bill-gates-hombre-mas-rico

Reblog: Putting Bill Gates in Proportion

[Feature photo above by Baluart.net.]

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…


Putting Bill Gates in Proportion

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.]


Bill Gates Proportions II

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?

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Do You Blog About Math?

by Mike Licht, NotionsCapital.com

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.

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

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Handshake_(Workshop_Cologne_'06)

Reblog: The Handshake Problem

[Feature photo above by Tobias Wolter (CC-BY-SA-3.0) via Wikimedia Commons.]

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 n people 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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Exam

Reblog: In Honor of the Standardized Testing Season

TakingTest

[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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72pencils

Math Teachers at Play #72 via Christy’s Houseful of Chaos

mathteachersplay72

[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….

Click here to go read the whole carnival.


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Natural Math Multiplication Course

NaturalMathMultiplication

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.

Preliminary Syllabus

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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Education Bloggers: Share Your Post!

photo by Omar Omar via flickr

photo by Omar Omar via flickr

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.

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…

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pi

Pi Day Roundup

WhyPi

[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

PiBiography

And Did You Know?

Pi Day is also Albert Einstein’s birthday.

A Pinch of Pi Day Humor

PiInSky

Favorite Pi Day Posts on Other Blogs

DragonOfPi

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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photo by Carla216 via flickr

Reblog: The Case of the Mysterious Story Problem

[Feature photo above by Carla216 via flickr (CC BY 2.0).]

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…


Case-of-the-Mysterious-Story-Problem
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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fraction pieces

Improper Fractions: A Mathematical Trauma

Feature photo (above) by Jimmie via flickr.

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:

\frac{1}{2} \times 8=\left[ \quad \right]

[Click here to go read the original post.]


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Math Teachers at Play #71 via Math Mama Writes

The February math education blog carnival is now posted for your browsing pleasure, featuring 71 playful ways to explore mathematics from preschool to calculus:

71 richard schwartzMath 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!

Click here to go read the whole, wonderful post.


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Quotable: Math as a Second Language

Wenninger 94photo by fdecomite via flickr (CC BY 2.0)

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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Math Teachers and Homeschool Bloggers: We Want You!

chica usando ordenador

[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.

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.

Click here to continue reading.

640px-Clifford_att1

Alexandria Jones and the Strange Attractor

[Feature photo above: Clifford Attractor by Yami89 (public domain) via Wikimedia Commons.]

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?”

The Mathematics of Chaos

Animation of a double compound pendulum showing chaotic behaviour.

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.”

Click here to continue reading.

Calling All Math Teacher Bloggers and Homeschoolers: Carnival Time!

by Bob Jagendorf via flickr

by Bob Jagendorf via flickr

The Math Teachers at Play (MTaP) math education blog carnival is almost here. If you’ve written a blog post about math, we’d love to have you join us! Each of us can help others learn, so in a sense we are all teachers.

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

Don’t procrastinate: The deadline for entries is this Friday. The carnival will be posted next week right here at Let’s Play Math.

We Need More Hosts for 2014

Help! I can’t keep the carnival going on my own. Would you volunteer to host the MTaP math education blog carnival some month this year? Hosting the 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.

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2014

2014 Mathematics Game

2014-Calendar

[Feature photo above by Artis Rams (CC BY 2.0) via flickr. Title background (right) by Dan Moyle (CC BY 2.0) via flickr]

Have you made a New Year’s resolution to spend more time with your family this year, and to get more exercise? Problem-solvers of all ages can pump up their (mental) muscles with the Annual Mathematics Year Game Extravaganza!

For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find.

Math Forum Year Game Site

Rules of the Game

Use the digits in the year 2014 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable by age: Young children can start with looking for 1-10, or 1-25.

  • You must use all four digits. You may not use any other numbers.
  • Solutions that keep the year digits in 2-0-1-4 order are preferred, but not required.
  • You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
  • You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
  • You may use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal.
  • You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.
  • You may use a double factorial, but we prefer solutions that avoid them. n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n.

[Note to students and teachers: If you want to take part in the Math Forum Year Game, be warned that they do not allow repeating decimals.]

Click here to continue reading.

Quotable: Focus on Being Silent

Children Reading Pratham Books and Akshara[Photo by Pratham Books via flickr (CC BY 2.0).]

I discovered this gem in my blog reading today. One of the secrets of great teaching:

Audrey seemed, for once, at a loss for words. She was thinking about the question.

I try to stay focused on being silent after I ask young children questions, even semi-serious accidental ones. Unlike most adults, they actually take time to think about their answers and that often means waiting for a response, at least if you want an honest answer.

If you’re only looking for the “right” answer, it’s fairly easy to gently badger a child into it, but I’m not interested in doing that.

Thomas Hobson
Thank You For Teaching Me

Learn Math by Asking Questions

The best way for children to build mathematical fluency is through conversation. For more ideas on discussion-based math, check out these posts:

And be sure to follow Christopher Danielson’s Talking Math with Your Kids blog!


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Math Teachers at Play Blog Carnival #69 via Kids Math Teacher

mtap69wordle

The new Math Teachers at Play blog carnival is up for your browsing pleasure. Featured articles include activities and enrichment from preschool through high school:

“While my site focuses on elementary level math concepts, I strongly think that young kids can understand complex concepts that are not taught until much later (and I think most math teachers feel that way. Do you agree?). The Math Teachers at Play Blog Carnival can contain math concepts/topics from Pre-school to Calculus.

“This month for December’s carnival there were 12 days of Christmas entries! I put them in order starting from earliest math to the most advanced math…”

Click here to go read the Blog Carnival post at Kids Math Teacher.


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Do You Blog About Math?

by Mike Licht, NotionsCapital.com

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 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.

To submit an entry, fill out this form:

Don’t procrastinate: The deadline for entries is this Saturday night! The carnival will be posted next week at Kids Math Teacher blog.

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2013 Advent Math from Nrich

Click the images below to visit the Advent calendars, and your children can play with math every day until Christmas! You may also enjoy:

Primary Advent Calendar

“This Advent Calendar has a new activity for each day in the run-up to Christmas. All the activities are based on the theme of Planet Earth.”

advent1

Secondary Advent Calendar

“Behind each door of the Advent Calendar is one of our favourite activities with videos. Watch and enjoy!”

advent2


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Happy Thanksgiving!

Thanksgiving at the Trolls

Give thanks to the Lord, for He is good;
His love endures forever.
Let the redeemed of the Lord say this —
those He redeemed from the hand of the foe,
those He gathered from the lands,
frome east and west, from north and south.

Whoever is wise, let him heed these things
and consider the great love of the Lord.

— Psalm 107:1-3 and 43

[Feature photo above by Martha_chapa95 (CC BY 2.0) via Flickr. Quotation from Holy Bible, New International Version, (c)1973, 1978, 1984 by the International Bible Society, used by permission of Zondervan Bible Publishers.]



Math Teachers at Play #68 via Mathematical Mischief

CERDEC Math and Science Summer Camp, 2013

[Photo by U.S. Army RDECOM CERDEC (CC BY 2.0) via Flickr.]

The Math Teachers at Play blog carnival is a monthly blogging round-up shared at a different blog each month, featuring posts from parents, teachers, homeschoolers, and students — anyone who is interested in playing around with school-level (preschool to pre-college) or recreational math.

This month’s edition is ready for your browsing pleasure:

Enjoy!

Good morning, everybody! This month’s edition of Math Teachers at Play is edition number 68. Also known as edition number {{2}^{2}}({{2}^{4}+1}). Or edition 31+37 or edition 7+61…. Alrighty, so… did you know that 68 is a happy number? That’s right, it’s not unhappy, it quite likes the way it is.

There’s certain numbers that exist that are ‘happy’ numbers. This is because the sum of the square of their digits is equal to 1. So, for 68, the two digits are 6 and 8. Adding the squares, we’re given {{6}^{2}}+{{8}^{2}}, which equates to 100. Adding the square of each of the digits makes 1, which is happy!

  • Can you find some more happy numbers?
    I’ll give you a hint – the first one is 1.

Anyway, back to the carnival. This carnival features 11 articles – smaller than last time, but still just as awesome and creative as ever….

Click here to go read the whole carnival: 11 great ideas for teaching math!
[By the way, did you notice? 11 is a happy number, too.]

You may also enjoy:


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