Secrets of Mental Math - The Mathemagicians' Guide to Lightning Calculation and Amazing Math Tricks
Author – Arthur Benjamin and Michael Shermer
If you need to find a math refresher, prepare for math competitions, find another way to teach basic arithmetic that clicks for at-risk students, or find ways to show off your mental math skills, take time to read a few chapters of Secret of Mental Math. If you do, you may find yourself saying, "Why didn't they teach me that in school?"
The authors share that "The fundamental principle of mental math arithmetic – namely, to simplify your problem by breaking it into smaller, more manageable parts. This is key to virtually every method you will learn in this book." As I read through some ideas I recognized that some tricks may not be new or secret to "math" people, but they are probably not common knowledge. Here's a quick one shared in chapter one, squaring a number ending in 5 requires two rules.
1) Multiply the first digit by the next higher digit
2) Append "25" to the answer
For example, 65 x 65 => the first digit is 6; so multiply 6 by the next higher number (7) to get "42" and attach "25" on the end. Thus, 65 x 65 = 4225.
Although some of the content towards the end of the book may take a few minutes to grasp, I like this book because as a teacher of Developmental Mathematics for adults and Tutor of other struggling math students, I believe my students could pick this book up on their own and be enlightened by the way Secrets of Mental Math proposes another way to approach arithmetic rather than the traditional methods that alluded them in school.
Also, I believe teachers and instructors should share some of these mental tips in their classrooms as alternative ways to work a problem. I call my math tips and alternative methods "Mrs. Mackie’s Math Commercials." And yes, I saw some of my commercials in this book. For instance, recently after giving a quiz, I notice some students were multiplying 2 digit by 2 digit numbers incorrectly. Now, that particular skill isn't part of the curriculum, but I addressed it in a math commercial showing the traditional algorithm and the method used in chapter 3 of Secrets of Mental Math. In fact, below is the full Table of Contents:
Chapter 0 Quick Tricks: Easy (and Impressive) Calculations
Chapter 1 A Little Give and Take: Mental Addition and Subtraction
Chapter 2 Products of a Mispent Youth: Basic Multiplication
Chapter 3 New and Improved Products: Intermediate Multiplication
Chapter 4 Divide and Conquer: Mental Division
Chapter 5 Good Enough: The Art of "Guesstimation"
Chapter 6 Math for the Board: Pencil-and-Paper Math
Chapter 7 A Memorable Chapter: Memorizing Numbers
Chapter 8 The Tough Stuff Made Easy: Advanced Multiplication
Chapter 9 Presto-digit-ation: The Art of Mathematical Magic
Chapter 10 Epilogue by Michael Shermer: How Math Helps Us Think About Weird
Take a look inside the book or buy it by clicking the link below.