Dividing by Two-Digit Numbers
A 50-minute Grade 5 lesson on dividing by a two-digit divisor, where the real skill is estimating each digit of the quotient rather than knowing a fact.
Dividing by Two-Digit Numbers is a free 50-minute Grade 5 maths lesson plan for Common Core standard 5.NBT.B.6 — divide by two-digit numbers. 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 5
- Length:
- 50 minutes
- Standard:
- 5.NBT.B.6
Grade 5 · Number & Operations in Base Ten
5.NBT.B.6
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
Objective
Students will be able to divide a multi-digit number by a two-digit divisor, using estimation to find each digit of the quotient.
Students are successful when they can
- Estimates the quotient before dividing.
- Uses rounding of the divisor to choose each quotient digit.
- Checks the answer by multiplying back.
What you need
- Squared paper for aligning columns
- Multiples tables for the divisor
- Calculation cards
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — build the multiples
6 min- Take a divisor such as 23 and list its first ten multiples as a class.
- Having the list in front of you turns a hard division into a lookup.
Teach — estimate each digit
15 min- Divide 1,472 by 23. Estimate first: 23 is about 20, and 1,472 is about 1,500, so the answer is around 70.
- Work through the algorithm, using the multiples list to choose each digit.
- At each step, say what is being asked: how many 23s in 147? About 6, because 23 rounds to 20 and 20 sixes is 120.
- Check 23 × 6 = 138, which fits under 147. Seven would give 161, which is too big.
- Continue to the end: 64, and check 23 × 64 = 1,472.
- Say the principle: rounding the divisor gives you a first guess, and you adjust it by testing.
“You are not expected to know how many 23s go into 147. You round to 20, guess six, and check. Guessing and adjusting is the method, not a sign of weakness.”
Guided practice — guess, test, adjust
14 min- Pairs build the multiples list for their divisor before starting.
- They estimate the whole quotient first, then work the algorithm.
- Every answer is checked by multiplying back.
Independent practice
12 min- Students complete a division page.
- Answers with a missing digit in the quotient are alignment errors and show as answers about a tenth too small.
Close
3 min- Give 2,016 ÷ 48 and ask only for the estimate.
- About 40, and having that before starting is what makes the rest possible.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Chooses a quotient digit that is too large and gets a negative remainder.
Why: The estimate from the rounded divisor overshoots when the divisor was rounded down, and no check was made before subtracting.
Fix: Test the product before writing the digit. If the product exceeds the number above it, the digit is too big and comes down by one.
Omits a zero in the quotient when a digit divides to nothing.
Why: Nothing was produced at that step, so nothing was written, and the remaining digits shift left.
Fix: Keep the columns aligned on squared paper. An empty column has to be filled with a zero because the position is visibly there.
Rounds the divisor and then forgets to use the real divisor for the subtraction.
Why: The rounded number was used for the estimate and has stayed in play.
Fix: Write the actual multiple being subtracted every time. The estimate chooses the digit; the real divisor does the arithmetic.
If they are not there yet
- Provide the multiples list for each divisor rather than requiring it to be built.
- Use divisors ending in 0 or 5, where the estimate is close and the adjustments are small.
If they finish early
- Divide with a remainder and express it as a fraction.
- Divide a four-digit number where the quotient contains an internal zero.
- Estimate the quotient to one significant figure before calculating, and compare.
Exit ticket
Work out 1,845 ÷ 15. Estimate first, then check by multiplying back.
What to look for: An estimate near 120 and the answer 123, checked as 15 × 123 = 1,845. An answer near 12 means a quotient digit was dropped.
Printable practice for 5.NBT.B.6
Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.
- Divide by a Two-Digit NumberWork out each answer.
- Divide with RemaindersWork out each answer.
Questions about Dividing by Two-Digit Numbers
How long does the Dividing by Two-Digit Numbers 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 Dividing by Two-Digit Numbers teach?
CCSS.MATH.CONTENT.5.NBT.B.6 — 5.NBT.B.6, Number & Operations in Base Ten for Grade 5: “Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.” In plain terms, divide by two-digit numbers.
What do I need to teach this lesson?
Squared paper for aligning columns, multiples tables for the divisor, calculation cards 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: chooses a quotient digit that is too large and gets a negative remainder; omits a zero in the quotient when a digit divides to nothing and rounds the divisor and then forgets to use the real divisor for the subtraction. 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: “Work out 1,845 ÷ 15. Estimate first, then check by multiplying back.” An estimate near 120 and the answer 123, checked as 15 × 123 = 1,845. An answer near 12 means a quotient digit was dropped. 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 Dividing by Two-Digit Numbers?
Yes — 2 printable 5.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 Dividing by Two-Digit Numbers 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 5.NBT.B.6 of the Common Core State Standards for mathematics.