Working Out Times and Durations: How to Teach "Minutes After", "Minutes Before" and "How Many Minutes" (Grades 2–3)
"What time is 30 minutes after 3:40?" "How many minutes is it from 2:45 to 3:20?" The elapsed-time unit in elementary school maths trips up many children because, unlike ordinary arithmetic, it carries over at 60. Answering "3:70", or working out a duration by plain subtraction and getting it wrong, is very common. This article explains the difference between a point in time and a length of time, how to find minutes after, minutes before and how many minutes using the "split at the hour" method, problems in hours and minutes, problems that cross noon, column calculation, and common mistakes and teaching tips.
The difference between a time and a duration
Before tackling elapsed-time problems, make the difference between a time (a point on the clock) and a duration (a length of time) clear. If that stays fuzzy, children can't tell what a question is asking.
| Time (jikoku) | Duration (jikan) | |
|---|---|---|
| Meaning | A single moment | The length from one time to another |
| Examples | 3:40, 8 a.m. | 30 minutes, 1 hour 20 minutes |
| How questions ask | "What time is it?" | "How many minutes?" "How many hours and minutes?" |
| Analogy | A mark on a ruler | The length between two marks |
Everyday examples that combine the two, such as "the time we left home" was 8:00, "the time it took to walk to school" was 15 minutes, and "the time we got to school" was 8:15, help children grasp the difference. Check the relationships between units at the same time: 1 hour = 60 minutes, 1 day = 24 hours, and 1 minute = 60 seconds.
Finding minutes after: split at the hour
To find the time so many minutes later, the most reliable way is to split at the next exact hour (X:00) and move forward in two steps. It simply puts into words what the clock does: when the minute hand passes 12, the hour goes up by one.
- 1
Count the minutes to the next exact hour
From 3:40, there are 20 minutes until 4:00 (60 − 40 = 20).
- 2
Split the time to add into two parts
For 30 minutes later, split it as 30 minutes = 20 minutes + 10 minutes.
- 3
Move forward to the exact hour
20 minutes after 3:40 is exactly 4:00.
- 4
Move forward by the rest
10 minutes after 4:00 is 4:10. The answer is 4:10.
With arrows, the thinking looks like this: "3:40 → 20 min → 4:00 → 10 min → 4:10". When the answer stays within the same hour (20 minutes after 3:10 = 3:30, for example), you can just add the minutes. Remember that the method changes depending on whether you cross the hour, and you won't get lost.
Finding minutes before: split at the hour, going backwards
Minutes before uses the same idea as minutes after, in reverse. First count how many minutes you can go back to the previous exact hour.
- 1
Count the minutes back to the previous exact hour
From 4:10, you can go back 10 minutes to exactly 4:00.
- 2
Split the time to go back into two parts
For 30 minutes earlier, split it as 30 minutes = 10 minutes + 20 minutes.
- 3
Go back to the exact hour
10 minutes before 4:10 is 4:00.
- 4
Go back by the rest
20 minutes before 4:00 is 20 minutes back from "3 o'clock and 60 minutes", which is 3:40.
With arrows: "4:10 → back 10 min → 4:00 → back 20 min → 3:40". The easy place to slip with minutes before is going back 20 minutes from the exact hour (4:00). Children forget to move the hour back by one and answer "4:40", or get stuck because they can't take 20 from 0 minutes. Rephrasing it as "4:00 is the same as 3 o'clock and 60 minutes" gives 60 − 20 = 40, so 3:40.
Finding how many minutes: count the gap between start and end
Finding how many minutes something took is also easy if you split at the hour. Add two durations: from the start time to the exact hour, and from the exact hour to the end time.
| Question | How to split | Answer |
|---|---|---|
| From 2:45 to 3:20 | 2:45 → 15 min → 3:00 → 20 min → 3:20 | 15 min + 20 min = 35 minutes |
| From 9:50 to 11:20 | 9:50 → 10 min → 10:00 → 1 hr → 11:00 → 20 min → 11:20 | 10 min + 1 hr + 20 min = 1 hour 30 minutes |
| From 5:10 to 5:55 | Same hour, so no need to split | 55 min − 10 min = 45 minutes |
A common mistake with how-many-minutes questions is simply subtracting the minutes. Treating 2:45 to 3:20 as "45 − 20 = 25 minutes" is the classic example. Drawing a clock and checking that the minute hand travels from 9 past 12 to 4 shows which part needs counting.
Hours-and-minutes problems and problems that cross noon
In Grade 3, children meet durations longer than an hour and problems that run from morning into afternoon. The split-at-the-hour idea works for both just as it is.
- Hours and minutes: "from 9:50 to 11:20" is 10 minutes + 1 hour + 20 minutes = 1 hour 30 minutes. Once you reach 60 minutes, turn them into 1 hour. Make sure children can rephrase 90 minutes as 1 hour 30 minutes.
- Crossing noon: "from 11:40 a.m. to 1:10 p.m." goes 11:40 a.m. → 20 min → 0:00 p.m. (noon) → 1 hr → 1:00 p.m. → 10 min → 1:10 p.m., a total of 1 hour 30 minutes.
- Minutes after where a.m. turns into p.m.: "20 minutes after 11:50 a.m." is noon (0:00 p.m.) after 10 minutes, and 0:10 p.m. after the remaining 10. Note that in Japanese schools this isn't written as "12:10 a.m.".
With problems that cross noon, the biggest stumbling block is that the a.m./p.m. label changes around 12 o'clock. How noon is written varies between textbooks and situations, so for details see Is noon 12 a.m. or 0 p.m.? A conversion table between a.m./p.m. and the 24-hour clock.
Solving with column calculation (carrying and borrowing at 60)
Adding and subtracting times can also be done in columns. The difference from ordinary column arithmetic is that when the minutes reach 60 you carry 1 to the hours, and when there aren't enough minutes you borrow 1 hour and turn it into 60 minutes.
| Question | Column method | Answer |
|---|---|---|
| 3:40 + 30 min | 40 + 30 = 70 min → carry 60 minutes as 1 hour, giving 4:10 | 4:10 |
| 4:10 − 30 min | 10 − 30 won't go → treat 4:10 as 3 h 70 min, then 70 − 30 = 40 | 3:40 |
| 11:20 − 9:50 | 20 − 50 won't go → treat it as 10 h 80 min, then 80 − 50 = 30 and 10 − 9 = 1 | 1 hour 30 minutes |
Common mistakes and teaching tips
- Forgetting to carry (3:70): actually move a clock and show the hour going up by one after 60 minutes.
- Forgetting to move the hour back with minutes before (answering 4:40 for 30 minutes before 4:10): check the rule "once you go back past the exact hour, the hour goes back by one".
- Finding a duration by subtracting the minutes only (25 minutes for 2:45 to 3:20): make what you are counting, from where to where, visible on a clock face or a number line.
- Mixing up a.m. and p.m.: draw a number line for the day (0:00 to 24:00) and check that a.m. switches to p.m. at noon.
- Misreading the question: check the form of the answer first; "What time is it?" asks for a time and "How many minutes?" asks for a duration.
Rather than going straight to word problems, understanding comes faster if children first practise checking answers visually while moving a clock: "What do you get if you move the minute hand 30 minutes on from 3:40?" If reading the clock itself is still shaky, go back to how to teach children to read a clock.
Practising elapsed-time problems with the tool
The "Practice quiz" in the Clock Reading Practice tool includes elapsed-time problems. It sets three types, minutes after, minutes before and how many minutes, in sets of 10 by level.
| Level | Content | Typical grade |
|---|---|---|
| Within the same hour | 10-minute steps, e.g. 20 minutes after 3:10 | Grade 2 to early Grade 3 |
| Across the hour | 5-minute steps, e.g. 30 minutes after 3:40 → 4:10 | Grade 3 |
| Crossing noon (AM / PM) | 1-minute steps, e.g. 20 minutes after 11:50 a.m. → 0:10 p.m. | Grade 3 |
| Hours and minutes | Durations longer than an hour | Grade 3 |
After each answer, the split-at-the-hour reasoning from this article is shown, like "3:40 → 20 min → 4:00 → 10 min → 4:10". If you set a start time in "Move the clock" and then move the hands on, the part the minute hand has travelled turns yellow so children can see how much time has passed. To practise on paper, you can also print elapsed-time worksheets with answers.
FAQ
- How do you work out the time so many minutes later?
- First count the minutes to the next exact hour (X:00), then split the time to add into two parts. For 30 minutes after 3:40, 20 minutes gets you to 4:00 and the remaining 10 minutes to 4:10. If you don't cross the hour, just add the minutes.
- I don't understand how to find how many minutes
- Split it into two parts, from the start time to the exact hour and from the exact hour to the end time, and add them. From 2:45 to 3:20 is 15 minutes + 20 minutes = 35 minutes. Subtracting the minutes directly (45 − 20 = 25) gives the wrong answer.
- What's the difference between a time and a duration?
- A time is a single moment, such as 3:40. A duration is the length from one time to another, such as 30 minutes. If a question asks "What time is it?", answer with a time; if it asks "How many minutes?", answer with a duration.
- What should I watch for when doing time calculations in columns?
- Minutes carry at 60 and borrow at 60. If 40 minutes + 30 minutes = 70 minutes, turn 60 of them into 1 hour to get 1 hour 10 minutes. In subtraction, if there aren't enough minutes, borrow 1 from the hours and add 60 to the minutes.
- How do you solve problems that cross noon?
- Split at noon (12 o'clock midday) as the exact hour. From 11:40 a.m. to 1:10 p.m., 20 minutes gets you to noon, 1 hour to 1:00 p.m. and 10 minutes to 1:10 p.m., a total of 1 hour 30 minutes. After noon, write the times as p.m.
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