* first decide the mathematical discovery/realization/leap you want them to make, or the concepts you want them to cement, and create a simple example which leads up to it then makes it happen
* do a warm-up example at the board first, which gives them the tools
* make the first part of the worksheet easy, a slight variation on what you just did at the board. Make sure everyone can do this.
* make the middle part of the worksheet where they have the new discovery. Make it the *simplest possible* example that illustrates the point. Make sure the numbers work out simply (not messy).
* at the end of the worksheet throw in an optional advanced question to keep the fast students busy while the others are finishing up. Make sure the others don't feel bad if they don't get to it!
* handwriting is quicker than LaTeX, and lets you draw figures quickly. Then throw it in the photocopier.
* you can do "coop learning lite" just by asking them to check with their neighbors if they are getting the same answers and resolve the conflicts by discussion. But I'm sure you have better plans...
* after they've had 2 mins to start off, go around and interact, give leading questions/hints if they are stuck. You have to know the answers well and take an answer key with you in case you forget.
* make sure that at the end the confused students (which there will be) get a chance to be shown & explained the answers (eg by gathering results at the board). Otherwise they will feel left out.
My Math 22 (linear algebra) worksheets are here, and Math 11 (multivariable calculus) worksheets are here.
Alex Barnett 7/5/12