Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

This article describes several ways to connect probability to other topics within mathematics, over a range of year levels, and across the curriculum. It includes a description of common issues and misconceptions, and practical learning activities to address them.

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

The goal of this geometry project is to use Voronoi diagrams, a powerful modeling tool across disciplines, and the integration of technology to analyze spring rainfall from rain gauge data over a region. In their investigation, students use familiar equipment from their mathematical toolbox: triangles and other polygons, circumcenters and…

In this article, the classic problem of finding three ways to determine the probability that the pieces of a stick randomly broken in two places will form a triangle is analyzed anew. To be useful in the classroom, an application must be incorporated into an often-crowded curriculum. What is nice about this triangle problem is that it fits in…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

The teacher's guide for the sixth unit of this SMSG series covers the two chapters on probability and on measurement. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives are stated, and a time schedule…

Topics covered in the probability chapter of the sixth unit in this SMSG series of student texts are fair and unfair games, outcomes and events, tree diagrams, and finding and estimating probability. The measurement chapter includes a discussion of length, units in the British and metric systems, perimeter, angle measure, circumference,…

This booklet contains suggestions for developing six of the twenty topics recommended for students in Secondary Forms III and IV in the schools of Victoria, Australia. These suggestions are intended for students for whom the standard course is unsuitable because of subject time allotments, ability levels, or vocational or educational needs. The…

Presents theorems about lines and lattice points, and relates these to combinatorial analysis. (RS)

Using license plates to generate random number pairs, students can calculate an approximate value for pi. The author views this approach as easier to understand than Buffon's needle. (SD)

Topics included in Part 2 of Course II are: real functions; descriptive statistics; transformations in the plane; length, area, and volume; combinatorics; and mass points. The chapter on real functions includes a discussion of properties of functions, composition of functions, inverses of functions and other topics. The chapter on descriptive…

This book is a sequel to MATHEMATICAL CHALLENGES, which was published in 1965. In this sequel are 100 problems, together with their printed solutions. The problems range from those that are quite simple to those that will challenge even the most ardent problem solver, and they include examples from algebra, geometry, number theory, probability,…

Five sets of activities for students are included in this document. Each is designed for use in junior high and secondary school mathematics instruction. The first is concerned with the use of models in mathematics. The second contains a variety of activities involving polygonal numbers. The third set of activities includes a variety of games for…