Paging Doctor Math: Shower Versus Bath Task

Last week's 6th grade task was courtesy of @ddmeyer and featured the price difference between taking a shower and taking a bath. This is a ratio heavy task and truthfully we have just started discussing ratios and proportions, so it was interesting to see how the students used what they already knew to come up with solutions.

Here is the modified task I displayed on my television before class for the students. As you will figure out from the student work, I changed the cost per gallon of water to 1/5 of a cent instead of the $0.19 I was using. I should have done some fact checking...

http://bit.ly/1A5Zcb7

Many of my students got off to a good start, and there are many paths to get to a reasonable response, but about 1/4 of my students made the mistake in some way of not realizing that the times displayed were minutes and seconds. I should rephrase that...I think they knew the time was minutes and seconds, but since the time per gallon was in seconds, answers for total gallons were off which made for a good discussion piece. Some students tried to divide the time (2:23) by the 26 or 27 seconds for the gallon in the shower, which wasn't correct because 2:23 isn't 223 seconds. I also had students count up or count down by seconds in a chart type fashion which would have been fine, but some of those students did not realize that minutes are not out of 100 but 60. I also had to have discussions on how to change minutes and seconds into seconds...which should give you an idea of the various levels of students that coexist in my classroom (and I am sure all of yours).

While not explicitly discussed, I like the estimation aspect to these tasks. Many students realized quickly that the bath is going to use more water due to the combination of longer length and a shorter amount of time to use a gallon of water making more gallons. This seems pretty trivial, but I am excited that my students take the time to think about these idea ahead of time. Most of my students have a good idea of the outcome before they arrive at the solution which is an important skill to have in my book.

If you are a 6th grade teacher and have not started discussing ratios, this is a great way to get started. Seeing the simplicity of 10 seconds being 1 gallon and trying to arrive at an ending time provides a nice visual to get the students primed.

Below are the standards I felt this task involved, along with student work and my discussion sheet I planned out prior to the task.