Excuse me Sir, do you have the time?

I am sitting here blogging in the best spot ever! 

On my couch, watching Ellen's birthday episode! Haha! 

I just LOVE her show! Every day. You know how people say when you work out you have to turn it into a lifestyle? Well...I maybe haven't mastered that yet...but watching Ellen is a lifestyle for me. 

If you haven't watched her...you need to!

This week I have been working on elapsed time with my students. For most of the first day or two we used their small dry erase boards to work out elapsed time problems that I was writing on the smart board. I tried a new technique this year ... don't tell them how to do it beforehand and see what happens!

(I have always been the type of math teacher that lets the students solve problems in whichever technique they like best...so this just cut out some of the work because I let them find the techniques!)

I tried this because time is something that students are familiar with... even though they may not realize it yet. I put a problem on the board and then I let them solve it however they want.

So your question probably is...why is she blogging about this?

Answer - I was amazed at what my students were able to do!! I absolutely loved walking around and seeing what techniques the students were coming up with. I have not been giving them enough credit, obviously, because it is like they don't even need me! They did such an awesome job!

The two boards above show work for the same problem:

 It is 3:16 now. What time was it 2 hours and 22 minutes ago?

The board with the red writing subtracted 2 hours and 22 minutes from the original time in order to find out what time is was before the elapsed time. This student showed amazing understanding of time and number sense when subtracting. If you follow along as I explain, you will see what I mean: 

6 - 2 is 4 ... 1 - 2 you cannot do, so the student changed the 3 hours to 2 hours and the 1 to a 7. 

This amazed me because this student knew not to carry over 10 and change the 1 to an 11...instead, he knew he was carrying over 6 (because there are 60 minutes in an hour), and changed the 1 to a 7... AWESOME that he knew to do that on his own! 

So, 7 - 2 is 5 ... 2 - 2 is 0 ... Zero in "time" is like saying 12.

The board with the blue writing did what I would have done if I were solving this mentally, except she showed her work. Starting with 3:16 she showed a loop to the time that is 2 hours prior to 3:16...which is 1:16. Then she went back 22 minutes to get to her answer.

The problem for this work is:

It is 9:17 now. What time will it be in 3 hours and 59 minutes?

The student who wrote in red is the same student in red in the first problem, so his work is done in the same technique as above.

The student with the black marker shows a similar technique to our blue marker in the prior problem. Starting with 9:17 and going over 3 hours, then 59 minutes. (Which he explained as going 1 hour and subtracting one minute).

The student with the pink marker skipped showing some work because a lot of it was in her head. I am okay with mental math as long as I can follow their thinking path, like I can with this work shown in pink. You can see that she ignored the 3 hour increase in time at first, by just worrying about the minutes (adding 17 and 59). Knowing that 76 was the total minutes we would have, she then added the 3 hours in her head (thinking "noon" out loud while she was at the board). She took away the 60 minutes, changing her hour time to 1:00. The minutes she still had left, she added to the 1:00 time, getting 1:16.

The purple marker did her work just like the problem in the black marker, but just showed it in a different way. Because she went this route, she ended up with 12:76 which she knew was not correct. She changed it to 1:16 mentally.

Above are two more examples with the problem:

It is 8:36 now. What time was it 4 hours and 49 minutes ago?

I will let you check out their work to see what technique they used!

Something I learned from this is that my students have enough number sense to try their own techniques sometimes. I think I will start each unit from now on with a few minutes of letting the students "try things" on their own to see if they can find solutions.