Back-of-the-Envelope Calculation

Author
Susannah Howe, Smith College, showe@smith.edu
NA Name
Back-of-the-Envelope Calculation (BotE)
Summary
Students have an individual assignment to do a rough calculation related to their project (or course or larger activity, etc.).  Emphasizes the need to do rough approximate calculations, making assumptions where needed. I have given students a few days to do it, but when I presented this at the 2010 Capstone Conference, someone suggested it could also be done with a very short (ten-minute) turnaround. I use it to get students diving into the technical depth of their projects early on, before they fully know the territory, but it could be used in other ways too. Main thing is that it is actually done on the *back of an envelope*--this constrains how much the students can write and also adds some humor. 
Topics
technical calculation, approximation
Audience
any--could be a whole course, could be a team on a project. Works across all years.
Strengths
·       Applicable to many courses & contexts.
·       Teaches students about the process and value of completing rough calculations/estimates.
·       Forces students to deal with unknowns and make assumptions.
Weaknesses
Needs some structuring to identify an appropriate back-of-the-envelope calculation. More advanced students can often identify and frame these themselves; other students may need more assistance.
Variants
·       Could be done over a period of a few days or as a 5-15 minute assignment in class or in a team meeting.
·       Could do a pre-activity with teams or a whole class to brainstorm possible back-of-the-envelope calculations that apply to their project or the current course material.  Then can divide up that list, assigning different calculations to different people.
·       Can return to the back-of-the-envelope calculations throughout the class; can also refer to the concept of BotE in the context of new calculations and students will better understand having done an initial one.