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Primary 4 Mathematics: HCF, LCM and Reading Word Problems
Sharing and re-meeting turn on one pair of ideas
The divide in Primary 4 word problems is highest common factor versus lowest common multiple: sharing a pile into equal groups takes the former, two events meeting again in time takes the latter. Marks are usually lost to choosing the wrong tool rather than to arithmetic, since a correct sum still answers the wrong question. Write one word beside each problem first: share, or re-meet.
How is Primary 4 Mathematics assessed, and what does each part carry?
Section A Quick computation: 12 short questions, 1 mark each: multiplication and division, H.C.F. a (12 marks); Section B Short questions: 5 questions, 2 marks each: two-digit multiplication, division, decimal (10 marks); Section C Word problems: 5 questions for 33 marks: H.C.F. context, L.C.M. context, square perim (33 marks)
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Section A Quick computation | 12 short questions, 1 mark each: multiplication and division, H.C.F. and L.C.M., decimals, equivalent fractions, perimeter and area, counting factors | 12 | 14 min |
| Section B Short questions | 5 questions, 2 marks each: two-digit multiplication, division, decimal multiplication and division, area | 10 | 14 min |
| Section C Word problems | 5 questions for 33 marks: H.C.F. context, L.C.M. context, square perimeter and area, shopping and change, area and perimeter of a cut-corner shape | 33 | 32 min |
The table above describes how this paper is laid out; it is not an official examination structure from the EDB or any school. P4 pacing: 22 questions in 60 minutes. The concept worth the most marks this year is choosing between H.C.F. and L.C.M.: sharing items into equal groups uses H.C.F., events happening together again uses L.C.M. The cut-corner question (perimeter unchanged) is the one most children get wrong – draw it by hand once.
What each paper is actually testing
| Paper | Drill focus | How marks are lost |
|---|---|---|
| Section A Quick computation | One minute per item; use short division for H.C.F. and L.C.M. | LCM and HCF are swapped, so correct arithmetic answers the wrong question. |
| Section B Short questions | Do decimal work in two stages: whole numbers first, then place the decimal point | A carry or borrow is dropped and the answer is out by a place value. |
| Section C Word problems | Answer (a) and (b) separately; for the cut corner, say area falls but perimeter stays the same | The answer carries a number with no unit. |
What is each Primary 4 Mathematics paper really testing, and what should you drill?
Section A Quick computation: One minute per item; use short division for H.C.F. and L.C.M; Section B Short questions: Do decimal work in two stages: whole numbers first, then place the decimal point; Section C Word problems: Answer (a) and (b) separately; for the cut corner, say area falls but perimeter stays the same
Drill order: by topic, then by year, then the mark scheme
| Step | What you do | Why |
|---|---|---|
| 1. By topic | Work through each topic, starting with the paper that allows least help (no calculator / closed book) | Exposes what is genuinely not understood |
| 2. By year | Whole papers to time, one or two a week | Trains pace, stamina and question selection |
| 3. Mark scheme | Go through the marking scheme question by question and log the scoring steps you missed | Most lost marks are written wrong, not thought wrong |
Should drilling go by topic first or by year?
By topic first, then whole papers by year, then the mark scheme. The first third of the time goes topic by topic (8-10 years of the same topic back to back), the middle switches to timed whole papers, and the last fortnight only redoes the recurring errors from your log.
A 12-week drilling timetable
| Week | Phase | What to do |
|---|---|---|
| Weeks 1-3 | By topic: foundation | Topic by topic, starting with the easiest marks, building habits and recall |
| Weeks 4-6 | By topic: core | 8-10 years of the same topic back to back, errors classified by topic |
| Weeks 7-8 | By topic: advanced and electives | Elective and higher-order topics, now under time pressure |
| Weeks 9-10 | By year: timed papers | One full paper a week, timed, no reference materials |
| Week 11 | Mark scheme work | Question by question against the marking scheme; list the scoring steps you omitted |
| Week 12 | Plug holes and simulate | Only the recurring errors from your log, then one full exam simulation |
Subject-specific weighting for this timetable: Weeks 1-3: sort word problems into share, re-meet and neither, naming the tool only, no calculating. Weeks 4-6: ten short questions against the clock, checking the tool before the digits. Weeks 7-9: vertical working and units, drilling carrying, decimal points and conversions, copying the correct form once per slip. Weeks 10-12: two timed papers a week, then only the question types already missed.
Use it properly: this is not a checklist to finish. Every week must keep time for redoing errors, or from week 9 you will be repeating the same batch.
Pacing
| Paper | Time | Suggested split |
|---|---|---|
| Section A Quick computation | 14 min | 14 min |
| Section B Short questions | 14 min | 14 min |
| Section C Word problems | 32 min | 32 min |
How should the time be split inside each Primary 4 Mathematics paper?
Section A Quick computation: 14 min; Section B Short questions: 14 min; Section C Word problems: 32 min
The drilling mistakes that cost the most marks
| Mistake | What it looks like | What actually happens | Instead |
|---|---|---|---|
| Swapping H.C.F. and L.C.M. | Using L.C.M. to share items, H.C.F. for things meeting again | The whole context is wrong | Sharing into equal groups = H.C.F.; meeting again = L.C.M. |
| Mixing up area and perimeter | Answering 12 x 9 as 42 cm | Both the number and the unit are wrong | Area in cm², perimeter in cm – read which is asked |
| Assuming the perimeter falls after a corner is cut | Writing 40 – 8 for the perimeter | Three to four marks lost | A cut corner reduces area only; draw it and the perimeter is unchanged |
| Misplacing the decimal point | 12.5 x 8 answered as 10 or 1000 | Out by a factor of ten | Work 125 x 8 = 1000 first, then put back one decimal place |
The error log and the mark scheme
Three columns: the problem with the words circled; the right tool and the first line of working; whether the loss was the tool, the arithmetic or a missing unit. Tool errors get the sentence rewritten in the pupil’s own words.
How many years should you drill?
Topic coverage at this level is stable and question shapes repeat across school papers, so three to five years covers the main forms, while school pacing and textbook editions differ, so the class timetable sets the order and the official curriculum frames the scope.
How many years of past papers is enough?
Topic coverage at this level is stable and question shapes repeat across school papers, so three to five years covers the main forms, while school pacing and textbook editions differ, so the class timetable sets the order and the official curriculum frames the scope.
Frequently asked questions
Is this page a mock paper or a drilling guide?
This is the Primary 4 Mathematics drilling guide: assessment structure, drill order, a 12-week timetable, pacing, common mark losses and the error-log method. For questions with answers, use the Primary 4 Mathematics mock papers linked under Related.
By topic or by year first?
By topic. Eight to ten years of the same topic back to back is what exposes repeating errors; going straight to whole papers just repeats the same batch under time pressure.
How should the error log be written?
Do not copy out questions. Per error record four things: question reference, which step failed (concept, wording, calculation), what the mark scheme requires, and the correct action next time.
What if the arithmetic is right but the answer is wrong?
Drill the choice, not the calculation: ten questions where only the tool and the first line are written, and full answers resume only when all ten are right.
Working or explanation first?
Both, in a fixed order: one self-explanatory line of working, then a sentence saying what each number stands for.
Official references
| Resource | What to use it for |
|---|---|
| https://www.edb.gov.hk/attachment/en/curriculum-development/kla/ma/curr/pmc2017_e.pdf | EDB Learning Content of Primary Mathematics (2017): P4 units 4N1-4D1 |
| https://www.tutorzone.com.hk/en-primary-maths-p3-mock-2027/ | Primary 3 paper: 5-digit numbers, multiplication, like fractions |
| https://www.tutorzone.com.hk/en-primary-maths-p5-mock-2027/ | Primary 5 paper: fraction operations, equations, area and volume |
Related: practice area · Primary 3 paper · Primary 5 paper
Next step: find a tutor / register as a tutor
After drilling, the hard part is telling a conceptual error from a writing error. Tell us the year group, the school and your available times, and TutorZone will match you with a tutor who knows the HKEAA assessment requirements.
Demand for tutors in this subject is steady, and those who can explain the marking scheme and where marks are won are especially sought after. Register free; you pay only when a match succeeds.