# 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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# Math Teachers at Play #70

[Feature photo above by David Reimann via Bridges 2013 Gallery. Number 70 (right) from Wikimedia Commons (CC-BY-SA-3.0-2.5-2.0-1.0).]

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

Welcome to the 70th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of 42+ 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 in honor of our 70th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

# Math Teachers at Play #66

[Feature photo above by Franz & P via flickr. Route 66 sign by Sam Howzit via flickr. (CC BY 2.0)]

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.

By tradition, we start the carnival with a couple of puzzles in honor of our 66th edition.

Let the mathematical fun begin!

## Puzzle 1

Our first puzzle is based on one of my favorite playsheets from the Miquon Math workbook series. Fill each shape with an expression that equals the target number. Can you make some cool, creative math?

Click the image to download the pdf playsheet set: one page has the target number 66, and a second page is blank so you can set your own target number.

# A Pretty Math Problem?

As we were doing Buddy Math (taking turns through the homework exercises) today, my daughter said, “Oooo! I want to do this one. It’s pretty!”

She has always loved seeing patterns in math. I remember once, years ago, when she insisted that we change the problems on a worksheet to make the answers come out symmetrical. :)

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# Logic Puzzle: Imbalance Problems

Kitten and I have been slogging through the decimals chapter in AoPS Pre-Algebra. She hates arithmetic, so I tried skipping ahead to the algebra puzzle in the exercises, but she refused to be taken in: a decimal problem with an x in it is still a decimal problem.

So I let her off early and pointed her toward these logical “algebra” puzzles instead:

Puzzle by Paul Salomon

By Denise Gaskins Posted in Puzzles

# Quotable: Why Study Algebra?

[Photo by AlphaTangoBravo / Adam Baker via flickr.]

One reason to study algebra: because it’s a building block. And just as it was really hard at first to get those blocks to do what you wanted them to do, so also it can be really hard at first to get algebra to work. But if you persevere, who knows what you might build someday?

Algebra is the beginning of a journey that gives you the skills to solve more complex problems.

So, try not to think of Algebra as a boring list of rules and procedures to memorize. Consider algebra as a gateway to exploring the world around us all.

— Jason Gibson
Why Study Algebra?

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# Rate × Time = Distance Problems

I love how Richard Rusczyk explains math problems. It’s a new school year, and that means it’s time for new MathCounts Mini videos. Woohoo!

# Math Teachers at Play #52

[Photo by bumeister1 via flickr.]

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! We have games, lessons, and learning activities from preschool math to calculus. If you like to learn new things and play around with mathematical ideas, you are sure to find something of interest.

Scattered between all the math blog links, I’ve included highlights from the Common Core Standards for Mathematical Practice, which describe the types of expertise that teachers at all levels — whether in traditional, experimental, or home schools — should seek to develop in their math students.

Let the mathematical fun begin…

## TRY THESE PUZZLES

By tradition, we start the carnival with a couple of puzzles in honor of our 52nd edition. Since there are 52 playing cards in a standard deck, I chose two card puzzles from the Maths Is Fun Card Puzzles page:

• A blind-folded man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up. How can he divide the cards into two piles (which may be of different sizes) with each pile having the same number of cards facing up?
• What is the smallest number of cards you must take from a 52-card deck to be guaranteed at least one four-of-a-kind?

The answers are at Maths Is Fun, but don’t look there. Having someone give you the answer is no fun at all!

# Math Teachers at Play #46

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! Here is a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college. Some articles were submitted by their authors, others were drawn from the immense backlog in my blog reader. If you like to learn new things, you are sure to find something of interest.

# How to Translate Word Problems

Hooray! The MathCounts Mini videos are back. September’s edition is all about translating word problems into algebra:

Download activity sheets and answers.

Do your students like making videos? This year, MathCounts is challenging students in grades 6-8 to create a math problem video. Check out the details:

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

# Math Teachers at Play #39

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.

Several of these articles were submitted by the bloggers; others were drawn from my overflowing blog reader. Don’t try to skim everything all at once, but take the time to enjoy browsing. Savor a few posts today, and then come back for another helping tomorrow or next week.

Most of the photos below are from the 2010 MAA Found Math Gallery; click each image for more details. Quotations are from Mike Cook’s Canonical List of Math Jokes.

Let the mathematical fun begin…

# Math Teachers at Play #35

35 is a tetrahedral number

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers.

Do you enjoy math? I hope so! If not, browsing these links just may change your mind. Most of these posts were submitted by the bloggers themselves; others are drawn from my overflowing Google Reader. From preschool to high school, there are plenty of interesting things to learn.

Let the mathematical fun begin…

# 10/10 is Powers of 10 Day

Sunday, October 10th is Powers of Ten Day!

# Sept-Oct 2010 Math Calendars

As I was preparing for Wednesday’s Homeschool Math Club Games & Activities meeting, I remembered my old math calendars and thought, that would be a fun activity to offer. So I pulled up the files and discovered that the days of the week matched perfectly. What a cool coincidence!

So in case you missed the math calendars last year, or in case it’s been long enough that your children have forgotten, here are the “new” versions:

## Addendum

Umm Ahmad created an easier version for young students:

By Denise Gaskins

# Rate Puzzle: How Fast Does She Read?

[Photo by Arwen Abendstern.]

If a girl and a half
can read a book and a half
in a day and a half,
then how many books can one girl read in the month of June?

Kitten reads voraciously, but she decided to skip our library’s summer reading program this year. The Border’s Double-Dog Dare Program was a lot less hassle and had a better prize: a free book! Of course, it didn’t take her all summer to finish 10 books.

How fast does Kitten read?

# Math Teachers at Play #24

[Photo by internets_dairy.]

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest. Let’s start the mathematical fun with an arithmetic card game in honor of our 24th edition and a few number puzzles:

# Game: Target Number (or 24)

[Photo by stevendepolo.]

Math concepts: addition, subtraction, multiplication, division, powers and roots, factorial, mental math, multi-step thinking
Number of players: any number
Equipment: deck of math cards, pencils and scratch paper, timer (optional)

# Math Teachers at Play #20

[Photo by shonk.]

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.

Let’s start the mathematical fun with a couple of puzzles in honor of our 20th edition: First, the shape to our right is an icosahedron, one of the Platonic solids. Each face is an equilateral triangle — can you count them? For more fun, make your own model.

# Algebra: A Problem in Translation

[Photo by *Irish.]

In my post Elementary Problem Solving: The Tools, I introduced word algebra as a way to help students think their way through a story problem. In the next two posts, I showed how the tool worked with simple word problems.

Now, before I move on to focus exclusively on bar diagrams, I would like to show how word algebra can help a student solve a typical first-year algebra puzzle.

A homeschooling friend who avoided algebra in high school, trying to help her son cope with a subject she never understood, posted: “Help! Our answer is different from the book’s.” Here is the homework problem:

Josh earned \$72 less than his sister who earned \$93 more than her mom. If they earned a total of \$504, how much did Josh earn?

# Math Teachers at Play #8

[Photo by jaaron.]

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! We accept entries from anyone who enjoys playing around with math, as long as the topic is relevant to students or teachers of preK-12th grade mathematics.

Some articles were submitted by their authors, other were drawn from the back-log in my blog reader, and I’ve spiced it all up with a few math jokes courtesy of the Mathematical humor collection of Andrej and Elena Cherkaev.

Let the mathematical fun begin…

# Math Facts: 5 Minutes a Day

Y of x reminded me about one of my old favorite websites for math fact practice with a purpose:

5-10 minutes of daily practice will cement the math facts in your student’s mind, while at the same time doing a good deed. For each correct answer, a Free Rice sponsor donates a very small amount of rice to feed hungry people worldwide through the UN World Food Program.

Even very small amounts of rice add up. Since Free Rice started in 2007, its sponsors have bought more than 63 billion grains of rice, just by paying for one right answer click at a time.

You and your students can practice other topics as well:

# Math Teachers at Play #5

[Photo by Alex Kehr.]

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest. Let the mathematical fun begin…

# April Math Calendar

My homeschool co-op classes had a lot of fun creating this April calendar to hand out at our end-of-semester party on Friday. It’s not as easy to read as a traditional calendar — it is more like a puzzle. The expression in each square simplifies to that day’s date, so families can treat each day like a mini-review quiz: “Do you remember how to calculate this?”

Download your own copy:

If you’ve been wanting to start your own math club, you will find plenty of helpful ideas here:

## Update

Check out my May Math Calendar post for more ideas about how to use these puzzles.

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

# Math Teachers at Play #2

[Photo by Sister72.]

Welcome to the second Math Teachers At Play blog carnival! Some articles were submitted by their authors, other were drawn from the back-log in my blog reader, and I’ve spiced it all up with a few of my favorite quotations.

Let the mathematical fun begin…

# Math Teachers at Play #1

[Photo by StuSeeger.]

Welcome to the inaugural edition of the Math Teachers At Play blog carnival! I hope you enjoy this collection of tips, tidbits, games, and activities for students and teachers of preschool-12th grade mathematics.

For this first carnival, I’ve drawn several recent posts from my blog reader as examples of the types of posts I’d love to include in future editions of Math Teachers at Play. I tried to find something for everyone, from multiplication drill for elementary students to advice for understanding high school math equations.

Let the mathematical fun begin…

# Review: Kiss My Math

Pre-algebra students stand at the threshold of adventure. Behind them lie the rocky plains of school arithmetic. Ahead, the trail winds into a murky, tangled woods and disappears in the shadows. Who knows what monsters might live in a place like that?

Actress and math maven Danica McKellar has traveled through the pre-algebra jungle and beyond, up the slopes to higher math. She survived the journey, and now, on the heels of her bestselling book for math-phobic middle schoolers, she has written Kiss My Math to guide uncertain students along their way.

Unlike the case with most Hollywood movies, this sequel is an improvement.

# Online Game: Math Caching

In the treasure-hunting game of Geocaching (pronounced “geo-cashing”), players use GPS systems to locate boxes hidden at different geographical locations across the country.

Now, the creative people at Mathbits.com have come up with an online treasure-hunting activity for junior high and high school students, called MathCaching. Students solve mathematical problems to find hidden “boxes” on the Internet. Each box reveals clues to the location of the next one.

The MathCaching game covers pre-algebra through trigonometry topics, with calculus levels under development. For more information, visit the MathCaching site, or read the post on my Frugal Homeschooling blog.

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

# Hit Me! (A Math Game)

Photo by paparutzi.

Math concepts: addition, subtraction, negative numbers, mental math, absolute value
Number of players: any number
Equipment: math cards (two decks may be needed for a large group)

# The Function Machine Game

Math concepts: odd numbers, even numbers, greater-than/less-than, rounding off, addition, subtraction, multiplication, division, fractions, negative numbers, prime numbers, square numbers, problem solving, mental math
Number of players: two or more
Equipment: pencil (or pen) and paper for every player