Discusses some surprising properties of the natural numbers set such as axioms for natural numbers and mathematical induction. (ASK)

Presents two activities on pentominoes using geoboards and rectangles. (ASK)

Presents an activity that engages children in thinking about the results of combining numbers. (ASK)

Presents activities for studying metric time where time is divided using base 10. (ASK)

Introduces an algebra lesson plan on two people saving money over the course of a week and the problems they encounter for early elementary school students. (YDS)

Tackles a tricky problem of probability based on the well-known carnival game Chuck-a-Luck which, at first glance, appears to favor the bettor. Presents an activity in which students correct a common fallacy in probabilistic reasoning and extend play to a gambler's ruin analysis. (Author/ASK)

While exploring the subject of geometric proofs, boolean logic operators AND and OR can be used to allow students to visualize their true-or-false patterns. An activity in the form of constructing electrical circuits is illustrated to explain the concept.

Different representations of rational numbers are considered and students are lead through activities that explore patterns in base ten and other bases. With this students are encouraged to solve problems and investigate situations designed to foster flexible thinking about rational numbers.

Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

Participants at the Summer Institute Pattern Exploration: Integration Math and Science in the Middle Grades used and developed a method treat arithmetic, algebra and geometry as one entity. The use of iterative geometric constructions is seen to reinforce the concepts of exponents, ratios and algebraic expressions for the nth stage of the…

Tennis is a sport in which the mathematics involves an unusual scoring system together with other applications pertinent to the draw for different types of tournaments and the relative ratios of points won and lost. The name of the sport is thought to have originated from the French word "tenez", which translates roughly as "to receive (the…

As a unifying feature of this Special Issue, we have asked proponents of each framework to analyse an empirical classroom account of one student's process of solving a mathematical problem. Here, for the case study of "Frank", we give the main data that were available to all authors.

This article describes a polyhedra construction project that illustrates how one activity can address several of the mathematics content standards in the NCTM Principles and Standards for School Mathematics.

In order to collaborate effectively in group discourse on a topic like mathematical patterns, group participants must organize their activities in ways that share the significance of their utterances, inscriptions, and behaviors. Here, we report the results of a ethnomethodological case study of collaborative math problem-solving activities…

This article introduces and explains probability games from diverse cultures. Activities are described and teacher-ready materials are included.