This article shows how simple instruments may be used to construct angles of certain measures and applies this procedure to more detailed problems. A proof of the Pythagorean Theorem is given using these procedures. (CT)

Children were pretested and assigned to one of three treatments: training with three dimensional manipulanda; the same program except that the instructional materials were line drawings; and a control. On the posttest, both experimental groups were significantly superior to control group. (Author)

The importance of having children manipulate small objects that can be grouped, arranged, and counted is discussed. Learning activities for one-to-one correspondence, numerals, and the four operations are given. (MNS)

Using squared paper as a concrete aid, children can explore important concepts about the perimeter and area of geometric figures. Activities are described and illustrated to develop several methods of finding perimeter and area. (MNS)

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

Ways to use popsicle sticks as concrete models of multiplication and division of fractions are given. (MK)

A geometric model used to teach properties of rational numbers to college students is described. (MK)

An activity for generating approximations of pi is described. (MK)