Sequential thinking is an essential element in one’s ability to experience success in various branches of math — and life, as well. Think of the sequence of steps one employs in the act of getting dressed in the morning to go to school or work: socks first, shoes second (not the other way around). The [...]
I have always believed, contrary to general public opinion, that “FRACTIONS ARE FANTASTIC”. I have no great trouble with adding, subtracting, multiplying, or dividing these marvelous little creatures. In fact, I even take a certain amount of pleasure in doing problems with them. Of course, nowadays with the calculators that have the ability to do [...]
Introduction While contemplating on the number curiosity below, I discovered that it possessed deeper and unexpected characteristics, structure, and patterns. I have not seen any discussion of these findings in the recreational literature I have read. Hence, it is being offered with the belief that I have uncovered a new recurrent operation pattern of a cyclic [...]
PALINDROMES: A Teacher’s Guide A number that remains unchanged in value upon writing it in reverse is called a palidromic number, or simply a palindrome. The idea is borrowed directly from a popular form of word play. Certain words, like dad, noon, radar, etc. possess this reversal invariant property. Even many sentences can be formed [...]
INTRODUCTION Before we can explain what a happy number is, you have to learn a new idea, called “recurrent operations.” As the word “recur” means “to happen again”, a recurrent operation must mean a mathematical procedure that is repeated. A very simple example would be the rule “add 5 to the result”. If we started [...]
On the 14th annual American Junior High School Mathematics Examination (1998) there appeared the following problem, which I share with you here: Problem #22: Terri produces a sequence of positive integers by following three rules. She starts with a positive integer, then applies the appropriate rule to the result, and continues in this fashion. Rule [...]
Stanislav Ulam was a famous and influential mathematician of the 20th century. Among other things, he even was a member of the team of scientists who developed the atomic bomb during the days of World War II. But like many mathematicians, he had a fascination for the simplest of things: whole numbers and basic operations. [...]
No, that is not someone’s telephone number up there in the title of this piece. It is the name of a numerical puzzle guaranteed to spark wonder and amazement in the minds of your students. It is called Kaprekar’s (pronounced kuh-PREE-kur) Constant*. This little, mysterious math activity is one of a family of math procedures called [...]
[Preface NOTE: The material presented below was lifted from an article I saw some time ago by Dan Brutlag, "Making Your Own Rules". THE MATHEMATICS TEACHER, November 1990. pp. 608-611. What is being given below is how I prepared a handout to give to my classes, mostly as anactivity for use by a substitute.] NUMBER [...]