Teacher Development

Number tricks are fun to perform and are an excellent way to enhance mathematical skills. When I was young, we used to discuss a lot of number tricks. One amongst those was as follows:

Take a number with a lot of digits. For example, suppose you think of 2134567. Add its digits: 2 + 1 + 3 + 4 + 5 + 6 + 7 = 28. Subtract 28 from the original number taken, 2134567. You’ll get some answer, say abcdefg.

We live in an era of data and information. Right from deciding what to read, what to wear, which restaurant to go to, which city to visit, whom to vote for, we consider ourselves rational human beings who rely on data to make all our decisions. How much of this data is based on facts rather than opinions and/or perceptions? This review looks at two websites, Gapminder and Our World in Data, which attempt to provide reliable global statistics and promote a fact-based worldview.

The following geometry problem is simple to state but challenging to solve!

In this edition of ‘Adventures’ we study a few miscellaneous problems.

A question about angle bisectors Consider a △ABC in which D, E and F are the midpoints of the sides BC, CA and AB respectively. Let G be the centroid of triangle ABC, i.e., the point of intersection of the medians AD, BE and CF. It is well-known that G is also the centroid of triangle DEF. If, instead of being the midpoints, the points D, E and F are the points of intersection of the internal bisectors of

The tasks of this set require you to get down to some actual cut and paste work. Arm yourself with a chart paper, a roll of cello tape and a pair of scissors.

In an article published in the November 2016 issue of At Right Angles we had seen how geometrical fractal constructions lead to algebraic thinking. The article had highlighted the iterative construction processes, which lead to the Sierpinski triangle and the Sierpinski Square carpet. Further the idea of self-similarity within these fractals was reinforced through the recursive and explicit relationships between various stages of the fractal constructions.

In this episode of “How To Prove It”, we consider two similar sounding terms which have great significance in higher mathematics: contradiction and contrapositive. Both of them arise in connection with proofs. We give several examples of proofs of both these kinds.

If two sides of a triangle have the same lengths as two sides of another triangle, and one angle of the first triangle has the same measure as one angle of the second triangle, what can be said about them? Under what circumstances will they be congruent to one another?

The ‘TearOut’ series is back, with perimeter and area. Pages 1 and 2 are a worksheet for students, while pages 3 and 4 give guidelines for the facilitator. This time we explore shapes with given perimeter or given area using the dots or the grid.

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