Add Within 1,000 Using Place Value | Grade 2 Math

Grade 2 Math ›  Addition & Subtraction Within 1,000  ›  Lesson 15

Grade 2 Math — Three-Digit Addition and Place Value

Add Within 1,000 Using Place Value

Learn to add within 1,000 by combining hundreds with hundreds, tens with tens, and ones with ones. Use base-ten blocks, place-value charts, expanded form, and open number lines to see why three-digit addition works.

Begin with sums that do not require trading ten ones for a ten or ten tens for a hundred. Build confidence with 25 fully worked examples, 30 independent practice problems, and a 15-question lesson test. You will learn to make those trades in Lesson 16.

Hundreds, tens & onesBase-ten blocksExpanded formAdd without regroupingNumber-line jumps

🎯 What You Will Learn

Combine matching place values
Add hundreds to hundreds, tens to tens, and ones to ones.

Read and build three-digit numbers
Use hundred flats, ten rods, and unit cubes to represent each addend.

Choose a helpful strategy
Connect drawings, expanded form, partial sums, and open number-line jumps.

Explain and check the result
Understand zeros as placeholders, use units carefully, and confirm the total.

For parents & teachers — standards alignment: This lesson focuses on the addition part of CCSS 2.NBT.B.7 (add and subtract within 1,000 with place-value models and strategies) and supports 2.NBT.B.9 (explain why those strategies work). Adding 10 or 100 connects to 2.NBT.B.8. In Texas, the word-problem practice supports the addition portion of TEKS 2.4(C), while place-value concepts connect to the Grade 2 number-and-operations expectations. Common Core is a reference framework; states may use different standards. Scope: This first lesson practices addition that does not require composing a new ten or hundred; the next lesson teaches those exchanges.

🧠 Key Vocabulary

addend
A number being added to another number.

sum
The total after all the addends are combined.

hundred flat
A model of 100 unit squares arranged in a 10-by-10 grid.

ten rod
A group of 10 unit cubes; ten rods make one hundred.

unit cube
A single unit, representing 1.

place value
The meaning of a digit in the hundreds, tens, or ones place.

expanded form
Writing a number as a sum of place-value parts: 324 = 300 + 20 + 4.

partial sums
Adding hundreds, tens, and ones in separate groups, then combining the results.

🟦 Build Three-Digit Numbers with Base-Ten Blocks

Remember: One hundred flat represents 100, one ten rod represents 10, and one unit cube represents 1. First combine like units: hundreds with hundreds, tens with tens, and ones with ones.

Hundreds1 flat = 100 ones

Tens1 rod = 10 ones

Ones1 cube = 1 one

Start with 324 + 253. The first addend is 3 hundreds, 2 tens, and 4 ones. The second addend is 2 hundreds, 5 tens, and 3 ones. Notice how the blocks match their place-value columns.

On a small screen, swipe sideways to see all the place-value columns. Keyboard users can focus the model and use the left and right arrow keys.

Number

Hundreds

Tens

Ones

324

+ 253

= 577

Blue flats = hundreds · Green rods = tens · Yellow cubes = ones

324 + 253 = (300 + 200) + (20 + 50) + (4 + 3) = 577

🏠 Add with a Hundreds–Tens–Ones Chart

Align the digits by place value. We add ones to ones, tens to tens, and hundreds to hundreds. In this example, each column totals fewer than ten units, so we do not need to exchange blocks.

Step	Hundreds	Tens	Ones
324	3	2	4
+ 253	2	5	3
Sum	5	7	7

Why the answer is 577: 5 hundreds = 500, 7 tens = 70, and 7 ones = 7. Since 500 + 70 + 7 = 577, both the drawing and the written method agree.

➕ Use Expanded Form and Partial Sums

Expanded form lets you see the value of each digit before you combine anything. For 512 + 246, add like-value parts in three small steps.

Step 1: Expand each addend

512 = 500 + 10 + 2

246 = 200 + 40 + 6

Step 2: Combine the same place values

500 + 200 = 700

10 + 40 = 50

2 + 6 = 8

Step 3: 700 + 50 + 8 = 758

Look at the value, not just the digits. The 5 in 512 means 500, not 5. Adding 5 + 2 without thinking about place value would not show the hundreds correctly.

➡️ Jump by Hundreds and Tens on an Open Number Line

To find 245 + 320, split 320 into 300 + 20. Start at 245. Jump forward 300 to 545, then forward 20 to 565.

245 → 545 → 565: the jumps +300 and +20 add up to +320.

🔢 What Happens When One Place Has Zero?

Zero keeps a place open. For example, 406 means 4 hundreds, 0 tens, and 6 ones. It does not mean 46.

406 = 400 + 0 + 6

There are no tens, but the hundreds are still worth 400.

230 = 200 + 30 + 0

There are no ones, but there are 3 full tens.

406 + 230 = 600 + 30 + 6 = 636

🧭 Choose the Best Addition Strategy

Base-ten blocks
Best when you need to see the hundreds, tens, and ones before adding.

Place-value chart
Best when keeping the three places aligned helps prevent errors.

Expanded form
Best when you want to explain why the partial sums fit together.

Number-line jumps
Best for adding whole hundreds, tens, or other convenient parts.

Important: This lesson uses examples where the total in each place is less than 10. When the ones make 10 or more, or the tens make 10 or more, we can compose a new ten or hundred. Lesson 16 will explain how to make those trades.

🌟 25 Worked Examples

Try each problem first, then open Show solution. We start with easy place-value combinations and move to three-digit sums, stories, missing addends, and error analysis.

1Warm up: add hundreds

Find 200 + 300.

Show solutionHide solution

Two hundreds and three hundreds make five hundreds.

Five hundreds equal 500.

Answer: 500

2Add 100 without changing tens or ones

Find 427 + 100.

Show solutionHide solution

427 is 4 hundreds, 2 tens, and 7 ones.

One more hundred gives 5 hundreds, 2 tens, and 7 ones.

Answer: 527

3Add a two-digit amount

Find 420 + 35.

Show solutionHide solution

Write 35 as 3 tens and 5 ones.

Start with 4 hundreds, 2 tens, and 0 ones. Add 3 tens and 5 ones.

Now there are 4 hundreds, 5 tens, and 5 ones.

Answer: 455

4Build the sum with base-ten blocks

Find 324 + 253.

Show solutionHide solution

324 has 3 hundreds, 2 tens, and 4 ones; 253 has 2 hundreds, 5 tens, and 3 ones.

Combine 3 hundreds with 2 hundreds to get 5 hundreds. Combine 2 tens with 5 tens to get 7 tens. Combine 4 ones with 3 ones to get 7 ones.

Read the new number: 5 hundreds, 7 tens, and 7 ones.

Answer: 577

5Write an expanded-form sum

Find 512 + 246.

Show solutionHide solution

Expand both addends: 512 = 500 + 10 + 2 and 246 = 200 + 40 + 6.

Add like units: 500 + 200 = 700; 10 + 40 = 50; 2 + 6 = 8.

Combine the partial sums: 700 + 50 + 8 = 758.

Answer: 758

6Use a hundreds–tens–ones chart

Find 413 + 265.

Show solutionHide solution

Line up each digit with the same place value.

Ones: 3 + 5 = 8. Tens: 1 + 6 = 7. Hundreds: 4 + 2 = 6.

Read 6 hundreds, 7 tens, and 8 ones.

Answer: 678

7Handle a zero in the tens place

Find 406 + 230.

Show solutionHide solution

Think of 406 as 4 hundreds, 0 tens, and 6 ones.

230 is 2 hundreds, 3 tens, and 0 ones.

Combine: 6 hundreds, 3 tens, and 6 ones.

Answer: 636

8Handle a zero in the ones place

Find 570 + 209.

Show solutionHide solution

The ones are 0 + 9 = 9. The tens are 7 tens + 0 tens = 7 tens.

The hundreds are 5 hundreds + 2 hundreds = 7 hundreds.

All three places show 7 hundreds, 7 tens, and 9 ones.

Answer: 779

9Keep zero as a placeholder

Find 305 + 104.

Show solutionHide solution

305 has 3 hundreds, 0 tens, and 5 ones; 104 has 1 hundred, 0 tens, and 4 ones.

The hundreds make 4 hundreds, the tens stay at 0 tens, and the ones make 9 ones.

Do not drop the middle zero: the result is four hundred nine.

Answer: 409

10Add two digits to three digits

Find 641 + 28.

Show solutionHide solution

Write 28 as 0 hundreds, 2 tens, and 8 ones.

Ones: 1 + 8 = 9. Tens: 4 + 2 = 6. Hundreds: 6 + 0 = 6.

Answer: 669

11Add close to 1,000

Find 713 + 264.

Show solutionHide solution

Hundreds: 7 + 2 = 9. Tens: 1 + 6 = 7. Ones: 3 + 4 = 7.

The sum is 977, which is within 1,000. No exchange is needed.

Answer: 977

12Add place-value parts first

Find 225 + 330.

Show solutionHide solution

Break the numbers into 200 + 20 + 5 and 300 + 30 + 0.

Hundreds total 500; tens total 50; ones total 5.

500 + 50 + 5 = 555.

Answer: 555

13Make open-number-line jumps

Find 245 + 320.

Show solutionHide solution

Start at 245. Add 300 to reach 545.

Add the remaining 20 to reach 565.

The jumps total 300 + 20 = 320, so every part was added.

Answer: 565

14Check with partial sums

Find 361 + 214.

Show solutionHide solution

Hundreds: 300 + 200 = 500. Tens: 60 + 10 = 70. Ones: 1 + 4 = 5.

Put the parts together: 500 + 70 + 5 = 575.

Check that 575 has the right hundreds, tens, and ones.

Answer: 575

15Add a three-digit and a two-digit number

Find 52 + 637.

Show solutionHide solution

Write 52 as 0 hundreds, 5 tens, and 2 ones.

Hundreds: 0 + 6 = 6. Tens: 5 + 3 = 8. Ones: 2 + 7 = 9.

The result has 6 hundreds, 8 tens, and 9 ones.

Answer: 689

16Add hundreds and tens

Find 342 + 150.

Show solutionHide solution

Break 150 into 100 and 50.

342 + 100 = 442 because one hundred is added.

442 + 50 = 492 because five tens are added.

Answer: 492

17See a repeating place-value pattern

Find 111 + 222.

Show solutionHide solution

The ones give 1 + 2 = 3. The tens give 1 ten + 2 tens = 3 tens.

The hundreds give 1 hundred + 2 hundreds = 3 hundreds.

The final number is 333.

Answer: 333

18Add when a number has zero tens

Find 702 + 185.

Show solutionHide solution

Expand 702 as 700 + 0 + 2. Expand 185 as 100 + 80 + 5.

Hundreds give 800, tens give 80, and ones give 7.

800 + 80 + 7 = 887.

Answer: 887

19Solve a library story

A school library has 313 picture books and 241 chapter books. How many books are in these two groups altogether?

Show solutionHide solution

The word altogether means combine the two given groups. Write 313 + 241.

Hundreds: 3 + 2 = 5. Tens: 1 + 4 = 5. Ones: 3 + 1 = 4.

The two groups have 554 books altogether.

Answer: 554 books

20Solve a craft-supply story

An art room has 420 sheets of blue paper and 135 sheets of green paper. How many sheets of blue and green paper are there in all?

Show solutionHide solution

Write 420 + 135 because the question asks for both sets together.

Hundreds: 4 + 1 = 5. Tens: 2 + 3 = 5. Ones: 0 + 5 = 5.

There are 555 sheets in all.

Answer: 555 sheets

21Combine two counts from a chart

A garden club plants 126 flowers in one section and 351 flowers in another section. How many flowers are planted in these two sections?

Show solutionHide solution

Use the equation 126 + 351.

Combine 100 + 300 = 400, 20 + 50 = 70, and 6 + 1 = 7.

Now add the partial sums: 400 + 70 + 7 = 477.

Answer: 477 flowers

22Find a missing second addend

Complete 430 + □ = 760.

Show solutionHide solution

The first addend has 4 hundreds and 3 tens; the total has 7 hundreds and 6 tens.

The missing addend needs 3 hundreds and 3 tens, with 0 ones.

Check: 430 + 330 = 760.

Answer: 330

23Find a missing first addend

Complete □ + 214 = 658.

Show solutionHide solution

Ask which hundreds, tens, and ones combine with 214 to make 658.

Hundreds: 6 − 2 = 4; tens: 5 − 1 = 4; ones: 8 − 4 = 4.

Check: 444 + 214 = 658.

Answer: 444

24Spot the missing place in an error

A student writes 504 + 170 = 574. Explain the error and give the correct sum.

Show solutionHide solution

The student overlooked one hundred. The hundreds are 5 + 1 = 6, not 5.

The tens are 0 tens + 7 tens = 7 tens, and the ones are 4 ones + 0 ones = 4 ones.

Six hundreds, seven tens, and four ones make 674, not 574.

Answer: 674

25Extension: choose two helpful methods

Find 623 + 356. Explain with place value and check with two jumps.

Show solutionHide solution

Expanded form: 600 + 300 = 900; 20 + 50 = 70; 3 + 6 = 9.

Combine: 900 + 70 + 9 = 979.

Check with jumps: 623 + 300 = 923, then +50 = 973, then +6 = 979.

Answer: 979

🎮 Independent Practice — 30 Problems

Directions: Solve using place value. Work with the hundreds, tens, and ones separately, and use a drawing, chart, or short equation when asked. Every sum in this set is within 1,000 and does not require composing a new ten or hundred. Keep the answer key closed until you finish.

1. 123 + 214 = ___.
2. 402 + 316 = ___.
3. 251 + 338 = ___.
4. 630 + 149 = ___.
5. 705 + 182 = ___.
6. 314 + 275 = ___.
7. 431 + 268 = ___.
8. 250 + 340 = ___.
9. 600 + 120 = ___.
10. 524 + 163 = ___.
11. 412 + 357 = ___.
12. 331 + 247 = ___.
13. 207 + 361 = ___.
14. 143 + 626 = ___.
15. 810 + 176 = ___.
16. 345 + 122 = ___.
17. 521 + 258 = ___.
18. 902 + 75 = ___.
19. 364 + 215 = ___.
20. 152 + 637 = ___.
21. Find 100 more than 638.
22. Find 10 more than 452.
23. Use expanded form to find 304 + 281.
24. Find 671 + 208 using hundreds, tens, and ones.
25. Complete 230 + □ = 560.
26. Complete □ + 124 = 587.
27. A class sorts 325 red cards and 142 blue cards. How many red and blue cards are there altogether?
28. A museum welcomes 440 visitors in the morning and 235 in the afternoon. How many visitors arrive during those two periods?
29. A student writes 503 + 264 = 707 and says there are no tens. Explain the mistake and give the correct sum.
30. Find 362 + 417. Explain why the hundreds, tens, and ones can be added separately.

🏆 Lesson Test — 15 Questions

Directions: Work independently. Explain your thinking for questions that mention expanded form, number-line jumps, missing numbers, stories, or errors. Open the test key only when you are done.

1. 132 + 246 = ___.
2. 423 + 154 = ___.
3. 610 + 249 = ___.
4. 304 + 275 = ___.
5. 251 + 427 = ___.
6. 720 + 136 = ___.
7. 83 + 605 = ___.
8. 530 + 168 = ___.
9. 214 + 365 = ___.
10. 407 + 372 = ___.
11. Use expanded form to solve 612 + 246.
12. Use helpful jumps to find 325 + 240.
13. Complete 341 + □ = 765.
14. A school plants 142 trees in spring and 327 trees in fall. How many trees are planted in these two seasons?
15. A student writes 508 + 241 = 709, forgetting to include the tens from the second addend. Explain the mistake and give the correct sum.

🔐 Complete Answer Key

Show practice answer keyHide practice answer key

Practice Answers

Teacher note: Students may use different mathematically correct models, equations, and orders of adding. Answers requiring an explanation should include a meaningful place-value reason.

1. 337. Hundreds: 1 + 2 = 3; tens: 2 + 1 = 3; ones: 3 + 4 = 7.

2. 718. 4 hundreds + 3 hundreds = 7 hundreds; 0 tens + 1 ten = 1 ten; 2 ones + 6 ones = 8 ones.

3. 589. Hundreds make 500, tens make 80, and ones make 9.

4. 779. 600 + 100 = 700; 30 + 40 = 70; 0 + 9 = 9.

5. 887. 700 + 100 = 800; 0 + 80 = 80; 5 + 2 = 7.

6. 589. 300 + 200 = 500; 10 + 70 = 80; 4 + 5 = 9.

7. 699. Add hundreds to 600, tens to 90, and ones to 9.

8. 590. 200 + 300 = 500 and 50 + 40 = 90.

9. 720. Add 100 to 600, then two tens.

10. 687. 500 + 100 = 600; 20 + 60 = 80; 4 + 3 = 7.

11. 769. Hundreds total 700, tens 60, ones 9.

12. 578. 300 + 200 = 500; 30 + 40 = 70; 1 + 7 = 8.

13. 568. Hundreds are worth 500, tens are worth 60, and ones are worth 8: 500 + 60 + 8.

14. 769. 100 + 600 = 700; 40 + 20 = 60; 3 + 6 = 9.

15. 986. 800 + 100 = 900; 10 + 70 = 80; 0 + 6 = 6.

16. 467. 300 + 100 = 400; 40 + 20 = 60; 5 + 2 = 7.

17. 779. Hundreds 7, tens 7, ones 9.

18. 977. 902 has 9 hundreds, 0 tens, and 2 ones; 75 has 0 hundreds, 7 tens, and 5 ones. Adding gives 9 hundreds, 7 tens, and 7 ones = 977.

19. 579. Hundreds 5, tens 7, ones 9.

20. 789. Hundreds 7, tens 8, ones 9.

21. 738. Add one hundred; the tens and ones stay 3 and 8.

22. 462. Add one ten; the hundreds and ones stay the same.

23. 585. 300 + 200 = 500; 0 + 80 = 80; 4 + 1 = 5.

24. 879. 600 + 200 = 800; 70 + 0 = 70; 1 + 8 = 9.

25. 330. The missing addend has 3 hundreds and 3 tens. Check 230 + 330 = 560.

26. 463. Subtract by place value to find the missing addend: 5 hundreds − 1 hundred = 4 hundreds; 8 tens − 2 tens = 6 tens; 7 ones − 4 ones = 3 ones.

27. 467 cards. Add 300 + 100, 20 + 40, and 5 + 2.

28. 675 visitors. Hundreds: 4 + 2 = 6; tens: 4 + 3 = 7; ones: 0 + 5 = 5.

29. 767. There are 0 tens + 6 tens = 6 tens. The correct total is 7 hundreds, 6 tens, and 7 ones, not 707.

30. 779. 300 + 400 = 700; 60 + 10 = 70; 2 + 7 = 9. Combine the equal-value units: 700 + 70 + 9.

Show test answer keyHide test answer key

Test Answers

Teacher note: Accept any correct place-value explanation; do not require children to use one particular order or method.

1. 378. 100 + 200 = 300; 30 + 40 = 70; 2 + 6 = 8.

2. 577. Hundreds 5, tens 7, ones 7.

3. 859. 600 + 200 = 800; 10 + 40 = 50; 0 + 9 = 9.

4. 579. Hundreds 5, tens 7, ones 9.

5. 678. 200 + 400 = 600, 50 + 20 = 70, 1 + 7 = 8.

6. 856. Hundreds 8, tens 5, ones 6.

7. 688. Write 83 as 0 hundreds, 8 tens, 3 ones; then add place by place.

8. 698. 500 + 100 = 600, 30 + 60 = 90, 0 + 8 = 8.

9. 579. 200 + 300 = 500, 10 + 60 = 70, 4 + 5 = 9.

10. 779. Hundreds 7, tens 7, ones 9.

11. 858. (600 + 10 + 2) + (200 + 40 + 6) = 800 + 50 + 8.

12. 565. 325 + 200 = 525, then +40 = 565.

13. 424. Find the missing place-value units: 7 hundreds − 3 hundreds = 4 hundreds; 6 tens − 4 tens = 2 tens; 5 ones − 1 one = 4 ones. Check: 341 + 424 = 765.

14. 469 trees. 100 + 300 = 400; 40 + 20 = 60; 2 + 7 = 9.

15. 749. The 4 tens in 241 must be counted. 500 + 200 = 700; 0 + 40 = 40; 8 + 1 = 9.

💡 Common Mistakes to Watch For

Adding digits from different places
Do not add a tens digit to a hundreds digit. Keep equal-value places together.

Forgetting what zero means
406 has 0 tens, not 4 tens. A zero still holds its place.

Writing 500 + 70 + 7 as 507
Seven tens are 70. Adding 500 + 70 + 7 gives 577.

Skipping part of a number-line jump
If you split +320 into +300 and +20, make both jumps.

Treating 100 as ten
One hundred is ten tens; one ten rod equals 10 ones.

Mixing up this lesson with regrouping
Here each place makes fewer than 10 units. Next, we will trade ten ones for one ten and ten tens for one hundred.

Family practice idea: Ask your child to build 324 and 253 with blocks, combine the matching columns, and explain how the drawing matches 324 + 253 = 577. The explanation matters as much as the answer.

🔗 Related Lessons

Grade 2 Lesson 14 — One- & Two-Step Word Problems Within 100Use stories to decide when two amounts should be combined.Grade 2 Lesson 13 — Mental Addition & Subtraction StrategiesReview adding tens, using helpful jumps, and explaining steps.Grade 2 Lesson 12 — Add Up to Four Two-Digit NumbersConnect friendly groupings and expanded form to larger numbers.Grade 2 Lesson 8 — Add Within 100 Using Place ValueRevisit tens and ones before extending to hundreds.Grade 2 Lesson 10 — Compose a Ten When AddingRefresh the meaning of trading ten ones for one ten.

🖨️ Printable Companion

A future Add Within 1,000 Using Place Value Practice Pack can include hundreds–tens–ones charts, cut-out base-ten blocks, expanded-form matching cards, open number lines, missing-addend puzzles, and a teacher answer key.

← Lesson 14: One- & Two-Step Word Problems Within 100Grade 2 Math Hub Next → Lesson 16: Add Within 1,000 — Compose Tens & Hundreds