Are certain individuals born to be teachers and can only those be truly competent? Or can people without such aspirations develop to become ‘great teachers’? Are there certain conditions, the presence of which foster such development?

# Area

Children are taught many kinds of measures in the primary grades, like length, weight, volume, money, time and finally area and perimeter (which is nothing but measurement of length). While for teaching length, weight and volume, efforts are made to give students an exposure to informal/ non-standard units of measurement (and thus some implicit understanding of what we may use to measure something), the other measurement ideas start with the standard units, conversions and formulae.

Interesting problem on area and triangle.

- Read more about A Triangle Area Problem
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The article talks about a simple activity which can be performed with students of primary, middle and high school. The shape that is used to discuss here is a square and hence it is expected that students know the basic properties of a square. The article also talks about using lines. Even if students don't have a Euclidean notion of definition of a line, that idea can be instilled as the teacher executes this activity.

- Read more about Cutting a Square into Equal Parts
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On the Facebook page (AtRiUM: At Right Angles, Us and Math) linked to this magazine, one of our contributors, Arsalan Wares, has been astonishingly prolific in posting problems. A good many of these have had to do with regular hexagons; more specifically, with the areas of polygonal regions drawn within such hexagons. It is both astonishing and pleasing to see such a rich diversity of problems arising from this simple and familiar structure.

- Read more about Arsalan’s Amazing Area Problems
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Websites and focus interest groups are a good source for interesting problems. But it’s rarely that one gets down to solving these; more often they go into a to-do list. We hope that the solution presented here will encourage you to try more of these. Look at the steps of the process: Visualization, definition of the problem, connection to known formulas and then good old mathematical processing. Problem solved!

- Read more about Area covered by Two Intersecting Circles
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In this article, we study the following problem. Three circles of equal radius r are centred at the vertices of an equilateral triangle ABC with side 2a. Here we assume that r > a. Find the area of the three-sided region DEF enclosed by all three circles, in terms of r and a.

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Consider a solid sphere of radius r. Suppose it is melted and the molten mass is recast into two solid spheres of radii r 1 and r 2 . Does the total surface area increase, decrease or remain the same, if it is assumed that there is no loss of matter in the whole process?

- Read more about On an Optimization problem
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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.

- Read more about Area, Perimeter and Congruency
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This article is the second in the ‘Inequalities’ series. We prove a very important inequality, the Arithmetic Mean-Geometric Mean inequality (‘AM-GM inequality’) which has a vast number of applications and generalizations. We prove it using algebra as well as geometry

- Read more about Inequalities in algebra and geometry 2
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Find the solution to the circle area problem posed in the earlier issue of AtRiA.

- Read more about Circle area problem
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