Division with remainders (age 10+)
Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate
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Teaching Table
Set out your lesson
Use long division by a two-digit divisor. Check the result and interpret a remainder for a stated purpose.
Ask for 84 ÷ 7 = 12 and for the check 12×7 = 84. Ask whether a remainder after division by 7 can be 8: no, another group of 7 is possible. If these are unclear, revisit the named short-division prerequisite. The earlier long-multiplication lesson is useful for checks but is a soft, not hard, canonical edge.
Check readiness directly. Prerequisite availability is not attainment.
Use these linked lessons over several short sessions. Start with the readiness check; if it is not secure, revisit the named prerequisites rather than treating source availability as learner readiness. Use Show, Guided, then Try. Read the active sheet on screen and answer on plain paper or by typing. No printer, cutting, purchase or internet is needed. The adult may read the exact prompt. Record any hints, scribing or calculation help. Oral explanations do not show independent reading or handwriting. Use extra space and time as needed; pause or split the lesson. Keep this adult guide and all keys private. Share only the active learner sheet. Before Try, put Show, Guided work and notes aside. Keep the Try givens available, including a unit table if supplied. Give no answer or target step during the first attempt. If help is needed, give it and mark the attempt supported. Review keys after the attempt. Record the actual response and help; do not invent success or infer mastery from one attempt. These are fictional paper or oral mathematics tasks. No personal information, public sharing, purchase, real transaction, physical experiment or real measurement is required.
Record the actual response and assistance. These tasks do not establish mastery.
Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.
Teaching limits and safe use
These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.
A small written-division sample, not general algorithm fluency. Try has new operands and reordered purposes, but the purposes are explicitly stated and follow modeled types. Treat the interpretation as supported purpose matching, not unaided real-world modelling. Fraction forms apply only when the amount is divisible.
Record the actual response and assistance. These tasks do not establish mastery.
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Teaching approaches
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1 approach
Use long division by a two-digit divisor. Check the result and interpret a remainder for a stated purpose.
Use long division by a two-digit divisor. Check the result and interpret a remainder for a stated purpose.
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Learning resources
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Check understanding
- Compute 4,752 ÷ 13 using long division and express the remainder as a fraction
- Decide whether to round up or down a division remainder in a real-life context (e.g. buses needed)
- Explain each step of the long division algorithm for a 4-digit ÷ 2-digit calculation
“Can your child use long division to work out something like '1,848 ÷ 24' — going through the steps of divide, multiply, subtract, and bring down until they reach the answer?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Multiplication & Division
- Age range
- Ages 10–11