Tag Archives: Algebra

Math Teachers at Play #76

76[Feature photo (above) by U.S. Army RDECOM. Photo (right) by Stephan Mosel. (CC BY 2.0)]

On your mark… Get set… Go play some math!

Welcome to the 76th edition of the Math Teachers At Play 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.

By tradition, we start the carnival with a puzzle in honor of our 76th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

PUZZLE: CRYSTAL BALL CONNECTION PATTERNS

K4 matchings

In the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call.

Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4-crystal system.

On the second line of the diagram, Joe (in the middle) wakes up from siesta and calls each of his friends in turn. Then the friends take turns calling each other, bringing the total number of possible connection-states up to seven.

Finally, Wizard Mathys imagines what would happen if one friend calls Joe at the same time as the other two are talking to each other. That’s the last line of the diagram: three more possible states. Therefore, the total number of conceivable communication configurations for a 4-crystal system is 10.

For some reason Mathys can’t figure out, mathematicians call the numbers that describe the connection pattern states in his crystal ball communication system Telephone numbers.

TheWizardBySeanMcGrath-small

  • Can you help Wizard Mathys figure out the Telephone numbers for different numbers of people?
    T(0) = ?
    T(1) = ?
    T(2) = ?
    T(3) = ?
    T(4) = 10 connection patterns (as above)
    T(5) = ?
    T(6) = ?
    and so on.

Hint: Don’t forget to count the state of the system when no one is on the phone crystal ball.

[Wizard photo by Sean McGrath. (CC BY 2.0)]


TABLE OF CONTENTS

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; I’ve drawn others from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, here’s a quick Table of Contents:

Continue reading Math Teachers at Play #76

The Linear Inequality Adventures of Ohio Jones

Ohio Jones 1

Last week, Kitten and I reached her textbook’s chapter on graphing linear equations, and a minor mistake with negative numbers threw her into an “I can’t do it!” funk. It’s not easy teaching a perfectionist kid.

Usually her mood improves if we switch to a slightly more advanced topic, and luckily I had saved these worksheets on my desktop, waiting for just such an opportunity. Today’s lesson:

  • Some fun(ish) worksheets
    “For tomorrow, students will be graphing systems of inequalities, so I decided to create a little Ohio Jones adventure (Indiana’s lesser known brother)…”

I offered to give her a hint, but she wanted to try it totally on her own. It took her about 40 minutes to work through the first few rooms of the Lost Templo de los Dulces and explain her solutions to me. I’m sure she’ll speed up with experience.

So far, she’s enjoying it much more than the textbook lesson. It’s fascinating to me how the mere hint of fantasy adventure can change graphing equations from boring to cool. Thanks, Dan!


Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.


Math Teachers at Play #70

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 Playtime With Blocks

Feature video by Stuart Jeckel via youtube.

DO Try This at Home

And ask questions!


Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.


Algebra for (Almost) Any Age

VisualPatterns-org2

Fawn Nguyen’s Visual Patterns website just keeps getting better and better. Check it out:

In addition to the 115 puzzle patterns (as of this writing), the site features a Gallery page of patterns submitted by students. And under the “Teachers” tab, Fawn shares a form to guide students in thinking their way through to the algebraic formula for a pattern.

How can you use these patterns to develop algebraic thinking with younger students? Mike Lawler and sons demonstrate Pattern #1 in the YouTube video below.


Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.


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)]
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

Puzzle: Algebra on Rectangles

Gordon Hamilton of Math Pickle recently posted these videos on how to make algebra 1 puzzles on rectangles. As I was watching, Kitten came in and looked over my shoulder. She said, “Those look like fun!”

They look like fun to me, too, and I bet your beginning algebra students will enjoy them:

Continue reading Puzzle: Algebra on Rectangles