Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Real problems rarely take one step. A class trip might involve buying tickets, adding the cost of lunch, and then splitting the bill. In fourth grade, students solve problems like these with whole numbers, choosing an operation for each step and keeping track of what every intermediate number means. They record the work with equations that use a letter for the unknown, for example 4 × 15 + 22 = c.
Division problems bring a special challenge: the remainder. If 50 students ride in vans that hold 8 each, 50 ÷ 8 is 6 remainder 2, yet the answer to "how many vans?" is 7, because the last 2 students still need a ride. Other contexts ask for the remainder itself (how many are left over) or ignore it (how many full boxes). Students must read the question to decide.
Finally, students judge whether an answer is reasonable by estimating with rounded numbers or mental math before and after calculating.
When 50 ÷ 8 gives 6 remainder 2, many students answer 6 vans even though 2 students would be left behind. Always ask what the remainder means for the people or objects in the story.
Students often solve the first part of a problem and give that number as the final answer. Underlining the actual question before starting helps them see what is still needed.
Some students combine the numbers left to right with whatever operation comes to mind. Drawing a quick diagram or acting out the story shows how the quantities really relate.
Without an estimate, an answer of 4,800 for a problem that should be near 480 goes unnoticed. Rounding first gives a target to compare against.
A school has 4 classes of 23 students. Every student gets a bus seat, and each bus holds 40 students. How many buses are needed?
Answer: 3 buses are needed, because the 12 students left over after 2 full buses still need seats.
Give the same division with different questions: 26 cookies shared into bags of 4 can ask how many full bags (6), how many bags to hold all the cookies (7), or how many cookies are left over (2). Comparing the three answers makes remainder interpretation a topic of discussion rather than a rule.
Encourage a three-part write-up: an estimate, the equations, and a sentence answer with units. Tests regularly offer the unrounded quotient or the intermediate total as distractors, so the sentence answer is a strong habit.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 53 (also accepted: $53)
Tickets: 5 × 9 = 45. Add popcorn: 45 + 8 = 53 dollars.
Answer: B) 7
50 ÷ 8 = 6 remainder 2. Six vans carry 48 students, and the other 2 students need a seventh van.
Answer: 6
38 ÷ 6 = 6 remainder 2. Only 6 boxes can be completely filled; the 2 extra muffins do not fill a box.
Answer: 2 (also accepted: 2 muffins)
Six full boxes use 36 muffins, and 38 - 36 = 2 are left over.
Answer: C) s = 120 - 3 × 25
She gives away 3 × 25 = 75 stickers in total, which is subtracted from 120. So s = 120 - 3 × 25 = 45.
Answer: B) 800
312 rounds to 300 and 489 rounds to 500, so the estimate is 800. The exact sum, 801, is very close.
Answer: 75 (also accepted: 75 plants)
Plants at the start: 7 × 12 = 84. After the rabbits: 84 - 9 = 75.
A full lesson with slides, activities and an exit ticket on multistep word problems and remainders, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.OA.A.3 with an answer key, ready in about a minute.
Make a worksheet →Turn multistep word problems and remainders into a quiz students answer online that marks itself, with a class summary for you.
Build a test →It means deciding what the leftover amount means in the story. Depending on the question, you may round the quotient up, drop the remainder, or give the remainder itself as the answer.
Not usually under this standard. Fourth graders give whole-number answers and interpret remainders in context. Writing a remainder as a fraction comes in fifth grade with 5.NF.B.3.