Naught Much

Today I discovered and downloaded a new program, Google SketchUp. This program is free and is for drawing all sorts of 3-dimensional figures. The tools are very intuitive and the whole program is easy to use. You can save your work in a 3D file to come back to later, or you can export to a 2D image file (.jpg, .png, .gif, etc.). I wish I had this when I was teaching geometry a few years ago. My handouts and tests would have looked so much better!

Here are a few drawings that I made using SketchUp. All of these were made today, the first day I ever used this program. [Click on each thumbnail for a full-size image.]

Conic section - parabola.

Conic Section - bottom view.

Golden spiral.

Golden spiral in three dimensions.

Home sweet home. Yes, I do have stairs on the front of my house. They just were too tedious to draw.

Here’s a quick (maybe) brainteaser from Elias over at Ramblings of an Australian Teacher.

In the multiplication

P Q R
x 3
——
Q Q Q

each of P, Q and R represents a different digit. The sum of P, Q and R is
(A) 16 (B) 14 (C) 13 (D) 12 (E) 10

Think you know the answer and can give a clear explanation? Then email Elias the solution (and post it in a comment here).

My school is one that operates on a “block” schedule. That is, one that has only four classes per day, each of which meet for one hour and twenty-five minutes. Students will take four classes in the fall semester, and then four different classes in the spring. There are some advantages to this schedule (so I’m told), but from my perspective it is a detriment to mathematics education.

In secondary mathematics, the course of study is very sequential — each class building upon skills and ideas from the previous. But what often happens to students in a block schedule is that they will take a math class during the first semester one year and then not take the next course until second semester of the next year. If you do the math, that is a full twelve months that pass with the student not taking a math course. Therein lies the major fault of block scheduling. So much can be, and usually is, forgotten during that “time off” from math.

Recently, the English department at my school has seen the need for ninth graders to take a full year of English classes. They voiced their concerns to the school leadership team and were able to get 9th grade English converted to a full year course, even though every other class remains a one-semester course. I believe the math department is close to accomplishing the same thing for Algebra 2.

Ever since our school implemented block scheduling several years ago, we have seen a decrease in the number of students enrolling in Calculus. I believe this can be attributed to the fact that students are not receiving a “continuous” mathematics education. Even the administrator in charge of the master schedule, a self-proclaimed math phobic, is beginning to see the benefits that would come with teaching Algebra 2 (if not other courses as well) for a full year.

Sometimes I wish that as a teacher I got paid by the hour. Yesterday morning started off with an 8:00am advisory team meeting (as does every Tuesday). An hour later, classes began. After a full day of classes ending at 4:00pm, the faculty had to stay another four and one-half hours. The reason for staying late was that it was our school’s first PTSA meeting of the year, immediately followed by open house. So after sitting through a arduous meeting where no one spoke loud enough to be heard, I had to entertain the parents as they cycled through their children’s classes.

Honestly though, I really do like meeting the parents of my students. It usually gives me quite a bit of insight into what makes them the way they are. Some students look just like their parents, some talk just like their parents, some smell like their parents, and some act like their parents.

Even though I enjoyed meeting the parents that made it out for open house, it was still a darn long day.

Here’s to punching the timeclock!

The last post contained a fairly easy problem. Now here’s one that is a bit more challenging.

In the figure below, a circle with a center at O and a radius of 4 is inscribed in triangle ABC. Point D is a point of tangency. Segment AD has a length of 8 and segment BD has a length of 6. Find the lengths of the three sides of the triangle — without using trigonometry (sine, cosine, tangent).

[This problem was posed to some mathematics teachers by Victor Katz at the San Antonio national conference of the NCTM.]

Here’s a problem that is a good one to give your Algebra 2 students (or anyone who’s interested).

Find the two distinct numbers whose product, quotient, and difference are all equivalent.

[in layman’s terms] Find two different numbers that, when you multiply them, you get the same thing you do when you subtract them or divide them.

I’ll not give the answer in this post. You give it to me in a comment.

If you’re one of my regular readers (assuming I have any), you might have noticed a couple changes to the site. First, the title has changed from Naught Much to Naught Much.com. That’s right, you can now access this site through its very own domain at www.naughtmuch.com.

Second, there are two new pages: About and Contact. You can find these links at the top navigation bar. In the About page, you’ll find links to some places that describe me.

Son

Daughter