How could I forget:

8. Mark Driscoll’s *Fostering Algebraic Thinking* and *Fostering Geometric Thinking*. If you don’t have a copy, order these now, or see if your school can order these for your department. Along the lines of the Problem of the Week (POW) problems from IMP, these books are great resources for groupworthy problems and include informative commentary about the mathematics involved. I don’t have my copy handy, so my apologies if the following reference is too cryptic, but the number puzzles that deal with solving systems of equations and the problem with the snake rings for looking at geometric sequences are perennial favorites of mine.

8 is a good place to pause. Now I’ll get some sleep.

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## About Clint

Looking for answers and enjoying the journey.

The Math Forum keeps a list of “other problems” here:

http://mathforum.org/pow/other.html

I’ve seen these books mentioned enough by now to know that I should get a copy myself. Can you post an example of something in there that you’ve seen success with?

When I get back home, I’ll be able to give more specifics. But these are some things that have worked for me in the past:

1a. Algebra 1 (Solving Systems of Linear Equations, see “Chapter 7” at http://home.comcast.net/~chan0809/alg1/) – 1st day of 2nd semester started with Henri Picciotto’s “Make These Lines” as a way to review the linear equation to graphical representation connection. In the discussion, I was looking for the following ideas to come up: parallel lines have the same slope, how do you know when 2 lines will intersect, and what is special about their point of intersection.

1b. At the beginning of PS#7G, those number puzzles came from Driscoll’s Algebra book. I don’t remember why I waited so long to introduce those – previously (in Extended-B, like an Alg 1B class) I had students working on those puzzles for a couple weeks as a “side” topic before we formally hit solving linear systems.

2. In College Transition Math, especially during the 2009-10 school year, I tried incorporating more POWs from IMP as a way to develop the skills of explaining a process, working together, and increasing stamina/persistence in problem solving. (http://home.comcast.net/~chan0910/ctm/) What often worked as a 3-5 day POW assignment in Math 1 or 2 seemed to fit nicely anywhere from 40 minutes to about 100 minutes for the more difficult POWs in CTM.

2a. Spiralateral Investigation (modified from IMP 1) – the entire math department did this activity to start the school year. Great problem that can be taken to different levels of depth, depending on the group.

2b. Ch4 – Snakes Alive! (from Driscoll’s Algebra book) – great problem that can tie in exponential growth, sums of geometric series, and divisibility.

2c. Problems for general problem solving / explaining process / group norms: The Coin Problem (a former student actually shared this one with me – I don’t know the original source); Around the Horn Problem (from IMP1); Jackals and Coyotes (from a book I actually forgot to list in the resources: Key Curriculum Press’ “Crossing the River with Dogs”) – this one worked particularly well and once students decide to use manipulatives instead of just words, the discussion really blossoms; Ch8 Logical Reasoning Activity (I forget the title of the book this came from – it’s on my shelf at home…) – great discussion starter for the idea of proof and the whole converse/contrapositive/inverse discussion; The Candle Problem (from Driscoll’s Algebra book) – there was something I wanted to change about this, but I don’t remember what it was… my notes are all 800 miles away.

Those are some of the ones that I think worked well. There were also a bunch that I need to rethink for next time around. A lot of the worksheets I have on my website might be hard to use “as-is” – there is a lot of setup and discussion that happens in class around what might be a half-sheet containing a handful of problems. So if there’s any background about how any specific set was used or anything, please feel free to ask.

I did a similar search after returning from PCMI. The best ones I found, not yet mentioned, are…

http://www.1000problems.org/

What it sounds like.

http://ohiorc.org/for/math/

Ohio Math Resource Center… I haven’t searched too much, but it looked promising.

http://samjshah.com/worksheets-projects/

This is a list maintained on Sam Shah’s blog.

http://www.exeter.edu/academics/84_9408.aspx

Exeter uses problem sets for its entire curriculum (as far as I can tell). You can download the entire thing in PDF.

cheers,

Joe