**Who is 109?**109 is a twin prime, twinned with 107. (from numbergossip.com)

If 109 is written in Roman notation (CIX), then it becomes reflectable along the line it is written on.

The pipe organ at the Cathedral of Notre Dame in Paris has 109 stops.

When chilled below minus 109°F, CO

_{2}becomes a solid, called dry ice.

109 equals the square root of 11881 or 118 - 8 - 1.

The only three-digit prime formed by concatenation of consecutive numbers. [Silva]

109 = 1*2+3*4+5*6+7*8+9. [Silva]

The Sun is just over 109 times the diameter of the Earth. [Friedman]

(from https://primes.utm.edu/curios/page.php/109.html)

**A Puzzle**: Can you make 109 from four 4's? (I don't promise that it's possible...)

At age 109, Augusta Bunge became the youngest living great great great great grandmother. Is that mom to the fifth power?

*is a monthly blog carnival, hosted at a different blog each month. I was hoping to give you 109 math links this month, but life intervened (parenting...) long before I got through my storehouse of cool stuff. There are plenty of goodies here, but not as many as I'd hoped.*

**Math Teachers at Play****Books**

There has been an explosion of super cool mathy books since I last hosted MTAP. Here are some I know about. I am embarrassed to admit that I haven't read most of them, and so I can't guarantee how cool they are. Let me know in the comments.

- Math and Magic in Wonderland, by Lilac Mohr (This is volume 1, there is now a volume 2. I've been meaning to buy this for the past year, and finally did, just now.)
- Avoid Hard Work, by Maria Droujkova, James Tanton, and Yelena McManaman
- Beast Academy (Fabulous curriculum, don't believe the grade levels (3 to 5), adults can find challenges in these)
- Math Girls 3, by Hiroshi Yuki (I love the first two. Turns out the 3rd one is out.)
- This is Not a Math Book, by Anna Weltman
- Any of Denise Gaskins books

**Animations**

- GIFs for Trig concepts
- A simulation of money moving randomly
- Explore Euclid's Algorithm for finding GCF, using a diagram instead of numbers.
- I do not yet understand this animation of 'involutes', but I want to read it and think about it again.

**Puzzles & Games**

- Solving equations as represented by mobiles (online)
- Reduce the perimeter game (John Golden)
- Find the number: Primes, Triangle Numbers, more
- Equation Crossnumber puzzles
- Rate, Time, and Distance Puzzle
- Highest / Lowest Result Game
- Pirate Puzzle

**Early Math**

- Skip counting and lots more: If you like Greg Tang's books, he's provided a page full of lovely resources for you to play with.
- A good problem to help resistant adults take a fresh look at multi-digit multiplication
- Why Number Sense is the most important math skill
- Fractions (Henri Picciotto)
- Number Sense (Kristin LaBeau)
- Play Math with Play Doh (Lucy Ravitch)

**Geometry**

- Triangles and Pythagorean Triples in Math Club
- Solution process for a hard problem involving three triangles
- What shapes can you get with one cut on a folded paper?
- Insight: How deep can you go? Painted Block Problem (Sam Shah)
- Some lovely tesselations (Luis Iglesias)

**Probability & Statistics**

- Misleading Interpretations (Stack Exchange)
- Fun Probability Question
- Math Club Probability Problem
- Estimating Population Size with Capture / Recapture

**Writing in Math Class**

- Problem Elaborations: One way to get students writing in math class (Maria Andersen)
- Math Haiku
- Math Copywork and Humor (Denise Gaskins)

**Math and ...**

- Ending the Curse of Remedial Math (NYT)
- How logarithms explain economics
- Is it hard for you to understand how math tests can be culturally biased? Here's an example. (James Cleveland)
- Family Tree Numbering (John D. Cook)

**On Teaching**

- 'Showing' doesn't work. (Mike Thayer)
- Playing with slide rules improves estimating skills.
- Forward and Backward Design (Henri Picciotto)
- Designing a Course with Peer Instruction and Project-Based Learning
- Getting students excited about higher math (Sam Shah)
- Improvisational Theater and Improvisational Teaching
- One of the principles of improv is "Yes, and...". Here's a way to use that to get students playing with math.
- Encouraging discussion with Always, Sometimes, Never

**Random Stuff**

- Links to people doing good work in Open Resources
- Calculus Lab Manual
- Using Newton's Method for a game
- Fermat's Last Theorem was proved by Andrew Wiles in 1994. Though Fermat thought he had proved it, we are pretty sure he didn't. James Propp writes a lovely summary of what Fermat probably knew.

I have more but it's bedtime and June is ending. Would you like to see your favorite blog post in next month’s playful math blog carnival? Submissions are always open!

(Note: Edited on 7/1 to add a few forgotten links, and fix a few broken links.)