Year 8MeasurementMeasuringYear 8 Maths

Duration, timetables and telling the time properly

What this lesson covers

  • Duration questions can involve fractions of time and converting between units of time.
Key idea

Two and a half hours is not 2 h 50

  • Write 2.5 hours on a page and it looks like 2 and a bit.
  • The bit is half an hour, and half an hour is 30 minutes.
  • So 2 h 30. Not 2 h 50. That gap causes real trouble.
WrittenBecauseMeans
2.5 hourshalf of 60 is 302 h 30 min
Not2 h 50 min
Key idea

Time is the odd one out

  • Every other unit you have converted runs in tens.
  • 100 centimetres in a metre. 1000 millilitres in a litre.
  • But 60 minutes in an hour. And 24 hours in a day.
MeasuringConverts byPattern
Length1 m = 100 cmtens
Volume1 L = 1000 mLtens
Time1 h = 60 minsixties
And1 day = 24 hneither
Key idea

Which is exactly why the trap works

  • You have spent two lessons multiplying by powers of ten.
  • A decimal point in an hour is a fraction of sixty.
  • 2.5 hours is 150 minutes. 2 h 50 would be 170. Different.
WrittenBecauseMeans
2.5 hourshalf of 60 is 302 h 30 min
Not2 h 50 min
In minutes2.5 × 60150 min
2 h 50 would be170 min
Key idea

Fractions of an hour, through 60

  • Half an hour is half of 60, so 30 minutes.
  • A quarter is 15. Three quarters is 45.
  • A third is 20, so two thirds is 40. Always via 60.
FractionWorkingMinutes
1/2 hourhalf of 6030 min
1/4 houra quarter of 6015 min
3/4 hourthree quarters of 6045 min
1/3 hour60 ÷ 320 min
2/3 hourtwo lots of 2040 min
Key idea

So what is 1.75 hours?

  • 0.75 is three quarters.
  • Three quarters of 60 minutes is 45.
  • So 1 hour 45 minutes. Never 1 h 75.
So what is 1.75 hours?
Worked example

Hours and minutes into minutes

  • Turn the hours into minutes first, then add the rest.
  • 2 h 45 is 120 plus 45, which is 165 minutes.
  • 3 h 20 is 180 plus 20, so 200 minutes.
TimeWorkingMinutes
2 h 45 min2 × 60, then + 45165 min
3 h 20 min3 × 60, then + 20200 min
1 h 05 min60 + 565 min
Worked example

And minutes back into hours

  • Ask how many whole 60s fit in.
  • 135 minutes: 60 goes in twice, leaving 15.
  • So 2 hours 15 minutes.
MinutesWorkingGives
135 minhow many whole 60s?2, with 15 left
So2 h 15 min
90 min1 whole hour, 30 left1 h 30 min
Key idea

Now a timetable

  • A timetable never prints the number you actually want.
  • It gives departure and arrival. You work out the gap.
  • These times are made up, but the stations are real enough.
StationMorningAfternoon
Avondale09:4514:50
Mount Albert09:5815:03
Kingsland10:1215:18
Britomart11:2016:05
Key idea

Do not subtract 9:45 from 11:20

  • Treat those as decimals and you get 1.75, which means nothing.
  • Subtract properly and you have to borrow 60, not 10.
  • There is an easier way that never borrows at all.
MethodProblem
11.20 − 9.45 as decimalsgives 1.75, which is wrong
Column subtractionborrowing in base 60error-prone
Counting upno borrowing at alluse this
Worked example

Count up through the whole hours

  • 09:45 to 10:00 is 15 minutes.
  • 10:00 to 11:00 is a whole hour.
  • 11:00 to 11:20 is 20 more. So 1 hour 35 minutes.
FromAdds
09:45 to 10:0015 min
10:00 to 11:001 hour
11:00 to 11:2020 min
Total1 h, 15 + 201 h 35 min
Key idea

You have done this before

  • It is how you worked out change from a $50 note.
  • Get to the next round number, then jump.
  • No borrowing, and it is how people actually do it.
SituationGet toThen
Change from $50the next whole dollarjump in tens
Duration from 09:45the next whole hourjump in hours
Worked example

The afternoon service, same method

  • 14:50 to 15:00 is 10 minutes.
  • 15:00 to 16:00 is an hour.
  • Then 5 minutes to 16:05. One hour 15.
FromAdds
14:50 to 15:0010 min
15:00 to 16:001 hour
16:00 to 16:055 min
Total1 h 15 min
Worked example

Comparing two journeys

  • The morning trip took 1 h 35. The afternoon took 1 h 15.
  • So the afternoon one is 20 minutes quicker.
  • Both in the same units before you compare. Always.
ServiceDurationIn minutes
Morning1 h 35 min95
Afternoon1 h 15 min75
Difference20 min20
Worked example

Adding durations, and carrying 60

  • 45 minutes plus 50 minutes is 95 minutes.
  • 95 is more than an hour, so it is 1 h 35.
  • 2 h 45 plus 1 h 30 gives 3 h 75, which carries to 4 h 15.
SumWorkingGives
45 min + 50 min95 min
95 min60 into 95 once, 35 left1 h 35 min
2 h 45 + 1 h 30gives 3 h 75 min
Carry the 604 h 15 min
Key idea

Three answers that are never right

  • Anything with 60 or more minutes in it, like 3 h 75.
  • 2.5 hours written as 2 h 50.
  • A duration got by subtracting clock times as decimals.
WrittenShould be
3 h 75 min4 h 15 min
2.5 h = 2 h 502 h 30 min
11.20 − 9.45 = 1.751 h 35 min
Your turn

Your turn: four questions

  • Pause here and try all four.
  • For question 3, count up through 09:00 and 10:00.
  • Question 2 is a fraction of 60, not of 100.
Question
1How many minutes is 3 hours 20 minutes?
2How many minutes is two thirds of an hour?
3A train leaves at 08:50 and arrives at 10:15. How long is the trip?
4Write 135 minutes in hours and minutes.
Show answer

1. 200 minutes. Three hours is 180, plus the 20. 2. 40 minutes. A third of 60 is 20, so two thirds is 40. 3. 1 hour 25 minutes. Count up: 10 minutes to 09:00, an hour to 10:00, then 15 more. 4. 2 hours 15 minutes. Sixty goes into 135 twice, leaving 15.

Worked example

The answers

  • 3 h 20 is 180 plus 20, which is 200 minutes.
  • Two thirds of an hour is 40 minutes.
  • 08:50 to 10:15 is 1 h 25. And 135 minutes is 2 h 15.
Answer
1200 min
240 min
31 h 25 min
42 h 15 min
Summary

What to take away

  • Time runs in 60s, so a decimal hour is a fraction of 60.
  • Count durations up through the whole hour. Never subtract.
  • And if your answer has 60 or more minutes in it, carry.
Remember
Timeruns in 60s and 24s, never in tens
2.5 hoursis 2 h 30 min, because half of 60 is 30
A fraction of an houris that fraction of 60 minutes
Durationscount up through the whole hour
Over 60 minutescarry an hour, do not write 75

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