# Odd

## Using Ten Frames inside your Classroom

Ten-frames are relatively new to India. They are very useful at the beginning for learning the single-digit numbers. They also facilitate automatization of addition facts with single digit numbers. In addition, they can provide a lot of conceptual clarity wrt odd-even.

Three versions are included:

## Pythagorean Triples and Composition

We know that Pythagorean triples are infinite in number, and the most common formula for generating triples is to take two relatively prime odd numbers s and t, where s > t ≥ 1, and produce the triple (st, (s2−t2)/2 , (s2+t2)/2 ). However, can we generate all possible triples from just one triple? Can we generate infinitely many triples from just one triple? These might be questions worth investigating.

## Functional Equations - Part 2

In Part 1, I explained the different techniques to solve functional equations. In most cases, the steps to solve them are similar to those in solving algebraic equations. However there is one scenario where using the algebraic method to solve a functional equation may lead to an incomplete solution; i.e., only a subset of functions that solve the FE may be identified and not the complete list. This error is known as pointwise trap.

## The Odd-Even Tale

W e are introduced to the concept of an even number and an odd number in primary school or even earlier. Any natural number divisible by 2 is even; if it is not, it is odd. The definition is extended to integers once we learn the arithmetic of negative whole numbers. Then we make simple observations such as: the sum of two even numbers is even, as is the sum of two odd numbers, and sum of an even number and an odd number is odd.

## Generating the n-th Prime

Here is an unusual way of generating the prime numbers. It is taken from a letter written by Ronald Skurnick of Nassau
Community College (New York, USA) to Mathematics Teacher (National Council of Teachers of Mathematics) and published in the November 2009 issue of the journal.

## 64 Squares

Use a chess board to learn Math!

Getting even on a chess board : See how odd numbers & even number pattern show up on a chess board.