by C. Elkins, OK Math and Reading Lady

In my last post, I shared my favorite model for elapsed time (Mountains, Hills, and Rocks) using an open number line. In this post I will share another version of the # line some of you might like — I’ll list the pros and cons of it as well as show the std. algorithm / convert version.

I hope all of you are doing well. I realize many of you are involved in distance learning with your students – and this may be in addition to taking care of your own children’s needs at home. So I understand my blog might not be on your top list of priorities, but I do hope you will bookmark it and keep it for future reference. But again, if you are home with kid, then dealing with elapsed time is a perfect real-life math situation they can apply on a daily basis.

**The Z Model:**

The Z model is a straight number line “bent” into 3 parts of the Z:

- 1st “leg”: From start time to next full hour – determine how many minutes
- 2nd “leg”: From hour to hour – determine how many whole hours
- 3rd “leg”: From last hour to end time – determine how many minutes

Here is an example to see the steps involved:

Here’s another in one single view to determine elapsed time between 7:50 and 1:10:

**Pros:**

- It helps break time down into smaller chunks.
- It’s a visual model which can help a child mentally process the elapsed time in these chunks.

**Cons:**

- Students would more likely have to know automatically how much time has elapsed on the first “leg” of the Z. In other words, can they mentally figure that the time from 8:25 to 9:00 (the nearest hour) is 35 minutes? Or the elapsed time from 3:47 to 4:00 is 13 minutes?
- In my opinion, this model is mostly just helpful when start and end times are given and the task is to compute the total elapsed time. It would not be very helpful if the task was to determine the start or end time.
- If a child can figure the minutes of elapsed time of the first “leg” of the Z, they might not need the visual model to solve.

**The Std. Algorithm / Converting Model**

This model resembles a std. algorithm problem because time is aligned vertically and added or subtracted.

- When adding, any minutes which total 60 or over would be converted to hours.
- When subtracting, exchange 1 hour for 60 minutes.

Here is an example to see the progression from start to finish when start time and elapsed time are the known parts:

Here’s another example in one view:

**Here’s an example that involves a known end time and elapsed time. The problem is to determine the start time which involves subtracting time:**

And another problem in one view:

**Pros:**

- Students who are ready for more abstract strategies might enjoy this model.
- This model is more useful when solving problems in which the task is to find the end time or start time.
- This can be utilized with hours, minutes, and seconds problems.

**Cons:**

- Having strong knowledge of number combinations that equal 60 is needed.
- There may be two or three steps involved to arrive the final answer.
- The regrouping in the subtraction version may involve two types which could be confusing: minutes vs. base 10 (as shown in picture directly above)
- Understanding what converting time means and why we subtract and add within the same problem (subtract 60 minutes, but add 1 hour).

**I miss seeing my friends in person! ****Let me know how you are coping during these crazy times!**