Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

Simple, classroom-tested probability activities that capture students' interest, develop critical thinking skills, and reinforce addition facts are suggested. All activities involve investigating the probabilities of the sums that come up when two dice are tossed. (MT)

The concept of statistical significance is explained, with specific numerical illustrations. (MNS)

Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)

The history of probability from ancient times is presented. The relationship between the mathematical and experimental definitions of probability are detailed. (MP)

Presents examples illustrating how to teach statistics in connection with mathematical concepts. Describes using percentage problems and graphing problems in the classroom. (YP)

Describes the "Buffon's Needle" problem, which is calculating the probability that a needle will cross one of two separated lines. Calculates the probability when the length of the needle is greater than the space of the two lines. Provides an analytic solution and the results of a computer simulation. (YP)

Discusses student difficulties with probability concepts and argues that a key difficulty is the lack of transferability of pupils' curriculum-based knowledge. Presents several probability game activities to help students with these difficulties. (MKR)

Activities related to content areas important to the primary mathematics program, but outside the scope of arithmetic, geometry and measurement, are presented. Topics include relations, number sentences, solving sentences, logic, probability, statistics, number theory, and the system of integers, Inclusion of these topics is justified and…

A hypothetical classroom discussion is used to present concepts and problems students can master. Three computer programs are listed for binomial probabilities. (MNS)

The use of indicator functions is promoted as a vehicle for providing students with greater appreciation and understanding of the function concept, which might be good preparation for the functional concepts of probability and random variable. The use is seen to provide a reasonably accessible method of verifying set-theoretic statements. (MP)

Developed are simple recursion formulas for generating the exact distribution of the longest run of heads, both for a fair coin and for a biased coin. Discusses the applications of runs-related phenomena such as molecular biology, Markov chains, geometric variables, and random variables. (YP)

Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

Activities involving rolling dice and recording results in diverse ways introduce children to a variety of basic mathematical concepts. Several games and activities are described. (SD)

The lesson described first involved tossing a pair of dice and recording on a graph the sum produced on each roll. Pupils examined questions such as which sum occurred most often. The second part involved a graph that indicated which types of sums were most likely to occur. (Author/MP)