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# Time zones

Area, volume, circles and Pythagoras · Time zones

<!-- Speaker note: Students move one city's time and watch the others follow, convert between time zones using UTC offsets, and plan flights and a call across zones (AC9M8M04, nodes 1 and 2). About 35 minutes (Predict and Run 8 min · Investigate 8 min · Modify 10 min · Practise and Make 9 min). Sources: Daylight saving in NSW: starts 4 October 2026, ends 4 April 2027 (NSW Government), https://www.nsw.gov.au/about-nsw/daylight-saving (checked 12 October 2026); When do the clocks change: back on 25 October 2026 (GOV.UK), https://www.gov.uk/when-do-the-clocks-change (checked 12 October 2026); Los Angeles clock changes: daylight saving ends 1 November 2026 (timeanddate.com), https://www.timeanddate.com/time/change/usa/los-angeles (checked 12 October 2026). -->

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## Today

**We are learning to** a city with a bigger UTC offset is ahead; a smaller offset is behind. Find the difference between the two offsets, then add or take it away; the day changes when you cross midnight. A flight's arrival time is the departure time plus the flight, changed to the local time where it lands.

- I can change a time from one time zone to another using UTC offsets.
- I can tell when the day changes.
- I can work out when a flight lands, in local time.

<!-- Speaker note: Before class: Do the Run board yourself first. The one idea: the city with the bigger offset is ahead; find the difference, add or take it away, and change the day at midnight. The common mistake is adding when the other city is behind (Kim's mistake). The offsets in this lesson hold from 4 October to 25 October 2026: Sydney UTC+11 (daylight saving, from 4 October; +10 before), Perth +8, Tokyo +9, London +1 (British Summer Time ends 25 October), Los Angeles −7 (until 1 November). Go by offsets, not east and west on a map: Los Angeles is east of Sydney but behind, across the date line. Daylight saving changes them through the year, and not every Australian state uses it; check current offsets for real planning. Wider: the International Date Line, why some zones are offset by half an hour (Adelaide, India), and planning a fair regular meeting for staff in several states and another country. -->

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## Why it matters

> You call your cousin in London after school and wake her up at 5 am. A flight from Sydney lands in Los Angeles before it took off. Time zones explain both.

<!-- Speaker note: Each place keeps its own clock, set by its **time zone**. A zone is written as its **offset** from UTC (Coordinated Universal Time). This lesson uses the offsets for most of October: Sydney UTC+11 (daylight saving, from early October to early April; UTC+10 the rest of the year), Perth UTC+8, Tokyo UTC+9, London UTC+1 (until late October) and Los Angeles UTC−7 (until early November). To change a time from one zone to another, find the **difference** between the offsets. A place with a bigger offset is **ahead** (later); a smaller offset is **behind** (earlier). Go by the offsets, not the map: Los Angeles is east of Sydney across the Pacific, but across the International Date Line, so it is 18 hours behind. Add or take away the difference, and change the **day** if you cross midnight. **24-hour time** (21:30, not 9:30 pm) avoids mixing up morning and night. For a flight: add the flight time to the departure time (in the departure zone), then change to the arrival zone. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Predict

**It is 9:00 am Monday in Sydney (UTC+11). What time is it in London (UTC+1)?**

- 10:00 am Monday
- 7:00 pm Sunday
- 11:00 pm Sunday
- 7:00 pm Monday

<!-- Speaker note: What happens: 11:00 pm Sunday. London is 10 hours behind Sydney: 9:00 am − 10 hours goes back past midnight to 11:00 pm the day before. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: ask which offset is bigger. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fmeasurement%2Ftime-zones%2Fstep-2&code=widget%3A+timezone%0Acities%3A+Sydney+%2B11%3B+Perth+%2B8%3B+London+%2B1%3B+Tokyo+%2B9%0Aslider+t%3A+0%2C+23.75%2C+9%2C+0.25%0Aday%3A+Monday%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/measurement/time-zones/?full=step-2#step-2)

<!-- Speaker note: The slider sets Sydney's time; the other cities follow. -->

<!-- Speaker note: Teacher: ask what happens to London's day as Sydney's time moves. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What happened?

* 11:00 pm Sunday. London is 10 hours behind Sydney: 9:00 am − 10 hours goes back past midnight to 11:00 pm the day before.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Perth

Here is the routine.

Now find Perth's time.

$$+11 - (+1) = 10$$

1) $\text{London's offset is smaller}$ — So London is behind Sydney.
2) $09{:}00 - 10\ \text{h} = 23{:}00\ \text{the day before}$ — Take it away, crossing midnight back to Sunday.

<!-- Speaker note: Model this live on the board before revealing anything: write each line and say why, pausing to ask the class what comes next. Then click to reveal the lines and compare. Script. Start: write +11 - (+1) = 10 and say "The difference between the offsets: 10 hours." Line 1: write London's offset is smaller and say "So London is behind Sydney." Line 2: write 09:00 - 10h = 23:00the day before and say "Take it away, crossing midnight back to Sunday." -->

<!-- Speaker note: Teacher: ask Kim to check her answer on the board. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Perth

**It is 14:00 in Sydney (UTC+11). What hour is it in Perth (UTC+8), in 24-hour time?**

* Answer: 11

<!-- Speaker note: Perth is 11 − 8 = 3 hours behind: 14:00 − 3 = 11:00. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the mistake

**Kim finds the time in London. Click the line where her working goes wrong.**

```
 1  It is 9:00 am Monday in Sydney (UTC+11). Kim wants the time in London (UTC+1).
 2  The zones are 10 hours apart, so she adds 10 hours.
 3  London time is 7:00 pm Monday.
```

* Answer: line 2

<!-- Speaker note: Line 2: London's offset (+1) is smaller than Sydney's (+11), so London is behind: take 10 hours away. 9:00 am Monday becomes 11:00 pm Sunday. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## 24-hour time

**Why do flight times use 24-hour time?**

- It is shorter to write
- Airports are open 24 hours
- 21:30 cannot be mixed up with 9:30 in the morning
- It changes the time zone

* Answer: 21:30 cannot be mixed up with 9:30 in the morning

<!-- Speaker note: With 12-hour time, a missing am or pm causes 12-hour mistakes. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Going the other way, and flights



- **London to Sydney:** 
- **A flight:** 
- **Two offices:** 
- **Plan a call:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/measurement/time-zones/?full=step-4#step-4)

<!-- Speaker note: What this step is for: Converting into the starting city, a flight across the date line, a working-hours overlap and a target time in another city. Hints, in order: Sydney is 10 hours ahead of London. / 9:00 + 10 hours. / Add the 14 hours on Sydney's clock first. / Then take away the 18 hours between Sydney and Los Angeles. / Perth is 3 hours behind Sydney. / Perth's 9:00 is Sydney's 12:00. For students who need more support: A printed strip of 24-hour lines for each city, to slide against each other. For early finishers: Plan a video call between Sydney, Perth and London that falls between 8:00 and 21:00 for everyone. Is there one? Which city has to compromise most? The hard part, on purpose: Ahead or behind. Ask students to compare the two offsets and say whose clock is later before they add or take away. When students get stuck: A student adds the difference for a city that is behind. Ask: Which offset is bigger? Which clock is later? Fix: Bigger offset: ahead (add). Smaller: behind (take away). / A student gets the right hour but the wrong day. Ask: Did you cross midnight? Fix: Going past 24:00 is the next day; going below 00:00 is the day before. / A student adds the flight time but does not change to the arrival zone. Ask: Whose clock is your answer on? Fix: Add the flight on the departure clock, then change to the arrival zone (or change first, then add). -->

<!-- Speaker note: Teacher: ask how a flight can land before it took off. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Sydney to Perth

**It is 10:00 in Sydney (UTC+11). What hour is it in Perth (UTC+8), in 24-hour time?**

* Answer: 7

<!-- Speaker note: Perth is 3 hours behind: 10:00 − 3 = 07:00. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## A trip's length

**A train leaves at 08:45 and arrives at 17:20 the same day (one time zone). How many minutes is the trip?**

* Answer: 515

<!-- Speaker note: 08:45 to 17:00 is 8 h 15 min; plus 20 min is 8 h 35 min = 515 minutes. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## 12-hour time

**What is 21:45 in 12-hour time?**

- 11:45 pm
- 10:45 pm
- 9:45 pm
- 9:45 am

* Answer: 9:45 pm

<!-- Speaker note: 21 − 12 = 9: 9:45 pm. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Past midnight

**It is 23:00 on Sunday in Perth (UTC+8). What hour is it in Sydney (UTC+11), in 24-hour time? (It is Monday there.)**

* Answer: 2

<!-- Speaker note: 23:00 + 3 hours = 02:00 on Monday. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## A flight's length

**A flight leaves Perth at 06:00 Perth time and lands in Sydney at 13:00 Sydney time. How many hours is the flight?**

* Answer: 4

<!-- Speaker note: 06:00 in Perth is 09:00 in Sydney; 09:00 to 13:00 is 4 hours. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Make: plan an arrival

Then write both times for your flight, in 24-hour time with the day, as you would on a ticket.

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/measurement/time-zones/?full=step-6#step-6)

<!-- Speaker note: What this step is for: Choosing a departure so an arrival lands in a window brings the offset, the flight and the day together. Hints, in order: The flight is 14 hours and Los Angeles is 18 hours behind Sydney. / Arrival (LA time) = departure + 14 − 18 = departure − 4. -->

<!-- Speaker note: Teacher: ask for the times as they would appear on a ticket. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Exit ticket

**It is 18:30 Tuesday in Sydney (UTC+11). What time and day is it in Los Angeles (UTC−7)?**

* Los Angeles is 18 hours behind: 00:30 Tuesday.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: This completes AC9M8M04. Where it leads: rates such as speed and time (Rates), and planning tasks in other subjects (Geography's time zones and the date line). -->