In this article, we draw on assemblage theory to investigate how children aged 5 engage with different material surfaces to explore ordinal and relational aspects of number. The children participate in an activity in which they first interact with a strip on the floor, then with a multi-touch iPad application, to work with numbers in expressive…

The purpose of this study was to examine patterns of mathematical practices evident during children's interactions with touchscreen mathematics virtual manipulatives. Researchers analyzed 33 Kindergarten children's interactions during activities involving apps featuring mathematical content of early number sense or quantity in base ten, recorded…

Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

This paper discusses the use of Numicon number teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined. (Contains 4 figures.)

A set of square counters is described as a simple way to introduce new concepts and as a concrete way for students to learn. (MP)

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)

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)

A concrete approach to prime numbers is presented using rectangles and triangles to construct a building for each number so that each story represents a pair of factors and the triangular-shaped roof represents the number. (MP)

The importance of using concrete materials to teach fractions is emphasized. Suggestions for preparing inexpensive sets of such materials are given, with nine activities for their use. (MNS)

Topics covered include: a game involving dice, using curve stitching to teach number concepts, and an activity to introduce rectangular coordinate systems. (MP)

A game for two teams employs dice, meter sticks, and Cuisenaire rods. The game gives practice in number facts, regrouping, and use of rods; it can also serve as an introduction to the metric system. (SD)

Games which use dominoes, dice, and playing cards to promote computational skill are described. (SD)

Activities and manipulative materials that teach pupils regrouping, also known as borrowing or carrying, are reviewed. Several examples of typical student errors and the reasons for these mistakes are outlined. (MP)

Several problem-solving activities involving only 0-9 to be used with sets of ceramic tiles are presented. Finding specified sums, differences, or products is the object of most of the problems. (MNS)

Presents an activity using base-10 blocks and the TI Explorer calculator to help fifth and sixth graders represent their ages in different numerical bases to appear older or younger than their real age. (MKR)