Math Teachers at Play 65: Teach, Learn and Enjoy

Welcome to the 65th edition of Math Teachers at Play. First let us have some trivia about 65. First, 65 is the smallest integer that can be expressed as the sum of two distinct positive squares in two ways 65 = 82 + 12 = 72 + 42. Second, 65 is the length of the hypotenuse of 4 different Pythagorean Triangles:  652 = 162 + 632 = 332 + 562 = 392 + 522 = 252 + 602. Third, 65=15+24+33+42+51. Lastly, 65 is the traditional age for retirement in the United States, the United Kingdom, and other countries including my beloved Philippines.

And now, let the math carnival begin!

Math Teachers at Play 65 Entries

Ing shares how she prepares her 5-year old to before studying preschool elementary. I really like her activity on Number Bonds in her blog Inspirations.

Given a shape made of straight lines, can you fold a piece of paper that you can cut out the shape with one straight line? This is Bowman Dickson’s One Cut Problem in his blog Bowman in Arabia. » Read more

How to Play and Enjoy the Dots and Boxes iPad App

The Dots and Boxes iPad App is one of the latest logic iPad app that I play and enjoy very much. The game consists of a 7 x 7 rows of dots where the players connect two dots horizontally or vertically. The objective of the game is to close as many squares as you can. When you place the fourth segment in a 1 x 1 square, the square becomes yours and is filled when your color regardless of who placed the other three segments of that box.

You play in turns with your opponent, but whenever a player gains a box, he/she can continue to play. » Read more

Proof that Out of 6 Persons Either 3 are Friends or 3 are Strangers

Did you know that out of 6 people, either 3 are friends or 3 are strangers? Three are friends in the question means mutual friends: A and B are friends, B and C are friends, and A and C are friends.  Three are strangers also mean that out of three persons, none of whom know each other.

In the mathematical proof below, we represent the individuals by vertices and the relationships by edges. As we can see, we can form triangles. In the triangles below, a green edge connecting two vertices means that the persons represented by two vertices are friends and a red edge connecting two vertices means that the persons represented by two vertices are strangers. A triangle formed by edges of the same color represents three mutual friends or three mutual strangers. We highlight this relationship by filling the interior of the triangle with the appropriate color. » Read more

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