*Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers*is on Amazon now! But we don't yet have any reviews. If you've gotten a copy of the book, can you write a review on Amazon? We would be so grateful.

Warmly,

Sue

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#
Math Mama Writes...

## Pages

## Sunday, July 12, 2015

###
Playing with Math: Can you write a review?

*Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers*
is on Amazon now! But we don't yet have any reviews. If you've gotten a
copy of the book, can you write a review on Amazon? We would be so
grateful.

Warmly,

Sue
## Friday, July 10, 2015

###
Links on Friday

I'll be leading a Math Jam for eight days just before Fall semester starts, helping students prepare to succeed in Beginning Algebra. My eight topics:

For fractions, I plan to do a bit with Egyptian Fractions. Here's a site that looks good for that. I looked at the Beast Academy site to see if they had anything good. I found 5 things I liked: one game and two puzzles using the area meaning of multiplication, one puzzle on ordering of decimals, and one game like Taboo for communicating about shapes.

## Thursday, July 2, 2015

###
Playing with Math: Inspiring Online Conversations

## Saturday, June 20, 2015

###
Book Review: The Archimedes Codex

## Monday, June 1, 2015

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Imbalance Abundance Puzzles (We're in the New York Times!!)

## Wednesday, May 27, 2015

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Preparing for the Fall Semester: How to Get Students to Participate More

## Tuesday, May 26, 2015

###
Machinery, Lines and Circles

On Facebook, someone posted an animation of how a sewing machine works. It wasn't enough to help me understand how the top thread manages to get around the bobbin mechanism. I searched on youtube, and nothing helped. This article on math and the sewing machine made me think for a moment that I was getting it, but I still am not. How is that bobbin mechanism held in place in a way that allows the thread to get around it? (Do you see how the top thread moves past the whole back of the bobbin? How is that possible?) They say that the bobbin is held snugly inside its case, but how is the out part attached?

I think I need a transparent sewing machine, so I can really see how this is working.

On thing leads to another (especially online!), and I ended up at this site from a museum for mathematics, called The Garden of Archimedes, in Florence, Italy, where I encountered this very simple statement about the difference between constructing a circle and a line - something I had never thought about before.

## Tuesday, May 19, 2015

###
Teaching My Son (Post One of Many?)

## Thursday, May 14, 2015

###
Moebius Noodles is Delightful

*Moebius Noodles* is headed into its second printing soon. For the past few days I've been reading it over carefully to offer suggested edits. What a delightful task I gave myself! It has been so fun to remind myself of all the activities for young children Maria Droujkova and Yelena McManaman have put together.

Their suggestion for creating an iconic times table got me dreaming. How can I get my son (who "hates" math, unfortunately) inspired to take photos for a times table collection? I was dreaming of a website that would show the whole table on one page, with each photo pretty small. And when you hover over a photo, that one would show up big. I don't know how to do that, though...

Here's a photo (from lernertandsander.com/cubes) that feels like it belongs in the Grid section of*Moebius Noodles*, except that there's no pattern to the pieces. Well, the rows and columns are a bit wonky too. Hmm...

Kate Nowak posted this on Facebook. The question that came to her mind (among other less mathy questions) was ... How do*you* count these?

[Edited to add: In the comments, Joshua described a very cool pattern he saw, and suggested that it's like 9 plus 4 is 13, which looks like my diagram below.]

*Moebius Noodles* has four sections: Symmetry, Number, Function, and Grid.

The mirror book introduced in the symmetry section is so simple, and so cool to play with. Just get two small rectangular mirrors (at a dollar store), tape them together along one side, and use with photos or drawings, to see lots of symmetrical designs.

My favorite game in the function section is Silly Robot. The grownup plays the robot, and follows orders exactly (while always trying to find a way to mess up the intention of the orders).

If you know anyone with a child from one to eight who'd like to find ways to play around with mathematical ideas,*Moebius Noodles* is a great resource.

And my book,*Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers*, is delighting readers across the U.S. (and hopefully around the world). Here are a few photos of happy readers. Send me a photo of you with the book, and I'll add it to my collection (especially if you live far from me!).

This is shaping up to be a very fun summer...

## Tuesday, May 5, 2015

###
Aunty Math

**Welcome to the world of**

**Math Challenges for K-5 Learners**

One of the reasons I put together a book was my fear that good online writing often just disappears. One of the sites I had really liked - and thought of including somehow in the book - was a site with stories from Aunty Math (Aunt Mathilda). It disappeared before I could contact the author. And for years, I thought it was just plain gone.

This evening I searched for Aunty Math, and found that someone had managed to get to this site through the Wayback Machine. It is now available as an archive. Check out all eleven past challenges. I think you'll enjoy them.

I would love to be in touch with the author, Angela G. Andrews. I googled her, but I don't see an email address. I'll just thank her here for her lovely stories. Thanks, Angela!

My book,*Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers*, won't disappear. If you want a copy to appear in your mailbox, order one now.

## Playing with Math - the Book

## My Favorite Posts

## Resources

## Blog Archive

## About Me

## Education Blogs I follow

## My Other Blog

Warmly,

Sue

- What is the Golden Ratio? A boy thought a museum had it wrong, and got in the news for correcting them. Really, they used the less common version of the ratio, still right. Read about it at Sense Made Here.
- Jonathan Halabi blogged about how crazy the scores on the NY common core math tests are. I wonder how other states report scores.
- I've been wondering whether I can use the principles of storytelling to improve my teaching.
- I wonder if I can modify any of these math movement games for kids, so they'd work well with adults students.
- How can we shift math education from memorizing to problem solving? How can we help students learn problem solving? (NY Times article)
- I've figured this out before, and the answer is even somewhere on my blog maybe. But I am once again stuck. Flipping coins to one side without looking... (on a Math Riddles blog)

I'll be leading a Math Jam for eight days just before Fall semester starts, helping students prepare to succeed in Beginning Algebra. My eight topics:

- Number Sense
- Fractions
- Negatives
- Algebra
- Percents
- Graphing
- Slopes
- Problem-Solving

For fractions, I plan to do a bit with Egyptian Fractions. Here's a site that looks good for that. I looked at the Beast Academy site to see if they had anything good. I found 5 things I liked: one game and two puzzles using the area meaning of multiplication, one puzzle on ordering of decimals, and one game like Taboo for communicating about shapes.

First sighting of a comment on a mathematical blog post that was inspired by seeing the content in my book...

Jonathan Halabi writes jd2718. His post, Puzzle: Who am I?, became one of the puzzles in*Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers*.

Today Lara H replied to his post:

I responded with:

We are hoping that the book will inspire online conversations. This is the first drop of what we hope will eventually become a deluge.

Jonathan Halabi writes jd2718. His post, Puzzle: Who am I?, became one of the puzzles in

Today Lara H replied to his post:

I came across this puzzle in the book “Playing with Math.” I found a different solution based on a wrong assumption I made at the beginning of solving the puzzle. I was thinking that a number with 3 digits also has 2 digits so I made both of those statements true and came up with 4097, which works for all the other conditions.

I responded with:

I’d say ‘different interpretation’ instead of ‘wrong assumption’. I wonder how many solutions the puzzle has using your interpretation. (Pretty exciting to see my book has inspired new discussion on Jonathan’s blog post!)

We are hoping that the book will inspire online conversations. This is the first drop of what we hope will eventually become a deluge.

I bought this book because I wanted to understand more about Archimedes' role in the ancient development of calculus ideas. When I got it, I was worried it would be another book I wouldn't want to wade through. I was so wrong!

*The Archimedes Codex*, by Reviel Netz and William Noel, is fascinating. Like much *g*ood science writing these days, *The Archimedes Codex* reads like a detective story. It is gripping! Netz writes chapters about Archimedes, his math, and translation issues. Noel writes chapters about the travels of the manuscript, and the attempts to use modern technology to get better images of Archimedes' writing.

In 1998 Christie's auctioned off this battered medieval manuscript which on its face was a prayer book, but also contained traces underneath of Archimedes work, which had been scraped off. It sold for two million dollars to an anonymous bidder. William Noel, of the Walters Art Museum in Boston, followed the story and emailed the agent of the buyer. The buyer agreed to work with the museum to attempt restoration of the manuscript. Most experts expected little from the work, since the manuscript was in such bad condition. But the project, which took years, brought to light previously unknown work by Archimedes.

Archimedes had explored the idea of infinity more carefully than had ever been realized. He also did work in combinatorics, which no one had even suspected. The math is pretty easy to follow, and it's amazing. I've dogeared about a dozen pages, so I can read passages to my calculus students.

This is perfect summer reading. Enjoy!

In 1998 Christie's auctioned off this battered medieval manuscript which on its face was a prayer book, but also contained traces underneath of Archimedes work, which had been scraped off. It sold for two million dollars to an anonymous bidder. William Noel, of the Walters Art Museum in Boston, followed the story and emailed the agent of the buyer. The buyer agreed to work with the museum to attempt restoration of the manuscript. Most experts expected little from the work, since the manuscript was in such bad condition. But the project, which took years, brought to light previously unknown work by Archimedes.

Archimedes had explored the idea of infinity more carefully than had ever been realized. He also did work in combinatorics, which no one had even suspected. The math is pretty easy to follow, and it's amazing. I've dogeared about a dozen pages, so I can read passages to my calculus students.

This is perfect summer reading. Enjoy!

Paul Salomon posted some delightful puzzles a few years back, I got in touch with him about including them in the book, and now his puzzles are featured in the New york Times' Numberplay column!

I met Gary Antonick (who writes Numberplay) in person a month or two ago at a lovely meeting of math popularizers. We were both excited to meet each other*, and he asked if he could share some of the book's material in his column. Of course I said yes.

I knew the column was coming today, but forgot to look until I saw Mike South's Facebook post mentioning it. Mike writes great math explanations on Living Math Forum, but doesn't blog. I wanted to include something of his in the book, but didn't manage it. (Here's Mike on thinking about zero.)

Gary included a great photo that goes so well with the puzzles, I want to make up a new puzzle to go with it. Hmm.

If you don't already have your own copy of*Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers*, you can buy one here.

_____________

*I finally got to meet the fabulous Fawn Nguyen in person, too! What an exciting day that was!

I met Gary Antonick (who writes Numberplay) in person a month or two ago at a lovely meeting of math popularizers. We were both excited to meet each other*, and he asked if he could share some of the book's material in his column. Of course I said yes.

I knew the column was coming today, but forgot to look until I saw Mike South's Facebook post mentioning it. Mike writes great math explanations on Living Math Forum, but doesn't blog. I wanted to include something of his in the book, but didn't manage it. (Here's Mike on thinking about zero.)

Gary included a great photo that goes so well with the puzzles, I want to make up a new puzzle to go with it. Hmm.

If you don't already have your own copy of

_____________

*I finally got to meet the fabulous Fawn Nguyen in person, too! What an exciting day that was!

Last summer, at a conference for the California Acceleration Project, Myra Snell used a cool way to set up random groups of participants/students. I wanted to use it in my classes, but just didn't get around to it. It seems, after almost 30 years of teaching, that it has become hard to change the way I run my classroom.

But I did change one thing this past semester. I noticed, while sitting in on a colleague's Calc III class, that I really appreciated the notices he wrote on the board at the beginning of each class. So I began to do it too. Maybe I could implement a few more good habits by watching other teachers during the second and third weeks of class.

Coming back to those random groups... I recently read research that found two effective strategies for getting students to participate more. One is visibly random groups. 'Visibly' means that they can't suspect the teacher of manipulating the group memberships. Myra's method is clearly random, looks easy to implement, and allows for up to four different groupings per class day. You have a slip for each student, with a number, a letter, an animal, and a food on it (for example). Those slips are set up so that no one is with any of the same other people more than once. I've asked Myra for her slips, but last night I was eager to think about it, and created my own. I don't know if this is the best way to do it, but I think it will work. Myra's slips had the 4 terms in a square and mine will be all in a row. I don't think that's a problem.

The second strategy which made a difference in student participation was student use of vertical whiteboards. The researcher(s?) compared paper and whiteboard, used vertically and horizontally. [Unfortunately, I can't find the research I originally read, which mentioned both the visibly random groups and the vertical whiteboards.] I'd like to try this out with the class I'll be teaching for the first time this fall, a compressed version of beginning algebra (first half of the semester) and intermediate algebra (second half of the semester). It's officially the same courses we've always taught, but I get to use a different curriculum, and will be using something project-based. I'm excited about implementing this.

But I did change one thing this past semester. I noticed, while sitting in on a colleague's Calc III class, that I really appreciated the notices he wrote on the board at the beginning of each class. So I began to do it too. Maybe I could implement a few more good habits by watching other teachers during the second and third weeks of class.

Coming back to those random groups... I recently read research that found two effective strategies for getting students to participate more. One is visibly random groups. 'Visibly' means that they can't suspect the teacher of manipulating the group memberships. Myra's method is clearly random, looks easy to implement, and allows for up to four different groupings per class day. You have a slip for each student, with a number, a letter, an animal, and a food on it (for example). Those slips are set up so that no one is with any of the same other people more than once. I've asked Myra for her slips, but last night I was eager to think about it, and created my own. I don't know if this is the best way to do it, but I think it will work. Myra's slips had the 4 terms in a square and mine will be all in a row. I don't think that's a problem.

The second strategy which made a difference in student participation was student use of vertical whiteboards. The researcher(s?) compared paper and whiteboard, used vertically and horizontally. [Unfortunately, I can't find the research I originally read, which mentioned both the visibly random groups and the vertical whiteboards.] I'd like to try this out with the class I'll be teaching for the first time this fall, a compressed version of beginning algebra (first half of the semester) and intermediate algebra (second half of the semester). It's officially the same courses we've always taught, but I get to use a different curriculum, and will be using something project-based. I'm excited about implementing this.

On Facebook, someone posted an animation of how a sewing machine works. It wasn't enough to help me understand how the top thread manages to get around the bobbin mechanism. I searched on youtube, and nothing helped. This article on math and the sewing machine made me think for a moment that I was getting it, but I still am not. How is that bobbin mechanism held in place in a way that allows the thread to get around it? (Do you see how the top thread moves past the whole back of the bobbin? How is that possible?) They say that the bobbin is held snugly inside its case, but how is the out part attached?

I think I need a transparent sewing machine, so I can really see how this is working.

On thing leads to another (especially online!), and I ended up at this site from a museum for mathematics, called The Garden of Archimedes, in Florence, Italy, where I encountered this very simple statement about the difference between constructing a circle and a line - something I had never thought about before.

The simplest curves are doubtless the line and the circle. To draw circles, one uses a compass. It's sufficient to keep a constant distance between the tracing point and the centre, and one obtains a near-perfect circle, even with a primitive compass. At first sight, one would think that tracing a segment is also a very simple operation: you just need to use a ruler or pull a string taut. In fact, things don't work exactly like that. In order to draw a good straight line with a ruler, one needs the ruler itself to have a "straight" side, but the value of a ruled line depends on the ruler that was used to make it. So, who made the first ruler? To apply the same method to the circle would mean, for example, to take a coin and trace its edge - the circular profile would be "intrinsic" to the instrument itself.Inatead of using a ruler or straightedge, can't you use the "pull a string taut" method, with something a bit less flexible than string? Maybe something that freezes into position? Hmm... Apparently that's not the avenue that was followed. You can find out the fascinating history of the solutions people found for this problem by going to the Garden of Archimedes site.

It would be better to apply to the straight line the principle used to draw the circle, rather than vice versa.

I started out really believing in unschooling. (Advice to self: Beliefs are dangerous.) My son has attended a free school, where he didn't have to attend classes (K-2), and then was homeschooled at the homes of friends (I'm a single parent), in groups of 2 to 8, with very little required of him. He has learned a lot over the years, but not in the conventional ways. If you're an advocate of unschooling, that may not sound like a problem at all. But for him it was. He thought he was 'behind' in reading, and felt bad about that. He totally avoided math because of how far behind he thought he was. He thinks he's dumb because he hasn't done the conventional academics.

Now he wants to go to a 'normal' school. So I signed him up for 8th grade at a charter school his friend goes to. (I've heard great things about it, and it is supposed to be project-based.*) Part of going to a regular school means catching up on all the 'regular subjects.' So I've begun requiring him to do 'academics' daily. (He asks if he has to. I say yes. He then shows subtle signs of relief. He really wants me to make him do this. This blows my mind.)

About a month ago, we started with 15 minutes of reading and 15 minutes of handwriting practice each day. I don't care about his handwriting. He does. He is so embarrassed about it that he resisted signing in for his trampoline class. A few weeks ago, I added spelling (his desire), geography (identifying the states), and math. This week we're adding science and an essay of the history of bikes. My opinion is that the only things he really needs to catch up on are math and writing (essays, stories, ...). It helps that we're doing this, because he also needs to become more aware of conventions - how to write dates, what schoolwork looks like.

For math, we're using*Beast Academy*. We started with book 3A. Yes, the 3 means third grade. We don't mention it, but he knows this is "supposed to be" for younger kids. *Beast Academy* has challenging work, though, and if we make it though all eight of the levels (3A-D and 4A-D), I think he'll be pretty well-prepared to join a class of 8th graders. I will look over the 'standards' for 5th to 7th grade later this summer, and see what might be missing from what we're doing. I have made a math plan for the next 14 weeks, leaving out some of the topics in the *Beast Academy* books (perfect squares, variables, counting, logic, probability). I'm sure they are excellent, but my goal was to find a way to pare it down, so he gets as much as possible of the foundational skills he'll need, in the short time we have before he starts 8th grade.

The first day that we did math, he was sitting next to me, saying his answers, waiting for me to confirm before he'd write them down. I did. (What he needs, as he takes on this huge emotional challenge, is support. Once he feels more secure, I'll be able to say things like "How can you decide whether that answer is right or not?")

On the second and third days, I noticed that his wrong answers were usually one off. To me, that meant he wasn't noticing things I notice about even and odd numbers. I printed out something from the nrich site that looked good. We haven't tried it yet.

It's very fun for me to be planning out his math curriculum. But this is very stressful for him, so our work time can be full of conflict. Once he buckles down and gets started, I get to quietly support him. Mostly I just confirm his answers. He is already seeing progress, and feeling good about it. I am trying to use Denise's technique of buddy math, offering to do every other problem myself, and then talking my way through it. He seems to prefer doing the problems himself most of the time, but let me do one problem last night.

The lessons he's working on are about finding perimeters. It has been a great way for him to work on adding numbers, with something extra thrown in. Most of the shapes have more than six sides. While we were working last night, I told him I noticed that he picked numbers that add to ten, which is a good strategy. I said that some people call those ten-bonds. He said he didn't know them all. I asked him for numbers that add to ten, and he got a bunch. The ones he hadn't mentioned, I asked him about: "Eight and ...?" He was surprised that there were only 5 pairs, I think. (At least two different stories in*Playing with Math* address this issue - Prison Math Circle and The Math Haters Come Around.) When he was unsure of 5 plus 8, I told him that I sometimes forget that one myself, and one way to figure it out is to move 2 from the 5 to the 8, so you get 3 and 10.

I am exploring the balance between telling (ten bonds) and helping him to discover (hopefully we'll do that with odds and evens). I am so happy to be doing this, and marveling at how hard it was for me to see that he actually wanted me to make him do it.

_____

*Yes, I agree that charter schools are being used to mess up the regular public schools. Difficult situation all around.

Now he wants to go to a 'normal' school. So I signed him up for 8th grade at a charter school his friend goes to. (I've heard great things about it, and it is supposed to be project-based.*) Part of going to a regular school means catching up on all the 'regular subjects.' So I've begun requiring him to do 'academics' daily. (He asks if he has to. I say yes. He then shows subtle signs of relief. He really wants me to make him do this. This blows my mind.)

About a month ago, we started with 15 minutes of reading and 15 minutes of handwriting practice each day. I don't care about his handwriting. He does. He is so embarrassed about it that he resisted signing in for his trampoline class. A few weeks ago, I added spelling (his desire), geography (identifying the states), and math. This week we're adding science and an essay of the history of bikes. My opinion is that the only things he really needs to catch up on are math and writing (essays, stories, ...). It helps that we're doing this, because he also needs to become more aware of conventions - how to write dates, what schoolwork looks like.

For math, we're using

The first day that we did math, he was sitting next to me, saying his answers, waiting for me to confirm before he'd write them down. I did. (What he needs, as he takes on this huge emotional challenge, is support. Once he feels more secure, I'll be able to say things like "How can you decide whether that answer is right or not?")

On the second and third days, I noticed that his wrong answers were usually one off. To me, that meant he wasn't noticing things I notice about even and odd numbers. I printed out something from the nrich site that looked good. We haven't tried it yet.

It's very fun for me to be planning out his math curriculum. But this is very stressful for him, so our work time can be full of conflict. Once he buckles down and gets started, I get to quietly support him. Mostly I just confirm his answers. He is already seeing progress, and feeling good about it. I am trying to use Denise's technique of buddy math, offering to do every other problem myself, and then talking my way through it. He seems to prefer doing the problems himself most of the time, but let me do one problem last night.

The lessons he's working on are about finding perimeters. It has been a great way for him to work on adding numbers, with something extra thrown in. Most of the shapes have more than six sides. While we were working last night, I told him I noticed that he picked numbers that add to ten, which is a good strategy. I said that some people call those ten-bonds. He said he didn't know them all. I asked him for numbers that add to ten, and he got a bunch. The ones he hadn't mentioned, I asked him about: "Eight and ...?" He was surprised that there were only 5 pairs, I think. (At least two different stories in

I am exploring the balance between telling (ten bonds) and helping him to discover (hopefully we'll do that with odds and evens). I am so happy to be doing this, and marveling at how hard it was for me to see that he actually wanted me to make him do it.

_____

*Yes, I agree that charter schools are being used to mess up the regular public schools. Difficult situation all around.

Their suggestion for creating an iconic times table got me dreaming. How can I get my son (who "hates" math, unfortunately) inspired to take photos for a times table collection? I was dreaming of a website that would show the whole table on one page, with each photo pretty small. And when you hover over a photo, that one would show up big. I don't know how to do that, though...

Here's a photo (from lernertandsander.com/cubes) that feels like it belongs in the Grid section of

Kate Nowak posted this on Facebook. The question that came to her mind (among other less mathy questions) was ... How do

[Edited to add: In the comments, Joshua described a very cool pattern he saw, and suggested that it's like 9 plus 4 is 13, which looks like my diagram below.]

The mirror book introduced in the symmetry section is so simple, and so cool to play with. Just get two small rectangular mirrors (at a dollar store), tape them together along one side, and use with photos or drawings, to see lots of symmetrical designs.

My favorite game in the function section is Silly Robot. The grownup plays the robot, and follows orders exactly (while always trying to find a way to mess up the intention of the orders).

If you know anyone with a child from one to eight who'd like to find ways to play around with mathematical ideas,

And my book,

This is shaping up to be a very fun summer...

One of the reasons I put together a book was my fear that good online writing often just disappears. One of the sites I had really liked - and thought of including somehow in the book - was a site with stories from Aunty Math (Aunt Mathilda). It disappeared before I could contact the author. And for years, I thought it was just plain gone.

This evening I searched for Aunty Math, and found that someone had managed to get to this site through the Wayback Machine. It is now available as an archive. Check out all eleven past challenges. I think you'll enjoy them.

I would love to be in touch with the author, Angela G. Andrews. I googled her, but I don't see an email address. I'll just thank her here for her lovely stories. Thanks, Angela!

My book,

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- Sue VanHattum
- Richmond, CA, United States
- Math Mama is Sue VanHattum, a community college math teacher interested in all levels of math learning, and the mama of a young son. I entered the blogging world as I began work on an anthology about learning math. Contact me at mathanthologyeditor on gmail etc.