Measurement - Calculating with Time

Units of Time and Conversion: Time is measured in seconds ($s$), minutes ($min$), hours ($h$), days, weeks, and years. To convert from a larger unit to a smaller unit, such as hours to minutes, multiply by $60$. To convert from a smaller unit to a larger unit, such as seconds to minutes, divide by $60$. Imagine a conversion ladder where moving down from hours to minutes involves multiplying by $60$, and moving up from minutes to hours involves dividing by $60$.

12-hour vs. 24-hour Clock: The 12-hour clock uses 'am' for morning and 'pm' for afternoon/evening, resetting at $12:00$. The 24-hour clock continues from $12:00$ to $13:00$ and goes up to $23:59$. To convert pm times to 24-hour format, add $12$ to the hours (e.g., $3:00$ pm becomes $15:00$). Visually, you can think of a double-layered clock face where the inner circle shows $1$ to $12$ and the outer circle shows $13$ to $24$.

Time Intervals and Elapsed Time: This is the amount of time that passes between a start time and an end time. A helpful visual strategy is the 'Empty Number Line' method: mark the start time, make 'jumps' to the next whole hour, then jump in hour blocks, and finally jump the remaining minutes to reach the end time.

Adding Time: When adding time durations, add the minutes and hours separately. If the minutes total $60$ or more, you must 'regroup' or carry over. For every $60$ minutes, add $1$ to the hours column and keep the remaining minutes. For example, $50 \text{ min} + 20 \text{ min} = 70 \text{ min}$, which is visually regrouped as $1 \text{ hour}$ and $10 \text{ minutes}$.

Subtracting Time: When subtracting time, if the minutes in the second time are greater than the first, you must 'borrow' $1$ hour from the hours column and add $60$ minutes to the minutes column. Visually, this is like taking a $1$-hour block and breaking it into $60$ smaller $1$-minute pieces to make the subtraction possible.

The Calendar System: A standard year has $365$ days, while a leap year has $366$ days (occurring every $4$ years). Months vary in length ($28$, $30$, or $31$ days). A common visual aid is the 'Knuckle Rule': peaks on your knuckles represent $31$-day months, while the dips between them represent shorter months.

Time Zones: The world is divided into time zones based on Longitude. The starting point is the Prime Meridian ($0^{\circ}$ longitude) in Greenwich, known as GMT or UTC. As you move East, you add hours; as you move West, you subtract hours. Imagine a world map divided into vertical strips, each representing a $1$-hour difference.