This article describes a hands-on geometric tiling art activity used in two third-grade classes and four fifth-grade classes in a rural public elementary school with class sizes of around 20 students each. The lesson investigates concepts in geometry, number sense, and probability. Examples of student work and takeaways for other teachers…

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.

In this paper, we give possible suggestions for a classroom lesson about an application of probability using basic mathematical notions. We will approach to some combinatoric results without using "induction", "polynomial identities" nor "generating functions", and will give a proof of the "Vandermonde…

Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…

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…

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)

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…

Discusses methods for integrating mathematics with study of culture and history to encourage awareness of its role in everyday life: comparing number words in foreign languages; discussing number origins, numerical symbols of ancient societies, games of skill and chance; and examining different housing styles to develop geometry and measurement…

Presents an activity on probability and area in which students try to decide which door to buy. (ASK)

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

These materials on geometric probability are the first unit in a course being developed by the Mathematics Department at the North Carolina School of Science and Mathematics. This course is designed to prepare high school students who have completed Algebra 2 for the variety of math courses they will encounter in college. Assuming only a knowledge…

Describes three activities to teach mathematical concepts involving probabilities related to outcomes using "Sicherman" and other dice; geometric representations of algebraic identities; and the volume of a cone. (MDH)