Here’s an interesting summer learning opportunity for homeschooling parents and classroom teachers alike. Stanford Online is offering a free summer course from math education professor and author Jo Boaler:
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:
Collect a bunch of empty cereal boxes. Cut the boxes open to make big sheets of cardboard.
Print out the template page (→) and laminate. Cut out each polygon shape, being sure to include the tabs on the sides.
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.
Draw the dark outline of each polygon with a ballpoint pen, pressing hard to score the cardboard so the tabs will bend easily.
Cut out the shapes, being careful around the tabs.
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:
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:
Remodel the house. From financing to floor coverings, that is real math in action.
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?
After teaching co-op math classes for several years, I’ve become known as the local math maven. Upon meeting one of my children, fellow homeschoolers often say, “Oh, you’re Denise’s son/daughter? You must be really good at math.”
The kids do their best to smile politely — and not to roll their eyes until the other person has turned away.
I hear similar comments after teaching a math workshop: “Wow, your kids must love math!” But my children are individuals, each with his or her own interests. A couple of them enjoy an occasional geometry or logic puzzle, but they never voluntarily sit down to slog through a math workbook page.
In fact, one daughter expressed the depth of her youthful perfectionist angst by scribbling all over the cover of her Miquon math workbook:
“I hate math! Hate, hate, hate-hate-HATE MATH!!!”
Translation: “If I can’t do it flawlessly the first time, then I don’t want to do it at all.”
Check out my newest home decor item, a hundred chart. The amount of work I put into it, I consider getting it framed to be proudly displayed in the living room. The thing is monumental in several ways:
1. It is monumentally different from my usual approach to choosing math aids. My rule is if it takes me more than 5 minutes to prepare a math manipulative, I skip it and find another way.
2. It is monumentally time-consuming to create from scratch all by yourself.
It began with a humble list of seven things in the first (now out of print) edition of my book about teaching home school math. Over the years I added new ideas, and online friends contributed, too, so the list grew to become one of the most popular posts on my blog:
Can you think of anything else we might do with a hundred chart? Add your ideas in the Comments section below, and I’ll add the best ones to our master list.
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:
It’s important to teach our children to ask questions, about math and about life. As I wrote in my series about homeschooling with math anxiety, “School textbooks only ask questions for which they know the answer. When homeschoolers learn to think like mathematicians, we will ask a different type of question.”
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.
Multiplication is taught and explained using three models. Again, it is important for understanding that students see all three models early and often, and learn to use them when solving word problems.
I hope you are playing the Tell Me a (Math) Story game often, making up word problems for your children and encouraging them to make up some for you. As you play, don’t fall into a rut: Keep the multiplication models from our lesson in mind and use them all. For even greater variety, use the Multiplication Models at NaturalMath.com to create your word problems.
While I was working on the next post in my PUFM Series, I stumbled on an old favorite video. Since I couldn’t think of an excuse to use it in a post about multiplication, I decided to share it today. Enjoy!
[Feature photo (above) by Alex Kehr. Photo (right) by kirstyhall via flickr.]
Denise Gaskins' Let's Play Math 