TOPIC 6: MEASUREMENT OF TIME – MATHEMATICS STANDARD THREE NOTES
UNITS OF TIME
Time is measured in seconds, minutes, hours, days, weeks, months or years. The relationship between the units of time is as follows:
(a) There are 60 seconds in one minute.
(b) There are 60 minutes in one hour.
(c) There are 24 hours in one day.
(d) There are 7 days in one week.
(e) There are 12 months in one year.
TOOLS FOR MEASURING TIME
Tools for measuring time are clocks, watches and calendars.
A clock is used for measuring time based on the twenty-four hours of a day. There are two types of clocks, namely analogue and digital.
A calendar is used for measuring days, weeks and months of a year.
EXERCISE
The following table shows the time spent by pupils in a game.
Read the information and answer the questions that follow.
1. Who spent the longest time?
2. Who spent the least amount of time?
3. How many seconds did Neema spend?
4. How many seconds did Musa spend?
5. How many seconds did Hassan spend?
6. How many minutes and seconds did Sofia spend?
READING TIME IN THE 12-HOUR FORMAT
When reading an analogue clock, the shortest arrow is the hour-hand.
The longer arrow is the minute-hand; while the longest and thinnest is the second-hand.
All the clock arrows rotate in the clockwise wise direction.
The face of a digital clock displays two pairs of digits. The pairs are separated by a colon (:). The first pair is for hours and the other for minutes. This is illustrated in the following figure.
Study the following diagram, and learn how the clock face is divided.
The minute-hand takes five minutes to rotate from one number to the next on the clock face.
You can read 30 minutes as half an hour, and 15 minutes as quarter an hour. This is illustrated in the following figures.
.
Example l
Draw an analogue clock face that shows 04:00.
Steps:
1. Take a circular object like a 200-shilling coin.
2. Use the circular object and a pencil to draw a circle paper.
3. Divide the circle into 12 equal parts. Put twelve thick marks on the circle to form a clock face.
4. Write the numbers 1, 2, 3 up to 12 facing the thick marks you have placed as shown in the following figure.
5. Draw an hour hand arrow pointing at number 4 from the centre of the circle.
6. Draw a minute-hand arrow pointing at number 12 from the center of the circle.
7. Draw a second-hand arrow pointing number 12.
8. The clock face shows 4 O’clock.
READING THE TIME IN HOURS AND MINUTES
Start reading hours followed by minutes. To read minutes, start at number 12 in the clockwise direction, until the minute-hand is reached.
Example
Draw an analogue clock face that shows 07:15.
Answer
Example
Study the following analogue and digital clock faces, then read the time.
Exercise 2
1. Study the following clock faces and then answer the questions that follow:
(a) Identify the type of clock face in A?
(b) What time does the clock face in B show?
(c) What time does clock face in A show?
(d) What is the difference between clock faces in A and B?
2. Read the following clock faces and then write the time in numerals and in words.
READING TIME IN THE 24-HOUR FORMAT
The following figure shows the 24-hour format that is not read on analogue clock faces.
A day has 12 hours and a night has 12 hours. In the 24 hours format, a day starts after 12:00 midnight.
The 24-hour format is written in four digits. The first two digits on the left indicate hours and the remaining digits indicate minutes.
The following table shows the relationship between time in 12-hour and 24-hour format.
Note: A.m. is a short form of the Latin word “ante- meridian” (before mid-day) and p.m. for “post- meridian” (after mid-day).
Example l
Write 12:30 pm in the 24-hour format and read it.
Answer
12:30 pm is written as 1230 hours in the 24-hour format. It is read as “twelve thirty hours”.
Example 2
Write 0235 hours in the 12-hour format.
Answer
0235 hour is written as 2:35 am in the 12-hour format.
Example 3
Write 10:45 pm in 24-hour format and read it.
Answer
10:45 pm is written as 2245 hours in 24 hour format. It is read as “twenty-two forty-five hours”.
Exercise 3
1. Change 3:47 am to 24-hour format.
2. Write 8:00 pm in 24-hour format.
3. Write 7:00 pm in 24-hour format.
4. Change the 0400 hours to 12-hour format.
5. Write 1700 hours in 12-hour format.
6. Write 2200 hours in 12-hour format.
7. Write the following times in the 24-hour format:
(a) 9:00 am
(b) 6:01 pm
(c) 11:00 am
(d) 12:50 am
(e) 8:34 am
(f) 1:00 pm
(g) 3:45 pm
(h) 4:00 pm
(I) 8:00 am
(j) 5:55 am
RELATIONSHIP BETWEEN UNITS OF TIME
The following diagram shows the relationship of the number of days in a week, weeks in a month, and months in a year.
Note: Time can be measured by counting the number of days, weeks, months or years.
(a) A day has 24 hours.
(b) A week has 7 days.
(c) A month has 4 weeks.
(d) A month has either 28, 29, 30 or 31 days.
(e) A year has 12 months.
NAMES OF WEEK DAYS
One week has seven days. The names of the days are as shown in the following table:
NAMES OF MONTHS IN A YEAR
A year has twelve months. Each month has its own name as shown in the following table.
Exercise 5
1. How many days are there in 24 hours?
2. How many week(s) are there in 7 days?
3. How many weeks are there in a month?
4. How many days are there in a month?
5. Twelve months are equal to ___ years?
6. Bakari bought an airtime for his mobile phone which lasted for 48 hours. How many days do the hours represent?
Calendar
A calendar displays dates, weeks, months and years. It also highlights national and international public holidays.
A calendar helps to identify two types of years:
A short year
A short year is the year in which February has 28 days.
A leap year.
A leap year is the year in which February has 29 days.
The following are the calendars for the year, 2019 and-2020.
Exercise 6
1. Write the names of the months with 30 days.
2. Write the names of the months with 31 days.
3. How many Sundays are there in the month of July this year?
4. Mention the month in which normally schools close for the end of the year holiday.
5. How many days are there in February this year?
Activity: My day in clocks
Instructions: Use a basic drawing software (example, Paint) to create a digital timetable illustrating your daily activities. Draw both analogue and digital clock faces to depict the times you engage in each activity.
Summary
1. On the clock face, the short arrow shows hours, the long arrow shows minutes.
2. One hour is equal to 60 minutes.
3. Time can be measured by counting number of days, weeks, month or year
Vocabulary
Half an hour
A quarter of an hour
30 minutes
15 minutes
REVISION EXERCISE
1. Draw the face of an analogue clock for each of the following times:
(a) Quarter past six (6:15)
(b) Ten o’clock (10:00)
(c) Half past two (2:30)
(d) Forty-five minutes past three or quarter to four (3:45).
2. Write the following times in words:
(a) 12:15
(b) 1:00
(c) 11:30
(d) 2:00
(e) 8:15
(f) 10:15
(g) 1:20
(h) 2:45
3. Choose the item from list B that matches an item from
4. Write the following times in the 12-hour format:
(a) 1930 hours
(b) 2324 hours
(c) 2127 hours
(d) 1513 hours
(e) 0712 hours
(f) 0835 hours
5. Write the following times in the 24-hour format:
(a) 8:10 am
(b) 8:34 pm
(c) 1:05 pm
(d) 11:30 am
(e) 5:55 am
6. Write the total number of days in June, July and August.
7. Write the months that follow each other and each has 31 days.
8. Write 4:45 am in the 24-hour format.
9. What time is 1945 hours in the 12-hour format?
10. How many hours are there from 1500 to 2300?
11. How many days are there in 72 hours?
10. Is this year a leap or a short year:
MORE EXERCISES
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