Maryland Math 5.NOS.B.5.b
The Standard
- 5.NOS.B.5
- Divide multi-digit whole numbers with up to four-digit dividends and two-digit divisors.
Use partial quotients efficiently to divide.
Maryland College and Career Ready Standards for Mathematics (2025) · PERFORM OPERATIONS ON MULTI-DIGIT WHOLE NUMBERS AND WITH DECIMALS TO HUNDREDTHS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students divide by subtracting easy multiples of the divisor. They add the partial quotients to find the answer and choose large multiples to work efficiently.
What Mastery Looks Like
- For 864 ÷ 24, a student subtracts 720 and 144, then adds 30 and 6 to get 36. They check that 36 × 24 = 864.
Common Misconceptions
- Students may add the amounts subtracted, 720 and 144, instead of the partial quotients, 30 and 6. They may also stop while the amount left is still greater than the divisor.
How to Assess It
- Exit ticket: Solve 864 ÷ 24 using partial quotients. Label each multiple you subtract and check your answer with multiplication.
Lesson moves
Ways to Teach It
Use base-ten blocks to share 156 among 12 groups, trading blocks as needed, then record partial quotients of 10 and 3.
Ask which takes fewer steps for 936 ÷ 24: subtracting 24 repeatedly or subtracting 720 then 216, and why.
Give pairs 648 ÷ 18 and 936 ÷ 24; challenge them to solve each with two partial quotients and check by multiplication.
Ask how many books go on each shelf if a librarian places 672 books equally on 21 shelves; solve with partial quotients.
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Printable 5.NOS.B.5.b Worksheet
A ready-to-print activity worksheet aligned to 5.NOS.B.5.b, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 5.NOS.B.5.a
Apply estimation strategies to estimate quotients.
- 4.NOS.B.6.a
Apply estimation strategies to estimate quotients.
- 4.NOS.B.6.b
Use strategies based on place value (e.g., partial quotients) to divide.
- 6.NOS.B.2.b
Use strategies (e.g., partial quotients, inverse relationship between multiplication and division) to divide.
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