中文（繁體）
中文（简体）
English
Primary 6 Maths | Speed, Time and Distance: Tutor Lesson Guide | Unit Conversion
Nine out of ten speed errors are unit errors. Put 45 minutes into a formula that wants hours and the answer is sixty times too big, yet the numbers still look plausible.
Objectives — Pupils can: (1) use distance equals speed times time, speed equals distance over time, and time equals distance over speed; (2) convert minutes to hours, so 45 minutes is 0.75 hours; (3) convert between kilometres per hour and metres per second by dividing by 3.6; (4) explain that average speed is total distance over total time, not the mean of the two speeds.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Decimal multiplication and division | 60 times 2.5, 150 divided by 2.5 | the arithmetic of every speed question |
| Time conversion | 45 minutes is 0.75 hours | the step that goes wrong most |
02 Lesson flow (40 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-5 min | Diagnostic | 60 km/h for 2 hours | answer 120 km |
| 5-14 min | The formula triangle | distance on top, speed and time below | derive all three forms |
| 14-24 min | Unit conversion | rewrite 45 minutes in hours | 0.75 hours |
| 24-33 min | Average speed | out at 60, back at 40, same road | 48 km/h, not 50 |
| 33-40 min | Exit check | three questions | all correct |
03 Teaching script (read it out)
Scene 1: Act 1: Draw the triangle once
Draw a triangle with distance on top and speed and time at the bottom left and right. Cover distance and you see speed times time. Cover speed and you see distance over time. Cover time and you see distance over speed. Sixty kilometres per hour for 2.5 hours is 60 times 2.5, which is 150 km. Use the same triangle for the whole lesson instead of re-deriving each time.
Tutor line: “Distance on top, speed and time below. Cover the one you want and you can see whether to multiply or divide.”
Scene 2: Act 2: Unify the units before substituting
A 12 km walk at 4 km/h takes 12 divided by 4, which is 3 hours. Now ask: 12 km took 45 minutes, what was the speed? Pupils write 12 divided by 45. Stop and ask what unit the 45 carries. Speed is per hour, so the time must be in hours. 45 divided by 60 is 0.75, and 12 divided by 0.75 is 16 km/h. Units that do not match make the arithmetic meaningless, however neat the numbers.
Tutor line: “45 minutes is not 45 hours. You want kilometres per hour, so turn the minutes into hours first: 45 over 60 is 0.75.”
Scene 3: Act 3: Average speed is not the mean of the speeds
Out at 60 km/h and back at 40 km/h along the same road. Pupils answer 50. Take a 120 km road: out takes 120 over 60, which is 2 hours; back takes 120 over 40, which is 3 hours. Total distance 240 km over 5 hours is 48 km/h. The slow leg occupies more time, so it drags the average down. Walk through the concrete numbers or pupils will not believe it.
Tutor line: “The slow leg takes longer, so it carries more of the time and pulls the average below 50. Total distance over total time gives 48.”
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Find distance | unify units, multiply speed by time, give km | 60 times 2.5 is 150 km | |
| Find time | unify units, divide distance by speed, give hours | 12 over 4 is 3 hours | |
| Find speed | minutes into hours first, divide, give km/h | 12 over 0.75 is 16 km/h | |
| Convert km/h to m/s | divide by 3.6 | 72 km/h is 20 m/s |
Sanity check (teach this): Units must match before substitution. Every answer carries a unit (km, h, km/h). Average speed uses total distance over total time only. Any time given in minutes must be divided by 60 first.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| 60 km/h for 2.5 hours. Distance? | 150 km | 60 times 2.5 |
| How many hours is 45 minutes? | 0.75 hours | 45 over 60 |
| 12 km at 4 km/h takes how long? | 3 hours | 12 over 4 |
| 72 km/h in metres per second? | 20 m/s | 72 over 3.6 |
| Out at 60 and back at 40 on the same road. Average speed? | 48 km/h | 240 over 5 |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Substituting minutes directly | 12 divided by 45 giving 0.27 km/h | 45 minutes is 0.75 hours; different units cannot be divided |
| Mixing km/h and m/s | treating 72 km/h as 72 m/s | kilometres to metres is times 1000, hours to seconds is times 3600, so divide by 3.6 |
| Averaging the two speeds | writing 50 km/h for 60 and 40 | use total distance over total time; the slow leg takes longer, so the answer is under 50 |
| Dropping the unit | answering 150 with no unit | 150 what? Distance takes km, speed takes km/h |
07 Homework (paper, section and question numbers)
- Independent practice in this chapter (questions 1 to 5 above) — questions 1 to 3: one of each formula; 4 to 5: conversion and average speed
- Primary Maths chapter index (related chapters at this level) — questions 6 to 8: write one time, one speed and one average speed question
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| 80 km/h for 1.5 hours. Distance? | 120 km | if wrong: reteach distance equals speed times time |
| 30 km at 5 km/h takes how long? | 6 hours | if wrong: reteach distance over speed |
| 36 km/h in metres per second? | 10 m/s | if wrong: reteach dividing by 3.6 |
09 Tutor FAQ
Must pupils memorise three formulas?
No. Draw the triangle once and all three follow, so there is nothing to memorise three times over.
Why must 45 minutes become 0.75 hours?
Speed is per hour. Kilometres over hours gives km/h, and mixing the units destroys the meaning of the number.
Can average speed be the midpoint of the two speeds?
Only when both legs take the same time. On the same road the legs take different times, so use total distance over total time.
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.