My class is self-paced for the most part, but at the current time most students are somewhere in our ratio unit. The task took longer for some students because they were at the very beginning of the unit and the task actually acted as both instruction and application. It was interesting to see the comparison between student's work who had already completed the ratio unit compared to those just starting. The only really difference was how long the task took...the learning was solid both ways.
Here is the original page for the task...
Here is the modified version the students were presented with...
I actually predicted this in a Tweet prior to the start of this task (which is more of a reason for teachers to plan obsessively to try to predict anything your students may come up with or struggle with so you are prepared...you won't, but try), but my students had a hard time grasping how if you were on the 4th floor, you really only had 3 flights of stairs to the 1st floor (same goes for the elevator).
Even though I push like crazy for as many labels and explanations as I can get, this concept is not as automatic with my 6th grade as I would like for a few select students. I noticed the two different sets of labels on the ratios were getting a little confusing to some. Seconds and stairs versus seconds and feet...this problem was most prevalent with those not using labels, so make sure to encourage labels and a key point of mathematical understanding.
The differences in methods were also interesting. When providing instruction with ratios, I always start with the ratio table. I feel like this makes the most sense to students, and also provides the base understanding needed to eventually shift to a quicker method. In the student work you will notice many students using the table, but other students who graduated to something else. I do not explicitly teach any shortcuts with ratios. I have found that this only skews the learning and prevents long-term understanding. When students are ready for the shortcuts, they will intuitively discover them.
Question two ended up being one of the most difficult questions the 6th grade had to encounter this year task-wise. I think most of this was due to the sheer amount of information each student had to keep track of. Again, having everything labeled really helps with the confusion. Students who were probably the most successful quickly figured out how many seconds it took to traverse one floor with the dueling modes of transportation, essentially creating their own usable ratio. Many students opted for a large scale chart which worked well but was time consuming.
We addressed many interesting questions like how the speed going down the stairs might change if you had a large number of flights, and what if you had to stop on the elevator to pick someone up? All of these are the unforeseen variables of life. Math is normally presented a lot cleaner than life. That is why I like these tasks so much. You can really dive into the all the variables at play and decide how much each one would change the outcome. Below is our student work, standards, as well as my help sheet for the task. Hopefully now you will be better prepared for when math and life collide!
|My notes to help with the discussion|