Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
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
Fifth graders extend division to two-digit divisors, finding whole-number quotients for problems such as 1,728 ÷ 24. The standard deliberately stops short of requiring the standard long division algorithm, which is a sixth grade fluency goal. Instead students use strategies grounded in place value, the properties of operations and the link between multiplication and division.
A common strategy is partial quotients: subtract friendly multiples of the divisor, such as 24 × 50 = 1,200 and then 24 × 20 = 480, and keep track of how many 24s have been removed. Area models show the same thinking as a rectangle with one side 24, split into pieces whose areas add to the dividend. Students should be able to illustrate and explain their calculation with equations, arrays or area models and check a quotient by multiplying it back. Interpreting a remainder in a word problem is also part of the work.
Students who subtract several chunks of the divisor sometimes forget to add up the multiples they used. Recording each multiple in a column beside the work fixes this.
If 350 students ride buses that hold 48, the quotient 7 remainder 14 means 8 buses are needed. The context decides whether to round up, drop or report the remainder.
Students may try to divide 1,728 by 2 and then by 4 separately, as if dividing by 24 were two separate steps on digits. Estimating with multiples of 24 keeps the divisor whole.
A quotient of 7 for 1,728 ÷ 24 should feel wrong, since 24 × 7 is under 200. A quick estimate (about 1,700 ÷ 25 ≈ 70) catches it.
Find 1,728 ÷ 24 and check the answer by multiplication.
Answer: 1,728 ÷ 24 = 72.
Give students a short list of easy multiples of the divisor (×1, ×2, ×5, ×10, ×20, ×50) before they divide. This makes partial quotients efficient and shows how the strategy rests on multiplication facts they already know.
Tests typically ask for a quotient, ask which model or equation represents a division, or embed division in a context with a remainder that must be interpreted, such as packing items into boxes.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 78
12 × 70 = 840, leaving 96. 12 × 8 = 96. So the quotient is 70 + 8 = 78.
Answer: 75
33 × 70 = 2,310, leaving 165. 33 × 5 = 165. So 2,475 ÷ 33 = 75.
Answer: D) 62 remainder 8
16 × 60 = 960, leaving 40. 16 × 2 = 32, leaving 8. So 1,000 ÷ 16 = 62 remainder 8. Check: 16 × 62 + 8 = 1,000.
Answer: A) 8
350 ÷ 48 = 7 remainder 14. Seven buses leave 14 students without a seat, so 8 buses are needed.
Answer: 72 (also accepted: 72 cartons)
18 × 70 = 1,260, leaving 36. 18 × 2 = 36. So 70 + 2 = 72 cartons.
Answer: C) 2,400 ÷ 40 = 60
Rounding to compatible numbers gives 2,400 ÷ 40 = 60. The exact quotient is about 58, so the estimate is close.
A full lesson with slides, activities and an exit ticket on division with two-digit divisors, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NBT.B.6 with an answer key, ready in about a minute.
Make a worksheet →Turn division with two-digit divisors into a quiz students answer online that marks itself, with a class summary for you.
Build a test →No. The standard asks for strategies based on place value, properties and the multiplication link, illustrated with equations, arrays or area models. Fluency with the standard division algorithm is expected in sixth grade (6.NS.B.2).
Yes. Quotients are whole numbers, so many problems have remainders, and word problems ask students to decide what the remainder means.