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Time & Timetable Problems

Maths · Y4 OC Prep
Year 4 OC
Lesson Guide
Explanation
OC style: board at 'ten to eleven at night' (10:50 pm), leave at 1:20 pm the next day — how long aboard? Use stepping stones: 10:50 pm to midnight is 1 hour 10 minutes; midnight to noon is 12 hours; noon to 1:20 pm is 1 h 20. Total: 14 hours 30 minutes. Notice the two skills stacked: decoding 'ten to eleven', then hopping through midnight AND noon. The wrong options (2 h 30, 13 h 30…) punish anyone who miscounts the 12-hour blocks.
Your Turn
From 10:50 pm to 7:20 am: how long? Check: 10 min → 11 pm, 1 h → midnight, 7 h 20 → total 8 h 30 min.
Watch Out
Noon and midnight are the two 12 o'clocks — crossing BOTH means a full 12-hour block sits in the middle. Count it once, not twice.
Explanation
OC style: 7 May was a Thursday — what day was 30 June? The insight: every 7 days lands on the same weekday, so only the REMAINDER matters. Count the gap: May 7→31 is 24 days, plus 30 June days = 54. Divide: 54 ÷ 7 = 7 weeks remainder 5. Walk five days from Thursday: Friday, Saturday, Sunday, Monday, Tuesday. You need month lengths by heart: 30 days hath September, April, June and November; the rest 31 — except February.
Your Turn
Today is Friday. What day is it in 16 days? Check: 16 ÷ 7 = 2 r 2 → Sunday.
Watch Out
Counting 7 May → 31 May: that's 31 − 7 = 24 days AFTER the 7th. Off-by-one here shifts your final day — recount if unsure.
Explanation
Timetables are grids: read DOWN a column to ride one bus, ACROSS a row to compare buses at the same stop. Bus A leaves School 3:10 and reaches Station 3:51 — journey 41 minutes. Classic OC questions: 'How long from Library to Pool on Bus B?' (13 min), 'You arrive at the Library at 3:30 — which bus can you catch?' (Bus B at 3:52 — you missed A by 8 minutes!). Always anchor: which column am I riding, which row am I standing at?
Your Turn
You reach the Pool at 3:36. Which is the next bus, and how long do you wait? Check: Bus B at 4:05 — a 29-minute wait.
Watch Out
A bus you missed by ONE minute is still missed. "Arrive 3:23, bus left 3:22" means waiting for the next one.
Explanation
OC times come dressed as fractions: 1¾ hours, half past, quarter to. Convert to minutes FIRST — ¼ h = 15, ½ h = 30, ¾ h = 45 — then hop. A 1¾-hour movie from 6:50 pm: add the hour (7:50), then 45 minutes via the 8:00 stepping stone (10 + 35): ends 8:35 pm. Never add '1.75' to a clock time — clocks don't speak decimal; they speak hours-and-minutes.
Your Turn
Soccer training is 1½ hours starting 4:45 pm. Finish time? Check: 4:45 + 1 h = 5:45, + 15 → 6:00, + 15 → 6:15 pm.
Watch Out
Minutes roll at 60: 7:50 + 45 is 8:35, never "7:95". The o'clock stepping stone keeps you honest.
Explanation
The last time skill: planning backwards from a deadline. Party at 3:00 pm; the cake needs 45 minutes baking, 30 cooling, 20 decorating. Start at the deadline and subtract task by task: 3:00 − 20 = 2:40, − 30 = 2:10, − 45 = 1:25 pm — the latest possible start. It's the working-backwards engine from Chapter 4 driving through a schedule. OC asks it as 'what is the LATEST time…' — and the trap options come from subtracting in the wrong order or dropping a task. Quiz and exercises!
Your Turn
School starts 8:55. Walk: 15 min, breakfast: 20 min, dressing: 10 min. Latest wake-up? Check: 8:55 − 15 − 20 − 10 = 8:10 am.
Watch Out
Subtract EVERY task — planners who forget the cooling step arrive with molten cake. Tick each task as you subtract it.
Step 1: Introduction
Step 1 of 5
The night coach "Ava got on a coach at ten to eleven at night and got off at 1:20 pm the NEXT DAY. How long was she on the coach?" 10:50 pm midnight noon 1:20 pm 1 h 10 12 h 1 h 20 Stepping stones: 10:50 pm → midnight (1 h 10 min) → noon (12 h) → 1:20 pm (1 h 20 min). Total: 14 hours 30 minutes ✓
What day of the week is it? "7 May was a Thursday. What day was 30 June?" Step 1 — count the days between: May has 31 days → 7 May to 31 May = 24 days, + 30 in June = 54 days. Step 2 — throw away whole weeks: 54 ÷ 7 = 7 weeks remainder 5 — only the remainder matters! Step 3 — walk 5 days from Thursday: Fri, Sat, Sun, Mon, TUESDAY ✓ Whole weeks land on the SAME weekday — only remainders move the day.
The bus timetable grid Stop Bus A Bus B School 3:10 3:40 Library 3:22 3:52 Pool 3:35 4:05 Station 3:51 4:21 Down a column = one bus's journey · Across a row = same stop, later buses. School → Station on Bus A: 3:51 − 3:10 = 41 minutes.
Quarter, half, three-quarter hours ¼ h = 15 min quarter hour ½ h = 30 min half hour ¾ h = 45 min three-quarter hour "A movie runs 1¾ hours, starting at 6:50 pm. When does it end?" 1¾ h = 1 h 45 min. 6:50 + 1 h = 7:50. Then +45: 10 min → 8:00, +35 more → 8:35. Ends 8:35 pm ✓ Fraction-hours → minutes FIRST, then hop through the o'clocks.
Work backwards from the deadline "The party starts at 3:00 pm. The cake needs 45 min to bake and 30 min to cool, and I need 20 min to decorate. Latest start time?" 3:00 ← 20 2:40 ← 30 2:10 ← 45 1:25 Start at the DEADLINE, subtract each task backwards: 3:00 − 20 = 2:40 · − 30 = 2:10 · − 45 = 1:25 pm. Start baking by 1:25 pm at the latest! Working backwards strikes again — this time through a schedule.
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