# exploration

## T-LAB: Dream Yard for Happiness

Pramod Maithil

‘When students were asked whether they have ever been bored in class, 83 percent of NAIS students answered that they were bored sometimes (50 percent) or often (33 percent), compared with 86 percent of public-school students (36 percent) were bored sometimes; 50 percent were bored often.’ HSSSE Report 2016.i

## Joining the Dots...

In our last Low Floor High Ceiling article, we had looked at Squaring the Dots... a series of questions on counting the dots inside squares of different sizes and orientations drawn on dotted paper with the dots as lattice points. The focus of the activity was to tilt squares and try to find a general formula for the number of dots inside the square of a particular tilt, as the side of the square changed.

## Finding the Square Root of a Four-Digit Perfect Square

On the web page [1] belonging to A2Y Academy For Excellence, there appears a curious method to find the square root of a four-digit number if it is known that that number is a perfect square. We describe the method here using two examples and then consider how to explain it.

## Area, Perimeter and Congruency

The topic of Perimeter and Area provides rich ground for teachers to examine the truth values of statements and then introduce the crucial ‘What-If ’ which can change a situation around completely.

## Teaching geography through current events

Geography as a subject entails the study of the Earth as the home of man; hence a framework of geographical knowledge is indispensable in the conduct of human affairs. Professor K. Mason from Oxford once said, “Many of our present-day troubles can be traced to the neglect of the teaching of geography.” A geographer can make a definite contribution to numerous modern problems. Teaching geography through current events and practical examples will help students understand geography, society, and culture better.

## 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.

## Exploration with Surds

In this short note we present a classroom vignette involving surds.

## Solution to the ‘Origamics’ Problem

In this note, we offer an explanation to the observations made in the ‘Origamics’ article (November 2013 issue of At Right
Angles).

## Folding and Mapping Turned-Up Folds

Haga’s Origamic activities require students to explore simple, geometric properties found when we fold paper in prescribed ways. The aim of these activities is to give students easy-to-explore paperfolding puzzles so that they can experience a micro-version of the three stages of mathematical research: exploration, conjecture and proof. In this article, we take up another ‘origamics’ exploration by Dr. Kazuo Haga from the chapter 'Intrasquares and Extrasquares' of his book.

## Explorations in Teaching

In this short note we describe some incidents in mathematics teaching— as they actually occurred in the classroom.

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