Let's Play Math!

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 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:

• Early Learning Activities
• Elementary Exploration and Middle School Mastery
• Adventures in Basic Algebra and Geometry
• Advanced Mathematical Endeavors
• Puzzling Recreations
• Teaching Tips

EARLY LEARNING ACTIVITIES

Mathematics depend upon the teacher rather than upon the textbook and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls the ‘Captain’ ideas, which should quicken imagination.

— Charlotte Mason
Toward A Philosophy of Education

• The Girl Who Painted Trees discovers that “5 minutes here and there” add up to a pretty full course of Kindergarten Math.

• Donna Boucher shares a simple Ten Plus Card Game for cooperative play.

• Alice challenges parents of young children to Explore Really Big Numbers with an Abacus.

• Margo finds a great use for dollar-store plates: Dish Up Some Multiplication on Partitioned Plates.

• Is different from ? Join Yelena McManaman and friends in playing What Would You Rather Have – Commutative Property Game.

• Christopher Danielson probes his children’s understanding of fractions in Zero=half and Not really ready for fractions. And I like Michael Paul Goldenberg’s comment: “The great thing is that your daughter has really good wrong ideas and is able to articulate them. If we could get all kids to articulate their wrong ideas and pursue them with other kids and knowledgable adults, 90% of our national difficulties in mathematics education would vanish.”

• Encourage your children to ask questions with Paul Salomon’s beautiful Stars of the Mind’s Sky. What do they notice? What do they wonder?

• Cindy updates her Math in Children’s Literature book list page. So many wonderful books!

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ELEMENTARY EXPLORATION AND MIDDLE SCHOOL MASTERY

The child may learn the multiplication-table and do a subtraction sum without any insight into the rationale of either. He may even become a good arithmetician, applying rules aptly, without seeing the reason of them; but arithmetic becomes an elementary mathematical training only in so far as the reason why of every process is clear to the child.

— Charlotte Mason
Home Education

• Malke Rosenfeld discovers once more that math is personal (and that sometimes Mom should keep her mouth shut) in Her Own Math, Not Mine.

• I love Lula B’s description of her family’s week in 5 Days of Maths Playtime. And the fun didn’t stop: her children continued to explore mathematical relationships in Pythagoras and the Knotted Rope.

• Measurement gives children an opportunity to use numbers in a practical task. Penny Ryder shares the downloadable activity guide, Comparing and Ordering Capacity, with the bonus puzzle of folding an origami cup with a specified volume.

• What are your goals in teaching math facts? Cindy rethinks Multiplication Fact Memorization.

• Sarah clearly demonstrates the process of Long Division with Manipulatives.

• Maria Miller shares a Prime Factorization forest game.

• William Emeny addresses a common student mistake in Decimal line zooming.

• John Golden tells how he developed a game for 5th graders just starting with fraction multiplication and adds several fun scenarios invented by the students: Find It!

• Ben Orlin answers the perennial question, Why can’t you divide by zero? (And don’t miss What It Feels Like to Be Bad at Math.)

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ADVENTURES IN BASIC ALGEBRA & GEOMETRY

We take strong ground when we appeal to the beauty and truth of Mathematics; that two and two make four and cannot conceivably make five, is an inevitable law.

It is a great thing to be brought into the presence of a law, of a whole system of laws, that exist without our concurrence — that two straight lines cannot enclose a space is a fact which we can perceive, state, and act upon but cannot in any wise alter.

— Charlotte Mason
Toward A Philosophy of Education

• Have your students experienced how surface area and volume change when a shape grows? Check out Tina C’s Volume Lesson, Crowd Sourced.

• Guillermo Bautista shows that The Product of Negative Number and a Positive Number is Negative and challenges the reader to prove a corollary.

• Jonathan Newman’s pre-calculus students are working so hard on new ideas that they forgot basic algebra: What Precal Students Can’t Do. Can your students explain how to figure it out?

• Many students have a hard time understanding exponents. I’m looking forward to trying Michael Pershan’s Visual Exponential Patterns with my daughter.

• Brian Miller offers advice for Teaching Mixture Problems With The Mixture Picture.

• Lois Lindemann comes up with a creative way to emphasize justification in beginning geometry proofs: Who knew that learning parrot fashion could be this much fun?

• Rodi Steinig introduces a series of explorations of proof to her Math Circle by not proving the Pythagorean Theorem in Aspect Ratios, the Golden Ratio, and Z’s TV. [Sessions #2 and #3 are now posted.]

• Jonathan Halabi is also teaching proof-based geometry, with an emphasis on logic and constructions: Shaking up traditional geometry.

• Josh ponders the relationship between Ferris Wheels and Euclid. For more on geometric constructions, did you notice Paul Salomon’s Stars of the Mind’s Sky, mentioned earlier? Your students may also enjoy exploring the Math Open Reference website.

• Textbook questions got you down? Fawn Nguyen shares what happened When I Let Them Own the Problem.

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ADVANCED MATHEMATICAL ENDEAVORS

In a word our point is that Mathematics are to be studied for their own sake and not as they make for general intelligence and grasp of mind. But then how profoundly worthy are these subjects of study for their own sake, to say nothing of other great branches of knowledge to which they are ancillary!

— Charlotte Mason
Toward A Philosophy of Education

• Studying Statistics? Check out Colleen Young’s long list of Statistics Resources.

• Alexander Bogomolny shows us some Jewels in the Bride’s Chair: for any triangle, there are three points where four straight lines meet forming successive angles of 45°.

• I love Patrick Honner’s Proof Without Words: Two Dimensional Geometric Series.

• Do your students have trouble with logarithms? Whit Ford hits all the key point of this important topic in Summary: Logarithms.

• Rebecka Peterson’s pre-calc class tries to create the best error in Mistakes mean we’re getting better, right?

• Calculus asks seemingly impossible questions, and limits give a strategy for answering “impossible” questions. See Kalid Azad’s Intuitive Introduction To Limits.

• Andrew Chambers considers the question, Does it Pay to be Nice? Game Theory and Evolution.

• Math Curmudgeon posts a series of problems to challenge your students (or yourself!): UVM 2013.

• And don’t miss the 98th Carnival of Mathematics!

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PUZZLING RECREATIONS

The Principality of Mathematics is a mountainous land, but the air is very fine and health-giving, though some people find it too rare for their breathing. It differs from most mountainous countries in this, that you cannot lose your way, and that every step taken is on firm ground. People who seek their work or play in this principality find themselves braced by effort and satisfied with truth.

— Charlotte Mason
Ourselves

• Gary Antonick reports on a coloring puzzle simple enough for children to understand, yet interesting enough to be featured in the current issue of The Mathematical Intelligencer: Triangle Mysteries.

• Not a puzzle, but a refreshing treat: Guillermo Bautista shares 10 Math Quotes That Will Make You Giggle.

• What can you see, and how many ways can you see it? Don Steward offers a fun set of angles in polygons by chopping.

• Looking for summer reading to inspire you mathematically? Sue VanHattum reviews Measurement, by Paul Lockhart and Math from Three to Seven, by Alexander Zvonkin.

• Mashka relates a variety of math circle puzzles: Tricky Pre-K Math Lesson 18 and Lesson 19—Everything Math.

• Glen Whitney transforms coffee stirrers and rubber bands into a 3-D puzzle in Math Monday: DIY Tensegrity.

• Justin Lanier shares a selection of interesting math explorations in Circling, Squaring, and Triangulating.

• Gene Chase explores the topology of a computer game screen in Flat Donuts.

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TEACHING TIPS

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

• David Wees lists eight Powerful ideas in math, based on Seymour Papert’s book Mindstorms. Then Shecky Riemann adds a short video about Ideas… The Stuff of Math.

• Katherine Cook ponders the intersection of Math education in two themes and warns parents and teachers about Processed Math: Don’t Eat This.

• Christopher Danielson contrasts two teaching styles in Skills practice [#NCTMDenver] and sparks a (mostly) thoughtful debate in the comments.

• Jason Dyer launches a wonderful discussion in Tiny Games, mathematics edition? Dan Myer brings the project to everyone’s attention with Tiny Math Games. And John Golden attempts to collect the tsunami of ideas in one place for easy reference.

• Nico Rowinsky explores one of math’s great mysteries in Some Equal Signs Are More Equal Than Others.

• Caroline Mukisa says, “Listening to podcasts is a great way of taking in new information and taking a fresh look at old information.” Listen Up! 8 Fascinating Podcasts to Spark a Love of Math in your Teen.

• Are you looking for a good homeschool math program? Check out Amy’s MEP Math Story.

• Most homeschoolers feel at least a small tinge of panic as their students approach high school. For my entry to this month’s carnival, I offer an assortment of links and tips on Homeschooling High School Math.

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FINAL CREDITS

The Robert Webb rhombicosidodecahedron graphic is from Wikimedia Commons, and the Charlotte Mason quotations are from Ambleside Online’s Annotated Charlotte Mason Series.

Most of the book covers link to Amazon.com, where you can read descriptions and reviews of these and many other living books for math (and where I receive a small commission through Skimlinks if you actually buy one of them). All the books included in this post — except for Moebius Noodles, which is too new — should be available through any well-stocked public library or library loan system.

And that rounds up this edition of the Math Teachers at Play carnival. I hope you enjoyed the ride.

The next installment of our carnival will open sometime during the week of June 10-14 at Math Jokes 4 Mathy Folks. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Past posts and future hosts can be found on our blog carnival information page.

We need more volunteers. Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn hosting the Math Teachers at Play blog carnival, please speak up!

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