This is the **72nd Edition of the Math Teachers at Play (MTaP) blog carnival**!

The number 72 is a Harshad number in number bases from binary up to but excluding base 13. Harshad numbers are numbers that are divisible by the sum of their numbers. They are base-dependant. In binary 72 is expressed 1001000. Add the digits together to get 2, one of the factors of 72. With a base of 5, 72 is expressed 242. With base 6 it is expressed 200. You can play around checking the bases of different numbers with an online calculator.

### Now on to the math posts….

Currency of the Weekly Art Show – This post starts off describing math as a “soul crushing experience” for artistically creative students with teachers “forcing repetitive routines where there’s no margin for creativity.” Hardly the type of beginning one would expect for a blog carnival about math teachers at play, and hopefully the rest of the posts here will prove the incredible potential for creative fun during math, but moving beyond that slight towards math teachers, the post shares an idea for encouraging artists to interact with their math homework in a different way.

Math story books are one way of making math fun. What are your favorite math story books? Caroline Mukisa shares her list of favorites here at Math Story Books to Help Build Your Child’s Love of Math. Becky’s list of 10 math books at the blog This Reading Mama includes some overlap and some different books. Another list of mathematical chapter books was put together by Erica at What Do We Do All Day.

Crystal Wagner writes about the importance of manipulatives for both younger and older students. Her blog includes Amazon links to manipulatives you can buy. Other bloggers wrote about manipulatives you might have at home already or about making use of chance opportunities. Julie was inspired to use a rope ladder for an Active Patterning Activity. In Place Value Fun a homeschooler describes the math her four year old is exploring with the the *Math You See* curriculum, playdough, beads and marshmallows. Multiplication towers can be built with beads, lego or modeled on minecraft.

How else can one encourage practice of multiplication? Karyn Tripp shares her way of helping kids practice with multiplication houses. Rebecca Reid shares the first level of her multiplication game Splat as a free download – other levels can be purchased. There’s also instructions for how to make a multiplication strategy game over at Crafting a Green World.

Positively Potatoes Math Activities includes potato-themed activities for anyone who might be studying the Irish potato famine this month, or for that matter is just looking for ways kids to practice various skills.

Over at the blog Gluten Free Mama, there’s a great post about fractals looking at trees, the Koch snowflake and the self-similarity of clouds.

Inspired by Calculus – Objects of Revolution, a post over at Moebius Noodles, begins with “**What does calculus for young kids look like? And what can kids do with calculus?** These are the questions we get a lot. So over the next 5 weeks we will be publishing a series of “Inspired by Calculus” posts. These are notes from a local math circle for 7-11 year olds, led by Maria Droujkova. Do try these activities at home by yourself (good), with your child (better) or invite some friends over (the best). If you do, please share your experience with us. As always, we welcome your questions and comments.” I can’t wait to check out the rest of their series!

Sue Vanhatten has provided a post titled: “Calculus – Optimizing the goodness.” She used origami boxes to give the students some hands-on exploration. About the post she writes: “Optimization problems, where we figure out things like the least material we can use to make a can with a given volume, or the most area we can enclose with a given amount of fencing, are probably the most useful problems we consider in calculus I. I loved how this lesson went.”

Glenn posted “Connecting Alg 1 through Stats & Calc – Lesson ideas.” These ideas use Graph Stories*, *a webpage worth checking out as well if you haven’t yet.. Regarding the post he writes: “This is an idea that I have been working on in and outside of class. Creating a consistent vocabulary of problem ideas / methods from Algebra 1 through the AP classes is important to allow for learners to see the connections between subjects.”

Robert Woodley wanted a simple tool for drawing 3D mathematical surfaces, and when he didn’t find one that met his requirements he made his own. Check out his fabulous Formula Toy. Even without understanding all the formulas it is fun to reach in and alter a detail then watch the results. Playing with this I was surprised how quickly my nine year old started to notice which parts of the fomula controlled which aspects of the shapes.

There are so many great ideas on making math fun and allowing exploration. Still, some people talk about finding math challenging and a couple of the posts submitted are about dealing with the challenges.

Do word problems puzzle you or your students? Denise of Let’s Play Math writes about approaching them like a detective: The Case of the Mysterious Story Problem.

Or perhaps the challenge faced is getting past careless mistakes. In that case check out this post by William Wu: Check for Careless Mistakes Using the Substitution Method.

Sue VanHattum wrote: “Some math educators were discussing whether or not multiplication is repeated addition. (My opinion: multiplication should be modeled many ways, repeated addition, area, arrays, …) I thought that was not the most pressing issue in math education, so I wrote this list.” Read her list here: Top Ten Issues in Math Education. Then tell me, what do you think are the important issues in math education? For the homeschoolers reading this, what are the biggest math issues in your family?

*Math Teachers at Play is a traveling blog carnival. It moves around from month to month but its home base is http://letsplaymath.net/mtap/. From there you can visit the archives, submit your blog post for inclusion in a future edition, and volunteer to host the site. You can also check out the Carnival of Mathematics. Thanks for visiting!*

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Thanks for sharing on the Homeschool Linky Party! There are many great ideas here. Hope you come by and link up again come Thursday!

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Thanks for writing up Formula Toy.

Note that I’ve made it into a Chrome App too since so many schools are adopting chrome books:

https://chrome.google.com/webstore/detail/formula-toy/nlokcbhiaandlmgclipefjalpolicngo

For my 7 year old, I became quite interested in visualizing multiplication as operations on prime factors. A post I wrote about it is here:

http://rwoodley.org/?p=492

I’d be interested in your thoughts. The relevant chrome app is here:

https://chrome.google.com/webstore/detail/visual-calculator/gjhgkallojkgahkjhppaldkbngihhnnj

Bob Woodley