Today we wrapped up the model-making activity and ended with up a couple more models to help visualize this 3D construction of a solid object with cross-sections of known shapes. Some people didn't finish all but I made the executive decision to stop and start talking about how to find the volume of the solids in the last 15 minutes of class. (We are also in the midst of AP testing so some students had missed class the previous day)
To have them "save" their models (since we deconstructed each one to save materials) I had them take a picture of each one and dump it into a Google Slide Deck and I will go through and pick the best ones to display on our Haiku Class Webpage. Since they did this in partners, they shared the document with their partner so they could both access it.
It is especially helpful for those slower students who made less of the models, or for students who were absent.
|This is what the assignment looked like. I pushed it out through Google Classroom .|
(So every student had a copy of this already ready to go, I made the template)
I loved trying out this activity for the first time this year! (Especially something this hands-on)
I definitely wouldn't do this 100% the same for next year, however. Specifically I was not entirely satisfied with the sheer amount of class time it took to make these, and how I felt at certain times there was a large gap between the students who were on task, or just worked faster, and how much they had completed as compared with the others.
Things that went great! (and I want to keep):
- Students getting hands-on practice constructing models
- Thinking in 3D is hard, and this allows an entire day to "play" and see what different types of scenarios would look like on a physical model that they can touch. I want to still have this be a conserved day with no official "formula" to speak of.
- Students seeing how even objects with the same base can look different with different cross sections
- Having them all use the same base function and interval region allows them to see how just changing the type of cross section can effect the solid. It also allows them to see and predict whether or not they think they will all have the same volume or not... (they don't)
- Students seeing the repeated shape generates the entire solid
- This means the discussion of where the volume formula comes from is more fluid and seamless, as they cannot look at a single model without seeing the same cross section repeatedly shown.
- Reviewing the concept of integration before the activity
- I could feel that they needed a reminder of what an integral really represented, even though we had come out of a unit of calculating them. The important thing we discussed as a sort of warm-up and again after we finished the models, was that an integral allowed us to take the infinite sum of repeated things (the "things" before being rectangles for Riemann sums)
- Organizing the materials into buckets
- This allowed for easy distribution and cleanup. I go from Applied Calculus to Algebra 2H and then back to Applied Calculus so I had to collect and distribute materials often.
Things I would change for next time:
- The number of models they build and what they do with them
- It would be more efficient if each table group had a different cross-section model to build, and then we had a "gallery walk" at the end to see them all to take pictures and answer questions about them. I could then save the best models from the last period of the day to have them go back through and calculate the volume of each one the next day, in a station activity.
- The distribution and subsequent collection of the Play-doh.
- This might not be an issue for you, but for my classes they are 5 weeks away from graduating and in the midst of AP testing so given any opportunity to "play" in class they will run with it. (I love them but at the same time I don't at this time of year...) I had several groups slack off and have one person build all the cross sections, which set them far behind every other group, all because they wanted to play with the play-doh. Next year I want to collect it as soon as they have molded their base, or have them put it in the bucket and put that on the floor. Your results may vary, and classroom management is definitely a growth area for me.
- The "Storytelling" aspect of building this concept
- I didn't do as good of a job as I could have with creating a sense of "need" for this sort of application. I kind of just said "Look at this neat solid we created! How can we find the volume?" That isn't the worst thing I could have done, I suppose, but definitely I wanted students to have more interest in what this could be used for than they did in this unit.
Let me know if you have any feedback when you try it out! (And thanks for reading if you got this far!)