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

Subtract Within 1,000 Using Place Value
Learn to subtract three-digit numbers by working with hundreds, tens, and ones. Use base-ten blocks, place-value charts, expanded form, and helpful backward jumps on an open number line to understand what a difference means.
Begin with problems that do not require decomposing a ten or a hundred. Then practice finding missing amounts, solving simple stories, checking subtraction with addition, and explaining why each step works. Includes 25 step-by-step worked examples, 30 practice problems, and a 15-question lesson test.
๐ฏ What You Will Learn
Take hundreds from hundreds, tens from tens, and ones from ones.
Show the amount you start with, what is taken away, and what remains.
Use a place-value chart, expanded form, or backward jumps on a number line.
Explain why the parts match the whole number and check with addition.
๐ง Key Vocabulary
The starting number in a subtraction equation, such as 652 in 652 − 231.
The number taken away, such as 231 in 652 − 231.
The amount remaining or the distance between two quantities; 421 in 652 − 231 = 421.
The value of a digit because it is in the hundreds, tens, or ones place.
A hundred flat is 100, a ten rod is 10, and a one cube is 1.
Writing 652 as 600 + 50 + 2 to make the place values visible.
A way to show useful backward jumps without drawing every number.
A way to check: difference + amount taken away = starting amount.
๐ฆ Start with Base-Ten Blocks: 652 − 231
Imagine 652 built with six hundred flats, five ten rods, and two one cubes. We want to take away 231: two hundred flats, three ten rods, and one one cube. Each place has enough units to remove the matching amount.
Read the rows: the middle row shows the blocks removed from the first row; the last row shows only the blocks left over.
↔ On a phone, swipe sideways inside the model; with a keyboard, focus it and use the arrow keys.
652
231
421
6 hundreds − 2 hundreds = 4 hundreds; 5 tens − 3 tens = 2 tens; 2 ones − 1 one = 1 one.
๐ Subtract in Three Place-Value Steps
Subtracting 652 − 231 can be explained by taking away hundreds, then tens, then ones.
๐ Read a Place-Value Chart
The chart describes the same subtraction as the blocks above. Be sure the hundreds, tens, and ones stay aligned.
↔ On a phone, swipe sideways across the table; with a keyboard, focus it and use the arrow keys.
| What happens | Hundreds | Tens | Ones |
|---|---|---|---|
| Start with 652 | 6 | 5 | 2 |
| Take away 231 | 2 | 3 | 1 |
| Remain: 421 | 4 | 2 | 1 |
๐งฉ Use Expanded Form and Partial Differences
Expanded form helps us explain each place rather than guessing a final number. Here is another example, 864 − 321.
864 = 800 + 60 + 4.
321 = 300 + 20 + 1.
800 − 300 = 500.
60 − 20 = 40.
4 − 1 = 3.
⬅️ Subtract with Backward Jumps on an Open Number Line
To subtract 231 from 652, split 231 into 200, 30, and 1. Move backward by those amounts in any helpful order. The path below shows 652 → 452 → 422 → 421.
๐ข What If a Place Has Zero?
Hundreds: 8 hundreds − 3 hundreds = 5 hundreds. Tens: 0 tens − 0 tens = 0 tens. Ones: 6 ones − 2 ones = 4 ones.
Hundreds: 9 hundreds − 4 hundreds = 5 hundreds. Tens: 8 tens − 6 tens = 2 tens. Ones: 0 ones − 0 ones = 0 ones.
✅ Check with the Related Addition Fact
Subtraction and addition undo each other. If 652 − 231 = 421, adding the difference and the removed amount should return the starting number.
๐งญ Know When Decomposing Is Needed
Before starting, compare the digits in the same places. In this lesson, we choose problems where each place in the starting number has enough units.
Example: 758 − 324. Eight ones can lose four, five tens can lose two, and seven hundreds can lose three.
Example: 503 − 127. The starting number has only 3 ones, but we need to take away 7 ones. We cannot finish by subtracting each digit directly.
๐ 25 Worked Examples
Show solution
We have 7 hundreds, 6 tens, and 3 ones. Remove 2 hundreds, 4 tens, and 1 one. That leaves 5 hundreds, 2 tens, and 2 ones. So 763 − 241 = 522.
Show solution
Subtract matching units: 8 hundreds − 3 hundreds = 5 hundreds; 7 tens − 5 tens = 2 tens; and 4 ones − 2 ones = 2 ones. Therefore the difference is 522. Check: 522 + 352 = 874.
Show solution
Write 598 as 500 + 90 + 8 and 276 as 200 + 70 + 6. Take away equal place-value units: 500 − 200 = 300, 90 − 70 = 20, and 8 − 6 = 2. Combine 300 + 20 + 2 = 322.
Show solution
Take away 400 first: 735 − 400 = 335. Take away 10 next: 335 − 10 = 325. Take away the last 2 ones: 325 − 2 = 323. The total amount removed was 400 + 10 + 2 = 412.
Show solution
Start at 846. Count backward 300 to 546, then 20 to 526, and then 5 to 521. These jumps remove 325 altogether. The result has 5 hundreds, 2 tens, and 1 one.
Show solution
Subtract by place value: 9 hundreds − 5 hundreds = 4 hundreds, 6 tens − 4 tens = 2 tens, and 3 ones − 1 one = 2 ones. The difference is 422. Confirm with the related addition fact 422 + 541 = 963.
Show solution
The ones place has enough ones: 6 − 5 = 1. The tens place has enough tens: 8 − 3 = 5. The hundreds place has enough hundreds: 7 − 4 = 3. So the answer is 351; no place-value trade was needed.
Show solution
Seven ones minus four ones leaves 3 ones. Eight tens minus five tens leaves 3 tens. Six hundreds minus two hundreds leaves 4 hundreds. The answer is 433.
Show solution
Subtract the 3 ones from 5 ones, leaving 2 ones. Subtract the 2 tens from 4 tens, leaving 2 tens. Subtract the 6 hundreds from 9 hundreds, leaving 3 hundreds. Therefore 945 − 623 = 322.
Show solution
The number 709 has 7 hundreds, 0 tens, and 9 ones. Remove 2 hundreds, 0 tens, and 4 ones. We have 5 hundreds, 0 tens, and 5 ones left, which is 505. Keep the 0 in the tens place; writing 55 instead would change the number.
Show solution
Subtract 3 hundreds from 8 hundreds to get 5 hundreds. There are no tens to remove from the 0 tens. Six ones minus 2 ones leaves 4 ones. The result is 504.
Show solution
Nine hundreds minus four hundreds leaves 5 hundreds. Eight tens minus six tens leaves 2 tens. Zero ones minus zero ones leaves 0 ones. Put the digits together: 520.
Show solution
Forty means 4 tens and 0 ones. Subtract 4 tens from the 6 tens in 764, leaving 2 tens. The 7 hundreds and 4 ones do not change. Thus 764 − 40 = 724.
Show solution
Two hundred is 2 hundreds, 0 tens, and 0 ones. Take 2 hundreds from the 8 hundreds in 853. Five tens and 3 ones stay the same, so 853 − 200 = 653.
Show solution
The number 5 represents only ones. Remove 5 ones from the 8 ones in 698; 3 ones remain. The 6 hundreds and 9 tens stay unchanged, so the difference is 693.
Show solution
Remove 2 hundreds from 7 hundreds, leaving 5 hundreds. Remove 3 tens from 5 tens, leaving 2 tens. Subtracting 0 ones leaves the original 9 ones. The difference is 529.
Show solution
Six ones can lose 4 ones; 3 tens can lose 1 ten; and 9 hundreds can lose 7 hundreds. Subtract in each place: 6 − 4 = 2, 3 − 1 = 2, 9 − 7 = 2. Therefore 936 − 714 = 222. No place needs more units than it already has.
Show solution
Subtract 400 to get 389. Subtract 50 to get 339. Subtract 6 to get 333. Check by adding 333 + 456 = 789. You may also subtract hundreds, tens, and ones in separate columns.
Show solution
Separate place values: (800 − 400) + (30 − 20) + (2 − 1) = 400 + 10 + 1. The difference is 411. In the block model, 4 hundred flats, 1 ten rod, and 1 one cube remain.
Show solution
Remove 3 hundreds, 5 tens, and 1 one from 5 hundreds, 6 tens, and 8 ones. The remaining 2 hundreds, 1 ten, and 7 ones make 217. Check: 217 + 351 = 568.
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Place-value method: 700 − 300 = 400, 60 − 20 = 40, and 4 − 1 = 3, so the difference is 443. Backward-jump method: 764 − 300 = 464, then −20 = 444, then −1 = 443. Both methods remove exactly 321.
Show solution
The missing number is the amount taken away. Compare 874 and 542 by place: 8 hundreds − 5 hundreds = 3 hundreds, 7 tens − 4 tens = 3 tens, and 4 ones − 2 ones = 2 ones. So □ = 332. Check: 542 + 332 = 874.
Show solution
We need the starting amount before 231 was removed. Add the removed amount to what remains: 452 + 231. Add units: 4 hundreds + 2 hundreds = 6 hundreds, 5 tens + 3 tens = 8 tens, 2 ones + 1 one = 3 ones. Therefore □ = 683. Check: 683 − 231 = 452.
Show solution
The sticks removed are 3 hundreds, 4 tens, and 7 ones. From the starting 9 hundreds, 5 tens, and 8 ones, we have 6 hundreds, 1 ten, and 1 one left. So 611 craft sticks remain. Check: 611 + 347 = 958.
Show solution
The student seems to have written 4 in the hundreds place, but 7 hundreds − 2 hundreds equals 5 hundreds, not 4. In the tens place, 5 tens − 4 tens = 1 ten; in the ones place, 6 ones − 3 ones = 3 ones. So the correct difference is 513. Check: 513 + 243 = 756.
๐ฎ Independent Practice — 30 Problems
Directions: subtract using hundreds, tens, and ones. For problems that ask for a missing number or explanation, show how the number or error can be found. Use another strategy or addition to check. Keep the answer key closed until you finish.
- 754 − 231 = ____.
- 863 − 412 = ____.
- 976 − 543 = ____.
- 695 − 263 = ____.
- 847 − 326 = ____.
- 568 − 245 = ____.
- 789 − 356 = ____.
- 934 − 512 = ____.
- 679 − 348 = ____.
- 846 − 703 = ____.
- 807 − 306 = ____.
- 905 − 403 = ____.
- 970 − 350 = ____.
- 890 − 470 = ____.
- 764 − 20 = ____.
- 835 − 300 = ____.
- 698 − 7 = ____.
- 984 − 60 = ____.
- 758 − 124 = ____.
- 975 − 432 = ____.
- 897 − 675 = ____.
- 668 − 346 = ____.
- 743 − 421 = ____.
- 886 − 263 = ____.
- 777 − 555 = ____. Name the hundreds, tens, and ones that remain.
- A school had 864 crayons. It gave 341 crayons to a class. How many crayons were left?
- A library had 786 books on a display. Staff moved 254 books to a different room. How many stayed on the display?
- Complete the subtraction: 957 − □ = 624. Find the missing number.
- Complete the subtraction: □ − 324 = 541. Find the starting number.
- A student claims 875 − 342 = 532. Explain the error and write the correct difference.
๐ Lesson Test — 15 Questions
Directions: complete the lesson test independently. Use place-value reasoning to explain the missing-number, story, and error-analysis problems. Open the test answer key only after you have finished.
- 865 − 342 = ____.
- 794 − 263 = ____.
- 958 − 436 = ____.
- 687 − 345 = ____.
- 975 − 651 = ____.
- 839 − 417 = ____.
- 760 − 240 = ____.
- 908 − 405 = ____.
- 850 − 300 = ____.
- 967 − 20 = ____.
- 759 − 408 = ____.
- 869 − 547 = ____.
- Complete 986 − □ = 543. What is the missing number?
- A bake sale prepared 968 cupcakes and sold 324 cupcakes. How many cupcakes remained?
- A student says 753 − 241 = 612. Is the answer correct? Explain and give the right difference.
๐ Complete Answer Key
Show practice answer key
Practice Answers
Teacher note: Accept any accurate subtraction method that preserves the meaning of hundreds, tens, and ones. For a word problem, include the appropriate unit; for an error-analysis problem, explain the incorrect place-value step.
Show test answer key
Test Answers
Teacher note: Accept equivalent correct place-value equations or backward jumps, as long as the reasoning is complete for the questions that request it.
๐ก Common Mistakes to Watch For
Take 3 tens from tens, not 3 ones. In 652 − 231, the 3 represents 30, not 3.
806 − 302 = 504. The zero in the tens place keeps the four in the ones place.
6 hundreds − 2 hundreds = 4 hundreds, which means 400, not 4.
The difference is the amount left or the distance between the numbers, not the number taken away.
If the top ones digit is smaller than the ones taken away, we need to decompose a place-value unit. This is covered in Lesson 18.
To check 652 − 231 = 421, use 421 + 231 = 652, not 652 + 231.
๐ Related Lessons
๐จ️ Printable Companion
A future Subtract Within 1,000 Using Place Value Practice Pack can include base-ten subtraction mats, hundreds–tens–ones charts, backward-jump number lines, expanded-form questions, missing-number puzzles, word problems, error analysis, and complete answer keys.
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