Five sets of activities for students are included in this document. Each is designed for use in junior high and secondary school mathematics instruction. The first Note concerns mathematics on postage stamps. Historical procedures and mathematicians, metric conversion, geometric ideas, and formulas are among the topics considered. Successful simulation is the focus of the second Note, with activities on planning a supermarket, bowling and random digits, and other suggestions for using a random digit table. The third set of activities concerns proof; geometric, algebraic, and numerical formulas are each considered. Golden rectangles and ratios are included in the fourth topic, with a physical model for generating golden rectangles, directions for constructing a golden rectangle and generating golden ratios via Logo, and comments on the divine proportion. Finally, the fifth Note concerns primes, and includes work with the Sieve of Eratosthenes, twin primes, and other problems. (MNS)