These 18 standards-based activities with mystery-picture drawings really motivate students to practice key math skills. After students complete each skill sheet, they use their answers to follow step-by-step directions that guide them to draw a hidden picture. Since only correct answers will create the right picture, these activities are self-checking and make great independent work or homework. Topics include addition, subtraction, multiplication, division, fractions and decimals, geometry, measurement, and more. For use with Grades 3-5.
This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.
In May 2014, Presh Talwalkar made a YouTube video about how to multiply numbers by drawing lines. By the end of the month, the video received over a million views.Multiplying by lines is an innovative visual method to multiply numbers. It works like magic and gets people excited about math.This book illustrates how you can multiply by lines, enumerates the precise steps in the process, and offers examples of how to use the method. There are also novel applications of how one diagram can solve additional problems and how multiplying by lines can be used for algebraic expressions. The book includes 35 exercises with solutions.
"Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams."--Back cover.
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
