A series of problems involving number theory, the law of cosines, and geometric interpretations of solutions to equations is discussed. (SD)

The author observes that checking the closure property is redundant for most number systems and therefore hard for students to understand. He defines several systems which are not closed, develops two concepts related to closure, and provides many related examples. (SD)

Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

Behavioral objectives are listed for the primary, intermediate and junior high mathematics curriculum in the Mesa Public Schools (Arizona). Lists of specific objectives are given by level for sets, symbol recognition, number operations, mathematical structures, measurement and problem solving skills. (JP)