Class 11-12

New educational portal Math4U - http://math4u.vsb.cz offers attractive and complex training materials for students and also offers tools for teachers to prepare tests and exams.

Math4U portal is divided into three main sections - Math for Student (Math4S), Math for Teacher (Math4T) and Math for Class (Math4C).

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.

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).

On the web page [1] belonging to A2Y Academy For Excellence, there appears a curious method to find the square root of a four-digit number if it is known that that number is a perfect square. We describe the method here using two examples and then consider how to explain it.

A classroom observation. A colleague a shared an observation that had come up during an exploratory class he was taking at the middle school level. The topic being discussed was Pythagorean Triples, i.e., triples (a, b, c) of positive integers satisfying the relation a 2 + b 2 = c 2 . If the three integers also happen to be relatively prime to each other, i.e., share no common factors exceeding 1, then the triple is called a ‘Primitive Pythagorean Triple’ (PPT for short).