Explain, Estimate & Check Addition and Subtraction Strategies | Grade 2 Math

Explain, Estimate and Check Addition and Subtraction Strategies for Grade 2 students
Grade 2 Math ›  Addition & Subtraction Within 1,000  ›  Lesson 19
Grade 2 Math — Explain, Estimate & Check

Explain, Estimate & Check Addition and Subtraction Strategies

Being good at math means more than finding a number. Learn to explain how a strategy works, use friendly numbers to estimate whether an answer makes sense, and check an exact answer with a related fact or another method.

Review three-digit addition and subtraction within 1,000 through base-ten models, place-value explanations, benchmarks, missing-number puzzles, mistake analysis, and word problems. Work through 25 detailed examples, 30 independent exercises, and a 15-question test.

Explain a strategyFriendly-number estimatesCheck with inverse operationsPlace-value reasoningSpot and fix errorsSums and differences within 1,000

๐ŸŽฏ What You Will Learn

Explain your thinking
Use hundreds, tens, and ones to show why a chosen addition or subtraction strategy works.
Estimate with friendly numbers
Use nearby tens or hundreds to make a quick approximate total or difference.
Check exact answers
Use an inverse operation, a second strategy, or a place-value model to test a result.
Spot mistakes and justify corrections
Decide whether an answer is reasonable, then explain precisely how to fix it.
For parents & teachers — standards alignment: This lesson directly emphasizes CCSS 2.NBT.B.9 (explain why addition and subtraction strategies work using place value and properties of operations) and reinforces CCSS 2.NBT.B.7 (add and subtract within 1,000 with visual models and written strategies). Friendly-number estimates are used here as a reasonableness-checking aid; the lesson does not claim that formal nearest-ten or nearest-hundred rounding is a separate CCSS Grade 2 requirement. The focus is explaining, approximating, and checking, not speed or a single algorithm.

๐Ÿง  Key Vocabulary

explain
Tell which method you chose, what each step represents, and why it keeps the right value.
estimate
A sensible approximate answer, often found with easier nearby numbers.
benchmark / friendly number
A helpful, easy-to-calculate number, such as 200, 400, or 650.
reasonable
Close enough to what the numbers suggest; an estimate alone cannot prove exact correctness.
exact answer
The precise sum or difference found through a valid calculation.
inverse operations
Addition and subtraction undo each other; they can be used to check answers.
place value
The value of a digit based on hundreds, tens, and ones.
strategy
A planned way to solve a problem, such as breaking apart, compensation, or using related facts.

๐ŸŒˆ Three Moves: Explain → Estimate → Check

๐ŸŸฃ ExplainShow what happens to hundreds, tens, and ones, or draw helpful jumps.
๐ŸŸ  EstimateChoose easy, nearby numbers to predict approximately how large the answer should be.
๐ŸŸข CheckFind the exact answer and verify it using the opposite operation or another method.
Big idea: Estimating and checking are two different jobs. An estimate helps you notice answers that seem too large or too small. An inverse-operation check confirms an exact answer when the check itself is computed correctly. A good explanation tells why the strategy works.

๐ŸŸฃ EXPLAIN: Why Do Place-Value Strategies Work?

Consider 342 + 215. We group the pieces by their values, not merely by the printed digits. Hundreds join hundreds, tens join tens, and ones join ones.

Hundreds
Tens
Ones
342
+ 215
= 557

On a phone, swipe sideways inside the model. Keyboard users: focus the model and use the arrow keys.

Each blue flat = 100; green rod = 10; yellow cube = 1. Counts are exact: 3 hundreds + 2 hundreds = 5 hundreds; 4 tens + 1 ten = 5 tens; and 2 ones + 5 ones = 7 ones.

342 + 215 = (300 + 200) + (40 + 10) + (2 + 5) = 557
Why regrouping works: Ten ones and one ten are equal in value. Ten tens and one hundred are equal in value. These are exchanges of units, not extra amounts. To explain a regrouped sum or difference, name the units before and after exchanging.

๐ŸŸ  ESTIMATE: Use Friendly Numbers to Test Reasonableness

For 426 − 189, we might use 400 and 200 to make a quick rough estimate. The approximate difference is 200. Then we calculate the exact difference, 237. An estimate helps us notice the size of an answer, but it is not itself proof.

Friendly-number estimate400 − 200 = 200Estimate for 426 − 189: about 200
Exact difference426 − 189 = 237Verified below using addition

We can use closer friendly tens for a more useful estimate: 430 − 190 = 240, so about 240 is a closer estimate for 426 − 189. Different reasonable estimates may have different accuracy. We are choosing convenient nearby numbers, not learning a formal rounding rule in this lesson.

Exact check: 237 + 189 = 426
Important: A reasonable estimate can reveal an obvious mistake, but a wrong answer might also be close to an estimate. For example, 231 is close to 240 yet 426 − 189 is 237. Use exact arithmetic and a valid check to know the answer is correct.

๐ŸŸข CHECK: Use the Opposite Operation

Check an addition

For 356 + 287 = 643, subtract one addend from the sum.

643 − 287 = 356 ✓

The remaining part matches the original addend.

Check a subtraction

For 731 − 286 = 445, add the difference and the amount removed.

445 + 286 = 731 ✓

The check returns to the starting amount.

You can also check an addition using another strategy. For example, start at 462 and add 183 in three helpful jumps. Each jump records part of the second addend.

Starting from 462, add 100 to 562, then 80 to 642, then 3 to 645. Jump lengths are schematic and not drawn to scale. +100+80+3 462562642645

On a phone, swipe sideways inside the number line. Keyboard users: focus it and use the arrow keys.

462 → 562 → 642 → 645. These jumps show added amounts, not distances drawn to scale.
462 + 183 = 462 + 100 + 80 + 3 = 645

๐Ÿงญ Choose a Useful Strategy

Notice this...Try this...Then check...
Easy hundreds, tens, and onesBreak apart place valuesRecombine the same units or use the inverse operation
Ten ones or ten tensCompose a new ten or hundredCheck that trading keeps the same value
Too few ones or tens for subtractionDecompose a ten or hundredAdd difference + amount taken away
Addend is near 10, 100, 200, ...Compensation with an adjustmentUse inverse subtraction
You want to predict the size of an answerUse nearby friendly tens or hundredsCompare with the exact answer—do not stop at the estimate
A proposed result might be wrongEstimate first, then compute exactlyUse the inverse operation to verify

On a phone, swipe sideways in the chart. Keyboard users: focus it and use arrow keys.

The most useful explanation often has three parts: I chose... (strategy), because... (reason), and I checked by... (verification). An efficient method need not be the same method another student chooses.

๐ŸŒŸ 25 Worked Examples

Try each question first. Then open Show solution to compare your explanation, estimate, and check with a complete worked method. A different mathematically correct method is welcome.
1Explain hundreds, tens, and ones
Explain why 342 + 215 = 557.
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342 is 3 hundreds, 4 tens, and 2 ones. The number 215 is 2 hundreds, 1 ten, and 5 ones.

Add matching places: 3 hundreds + 2 hundreds = 5 hundreds; 4 tens + 1 ten = 5 tens; 2 ones + 5 ones = 7 ones.

So the sum is 557. This works because each place has its own value.

2Explain composing a new ten
Find 257 + 126 and explain the new ten.
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Ones: 7 ones + 6 ones = 13 ones. Rename 13 ones as 1 ten and 3 ones.

Tens: 5 tens + 2 tens + 1 new ten = 8 tens. Hundreds: 2 hundreds + 1 hundred = 3 hundreds.

The answer is 383. The new ten did not change the total; 10 ones and 1 ten have the same value.

3Explain composing a hundred
Find 460 + 370 using place value.
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The ones are 0. Add the tens: 6 tens + 7 tens = 13 tens.

Rename 13 tens as 1 hundred and 3 tens. Combine the hundreds: 4 hundreds + 3 hundreds + 1 new hundred = 8 hundreds.

The sum is 830. Ten tens and one hundred represent the same amount.

4Explain two trades in addition
Find 348 + 276 and explain both trades.
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Ones: 8 ones + 6 ones = 14 ones, so make 1 ten and leave 4 ones.

Tens: 4 tens + 7 tens + 1 new ten = 12 tens, so make 1 hundred and leave 2 tens.

Hundreds: 3 hundreds + 2 hundreds + 1 new hundred = 6 hundreds. The exact sum is 624.

5Explain subtraction without trading
Explain 765 − 324 by subtracting like places.
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Subtract hundreds: 7 hundreds − 3 hundreds = 4 hundreds.

Subtract tens: 6 tens − 2 tens = 4 tens. Subtract ones: 5 ones − 4 ones = 1 one.

The difference is 441. We subtracted amounts of the same place value.

6Explain trading a ten for ones
Find 642 − 215 and explain the trade.
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We cannot take 5 ones from 2 ones. Trade 1 ten for 10 ones: 6 hundreds, 3 tens, and 12 ones still represent 642.

Now subtract: 12 ones − 5 ones = 7 ones; 3 tens − 1 ten = 2 tens; 6 hundreds − 2 hundreds = 4 hundreds.

The difference is 427. The trade changed the units, not the starting number.

7Explain trading a hundred for tens
Find 632 − 271 and explain the trade.
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Ones: 2 ones − 1 one = 1 one. We cannot take 7 tens from 3 tens.

Trade 1 hundred for 10 tens. Now 632 is 5 hundreds, 13 tens, and 2 ones.

Subtract: 13 tens − 7 tens = 6 tens and 5 hundreds − 2 hundreds = 3 hundreds. The difference is 361.

8Explain subtracting across zero tens
Find 503 − 178 and explain the two trades.
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The tens place has zero, so first trade 1 hundred for 10 tens: 4 hundreds, 10 tens, and 3 ones.

Trade 1 of those tens for 10 ones. We now have 4 hundreds, 9 tens, and 13 ones, still worth 503.

Subtract: 13 ones − 8 ones = 5 ones; 9 tens − 7 tens = 2 tens; 4 hundreds − 1 hundred = 3 hundreds. The difference is 325.

9Explain helpful compensation
Explain why 248 + 132 = 380 also equals 250 + 130.
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Move 2 from the second addend to the first: 248 + 2 = 250 and 132 − 2 = 130.

One addend went up by 2 and the other went down by 2, so the total stays unchanged.

250 + 130 = 380. This is a way to make an easier addition without changing its sum.

10Use a related fact to explain subtraction
Explain why 684 − 239 = 445.
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Break 239 into 200 + 30 + 9. Subtracting these parts one at a time removes exactly 239: 684 − 200 = 484; 484 − 30 = 454; and 454 − 9 = 445.

Check with a related addition fact: 445 + 239 = 684.

Because the difference plus the amount removed returns to the starting amount, 445 is correct.

11Use a friendly-hundreds estimate
Estimate 398 + 207, then find the exact sum.
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398 is close to 400, and 207 is close to 200. The friendly-number calculation is 400 + 200 = 600. So an estimate for the original sum is about 600.

For an exact answer, 398 + 200 = 598, then 598 + 7 = 605.

605 is near 600, so the estimate supports the reasonableness of the answer. An estimate is not the exact sum.

12Estimate a subtraction with hundreds
Estimate 426 − 189, then calculate exactly.
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426 is near 400 and 189 is near 200. The friendly-number calculation is 400 − 200 = 200. So a rough estimate for the original difference is about 200.

Compute the exact difference: 426 − 200 = 226; because 200 is 11 more than 189, add 11 back: 226 + 11 = 237.

The estimate 200 is rough, while 237 is exact. For a closer estimate, use 430 − 190 = 240.

13Choose the reasonable answer
A student says 283 + 216 is either 499 or 699. Which is correct?
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283 is near 300, and 216 is near 200. Since 300 + 200 = 500, the original sum should be about 500. That makes 499 more reasonable than 699.

Compute: 283 + 200 = 483; 483 + 16 = 499.

Check: 499 − 216 = 283. Estimation helped us choose, and exact arithmetic proved the answer.

14Estimate with friendly tens
Estimate and solve 147 + 349.
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Choose close, friendly tens: 147 is close to 150 and 349 is close to 350. The calculation 150 + 350 = 500 gives an estimate of about 500 for the original sum.

Exactly, 147 + 349 = 147 + 350 − 1 = 496.

The exact sum is just 4 away from the friendly estimate of 500.

15Estimate a difference near 400
Estimate and solve 702 − 296.
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Use nearby easy numbers: 702 is close to 700, and 296 is close to 300. The calculation 700 − 300 = 400 gives an estimate of about 400 for the original difference.

For the exact answer, 702 − 300 = 402. We subtracted 4 too much, so add 4 back: 402 + 4 = 406.

406 is near the estimate, and 406 + 296 = 702 checks the exact difference.

16Use a closer estimate for subtraction
Estimate and solve 451 − 249.
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The nearby tens give 450 − 250 = 200, so the original difference is estimated at about 200.

Find the exact difference by subtracting 250 then adding 1 back: 451 − 250 = 201; 201 + 1 = 202.

The difference 202 is close to 200. Nearby friendly numbers make estimates easier to interpret.

17Compare an estimate with a proposed sum
A student reports 263 + 328 = 791. Is that reasonable?
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Use nearby friendly tens: 263 is close to 260, and 328 is close to 330. The calculation 260 + 330 = 590 gives an estimate of about 590 for the original sum.

791 is far from that estimate. Compute exactly: 263 + 300 = 563, and 563 + 28 = 591.

So 791 is incorrect. Check 591 − 328 = 263. The estimate helped us spot the error before checking.

18Use a quick approximate total
Estimate and solve 184 + 395.
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Use easy hundreds: 184 is near 200 and 395 is near 400. The calculation 200 + 400 = 600 gives an estimate of about 600 for the original sum.

Compute: 184 + 400 = 584, then subtract the 5 added too much: 584 − 5 = 579.

579 is reasonably close to the rough estimate of 600. It need not equal the estimate.

19Check addition with subtraction
Solve 356 + 287 and check with the inverse operation.
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Add by place value: 356 + 200 = 556; +80 = 636; +7 = 643.

Check with subtraction: 643 − 287 = 356. The difference matches the original first addend.

The check shows that 643 is a correct sum.

20Check subtraction with addition
Find 731 − 286 and check.
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Subtract in friendly parts: 731 − 200 = 531; −80 = 451; −6 = 445.

Add the difference to the amount taken away: 445 + 286 = 731.

This returns to the original number, so the difference is correct.

21Check with a second addition strategy
Find 275 + 468 in two ways.
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First method: 275 + 400 = 675; +60 = 735; +8 = 743.

Second method: add place values. Ones: 5 ones + 8 ones = 13 ones (1 new ten, 3 ones). Tens: 7 tens + 6 tens + 1 new ten = 14 tens (1 new hundred, 4 tens). Hundreds: 2 hundreds + 4 hundreds + 1 new hundred = 7 hundreds.

Both methods give 743. The agreement is a useful check.

22Find the wrong subtraction result
A student writes 564 − 237 = 437. Explain and correct the error.
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Check the proposed answer: 437 + 237 = 674, not 564, so the result cannot be correct. The final answer alone does not reveal which step the student did incorrectly.

Since 237 = 200 + 30 + 7, subtract those parts: 564 − 200 = 364; then 364 − 30 = 334; and 334 − 7 = 327.

Check: 327 + 237 = 564. The corrected difference is 327.

23Find the wrong addition result
A student writes 389 + 246 = 525. Explain and correct the error.
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Adding ones gives 9 ones + 6 ones = 15 ones, so 10 of those ones are traded for 1 new ten.

Tens: 8 tens + 4 tens + 1 new ten = 13 tens, so 10 of those tens make 1 new hundred. Hundreds: 3 hundreds + 2 hundreds + 1 new hundred = 6 hundreds. The sum is 635.

Check by subtraction: 635 − 246 = 389. A possible mistake was forgetting a new ten or hundred; we cannot know the exact mistake from the answer alone.

24Find a missing addend and check
Complete 246 + □ = 610 and explain your check.
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The missing number is the amount that must be added to 246 to make 610. Find that amount by subtracting 246 from 610.

Subtract 246 in parts: 610 − 200 = 410; 410 − 40 = 370; 370 − 6 = 364. We subtracted 200 + 40 + 6 = 246 in all.

Check with the opposite operation: 246 + 364 = 610. The two addends make 610, so □ = 364.

25Explain, estimate, and check a story
A library begins with 685 books on its shelves. Students check out 248 books; later 119 of those books are returned. How many books are on the library shelves now?
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Plan the two changes in order: begin with 685, subtract the 248 books checked out, then add the 119 returned.

Exact calculation: 685 − 248 = 437, and 437 + 119 = 556 books.

Use friendly numbers to estimate: 700 − 250 + 100 = 550. That suggests about 550 books on the shelves. The exact count, 556 books, is close to this estimate.

Reverse the changes to check: 556 − 119 + 248 = 685. Both the estimate and check support the answer.

๐ŸŽฎ Independent Practice — 30 Problems

Directions: solve each problem and write the explanation, estimate, or check requested. For estimation questions, choose convenient nearby numbers and say why your estimate makes sense. Open the key only after finishing.

  1. Explain 526 + 143 by hundreds, tens, and ones.
  2. Add 438 + 175. Explain both regroupings.
  3. Explain how 380 + 460 makes a new hundred.
  4. Find 574 − 329. Describe the needed trade.
  5. Find 801 − 264. Explain how zero tens are handled.
  6. Explain 724 − 381 using a place-value trade.
  7. Show why 147 + 253 makes 400.
  8. Explain 824 − 312 without trading.
  9. Estimate 298 + 301 with friendly hundreds and find the exact sum.
  10. Estimate 946 − 512 and find the exact difference.
  11. Estimate 524 + 169 and calculate exactly.
  12. Choose friendly tens to estimate 531 − 228, then solve.
  13. Estimate and calculate 338 + 427.
  14. Use friendly hundreds to estimate 912 − 388, then solve.
  15. Estimate 236 + 452, then give the exact result.
  16. Estimate 743 − 199 and explain your exact calculation.
  17. Find 327 + 456, then check by subtraction.
  18. Find 865 − 417, then check by addition.
  19. Find 436 + 228 and check with the inverse operation.
  20. Find 902 − 357, then check.
  21. Explain how you can check 178 + 609.
  22. Solve 830 − 574 and check with addition.
  23. Find 269 + 407 and check by subtraction.
  24. A student says 472 + 189 = 651. Explain why the result is incorrect, find the correct sum, and check.
  25. A student says 845 − 376 = 569. Show that the result is incorrect, find the correct difference, and check.
  26. A student says 456 + 129 = 575. Explain and correct.
  27. A student says 803 − 176 = 637. Explain and correct.
  28. Find the missing addend: □ + 358 = 704. Check.
  29. Find the missing amount taken away: 625 − □ = 287. Check.
  30. Mia has 462 marbles, receives 185 more, then gives away 230. How many remain? Estimate and check.

๐Ÿ† Lesson Test — 15 Questions

Directions: work independently. Show a clear strategy for each question that asks you to explain, estimate, or check. Exact answers are required even when you give an estimate.

  1. Explain using place value: 417 + 352 = ?
  2. Find 728 − 413 and show matching places.
  3. Compute 257 + 368 and explain composing.
  4. Find 706 − 459, explaining needed decomposing.
  5. Add 490 + 270. Explain the new hundred.
  6. Find 753 − 486. Check by addition.
  7. Solve 516 + 237. Explain one helpful strategy.
  8. Solve 936 − 578. Check with addition.
  9. Find 584 + 179. Explain how a new ten and a new hundred are formed.
  10. Find 956 − 398. Explain and check.
  11. Estimate 512 + 284 using friendly hundreds, then solve.
  12. Estimate 779 − 356 using friendly tens, then solve.
  13. Find 629 + 184 and write its inverse-operation check.
  14. A student says 812 − 465 = 457. Correct and check.
  15. A school has 735 stickers, gives away 268, then gets 149 more. How many now? Estimate and check.

๐Ÿ” Complete Answer Key

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Practice Answers

Teacher note: Accept equivalent correct explanations and estimates using other nearby friendly numbers. An estimate and an exact answer should be labeled differently; an inverse check must match the original numbers.

1. 669. 5 hundreds + 1 hundred = 6 hundreds; 2 tens + 4 tens = 6 tens; 6 ones + 3 ones = 9 ones, so the exact sum is 669.
2. 613. 8 ones + 5 ones = 13 ones; make 1 new ten and leave 3 ones. 3 tens + 7 tens + 1 new ten = 11 tens; make 1 new hundred and leave 1 ten. 4 hundreds + 1 hundred + 1 new hundred = 6 hundreds, so 613.
3. 840. 8 tens + 6 tens = 14 tens, or 1 new hundred and 4 tens. Add the hundreds: 3 hundreds + 4 hundreds + 1 new hundred = 8 hundreds. With 0 ones, the exact sum is 840.
4. 245. Trade 1 ten for 10 ones: 574 becomes 5 hundreds, 6 tens, and 14 ones. Then 14 ones − 9 ones = 5 ones, 6 tens − 2 tens = 4 tens, and 5 hundreds − 3 hundreds = 2 hundreds. The difference is 245.
5. 537. Trade 1 hundred for 10 tens, then 1 ten for 10 ones: 7 hundreds, 9 tens, 11 ones. Subtract 2 hundreds, 6 tens, 4 ones to get 5 hundreds, 3 tens, 7 ones = 537.
6. 343. Exchange 1 hundred for 10 tens: 724 becomes 6 hundreds, 12 tens, and 4 ones. Remove 3 hundreds, 8 tens, and 1 one. That leaves 3 hundreds, 4 tens, and 3 ones, or 343. Check: 343 + 381 = 724.
7. 400. 7 ones + 3 ones = 10 ones, which make 1 ten. Then 4 tens + 5 tens + 1 new ten = 10 tens, which make 1 hundred. Then 1 hundred + 2 hundreds + 1 new hundred = 4 hundreds with no tens or ones: 400.
8. 512. Subtract equal place-value units: 8 hundreds − 3 hundreds = 5 hundreds; 2 tens − 1 ten = 1 ten; and 4 ones − 2 ones = 2 ones. No trade is needed; the difference is 512.
9. 599. Use 300 + 300 = 600 to estimate about 600. Exactly 298 + 301 = 599. This is just one less than 600.
10. 434. Use nearby hundreds: 900 − 500 = 400, so the original difference is roughly 400. Calculate exactly by place value: 9 hundreds − 5 hundreds = 4 hundreds; 4 tens − 1 ten = 3 tens; 6 ones − 2 ones = 4 ones. Thus 946 − 512 = 434. Check: 434 + 512 = 946.
11. 693. Use nearby friendly hundreds: 524 is near 500 and 169 is near 200. Calculate 500 + 200 = 700, so an estimate for the original sum is about 700. The exact calculation is 524 + 169 = 693.
12. 303. 531 is near 530 and 228 is near 230: 530 − 230 = 300, so estimate about 300. Exact difference 531 − 228 = 303.
13. 765. Use nearby friendly tens: 340 + 430 = 770, so estimate about 770 for the original sum. Exactly, 338 + 427 = 765. The exact total is 5 less than the estimate.
14. 524. Use 900 − 400 = 500 to estimate about 500. Exactly 912 − 388 = 524, which is near the rough estimate.
15. 688. Use friendly hundreds: 200 + 500 = 700, so the original sum is about 700. Calculate exactly: 236 + 452 = 688. The exact answer is 12 less than the estimate.
16. 544. Use 740 − 200 = 540 to estimate about 540. Exactly subtract 200 then add 1 back: 743 − 200 + 1 = 544.
17. 783. 327 + 456 = 783. Check: 783 − 456 = 327.
18. 448. 865 − 417 = 448. Check: 448 + 417 = 865.
19. 664. 436 + 228 = 664. Check: 664 − 228 = 436.
20. 545. 902 − 357 = 545. Check: 545 + 357 = 902.
21. 787. 178 + 609 = 787. Check: 787 − 609 = 178.
22. 256. In 830 − 574, trade 1 ten for 10 ones, then 1 hundred for 10 tens. The 830 becomes 7 hundreds, 12 tens, and 10 ones. Subtract 5 hundreds, 7 tens, and 4 ones to leave 2 hundreds, 5 tens, and 6 ones = 256. Check: 256 + 574 = 830.
23. 676. 269 + 407 = 676. Check: 676 − 407 = 269.
24. 661. The claim 651 is wrong. In 472 + 189, 2 ones + 9 ones = 11 ones, giving 1 new ten and 1 one. Next, 7 tens + 8 tens + 1 new ten = 16 tens, giving 1 new hundred and 6 tens. The hundreds are 4 hundreds + 1 hundred + 1 new hundred = 6 hundreds, so the correct sum is 661. Check: 661 − 189 = 472.
25. 469. The stated result 569 is too large by 100. Subtract in parts: 845 − 300 = 545; 545 − 70 = 475; 475 − 6 = 469. Check: 469 + 376 = 845. Therefore the correct difference is 469.
26. 585. The proposed 575 is too small by 10. Add the ones: 6 ones + 9 ones = 15 ones, which gives 1 new ten and 5 ones. Then 5 tens + 2 tens + 1 new ten = 8 tens; 4 hundreds + 1 hundred = 5 hundreds. The corrected sum is 585. One possible error was omitting the composed ten, but the student’s exact mistake cannot be known from the answer alone. Check: 585 − 129 = 456.
27. 627. The stated difference 637 is wrong. Exchange 1 hundred for 10 tens, then 1 ten for 10 ones: 803 becomes 7 hundreds, 9 tens, and 13 ones. Subtract: 13 ones − 6 ones = 7 ones; 9 tens − 7 tens = 2 tens; 7 hundreds − 1 hundred = 6 hundreds. The corrected difference is 627. Check: 627 + 176 = 803.
28. 346. 704 − 358 = 346. Check by addition: 346 + 358 = 704.
29. 338. 625 − 287 = 338, so □ = 338. Check: 625 − 338 = 287.
30. 417. 462 + 185 = 647; 647 − 230 = 417 marbles. Use 460 + 190 − 230 = 420 to estimate about 420. Reverse to check: 417 + 230 − 185 = 462.
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Test Answers

Teacher note: Accept equivalent correct explanations and estimates using other nearby friendly numbers. An estimate and an exact answer should be labeled differently; an inverse check must match the original numbers.

1. 769. 4 hundreds + 3 hundreds = 7 hundreds; 1 ten + 5 tens = 6 tens; 7 ones + 2 ones = 9 ones. The sum is 769.
2. 315. 7 hundreds − 4 hundreds = 3 hundreds, 2 tens − 1 ten = 1 ten, and 8 ones − 3 ones = 5 ones. Difference 315.
3. 625. 7 ones + 8 ones = 15 ones, so make 1 ten. 5 tens + 6 tens + 1 new ten = 12 tens, so make 1 hundred. 2 hundreds + 3 hundreds + 1 new hundred = 6 hundreds: 625.
4. 247. Start with 7 hundreds, 0 tens, and 6 ones. Trade 1 hundred for 10 tens, then 1 ten for 10 ones: 6 hundreds, 9 tens, and 16 ones still make 706. Subtract 4 hundreds, 5 tens, and 9 ones to leave 2 hundreds, 4 tens, and 7 ones. Thus 706 − 459 = 247.
5. 760. 9 tens + 7 tens = 16 tens = 1 hundred + 6 tens. 4 hundreds + 2 hundreds + 1 new hundred = 7 hundreds, so 760.
6. 267. First trade 1 ten for 10 ones, then 1 hundred for 10 tens. Now 753 is 6 hundreds, 14 tens, and 13 ones. Subtract 4 hundreds, 8 tens, and 6 ones to get 2 hundreds, 6 tens, and 7 ones: 267. Check: 267 + 486 = 753.
7. 753. Break 237 into 200 + 30 + 7. First 516 + 200 = 716; then 716 + 30 = 746; finally 746 + 7 = 753. This is valid because the three added parts make exactly 237. Check: 753 − 237 = 516.
8. 358. To subtract 578 from 936, trade 1 ten for 10 ones, then 1 hundred for 10 tens. Now 936 is 8 hundreds, 12 tens, and 16 ones. Subtract 5 hundreds, 7 tens, and 8 ones to get 3 hundreds, 5 tens, and 8 ones: 358. Check: 358 + 578 = 936.
9. 763. First compose a ten: 4 ones + 9 ones = 13 ones, or 1 new ten and 3 ones. Next compose a hundred: 8 tens + 7 tens + 1 new ten = 16 tens, or 1 new hundred and 6 tens. Then 5 hundreds + 1 hundred + 1 new hundred = 7 hundreds. So 584 + 179 = 763.
10. 558. To use compensation, subtract 400 rather than 398: 956 − 400 = 556. Because 400 is 2 more than 398, add 2 back: 556 + 2 = 558. Check with the inverse operation: 558 + 398 = 956.
11. 796. Use nearby friendly hundreds: 500 + 300 = 800, so the original sum is about 800. Exactly 512 + 284 = 796, just 4 less than the estimate.
12. 423. Use 780 − 360 = 420 to estimate about 420. Exactly 779 − 356 = 423, which is 3 more than the friendly estimate. Check: 423 + 356 = 779.
13. 813. 629 + 184 = 813. Check by subtracting one addend from the sum: 813 − 184 = 629.
14. 347. The claimed 457 is wrong. 812 − 465 = 347. Check: 347 + 465 = 812.
15. 616. 735 − 268 = 467; 467 + 149 = 616 stickers. Use 735 − 270 + 150 = 615 to estimate about 615. Reverse check: 616 − 149 + 268 = 735.

๐Ÿ’ก Common Mistakes to Watch For

Treating an estimate as an exact answer
An estimate predicts approximate size; it cannot replace the actual calculation.
Using the wrong inverse check
For 356 + 287 = 643, check 643 − 287 = 356. For 731 − 286 = 445, check 445 + 286 = 731.
Ignoring place value
A 7 in the hundreds place means 700, not 7. Explain the value of each unit.
Dropping a composed or decomposed unit
When trading, record both the decrease in one unit and the increase in another.
Trusting any answer near an estimate
An incorrect result may still be close. Complete an exact calculation and check.
Confusing explanations with digit rules
Say what each step represents: hundreds, tens, ones, compensation, or jumps—not just “carry” or “borrow.”
Family practice idea: Ask your student to finish three sentences: “My strategy was...”, “My estimate was...”, and “I checked by...”. These answers reveal number sense and reasoning more clearly than speed alone.

๐Ÿ”— Related Lessons

Grade 2 Lesson 18 — Subtract Within 1,000: Decompose Tens & HundredsReview why decomposing place-value units preserves value. Grade 2 Lesson 17 — Subtract Within 1,000 Using Place ValueConnect differences to hundreds, tens, and ones. Grade 2 Lesson 16 — Add Within 1,000: Compose Tens & HundredsExplain how ones make tens and tens make hundreds. Grade 2 Lesson 15 — Add Within 1,000 Using Place ValueReview place-value strategies before comparing methods. Grade 2 Lesson 13 — Mental Addition & Subtraction StrategiesUse friendly numbers, related facts, and compensation. Grade 2 Lesson 14 — One- & Two-Step Word Problems Within 100Practice making equations that match a story.

๐Ÿ–จ️ Printable Companion

A future Explain, Estimate & Check Practice Pack can include think-aloud prompts, place-value reasoning cards, friendly-number estimate puzzles, inverse-operation check sheets, two-method challenges, and error-analysis tasks with complete answer keys.

← Lesson 18: Subtract Within 1,000 — Decompose Tens & HundredsGrade 2 Math Hub Next → Lesson 20: Even & Odd Numbers

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