The topic of ‘Equations’ can be approached in several ways. The choice of approach has a strong impact on the conceptual image which a student builds about a given concept. Hence, the choice is crucial in helping a student in understanding the concept as well as in developing the procedure for solving the problems. However, every approach has its limitations and can be used only for solving certain types of problems. Its use is limited and it may become necessary to expose students to other approaches when the type or complexity of the problems alters.

For the middle school student, the transition from arithmetic to algebra is often quite daunting. In grade VI, the concept of a ‘variable’ is encountered for the first time. This is the stage where either a child embraces the newly introduced ‘Algebra’ or gets overwhelmed with the idea of numbers being replaced by letters of the alphabet. This is also the stage where the students learn to solve equations and find the value(s) of the unknown(s).

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.

Find the area of an inscribled triangle...

In this edition of “Adventures” we consider some problems from various mathematics contests...

The problems in this set are adapted from the Romanian Mathematical Competitions, 2014. Also find solutions to the problems in the November 2014 issue.

Here's what Sringeri Srinivas does when he finds the noise getting too much. What would you do?

Mathematical puzzles are generally perceived to be at the periphery of mathematics, and not part of the core of the discipline. This may be related to the fact that we sometimes come across puzzles that have no solution. The general expectation among mathematics practitioners and school children seems to be that problems in mathematics should have a solution. In this paper, we argue that puzzles can be an important source of learning some core mathematical ideas. 

Here are some problems for the Middle School. Also find the solutions to the problems given in AtRiA Mar 2014 issue.

Readers were asked to prove the observation made in the Nov 2013 issue of AtRiA. Here is a proof contributed by Swati Sircar.


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