CCSS.MATH.CONTENT.3.NF.A.2.A: Clock Math and Unit Fractions

We use the terms seconds, minutes, and hours to provide a context for the numbers related to time. Each of these quantities sit on a number line, which allows us measure the distance between two times. The most common use of this measurement is the expression of the time elapsed since midnight.

In this activity, we are focusing on the language related to time. We will look at each time segment and express that quantity as a unit fraction.

There are 60 seconds in one minute. Therefore, each second is 1/60 (“one-sixtieth”) of a minute. In most contexts, saying “one second” makes more sense than saying “1/60” of a minute. We know that if we add 59 more seconds, we will have a total of 60 seconds. We would have a full minute.

We can use an expression to describe this addition:

In both fractions, the numerator indicates what part of the minute is being considered. Also, the denominator is providing the total number of seconds in every minute. When we add all the parts in the above expression, we get a whole minute.

There are also 60 minutes in one minute. Each minute is 1/60 of an hour. We have 24 hours in a day, and each of those hours equals 1/24 (“one-twenty-fourth”) of a day. There are 7 days in a week, so each day is 1/7 (“one-seventh”) of a week.

CCSS.MATH.CONTENT.3.NF.A.2.A: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

BONUS: The 12 Unequal Months

There are 12 months in a year. This means each month is considered 1/12 (“one-twelfth”) of a year. Right? Well, yes and no.

The length of a month can vary between 28 and 31 days. This can be confusing because each month of the year can divided into an unequal amount of days.

We know that unit fractions must represent a single part of a whole quantity that has equal parts.

Interesting. Let’s work through this.

The months are containers, and the contents in those containers are days. We have 12 equal containers, but the contents in each of those 12 containers may not be equal.

The good news is that banks have created a special convention to help each month have equal parts. It is called the 360-day convention (or the banker’s year).

To make things easier (and to reduce the cost of extra math), banks say that every month has 30 days. Thus, each banker’s month is 1/12 of a 360-day banker’s year.

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