# Time Passage

Once students gain time sense, it's time to learn how to calculate time passage. (Most of the time passage worksheets below deal with time passage and analog clocks -- they may be too much for students who really struggle with analog clocks. For some students, it might be wiser to teach time passage without the additional complication of analog clocks!).

Before students start working with complicated time passage problems, have them work with time passage problems that deal with hour-long increments. (There are worksheets with hour-long, and hours-long passages below.) Those exercises will give them practice counting up and down hours (and counting over the 12s). Once students master that, they can start working on time passage problems that include minutes.

When working with time passage, students need to be able to think in base-12 and base-60 number systems, which can be very confusing to children. When students first start working on time passage, they tend to set problems up like a regular addition or subtraction problems, and then regroup like a regular math problem. But, our regrouping processes are based in a base-10 system, so they do not work for time (base-12 hours or base-60 minutes or seconds)! The best way to teach time passage is to have students deal with minutes and hours separately and then combine them to create a form of time that makes sense (just like when adding mixed numbers, you add the fractions and the whole numbers separately, then you combine the two).

Here's an example of how students often try to figure out how much time has passed and how they should do it.

Example:

**If your class begins at 8:15am and ends at 1:35 pm, how much time did you spend in class?**

Students' first instinct is often to do a subtraction problem: $$\eqalign{1\text{:}35\\\underline{-8\text{:}15}}$$

As you can see, that process will fail in several ways. Try this instead:

First get to whole hours.

The class started at 8:15, so it was **45 minutes** until 9:00 am.

The class ended at 1:35, so it lasted **35 minutes** after 1:00 pm.

**45 minutes + 35 minutes = 80 minutes**

Now find the time passage between the hours:

How many hours are there from **9:00 am to 1:00 pm? 10, 11, 12, 1 = 4 hours.**

Add the hours and minutes together: **4 hours and 80 minutes**.

If there are any hour wholes (60 minutes) in the minutes, put them in the hours: 4 hrs + 80 min = 4 hrs + (1 hr + 20 min)=** 5 hours and 20 minutes**

Figuring out time passage takes some time and practice. But, it is one of those math skills that students will probably use in real life, so it's worth getting right. For what it's worth, many students use their fingers when they count hours (especially when they count over a 12) and that's ok. Encourage them to do whatever works for them.