The notion of partitioning is used to help develop simple number concepts, counting skills, place value concepts, and division with two-digit divisors. Working with counters, base blocks, and other materials is carefully explicated. (MNS)

A developmental sequence of activities is presented that introduce children to linear measurement and the use of rulers. Activities enable children to understand the nature of measurement, the construction of a ruler, and how rulers simplify measurement. (MNS)

How the manipulative aid called the "10 frame" can be used to teach the number combinations for 10, the addition facts that bridge 10, and the place value nature of our number system is described. (MNS)

Fraction strips are suggested as good conceptual models to focus on the meaning of fractions. Making the strips, beginning activities, connecting symbols, more concept activities, and working with two fractions are each illustrated. (MNS)

Described are activities using paper plates with dots drawn on them which place a heavy emphasis on matching and ordering sets, on developing mental images of sets, and on perceiving sets of a certain size as composed of smaller subsets. Also suggested are activities involving numerals. (Author/TG)

Described are activities for thinking through patterns using toothpicks, paper strips, wooden cubes, and people patterns; thinking with attribute items such as geocards, namestrips, and treasures; and thinking with geometric materials such as geoboards and dot paper, cubes, and simple puzzle pieces. (MNS)

A method is presented for helping children make a smooth transition from using manipulative materials to using symbols only in solving multidigit addition problems. (MP)

Activities are given for solving verbal subtraction problems. Take-away and comparison situations are described, and three levels of activities to model the situations are given: one involving concrete materials and verbal descriptions; the second with these plus written symbols; and the third encouraging mental images. (MNS)

The construction and use of bean sticks, an easily produced and inexpensive manipulative material, is promoted. Activities and games designed to teach place value and related mathematical concepts are also presented. (MP)

Manipulative materials designed to instruct pupils on fractions are presented. The use of unit holders in teaching fundamental concepts of fractions and equivalent fractions are reviewed. (MP)

Five different triangle shapes cut from poster board or construction paper provide the springboard for student activities and discussions of a variety of geometric concepts from kindergarten to grade 8. (MP)