Time & Base

This week we only had one day of class so I'll only have information to cover for Tuesday's class period. We went over many different time problems as well as base systems when doing a problem like time.

We are used to a base system of 10. When we were taught to subtract, we always had to "borrow" a group of ten from the next number to in a sense "roll over." We practiced that this week in class but changing the base systems to be something completely different like 3, 8, or 6. These type of systems don't exist, at least we don't use them in our math, it's just a way to get us as future teachers to understand how difficult it can be for a kid to learn these concepts as well.

When dealing with time, there are multiple base systems to keep in mind. The first is that there are 60 seconds in one minute, and 60 minutes in one hour. It is also crucial to remember that we work in a 12 hour system. So we start at start at 1, and then continue until 12 and start over again after that at 1 to end up with 24 hours in one day. Now that is confusing! Here is an example of a time problem:

Jessie started baseball practice 3 hours and 45 minutes ago. It is now 5:15. What time did Jessie's baseball practice start at? 

Possible Mistakes

In class we were assigned to think about the possible errors that a kid could make. I came up with at least three different things that could have gone wrong. 

1. a kid could forget that the base system is 60 for time rather than 10 which they are used to

2. a kid could have done 5 hours - 3 hours = 2 hours

3. try to use the traditional method of borrowing and carrying and get confused

Number Line Method:

I first did the problem on a number line because that is the easiest tool for me to understand how time works with the visual of seeing each jump of time in either minutes or numbers.

So I first started at 3:45 and jumped up 15 minutes to get to 4 o'clock because that was the next easier time to deal with. Remember my goal here is to end up at 5:15 because that is the current time. Once I was at 4 o'clock I jumped 1 hour to 5 o'clock. Our goal is 5:15 so then I knew I only needed to jump 15 minutes more to get there. Last, I added up the numbers above each jump which were 15 min + 15 min + 1 hr. = 1 hour and 30 minutes, or 1:30 which is the correct answer for what time Jessie's baseball practice started.

Algorithm Method: 

After completely the problem on the number line, Christina asked us to do it with the algorithm. This is really confusing to explain so try and stay with me! 

I lined up the numbers the old school way and then stared because I could not figure out how to borrow time! The base was in 60 minutes not 10 so how the heck does that work?! 

I took one group of 60 minutes away from 5 hours making it 4 hours. Are you following?

Then naturally we have to add the one to 15 minutes, but thats confusing because its not a base 10 still. So what really happened to the 15 minutes was I added 60 minutes to it because we took 60 minutes away from the 5 hours. So the 15 minutes became 75 minutes by doing 15 min + 60 min = 75 minutes. Confused yet?

Then I rewrote the problem as you can see in the picture above with 4:75 - 3:45. NOW you are able to subtract as we normally would to get 1:30 for the start time of Jessie's practice. I absolutely hated doing it this way! My friend sitting next to me in class has to keep explaining it to me over and over until I fully understood. Think about how frustrated an elementary aged kid would be trying to do this method! I'm going to stick to the number line, what about you?

I have had such a fun time blogging about math these past six weeks.  I hope my blog has been helpful to you and understanding the concepts you learned as a kid. To conclude this lesson on algorithms and confusing base systems, I'll leave you with this cheesy math cartoon :