Mathematics

Fraction additon can be made interesting , easy and fun using this worksheet.

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The topic of ‘Equations’ can be approached in several ways. The choice of approach has a strong impact on the conceptual image which a student builds about a given concept. Hence, the choice is crucial in helping a student in understanding the concept as well as in developing the procedure for solving the problems. However, every approach has its limitations and can be used only for solving certain types of problems. Its use is limited and it may become necessary to expose students to other approaches when the type or complexity of the problems alters.

It was during lunch on a pleasant day that I was told about this popular book on Mathematics called “Mathematician’s Delight.” I was chatting with a professor who said that his choice to become a mathematician was influenced by this book. The story went like this: When the professor was a teenager, just after high school, during the summer vacation, he found this book and wanted to give it a try. He could follow most of it without much difficulty, and solved most of the exercises which led him to ‘experiment’ with mathematical ideas on his own.

Pure geometry or Euclidean geometry is a body of theorems and corollaries logically derived from certain axioms and postulates as presented in Euclid’s Elements. Later geometers, both Greek and others, have added to this. Occasionally some algebra is brought in but not trigonometry. Abraham Lincoln is said to have read the Elements just for the reasoning.

Some problems for the Senior School.

In this edition of ‘Adventures’ we study a few miscellaneous problems, some from the PRMO and some from the AIME (the ‘American Invitational Mathematics Examination’). As usual, we pose the problems first and present the solutions later.

We know that Pythagorean triples are infinite in number, and the most common formula for generating triples is to take two relatively prime odd numbers s and t, where s > t ≥ 1, and produce the triple (st, (s2−t2)/2 , (s2+t2)/2 ). However, can we generate all possible triples from just one triple? Can we generate infinitely many triples from just one triple? These might be questions worth investigating.

Graphics calculators have been available to students in secondary school in some countries now for more than thirty years, although of course their capabilities have been developed in various ways to support the school curriculum over that time. The most frequent use of these devices seems to be concerned with the representation of functions, including in particular their graphical representation, which was an important component of a previous paper in this magazine (Kissane, 2016).

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