Fluently add and subtract multi-digit whole numbers using the standard algorithm.
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
By fourth grade, students are expected to add and subtract multi-digit whole numbers fluently using the standard algorithm, the familiar column method. Fluency here means accurate, efficient and flexible: students line up digits by place value, work from the ones place leftward, and regroup when a column sum reaches ten or a column does not have enough to subtract from.
Earlier grades built the understanding with base-ten blocks, place value strategies and partial sums. This standard asks students to compress those ideas into the efficient written method and apply it to numbers up to one million. Subtraction across zeros, as in 6,003 - 2,748, is a well-known sticking point, because regrouping has to travel through several places before the ones column can be subtracted. Checking subtraction by adding the answer back to the number subtracted is part of being fluent. The same algorithm works no matter how many digits the numbers have, which is exactly why it is worth mastering.
In 532 - 278, a student may compute 8 - 2 in the ones column. Each column must subtract the bottom digit from the top, regrouping when the top digit is smaller.
With 6,003 - 2,748, students often borrow from the 6 but forget to turn the zeros into 9s. Modeling with blocks shows that one thousand becomes 9 hundreds, 9 tens and 10 ones.
Adding 4,325 + 68 with the 68 lined up under the 43 gives a wildly wrong answer. Writing numbers on grid paper or with place value headings keeps columns straight.
Find 6,003 - 2,748 using the standard algorithm.
Answer: 6,003 - 2,748 = 3,255.
Keep a place value explanation attached to the algorithm. Ask students to narrate one regrouping in each problem ("I traded 1 hundred for 10 tens") so the procedure never becomes a string of crossed-out digits with no meaning.
Fluency grows with short, frequent practice rather than long worksheets. Mix addition and subtraction, include zeros in the minuend, and add a quick estimate so students catch answers that are off by a place.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 8413 (also accepted: 8,413)
Ones: 7 + 6 = 13, write 3 carry 1. Tens: 8 + 2 + 1 = 11, write 1 carry 1. Hundreds: 5 + 8 + 1 = 14, write 4 carry 1. Thousands: 4 + 3 + 1 = 8. The sum is 8,413.
Answer: 3255 (also accepted: 3,255)
Regroup 1 thousand into 9 hundreds, 9 tens and 10 ones, so the ones become 13. Then 13 - 8 = 5, 9 - 4 = 5, 9 - 7 = 2, 5 - 2 = 3. The answer is 3,255.
Answer: C) 71,104
Ones: 9 + 5 = 14. Tens: 0 + 9 + 1 = 10. Hundreds: 3 + 7 + 1 = 11. Thousands: 2 + 8 + 1 = 11. Ten thousands: 5 + 1 + 1 = 7. The sum is 71,104.
Answer: B) Subtracted the smaller digit from the larger in each column instead of regrouping
The student did 8 - 2 = 6, 7 - 3 = 4 and 5 - 2 = 3 without regrouping. The correct answer is 254.
Answer: 6584 (also accepted: 6,584)
45,000 - 38,416 = 6,584. Check: 6,584 + 38,416 = 45,000.
Answer: 3383 (also accepted: 3,383)
Ones: 10 - 7 = 3 after regrouping. Tens: 14 - 6 = 8 after regrouping. Hundreds: 11 - 8 = 3 after regrouping. Thousands: 6 - 3 = 3. The answer is 3,383.
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.
A full lesson with slides, activities and an exit ticket on adding and subtracting with the standard algorithm, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 4.NBT.B.4 with an answer key, ready in about a minute.
Make a worksheet βTurn adding and subtracting with the standard algorithm into a quiz students answer online that marks itself, with a class summary for you.
Build a test βIt is the column method for adding or subtracting, working from the ones place to the left and regrouping (carrying or borrowing) when needed.
Not only speed. Fluency means accuracy, efficiency and flexibility, including understanding why each regrouping step works.