Classroom Resources

In this short note, we present a proof of the generalised Pythagoras theorem. We use the ‘ordinary’ Pythagoras theorem for the proof.

Theorem. In any triangle ABC, we have:

AC2 + BC2 > AB2 ⇐⇒

This book is particularly a preparation for understanding Science. Science is built from curiosity, experience, analysis and finally the expression of a discovery. The main part of this process is arranging objects, activities and ideas so as to create a new order or pattern. Science is the discovery of new patterns. This book is to help children discover the patterns and arrangements of the world around them by using their hands, senses and minds.

The whole of plane geometry is based on two figures, the straight line and the circle. Both these figures are defined by two points, say A and B. For drawing these figures, two instruments are available: (i) an unmarked straight edge for drawing a straight line joining A and B and, if necessary, extending the straight line beyond the segment AB on both sides; (ii) a compass for drawing a circle with one of the points A (or B) as centre and passing through the other point B (or A).

In this short note, we present a proof of the generalised Pythagoras theorem. We use the ‘ordinary’ Pythagoras theorem for the proof.

Theorem. In any triangle ABC, we have:

AC2 + BC2 > AB2 <--> C < 90 ,

AC2 + BC2 < AB2  <--> C > 90◦ .

In this short note, we present a proof of the generalised Pythagoras theorem. We use the ‘ordinary’ Pythagoras theorem for the proof.

Theorem. In any triangle ABC, we have:

AC2 + BC2 > AB2 ⇐⇒

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.

Wikipedia [1] defines a semi-prime as a natural number that is the product of two prime numbers. The definition allows the two primes in the product to be equal to each other, so the semi-primes include the squares of prime numbers. Displayed below are the first forty semi-primes.

 

Problem-solving, which has always been an important part of learning mathematics, received considerable attention after it was recognised as a route for promoting mathematical thinking in the Position Paper on Teaching of Mathematics (NCERT, 2005). For problem-solving to flourish in its true spirit, two ingredients are essential: adequate knowledge and skill to solve the problems and acumen to generate good meaningful problems

 

Problem-solving, which has always been an important part of learning mathematics, received considerable attention after it was recognised as a route for promoting mathematical thinking in the Position Paper on Teaching of Mathematics (NCERT, 2005). For problem-solving to flourish in its true spirit, two ingredients are essential: adequate knowledge and skill to solve the problems and acumen to generate good meaningful problems

Fractions have long been earmarked as a danger zone for both students and teachers – while one needs to tread carefully here, the topic should not be shied away from or treated with so much caution that students tend to handle it with reservation. Misconceptions are a natural stage of conceptual development and should not be viewed as an undesirable occurrence. What is important is that the teacher is aware of them and addresses them to the extent possible.

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