Primary 3 Maths | Long Division with Remainder Lesson-Prep Guide (for tutors) | 45-minute flow, teaching script, common errors

2026-11-15

Tutor lesson-prep guides · Primary Maths

Pupils know their times tables but freeze the moment a long division layout appears, because they guess the whole quotient at once instead of one digit at a time. This lesson drills one routine: estimate, multiply back, subtract, bring down.

Objectives — By the end of the lesson the pupil can: (1) name the four steps of long division in order and say where the quotient digit is written; (2) divide a three-digit number by a one-digit number with a two or three digit quotient; (3) handle a remainder and check the answer with divisor times quotient plus remainder; (4) state that a remainder must be less than the divisor and use that as a self-check.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Times tables	says what 7 times 8 is	answers 56
Subtraction with borrowing	works out 43 minus 28	answers 15
Place value	names the hundreds digit of 456	answers 4

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Entry check	asks three quick items and writes them on the right of the board	answers aloud and points to hundreds, tens and ones
6-14 min	The four-step routine	models 96 divided by 8, naming each step	repeats the four step names and points to each number
14-23 min	Three digits by one digit	models 456 divided by 3 and pauses to ask for each estimate	gives the estimate and writes 152
23-32 min	With a remainder	models 800 divided by 7 and stresses where the remainder is written	writes 114 remainder 2 and checks 7 times 114 plus 2
32-41 min	Independent practice	reads the questions only	works three layouts alone
41-45 min	Exit check	collects and marks at once	says which step went wrong

03 Teaching script (read it out)

Scene 1: Act 1: One digit at a time, not the whole number

“In long division you handle one place at a time. Look at the highest place and ask how many of the divisor fit inside it. That answer is your quotient digit, and it goes above the line in line with that place. So for 456 divided by 3, look at the hundreds digit 4, which holds one 3, so the first quotient digit is 1.”

When you start a long division, which single place do you look at first, and why not the whole number?

Scene 2: Act 2: Multiply back, subtract, bring down

“After you write the quotient digit you must multiply back and write it under the dividend: 1 times 3 is 3, written under the 4, then subtract, 4 minus 3 is 1. Now bring down the next digit 5 to make 15. Fifteen holds five 3s, so the next quotient digit is 5, 5 times 3 is 15, nothing left, bring down 6. Six holds two 3s, so the last digit is 2. The answer is 152. The order never changes: multiply, subtract, bring down.”

After you write a quotient digit, which three actions come next?

Scene 3: Act 3: The remainder must be less than the divisor

“Not every division comes out exact. For 800 divided by 7, 7 times 114 is 798, leaving 2, so the remainder is 2. If the remainder is equal to or bigger than the divisor, your quotient digit was too small and you must estimate again. Check with divisor times quotient plus remainder: 7 times 114 plus 2 must give 800. The check is not extra work, it is your only tool for catching errors.”

When does a remainder tell you the quotient digit is wrong, and how do you check the answer?

04 Question types and worked steps

Type	Example	Steps	Answer
Three digits by one digit, exact	456 divided by 3	estimate each place, multiply back, subtract, bring down	152
Three digits by one digit, with remainder	800 divided by 7	what is left at the end is the remainder	114 remainder 2
A zero in the quotient	702 divided by 6	when the brought-down number is too small, write 0 then bring down again	117
Checking an answer	check 512 divided by 5	5 times 102 plus 2 must equal 512	102 remainder 2, check holds

Sanity check (teach this): Three checks: a remainder must always be less than the divisor, so a larger remainder means the estimate was too small; divisor times quotient plus remainder must rebuild the dividend, so a different number means a copying slip; and the size of the quotient must make sense, since 456 divided by 3 gives three digits because the hundreds digit 4 is bigger than 3, while a two-digit answer means a place was skipped.

05 Independent practice (3 questions)

Question	Answer	What to watch
What is 738 divided by 6?	123	whether the pupil estimates place by place rather than guessing
What is 945 divided by 7?	135	whether the multiplied-back number lands under the right place
What is 512 divided by 5, and what is the remainder?	102 remainder 2	whether the pupil writes a remainder and checks it

06 Common mistakes and what to say

Mistake	Student writes	Say this
Guessing the whole quotient	writes 456 divided by 3 as 132	You work one place at a time. Look at the hundreds digit 4 and ask how many 3s fit inside.
Writing the product out of line	writes the 3 from 1 times 3 under the 5	The product goes directly under the place you just looked at. Wrong place, wrong answer.
Remainder bigger than the divisor	writes 800 divided by 7 as 113 remainder 9	A remainder of 9 is bigger than 7, so your estimate was too small. Estimate again.
Skipping the zero	writes 702 divided by 6 as 17	When the brought-down number is too small, write 0 in that place and bring down the next digit.

07 Homework (paper, section and question numbers)

Primary 3 maths paper 1: four operations section — Section B, questions 1 to 4

08 Exit check (last 5 minutes)

Question	Answer	Decision
What is 468 divided by 9?	52	wrong: reteach the place-by-place estimate from Act 1
What is 801 divided by 4, and what is the remainder?	200 remainder 1	wrong: reteach the remainder and check from Act 3
How many digits does 1000 divided by 7 have?	three digits, 142	wrong: reteach judging the size of the quotient

09 Tutor FAQ

Which year group is this for?

Hong Kong primary schools introduce long division in Primary 3 with a one-digit divisor. Primary 4 moves on to two-digit divisors, so the remainder and the check must be solid here.

Is 45 minutes enough?

Yes, provided the entry check is actually done. A pupil who is shaky on times tables will stall at the estimating step, so patch three facts on the spot rather than skipping.

Is there a practice paper?

Yes. The homework line links straight to the matching section and question numbers of the site practice paper, with an answer version.

Find a tutor — free Tutor Registration →

A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.