#MTBoSBlaugust To Infinity and Beyond! An enrichment project idea

A favorite picture book is,Infinity and Me, by Kate Hosford.  If you haven't read it, do so!  If you teach math, buy it for your classroom.  Many of us teach sets of numbers early in the year.  We talk about infinity in domain and range.  Infinity is one of those topics that makes for a great enrichment project!

Here is an example of a "choice board" that you could use as a project in your class ...

You can access the Google Doc here ... just copy it to your Google Drive.

To INFINITY, and BEYOND!

Complete three activities making a tic-tac-toe from the Choice Board.  Use at least three of the following resources. Create a reference page for the resources you use.

• Angier, N. (2012, December 31). The Life of Pi, and Other Infinities. Retrieved August 24, 2016, from http://www.nytimes.com/2013/01/01/science/the-life-of-pi-and-other-infinities.html
• Chartier, T. (2014, April 14). Mime-matics - the infinite rope. Retrieved August 24, 2016, from https://www.youtube.com/watch?v=--nbhhuabHo
• Hosford, K., & Swiatkowska, G. (2012). Infinity and me. Minneapolis: Carolrhoda Books.
• How big is infinity? - Dennis Wildfogel. (n.d.). Retrieved August 24, 2016, from http://ed.ted.com/lessons/how-big-is-infinity
• The Infinite Hotel Paradox - Jeff Dekofsky. (n.d.). Retrieved August 24, 2016, from http://ed.ted.com/lessons/the-infinite-hotel-paradox-jeff-dekofsky
• Vi Hart. (2014, June 6). Retrieved August 24, 2016, from http://vihart.com/how-many-kinds-of-infinity-are-there/
• Weltman, A. (2014, February 20). Talk Like a Computer, Infinite Hotel, and Video Contest. Retrieved August 24, 2016, from https://mathmunch.org/2014/02/20/talk-like-a-computer-infinite-hotel-and-video-contest/

To INFINITY, and BEYOND! Choice Board

Define infinity for a 1st grader.  Define it for a 6th grader.  Define it for a high schooler.  How do your definitions change?	Explain the infinity symbol.  What is it’s name?  How did it originate?	What does infinity look like to you? Draw a picture that captures infinity.
N. Angier says in her New York Times post, “... there are infinities, multiplicities of the limit-free that come in a vast variety of shapes, sizes, purposes and charms.”  What is meant by “different” infinities?	Select either the infinite hotel paradox or Zeno’s Paradox.  Write a story, poem, or essay about the one your choice.	What is a doppelgänger, and why does the existence of an infinite universe suggest yours might exist?
Make a list of quantities that you believe are infinite and present that list to a group of classmates. Invite your classmates to debate whether or not the quantities are finite or infinite, and if infinite, which kind of infinity.	Mime Tim Chartier uses movement to explore and express the idea of infinity. Watch his youtube video.  Then, create your own skit or mime to convey how you see infinity.	Is it possible to find the sum of an infinite series?  Explain.

Reference:  Teaching the Mathematics of Infinity. (0604). Retrieved August 24, 2016, from http://learning.blogs.nytimes.com/2013/01/30/teaching-the-mathematics-of-infinity/

First Week Idea - Chessboard Squares Extension

I love the YouCubed Week of Inspirational Math ideas!  I love the idea of starting at the very beginning of the year inviting our students to explore patterns, create generalizations, and communicate math!!

With that in mind, I love to stumble on ideas ... some olds ones that need revamping ... like the one I'm sharing today!

I imagine many of us have challenged students with the question - "How many squares are on a Chess board?"  And of course, the first response is often 64, which allows us the opportunity for a sly smile, raised eyebrows, and the comment, "Really?  Are you sure?"

One of the fun things I am doing in retirement is sharing Usborne Books & More with folks ... yes, I'm not just a math lady ... I'm also a book lady!  So I was pleasantly surprised the other day when I was looking through Anna Weltman's, This is Not Another Math Book**, I found a great extension of the question about squares on a Chess board!

Obviously in doing this activity, you want to start with the basic challenge!  And have you ever noticed the pattern??

1    8x8 square

4    7x7 squares

9    6x6 squares

16  5x5 squares ... YES!

The number of subsequent numbers of squares are all square numbers!!  WooHoo!

The extension in Weltman's book above asks students to consider a rectangular board.  How many squares are on a 5 x 8 board or a 4 x 6 board?  Can they not only answer those questions ... but can they generalize the rule??!  Can you make a rule for how many square there are in ANY SIZE rectangular chessboard!

**If you are interested in knowing more about the book I've referenced, let me know.  It is currently on special.  Publisher's Weekly says this about the book:  This companion to THIS IS NOT A MATH BOOK continues to explore the connections between mathematics and art via more than two dozen step-by-step projects. Most of the projects require only the paper templates provided, along with writing utensils, a ruler, tape, and scissors. They include drawing kaleidoscopic patterns (as part of an exploration of symmetry), making a forest of fractals trees, and assembling five-square pentomino shapes (they resemble Tetris pieces) into pictures. There isn’t much discussion of how artists use math (Mondrian is the only fine artist mentioned), but Weltman’s projects ably demonstrate how creative mathematics can be.  

#BLAugustChallenge2018

#MTBOS

#ITeachMath

#UsborneBooks&More

The Number Hunter

This week I learned about a new project that sounds awesome! I am always looking for video that inspires students to want to learn math.

Introducing The Number Hunter!

Stephanie Glen is creating a web-based TV show that’s both fun and educational. She wants to use the same idea that made science fascinating to children.   Stephanie uses Bill Nye, the science guy, as her example.  He introduced cool experiments in video and students were enticed to learn more!  

Check out The Number Hunter project!

And while you are exploring math online, peruse Stephanie's website on statistics!

math club memories!

In past years I had great fun with math clubs.  I did not sponsor clubs that were intensely competitive.  Instead, I sponsored clubs at grades 4 - 8 that were exploratory.   We would explore math topics that were not commonly included in the core curriculum.

A few of my favorite resources included:

• NCTM's Student Math Notes (now called Student Explorations in Math)  These are copyright protected but available with a small membership fee.


• Cynthia Lanius' website has fun math explorations suitable for class or clubs.


• For my elementary students we worked various puzzles - like these or these!


• We worked sample contest problems - samples at Math Olympiad


• And we played favorite games like Set, 24, and Equate!  There is a SET tutorial and daily game online.  There is a 24 game online as well!


• We read Theoni Pappas' stories about Penrose, the mathematical cat!

I haven't sponsored a math club for several years.  Instead I sponsored a writing club ... which was different and fun!  If I were in an elementary school this year I would consider combining the two ideas ... math stories, math poems, and math problems!