The Birthday Paradox problem can be investigated either with a carefully constructed spreadsheet (for greatest precision) or a calculator process (for reasonable precision). A number of ways of approaching this problem as a class activity are provided.

The statistical output of interest to most elementary statistics students is the p-value, outputted in computer programs like SPSS, Minitab and SAS. Statistical decisions are sometimes made using these values without understanding the meaning or how these values are calculated. Most elementary statistics textbooks calculates p-values for z-tests…

Tossing a fair coin 1000 times can have an unexpected result. In the activities presented here, players keep track of the accumulated total for heads and tails after each toss, noting which player is in the lead or whether the players are tied. The winner is the player who was in the lead for the higher number of turns over the course of the game.…

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Although a plethora of research evidence highlights positive and significant outcomes of the incorporation of the Graphing Calculator (GC) in mathematics education, its use in the teaching and learning process appears to be limited. The obvious need to revisit the teaching and learning of Probability has resulted in this study, i.e. to incorporate…

Simulation is an important learning tool that allows students to grasp probability concepts, especially when the actual scenario does not need to be replicated entirely. In the cases of tossing coins and rolling dice, gathering the data before analyzing them can be laborious and might be a waste of precious class time--time that might be better…

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The modules also introduce students to real world math concepts and problems that property and casualty actuaries come across in their work. They are designed to be used by teachers and…

Student access to programmable calculators and computer terminals, coupled with a familiarity with baseball, provides opportunities to enhance their understanding of the binomial distribution and other aspects of analysis. (MP)

One problem that students have with mathematics is that they often view the topic as a series of unrelated ideas. Sometimes they are aware that they have to know one concept to move to the next, but what is done in geometry is not necessarily related to anything in algebra. This failure to recognize mathematical connections limits students'…

Describes an activity designed to demonstrate the birthday paradox and introduce students to real-world applications of Monte Carlo-type simulation techniques. Includes a sample TI-83 program and graphical analysis of the birthday problem function. (KHR)

This article describes a project in which certain key concepts in probability were explored using graphics calculators with year 10 students. The lessons were conducted in the regular classroom where students were provided with a Casio CFX 9850 GB PLUS graphics calculator with which they were familiar from year 9. The participants in the…

Presents a game to capture student interest in probability by giving them an opportunity to explore the idea of various outcomes and the likelihood of the occurrence of one of those outcomes to explain the benefits of using a large sample rather than a small one. (ASK)

Some examples of typical nonrelevant textbook problems on probability are followed by more complex problems pulled from the real world. The resource used in this report is Newsweek magazine; and is used to help demonstrate that from the very beginning, lessons on conditional probability can have relevance. (MP)