Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
In third grade, students become fluent adding and subtracting three-digit numbers, such as 485 + 267 or 703 - 258. Fluency here means choosing a sensible method and carrying it out accurately, whether that is a mental strategy, a number line, partial sums or the standard algorithm. All of these methods rest on the same base-ten ideas: hundreds combine with hundreds, tens with tens and ones with ones, and ten of any unit can be traded for one of the next larger unit.
Subtraction across zeros (like 600 - 274) is where understanding is tested hardest, because the student must decompose a hundred into tens and then a ten into ones. Students who can explain the trade with base-ten blocks make far fewer errors than those who only follow steps. Flexible thinking also pays off: 703 - 698 is easiest by counting up 5, and 499 + 238 is quick as 500 + 237. The relationship between addition and subtraction gives a built-in check, because every difference can be confirmed by adding it back.
For 532 - 178, a student may compute 8 - 2 in the ones place and get 446. Insist on reading each column from the top number down, trading when the top digit is too small.
In 600 - 274, students often borrow from the hundreds but forget to make the tens 9. Model the trade with blocks: 6 hundreds become 5 hundreds, 9 tens and 10 ones.
When adding 457 + 386 a student may write 13 in the ones and never add the carried ten. Labeling columns H, T and O helps.
Adding 63 to 418 with the 6 under the 4 produces errors. Line up digits by place value from the right.
Find 704 - 258 and check the answer.
Answer: 704 - 258 = 446.
Begin with base-ten blocks and place value charts, then record the same steps with numbers so the algorithm grows from the model. Introduce partial sums and open number lines alongside the standard algorithm, and ask students to compare methods for the same problem.
Fluency checks can include mixed sets where some problems are easiest mentally (500 - 499) and others need careful regrouping. Expect word problems that combine this standard with rounding and estimation.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 752
Ones: 5 + 7 = 12, write 2 carry 1. Tens: 8 + 6 + 1 = 15, write 5 carry 1. Hundreds: 4 + 2 + 1 = 7. Answer 752.
Answer: 326
Trade 1 hundred to make 5 hundreds, 9 tens and 10 ones. 10 - 4 = 6, 9 - 7 = 2, 5 - 2 = 3. Answer 326.
Answer: A) 354
Trade for ones: 12 - 8 = 4. Trade for tens: 12 - 7 = 5. Hundreds: 4 - 1 = 3. Answer 354. The option 446 comes from subtracting the smaller digit in each column.
Answer: 467 (also accepted: 467 books)
812 - 345: ones 12 - 5 = 7, tens 10 - 4 = 6 after trading, hundreds 7 - 3 = 4. 467 books remain.
Answer: C) Add 500 + 236 and then subtract 1
499 is 1 less than 500. 500 + 236 = 736, minus 1 is 735.
Answer: 570
368 + 157 = 525, and 525 + 45 = 570.
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Explain why addition and subtraction strategies work, using place value and the properties of operations.
A full lesson with slides, activities and an exit ticket on adding and subtracting within 1000, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 3.NBT.A.2 with an answer key, ready in about a minute.
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Build a test βNo. Students add and subtract fluently using strategies and algorithms based on place value, properties and the addition-subtraction relationship. The standard algorithm for addition and subtraction is required by 4.NBT.B.4.
Accurate, efficient and flexible. Students choose a method that suits the numbers and carry it out correctly without excessive time.