E. Spatial Sense · Angles, Rectangles, Grids and Measurement

Elapsed Time: How Long Did It Take?

E2.3 A1About 40 minutes

Learning goals

I can find how much time has passed between a start time and an end time.
I can find an end time when I know the start time and how long something lasts.
I can find a start time by working backward.
I can use a timeline to solve elapsed time problems, even across noon, midnight and days.

Words to know

elapsed time
The amount of time that passes from the start of something to the end.

start time
The time something begins.

end time
The time something finishes.

timeline
A number line for time. We draw jumps on it to count time.

a.m. and p.m.
a.m. is from midnight to noon. p.m. is from noon to midnight.

noon and midnight
Noon is 12:00 in the middle of the day. Midnight is 12:00 in the middle of the night.

Let's start with a field trip

Your class leaves for the science centre at 9:40 a.m. and arrives at 11:15 a.m. How long was the bus ride?

The time that passes from start to end is called elapsed time. You can't just subtract 9:40 from 11:15 like ordinary numbers, because an hour has 60 minutes, not 100. Instead, we count on using friendly times.

The bus leaves at 9:40 a.m. and arrives at 11:15 a.m.

Count on with a timeline

Write the start time at the left of a line.
Jump to the next o'clock time (the next hour).
Jump by whole hours as far as you can without passing the end time.
Jump the minutes that are left to reach the end time.
Add all the jumps.

Worked example

Example 1: The bus ride

How long is it from 9:40 a.m. to 11:15 a.m.?

From 9:40 to 10:00 is 20 minutes.
From 10:00 to 11:00 is 1 hour.
From 11:00 to 11:15 is 15 minutes.
Add the jumps: 1 h + 20 min + 15 min = 1 h 35 min.

The bus ride took 1 hour 35 minutes.

A timeline from 9:40 to 11:15: jump 20 minutes to 10:00, 1 hour to 11:00, then 15 minutes to 11:15.

Worked example

Example 2: Find the end time

Soccer practice starts at 4:45 p.m. and lasts 1 h 30 min. When does it end?

Add the hour first: 4:45 + 1 h = 5:45.
Now add 30 minutes. Jump 15 minutes to the next hour: 5:45 + 15 min = 6:00.
There are 30 − 15 = 15 minutes left: 6:00 + 15 min = 6:15.

Practice ends at 6:15 p.m.

Worked example

Example 3: Across noon

A skating party goes from 10:50 a.m. to 1:20 p.m. How long is it?

10:50 to 11:00 is 10 minutes.
11:00 to 1:00 is 2 hours (11 to 12 is 1 hour, and 12 to 1 is another hour).
1:00 to 1:20 is 20 minutes.
Add: 2 h + 10 min + 20 min = 2 h 30 min.

The skating party is 2 hours 30 minutes long.

A timeline from 10:50 a.m. to 1:20 p.m. It crosses noon (12:00). Jump 10 minutes, then 2 hours, then 20 minutes.

Worked example

Example 4: Find the start time (work backward)

A movie ends at 8:10 p.m. It is 1 h 45 min long. When did it start?

Go back 1 hour: 8:10 − 1 h = 7:10.
Now go back 45 minutes. Go back 10 minutes to the hour: 7:10 − 10 min = 7:00.
There are 45 − 10 = 35 minutes left: 7:00 − 35 min = 6:25.
Check by counting on: 6:25 + 1 h = 7:25. Then 7:25 + 35 min = 8:00, and 8:00 + 10 min = 8:10. That is 1 h 45 min in all. ✔

The movie started at 6:25 p.m.

Worked example

Example 5: Overnight

Zara goes to bed at 8:30 p.m. and wakes up at 7:00 a.m. How long does she sleep?

8:30 p.m. to midnight (12:00): 30 min to 9:00, then 3 hours to 12:00. That is 3 h 30 min.
Midnight to 7:00 a.m. is 7 hours.
Add: 3 h 30 min + 7 h = 10 h 30 min.

Zara sleeps 10 hours 30 minutes.

A timeline from 8:30 p.m. to 7:00 a.m., crossing midnight: 3 h 30 min, then 7 h.

Worked example

Example 6: Elapsed time in days

In 2026, Thanksgiving is on Monday, October 12. Halloween is on Saturday, October 31. How many days is it from Thanksgiving to Halloween? How many weeks and days?

Both dates are in October, so subtract: 31 − 12 = 19 days.
19 days = 2 weeks (14 days) and 5 days left over.

19 days, or 2 weeks 5 days.

Watch out!

Don't subtract times like regular numbers. If you work out 1115 − 940, you get 175, which looks like "1 hour 75 minutes". That can't be right, because an hour has only 60 minutes! The real answer is 1 h 35 min. Use a timeline and jump to friendly o'clock times.

Math talk: check your answer

After you find an elapsed time, check it the other way. If you counted on from the start, count back from the end (or add the elapsed time to the start time). If both ways match, you can be confident. If not, look for the jump that went wrong. Don't give up!

Just for fun

Q: Why did the student stare at the clock all through recess?

A: She wanted to see time fly! (It doesn't, but a number line will tell you exactly how much went by.)

Hands-on activity

My day timeline

You need: a long strip of paper (or tape two sheets together), a pencil, a ruler and a clock.

On a Saturday or Sunday, write the start time and end time of 5 things you do: breakfast, playing outside, a show, reading, dinner.
For each one, draw a small timeline and find the elapsed time with jumps.
Which activity took the longest? The shortest?
Find how long it was from when you woke up to when you went to bed.
Bonus: use a calendar to find how many days until your birthday, or until the next holiday. Write it in weeks and days.

Math talk: "Which problem was hardest? What strategy helped you?"

Your turn

How long is it from 2:15 p.m. to 4:00 p.m.?

How long is it from 8:50 a.m. to 10:20 a.m.?

A hockey practice starts at 5:30 p.m. and lasts 1 h 15 min. When does it end?

Recess is 20 minutes long and ends at 10:35 a.m. When did it start?

How long is it from 11:40 a.m. to 2:10 p.m.?

A pie goes in the oven at 3:50 p.m. and needs 45 minutes. When should it come out?

More practice: warm-up

How long is it from 3:00 to 5:00?

How long is it from 7:30 to 8:00?

What time is it 1 hour after 9:20?

What time is it 15 minutes after 6:45?

Is 10:00 p.m. in the morning or at night?

More practice: on your own

A swim lesson goes from 6:25 p.m. to 7:10 p.m. How long is it?

A train leaves at 9:35 a.m. The trip takes 2 h 40 min. When does it arrive?

Leo read from 7:45 p.m. to 8:20 p.m. Mia read for 40 minutes. Who read longer, and by how much?

A camp starts on Monday, July 6 and ends on Friday, July 17. How many days is that, counting both the first and last days?

A baker starts bread at 10:30 p.m. and it is ready at 6:00 a.m. How long does it take?

Challenge

A family drives to a cottage. They leave at 8:45 a.m., stop for lunch for 50 minutes, and arrive at 2:05 p.m. How much time did they spend driving?

Winter break starts on Saturday, December 19, 2026 and school starts again on Monday, January 4, 2027. How many days are there from December 19 to January 4?

Kim says: "From 9:50 to 11:10 is 1 hour 60 minutes because 11:10 − 9:50 is 1:60." What is wrong, and what is the right answer?

Check your understanding

Quiz

How long is it from 1:30 p.m. to 3:00 p.m.?

A game starts at 6:40 p.m. and lasts 2 hours. When does it end?

How long is it from 10:45 a.m. to 12:15 p.m.?

A movie is 1 h 20 min long and ends at 4:00 p.m. When did it start?

What is the first jump you should make to find the time from 7:35 to 9:10?

How long is it from 9:00 p.m. to 6:00 a.m.?

For parents and teachers

Big idea: The Ontario curriculum (E2.3) asks Grade 4 students to solve problems involving elapsed time by applying the relationships between units of time. A reliable strategy is to count on with a timeline: jump to the next hour, jump whole hours, then jump the remaining minutes.

Common difficulties:

Subtracting times like regular numbers. 11:15 − 9:40 is not 1:75 or 175. Time uses groups of 60.
Crossing noon or midnight. Children may think 11:00 to 1:00 is "10 hours". Count the hours on a clock face.
Calendar problems. Decide whether to count both the first and last day ("Monday to Friday" camp is 5 days, but from Monday to Friday is 4 days later).

How to help: Ask elapsed-time questions in daily life: "Dinner is at 5:45. It's 4:50 now. How long until dinner?" Let your child set an oven timer and figure out when food will be ready. A clock with hands is very helpful for seeing jumps.