Class 9-10

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

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

Interesting problem on area and triangle.

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

Some problems for the Senior School.

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?

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.

In this article, I have argued that it is important not to bunch all the students’ errors as “careless mistakes” or “over-generalisations”. We can classify the errors to understand – (a) what is their mathematical source and (b) what could be the student’s thinking underlying such responses. This will help us in designing appropriate interventions for handling these errors in classroom.

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