Reblog: The Handshake Problem

Posted on by Denise Gaskins

[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.]

Math Teachers at Play #70

Posted on by Denise Gaskins

800px-Brauchtum_gesteck_70_1[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.

Click here to continue reading.

Math Teachers at Play #66

Posted on by Denise Gaskins

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

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

how crazy 66

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.

Continue reading Math Teachers at Play #66

A Pretty Math Problem?

Posted on by Denise Gaskins

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!”

CodeCogsEqn

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. 🙂

Logic Puzzle: Imbalance Problems

Posted on by Denise Gaskins

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

Continue reading Logic Puzzle: Imbalance Problems

Quotable: Why Study Algebra?

Posted on by Denise Gaskins

Blocks

[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?

Rate × Time = Distance Problems

Posted on by Denise Gaskins

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!

Continue reading Rate × Time = Distance Problems

Math Teachers at Play #52

Posted on by Denise Gaskins

[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!

Continue reading Math Teachers at Play #52

Math Teachers at Play #46: Living Books for Math

Posted on by Denise Gaskins

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.

Living Books for Math

A child’s intercourse must always be with good books, the best that we can find… We must put into their hands the sources which we must needs use for ourselves, the best books of the best writers.
…
For the mind is capable of dealing with only one kind of food; it lives, grows and is nourished upon ideas only; mere information is to it as a meal of sawdust to the body.

— Charlotte Mason
Toward A Philosophy of Education

Princess Kitten and I took a longer than usual holiday break from homeschooling, but now I’m in plan-for-the-new-semester mode. I hope to include more living math in our schedule, so I decided to illustrate this edition of the MTaP carnival with a few of my favorite living math books. I’d love to hear more living book suggestions in the comments!

If you click on a book cover, the links take you to Amazon.com, where you can read reviews and other details (and where I earn a small affiliate commission if you actually buy the book), but all of these books should be available through your public library or via inter-library loan.

Let the mathematical fun begin…

Continue reading Math Teachers at Play #46: Living Books for Math