Time and time zones: a week of ready-to-teach maths

Five lessons for Year 8 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet with practice and a stretch section, plus a train timetable, the Australian time zones in June and January, twelve duration loop cards, twelve same-instant cards, a mini-check and every answer with its working.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Print the two cut-out sheets: the loop cards are for Day 2 (one set for the class), the same-instant cards for Day 3 (one set per pair).
4. Open the free interactive unit on the board. Every plan says which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and worked answers are all on the one page.

The idea in plain words

A 24-hour clock counts the hours of the day from 00:00 at midnight to 23:59, so it needs no am or pm: after noon, add 12 to the hour. A duration is found by counting up in hops, to the next hour, then whole hours, then the minutes left, and a duration across noon or midnight is easiest in 24-hour time. A time zone is an offset from Coordinated Universal Time (UTC): Perth is UTC+8, Adelaide and Darwin UTC+9:30, and the eastern states UTC+10. To convert, find the gap between the offsets and add it going east or subtract it going west. In summer, the states that use daylight saving move their clocks an hour forward, so the gaps change.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 60 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point for two shorter sessions, and every worksheet ends with a stretch section for students who finish early.

Daylight saving in this pack

Questions say whether they are in June (standard time everywhere in Australia) or January (daylight saving in NSW, the ACT, Victoria, Tasmania and South Australia; not in Queensland, the Northern Territory or Western Australia). Daylight saving runs from the first Sunday in October to the first Sunday in April. World questions are set in January and give each offset.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 makes 24-hour time automatic; Day 2 uses it to find durations, even across midnight; Day 3 adds the Australian time zones and daylight saving; Day 4 goes round the world, where the date can change; and Day 5 plans trips and calls that cross zones. It builds on 12- and 24-hour time and elapsed time in Years 5 and 6, and prepares rates (time in a ratio with distance) later in Year 8.

Materials for the week (one trip)

• From the classroom: pencils, calculators, scissors, this pack printed. A wall clock helps on Day 1.
• Cut-out sheet 1, one set for the class: 12 duration loop cards (Day 2).
• Cut-out sheet 2, one per pair: 12 same-instant cards (Day 3).
• Optional: a world time zone map or an online world clock for Day 4.

Words for the word wall

12-hour time, 24-hour time, am, pm, midnight, noon, timetable, duration, elapsed time, bridging, time zone, offset, UTC, AWST, ACST, AEST, daylight saving, ahead, behind, date line

Dear families

This week in maths, Year 8 is working with time: changing between 12- and 24-hour time, finding how long things take, and converting times between Australian states and other countries. They learn why Perth is two hours behind Sydney in winter but three in summer, and why a flight can land before it took off by the clocks.

Try this at home

• Read a TV guide or a bus timetable together and change three times to 24-hour time.
• Ask: a game starts at 7:45 pm and runs for 2 h 30 min. When does it finish? (10:15 pm.)
• Ask: in June it is 6:00 pm in Sydney. What time is it in Perth? (4:00 pm.)
• If you have family or friends in another state or country, work out what time it is there right now.

My times this week

Fill one row a day. Write a time you noticed in both forms, and one duration you worked out.

Printed from the free seegongsik Time and time zones teaching pack · seegongsik.com/au/y8/measurement/AC9M8M04/pack

12-hour and 24-hour time

The 24-hour clock counts from 00:00 at midnight to 23:59, so it never needs am or pm. Students change times both ways, take care with midnight and noon, and read a train timetable.

We are learning to

• change a 12-hour time to 24-hour time and back,
• write midnight as 00:00 and noon as 12:00, and the minutes after them,
• read a timetable in 24-hour time and use it to plan a trip.

Success criteria

• I can write 6:25 pm and 12:10 am in 24-hour time.
• I can find a train in a 24-hour timetable and say when it arrives.

You need

The worksheet and a pencil each.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part A; start the second with the timetable.

Watch for these ideas

• Writing 12:15 am as 12:15: just after midnight is 00:15.
• Adding 12 to a morning time.
• Dropping the first zero: in 24-hour time the hour always has two digits, 08:05.

Answers

• Part A: 7:05 am = 07:05, 12:30 pm = 12:30, 4:20 pm = 16:20, 12:15 am = 00:15, 11:50 pm = 23:50; 13:40 = 1:40 pm, 00:05 = 12:05 am, 09:00 = 9:00 am, 20:35 = 8:35 pm, 12:00 = 12:00 pm.
• Part B: 1. 12:37; 2. 06:42 to 08:47 is 2 h 5 min; 3. the 11:15 from Central, at Bay Point at 13:20; 4. 7:34 pm.
• Part C: 12:45 am; 11:50 am; 12:30 am.
• Part D: from 1:00 am to 12:59 pm the digits match (24-hour time just adds a 0 before a one-digit hour); after 1:00 pm and before 1:00 am they differ.

12-hour and 24-hour time

A. Both ways

B. The train timetable

1. When does the 11:15 from Central reach Hill Junction? ____________
2. How long does Train 1 take from Central to Bay Point? ____________
3. Which train should you catch from Central to be at Bay Point by 13:30? ____________
4. Write Train 3’s time at Bay Point in 12-hour time. ____________

C. Which is earlier in the day?

D. Stretch: same digits

For which times of day does a 12-hour clock show the same digits as a 24-hour clock (ignoring a 0 at the front)? Explain.

Durations

A duration is found by counting up, not by subtracting like ordinary numbers. Students count up in hops, across noon and midnight, find finishing times, and play a duration loop as a class.

We are learning to

• count up in hops: to the next hour, then whole hours, then the minutes left,
• use 24-hour time to find a duration across noon or midnight,
• add a duration to a start time, and change decimal hours to hours and minutes.

Success criteria

• I can find how long it is from 9:50 am to 2:20 pm.
• I can say why 1.5 hours is not 1 hour 50 minutes.

You need

The worksheet each; the twelve loop cards from cut-out sheet 1, one set for the class, cut out and handed round.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after the loop; start the second with Part A.

Watch for these ideas

• Subtracting times like decimals: 11.15 − 9.40 = 1.75 is not a duration.
• Reading 1.5 hours as 1 hour 50 minutes: the .5 is half an hour.
• Losing a day when a duration crosses midnight.

Answers

• Part A: 08:35 to 11:10 is 2 h 35 min; 10:50 to 14:25 is 3 h 35 min; 13:15 to 17:05 is 3 h 50 min; 22:40 to 06:15 is 7 h 35 min.
• Part B: 10:05 pm; 2:05 pm; 07:15, the next day.
• Part C: 1.5 h = 1 h 30 min; 2.25 h = 2 h 15 min; 0.75 h = 45 min; 3.2 h = 3 h 12 min.
• Part D: 1 h 45 min + 2 h 50 min + 55 min + 2 breaks of 20 min = 6 h 10 min, so the ride ends at 12:50 pm.

Durations

A. Count up in hops

Draw your hops above each line and write the duration in hours and minutes.

B. When does it finish?

C. Decimal hours

A phone or a calculator may show a time in decimal hours. Write each in hours and minutes.

D. Stretch: a long ride

A cyclist starts at 6:40 am and rides three legs of 1 h 45 min, 2 h 50 min and 55 min, with a 20-minute break between legs. When does the ride end?

Australian time zones

A time zone is an offset from UTC, and in summer some states move their clocks an hour forward. Students convert between Australian cities in June and in January, and sort cards into groups that show the same instant.

We are learning to

• find the gap between two zones from their offsets, and add it going east or subtract it going west,
• use the right offsets in summer, when some states use daylight saving and others do not,
• tell when a conversion crosses midnight into a different day.

Success criteria

• I can say what time it is in Perth when it is 6:00 pm in Sydney in June.
• I can explain why Perth is 2 hours behind Sydney in June but 3 hours behind in January.

You need

The worksheet each; the same-instant cards from cut-out sheet 2, one set per pair, cut out.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part B; start the second with Part C and the cards.

Watch for these ideas

• Adding when going west: places to the west are behind.
• Using daylight saving for Queensland, Western Australia or the Northern Territory, which do not use it.
• Forgetting the half hour for Adelaide and Darwin.

Answers

• Part A (June): 9:00 am in Sydney is 7:00 am in Perth; 2:30 pm in Perth is 4:00 pm in Adelaide; 6:45 pm in Brisbane is 6:15 pm in Darwin; 11:20 pm in Adelaide is 11:50 pm in Sydney.
• Part B (January): 9:00 am in Sydney is 6:00 am in Perth; 7:30 pm in Sydney is 6:30 pm in Brisbane; 12:00 pm in Adelaide is 9:30 am in Perth; 10:15 pm in Perth is 1:15 am in Hobart, the next day.
• Part C: 6:00 pm to 8:00 pm in Sydney is 3:00 pm to 5:00 pm in Perth (3 hours behind in January). Cards: A: 3, 8, 11; B: 2, 5, 9, 12; C: 1, 4, 6, 7, 10.
• Part D: Brisbane 6:30 pm, Adelaide 7:00 pm, Darwin 6:00 pm, Perth 4:30 pm.

Australian time zones

A. In June (standard time)

B. In January (daylight saving where it is used)

C. A good time to ring, and the cards

In January, a cousin in Sydney is free to talk from 6:00 pm to 8:00 pm, Sydney time. Between which times should they be rung from Perth?

D. Stretch: one show, five clocks

In January a show starts at 7:30 pm in Sydney, live across Australia. When does it start in Brisbane, Adelaide, Darwin and Perth?

Across the world

Overseas, the safe way is through UTC: back to UTC first, then on to the other city. Students convert times from Los Angeles to Auckland, watch the date change, and work out when flights land.

We are learning to

• change a local time to UTC (take away the offset) and UTC to local time (add the offset),
• say which day a converted time falls on,
• find a flight’s arrival time on the clocks where it lands.

Success criteria

• I can change 09:00 in Sydney to London time in January, through UTC.
• I can explain how a flight can land at an earlier clock time than it left.

You need

The worksheet each. A world time zone map helps but is not needed: the offsets are on the sheet.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part A; start the second with the flights.

Watch for these ideas

• Adding the offset to get to UTC: for a city ahead of UTC, take it away.
• Forgetting that the date can change, a day ahead or a day behind.
• Adding the flight time to the departure time and stopping there: that is still the departure city’s clock.

Answers

• Part A: 08:00 London = 08:00 UTC = 19:00 the same day in Sydney; 21:00 Sydney = 10:00 UTC = 10:00 the same day in London; 14:00 New York = 19:00 UTC = 06:00 the next day in Sydney; 07:30 Tokyo = 22:30 UTC = 14:30 the day before in Los Angeles.
• Part B: Sydney 10:00 + 9 h 30 min lands in Tokyo at 17:30 local time, the same day; Auckland 07:00 + 3 h 20 min lands in Sydney at 08:20 local time, the same day.
• Part C: 20:00 Monday in Auckland is 07:00 UTC, which is 23:00 on Sunday in Los Angeles.
• Part D: Auckland, Sydney, Tokyo, Perth, London, New York, Los Angeles; Los Angeles sees the New Year 21 hours after Auckland.

Across the world

Offsets in January: Sydney UTC+11 · Perth UTC+8 · Auckland UTC+13 · Tokyo UTC+9 · London UTC+0 · New York UTC−5 · Los Angeles UTC−8

A. Through UTC

B. When does it land?

C. Across the date line

It is 20:00 on Monday in Auckland. What time and day is it in Los Angeles?

D. Stretch: the New Year

Put the cities in the order they see the New Year, first to last. How many hours after the first city does the last one see it?

Planning across zones

Trips and calls that cross zones mix durations and conversions. Students work out when flights land, plan a call for three cities, catch a daylight-saving mistake, and play the quiz as a class game.

We are learning to

• combine a duration and a time-zone change in one problem,
• find times that suit people in several zones at once,
• check whether daylight saving applies before converting.

Success criteria

• I can find when a flight from Perth to Sydney lands, by Sydney’s clocks.
• I can say why the gap between two cities can change during the year.

You need

The worksheet each; the self-check quiz at the bottom of the unit page for the game.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part B; start the second with Part C and the quiz.

Watch for these ideas

• Adding the flight time but forgetting the change of zone.
• Giving one city’s time for the whole group of callers.
• Assuming the gap between two cities is the same all year.

Answers

• Part A: Perth 23:55 + 4 h 15 min lands at 07:10 in Sydney, the next day; Sydney 09:30 + 5 h 10 min lands at 11:40 in Perth, the same day; Sydney 21:30 + 13 h 40 min lands at 16:10 in Los Angeles, the same day.
• Part B: any time from 20:00 to 22:00 UTC works, from Sydney 07:00, London 20:00, New York 15:00 to Sydney 09:00, London 22:00, New York 17:00.
• Part C: right in June (2 h); in January Sydney uses daylight saving and Perth does not (3 h).
• Part D: Los Angeles is 19 h behind, more than the 13 h 40 min flight: 16:10, the same day.

Planning across zones

Offsets in January: Sydney UTC+11 · Perth UTC+8 · Auckland UTC+13 · Tokyo UTC+9 · London UTC+0 · New York UTC−5 · Los Angeles UTC−8

A. When do they land?

B. A call for three cities

A class in Sydney wants a video call with schools in London and New York in January. Everyone must be between 7:00 am and 10:00 pm local time. Find a time that works, and give it in all three cities.

C. Find the mistake

Tom says, “Perth is always 2 hours behind Sydney.” When is Tom right, and when not? Explain.

D. Stretch: landing before take-off

Look at your answer for the flight to Los Angeles. Explain how it can land at an earlier clock time than it left, on the same date.

The duration loop

For Day 2, one set for the class: twelve cards

Give out every card. The student with “Start” reads both lines aloud. Whoever has the time that answers the question reads their card next, and so on until the loop comes back to the start.

Teacher note: the loop runs 06:15 → 09:05 → 12:45 → 13:30 → 16:10 → 17:55 → 21:10 → 23:45 → 00:20 → 03:20 → 04:30 → 05:20 → 06:15, twelve hops that add to 24 hours.

Same-instant cards (June)

For Day 3, one set per pair: twelve clocks at three instants

Every card shows a local time in June. Sort the cards into three groups, A, B and C, so that the clocks in each group show the same instant. The groups are not the same size. Use the offsets on your worksheet; Tokyo is UTC+9, Singapore UTC+8 and Auckland UTC+12 in June.

Teacher note: A = 01:00 UTC: cards 3, 8, 11; B = 06:30 UTC: cards 2, 5, 9, 12; C = 11:00 UTC: cards 1, 4, 6, 7, 10.

What we know: Time and time zones

Work on your own. Show your hops and conversions.

1. Write 7:35 pm in 24-hour time, and 00:40 in 12-hour time. ______________________
2. How long is it from 08:50 to 13:25? ______________________
3. A plane leaves at 21:40 and lands at 06:15 the next morning, in the same time zone. How long is the flight? ______________________
4. A concert starts at 7:45 pm and runs for 2 h 25 min. When does it finish? ______________________
5. In June it is 4:00 pm in Brisbane. What time is it in Perth? ______________________
6. In January it is 4:00 pm in Brisbane. What time is it in Sydney? ______________________
7. In January, London is UTC+0 and Tokyo is UTC+9. When it is 10:00 in London, what time is it in Tokyo? ______________________
8. Kai says, “1.5 hours is 1 hour 50 minutes.” Is Kai right? Explain. ______________________

Answers and marking guide

Answers with working

1. 7:35 pm = 19:35 (add 12 after noon); 00:40 = 12:40 am (just after midnight).
2. 4 h 35 min: 08:50 to 09:00 is 10 min, to 13:00 is 4 h, to 13:25 is 25 min.
3. 8 h 35 min: 21:40 to midnight is 2 h 20 min, then 6 h 15 min to 06:15.
4. 10:10 pm.
5. Perth is 2 hours behind Brisbane in June: 2:00 pm.
6. Sydney uses daylight saving in January and Brisbane does not, so Sydney is 1 hour ahead: 5:00 pm.
7. 10:00 + 9 h = 19:00 the same day.
8. No: 1.5 hours is 1 hour and half an hour, 1 hour 30 minutes.

A quick three-level guide

Eight questions, four ideas. A student at standard answers most questions with hops or a conversion shown.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: 12- and 24-hour time, durations, Australian zones, world zones and planning.