Year 6MeasurementMeasuringYear 6 Maths

Time, timetables and elapsed time

What this lesson covers

Vertically opposite angles are equal.
Time and duration arise in a range of situations including solar calendars (e.g. Roman, Gregorian) and lunar calendars (e.g. maramataka Māori, Chinese).
Timetables can be used to record the time and duration of events.

Key idea

How long from 2:53 pm to 3:28 pm?

Two clock faces, thirty-something minutes apart.
Try subtracting: 28 minutes take 53 minutes.
That goes negative, which cannot be right.

Key idea

Because time is not base ten

Last lesson everything divided by 10, 100 or 1000.
Time does not. It counts in sixties.
So 3.28 minus 2.53 is not a time calculation at all.
Doing it that way gives 75 minutes, which is over an hour.

Method	Gives	Sensible?
28 − 53	negative	no
3.28 − 2.53 as decimals	75 min	no
Bridge the hour	35 min	yes

Worked example

Count up to the hour first

From 2:53, how far to 3:00?
53 and 7 make 60, so 7 minutes.
That gets you to a round hour, where counting is easy.

Worked example

Then carry on from the hour

From 3:00 to 3:28 is just 28 minutes.
No borrowing, no sixties: you read it straight off.

Worked example

Add the two pieces

7 minutes up to the hour, then 28 minutes after it.
7 + 28 = 35.
So 2:53 pm to 3:28 pm is 35 minutes.
Two easy steps instead of one impossible subtraction.

Piece	How	Minutes
2:53 pm to 3:00 pm	up to the hour	7 min
3:00 pm to 3:28 pm	then onwards	28 min
Total	7 + 28	35 min

Key idea

This works every time

Up to the next hour, then on to the finish.
If both times are in the same hour, you do not need it.
If they cross an hour, always bridge it.

Key idea

Sixties all the way up

60 seconds in a minute. 60 minutes in an hour.
Which makes 3600 seconds in an hour.
Nothing here is a ten, a hundred or a thousand.

One	Is
1 minute	60 seconds
1 hour	60 minutes
1 hour	3600 seconds

Worked example

Minutes into hours and minutes

150 minutes. How many whole hours fit?
150 ÷ 60 = 2, with 30 left over.
So 150 minutes is 2 hours 30 minutes.
A division with a remainder, exactly as in the division lesson.

Convert	Working	Answer
150 min	150 ÷ 60	2 h 30 min
2.5 hours	half of 60 is 30	2 h 30 min
3 min	3 × 60	180 s
90 s	90 − 60	1 min 30 s

Key idea

2.5 hours is not 2 hours 50

Half of an hour is half of 60, which is 30.
So 2.5 hours is 2 hours 30 minutes.
The 5 after the point means half, not fifty.
Same for 1.25 hours: a quarter of 60 is 15 minutes.

Written	Means	Not
2.5 h	2 h 30 min	2 h 50 min
1.25 h	1 h 15 min	1 h 25 min

Worked example

And down to seconds

3 minutes into seconds: 3 × 60 = 180 s.
90 seconds back into minutes: 60 and 30 left, so 1 min 30 s.
Multiply going down, divide going up. Always by 60.

Key idea

12-hour time needs am or pm

A clock face only goes up to 12, so each number happens twice a day.
am is before midday. pm is after it.
Leave them off and 3:28 could be either.

Key idea

24-hour time does not

The hours run 00 to 23, so every one is different.
Morning hours look the same: 09:15 is 9:15 am.
Afternoon ones have 12 added: 15:28 is 3:28 pm.
No am, no pm, no confusion.

12-hour	24-hour	When
9:15 am	09:15	morning
12:00 pm	12:00	midday
3:28 pm	15:28	afternoon
11:40 pm	23:40	night

Worked example

Swapping between them

Afternoon into 24-hour: add 12 to the hour. 3:28 pm → 15:28.
24-hour into afternoon: subtract 12. 19:45 → 7:45 pm.
Morning times need no change at all.
Watch midnight: that is 00:00, not 24:00.

From	Do this	To
3:28 pm	add 12	15:28
19:45	subtract 12	7:45 pm
9:15 am	nothing	09:15

Key idea

Which is why timetables use it

A bus at 7:30 is very different from a bus at 19:30.
Timetables cannot afford that kind of doubt.
So schedules, hospitals and the army all use 24-hour time.

Key idea

Reading a timetable

Each row is a stop. Each column is one bus.
Read down a column to follow one bus along the route.
Read across a row to see when each bus reaches that stop.
These times are made up, but the stops are real.

Stop	Bus 1	Bus 2
Avondale	8:15	8:45
Mount Albert	8:32	9:02
Kingsland	8:49	9:19
Britomart	9:05	9:35

Worked example

How long is the whole trip?

Bus 1 leaves Avondale at 8:15 and reaches Britomart at 9:05.
Bridge the hour: 45 minutes to 9:00, then 5 more.
45 + 5 = 50 minutes.
Check Bus 2: 8:45 to 9:35 is also 50. Same trip, same time.

Stop	Bus 1	Bus 2
Avondale	8:15	8:45
Mount Albert	8:32	9:02
Kingsland	8:49	9:19
Britomart	9:05	9:35

Worked example

And part of the trip

Mount Albert to Britomart on Bus 1: 8:32 to 9:05.
8:32 to 9:00 is 28 minutes.
Then 9:00 to 9:05 is 5 more.
33 minutes. The bridge again.

Piece	How	Minutes
8:32 to 9:00	up to the hour	28 min
9:00 to 9:05	then onwards	5 min
Total	28 + 5	33 min

Worked example

And how long you would wait

Miss Bus 1 at Avondale (8:15) and the next is 8:45.
Both times are in the same hour, so no bridging needed.
45 − 15 = 30 minutes of waiting.
Every stop is 30 minutes apart, because the buses are.

Stop	Bus 1	Bus 2
Avondale	8:15	8:45
Mount Albert	8:32	9:02
Kingsland	8:49	9:19
Britomart	9:05	9:35

Key idea

Bigger units of time

A solar calendar counts a year by the sun (the Gregorian one).
A lunar calendar counts months by the moon.
Maramataka Māori follows the moon’s phases.
It has long guided the best times for planting and fishing.

Calendar	Kind	Counts by
Gregorian	solar	the 365-day year most of the world uses
Maramataka Māori	lunar	follows the phases of the moon
Chinese	lunar	months set by the moon, year by the sun

Your turn

Four to try

1. How long from 4:47 pm to 5:12 pm?
2. Write 21:05 as 12-hour time.
3. How many minutes is 3.5 hours?
4. On the timetable, how long is Kingsland to Britomart?

Show answer

Answers: 1. 25 minutes: 13 up to 5:00, then 12. An answer of 35 means they subtracted 47 from 12 and flipped the sign. 2. 9:05 pm. 3. 210 minutes: 3 × 60 is 180, plus half an hour. An answer of 350 is the decimal trap. 4. 8:49 to 9:05; 11 minutes up to the hour, then 5, so 16 minutes.

Summary

Bridge the hour, and count in sixties

Crossing an hour? Go up to it, then on from it.
Everything is 60s, never 10s, 100s or 1000s.
And 24-hour time exists so nobody has to guess.

Piece	How	Minutes
2:53 pm to 3:00 pm	up to the hour	7 min
3:00 pm to 3:28 pm	then onwards	28 min
Total	7 + 28	35 min

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