Let's talk about what we did do shall we, not what we didn't, at least at first.

Attending to Precision and Excel:

I did get my Precalculus students in the computer lab to have them run a spreadsheet for estimated area under a curve. Their homework was to graph and find the following:
The next day we went into the lab and I gave them some basic Excel Spreadsheet how to's and let them try to organize the information and check their answers.

We came up with the following columns:

I find it super good brain food to get the students to recognize and articulate the subtleties between rectangle number, index number, and sub interval. Do you want index 0 to 7 or 1 to 8? Do you want to multiply by cell A2 or by cell A3? Do you want the spreadsheet to calculate the x-value and then the height, or do you want the argument to do it all? The feedback is immediate with an ERROR message or some weirdness like #########. The students appreciated the challenges and intricacies of attending precision and perhaps what coding is like.

One groups final product for problem number 5:

















Student K went a bit overboard here, but she caught herself in the LH area and RH area cells.

Not the most exciting thing ever, but really gave me pause for attending to precision and the value of giving students an opportunity to learn a real world skill.



Here is another group's final product for number 3. I like that the area cell for Right hand Area is blank.



Speaking of Attending to Precision:

I am pretty sure I want to try this activity, using Excel in Geometry too. Again, I am just convinced that find the surface area and volume of ANY regular polygonal prism is a good place for students to look for and make use of structure and attend to precision. How can each problem be soooooo different? How can I get the students to slow down, ask themselves, what do I need, what do I have, How can the I make this as simple as possible? (It also occurred to me that the entire final could be one regular pentagonal prism and one regular pentagonal-based pyramid to find the surface area and volume of and the student knowledge of just about all of the second semester would be used (the students are speaking of isosceles triangles as two congruent triangles that are reflected from a vertex perpendicular to a base!).

Which leads me to Number Sense and Spatial Reasoning:

Since it is late and I need to go to bed, I will leave you all with this one last thought, what is the best final product you've asked for to convince you that a student can imagine, picture, draw, internalize the height of a prism? I so badly want them to have an internal vision. We have built, drawn, and broken down many a pyramid, and really, it isn't so much about the "usefulness" of knowing the volume of pyramid, as it is for me at least, that a student can reach into their toolbox, the ones I know they have, and SEE what needs to be done and make something of a problem on their own.

Comments welcome!