128. Time Units, Time Formats and Time Zones

Learning Intentions

• convert between different units of time
• convert between times in 24-hour time and a.m./p.m.
• Use a time zone map to relate times in different locations in the world

Pre-requisite Summary

• Know that time is measured in units such as seconds, minutes and hours
• Know that minute seconds and hour minutes
• Know that there are hours in a day
• Be able to read analogue and digital times
• Understand the meaning of a.m. and p.m.
• Know that places around the world can have different local times
• Be able to add and subtract whole numbers when calculating time differences
• Understand that a time zone map shows offsets from a reference time

Worked Examples

Worked Example 1

Convert between units of time:

a) hours to minutes

b) minutes to hours and minutes

c) days to hours

Worked Example 2

Convert between units of time:

a) seconds to minutes

b) weeks to days

c) hours to days

Worked Example 3

Convert between 24-hour time and a.m./p.m.:

a)

b)

c)

Worked Example 4

Convert between 24-hour time and a.m./p.m.:

a) p.m.

b) a.m.

c) a.m.

Worked Example 5

Use a time zone map to relate times:

a) If it is p.m. in London and Tokyo is hours ahead, what time is it in Tokyo?

b) If it is a.m. in Sydney and Perth is hours behind, what time is it in Perth?

Worked Example 6

Use a time zone map to relate times:

a) If it is a.m. in Brisbane and Auckland is hours ahead, what time is it in Auckland?

b) If it is p.m. in New Delhi and Dubai is hours behind, what time is it in Dubai?

Problems

Problem 1

Convert between units of time:

a) hours to minutes

b) minutes to hours and minutes

c) days to hours

Problem 2

Convert between units of time:

a) seconds to minutes

b) weeks to days

c) hours to days

Problem 3

Convert between 24-hour time and a.m./p.m.:

a)

b)

c)

Problem 4

Convert between 24-hour time and a.m./p.m.:

a) p.m.

b) p.m.

c) a.m.

Problem 5

Use a time zone map to relate times:

a) If it is p.m. in London and Paris is hour ahead, what time is it in Paris?

b) If it is a.m. in Melbourne and Adelaide is hours behind, what time is it in Adelaide?

Problem 6

Use a time zone map to relate times:

a) If it is a.m. in Brisbane and Wellington is hours ahead, what time is it in Wellington?

b) If it is p.m. in Singapore and Bangkok is hour behind, what time is it in Bangkok?

Exercises

Understanding and Fluency

Exercise 1.

Complete each statement:

a) minute seconds

b) hour minutes

c) day hours

d) week days

Exercise 2.

Convert between units of time:

a) hours to minutes

b) minutes to hours

c) seconds to minutes

d) weeks to days

Exercise 3.

Convert between units of time:

a) minutes to hours and minutes

b) seconds to minutes and seconds

c) hours to days and hours

d) days to hours

Exercise 4.

Convert each 24-hour time to a.m./p.m.:

a)

b)

c)

d)

Exercise 5.

Convert each a.m./p.m. time to 24-hour time:

a) a.m.

b) p.m.

c) a.m.

d) p.m.

Exercise 6.

Use the given time zone difference to Solve the new time:

a) It is p.m. in Brisbane. Sydney is hour ahead. What time is it in Sydney?

b) It is a.m. in Perth. Brisbane is hours ahead. What time is it in Brisbane?

c) It is p.m. in Adelaide. Darwin is hours behind. What time is it in Darwin?

Exercise 7.

Use the given time zone difference to find the new time:

a) It is p.m. in London. Rome is hour ahead. What time is it in Rome?

b) It is a.m. in Tokyo. Seoul is in the same time zone. What time is it in Seoul?

c) It is p.m. in Dubai. Mumbai is hours ahead. What time is it in Mumbai?

Exercise 8.

Solve each:

a) A movie lasts minutes. Write this in hours and minutes

b) A flight leaves at . Write this in a.m./p.m. time

c) If it is a.m. in Brisbane and Auckland is hours ahead, what time is it in Auckland?

Reasoning

Exercise 9.

Explain why in 24-hour time is the same as p.m.

Exercise 10.

A student says that a.m. is midday. Explain the mistake.

Exercise 11.

Noah says that if one city is hours ahead, you subtract hours from the time. Is he correct? Explain.

Exercise 12.

Explain why a time zone map is useful when comparing times in different countries.

Exercise 13.

A student says that minutes is hours because the digits look similar. Describe the error.

Problem-solving

Exercise 14.

A train journey lasts minutes. Write the journey time in hours and minutes.

Exercise 15.

A concert starts at . Write this in a.m./p.m. time.

Exercise 16.

If it is a.m. in Brisbane and Tokyo is hour behind, what time is it in Tokyo?

Exercise 17.

If it is p.m. in New York and Los Angeles is hours behind, what time is it in Los Angeles?

Exercise 18.

A live event is shown at p.m. in London. If Johannesburg is hour ahead, what time is it there?

Exercise 19.

A lesson begins at a.m. and lasts minutes. What time does it finish, written in 24-hour time?

Potential Misunderstandings

• Students may confuse the conversion facts for seconds, minutes and hours
• Students may divide when they should multiply, or multiply when they should divide, when converting time units
• Students may think minutes equals hour because of the base- number system
• Students may confuse a.m. and p.m.
• Students may think a.m. is noon instead of midnight
• Students may think p.m. is midnight instead of noon
• Students may forget to add when converting p.m. times to 24-hour time after midday
• Students may incorrectly write as p.m.
• Students may add or subtract time zone differences in the wrong direction
• Students may ignore half-hour time differences on a time zone map
• Students may forget to adjust the day when a time crosses midnight