Ten hours til bed time, the Lions game is on now, three subjects of homework, a psychology and culture test tomorrow, a job interview at 3:00p.m, and it’s 1:00p.m now. What do I do? How can I possibly do well on my homework, and do all these things? What tasks will I not complete today? How can I plot out my time so that I can enjoy all of these tasks and fun activities? We will explore this problem in a short bit.

It is amazing to me the lack of time that is spent in mathematics exploring this unique math problem. The first time I was given truly helpful material to work through the math problem of time management was at CRU a student movement for Jesus that I am a part of on campus at Grand Valley State University. The worksheet pdf is below.

The idea of adding up the hours you spend on each activity in your life in order to see what areas of your life are dominating your time is an excellent one. I think that using math in this way is excellent for helping people most enjoy their lives. Adding up the hours you spend on various activities allows you to discover what parts of your life you want to spend less time in, and what you would enjoy and benefit from spending more time in. Understanding time management is crucial to leading a balanced life style, and math teachers should spend more time discussing this vital issue. If we are math teachers, then we should spend the time to solve the constantly evolving problem of time management. Math teachers should be “Time Masters”.

Time management has been shown to positively effect academic success(Britton and Tesser, 1991 and McKenzie and Gow, 2004). As a future math teacher, I think emphasizing strong time management skills through math should be one of our essential focuses. In an increasingly busy world, time management will be a key foundation for students’ success.

So back to the original problem, I have a given of 10 hours of time before bed. I know the Lions game will last about 3 hours. We are unsure how much time each of our three subjects of homework will take, and we have a test tomorrow that we probably should study for. The job interview also will take an unspecified amount of time, but from my previous experience probably about an hour. Perhaps, the uncertainty is just what makes time management problems so difficult to master. There are a number of events in our lives that are new experiences. Often times, we are unsure of how to quantify or measure these occurrences. I may express this situation algebraically as

10=3+3x+y+1

with y= the amount of time spent studying for PSY 355 test and x=the amount of time (time spent on homework subjects)

Does this equation accurately describe the scenario? Why? It seems it could, but likely it would not because the time needed for homework varies largely from subject to subject. Maybe the best way to show this component, would be

a+b+c=x with a=subject 1 homework time b=subject 2 homework time c= subject 3 homework time , so we would remove the coefficient 3 from the x in the original equation and x now means homework time for all subjects.

We now have a system of equations with which we can represent the scenario.

10=3+x+y+1 {1}

a+b+c=x {2}

By simplifying {1} we see that

6=x+y

We are assuming that we watch the whole Lions game and the interview only takes an hour. From this point the choice is mine, if I want to do everything I had hoped to do, I can quantify x and y as I want, but they should not exceed 6 hours or else I will miss my bed time. Today, I choose 2=y and 4=x. The values of a,b,and c I would have to estimate to the best of my ability, but if their sum is greater than 4, then I must determine an item to cut down on or remove from my schedule.

After approaching this problem I further came to understand that time management problems are much more difficult than meets the eye because there are many unknowns. This is why time management math is scarcely attempted in math classes. While not easy, I think it would be extremely helpful for students to train to become “Time Management Jedi” and their math teachers to be “Time Masters”.

Interesting. I see this as an argument for time management in linear equations. For sure it’s a nice number decomposition (out of 24…), and proportional thinking (do the times match your priorities). Will the students see this as a silly add on, or more relevant equations? In real life, you’d probably just say 10-3-1 means 6 hours to divide up. Maybe the context makes the equation more concrete to students?

I think it’s worth exploring. And definitely a good blogpost working your way through these thoughts.

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