Telling time
Read the clock to hour/half-hour → 5 min → minute; days/weeks/months/years; a.m./p.m.; durations; convert h/min/s; convert between decimal and sexagesimal systems.
Time is a measurement, just like length or weight — but instead of a ruler we read it off a clock and a calendar.
What it means
A clock divides the day into hours, minutes and seconds. An analogue clock has a round face marked 1 to 12 and two hands. The short hand is the hour hand; the long hand is the minute hand. There are 12 numbers but a day has 24 hours, so the hour hand goes around the face twice a day.
The face is split into 60 tiny steps. The minute hand points to how many minutes past the hour we are, and it moves one full loop — 60 minutes — every hour. Each numbered mark is 5 minutes apart (5 × 12 = 60), which is why we count round in fives: 5, 10, 15, and so on. Halfway round is 30 minutes, so “half past”. A second is a still smaller step: 60 seconds make one minute.
The key facts to hold onto:
60seconds =1minute60minutes =1hour24hours =1day
A digital clock skips the hands and writes the time as numbers, like 9:45, meaning 45 minutes past 9. Because a day has 24 hours, we split it into a.m. (midnight to noon) and p.m. (noon to midnight).
Longer stretches of time stack up too: 7 days = a week, about 4 weeks = a month, 12 months = a year.
Counting seconds and minutes in 60s is called a sexagesimal (base-60) system — unusual, because everyday numbers count in tens (base-10, or decimal). Converting between them is just multiplying or dividing: 2.5 hours is 2 hours plus half of 60 minutes, so 2 h 30 min.
Worked examples
Reading the hands. The hour hand sits just past 3; the minute hand points at 8. The 8 mark means 8 × 5 = 40 minutes. So the time is 3:40 — twenty to four.
A duration. A film starts at 2:15 p.m. and ends at 4:00 p.m. From 2:15 to 3:15 is one hour; 3:15 to 4:00 is another 45 minutes. Total: 1 h 45 min.
Convert to one unit. How many seconds in 3 minutes? 3 × 60 = 180 seconds.
Decimal ↔ sexagesimal. Write 90 minutes in hours-and-minutes: 90 ÷ 60 = 1 remainder 30, so 1 h 30 min, i.e. 1.5 h.
The generative-art connection
A clock face is already generative art: 12 numbers spaced evenly on a circle, and a hand that sweeps a full turn. That sweep is an angle. The minute hand travels 360° ÷ 60 = 6° every minute; the hour hand crawls 30° per hour. Telling time is reading an angle off a circle.
You can make this visible. Place 60 dots evenly around a ring and light one up each second — the dot circling the ring is the passing of a minute. This is exactly the radial, evenly-spaced structure behind dot-multiplier, where one dot fans out into a symmetric ring: swap “arms” for “minutes” and the starburst becomes a clock. Speed the hands up and the two hands trace looping curves against each other, turning base-60 counting into a moving pattern a child can watch and steer.
Common misconceptions
- “The 3 means 3 minutes.” On the minute hand, each number counts in fives — the 3 mark is
15minutes, not 3. - “A new hour has 100 minutes.” Time is base-60, not base-10: after
59minutes comes the next hour, not minute60. - “9:45 is nearly ten past nine.”
:45is three-quarters of the way round — quarter to ten, not past nine.
What a learner should be able to solve
The benchmark for mastering this concept — the problems a child at this stage is expected to be able to work through.
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An analogue clock has its short hand a little past `7` and its long hand pointing at the `9` mark. Write the time in two ways: as a digital time, and in words.
Answer
The `9` mark is `9 × 5 = 45` minutes past. Digital: `7:45`. In words: quarter to eight (`:45` is three-quarters round, so 15 minutes *to* the next hour). Correct if both the digital `7:45` and the "to" wording are given.
Art hook Draw a clock: 12 numbers evenly on a circle at 30 degrees apart, plus 60 tick dots. A slider sets minutes 0-59; the app snaps the long hand and shows where it points, and colours the swept-past arc so a child sees :45 as three-quarters of the ring filled.
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A swimming lesson starts at `3:50` p.m. and ends at `5:15` p.m. How long does it last?
Answer
From `3:50` to `4:50` is `1` h; `4:50` to `5:15` is `25` min. Total `1` h `25` min. (Or count up: `3:50`→`4:00` is 10 min, `4:00`→`5:15` is 1 h 15 min, sum 1 h 25 min.)
Art hook A horizontal time number line from 3:00 to 6:00 with hour ticks. The learner drags a start dot and end dot; the app arcs a coloured band between them and labels its length in h/min — a visual duration bar.
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How many seconds are there in `4` minutes `30` seconds? Give your answer as a single number of seconds.
Answer
`4 × 60 = 240` seconds, plus `30` = `270` seconds.
Art hook A ring of 60 dots. Click 'play' and one dot lights each second, sweeping round; each completed loop drops a tally mark. Set the target to 270 s and watch it fill 4 full loops plus half of a fifth.
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Write `2` hours `45` minutes as a decimal number of hours.
Answer
`45 ÷ 60 = 0.75` h, so `2` h `45` min `= 2.75` h. (45 min is three-quarters of an hour.)
Art hook Two side-by-side dials: one shows minutes 0-60, the other the same angle relabelled 0.00-1.00. Rotating one hand rotates the other, so a child sees 45 min and 0.75 h as the *same* turn.
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A train leaves at `08:40` and the journey takes `1` hour `35` minutes. At what time (using the 24-hour clock) does it arrive?
Answer
`08:40 + 1` h `= 09:40`; `09:40 + 35` min: 20 min to `10:00`, then 15 more `= 10:15`. Arrival `10:15`.
Art hook A 24-hour clock drawn as a full ring of 24 hour-marks. Two hands (start green, arrival orange) show departure and arrival; the coloured arc between them is the journey — bridging past the hour is visible as the arc crossing a tick.
Training exercises
Practice problems, easier first, that build toward the bar above. Each doubles as a seed for an interactive artwork.
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On a clock, the short hand points straight at the `9` and the long hand points straight up at the `12`. What time is it?
Answer
`9:00` — nine o'clock. The long hand on 12 means 0 minutes past, so it is exactly the hour the short hand shows.
Art hook A clock where clicking a number moves the hour hand there and the app reads out 'o'clock'. Twelve evenly spaced numbers on a circle is the seed shape.
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The long (minute) hand points straight down at the `6`, and the short hand is halfway between `2` and `3`. Read the time.
Answer
The `6` means `6 × 5 = 30` minutes, so half past. The hour hand is between 2 and 3, so it is `2:30` — half past two.
Art hook Split the clock face into a coloured half and a plain half, hinged at the 12-6 line, to show 'half past' as literally half the ring swept.
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Count round the clock in fives. The minute hand points at the `4` mark. How many minutes past the hour is that?
Answer
`4 × 5 = 20` minutes past.
Art hook Around the ring, label each numbered mark with its minute value (5,10,15,...) fading in as you count; clicking a number highlights the 5-count path from 12 to it.
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Put these in order from shortest to longest: a minute, a second, an hour, a day.
Answer
second, minute, hour, day. (`60` s = 1 min, `60` min = 1 h, `24` h = 1 day.)
Art hook Four nested rings sized by duration (second smallest, day largest); dragging them into the right order snaps them into a bullseye of time units.
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Spot the mistake. Sam says: "The minute hand is on the `3`, so it is `3` minutes past." What did Sam get wrong, and what is the real number of minutes?
Answer
Each number counts in fives, not ones. The `3` mark is `3 × 5 = 15` minutes past, not 3.
Art hook Toggle button flips every mark's label between the wrong reading (1,2,3...) and the right one (5,10,15...) so the error is visible as two different colourings of the same dots.
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A cartoon starts at `4:00` and finishes at `4:20`. How many minutes long is it?
Answer
`20` minutes (from :00 to :20).
Art hook A mini duration bar on a 0-60 minute number line: shade from 0 to 20 and label the length.
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How many minutes are there in `2` hours?
Answer
`2 × 60 = 120` minutes.
Art hook Two full loops of a 60-dot ring animate one after the other, a counter ticking up to 120.
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A morning club runs from `9:15` to `10:45`. How long is that?
Answer
`9:15`→`10:15` is `1` h; `10:15`→`10:45` is `30` min. Total `1` h `30` min.
Art hook Drag start and end dots on a time line from 9:00 to 11:00; the coloured span shows 1 h 30 min and can be split at the hour tick.
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Convert `90` seconds into minutes and seconds.
Answer
`90 ÷ 60 = 1` remainder `30`, so `1` minute `30` seconds.
Art hook A 60-dot second-ring: fill 90 dots and watch it complete one loop (1 min) with 30 dots into the next — remainder made visible.
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It is `11:50` a.m. now. What time will it be in `20` minutes? Is that a.m. or p.m.?
Answer
`11:50 + 20` min: 10 min reaches `12:00` (noon), then 10 more `= 12:10`. Noon flips to p.m., so `12:10` p.m.
Art hook A clock that dims to night-blue for a.m. and brightens to yellow for p.m.; sweeping the minute hand past 12 (noon) triggers the colour flip so the a.m./p.m. boundary is a visible sunrise.
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Write `1` hour `15` minutes as a decimal number of hours.
Answer
`15 ÷ 60 = 0.25` h, so `1` h `15` min `= 1.25` h. (15 min is a quarter of an hour.)
Art hook A quarter-slice of the clock lights up when you enter 15 min, and a second dial shows the same wedge relabelled 0.25 — matching the sexagesimal and decimal readings.
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A bus is due at `07:55`. It is `12` minutes late. Using the 24-hour clock, what time does it actually arrive?
Answer
`07:55 + 12` min: 5 min reaches `08:00`, then 7 more `= 08:07`. Arrival `08:07`.
Art hook On a 24-hour ring, a 'scheduled' hand and a 'late' hand; the small orange arc between them is the delay, shown crossing the 08:00 tick to make the bridge over the hour concrete.