Primary 4 Maths | Multiplication and Division as Inverse Operations Lesson-Prep Guide (for tutors) | 45-minute flow, teaching script, common errors

2026-11-15

Tutor lesson-prep guides · Primary Maths

Pupils stop the moment they have a quotient, because nobody showed them that division can prove itself. This lesson installs one move: multiply back before you raise your hand.

Objectives — By the end of the lesson the pupil can: (1) write two division sentences from one multiplication fact and say that multiplying and dividing undo each other; (2) check any division by multiplying the quotient by the divisor and adding any remainder; (3) judge whether a remainder is legal, saying that it must be smaller than the divisor; (4) find a missing factor by dividing the product.

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 9 times 7 is	answers 63
Meaning of a remainder	gives the quotient and remainder of 45 divided by 6	answers 7 remainder 3
Two-digit subtraction	works out 45 minus 40	answers 5

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Entry check	asks times tables and the quotient and remainder of 45 divided by 6, writing answers on the right of the board	answers aloud and names both parts
6-15 min	One product, two quotients	turns 7 times 8 equals 56 into 56 divided by 7 and 56 divided by 8	writes both divisions from 9 times 7
15-24 min	Checking by multiplying back	shows 96 divided by 8 as 12, then checks with 8 times 12	checks 63 divided by 9 by writing 9 times 7
24-33 min	Checking with a remainder	shows 45 divided by 6 as 7 remainder 3, then checks 6 times 7 plus 3	checks 50 divided by 8 with 8 times 6 plus 2
33-41 min	Independent practice	reads questions only and walks the room looking for a check line	works three items, each with one check line
41-45 min	Exit check	marks at once and names whether the slip was the check or the remainder	says which step went wrong

03 Teaching script (read it out)

Scene 1: Act 1: multiplying and dividing are one pair, not two topics

Seven times eight is fifty-six, and that single sentence hides three number sentences: 7 times 8 is 56, 56 divided by 7 is 8, and 56 divided by 8 is 7. The same three numbers, one product and two quotients. So there is only one fact to learn: know two of the numbers and the third is found. Hearing 9 times 7 equals 63, you should say at once that 63 divided by 9 is 7 and 63 divided by 7 is 9.

From 9 times 7 equals 63, how many division sentences can you write, and what are they?

Scene 2: Act 2: a check is the answer multiplied back

After dividing, do not put your hand up; check. There is one way: quotient times divisor. For 96 divided by 8 you get 12, so write 8 times 12 equals 96. It matches the dividend, so the answer stands. If it does not match, the quotient is usually wrong, not the check. That line is not decoration for the teacher; it is where you catch yourself, and in an exam it protects marks.

After 96 divided by 8, which two numbers do you multiply to check?

Scene 3: Act 3: with a remainder, add it back, and keep it smaller than the divisor

Division with a remainder takes one extra step: quotient times divisor, then add the remainder. 45 divided by 6 is 7 remainder 3, so 6 times 7 is 42, add 3 gives 45, and it stands. There is also a rule to keep: the remainder must be smaller than the divisor. Dividing by 6, the remainder can only be 0 to 5. Writing 6 remainder 9 breaks the rule, because 9 is larger than 6 and the quotient is one short.

Can the remainder of 45 divided by 6 be 9? Why not?

04 Question types and worked steps

Type	Example	Steps	Answer
One product, two quotients	7 times 8 equals 56	the product becomes the dividend, each factor takes a turn as divisor	56 divided by 7 is 8 and 56 divided by 8 is 7
Checking an exact division	96 divided by 8	quotient times divisor must equal the dividend	12, checked by 8 times 12 equals 96
Checking with a remainder	45 divided by 6	quotient times divisor plus remainder, with the remainder smaller than the divisor	7 remainder 3, checked by 6 times 7 plus 3 equals 45
Finding a missing factor	what times 7 equals 63	divide the product by the known factor	9

Sanity check (teach this): Three checks: the check line must exist, because a page without one has not been checked at all; the check must reproduce the dividend, since a mismatch means the quotient is wrong; and the remainder must be smaller than the divisor, so a larger remainder means adding one to the quotient and recomputing.

05 Independent practice (3 questions)

Question	Answer	What to watch
What is 56 divided by 7? Check it by multiplying.	8, checked by 7 times 8 equals 56	whether a check line was written at all
What is 63 divided by 9?	7, checked by 9 times 7 equals 63	whether 9 times 7 was used to check
What is 50 divided by 8?	6 remainder 2, checked by 8 times 6 plus 2 equals 50	whether the remainder 2 was added back

06 Common mistakes and what to say

Mistake	Student writes	Say this
Dropping the remainder in the check	45 divided by 6 answered as 7 remainder 3 but checked with 6 times 7 equals 42 and declared wrong	Add the remainder back: 6 times 7 plus 3 is 45, and without it the check can never match.
Writing a remainder larger than the divisor	45 divided by 6 answered as 6 remainder 9	The remainder must be smaller than the divisor, so 9 above 6 means one more group fits and the quotient rises.
Swapping dividend and divisor	writing 8 divided by 56 for 56 divided by 8	The dividend is always left of the division sign and the divisor right of it; swapping them changes the answer completely.
Hunting for a missing factor by trial	testing numbers one by one for what times 7 equals 63	Knowing the product and one factor, divide: 63 divided by 7 is 9 at once.

07 Homework (paper, section and question numbers)

Primary 4 maths paper 1: multiplication, division and checking section — Section B, questions 1 to 4

08 Exit check (last 5 minutes)

Question	Answer	Decision
What times 7 equals 63?	9	wrong: reteach Act 1, inverse operations
What is 144 divided by 12? Write the check.	12, checked by 12 times 12 equals 144	wrong: reteach Act 2, quotient times divisor
Give the quotient and remainder of 50 divided by 8.	6 remainder 2	wrong: reteach Act 3, remainder smaller than divisor

09 Tutor FAQ

Which year group is this for?

Hong Kong primary schools expect pupils in Primary 4 to check division using the inverse relationship and to handle remainders in three-digit division by one digit. Division and fraction simplifying in Primary 5 and 6 reuse the same habit, so it should be settled in Primary 4.

Is 45 minutes enough?

Yes, but Act 3 needs its full nine minutes. The commonest slip is a check that forgets the remainder, so demonstrate 45 divided by 6 twice, once wrong and once right, side by side.

Is there a practice paper?

Yes. The homework line links to the Primary 4 paper with the section and question numbers, and the page carries 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.