Dear Sirs,
I am preparing a 45 minutes class for K-12 students. The problem is to show that algebraic equivalent expressions are not always numerically equivalent. In particular I would like to show one of these dangers: cancellation that occurs during the subtraction of nearly equal quantities. Do you have a good reference I could use to prepare my class. In particular to be able to show some examples and how one can avoid this type of error. I also would like to show examples with practical use. I tried to look up in the web but did not find anyhting appropriate.

Many thanks
Yossi
Math Teacher

I dislike the claim that algebraicly equivalent expressions can somehow not be numerically equivalent. What is probably meant is that a calculator, and even a computer, will make rounding errors that become apparent when computing the value of an expression by two different methods. There is a lovely discussion of it (with nice examples) in the first two editions of CALCULUS by James Stewart (in the appendix entitled "Lies My Calculator Told Me"). He claims that the owner's manual that comes with a calculator often describes limitations. Otherwise, one finds such information in books on numerical methods.