Division with Remainders
A 50-minute Grade 4 lesson on dividing larger numbers by a one-digit divisor, and on the question that has no arithmetic answer: what to do with what is left over.
Division with Remainders is a free 50-minute Grade 4 maths lesson plan for Common Core standard 4.NBT.B.6 — divide larger numbers, including with remainders. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.
- Grade:
- Grade 4
- Length:
- 50 minutes
- Standard:
- 4.NBT.B.6
Grade 4 · Number & Operations in Base Ten
4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.
Objective
Students will be able to divide a multi-digit number by a one-digit divisor and interpret the remainder in context.
Students are successful when they can
- Divides accurately with a remainder.
- Checks by multiplying back and adding the remainder.
- Decides in context whether to round up, round down or report the remainder.
What you need
- Base ten materials
- Place value charts
- Word problem cards with different remainder interpretations
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — share and see what is left
6 min- Share 27 counters between 4. Six each, three left over.
- Ask what the three are. Not an error and not a fraction yet — just what did not fit.
Teach — divide, then decide
15 min- Divide 738 by 5 using partial quotients or the standard layout, narrating each place.
- Answer 147 remainder 3. Check: 147 × 5 = 735, plus 3 is 738.
- Say the check out loud as a rule. The remainder must be smaller than the divisor or the division is not finished.
- Now three word problems with the same numbers: 147 remainder 3.
- Buses holding 5 — you need 148, because the last three still have to travel. Round up.
- Full boxes of 5 — you get 147. Round down. Sweets shared out — 147 each and 3 left in the bowl. Report the remainder.
“The arithmetic gives you the same answer every time. What you do with the remainder depends entirely on the story, and there is no rule that covers all three.”
Guided practice — same numbers, three questions
14 min- Pairs solve a division, then answer three word problems built on it.
- They must state which interpretation each needs and why.
- Every division is checked by multiplying back.
Independent practice
12 min- Students complete a division page including contextual problems.
- The bus problem answered as 147 is the classic error and is a reading error, not a division one.
Close
3 min- Give a remainder problem and ask only whether it rounds up or down.
- The decision, not the calculation, is what this lesson was about.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Answers 'how many buses for 738 people at 5 each' with 147.
Why: The arithmetic answer has been handed in without the context being reconsidered. In most divisions so far the quotient was the answer.
Fix: Ask what happens to the three people left over. They still need a bus, and the pupil supplies the correction themselves.
Leaves a remainder larger than the divisor.
Why: The division was stopped early — another whole group could still have been made.
Fix: State the rule and check it every time: if the remainder is not smaller than the divisor, keep going.
Writes 738 ÷ 5 as 147.3 by treating the remainder as a decimal digit.
Why: The remainder has been appended after a decimal point because that is where leftover digits usually go.
Fix: Check by multiplying back. 147.3 × 5 is 736.5, not 738. The check exposes it without a rule being quoted.
If they are not there yet
- Divide two-digit numbers by 2, 5 and 10 where the facts are known and only the remainder is new.
- Use base ten materials so the leftover is physically present and cannot be misread.
If they finish early
- Divide a four-digit number by a one-digit divisor.
- Write a word problem for 53 ÷ 6 where the answer is 9, and another where it is 8.
- Express the remainder as a fraction of the divisor.
Exit ticket
245 pencils are packed in boxes of 6. How many full boxes? How many boxes are needed to pack them all?
What to look for: 40 full boxes, 41 boxes needed. The same answer to both questions means the remainder was not interpreted, only calculated.
Printable practice for 4.NBT.B.6
Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.
- Divide Two Digits by OneWork out each answer.
- Divide Three Digits by OneWork out each answer.
Questions about Division with Remainders
How long does the Division with Remainders lesson take?
50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 14 min, independent practice 12 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.
Which standard does Division with Remainders teach?
CCSS.MATH.CONTENT.4.NBT.B.6 — 4.NBT.B.6, Number & Operations in Base Ten for Grade 4: “Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.” In plain terms, divide larger numbers, including with remainders.
What do I need to teach this lesson?
Base ten materials, place value charts, word problem cards with different remainder interpretations and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.
What mistakes should I expect in this lesson?
Three, each a reasoning error rather than carelessness: answers 'how many buses for 738 people at 5 each' with 147; leaves a remainder larger than the divisor and writes 738 ÷ 5 as 147.3 by treating the remainder as a decimal digit. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.
How do I know whether the lesson worked?
The exit ticket asks: “245 pencils are packed in boxes of 6. How many full boxes? How many boxes are needed to pack them all?.” 40 full boxes, 41 boxes needed. The same answer to both questions means the remainder was not interpreted, only calculated. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.
Is there a worksheet to go with Division with Remainders?
Yes — 2 printable 4.NBT.B.6 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.
Is Division with Remainders free to use?
Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.
Last reviewed 2026-09-05. Aligned to 4.NBT.B.6 of the Common Core State Standards for mathematics.