Fluent adding and subtracting within 1000
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction
کارهایی که یادگیرنده بعد از این درس میتواند انجام دهد
- Add two numbers with a total within 1000 using place value or rounding and adjusting
- Subtract three-digit numbers fluently, including with regrouping
- Identify a subtraction that checks an addition total by returning the other addend
- Evaluate addition and subtraction expressions to identify an equation with equal values on both sides
- Arrange six given nonzero digits exactly once across two three-digit numbers to make the greatest difference
- Estimate a sum by rounding each addend to the nearest hundred
۱ · بخوان
You have grouped tens and ones before. For numbers within 1000, also use hundreds. Fluency means working accurately and efficiently. Look at the numbers before choosing a method. A nearby hundred may help, or you can use place-value columns.
To add 298 + 156, increase 298 by 2 to make 300. Now 300 + 156 = 456. This total includes 2 extra, so subtract 2: 456 - 2 = 454. When you increase an addend, subtract that increase from the total.
Line up hundreds, tens and ones. Add ones first. Trade 10 ones for 1 ten, and 10 tens for 1 hundred. For 367 + 258, the column totals including carries are 15 ones, 12 tens and 6 hundreds: 625. A carried 1 means 10 in tens or 100 in hundreds. You can also split an addend: 432 + 25 = 432 + 20 + 5 = 457.
Subtract 672 - 348 in place-value columns. Keep the subtraction order in every column. Exchange 1 ten for 10 ones: 672 becomes 6 hundreds, 6 tens and 12 ones. Then 12 - 8 = 4, 6 - 4 = 2 and 6 - 3 = 3, giving 324. If the tens also need an exchange, trade 1 hundred for 10 tens before subtracting.
A zero tens digit may need two exchanges. For 702 - 385, exchange 1 hundred for 10 tens. Then exchange 1 of those tens for 10 ones. You now have 6 hundreds, 9 tens and 12 ones. Subtract: 12 - 5 = 7, 9 - 8 = 1 and 6 - 3 = 3. The difference is 317.
You can adjust the number being subtracted too. To find 652 - 199, subtract 200 instead: 652 - 200 = 452. You took away 1 extra, so add 1 back: 453. Taking away extra makes the difference too small.
Another way to subtract is to add up from the smaller number. For 800 - 467, add 33 to reach 500, then 300 to reach 800. Add the amounts you used: 33 + 300 = 333. That is the difference.
Addition and subtraction undo each other. Check a sum by subtracting one addend from the total. For 358 + 264 = 622, check that 622 - 264 = 358. Check a difference by adding it to the number taken away. For 622 - 264 = 358, check that 264 + 358 = 622.
An equation with a calculation on each side is true only when both sides have the same value. Work out each side separately. For 240 + 130 = 600 - 230, both sides equal 370. The matching values make this equation true.
In a digit puzzle, read which digits you may use and how often. To make the greatest difference using six given nonzero digits once, make the top number from the three largest digits, largest first. Make the bottom number from the three smallest, smallest first. With digits 1 to 6, this gives 654 - 123 = 531.
To estimate, round each number to the nearest hundred. Choose the closer of the two hundreds around it. Halfway numbers round to the higher hundred. For 427 + 286, use 400 + 300 = 700. The exact total, 713, is close to 700. An estimate checks the size of an answer, but cannot prove every digit is correct.
Choose a method that fits the numbers. Track each exchange or adjustment, and check your answer with an estimate or the opposite operation.
Lessons, questions and flashcards written for this dataset.
Eight practice questions and five readings independently written for this dataset.
برای خواندن بیشتر
What a carried 1 is worth
Add 275 + 368 in columns. The ones make 13, so keep 3 ones and trade 10 ones for 1 ten. Include that ten in the next column: 7 + 6 + 1 = 14 tens. Keep 4 tens and trade 10 tens for 1 hundred. The hundreds are 2 + 3 + 1 = 6. The total is 643. The carried marks may both look like 1, but their values differ. One records a ten; the other records a hundred.
Two exchanges across a zero
For 806 - 479, begin with the ones. You cannot take 9 ones from 6 ones yet, and there are no tens to exchange. Exchange a hundred first. The 806 becomes 7 hundreds, 10 tens and 6 ones. Exchange one of those tens next, giving 7 hundreds, 9 tens and 16 ones. Now subtract: 16 - 9 = 7, 9 - 7 = 2 and 7 - 4 = 3. The difference is 327. Both exchanges keep the starting amount equal to 806.
Remember the ten you exchanged
Consider 571 - 246. The ones need an exchange because 1 is less than 6. Turn one of the 7 tens into 10 ones. You now have 5 hundreds, 6 tens and 11 ones. Subtract 11 - 6 = 5 ones, 6 - 4 = 2 tens and 5 - 2 = 3 hundreds. The answer is 325. The tens count dropped from 7 to 6 because one ten moved into the ones. Keeping all 7 tens as well would add 10 to the starting amount.
Decide which way to adjust
Use 400 to help find 397 + 226. First calculate 400 + 226 = 626. Increasing 397 by 3 made the total 3 too large, so subtract 3 to get 623. Now try 684 - 397. Subtracting 400 gives 284, but that takes away 3 too many. Add 3 back to get 287. Before adjusting, ask what your change did. Adding extra made the sum larger. Taking away extra made the difference smaller.
Two ways to check a total
For 536 + 278, rounding to the nearest hundred gives 500 + 300 = 800. The exact total is 814, close to the estimate. But 815 is close too, so closeness alone does not prove the answer. Use subtraction for an exact check. From 814, take away 278: the result is 536, the other addend. An estimate helps you check the size. The opposite operation checks whether the exact numbers fit together.
۲ · ببین
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