080i - 12- and 24-Hour Time and Duration

Lesson 80 — Explicit Instruction: 12- and 24-Hour Time and Duration

Strand: Measurement | Descriptor: AC9M8M04 | Duration: 45 minutes

Learning Intentions

• To convert times fluently between 12-hour (am/pm) and 24-hour notation.
• To calculate the duration between two times, and to calculate a finish time given a start time and a duration, within a single time zone.

Success Criteria

I can:

1. Convert a 12-hour time (am/pm) to 24-hour time, and vice versa.
2. Correctly handle midnight (12:00 am) and midday (12:00 pm) in both notations.
3. Calculate the elapsed duration between two given times, including when the times cross midday or midnight.
4. Calculate a finish time given a start time and a duration, and calculate a start time given a finish time and a duration.

Warmup

(5 minutes — mini whiteboards, rapid-fire)

1. Write down the time shown on a clock face displaying , if it is in the evening.
2. Is am the start of the day or the end of the day?
3. A train timetable shows a departure of . Is this morning or evening?
4. How many hours are there in one full day?

Teacher note: Question 2 is the hook — many students believe pm is midnight and am is midday. Do not resolve it yet; return to it explicitly in Activity 1.

Activities

Activity 1 — Explicit Instruction: Converting between 12-hour and 24-hour Time (12 min)

Explain that 24-hour time avoids the need for “am” or “pm” by counting hours from (midnight) through to , restarting at the next day. It is always written with 4 digits, e.g. , not .

Display the key reference points explicitly — this is the single most important anchor for the whole lesson:

12-hour time	24-hour time
am (midnight)
am
am
pm (midday)
pm
pm

I do — am times to 24-hour: For any am time other than am, the 24-hour time simply has the same hour value, written with a leading zero if needed and no “am”.

I do — pm times to 24-hour: For any pm time other than pm, add to the hour.

I do — 24-hour back to 12-hour: If the 24-hour time is or later, subtract and label pm. If it is before , keep the hour and label am (except , which becomes am).

We do: Convert together: am, pm, am, pm to 24-hour time. Then convert , , , back to 12-hour time.

You do: Convert to 24-hour time: (a) am (b) pm (c) am (d) pm. Convert to 12-hour time: (e) (f) (g) (h) .

(Answers: (a) (b) (c) (d) (e) am (f) pm (g) am (h) pm)

Activity 2 — Explicit Instruction: Calculating Duration and Finish times (13 min)

Explain the key strategy: it is usually easiest to work in 24-hour time for duration problems, since there is no am/pm boundary to trip over.

I do — duration within the same “half” of the day: A lesson starts at and finishes at . Find the duration.

I do — duration crossing midday/midnight (the tricky case): A flight departs at and lands at the next day. Find the duration.

Explicit strategy: break the journey into two parts — from departure to midnight, then from midnight to arrival.

I do — finding a finish time: A movie starts at and runs for h min. Find the finish time.

I do — finding a start time (working backwards): A flight lands at after a duration of h min. Find the departure time.

Explicit warning: When subtracting minutes and the minutes value is too small (e.g. min), “borrow” an hour: , then .

We do: Together, find the duration from to , and the finish time for an event starting at and lasting h min.

You do:

1. Find the duration from to .
2. Find the duration from to the next day.
3. A train departs at and takes h min. Find its arrival time.
4. A shift ends at and lasted h min. Find the start time.

(Answers: 1. h min 2. h min 3. 4. the previous day)

Activity 3 — Applied Task: Planning a Study Timetable (10 min)

Pairs, then whole-class share.

Maya is planning her Saturday. She wants to:

• Study Maths from am for h min.
• Take a -minute break.
• Study Science for h min.
• Have lunch at pm.

(a) Using 24-hour time throughout your working, find the exact time Maya finishes studying Science. (b) Does she finish in time for a pm lunch, or does she need to adjust her schedule? By how much?

Socratic scaffolding:

Prompt	Purpose
Understand: what is actually being asked?	Two things — a final finish time, and a comparison against a fixed target (1:00 pm lunch).
What should you convert first, and why?	Convert am to 24-hour time () so every step avoids am/pm confusion.
Devise a plan	Add each duration in sequence: Maths, then break, then Science.
Carry out the plan	; ; .
Looking back	Convert back to 12-hour time: pm. Compare to the pm target: she finishes minutes early, with time to spare.

Checks for Understanding

(6 minutes — exit ticket, collected)

1. Convert pm to 24-hour time.
2. Convert to 12-hour time.
3. Find the duration from to .
4. A bus departs at and the journey takes h min. Find the arrival time (state whether it is the same day or the next).

Answers: 1. ; 2. am; 3. h min; 4. — the next day.

Common Misconceptions

Misconception	How to pre-empt it
Believing am is midday and pm is midnight (or vice versa).	Return constantly to the reference table: am (midnight), pm (midday). Never let either pass without stating which is which.
Subtracting times as if they were base- decimals (e.g. treated like ).	Insist on converting minutes to a “borrow 60” strategy, not a “borrow 100” strategy — explicitly contrast with column subtraction of money.
Writing 24-hour times without the leading zero or without 4 digits (e.g. "" instead of "").	Model every 24-hour time with exactly 4 digits from the very first example.
Forgetting that a duration crossing midnight moves into “the next day”, and not stating this in the final answer.	Require students to explicitly write “(next day)” whenever a calculated time exceeds .
Adding hours and minutes separately without checking if minutes overflow past .	Model the explicit convert-carry step every time, e.g. minutes h min.

Enrichment — Competition-Style Problems

E1 (Kangaroo style). A clock shows pm. What is the size, in degrees, of the smaller angle between the hour and minute hands? (Hint: the minute hand moves per minute; the hour hand moves per minute.)

Answer

At : minute hand is at . Hour hand has moved from the () by minutes’ worth of hour-hand motion: .

Since , this is already the smaller angle.

E2 (AMC Junior style). A digital clock displays 24-hour time. How many minutes in a full day show a time where all four digits are the same (e.g. is close, but not all four digits match)? List them.

Answer

We need with all four digits identical: . Since hours only run –, the tens digit of the hour can only be or , and for all four digits to match, must equal that tens digit too.

Testing : — valid. Testing : — valid. Testing or higher: hour would be or ; is not a valid hour, and has hour digits but needs all four the same, which works: — valid (since is a valid hour). Testing upward: hour invalid.

So the valid times are , , — 3 times in a full day.

E3 (Challenge). A clock loses minutes every hour. It is set correctly at pm (noon). What time will it show when the correct time is am (midnight) that same night?

Answer

From noon to midnight is correct hours.

The faulty clock will show , i.e. pm.

Homework

1. Convert to 24-hour time: (a) am (b) pm (c) am (d) pm.
2. Convert to 12-hour time: (a) (b) (c) (d) .
3. Find the duration between each pair of times: (a) to (b) to (c) to the next day.
4. A ferry departs at am and the crossing takes h min. Find the arrival time in 12-hour notation.
5. Reasoning. Explain why 24-hour time is often preferred over 12-hour time for official timetables (trains, flights, hospitals), giving a specific example of a mistake 12-hour time could cause.
6. Challenge. A movie session begins at and the cinema needs the room clear and ready minutes before the next showing. If the film runs for h min and there are minutes of advertisements before it starts, at what time (24-hour) must the next showing begin at the earliest?

Answers: Q1 — (a) (b) (c) (d) . Q2 — (a) am (b) pm (c) am (d) pm. Q3 — (a) h min (b) h min (c) h min. Q4 — am hmin am. Q5 — 24-hour time removes ambiguity between am and pm; e.g. a “9:00” flight could be misread as either 9 am or 9 pm, causing a traveller to miss it by 12 hours, whereas and cannot be confused. Q6 — session starts , ads min then film hmin: ; ; add the required -minute clearing buffer: — the next showing can begin no earlier than .