Class 5 Mathematics Chapter 12: Racing Seconds

Race day at school

Three friends line up for the 200 metre walking race. Ira, Dev and Nila stand on the white line. Sir holds a stopwatch in his hand. He starts it the moment the whistle blows. All three walk fast and finish almost together.

Who won?

Sir looks at the stopwatch. Ira took 2 min 5 s. Dev took 2 min 8 s. Nila took 2 min 11 s. Every one of them took about two minutes. So how did Sir pick the winner?

The tiny unit

The numbers after the minutes are seconds. A second is a very short piece of time. One clap of your hands takes about one second. A quick breath in and out takes two or three. Seconds let us see small gaps that minutes would hide.

Sixty in a minute

Sixty seconds make one minute. We write it as 1 min = 60 s. That is the same pattern as the hour. An hour holds sixty minutes, and a minute holds sixty seconds.

The thin hand

Look at a wall clock. It has three hands. The short fat hand shows the hour. The longer hand shows the minutes. The thinnest hand is the fastest of all. It moves on one tick every second.

One round, one step

Watch the thin hand go round once. It passes all sixty little marks on the way. When it comes back to the top, the minute hand moves on by one step. One minute has gone.

Reading the seconds

The little marks round the face are seconds. The printed numbers help you count them in fives. The thin hand on the number 4 means twenty seconds. On the number 9 it means forty-five seconds.

Seconds or minutes?

Some jobs are over in seconds. Snapping your fingers, switching on a fan, writing your name. Other jobs need minutes. Brushing your teeth, filling a bucket, walking to the shop at the corner. Guess the unit first, then check it against a clock.

Back to the race

Now the stopwatch makes sense. Ira was quickest at 2 min 5 s. Nila was last at 2 min 11 s. Only six seconds lay between them. Without seconds, Sir could not have named a winner.

Remember

• One minute is sixty seconds.
• The thinnest hand on a clock counts seconds.
• One full round of that hand is one minute.
• Short jobs take seconds, longer jobs take minutes.

Scenario:

A class times how long each child can stand on one leg. Ravi counts out loud to sixty and says a minute has passed. His teacher asks the class to check against the clock's thinnest hand. Ravi's count took only forty seconds, because he was counting faster than the hand moved. The class tries again, matching each number to one tick. Now the counts agree. Ravi sees why the clock is needed. A second is a fixed length. A person counting can speed up without noticing. The hand is the measure, not the voice.

Analysis:

Ravi counted sixty and forty seconds passed. A second is fixed, and a voice is not, which is what the second hand settles.

Activity:

Count to sixty while watching a clock's second hand. Write how far off you were, then try again.

Title:

Make your own one minute

What You Notice:

Most children write far more names than they guessed. A minute feels short when you are busy and long when you sit still, but the thin hand always takes sixty ticks.

A stopwatch at a big sports meet can split one second into a hundred parts.

Your heart beats about once every second when you are sitting still.

Seconds in a minute — Sixty ticks, one minute gone. — Count sixty ticks of the thin hand and exactly one minute has passed.

One list, one unit

Sports day is on Friday. Meera has to read out the plan on the loudspeaker. The plan is a mess. The march past says one hour. The races say ninety minutes. The prize giving says two hours fifteen minutes. Meera wants every event in minutes.

The sixty rule

She writes the rule at the top of her page. One hour is sixty minutes. One minute is sixty seconds. Every change of unit in time uses that same number sixty. It is never a hundred, however much a hundred may feel right.

Hours into minutes

The march past takes one hour. That is sixty minutes. Two hours would be two lots of sixty, which is a hundred and twenty. Three hours would be three lots of sixty, which is a hundred and eighty.

The time ladder

Meera draws a ladder of hours with the minutes below. One hour sits above sixty. Two hours sit above a hundred and twenty. Each step to the right adds sixty more minutes. The ladder never skips.

A mixed time

Prize giving takes two hours fifteen minutes. Meera does it in two parts. Two hours give a hundred and twenty minutes. Then she adds the fifteen minutes. The answer is a hundred and thirty-five minutes.

Going back up

Now she meets ninety minutes. She wants hours. Sixty minutes make one whole hour. Thirty minutes are left over. So ninety minutes is one hour thirty minutes.

Sharing into sixties

The same works for bigger numbers. Take two hundred minutes. Three sixties make a hundred and eighty. Twenty minutes are left over. So two hundred minutes is three hours twenty minutes.

Minutes into seconds

The lower rung of the ladder works in the same way. One minute is sixty seconds. Four minutes are four lots of sixty, which is two hundred and forty seconds.

Seconds back to minutes

A relay took two hundred seconds. Three sixties make a hundred and eighty. Twenty seconds are left over. So the relay took three minutes twenty seconds. Meera checks it the other way round to be sure.

Why one unit helps

Meera now has one list in minutes only. She can add the times straight down the page. Mixed units cannot be added like that. A timetable printed in minutes saves everybody that trouble.

Remember

• One hour is sixty minutes, one minute is sixty seconds.
• Going down a rung, multiply by sixty.
• Going up a rung, share by sixty.
• The leftover stays as the smaller unit.

Scenario:

A film lasts 2 hours 30 minutes. A class is asked for that in minutes. Nita writes 230, putting the numbers together. Her teacher asks how many minutes are in one hour. Sixty. So two hours is 120 minutes, and 30 more makes 150. Nita sees that she had joined the digits instead of converting them. The class checks the other direction too. Turning 150 minutes back into hours means dividing by 60, which gives 2 with 30 left over. Going to a smaller unit multiplies, and going to a bigger unit divides.

Analysis:

Writing 230 treats the digits as a label rather than a quantity. Sixty is the conversion, and it works both ways.

Activity:

Convert three times from hours and minutes into minutes. Then convert each answer back and check it matches.

Title:

Turn your day into minutes

What You Notice:

The total in minutes looks much bigger than the same total in hours, yet both describe the very same day. Changing the unit changes the number, never the time.

A cricket over takes about four minutes, which is 240 seconds of play.

A school day of six hours is 360 minutes long.

Which way to work — Down we times, up we share. — Hours down to minutes means multiply. Minutes up to hours means share into sixties.

Meera plans her Sunday

Meera writes a plan for Sunday. Homework in the morning. Cricket in the evening. A film at night. Her mother asks three questions. When will you be back? How long will you play? When must you begin?

Going to play

Meera leaves for the ground at 4:20 in the afternoon. She will play for 1 hour 55 minutes. When will she be home? She hops forward from the start.

Hours first

One hour after 4:20 is 5:20. That is the big hop done. Now the small hop. Fifty-five minutes after 5:20 brings her to 6:15. So Meera is home at 6:15 p.m.

How long did it take?

Her homework began at 9:40 in the morning and ended at 11:15. How long was that? Hop from 9:40 to 10:40. That is one hour. Then hop from 10:40 to 11:15. That is thirty-five minutes more.

Never plain subtraction

Some children write 11:15 take away 9:40 in a column. That is wrong. An hour holds sixty minutes, not a hundred. The hopping way keeps the sixty rule safe. Her homework took 1 hour 35 minutes.

Working backwards

The film ends at 9:10 at night and runs for 2 hours 30 minutes. When did it start? Hop back two hours to 7:10. Then hop back thirty minutes to 6:40. So the film began at 6:40 p.m.

Two names, one moment

A station clock shows 18:15 hours. Meera is puzzled. That is the same moment as 6:15 in the evening. Railways count straight on past twelve instead of starting again. So every hour of the day gets one name of its own.

Reading the long clock

For a morning time the two clocks agree. Nine in the morning is 09:00 hours. For an afternoon or evening time, add twelve to the hour. Half past two becomes 14:30 hours.

Coming back down

To go the other way, take twelve off any hour above twelve. So 20:45 hours is 8:45 in the evening. Anything below twelve is a morning time already. Meera tries a few from her mother's bus ticket and gets them all right.

Remember

• Hop by hours first, then by minutes.
• Never subtract times like plain numbers.
• Add twelve for an afternoon hour on the long clock.
• Take twelve off to come back to the short clock.

Scenario:

The Konkan Railway runs beside the sea in Maharashtra. Aarti and her grandfather board a train at Ratnagiri. The station board shows the departure as 18:15 hours. Her grandfather says they will reach Madgaon at 21:40 hours. Aarti has never seen a clock counting past twelve. Her grandfather explains that every railway in India uses it, so that nobody mixes up a morning train with an evening one. Outside the window the light fades and fishing boats come home. Aarti wants to know how long she must sit before the train pulls in. She also wants to tell her mother the arrival time in the ordinary way, because her mother reads the short clock.

Analysis:

Time hops, the 24-hour clock and a real railway route join maths with the geography of the coast.

Activity:

Copy three timings from a bus or train ticket and write each one on an ordinary clock too.

Railway stations in India print every timing on the 24-hour clock.

Midnight is written as 00:00 hours, the very start of a new day.

Working out a time gap — Hours first, minutes after. — Take the big hour hops, then finish with the small minute hops.