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 = 8^{2} + 1^{2} = 7^{2} + 4^{2}. Second, 65 is the length of the hypotenuse of 4 different Pythagorean Triangles: 65^{2} = 16^{2} + 63^{2} = 33^{2} + 56^{2} = 39^{2} + 52^{2} = 25^{2} + 60^{2}. Third, 65=1^{5}+2^{4}+3^{3}+4^{2}+5^{1}. 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.

Do you know what mathematicians do? **Maria Boyko** describes the usual written of mathematicians in her blog Work Day of a Mathematician.

**Jeremy Seminoff** takes assessment to the next level by giving a situation and letting students create their own problems in his post Student Create Math Questions in his blog Making Learning Fun.

Watch how **Malke Rosenfelds** Teach Math and Dance at the Same Time and introduce the concept of sameness to kids in Not All the Same in the Map is not a Territory.

**Steph** presents how her students created their own and showed the path how to get a hole-in-one using reflections in her post Geometry Mini Golf Course Project posted at Critical Points.

**Maria Miller** discusses the Different Sizes of Infinities in her Home School Math blog.

**Caroline Mikusa** presents a guest post about mastering times table in Making Friends with Times Table at Maths Insider.

**Sue Vanhattum** invites to you to try Kenken, a numerical magic puzzle from Japan aim to improving skills in arithmetic in her post Kenken: A Puzzle that Goes Deep posted at Mama Writes.

**Mama Squirrel** talks about the questions about “being mathematical” and early experiences about her daughter in A Countdown to School: Interview with the Apprentice posted at Dewey’s Treehouse.

**
Shaun Klassen** discusses the basic of functions at Introduction to Functions as well as more advanced topics about Complex and Piecewise Functions at

**The Numerist.**

**Colleen Young** presents a couple of great Geoboard Actvities in Mathematics, Learning, and Web 2.0

**Denise Gaskins**, founder of Math Teachers at Play presents her new favorite math proof at Math That is Fun: Infinite Primes posted at Lets Play Math.

**Proofs from The Book** presents an interesting Proof of the Area of a Triangle.

I hope you enjoyed the Math Teachers at Play 65, you may also want to enjoy the following carnivals.

- Last month’s MTaP 64 at Mathematical Mischief
- Carnival of Mathematics (high school & up)
- Carnevale della Matematica

*Image Credits: Inspirations, Critical Points, Proofs from the Book*