factor game

Math Teachers at Play #79

79

[Feature photo above by Jimmie, and "79" image (right) by Steve Bowbrick via flickr (CC BY 2.0).]

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 79th edition of the Math Teachers At Play (MTaP) math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle, game, or trivia tidbits. If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Since I’ve been spending all my free time working on my upcoming Math You Can Play book series, I’m in the mood for games. So I found a few games featuring prime and nonprime numbers [which category is #79 -- do you know?], and I’ll sprinkle some of my best-loved math game books throughout the carnival.

TRY THESE NUMBER GAMES

Students can explore prime and non-prime numbers with two free classroom favorites: The Factor Game (pdf lesson download) or Tax Collector. For $15-20 you can buy a downloadable file of the beautiful, colorful, mathematical board game Prime Climb. Or try the following game by retired Canadian math professor Jerry Ameis:

Factor Finding Game

FactorFindingGame

Math Concepts: multiples, factors, composites, and primes.
Players: only two.
Equipment: pair of 6-sided dice, 10 squares each of two different colors construction paper, and the game board (click the image to print it, or copy by hand).

On your turn, roll the dice and make a 2-digit number. Use one of your colored squares to mark a position on the game board. You can only mark one square per turn.

  • If your 2-digit number is prime, cover a PRIME square.
  • If any of the numbers showing are factors of your 2-digit number, cover one of them.
  • BUT if there’s no square available that matches your number, you lose your turn.

The first player to get three squares in a row (horizontal/vertical/diagonal) wins. Or for a harder challenge, try for four in a row.

Hat tips: Jimmie Lanley.



TABLE OF CONTENTS

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.

Tweet: Math Teachers at Play #76: a smorgasbord of great ideas for learning, teaching, and playing around with math. http://ctt.ec/fU9Z2+

Click to tweet: Share the carnival with your friends.
(No spam, I promise! You will have a chance to edit or cancel the tweet.)

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640px-Horseshoes_game

Horseshoes: A Place Value Game

[Feature photo above by Johnmack161 via Wikimedia Commons (CC BY 2.5).]

I first saw place value games on the old PBS Square One TV show (video below). Many teachers have posted versions of the game online, but Snugglenumber by Anna Weltman is by far the cutest variation. Anna kindly gave me permission to use the game in my upcoming Math You Can Play book series, and I added the following variation:

Horseshoes

snugglenumber

Math Concepts: place value, strategic thinking.
Players: two or more.
Equipment: one deck of playing cards, or a double deck for more than three players.

Separate out the cards numbered ace (one) through nine, plus cards to represent the digit zero. We use the queens (Q is round enough for pretend), but you could also use the tens and just count them as zero.

Shuffle well and deal eleven cards to each player. Arrange your cards in the snugglenumber pattern shown here, one card per blank line, to form numbers that come as close to each target number as you can get it.

Score according to horseshoes rules:

  • Three points for each ringer, or exact hit on the target.
  • One point for each number that is six or less away from the target.
  • If none of the players land in the scoring range for a target number, then score one point for the number closest to that target.

For a quick game, whoever scores the most points wins. Or follow tradition and play additional rounds until one player gets 21 points (40 for championship games) — and you have to win by at least two points over your closest opponent’s score.

But Who’s Counting?


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


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.

Tweet: #Math Teachers and #Homeschool Bloggers: We Want You! Send a post to next week's math ed carnival. http://ctt.ec/daIO0+Don’t procrastinate: The deadline for entries is Monday, October 20. The carnival will be posted soon afterwards at — well, we don’t have a host for this month yet. Would you like to volunteer?

Click to tweet about the carnival:
(No spam, I promise! You will have a chance to edit or cancel the tweet.)

Would You Like to Host the Carnival?

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.

Explore the Other Math Carnivals

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

MathART Projects


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


Teddy Bear Hospital

Math Storytelling Day: The Hospital Floor

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

Have you ever heard of Math Storytelling Day? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system.

Check out these posts for more information:

My Math Story

tiles2

My story begins with an unexpected adventure in pain. Appendicitis sidewhacked my life last week, but that’s not the story. It’s just the setting. During my recovery, I spent a lot of time in the smaller room of my hospital suite. I noticed this semi-random pattern in the floor tile, which made me wonder:

  • Did they choose the pattern to keep their customers from getting bored while they were … occupied?
  • Is the randomness real? Or can I find a line of symmetry or a set of tiles that repeat?
  • If I take pictures from enough different angles, could I transfer the whole floor to graph paper for further study?
  • And if the nurse finds me doing this, will she send me to a different ward of the hospital? Do hospitals have psychiatric wards, or is that only in the movies?
  • What is the biggest chunk of squares I could “break out” from this pattern that would create the illusion of a regular, repeating tessellation?

I gave up on the graph paper idea (for now) and printed the pictures to play with. By my definition, “broken” pattern chunks need to be contiguous along the sides of the tiles, like pentominoes. Also, the edge of the chunk must be a clean break along the mortar lines. The piece can zigzag all over the place, but it isn’t allowed to come back and touch itself anywhere, even at a corner. No holes allowed.

I’m counting the plain squares as the unit and each of the smaller rectangles as a half square. So far, the biggest chunk of repeating tiles I’ve managed to break out is 283 squares.

tiles1

What Math Stories Will You Tell?

Have you and your children created any mathematical stories this year? I’d love to hear them! Please share your links in the comments section below.


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


Math Teachers at Play #78 via 1001 Math Problems

blog carnival 78 graphic

Math Teachers at Play is a traveling collection of math tidbits — games, lesson ideas, and more — from around the Internet. It moves around from month to month, and the September edition is now posted at 1001 Math Problems blog. What a fun list of math posts to browse!

Welcome to the 78th edition of the Math Teachers At Play math education blog carnival, which I am thrilled to be hosting this month in celebration of my soon-to-be-released book, Camp Logic. What is the blog carnival? It is a monthly snapshot of some interesting recent ideas and activities posted by math education bloggers all over the internet.

By tradition, I begin with a fun fact about the number 78:

Seventy-eight is the 12th triangle number, which means that it is the sum of the integers from 1 to 12. Therefore, it is also the total number of gifts given on the last day in the song “The Twelve Days of Christmas!” …

Click here to go read the whole carnival.


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


Calling All Math Teacher Bloggers and Homeschoolers: Carnival Time!

by Bob Jagendorf via flickr

by Bob Jagendorf via flickr

The monthly 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.

Tweet: Calling All Math Teacher Bloggers and Homeschoolers: Carnival Time! Join us by submitting your post today. http://ctt.ec/h3BOL+Don’t procrastinate: The deadline for entries is this Friday. The carnival will be posted next week at 1001 Math Problems blog.

Click to tweet about the carnival:
(No spam, I promise! You will have a chance to edit or cancel the tweet.)

We Need More Hosts to Fill Out this School Year

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.

Continue reading

Quotable: I Do Hate Sums

MrsLaTouche

I’ve been looking for quotes to put at the beginning of each chapter in my math games books. I found a delightful one by Mrs. LaTouche on the Mathematical Quotations Server, but when I looked up the original source, it was even better:

I am nearly driven wild with the Dorcas accounts, and by Mrs. Wakefield’s orders they are to be done now.

I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are Permutations and Aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of Number which it requires a mind like mine to perceive.

For instance, if you add a sum from the bottom up, and then again from the top down, the result is always different.

Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.

Try the experiment, and if you do not find it as I say, you are a mere sciolist*, a poor mechanical thinker, and not gifted as I am, with subtle perceptions.

Of course I find myself not appreciated as an accountant. Mrs. Wakefield made me give up the book to [my daughter] Rose and her governess (who are here), and was quite satisfied with the work of those inferior intellects.

— Maria Price La Touche
The Letters of A Noble Woman
London: George Allen & Sons, 1908

*sciolist: (archaic) A person who pretends to be knowledgeable and well informed. From late Latin sciolus (diminutive of Latin scius ‘knowing’, from scire ‘know’) + -ist.


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Capture

Math Teachers at Play # 77 via Math = Love

MTaP77

Math Teachers at Play is a traveling collection of math tidbits — games, lesson ideas, and more — from around the Internet. It moves around from month to month, and the August edition is now posted at Math = Love blog. What a fun list of math posts to browse!

Welcome to the 77th edition of the Math Teachers at Play Blog Carnival! I’m super excited to be hosting this carnival because I’ve been reading it for years! Yes, I am that crazy person who started reading math teacher blogs as a high school junior. I think you are going to enjoy going through the submissions. I know I found several new-to-me blogs to add to my RSS reader! …

Click here to go read the whole carnival.


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


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.

Tweet: Do You Blog About Math?: Share Your Post! Enter next week's #math education carnival. http://ctt.ec/5faeWDon’t procrastinate: The deadline for entries is this Friday. The carnival will be posted next week at Math = Love.

Click to tweet about the carnival:
(No spam, I promise! You will have a chance to edit or cancel the tweet.)

Would You Like to Host the Carnival?

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.

Explore the Other Math Carnivals

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

Sawyer--Vision in Elem Maths


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


dividing sausages

Fractions: 1/5 = 1/10 = 1/80 = 1?

[Feature photo is a screen shot from the video "the sausages sharing episode," see below.]

Fractions: 1/5 = 1/10 = 1/80 = 1?

How in the world can 1/5 be the same as 1/10? Or 1/80 be the same as one whole thing? Such nonsense!

No, not nonsense. This is real-world common sense from a couple of boys faced with a problem just inside the edge of their ability — a problem that stretches them, but that they successfully solve, with a bit of gentle help on vocabulary.

Here’s the problem:

  • How can you divide eight sausages evenly among five people?

Think for a moment about how you (or your child) might solve this puzzle, and then watch the video below.

What Do You Notice?

Continue reading

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Playing With Math — the Book

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Update: The crowdfunding campaign is now closed and the book is in the final stages. It should be headed to the printer soon. Check the Playing With Math homepage for publication and ordering information.


There are only a few days left to reserve your copy of Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers. I don’t have time to finish the review I hoped to write, so instead I’ll share some of my favorite quotes from the book:

What do mathematicians do? We play with math. What are little kids doing when they’re thinking about numbers, shapes, and patterns? They’re playing with math. You may not believe it yet, but you can have fun playing with math, too.

— Sue VanHattum, editor

We had a discussion at the end of the club on how we are all confused now, but pleasantly so, and how important it is to rejoice in confusion and to be comfortable with it. Adults often strive very hard to get rid of any and all possible traces of confusion for kids, making things dreadfully boring.

— Maria Droujkova, after a math circle exploration of infinity

All it talkes to do mathematics is opportunity, a frustrating problem, and a bit of stubbornness.

— Ellen Kaplan, math circle leader

Our own school experiences can make it hard for us to teach without being tempted to “help them master” a concept that they may or may not be ready to master. What we never learned in school was the concept of playing around with math, allowing ideas to “percolate,” so to speak, before mastery occurs, and that process may take time.

— Julie Brennan, homeschooler

4 hurricane learning lp md

The most profound learning often takes place silently and invisibly, in between activities and away from prying eyes. It is here that all those pieces of information, having been shaved from actual experience, are pulled inward to jostle against one another in various combinations and arrangements until gradually, or sometimes suddenly, a new understanding emerges.

— Holly Graff, unschooler

I do a mean T. Rex impression and the class was convulsed in giggles — the perfect way to enter a “hard” math lesson. I chucked the planned lesson for the day, and we went with the dinosaurs, and eventually various other creatures with different numbers of digits. I asked the class how the T. Rex would count. After all, it has only three fingers. I’ll admit to a lot of roaring and stomping as I, the T. Rex, became more and more frustrated trying to write a note to my mother in which I wanted to tell her that I had eaten those four velociraptors.

— Michelle Martin, elementary teacher

OLYMPUS DIGITAL CAMERA

It is the process of sharing — of not only creative and insightful problem-solving approaches, but also memorable moments filled with camaraderie, generosity, and incomparable joy. That is why I love math.

— Luyi Zhang, math major

Remember that joy and passion lead to more learning than duty ever did.

— Sue VanHattum, editor

This book truly captures the joy and passion of learning (and teaching) mathematics. Whether you love math and want to share it with your kids, or whether you fear and loathe math and need help getting over that hurdle so you won’t pass your fear on, Playing With Math will encourage you to see math more deeply and play with it more freely.

Excerpts from Playing With Math

If I’m reading the website aright, the crowdfunding campaign for Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers ends in the early wee hours of Sunday morning. Be sure to place your order by Saturday, July 19th!


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


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.

Tweet: #Math Teachers and #Homeschool Bloggers: Share Your Post! Enter next week's math ed carnival. http://ctt.ec/qJPXy+Don’t procrastinate: The deadline for entries is this Friday extended through the weekend. The carnival will be posted next week at Let’s Play Math.

Click to tweet about the carnival:
(No spam, I promise! You will have a chance to edit or cancel the tweet.)

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

Need an Idea-Starter?

  • 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 \left(a + b \right)^2 ? 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!

Would You Like to Host the Carnival?

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.

Explore the Other Math Carnivals

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


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


JoBoalerProportionalRelationships

Quotable: Math Connections

ConnectedGearsJoBoaler

It turns out that the people who do well in math are those who make connections and see math as a connected subject. The people who don’t do well are people who see math as a lot of isolated methods.

— Jo Boaler
Math Connections

If you or your children struggle with math, Boaler’s non-profit YouCubed.org may help you recover your joy in learning.


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


Sconic Sections

Math(s) Teachers At Play #75 via CavMaths

[Feature photo above "Sconic Sections" by Lenore Edman and "75" by R/DV/RS via Flickr (CC BY 2.0).]
75

The monthly math education blog carnival Math Teachers at Play features games, lessons, puzzles, activities, and teaching tips from classroom teachers, homeschoolers, and self-educated learners around the Internet world. Check out the 20 posts of mathematical fun in the June edition:

Math(s) Teachers At Play #75 via CavMaths

Hello, and welcome to the 75th issue of the Math(s) Teachers at Play Blog Carvinal! For those of you who are unaware, a “blog carnival” is a periodic post that travels from blog to blog and has a collection of posts on a certain topic.

This is the first time I’ve hosted a carnival and there were some excellent submissions. I enjoyed reading them all and have discovered some new blogs. I have also input some posts I’ve seen this month which I thought were excellent too…

Click here to go read Math(s) Teachers At Play #75 via CavMaths.


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


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Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers

body_Book_cover_for_upload

Update: The crowdfunding campaign is now closed and the book is in the final stages. It should be headed to the printer soon. Check the Playing With Math homepage for publication and ordering information.


There’s a problem: Most people don’t like math. Why is that? Perhaps it has something to do with the way math is taught in school. As a teacher to my own kids and mentor to homeschooling parents, I’ve been fighting math anxiety for decades.

This book is one part of the solution.

Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers features more than thirty authors who tell delightful stories of learning to appreciate math and of sharing their enthusiasm with their communities, families, or students. After every chapter is a puzzle, game, or activity to get you and your kids playing with math, too.

You can read a couple of excerpts at PlayingWithMath.org:

Whether you love math and want to share it with your kids, or whether you fear and loathe math and need help getting over that hurdle so you won’t pass your fear on, Playing With Math will encourage you to see math more deeply and play with it more freely.

I’ve been waiting for this book for years, and I’m thrilled to see it finally come together. As I read the advance copy (review coming soon!), I am amazed at how many different ways there are to think about math. Each writer has a new perspective and unique insight, and my quotes journal is filling up with inspiration.

A Word from the Editor

The idea of crowd-funding may be new to you. Here’s how it works:

Today is the first day of our crowd-funding campaign. For a contribution of $25, we’ll send you a book as soon as it’s printed.

You can contribute anything from $1 to $5000 (with rewards at each contribution level) to help us pay for our illustrators, editors, page layout person, and printing. This is our way of asking for community support for this book as part of the production process. We hope to build lots of energy around the ideas in the book through this campaign.

Besides contributing, here’s another way you can help: Think of five friends who would enjoy this book.

  • Do you have friends who get frustrated helping their kids with math homework?
  • Or who teach young kids but don’t feel comfortable with math themselves?
  • Do you have friends who enjoy math?
  • Or who want ideas to share with the kids in their lives?
  • Do you know someone who might want to start a math circle?

Would you send them a quick message, to let them know we’re here?

I’m hoping for the power of exponential growth with this. Our outrageous goal is to change the way people all over this country, and maybe even the world, think about math. If you each send this to five friends who might enjoy the book, and each of them sends it to five friends, and each of them … Well, pretty soon we cover the world, right?

In fact, if we kept it going through eleven steps, that would make 5 to the 11th power, or over 40 million people. Does Sue dream big? Yep.

Sue VanHattum


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


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.

Tweet: #Math Teachers and #Homeschool Bloggers: We Want You! Send a post to next week's math ed carnival. http://ctt.ec/ERdmu+Don’t procrastinate: The deadline for entries is this Friday, June 20. The carnival will be posted next week at CavMaths blog.

Click to tweet about the carnival:
(No spam, I promise! You will have a chance to edit or cancel the tweet.)

Would You Like to Host the Carnival?

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.

Explore the Other Math Carnivals

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

MathART Projects


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


calculus

Reblog: Calculus Tidbits

[Feature photo above by Olga Lednichenko via Flickr (CC BY 2.0).]

This week I have a series of quotes about calculus from my first two years of blogging. The posts were so short that I won’t bother to link you back to them, but math humor keeps well over the years, and W. W. Sawyer is (as always) insightful.

I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:


Finding the Limit

Eldest daughter had her first calculus lesson last night: finding the limit as delta-t approached zero. The teacher found the speed of a car at a given point by using the distance function, calculating the average speed over shorter and shorter time intervals. Dd summarized the lesson for me:

“If you want to divide by zero, you have to sneak up on it from behind.”


Harmonic Series Quotation

This kicked off my week with a laugh:

Today I said to the calculus students, “I know, you’re looking at this series and you don’t see what I’m warning you about. You look and it and you think, ‘I trust this series. I would take candy from this series. I would get in a car with this series.’ But I’m going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.”

—Rudbeckia Hirta
Learning Curves Blog: The Harmonic Series
quoting Alexandre Borovik


So You Think You Know Calculus?

Rudbeckia Hirta has a great idea for a new TV blockbuster:


Common Sense and Calculus

Sawyer-MathDelight

And here’s a quick quote from W. W. Sawyer’s Mathematician’s Delight:

If you cannot see what the exact speed is, begin to ask questions. Silly ones are the best to begin with. Is the speed a million miles an hour? Or one inch a century? Somewhere between these limits. Good. We now know something about the speed. Begin to bring the limits in, and see how close together they can be brought.

Study your own methods of thought. How do you know that the speed is less than a million miles an hour? What method, in fact, are you unconsciously using to estimate speed? Can this method be applied to get closer estimates?

You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply the same common sense to stones rolling down hillsides, and the calculus is at your command.


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


6260501380_7dbe7a7aed_z

Reblog: Patty Paper Trisection

[Feature photo above by Michael Cory via Flickr (CC BY 2.0).]

trisection2

I hear so many people say they hated geometry because of the proofs, but I’ve always loved a challenging puzzle. I found the following puzzle at a blog carnival during my first year of blogging. Don’t worry about the arbitrary two-column format you learned in high school — just think about what is true and how you know it must be so.

I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:


trisection

One of the great unsolved problems of antiquity was to trisect any angle using only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass. Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator or something.

One “cheat” that works is to fold your paper. I will show you how it works, and your job is to show why …

[Click here to go read Puzzle: Patty Paper Trisection.]



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Let’s Play Math on Scribd

letsplaymathcover-mini

Do you subscribe to the Scribd subscription reading service? My Let’s Play Math ebook is now available to Scribd subscribers:

Reviews of Let’s Play Math

Combined with all the linked resources, this book is going to transform how I teach my kids maths. No more dabbling in “real maths” but then running back to the workbooks when anxiety strikes — with this approach I can teach my kids to think like mathematicians without worrying about leaving gaps.

My favourite section of the book is “One Week of Real Mathematics”, which contains examples of what one week’s worth of math playtime might look like. I love having this starting point to show me what a balanced “maths diet” might look like.

I knew the well-travelled road (maths curricula) wasn’t for us, but I lacked confidence in my ability to guide my children through uncharted territory. Let’s Play Math is the map and the guidebook I’ve been looking for. With it in my hand I can’t wait to take my children by the hand and head off to explore the wonderful world of maths.

— Lucinda Leo
Navigating By Joy

A beautiful book that explains the “why” and “how” of teaching math from a Constructivist perspective. It is well researched, well annotated, and includes loads of activities that you can try with kids K-12 at home. While reading the book, I found myself remembering a lot of things I had forgotten from my teacher-training … I have to say that there were so many parts of this book that I highlighted that I really gave my Kindle a workout!

There is a whole section that I’m going to come back to this summer, to keep my kids busy. But was especially useful to me at this moment, were the talking points for helping kids solve problems on their own. Yes, I at one point learned all of talking points, but I really needed the refresher.

My son’s school does Continental Mathematics League, and those problems are really hard. I’m going to print up all of the talking points and post them in our kitchen so that my husband and I will have a list of questions to prompt our son’s thinking.

— Jennifer Bardsley
Teaching My Baby To Read


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old warrior dragon

Reblog: Solving Complex Story Problems

[Dragon photo above by monkeywingand treasure chest by Tom Praison via flickr.]

Dealing with Dragons

Over the years, some of my favorite blog posts have been the Word Problems from Literature, where I make up a story problem set in the world of one of our family’s favorite books and then show how to solve it with bar model diagrams. The following was my first bar diagram post, and I spent an inordinate amount of time trying to decide whether “one fourth was” or “one fourth were.” I’m still not sure I chose right.

I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:


Solving-Complex-Story-Problems

Cimorene spent an afternoon cleaning and organizing the dragon’s treasure. One fourth of the items she sorted was jewelry. 60% of the remainder were potions, and the rest were magic swords. If there were 48 magic swords, how many pieces of treasure did she sort in all?

[Problem set in the world of Patricia Wrede's Enchanted Forest Chronicles. Modified from a story problem in Singapore Primary Math 6B. Think about how you would solve it before reading further.]

How can we teach our students to solve complex, multi-step story problems? Depending on how one counts, the above problem would take four or five steps to solve, and it is relatively easy for a Singapore math word problem. One might approach it with algebra, writing an equation like:

x - \left[\frac{1}{4}x + 0.6\left(\frac{3}{4} \right)x  \right]  = 48

… or something of that sort. But this problem is for students who have not learned algebra yet. Instead, Singapore math teaches students to draw pictures (called bar models or math models or bar diagrams) that make the solution appear almost like magic. It is a trick well worth learning, no matter what math program you use …

[Click here to go read Solving Complex Story Problems.]



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mtap74

Math Teachers at Play #74 via Triumphant Learning

74 by Stephan Mosel

photo by Stephan Mosel (CC BY 2.0)

The new Math Teachers at Play math education blog carnival is up for your browsing pleasure. Each month, we feature activities, lessons, and games about math topics from preschool through high school. Check it out!

Here’s a peek at a few of the entries:

Origami
Learn how to make Origami Stars, Tessellation Stars, and Chaotic Stars at Math Munch. I think once your students or children see this, you will find Transforming Ninja Stars littering your house and classroom!

Pi
Here’s a fun activity to explore other ways to get the number Pi on the calculator from William Wu at Singapore Maths Tuition.

Math Games
Math Hombre shares a coordinate grid game that also calculates area of rectangles. And all you need is some grid paper and dice.

…And much more!

Click here to go read the entire blog carnival.

Would You Like to Host the Carnival?

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.


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


Basel spiral

More Than One Way To Find the Center of a Circle

[Feature photo above by hom26 via Flickr.]

My free time lately has gone to local events and to book editing. I hope to put up a series of blog posts sometime soon, based on the Homeschool Math FAQs chapter I’m adding to the paperback version of Let’s Play Math. [And of course, I'll update the ebook whenever I finally publish the paperback, so those of you who already bought a copy should be able to get the new version without paying extra.]

But in the meantime, as I was browsing my blog archives for an interesting “Throw-Back Thursday” post, I stumbled across this old geometry puzzle from Dave Marain over at MathNotations blog:

Is it possible that AB is a chord but NOT a diameter? That is, could circle ABC have a center that is NOT point O?

Jake shows Jack a piece of wood he cut out in the machine shop: a circular arc bounded by a chord. Jake claimed that the arc was not a semicircle. In fact, he claimed it was shorter than a semicircle, i.e., segment AB was not a diameter and arc ACB was less than 180 degrees.

Jack knew this was impossible and argued: “Don’t you see, Jake, that O must be the center of the circle and that OA, OB and OC are radii.”

Jake wasn’t buying this, since he had measured everything precisely. He argued that just because they could be radii didn’t prove they had to be.

Which boy do you agree with?

  • Pick one side of the debate, and try to find at least three different ways to prove your point.

If you have a student in geometry or higher math, print out the original post (but not the comments — it’s no fun when someone gives you the answer!) and see what he or she can do with it.

Dave offers many other puzzles to challenge your math students. While you are at his blog, do take some time to browse past articles.


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Related posts on Let’s Play Math! blog:

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 at Triumphant Learning blog.

Click to tweet about the carnival: Tweet: Math teachers and homeschool bloggers: Share your post! #Math education blog carnival deadline Friday.  http://ctt.ec/Cpcm1+
(No spam, I promise! You will have a chance to edit or cancel the tweet.)

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.

Explore the Other Math Carnivals

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


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wordle73

Math Teachers at Play #73 via Singapore Maths Tuition

Maze photo by woodleywonderworks (CC BY 2.0)

woodleywonderworks (CC BY 2.0)

The monthly math education blog carnival Math Teachers at Play features games, lessons, puzzles, activities, and teaching tips from classroom teachers, homeschoolers, and self-educated learners around the Internet world. Check out the 15 posts of mathematical fun in April’s edition:

Here’s a peek at a few of the entries:

Check out the following awesome blogs!

Math Strategies
There is such an emphasis on learning math facts that our children do not spend enough time learning strategies that will help them solve math problems. Read about two types of strategies for solving math problems—working left to right and regrouping into what you know.
– Crystal Wagner

Nim Games
This is a game that is generally used to show how math can be involved in game play. I explain the rules of the game as well as the mathematical strategy involved. There is also a script where users can compete against the computer
– Aftermath

Day 85 – Related Rates
Two separate trucks carrying a very long wind turbine blade need to turn the corner. Describe how their speeds vary throughout the turn. The blog is dedicated to these types of discussion starters, at all levels.
– Curmudgeon

Click here to go read the entire blog carnival!

Would You Like to Host the Carnival?

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.


Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.


bill-gates-hombre-mas-rico

Reblog: Putting Bill Gates in Proportion

[Feature photo above by Baluart.net.]

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 this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:


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?

Continue reading

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.

Continue reading

Handshake_(Workshop_Cologne_'06)

Reblog: The Handshake Problem

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

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 this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:


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 Skit: The Handshake Problem.]


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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.]

Quotations and comments about the perils of standardized testing, now part of my book Let’s Play Math.

I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:


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 In Honor of the Standardized Testing Season.]


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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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