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Measurement - Telling Time and Time Intervals

Grade 3IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Understanding the Analog Clock: An analog clock is a circular face with numbers from 11 to 1212. It features two main hands: the short 'hour hand' and the long 'minute hand.' The hour hand indicates the current hour, while the minute hand indicates how many minutes have passed in that hour. If the minute hand is at 1212, we say it is 'o'clock.'

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Telling Time to the Minute: Each large number on the clock represents a 55-minute interval (e.g., 1=51 = 5 mins, 2=102 = 10 mins). Between these numbers are 44 small tick marks, each representing 11 minute. To find the exact time, count by 55s to the nearest large number and then count the individual tick marks to reach the minute hand's exact position.

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Quarter Hours and Half Hours: A clock face can be visualized like a pie cut into four equal slices. 'Quarter past' refers to 1515 minutes past the hour (minute hand at 33). 'Half past' refers to 3030 minutes past the hour (minute hand at 66). 'Quarter to' refers to 4545 minutes past the hour (minute hand at 99), meaning there are 1515 minutes left until the next hour begins.

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AM and PM Cycles: A single day consists of 2424 hours, divided into two 1212-hour cycles. AMAM (Ante Meridiem) covers the time from midnight (12:00 midnight12:00 \text{ midnight}) until just before noon. PMPM (Post Meridiem) covers the time from noon (12:00 noon12:00 \text{ noon}) until just before midnight. For example, 7:00 AM7:00 \text{ AM} is breakfast time, and 7:00 PM7:00 \text{ PM} is dinner time.

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Time Intervals (Elapsed Time): Elapsed time is the duration or the 'amount of time' that passes between a start time and an end time. This can be visualized using a linear time-line where you make 'jumps' of hours and minutes. For instance, if you start a game at 2:002:00 and end at 2:452:45, you have made a 4545-minute jump on the timeline.

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Digital Clock Representation: Digital clocks display time using numbers separated by a colon (HH:MMHH:MM). The digits to the left of the colon represent the hour (11 through 1212), and the digits to the right represent the minutes (0000 through 5959). If the minutes are less than 1010, a leading zero is used, such as 4:084:08.

📐Formulae

1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes}

1 minute=60 seconds1 \text{ minute} = 60 \text{ seconds}

1 day=24 hours1 \text{ day} = 24 \text{ hours}

Half hour=30 minutes\text{Half hour} = 30 \text{ minutes}

Quarter hour=15 minutes\text{Quarter hour} = 15 \text{ minutes}

Elapsed Time=End Time−Start Time\text{Elapsed Time} = \text{End Time} - \text{Start Time}

💡Examples

Problem 1:

A clock shows the hour hand slightly past the 55 and the minute hand pointing exactly at the 88. What time is shown on the clock?

Solution:

Step 1: Look at the hour hand. It is past the 55 but has not reached the 66, so the hour is 55. \ Step 2: Look at the minute hand. It points at the 88. Since each number represents 55 minutes, calculate 8×5=408 \times 5 = 40 minutes. \ Step 3: Combine the hour and minutes to get the time: 5:405:40.

Explanation:

To tell time on an analog clock, identify the last hour the hour hand passed and multiply the number the minute hand points to by 55.

Problem 2:

Maya started her swimming lesson at 3:45 PM3:45 \text{ PM} and finished at 4:30 PM4:30 \text{ PM}. How many minutes long was her lesson?

Solution:

Step 1: Calculate the minutes from the start time (3:453:45) to the next full hour (4:004:00). 60−45=1560 - 45 = 15 minutes. \ Step 2: Calculate the minutes from the full hour (4:004:00) to the end time (4:304:30). This is 3030 minutes. \ Step 3: Add the two durations together: 15 minutes+30 minutes=45 minutes15 \text{ minutes} + 30 \text{ minutes} = 45 \text{ minutes}.

Explanation:

Using the 'jump' method on a timeline, we first move to the nearest hour to make calculations easier, then add the remaining minutes to find the total elapsed time.