones. Trade 10 of them for 1 new ten, leaving 2 ones.

Add the tens, including the new ten if there is one: 5 tens + 8 tens + 1 new ten = 14 tens. Trade 10 tens for 1 new hundred, leaving 4 tens.

Add the hundreds: 2 hundreds + 3 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 4 tens, and 2 ones.

Answer: 254 + 388 = 642.

Both trades are necessary: the ones make 12, and the tens make 14 after including the new ten. So the answer is 642.

24Find and fix a regrouping mistake

A student writes 365 + 278 = 533 by keeping only the last digit in each place and forgetting the trades. Explain the error and find the correct sum.

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Add the ones: 5 ones + 8 ones = 13 ones. Trade 10 of them for 1 new ten, leaving 3 ones.

Add the tens, including the new ten if there is one: 6 tens + 7 tens + 1 new ten = 14 tens. Trade 10 tens for 1 new hundred, leaving 4 tens.

Add the hundreds: 3 hundreds + 2 hundreds + 1 new hundred = 6 hundreds. The final places are 6 hundreds, 4 tens, and 3 ones.

Answer: 365 + 278 = 643.

The result 533 is incorrect: the student kept the leftover 3 ones and 3 tens, but did not count the newly composed ten and hundred. The correct sum is 643. Check: 365 + 278 = 643.

25Extension: Make exactly 1,000

Extension challenge: Find 575 + 425. Explain how 10 hundreds can become one thousand.

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Add the ones: 5 ones + 5 ones = 10 ones. Trade 10 of them for 1 new ten, leaving 0 ones.

Add the tens, including the new ten if there is one: 7 tens + 2 tens + 1 new ten = 10 tens. Trade 10 tens for 1 new hundred, leaving 0 tens.

Add the hundreds: 5 hundreds + 4 hundreds + 1 new hundred = 10 hundreds. Ten hundreds equal 1,000.

Answer: 575 + 425 = 1000.

This extension reaches the boundary of our number range. Composing 10 hundreds gives 1,000, not a three-digit answer. Check: 575 + 425 = 1,000.

🎮 Independent Practice — 30 Problems

Directions: Combine hundreds, tens, and ones. If a place has 10 or more units, trade ten of them for one unit in the next place. Show the trades or a place-value chart for questions that ask for reasoning. Keep the key closed until you finish.

1. 138 + 145 = ___.
2. 247 + 126 = ___.
3. 386 + 207 = ___.
4. 412 + 179 = ___.
5. 264 + 147 = ___.
6. 503 + 189 = ___.
7. 458 + 132 = ___.
8. 229 + 158 = ___.
9. 182 + 249 = ___.
10. 375 + 246 = ___.
11. 694 + 178 = ___.
12. 239 + 487 = ___.
13. 576 + 188 = ___.
14. 186 + 279 = ___.
15. 497 + 386 = ___.
16. 350 + 470 = ___.
17. 680 + 240 = ___.
18. 425 + 390 = ___.
19. 560 + 270 = ___.
20. 742 + 180 = ___.
21. Add 248 + 367. Explain where you composed a ten or a hundred.
22. Add 359 + 264. Explain where you composed a ten or a hundred.
23. Add 178 + 546. Explain where you composed a ten or a hundred.
24. Add 468 + 329. Explain where you composed a ten or a hundred.
25. Add 278 + 453. Explain where you composed a ten or a hundred.
26. A school gathered 286 cans in one week and 175 more cans the next week. How many cans did it gather in the two weeks?
27. A museum sold 349 tickets in the morning and 278 tickets in the afternoon. How many tickets did it sell altogether?
28. Find the missing tens digit: 3□7 + 285 = 622.
29. A student says 268 + 174 = 332, forgetting both trades. Explain the mistake and find the correct sum.
30. Extension: Find 594 + 406. Explain what 10 hundreds become.

🏆 Lesson Test — 15 Questions

Directions: Complete these questions on your own. Use a place-value picture, chart, or written explanation for the reasoning questions. Only open the test key after finishing.

1. 146 + 137 = ___.
2. 218 + 165 = ___.
3. 437 + 126 = ___.
4. 304 + 188 = ___.
5. 283 + 349 = ___.
6. 466 + 257 = ___.
7. 189 + 475 = ___.
8. 358 + 267 = ___.
9. 670 + 260 = ___.
10. 541 + 390 = ___.
11. Add 248 + 176. Show how the ones and tens are composed.
12. Find 362 + 279 using expanded form or a place-value chart.
13. A library received 287 picture books and 156 chapter books. How many books did it receive altogether?
14. Find the missing tens digit: 3□9 + 185 = 514.
15. A student writes 496 + 235 = 631. The student correctly trades 11 ones for a new ten but forgets to trade 10 of the 13 tens. Explain the error and correct the total.

🔐 Complete Answer Key

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Practice Answers

Teacher note: Equivalent, mathematically correct models and descriptions of the trades are acceptable. A correct answer should not be based on uncounted or double-counted units.

1. 283. 13 ones → 1 ten + 3 ones.

2. 373. 13 ones → 1 ten + 3 ones.

3. 593. 13 ones → 1 ten + 3 ones.

4. 591. 11 ones → 1 ten + 1 one.

5. 411. 11 ones → 1 ten + 1 one; 11 tens → 1 hundred + 1 ten.

6. 692. 12 ones → 1 ten + 2 ones.

7. 590. 10 ones → 1 ten + 0 ones.

8. 387. 17 ones → 1 ten + 7 ones.

9. 431. 11 ones → 1 ten + 1 one; 13 tens → 1 hundred + 3 tens.

10. 621. 11 ones → 1 ten + 1 one; 12 tens → 1 hundred + 2 tens.

11. 872. 12 ones → 1 ten + 2 ones; 17 tens → 1 hundred + 7 tens.

12. 726. 16 ones → 1 ten + 6 ones; 12 tens → 1 hundred + 2 tens.

13. 764. 14 ones → 1 ten + 4 ones; 16 tens → 1 hundred + 6 tens.

14. 465. 15 ones → 1 ten + 5 ones; 16 tens → 1 hundred + 6 tens.

15. 883. 13 ones → 1 ten + 3 ones; 18 tens → 1 hundred + 8 tens.

16. 820. 12 tens → 1 hundred + 2 tens.

17. 920. 12 tens → 1 hundred + 2 tens.

18. 815. 11 tens → 1 hundred + 1 ten.

19. 830. 13 tens → 1 hundred + 3 tens.

20. 922. 12 tens → 1 hundred + 2 tens.

21. 615. 15 ones → 1 ten + 5 ones; 11 tens → 1 hundred + 1 ten.

22. 623. 13 ones → 1 ten + 3 ones; 12 tens → 1 hundred + 2 tens.

23. 724. 14 ones → 1 ten + 4 ones; 12 tens → 1 hundred + 2 tens.

24. 797. 17 ones → 1 ten + 7 ones.

25. 731. 11 ones → 1 ten + 1 one; 13 tens → 1 hundred + 3 tens.

26. 461 cans. 11 ones → 1 ten + 1 one; 16 tens → 1 hundred + 6 tens.

27. 627 tickets. 17 ones → 1 ten + 7 ones; 12 tens → 1 hundred + 2 tens.

28. 3 (missing tens digit); 337 + 285 = 622. 7 + 5 = 12 ones, so carry 1 ten; the tens must make 12, so □ + 8 + 1 = 12 and □ = 3; 3 + 2 + 1 = 6 hundreds.

29. 442 (not 332). 8 + 4 = 12 ones, then 6 + 7 + 1 = 14 tens, so 2 + 1 + 1 = 4 hundreds.

30. 1000. 10 ones → 1 ten; 10 tens → 1 hundred; 10 hundreds → 1,000.

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Test Answers

Teacher note: Accept any equivalent grouping that explains all composed units and preserves the value of both addends.

1. 283. 13 ones = 1 new ten and 3 ones.

2. 383. 13 ones = 1 new ten and 3 ones.

3. 563. 13 ones = 1 new ten and 3 ones.

4. 492. 12 ones = 1 new ten and 2 ones.

5. 632. 12 ones = 1 new ten and 2 ones; 13 tens = 1 new hundred and 3 tens.

6. 723. 13 ones = 1 new ten and 3 ones; 12 tens = 1 new hundred and 2 tens.

7. 664. 14 ones = 1 new ten and 4 ones; 16 tens = 1 new hundred and 6 tens.

8. 625. 15 ones = 1 new ten and 5 ones; 12 tens = 1 new hundred and 2 tens.

9. 930. 13 tens = 1 new hundred and 3 tens.

10. 931. 13 tens = 1 new hundred and 3 tens.

11. 424. 14 ones = 1 new ten and 4 ones; 12 tens = 1 new hundred and 2 tens.

12. 641. 11 ones = 1 new ten and 1 one; 14 tens = 1 new hundred and 4 tens.

13. 443 books. 13 ones = 1 new ten and 3 ones; 14 tens = 1 new hundred and 4 tens.

14. 2 (missing digit); 329 + 185 = 514. 9 + 5 = 14 ones; the tens must make 11, so □ + 8 + 1 = 11 and □ = 2; 3 + 1 + 1 = 5 hundreds.

15. 731, not 631. The 11 ones become 1 ten and 1 one; 9 + 3 + 1 = 13 tens gives one new hundred; 4 + 2 + 1 = 7 hundreds.

💡 Common Mistakes to Watch For

Losing the new ten
After making 10 ones into 1 ten, include that ten when you add the tens.

Forgetting to make a hundred
When the tens total is 10 or more, exchange 10 tens for 1 hundred. Do not keep all ten of those rods too.

Confusing digits and units
The digit 4 in the tens place is 4 tens, or 40. Write and say the units to explain a trade.

Leaving too many units in a place
A finished hundreds–tens–ones numeral has fewer than 10 tens and fewer than 10 ones. Regroup first.

Counting the same blocks twice
An exchange changes the model, not the amount. The 10 ones that became a ten are no longer single ones.

Thinking the total cannot reach 1,000
Within 1,000 includes 1,000 itself. In a challenge such as 575 + 425, ten hundreds make one thousand.

Talk about your thinking: Ask a partner, “Which ten units did you trade? What new unit did you make? How many original units remain?” Explaining the trade is stronger evidence of understanding than just saying “carry the one.”

🔗 Related Lessons

Grade 2 Lesson 15 — Add Within 1,000 Using Place ValueBegin with hundreds, tens, and ones when no composing is needed. Grade 2 Lesson 10 — Compose a Ten When AddingReview why 10 ones can become 1 ten in two-digit addition. Grade 2 Lesson 2 — Compose & Decompose Three-Digit NumbersRevisit renaming the same number with different place-value units. Grade 2 Lesson 13 — Mental Addition & Subtraction StrategiesUse number relationships to explain regrouping and mental jumps. Grade 2 Lesson 14 — One- & Two-Step Word Problems Within 100Practice reading story problems and choosing the correct operation.

🖨️ Printable Companion

A future Compose Tens & Hundreds Practice Pack can include base-ten trading mats, place-value charts, regrouping puzzles, expanded-form problems, story tasks, error-analysis cards, and complete answer keys.

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