More Resources…

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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Resources for Good Problems

The excellent question that comes up often seems to be, “Where can I find problems that are rich, groupworthy, and with multiple entry points to use in my classes?”  Being a packrat, I keep accumulating stuff, so I figure I can kill 2 birds with one stone – partly as an organizational tool for myself and to share what I’ve accumulated, I’ll periodically post some pointers to resources that I find useful.  If you have other favorite sources of problems, I’d also love to get pointers to those items in the comments section.

Here’s a quick list of some resources I go to the most.  As time goes on, I hope to post links to more resources and point to some specific activities that I’ve used from the links below.

1.  Henri Picciotto’s Math Ed Page is one I visit often.  His “Make these Lines” and “Make these Parabolas” are ones I’ve used at many different levels.  I also have a copy of his “Geometry Labs” book and find the “Polyominos” activites good for both algebra and geometry.

2.  The Dana Center at UT Austin used to have a bunch of free activities for download from their assessment books.  Click on a link, such as “Algebra II” – the section headings are actually links (it wasn’t obvious to me) – the assessment links have good samples.  There used to be more free content available for download, it looks like they’re now available for purchase.

3.  One of my favorite series is Key Curriculum Press’ Interactive Mathematics Program.  I student-taught parts of Years 1 and 2.  Used copies are available for a reasonable price on  I often use their Problem-of-the-Week problems for group tasks (typically lasts anywhere from 1-4 class days).  I switch seats every 2 weeks and in my Intermediate Algebra class, I usually had them work through a .5 or 1 day group task when they were placed in new groups.  I also love the way the “Shadows” unit in Year 1 approaches the idea of similarity, and they way that they approach solving proportions.

4.  My go-to resource for PreCalculus is Foerster’s PreCalculus, also from Key Curriculum Press.  He has lots of great word problems, especially for Trig.  The way that he develops the Law of Cosines and Law of Sines is also great.  On my to-do list for next year is to look through his Calculus materials.

5.  Another resource I use heavily for PreCalculus is the University of Washington’s Math 120 materials.  There are lots of challenging problems and interesting application problems.

6.  On the subject of PreCalc, Connally, Hughes-Hallett, and Gleason’s Functions Modeling Change is another book I’d be happy to use as a course text.  Again, there are a number of excellent problems that elicit deep thinking.

7.  Also on my to-do list is to become more familiar with the CME Project materials.  What I have seen so far has been excellent.  At PCMI, I am in the functions working group and the project my partners and I are working on are lessons to help students understand general function transformations.  There is a particular method I used over the last 4 years, which I’ve never seen in any textbook.  That is until I had a chance to chat with someone on the CME Project development team.  It turns out that’s the approach they’re using to function transformations in Algebra 1 and 2, but in a better way.  When I get a chance, I’ll post more details.

7 seems like a good place to pause.  I should go to sleep soon anyway…

Posted in General, Resources | 3 Comments

AP Precalculus?

Recently, there have been discussions on the AP Calculus mailing list about whether or not there should be an AP Precalculus course. If done well, I think this is a unique opportunity for the College Board. I feel that one of the strengths of the AP program is the reputation it maintains for high standards, thereby allowing many 4-year universities to award credit based on student performance on the AP tests. Precalculus is a course that sits in that grey area. Many 4-year universities do not consider Precalculus to be a credit-bearing course if they offer it at all (evidence needed to support this assertion – I could just be talking out of a body part other than my mouth here). However, Precalculus is a credit-bearing course at community colleges. Oddly enough, I don’t believe that many community colleges award credit for a passing score on the AP Calculus exam. It seems like community colleges have been left out of the conversation at the College Board – is that true? Are 2-year institutions represented in those that read the AP exams? Do they have representation on the committees that determine the curriculum or write the AP test questions? Maybe this is an opportunity to bring the 2-year colleges into the AP conversation. It might also provide options or alternatives for “calculus readiness” tests that many 4-year institutions spend resources on administering.  Perhaps a passing AP Precalc score could count for credit at a 2-year college and count as a prerequisite for Calc I at a 4-year college?

These are the kinds of thoughts that literally keep me up at night.

Posted in AP, College Board | Tagged , | 7 Comments

A journey of a thousand miles begins with a single step…

Maybe a better inaugural quote is:  if a tree falls in a forest and no one is around to hear it, does it make a sound?

At PCMI, Sam Shah gave a 5-minute presentation about blogging and so this one was born.  It seems like a good way to reflect on one’s practice.  So why not, I say.

Posted in Blog Purpose | 5 Comments