Last bus from the fair

The fair ends at 3:48 and the last bus leaves at 4:15. Tanmay says 415 − 348 = 67, so they have over an hour. Do they?

About 30 minutes
Class 5
Mathematics and money

What you will learn: Work out how long it is from one time to another, across the hour, by counting up to the hour and then on.

What should I know first?

If this feels new, try this first. It is fine to go back.

Dadi's clock: o'clock, half past and quarter past Class 3

Small test at the end: scroll down to the end of this page for five short questions that check what you have learnt. Tap an answer, then press Check answer. Go to the questions ↓

Jump to: Check yourself · For grown-ups · For teachers

Safety first

Stay with a grown-up at bus stops and near roads.

Keep it safe:

Stay with a grown-up at bus stops and near roads. Use made-up timetables for practice.
If you use counters to mark the jumps, keep them away from babies: nothing goes in the mouth.

You will need

Paper and a pencilFor the time line.
A clock with handsA real one, or one drawn on paper with a cardboard hand.
A bus or train timetableReal or made up. The one on this page is made up.

Time: About 30 minutes.

What do you think?

Tanmay says 415 − 348 = 67, so there are 67 minutes from 3:48 to 4:15. Is he right?

Make a prediction and write one reason for it. Then tap the guess closest to yours to see how to test it. It is fine to change your mind after checking.

Yes, 67 minutes

Let's test it. Put a clock at 3:48 and turn the minute hand to 4:15, counting the minutes. Does it take more than an hour?

No, it is less than that

How much less? Count from 3:48 up to 4:00 first, then on to 4:15, and check your guess.

Not sure

That is fine. Try it on a clock face, or draw a line from 3:48 to 4:15 and mark 4:00 on it.

Need a hint?

From 3:48, how many minutes to get to 4:00? Then how many more to 4:15?

The story

The school fair is nearly over. Tara, Tanmay and Dhruv are helping Dadi pack up her chai stall. "The last bus leaves at 4:15," says Dadi. "What time is it now?" Dhruv looks at the clock: 3:48. Tanmay does a quick sum on his hand. "415 take away 348 is 67. We have 67 minutes. Plenty of time for one more cup!" Tara frowns. "An hour is not a hundred minutes."

The idea

Times on a clock count 60 minutes in an hour, then start again at 0.

So 4:15 − 3:48 is not 67 minutes. Ordinary subtraction treats 4:15 as 415, as if an hour had 100 minutes.

A safer way: jump from the start time up to the next hour, then from the hour to the end time, and add the jumps.

For longer times, jump to the next hour, then in whole hours, then the last few minutes.

A time line from 3:48 to 4:15 with a mark at 4:00. The first jump, from 3:48 to 4:00, is 12 minutes. The second jump, from 4:00 to 4:15, is 15 minutes. Together they make 27 minutes.

Worked example

How long is Dadi's stall open?

Dadi opens her chai stall at 6:30 in the morning and closes it at 9:10. How long is it open?

Jump from 6:30 to the next hour, 7:00: 30 minutes.
Jump in whole hours from 7:00 to 9:00: 2 hours.
Jump from 9:00 to 9:10: 10 minutes.
Add the jumps: 30 minutes + 2 hours + 10 minutes.

The stall is open for 2 hours 40 minutes.

Try it

Draw a time line.
Draw a long line. Write the start time at the left end and the end time at the right end.
Mark the hour.
Find the next o'clock after the start time. Mark it on the line.
Jump to the hour.
Count the minutes from the start up to the hour. Write the number over a curved jump.
Jump to the end.
Count the minutes (and any whole hours) from that hour to the end time. Write it over a second jump.
Add the jumps.
Add the jumps together. If the minutes make 60 or more, change 60 minutes into 1 hour.
Check on a clock.
Set a clock to the start time and turn the minute hand to the end time. Count as you go. Do you agree?

What you make (paper or offline)

Your timetable puzzle card

A made-up timetable of four buses from the fair, with the times each leaves and reaches home.

Copy the timetable, or make your own for a bus, train or tuition class.

Write two puzzles under it, like "How long is the journey?" or "I reach the stop at 4:20. How long do I wait?"

Swap cards with someone and check each other's answers with time lines.

Make it on paper. Keep it with you. Nothing to upload.

What did we find out?

Read this after you have tried it. Look back at your guess and your reason first.

An hour has 60 minutes, not 100, so taking one time from another like ordinary numbers can go wrong.

Jump to the next hour first, then jump on to the end time, and add the jumps.

From 3:48 to 4:15 is 12 + 15 = 27 minutes. They have time, but not for one more cup.

Think back

Why was Tanmay's 67 minutes too many?

When could the "jump to the hour" way save you from missing a bus or train?

Investigate further

Find a real bus or train timetable. Which journey is the longest?
How many minutes are there from 11:45 in the morning to 1:10 in the afternoon?

Can you use it here?

Look at when your school day starts and ends. How long is it? Jump to the hour first.

Ask someone at home

Ask someone at home when they leave for work or the market, and when they come back. Work out how long they are away.

No one free to join in? That's fine. You can do it by yourself with drawings, and ask a grown-up to help with the materials.

For grown-upsTap a heading to open it. The safety notes are at the top of the page.

Before you start

Paper, a pencil and a clock with hands (or a paper clock). Keep small counters away from babies; nothing in the mouth.
Find a real timetable if you can: bus, train, school or tuition.

Questions that help

"Where is the next o'clock?"
"How many minutes is the first jump? The second?"
"Does your answer look sensible on the clock?"

What's really going on

Children often subtract times like ordinary numbers (415 − 348). That fails because an hour has 60 minutes, not 100.

Counting up to the hour, then on, is the method adults use in their heads. The time line makes the jumps visible.

The same idea works for dates and days of the week: jump to the end of the month first.

Other ways to do it

No clock? Draw one, with a cardboard minute hand held by a pin (the grown-up handles the pin).
Use the times of a favourite TV programme or a cricket match.

For teachersLearning aims, classroom ideas and what to look for.

Learning aims

Find elapsed time across the hour using a time line.
Read and use a simple timetable.
Explain why subtracting times as ordinary numbers can give a wrong answer.

Subject links

Maths: number line, adding on, units of time.
Class 3 shelf activity "Clock time" (reading the clock).
Social science: travel and timetables in daily life.

These links are general. They have not been checked against a specific board syllabus.

In the classroom

Groups make timetables for a made-up school trip and swap puzzles.
Stand-up time line on the floor: children jump in 5-minute steps.

What to look for

Marks the next hour on the time line without being told.
Changes 60 minutes into 1 hour when adding.
Checks an answer by turning a clock's hands.