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.

Paper folding techniques have been successfully used to demonstrate multiplication of proper fractions in the classroom. This article may be used to make sense of the same techniques when applied to improper fractions. The problem at hand is to investigate how a product such as 3/2 x 4/3 may be demonstrated by paper folding.

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.
For each of these three means (arithmetic mean, geometric mean and harmonic mean) , there is a simple and well-known geometric construction that illustrates it, but is there a single diagram that illustrated all three at the same time?
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