Understanding The Game of Odd Numbers by Paul Chika Emekwulu

Understanding the Game of Odd Numbers

Introduction

The students featured in this dialogue are Helen, Jane, Idahosa, and .  The teacher’s name is Miss Francisca Awosika.  The school is Airewele High School, Benin, Edo state.

An odd number is of the form, 2n+1 where n is a whole number. Therefore, if 2n+1 is the first odd number, the next odd number is of the form, 2n+3.  The odd number game takes advantage of the fact that the difference between two consecutive odd numbers is equal to 2.

Objectives

At the end of the dialogue the students should be able to:

(a)  have fun with the trick.
(b)  use algebra to prove why the trick works.
(c)  use arithmetic to verify results.
(d)  search for counter examples of odd numbers that do not satisfy the requirements of the game.

Previous Knowledge or Prerequisite

The students are familiar with odd numbers.

The Dialogue Begins

Examples with One Digit Numbers

EXAMPLE 1

(a)  Start with any odd number say: 1.

(b)  Add the next odd number to your number in (a): 1+3=4.

(c)  Add 2 to your sum in (b): 4+2=6.

(d)  Subtract 4 from your sum in (c): 6-4=2.

(e)  Divide your answer in (d) by 2: 2/2=1.

EXAMPLE 2

(a)  Start with any odd number say: 3.

(b)  Add the next odd number to your number in (a): 3+5=8.

(c)  Add 2 to your sum in (b): 8+2=10.

(d)  Subtract 4 from your sum in (c): 10-4=6

(e)  Divide your answer in (d) by 2: 6/2=3.

EXAMPLE 3

(a)  Start with any odd number say: 53.

(b)  Add the next odd number to your number in (a): 53+55=108.

(c)  Add 2 to your sum in (b): 108+2=110.

(d)  Subtract 4 from your sum in (c): 110-4=106.

(e)  Divide your answer in (d) by 2: 106/2=53.

EXAMPLE 4

(a)  Start with any odd number say: 67.

(b)  Add the next odd number to your number in (a): 67+69=136.

(c)  Add 2 to your sum in (b): 136+2=138.

(d)  Subtract 4 from your sum in (c): 138-4=134.

(e)  Divide your answer in (d) by 2: 134/2=67.

Examples with Two Digit Numbers