# investigation

## A path to π

Consider the following situation. A regular polygon of n sides is placed symmetrically inside another regular polygon of n sides i.e. with corresponding sides parallel and with a constant distance between them. We now have a 'path of uniform width' running around the inner polygon. Now the following is asked: By how much does the perimeter of the outer polygon exceed that of the inner.

## π Enters the 5th Class

I write this to tell myself that it was not a dream...

This year I taught a bunch of fifth standard kids in Sahyadri School KFI (Krishnamurti Foundation India), who, like all others of their age, were high-energy kids; they were willing to explore but found it difficult to sit down in one place. I had a great relationship with them. The air in the classroom was of love, trust and wonder!

## Spiral of Square Roots

Take the perennial favourite Pythagoras theorem to the classroom and pose these investigative questions. Spiral of square roots perks up the proceedings!

Mathematical investigations are perfect for Low Floor High Ceiling activities. Here, we have described how a simple pattern can be recognized, investigated, played with and generalized. If your students have enjoyed DADS Rule, do let them try the same strategies with other number patterns; we hope they rule!

## The Difference of Two Squares Formula - A New Look

The difference-of-two-squares formula a2 − b2 = (a − b)(a + b) is so basic that it would seem a difficult task to say anything new about it! But Agnipratim Nag of Frank Anthony Public School, Bangalore (Class 8) has done just this. In this short note we describe his interesting and innovative approach to prove the identity. It has particular relevance for those who teach at the middle school level.

## A Diagonal Investigation

This task is designed to give students a feel of how mathematicians ‘work’. It develops the skills of documentation, communication, reasoning and conjecture.

## When does it have Maximum Area? ~ A GeoGebra Exploration

Use GeoGebra to check when will a rectangle have maximum area when it is inscribed in a triangle.

## Exploring Fibonacci Numbers using a spreadsheet

In this article we are going to explore a very interesting sequence of numbers known as the Fibonacci sequence.
The exploration of the sequence can lead to an absorbing classroom activity for students at the middle school and secondary school level. Students can explore many patterns within the sequence using a spreadsheet like MS Excel and the observations can lead to an enriching discussion in the classroom.

## Reflecting on projects

Having realized that students simply submit projects that their parents work on, this particular teacher devised a new way of getting the children to work on projects and one of her rules on submitting projects was that they should not be longer than two pages! But today, thinking back on those classes, she wonders whether she and her students satisfied the basic tenets of project work.

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