Here’s a blast from the *Let’s Play Math!* blog archives: Seven years ago, one of my math club students was preparing for a speech contest. His mother emailed me to check some figures, which led to a couple of blog posts on solving proportion problems. I hope you enjoy…

A friend gave me permission to turn our email discussion into an article…

Can you help us figure out how to figure out this problem? I think we have all the information we need, but I’m not sure:

The average household income in the United States is $60,000/year. And a man’s annual income is $56 billion. Is there a way to figure out what this man’s value of $1mil is, compared to the person who earns $60,000/year? In other words, I would like to say — $1,000,000 to us is like 10 cents to Bill Gates.

## Let the Reader Beware

When I looked up Bill Gates at Wikipedia, I found out that $56 billion is his net worth, not his income. His salary is $966,667. Even assuming he has significant investment income, as he surely does, that is still a difference of several orders of magnitude.

But I didn’t research the details before answering my email — and besides, it is a lot more fun to play with the really big numbers. Therefore, the following discussion will assume my friend’s data are accurate…

*[Click here to go read Putting Bill Gates in Proportion.]*

Another look at the Bill Gates proportion… Even though I couldn’t find any data on his real income, I did discover that the median American family’s net worth was $93,100 in 2004 (most of that is home equity) and that the figure has gone up a bit since then. This gives me another chance to play around with proportions.

So I wrote a sample problem for my Advanced Math Monsters workshop at the APACHE homeschool conference:

The median American family has a net worth of about $100 thousand. Bill Gates has a net worth of $56 billion. If Average Jane Homeschooler spends $100 in the vendor hall, what would be the equivalent expense for Gates?

In the last post, I explained that a proportion sets two ratios equal to each other. Each ratio must compare similar thing to similar thing in the same order. In this case, we are interested in the ratio “Expense : Net Worth”…

*[Click here to go read Bill Gates Proportions II.]*

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It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our *Math Teachers at Play* (MTaP) math education blog carnival.

Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday*. The carnival will be posted next week at Singapore Maths Tuition.

Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

- Last month’s Math Teachers at Play #72 at Christy’s Houseful of Chaos
- Carnival of Mathematics
- Carnaval de Matemáticas

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Here’s a blast from the *Let’s Play Math!* blog archives: Seven years ago, our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned. I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students voted to perform a skit. I hope you enjoy…

If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in all?

In general, if

npeople meet and shake hands all around, how many handshakes will there be?## Cast

1-3 narrators

7 friends (non-speaking parts, adjust to fit your group)## Props

Each friend will need a sheet of paper with a number written on it big and bold enough to be read by the audience. The numbers needed are 0, 1, 2, 3, … up to one less than the number of friends. Each friend keeps his paper in a pocket until needed.

*[Click here to go read the original post.]*

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*[Feature photo above by Alberto G. Photo right by Renato Ganoza. Both (CC-BY-SA-2.0) via flickr.]*

Here’s a blast from the *Let’s Play Math!* blog archives: Quotations and comments about the perils of standardized testing, now part of my book Let’s Play Math. I hope you enjoy…

The school experience makes a tremendous difference in a child’s learning. Which of the following students would you rather be?

I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours. I found it quite enthralling.

— Agatha Christie

An Autobiography…or…

“Can you do Addition?” the White Queen asked. “What’s one and one and one and one and one and one and one and one and one and one?”

“I don’t know,” said Alice. “I lost count.”

“She can’t do Addition,” the Red Queen interrupted. “Can you do Subtraction? Take nine from eight.”

“Nine from eight I can’t, you know,” Alice replied very readily: “but—”

“She can’t do Subtraction,” said the White Queen. “Can you do Division? Divide a loaf by a knife — what’s the answer to that?”

[Click here to go read the original post.]

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*[Feature photo above is 72 Pencils by fdecomite via flickr.]*

Math Teachers at Play is a traveling blog carnival. It moves around from month to month, and the March edition is now posted at Christy’s Houseful of Chaos. What a fun list of math posts to browse!

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….

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This April, the creative people at Moebius Noodles are inviting parents, teachers, playgroup hosts, and math circle leaders to join an open online course about multiplication. My preschool-2nd grade homeschool math group is eager to start!

Each week there will be five activities to help kids learn multiplication by exploring patterns and structure, with adaptations for ages 2-12.

The course starts April 6 and runs for four weeks.

**Week 1: Introduction.**

What is multiplication? Hidden dangers and precursors of math difficulties. From open play to patterns: make your own math. 60 ways to stay creative in math. Our mathematical worries and dreams.

**Week 2: Inspired by calculus.**

Tree fractals. Substitution fractals. Multiplication towers. Doubling and halving games. Zoom and powers of the Universe.

**Week 3: Inspired by algebra.**

Factorization diagrams. Mirror books and snowflakes. Combination and chimeras. Spirolaterals and Waldorf stars: drafting by the numbers. MathLexicon.

**Week 4: Times tables.**

Coloring the monster table. Scavenger hunt: multiplication models and intrinsic facts. Cuisenaire, Montessori, and other arrays. The hidden and exotic patterns. Healthy memorizing.

Sounds like lots of fun!

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If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s *Math Teachers at Play* (MTaP) math education blog carnival.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday*. The carnival will be posted next week at Christy’s Houseful of Chaos.

If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing…

**Elementary Concepts:**As Liping Ma showed, there is more to understanding and teaching elementary mathematics than we often realize. Do you have a game, activity, or anecdote about teaching math to young students? Please share!**Arithmetic/Pre-Algebra:**This section is for arithmetic lessons and number theory puzzles at the middle-school-and-beyond level. We would love to hear your favorite math club games, numerical investigations, or contest-preparation tips.**Beginning Algebra and Geometry:**Can you explain why we never divide by zero, how to bisect an angle, or what is wrong with distributing the square in the expression ? Struggling students need your help! Share your wisdom about basic algebra and geometry topics here.**Advanced Math:**Like most adults, I have forgotten enough math to fill several textbooks. I’m eager to learn again, but math books can be so-o-o tedious. Can you make upper-level math topics come alive, so they will stick in my (or a student’s) mind?**Mathematical Recreations:**What kind of math do you do, just for the fun of it?**About Teaching Math:**Other teachers’ blogs are an important factor in my continuing education. The more I read about the theory and practice of teaching math, the more I realize how much I have yet to learn. So please, fellow teachers, don’t be shy — share your insights!

We need more hosts! Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog.

If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

- Last month’s Math Teachers at Play #71 (with 71 links)
- Carnival of Mathematics (mostly high school & up)
- Carnaval de Matemáticas
- Carnevale della Matematica

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*[Feature photo above by Nicolo' Canali De Rossi.]*

**Math holiday alert:** March 14th is Pi Day. And why limit ourselves to a single day? As Tyler Jarvis pointed out, March 2014 (3/14) is Pi Month! Here are some ideas to help you celebrate…

**Pi Day Posts on Let’s Play Math! Blog**

- Happy Pi Day I
- Happy Pi Day II
- Happy Pi Day III: Visualizing Pi
- Poetry for Pi Day
- Do the Digits of Pi Encode Shakespeare’s Plays?
- Egyptian Math: Pi

**And Did You Know?**

Pi Day is also Albert Einstein’s birthday.

- Happy Birthday, Einstein!
- Happy Birthday, Einstein (Part 2)
- Happy Birthday, Einstein (Part 3)
- Happy Birthday, Einstein (Part 4)

**A Pinch of Pi Day Humor**

**Favorite Pi Day Posts on Other Blogs**

- Pi Day in America
- How to celebrate Pi Day: The geekiest time of the year
- Oh Number Pi – Celebrate Pi Day in style!
- Celebrate Pi Day: Seven Classroom Resources for Pi Learning
- π Day Activities (pdf) from Yummy Math
- Pi Day activity worksheets for primary and secondary students from the Australian Mathematics Trust
- Cool Math Games for π (Pi) Day
- 32 Pi Day Recipes/Activities/Games for March 14th
- Discovering Pi – the living maths of circles
- Math Art for Kids: Pi Skyline
- How I Spent Pi Day
- Pi Day Post on Irrational Numbers
- Pi is Beautiful – Numberphile

And if that’s not enough to keep you busy, Education World offers another huge round-up of Pi Day lesson plans and activity ideas.

**Do you have any favorite activities or blog posts about Pi Day? Please share in the comments!**

This post is featured in the Carnival of Homeschooling {Edition # 428}.

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Here’s a blast from the *Let’s Play Math!* blog archives: Seven years ago, I blogged a revision of the first article I ever wrote about homeschooling math. I can’t even remember when the original article was published — years before the original (out of print) editions of my math books. I hope you enjoy…

I love story problems. Like a detective, I enjoy sifting out clues and solving the mystery. But what do you do when you come across a real stumper? Acting out story problems could make a one-page assignment take all week.You don’t have to bake a pie to study fractions or jump off a cliff to learn gravity. Use your imagination instead. The following suggestions will help you find the clues you need to solve the case…

*[Click here to go read the original post.]*

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Here’s a blast from the *Let’s Play Math!* blog archives: My 8-year-old daughter’s first encounter with improper fractions…

*Photo (right) by Old Shoe Woman via Flickr.*

Nearing the end of Miquon Blue today, my youngest daughter encountered fractions greater than one. She collapsed on the floor of my bedroom in tears.

The worksheet started innocently enough:

*[Click here to go read the original post.]*

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Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from my About page. Background courtesy of Pinstamatic.

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Math teachers at play know that math is best learned when the student is thoroughly engaged, through their body, their imagination (story-telling), or the world of games. I’ve started out this month’s post with those three categories.

Most of the submissions this month described hands-on, or feet-on, activities. It’s as if there had been a theme agreed upon without anyone mentioning it. Some of the following posts are from submissions, and others are posts that I wanted to share from my internet wanderings.

This post has 71 links. (You might need to digest it in smaller bites.) Enjoy!

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I sat in class 3 days ago and though to myself, “They need a class called ‘Math as a second language’ or MSL for short.”

It is easy to understand what a median is, or what attributes a kite has, or why is a rectangle a square but a square not a rectangle… for a minute or a day.

It is easy to temporarily memorize a fact. But without true understanding of the concept those “definitions” fade. If the foundation of truly understanding is not there to begin with then there is little hope for any true scaffolding and even less chance of any true learning.

—Duncan

Comment on Christopher Danielson’s Geometry and language

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*[Photo by Olga Berrios via flickr.]*

Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The *Math Teachers at Play* (MTaP) math education blog carnival would love to feature your article!

We welcome math topics from preschool through the first year of calculus. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

- Click here to submit your blog post.

[Note: The Google Doc would not load in Firefox this morning. :( So if you have trouble, just leave a link to your entry in the comments here.] - Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday extended to Thursday, February 13*. The carnival will be posted on February 17th at Math Mama Writes.

Hosting the blog carnival is fun because you get to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival often brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

- Last month’s Math Teachers at Play Blog Carnival #70
- Carnival of Mathematics (mostly high school & up)
- Math Monday Blog Hop (preschool & up: back-issues on different topics are still open to submit!)
- Carnaval de Matemáticas
- Carnevale della Matematica

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Alexandria Jones collapsed onto the couch with a dramatic sigh. Her father, the world-famous archaeologist Dr. Fibonacci Jones, glanced up from his newspaper and rolled his eyes.

“I don’t even want to hear about it,” he said.

Alex’s brother Leonhard was playing on the floor, making faces at the baby. He looked up at Alex and grinned.

“I’ll take the bait,” he said. “What happened?”

“Mom called my bedroom a *Strange Attractor*.”

“Oh? What does it attract?”

“I don’t know. Mostly books and model horses. But what’s so strange about that?”

Dr. Jones laughed and put down his paper. “*Strange attractor* is a technical term from the branch of mathematics called *dynamical systems analysis* — often called chaos theory.”

“So my bedroom is a math problem?”

“No. I think Mom meant your bedroom was chaos.”

“Oh.” Alex looked like she might pout, then she shrugged. “I guess she’s right, at that. So what is a strange attractor, really?”

“Well, when scientists first drew graphs of classical, non-chaotic systems — like a planet’s orbit or the flight of a football — it was surprising how often they got an ellipse or parabola or some similar curve,” Dr. Jones explained. “For some reason, nature seemed to be attracted to the shapes of classical geometry.”

“Like bushes are spheres and mountains are pyramids?” Alex asked. “But they aren’t really — not even very close.”

He shook his head. “Neither does a football fly in an exact parabola, nor a planet orbit in an exact ellipse. But those two examples are close enough that we can predict their motion and send a man to the moon.”

“Classical geometry made science easy to understand,” Dr. Jones continued. “And it worked fairly well, until scientists tried to graph dynamical systems like the weather or an earthquake or the growth of a tree…”

Leon jumped up. “I know! Then they get a mess like Alex’s bedroom, right?”

“Not quite. Chaotic systems tend to hover around certain values in a complicated, fractal pattern. That fractal pattern is called the system’s strange attractor.”

Alex frowned. “But doesn’t chaos theory mean that everything in the universe comes from a chaotic jumble of energy left over from the Big Bang? And that we can’t really know anything, because it’s all chaos?”

“Yeah,” Leon said. “Chaos theory says that God isn’t really in charge of the universe — that everything happens by chance.”

“Watch out,” Dr. Jones warned. “You are both falling into a common fallacy.”

“Huh?” Leon said.

Alex nudged him with her elbow. “Fallacy means a mistake in logic.”

Dr. Jones nodded. “You are confusing two logically different ideas, just because they both use the word *chaos*. What chaos theory says is that some things are so complicated scientists will never be able to predict them. That is not the same as saying the universe is ruled by chaos, or that God himself cannot understand or control things.”

“Do you know the difference between physics and metaphysics?” Dr. Jones asked.

“Hmmm,” Alex said. “Physics is the study of how the universe works. Matter and energy and gravitation and stuff like that.”

“Right,” her father said. “Then you could say that metaphysics is the study of why the universe works. Physics works with things you can measure. But metaphysics deals with things that are impossible to measure.”

“I know,” Leon said. “What God is like, or how people are different from animals.”

“Those are just a couple of questions that metaphysics might try to answer,” Dr. Jones said. “Now, you see, your fallacy was to confuse the two. Chaos theory has to do with physics — with the world we can touch and measure. But the statement ‘Everything is chaos’ is a metaphysical statement. There is no way a scientist could measure or prove something like that.”

“Oh, I get it,” Alex said. “It’s like the difference between relativity and relativism.”

“What do you mean?” Leon asked. “Relativity is about warp speed, right?”

Alex laughed. “Warp speed is science fiction. Relativity means things look different from different angles, sort of. And that nothing can go faster than the speed of light. Albert Einstein discovered it.”

“So what is relativism?”

“Relativism says that there isn’t any true right or wrong,” Alex explained. “That means values are relative, and you can do whatever you want.”

“Exactly,” Dr. Jones said. “The problem is, many people think that Einstein’s Theory of Relativity proved that relativism is true. They are confusing physics with metaphysics. As I said, it’s a common fallacy.”

Read all the posts from the January/February 2000 issue of my ** Mathematical Adventures of Alexandria Jones** newsletter.

Don’t miss any of *“Let’s Play Math!”*: Subscribe in a reader, or get updates by Email.

- The Secret of Egyptian Fractions
- The Puzzling Pythagorean Pebbles
- The Mosaic Tile Mystery
- Alexandria Jones and the Mathematical Carnival
- Alexandria Jones and the Eighty-Yard Drive

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