Ohio Jones 2

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!


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Reimann-hexagon

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.

Carnival Parade in Aachen 2007

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.

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What Do You Notice? What Do You Wonder?

Drawing Star

If you want your children to understand and enjoy math, you need to let them play around with beautiful things and encourage them to ask questions.

Here is a simple yet beautiful thing I stumbled across online today, which your children may enjoy:

It reminds me of string art designs, but the app makes it easy to vary the pattern and see what happens.

  • What do your students notice about the patterns?
  • What questions can they ask?

I liked the way the app uses “minutes” as the unit that describes the star you want the program to draw. That makes it easier (for me, at least) to notice and understand the patterns, since minutes are a more familiar and intuitive unit than degrees, let alone radians.

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Math Teachers at Play #62

by Robert Webb

Do you enjoy math? I hope so! If not, browsing this post just may change your mind. Welcome to the Math Teachers At Play blog carnival — a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college.

Let the mathematical fun begin!

POLYHEDRON PUZZLE

By tradition, we start the carnival with a puzzle in honor of our 62nd edition:

An Archimedean solid is a polyhedron made of two or more types of regular polygons meeting in identical vertices. A rhombicosidodecahedron (see image above) has 62 sides: triangles, squares, and pentagons.

  • How many of each shape does it take to make a rhombicosidodecahedron?
Click for full-size template.

Click for template.

My math club students had fun with a Polyhedra Construction Kit. Here’s how to make your own:

  1. Collect a bunch of empty cereal boxes. Cut the boxes open to make big sheets of cardboard.
  2. Print out the template page (→) and laminate. Cut out each polygon shape, being sure to include the tabs on the sides.
  3. Turn your cardboard brown-side-up and trace around the templates, making several copies of each polygon. I recommend 20 each of the pentagon and hexagon, 40 each of the triangle and square.
  4. Draw the dark outline of each polygon with a ballpoint pen, pressing hard to score the cardboard so the tabs will bend easily.
  5. Cut out the shapes, being careful around the tabs.
  6. Use small rubber bands to connect the tabs. Each rubber band will hold two tabs together, forming one edge of a polyhedron.

So, for instance, it takes six squares and twelve rubber bands to make a cube. How many different polyhedra (plural of polyhedron) will you make?

  • Can you build a rhombicosidodecahedron?

And now, on to the main attraction: the 62 blog posts. Many of the following articles were submitted by their authors; others were drawn from the immense backlog in my blog reader. If you’d like to skip directly to your area of interest, here’s a quick Table of Contents:

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photo by Sphinx The Geek via flickr

Homeschooling High School Math

photo by ddluong via flickr

photo by ddluong via flickr

Feature photo (above) by Sphinx The Geek via flickr.

Most homeschoolers feel at least a small tinge of panic as their students approach high school. “What have we gotten ourselves into?” we wonder. “Can we really do this?” Here are a few tips to make the transition easier.

Before you move forward, it may help to take a look back. How has homeschooling worked for you and your children so far?

If your students hate math, they probably never got a good taste of the “Aha!” factor, that Eureka! thrill of solving a challenging puzzle. The early teen years may be your last chance to convince them that math can be fun, so consider putting aside your textbooks for a few months to:

On the other hand, if you have delayed formal arithmetic, using your children’s elementary years to explore a wide variety of mathematical adventures, now is a good time to take stock of what these experiences have taught your students.

  • How much of what society considers “the basics” have your children picked up along the way?
  • Are there any gaps in their understanding of arithmetic, any concepts you want to add to their mental tool box?

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Math That Is Beautiful

One of the sections in my book encourages parents to make beautiful math with their children. If you have trouble imagining that math can be beautiful, check out this video:

How many mathematical objects could you identify? Cristóbal Vila describes them all on his page Inspirations from Maths.


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fryeburg-fair-by-alex-kehr

Math Teachers at Play #58

No 58 - gold on blue[Feature photo (above) by Alex Kehr. Photo (right) by kirstyhall via flickr.]

Welcome to the Math Teachers At Play blog carnival — a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college. 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…

PUZZLE 1

By tradition, we start the carnival with a pair of puzzles in honor of our 58th edition. Click to download the pdf:

How CRAZY Can You Make It

PUZZLE 2

A Smith number is an integer the sum of whose digits is equal to the sum of the digits in its prime factorization.

Got that? Well, 58 will help us to get a better grasp on that definition. Observe:

58 = 2 × 29

and

5 + 8 = 13
2 + 2 + 9 = 13

And that’s all there is to it! I suppose we might say that 58′s last name is Smith. [Nah! Better not.]

  • What is the only Smith number that’s less than 10?
  • There are four more two-digit Smith numbers. Can you find them?

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 Google Reader. Enjoy!

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What Is a Proof?

I’ve been enjoying the Introduction to Mathematical Thinking course by Keith Devlin. For the first few weeks, we mostly talked about language, especially the language of logical thinking. This week, we started working on proofs.

For a bit of fun, the professor emailed a link to this video. My daughter Kitten enjoyed it, and I hope you do, too.

Full lesson available at Ted-Ed.


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Who Killed Professor X?

What a Fun Book!

professorX

Who Killed Professor X? is a work of fiction based on actual incidents, and its heroes are real people who left their mark on the history of mathematics. The murder takes place in Paris in 1900, and the suspects are the greatest mathematicians of all time. Each suspect’s statement to the police leads to a mathematical problem, the solution of which requires some knowledge of secondary-school mathematics. But you don’t have to solve the puzzles in order to enjoy the book.

Fourteen pages of endnote biographies explain which parts of the mystery are true, which details are fictional, and which are both (true incidents slightly modified for the sake of the story).

I ordered Who Killed Professor X? from The Book Depository (free shipping worldwide!), and it only took 5 days to arrive here in the middle of the Midwest. My daughter Kitten, voracious as always, devoured it in one sitting — and even though she hasn’t studied high school geometry yet, she was able to work a couple of the problems.


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Lockhart quadrilateral puzzle

Lockhart’s Measurement

After watching the video on the Amazon.com page, this book has jumped to the top of my wish list.

You may have read Paul Lockhart’s earlier piece, A Mathematician’s Lament, which explored the ways that traditional schooling distorts mathematics. In this book, he attempts to share the wonder and beauty of math in a way that anyone can understand.

According to the publisher: “Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living. Favoring plain English and pictures over jargon and formulas, Lockhart succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable.”

If you take any 4-sided shape at all — make it as awkward and as ridiculous as you want — if you take the middles of the sides and connect them, it always makes a parallelogram. Always! No matter what crazy, kooky thing you started with.

That’s scary to me. That’s a conspiracy.

That’s amazing!

That’s completely unexpected. I would have expected: You make some crazy blob and connect the middles, it’s gonna be another crazy blob. But it isn’t — it’s always a slanted box, beautifully parallel.

WHY is it that?!

The mathematical question is “Why?” It’s always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it.

So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems.

— Paul Lockhart
author of Measurement


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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!

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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.

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MAA Found Math for the week of June 21, 2010

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…

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Hyperbolic Crochet Coral Reef

Wow! And to think, I was proud of myself for finishing a crochet afghan. Once.

For More Details

Try It Yourself

Chain several. Leave straight to work in rows, or connect into a loop. Single crochet until your patience runs out, increasing every nth stitch (add an extra sc in the same place). Experiment with different colors and patterns. This pdf will give you more ideas.

The more frequently you increase, the frillier your hyperbolic plane will be, while a less-frequent increase makes it easier for students to see the structure. Daina Taimina recommends a 12:13 ratio (increase after every 12th stitch) for classroom use.

Hat tip: 2010 MAA Found Math Gallery, Week 45, and authentic arts by jenny hoople for the pdf.


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math notebooking clock, large

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…

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Graph-It Game

[Photo by Scott Schram via Flickr.]

For Leon’s Christmas gift, Alex made the Graph-It game. She wrapped a pad of graph paper and wrote up the instructions:

To play Graph-It, one person designs a picture made by connecting points on a coordinate graph. He reads the points to the other player, who tries to reproduce the picture.

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Renée’s Platonic Mobile

Alexandria Jones struggled to think of a Christmas gift that a one-month-old baby could enjoy, but finally she got an idea.

She cut empty cereal boxes to make regular polygons: 6 squares, 12 regular pentagons, and 32 equilateral triangles. Using small pieces of masking tape, she carefully formed the five Platonic solids. Then she mixed flour and water into a runny paste. She tore an old newspaper into small strips and soaked them in the paste. She covered each solid with a thin layer of paper.

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Math Project: Measure the Earth

Tomorrow, September 23, is the equinox — when night and day are equally balanced (or would be, if the sun appeared as a point, rather than a disc). If we lived on the equator, the sun would appear directly overhead at noon and would cast no shadow. Therefore, it’s a great day to perform Eratosthenes’ experiment of measuring the earth:

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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:

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found math triads wall hanging

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:

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Cardstock Geometry Puzzle

While browsing the Kim Komando website for ideas I could use in my blogging class, I followed a rabbit trail through Kim’s video archive. I think we will try this in Math Club next semester:

If the embedded video doesn’t work on your computer, you can find the original here: Unbelievable Paper Transformer.

Update

Simon posted a template for the puzzle at his MathsClass blog.


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