I win! : she always wins, it's not fair!
In this activity, students play a game and examine what it means for a game to be fair. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. In the game's 12 rounds, two six-sided die are rolled, the face values are subtracted, and data are recorded on a table. Player A wins if the difference is 0, 1, or 2, and Player B wins when the difference is 3, 4, or 5. The page contains a solution hint, the solution, and relat
Author(s): National Council of Teachers of Mathematics (NCTM)

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Content copyright 1999-2002 National Council of Teachers of Mathematics.

Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to think about angles as geometric shapes and to find the sizes of the angles between their fingers. It is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. For this challenge, the students trace a hand stretched to form an L-shape with the thumb and sketches angles of 90 degrees and 45 degrees between the thumb and index finger. They use the sketches to estimate the angles between their other fi
Author(s): National Action Council for Minorities in Engineer

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Copyright 2004 National Council of Teachers of Mathematics. Copyright 1999-2004 KnowNet Construction, Inc.

Middle School Portal: Math and Science Pathways (MSP2)
This web site contains descriptions and links to more than 60 virtual manipulatives, activities designed to function as concept tutorials. The virtual manipulatives, mostly in the form of Java applets, are designed to facilitate grades 6-8 mathematics learning. By encouraging active student exploration with computers, the virtual manipulatives can help students visualize mathematical relationships. They are organized into five categories based on the National Council of Teachers of Mathematics (
Author(s): Utah State University. National Library of Virtual

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Copyright 2003 MATTI Associates LLC. All rights reserved.

Logic for Computer Science: Foundations of Automatic Theorem Proving
This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. The book is self contained, and the level corresponds to senior undergraduates and first year graduate students. However,
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Mathematical Biology
These are my lecture notes for a course I teach on mathematical biology at the Hong Kong University of Science & Technology. My main emphasis is on mathematical modeling, with biology the sole application area.
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Statistical Methods in Biomedical Imaging
This resource contains the complete materials (syllabus, class notes, assignments, web-based software analysis and visualization tools) for a semester-long upper-division or graduate course on mathematical modeling, statistical analysis and visualization of biomedical imaging data.
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Missing Angle Puzzles
This lesson lays some of the ground work for eventually writing two column proofs. In the lesson students use known geometric facts to solve for missing angles. Students are asked to identify the key concepts required for the solution and to record the a path for finding the measure of a particular angle. Key concepts include the sum of the measures of the interior angles of a triangle and quadrilateral, parallel line relationships, and what can and cannot be assumed from a drawing.
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Geometry Formulas and Facts
This excerpt from the CRC Standard Mathematical Tables and Formulas covers geometry, excluding differential geometry. It is a reference for advanced students, and covers the material in quick, condensed sections of notes. Notes and diagrams are organized into sections and subsections, starting with coordinate systems, plane transformations, lines, and polygons in two-dimensional geometry. The section on three-dimensional geometry covers coordinate systems in space, space symmetries, directions,
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GeoMaths MathHelp Material
This site provides students with mathematics self-study material which is embedded within the context of the geosciences. The material consists of many MathHelp "notebooks" covering specific mathematical topics related to a relevant geological context, such as plate velocity or cliff erosion. The notebooks contain explanations, illustrations, and examples. A mathematical glossary is also constantly available, providing a brief explanation of mathematical keywords and links to the relevant notebo
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GeoMaths - 2nd Level Modules
The highest level of math on the University College London's GeoMath site, this covers skills such as complex numbers, partial differentiation, matrices, advanced vectors, and probability. Each section features a menu of topics and links to a glossary. Many have geology-based examples, using the mathematical skill within a realistic scenario. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/
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Division Races I
Practice your mental and mathematical agility with arithmetic races. A sequence of levels with timed questions. Each level gets progressively faster. The questions themselves are based on division and involve positive integers in the range 0 - 9999. There are a total of 11 levels, combing both multiple-task and single-task questions. Points available increase as the time decreases. Tracking of numerous performance measures is available for self-analysis and parental analysis.
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Arithmetic Races II
Practice your mental and mathematical agility with arithmetic races. A sequence of levels with timed questions. Each level gets progressively faster. The questions themselves are based on the four main arithmetical operations (addition, subtraction, multiplication and division) and involve positive integers in the range 0 - 1000. There are a total of 11 levels, combing both multiple-task and single-task questions. Points available increase as the time decreases. Tracking of numerous performance
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Applied Mathematics II
In this applied maths quiz, some children set out to complete their toy zoo. While out shopping they encounter numerous arithmetical problems involving addition, subtraction, multiplication and division of currency units. This helps your child gain the independence required to manage their own pocket money. Currencies used in the module are dollars, pounds and euros. The module includes many puzzles, involving sums of money up to about 20 to 30 dollars, euros and pounds, including calculation wi
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Applied Mathematics I
The quiz is set in Ancient Egypt. A group of ancient Egyptians set about their everyday lives and encounter mathematical problems. Solve them and help them on their way to the afterlife. Seven levels of randomized applied mathematical problem are included. Randomisation and fresh generation of new material maintains a high level of replayability until the underlying skills are mastered. Tracking systems are included for parental supervision. Rewards maintain student interest.
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S.O.S. Mathematics
This site is a free resource for math review material from algebra to differential equations. It provides more than 2,500 pages of short and easy-to-understand explanations for subjects including algebra, trigonometry, calculus, differential equations, complex variables, matrix algebra, and various mathematical tables. The materials on this site are designed for high school students, college students, and adult learners. Links to recommended books and other math education websites are also provi
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Environmental Decision Making
Using the Extend 'connect-the-components' visual programming, students can model and simulate ecosystems including social and economic forces as well as study parameter variations to develop an understanding of ecosystem function and productivity. By making 'what if...' changes in the model, the effects of various proposed decisions about the environment can then be shown. EDM includes three ecological systems: Ponds, Grasslands, and Logging. Students can predict results of changes in the mode
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Linear Algebra
When I started teaching this subject I found three kinds of texts. There were applications books that avoid proofs and cover the linear algebra only as needed for their applications. There were advanced books that assume that students can understand their elegant proofs and know how to answer the homework questions having seen only one or two examples. And, there were books that spend a good part of the semester multiplying matrices and computing determinants and then suddenly change level to wo
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Applied Probability
Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) i
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Private Universe Project in Mathematics: Workshop 3. Inventing Notations
We learn how to foster and appreciate students’ notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New Jersey
Author(s): Harvard-Smithsonian Center for Astrophysics

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Smithsonian Institution-Astrophysical Observatory "All Rights Reserved"

Private Universe Project in Mathematics: Workshop 1. Following Children's Ideas in Mathematics
An unprecedented long-term study conducted by researchers at Rutgers University followed the development of mathematical thinking in a randomly selected group of students for 12 years—from first grade through high school—with surprising results. In an overview of the study, we look at some of the conditions that made the students’ math achievement possible.,10 min Building Towers Five-High The Kenilworth students in the fourth grade are seen working on the Towers problem (“How many different
Author(s): Harvard-Smithsonian Center for Astrophysics

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Smithsonian Institution-Astrophysical Observatory "All Rights Reserved"