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Thought Provokers
Paradoxes and Problems to Intrigue Your Students One equals zero! Every number is greater than itself! All triangles are isosceles! Surprised? Welcome to the world of One Equals Zero and Other Mathematical Surprises. In this book of blackline activity masters, all men are bald, mistakes are lucky, and teachers can never spring surprise tests on their students! The paradoxes and problems in each One Equals Zero activity will perplex your students, arouse their curiosity, and challenge their intellect. Each counterintuitive result, false analogy, and answer that defies expectation will encourage students to look at familiar mathematical situations in a new light. By solving the paradoxes, your students will come to better understand both the possibilities and the limitations of mathematics. Many of the paradoxes, fallacies, and mind bogglers in One Equals Zero are based on classic paradoxes and can be used in algebra, geometry, trigonometry, statistics, or calculus classes. The one- and two-page activities in One Equals Zero can be used:- To reinforce, refine, or clarify a concept your students are studying
- To add an element of surprise to your mathematics class
- To stimulate problem-solving skills
- As discussion topics and extra-credit assignments Remind students about the perils of dividing by zero with Activity 14: A Question of Quadratics. Show them that deceptive geometric figures can lead to false conclusions with Activity 26: Every Trapezoid Is a Parallelogram. Encourage your students to stretch their minds around the concept of infinity with Activity 49: The Paradox of the Locked Boxes. Each of the activities in One Equals Zero can be completed in less than one class period and requires no additional materials, although several of the books geometry activities can be enhanced by the use of The Geometers Sketchpad software. With One Equals Zero, you can transform mathematical errors and quandaries into positive learning experiences. Along the way, youll encourage your students to see that the development of mathematical skill is a process of creative struggle and spirited debate. Detailed teachers notes that accompany each activity provide:
- Thorough explanation of the paradox or problem
- In-depth pedagogical and mathematical comments
- Suggestions for extensions
- Related historical material for many activities
- List of the activitys key concepts (A matrix of these concepts at the beginning of the book allows you to place each activity in a suitable context.)
- List of recommended related readings
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