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!


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:



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.
  • 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?

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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.
  • 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.
  • 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!

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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

  • 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.

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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

  • 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°.
  • Do your students have trouble with logarithms? Whit Ford hits all the key point of this important topic in Summary: Logarithms.
  • Calculus asks seemingly impossible questions, and limits give a strategy for answering “impossible” questions. See Kalid Azad’s Intuitive Introduction To Limits.
  • Math Curmudgeon posts a series of problems to challenge your students (or yourself!): UVM 2013.

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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

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

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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

  • 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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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, where you can read descriptions and reviews of these and many other living books for math (and where I receive a small affiliate commission 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!

4 thoughts on “Math Teachers at Play #62

  1. Thanks for acknowledging my comment on Chris’ blog. It’s an oblique reference to Goro Shimura’s comment about his late colleague, Taniyama. He says in THE PROOF, “He was not a very careful person as a mathematician. He made a lot of mistakes. But he made mistakes in a good direction. I tried to emulate him. But I’ve realized that it’s very difficult to make good mistakes.”

  2. I’m really excited to get exploring all these ideas – thank you so much for the way you’ve carefully put this together, Denise. We’re continuing to love our maths playtimes, I can’t thank you enough for the difference you’ve made to this homeschooling family 🙂
    I’m linking to the carnival on my blog today. Lucinda

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