中文（繁體）
中文（简体）
English
P4 Maths | Long Multiplication and Division Lesson-Prep Guide (for tutors) | 45 minutes from place value to long division and checking
The written layout is not decoration; it records place value. When students get these wrong it is rarely weak tables, it is a missing zero, a misaligned column, or a remainder written in the wrong place.
Objectives — Students can: (1) complete a two-digit by two-digit long multiplication and explain why the second row shifts one place left; (2) complete a three-digit by one-digit long division and record quotient and remainder correctly; (3) check with quotient times divisor plus remainder; (4) state that a remainder is always smaller than the divisor.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Times tables | 7 times 8 | 56 |
| Place value | What does the 3 in 36 stand for? | 30, that is three tens |
| Subtraction with borrowing | 302 minus 8 | 294 |
| Meaning of division | 12 shared into 3 groups | 4 in each group |
02 Lesson flow (45 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-7 min | Opening: place value warm-up | Split 24 times 36 into 24 times 30 and 24 times 6 | State both partial products |
| 7-17 min | Two-digit by two-digit layout | Show 24 times 36, write the second row one place left and explain why | Three questions, labelling what each row means |
| 17-26 min | Long division layout | Show 135 divided by 5 using estimate, multiply, subtract, bring down | Four questions with the remainder noted |
| 26-34 min | Remainders and checking | Show 137 divided by 5 as 27 remainder 2 and check with 27 times 5 plus 2 | Three questions with a check line |
| 34-43 min | Word problems and traps | Questions asking for the minimum number of boxes need rounding up | Four questions, circling the key phrase |
| 43-45 min | Exit check | Three quick oral questions | Independent answers |
03 Teaching script (read it out)
Scene 1: Why the second row shifts
Students copy the layout without knowing why, so the columns drift and the answer is out by a factor of ten. Unpack it: 24 times 36 is 24 times 30 plus 24 times 6; the second row is really multiplying by three tens, so it is 720 and must sit one place left.
Have them write a small zero or the word tens beside the second row until the habit sticks.
Have them write a small zero or the word tens beside the second row until the habit sticks.
Students do: say that the second row means 24 times 30.
Scene 2: Long division in four moves
Students stall in long division because they do not know the next action. Fix the cycle: estimate how many fit, multiply back, subtract, bring down the next digit.
Every piece goes in its correct position: the quotient above the line, the product under the dividend, the remainder smaller than the divisor. Say the same four words each time until it becomes a habit.
Every piece goes in its correct position: the quotient above the line, the product under the dividend, the remainder smaller than the divisor. Say the same four words each time until it becomes a habit.
Students do: say the four steps aloud before writing.
Scene 3: The check line is the brake
Once remainders appear, mistakes are invisible. One line is enough: quotient times divisor plus remainder equals the dividend.
Require a check after every question, and check in the other direction where possible. It costs less than redoing the work and catches place-value slips immediately.
Require a check after every question, and check in the other direction where possible. It costs less than redoing the work and catches place-value slips immediately.
Students do: write the check line beside every answer.
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Two-digit by two-digit | 24 times 36 | Two rows, second row shifted left | 864 |
| Three-digit by one-digit | 135 divided by 5 | Estimate, multiply, subtract, bring down | 27 |
| Division with a remainder | 137 divided by 5 | Remainder smaller than the divisor | 27 remainder 2 |
| Checking and context | Is 27 times 5 plus 2 equal to 137? How many boxes at minimum? | Check line, round up for a minimum | 137; 28 boxes needed |
Sanity check (teach this): Sanity checks: the remainder is smaller than the divisor; the magnitude of a product is plausible (24 times 36 lies between 700 and 900, not 8,640); columns line up digit for digit; the check line is complete; “minimum number” rounds up and “maximum number” rounds down; answers carry units.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| Three two-digit products | One with a zero in the middle | Check the second row shifted |
| Four long divisions | Two exact, two with remainders | Check remainder smaller than divisor |
| Four word problems | Two needing a round up, two a round down | Check the key phrase was circled |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Second row not shifted | 24 times 36 answered as 264 | The second row multiplies by three tens, that is 720, so it moves one place left. The units column of that row should be empty. |
| Remainder larger than the divisor | 137 divided by 5 answered as 26 remainder 7 | Another 5 still fits, so the quotient goes up by one and a remainder is always less than the divisor. |
| Quotient in the wrong column | Digits placed above the wrong digit | Each quotient digit sits above the digit just brought down; shift it and the value changes. |
| No rounding up in context | Needing 27.4 boxes answered as 27 | Boxes cannot be cut, so even 0.4 of a box means one more: 28. |
07 Homework (paper, section and question numbers)
- Primary maths chapter index — All chapters for this subject
- Lesson-prep guides index — Similar chapters in other subjects
- Redo this chapter — Redo three long divisions with a check line each
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| Why shift the second row | It multiplies by tens | Answering “because that is the format” means going back to the second stage |
| The four moves | Estimate, multiply, subtract, bring down | Missing one means going back to the third stage |
| Limit on a remainder | Always smaller than the divisor | Answering “no limit” means going back to the fourth stage |
| How to check | Quotient times divisor plus remainder | Answering “just recalculate” means going back to the fourth stage |
09 Tutor FAQ
What if the tables are slow?
Run a five-minute tables drill daily and cut the volume of written work but demand accuracy; speed follows fluency, and volume is a poor substitute.
May students use a calculator?
Long multiplication is a core P4 skill, so no calculator during practice; a calculator is fine for a final check, but the check line is still written by hand.
Must every subtraction be shown?
Yes. Showing it makes the remainder traceable and keeps columns aligned; skipping it is the main cause of later place-value errors.
Find a tutor — freeTutor 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.