Is Geometry the Unsung Hero of Mathematics Instruction?
Geometiles at the Julia Robinson Mathematics Festival
3 common classroom challenges and suggestions for handling them
In the footsteps of Archimedes: celebrating Pi day
Math Club Materials: academic programs and competitions
Math Club Materials: recreational math
Math Club staff: the parent volunteers
To compete or not to compete: that is the question
When I first became the coach of our math club, I was not sure if math competitions were a good idea. What if the students get the impression that learning math is just about competing? What if our sessions become just a bunch of competition drills? These and similar questions were in the back of my mind as I began coaching.
Geometry Installation by Hybycozo and Truncation
I was fortunate enough to visit downtown Los Angeles just in time to see this beautiful geometry installation by Hybycozo at the City National Plaza. The purple object on the left is an icosahedron, and the green one on the right -- a truncated octahedron. The icosahedron is one of the 5 Platonic solids discovered several thousand years ago. Here is a picture of the Platonic solids from Johannes Kepler's work, Harmonices Mundi, in 1619:
Here’s an idea: start a Math Club at your school!
Parents often ask me advice on how to expose their children to math concepts outside of what is being taught in schools. Some feel like their children are ready for an extra challenge, while others would like to spark and foster their children’s interest in math.
Gift wrap and symmetry
This is a time of year when many of us are running around frantically shopping for gifts. Caught up in the spirit of the holidays, I was looking for some math-themed gift wrap as part of a holiday promotion for Geometiles. In the middle of all the madness, this winter holiday giftwrap caught my eye because of its rotational symmetry. To most people "symmetry" means "mirror symmetry". But to mathematicians, mirror symmetry is just one of the four types of symmetry used to classify patterns. The other three types of symmetry are rotational, translational, and glide reflection.
Bagels, pretzels... cubical frames?
This year's Nobel Prize in physics brought into the limelight the subject of topology, which studies the property of figures that remain unchanged under stretching and twisting, as long as there is no tearing. As a member of the Nobel Prize committee explained in this article, a topologist is concerned with distinguishing a Swedish pretzel from a bagel not due to their taste differences, but due to the fact that a pretzel has two holes and a bagel has one. To a topologist, the pretzel is a surface of genus 2, and a bagel is a surface of genus 1, where the genus number simply corresponds to a number of holes.
Math Lesson from the Olympic Games
Among the myriad math lessons offered to us by the Olympic Games, here's one involving just the rings. I recently challenged myself to model the rings using Geometiles, and came up with what you see against the background of the UCSD Track and Field Stadium. When Susan Lopez of LopezLandLearners saw this picture, she realized that it would make a great estimation problem: How many triangles and squares does it take to make one of these rings, just by looking at it? What a great way to start children thinking about estimates.
Math and Economics at the Farmers Market
There's still nothing like experiencing math in the context of of simple cash purchases. I say "still" because of the plethora of available extra-curricular math resources like competitions, online programs, manipulatives, etc. In our age dominated by credit card and online purchases, many kids don't have the opportunity to develop the skills of making simple arithmetic computations in real time while talking to people.
An exercise in modeling a real life tile pattern
What a great exercise it would be for a child to figure out how to "model" this wall with only equilateral triangles and squares. This is exactly the kind of thinking that the writers of the Common Core Math standards illustrate in the draft of their Geometry Progression for Grades K-6, pp. 7, 11-12. Geometiles™ were used for the modeling task, as shown above.
Three sisters and their PJ's
Platonic Solids: Antiquity to Now
Shapes have fascinated humans since the beginning of time. The Polyhedra, or solid shapes with flat polygonal faces, is one of such shapes. One of the most appealing types of polyhedra is the icosahedron, most likely due to its high degree of symmetry. In the image above, you can see that the view from the center of each face, as well as the view from each corner, is precisely the same. This is what we mean by "high degree of symmetry" – many places on the polyhedron have identical views.
A prism of a bathroom sink
A trip to the ladies room of the Arclight Cinemas in the local mall revealed a rather unusually shaped sink...
In case you're wondering where the water drains, there's a slit right along the back edge, shown by the blue arrow. But what happens if the drain backs up; how much water can a sink like this hold before it spills over? Let's figure out its approximate volume.
Before we start the calculations, let's identify the shape of the sink. Recognizing the shape will help us get a better grip on the volume problem. The shape of the sink is a trapezoidal prism.
A generous uncle?
When my daughter was 6 years old, her uncle gave her this figurine, a couple of inches tall.
She asked if it was made of pure gold. Well, let's see how much it would cost if it were.
Driving by the Embarcadero
A teachable moment at the top of Filbert Street