Grade 5/Division
Long Division with Remainders: 2–3 Digit ÷ 1-Digit (870)
Students practice long division of 2- and 3-digit dividends by 1-digit divisors where remainders appear. Each answer is written with R notation (for example, 23 R2) and the worked-out solutions show multiplication and subtraction steps clearly. This worksheet helps Students understand what a remainder means and how to check that divisor × quotient + remainder matches the original dividend.
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⭐ Easy2
| # | Name | Qs | Actions |
|---|---|---|---|
1 | ID: 12359 | 9 Qs | |
2 | ID: 12360 | 9 Qs |
📊 Medium2
| # | Name | Qs | Actions |
|---|---|---|---|
1 | ID: 12361 | 9 Qs | |
2 | ID: 12362 | 9 Qs |
🔥 Hard2
| # | Name | Qs | Actions |
|---|---|---|---|
1 | ID: 12363 | 9 Qs | |
2 | ID: 12364 | 9 Qs |
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Teacher Resources
Teaching Notes
Use this worksheet to extend long division into problems with remainders. Emphasize that the remainder must always be smaller than the divisor and that it represents what is left over after making as many equal groups as possible. Have students interpret a few remainders in words ("2 left over") even though they record answers with R notation. Connect to the idea that the original dividend equals divisor × quotient + remainder.
Vocabulary
Remainder: What is left over after division.
Quotient: The whole number result of division.
Common Mistakes
- Writing a remainder that is equal to or larger than the divisor
- Dropping the remainder or forgetting to include it in the final answer
- Incorrectly multiplying divisor and quotient when checking the work
- Incorrect multiplication in steps
- Subtracting incorrectly
- Forgetting to bring down digits
- Misinterpreting the remainder
Differentiation
SupportBegin with a quick review of problems that divide evenly, then show how the last subtraction step can leave a non-zero result. Provide a sentence frame such as "dividend = divisor × quotient + remainder" and have students check their own answers with it.
ChallengeAsk students to create their own problems that produce a specific remainder. Have them rewrite a few answers as mixed numbers for enrichment, or explain how the remainder would be interpreted in a word problem.
Discussion Questions
- How can you quickly tell whether your quotient is reasonable?
- Why must the remainder always be less than the divisor?
- How does checking with multiplication help you catch division mistakes?
- What step in the algorithm do you find most important to double-check?
- What does the remainder represent in a division problem?
- How do you know if your remainder is correct?
- When might you not want a remainder?
- How does multiplication help with division?
Extension Activities
- Have students check three completed problems by multiplying divisor and quotient and adding the remainder.
- Ask students to write a short explanation of what the remainder means in one of the problems.
- Use base-ten blocks or sketches to model one of the division problems.
- Let students design a challenge problem for a partner using a chosen divisor.
Parent Tip
Use small objects like buttons to practice sharing and finding leftovers.
Learning Path
Skill Cluster
Number Operations - Division
Estimated Time
15 minutes
Skills Practiced
long division with remainderscheck division with multiplication
Prerequisites
- Multiplication Facts Fluency
- Subtraction with Regrouping
- Basic Division Facts
Next Steps
- Long Division with 2-Digit Divisors
- Interpreting Remainders in Word Problems
- Long Division Without Remainders
- Division with 4-Digit Dividends
- Interpreting Remainders in Context