Dave @ MathNotations posted this nice problem today, good for an Algebra 2 or Precalculus class. I like it:
Consider the following problem:
If -5 ≤ x ≤ 4, and f(x) = 2x2 – 3, how many integer values are possible for f(x)?
For the solution, and some added pedagogical discussion, visit the original post here. Thanks, Dave!
I think this is good news for our county schools in Montgomery County, Maryland:
Montgomery County schools to push basic math to prepare students for algebra
By Michael BirnbaumWashington Post Staff Writer
Friday, November 5, 2010; 12:00 AMMontgomery County long has pushed its students to take ever-more-challenging math at ever-younger ages. Now educators will back off in the hope that more time and depth with the basics will yield payoffs in high school and beyond, school officials said Thursday.
Elementary and middle school students will no longer skip grade levels in math in large numbers. Instead, they will spend extra time on fundamental mathematical concepts that will better prepare them for Algebra I in the eighth grade and advanced math topics in high school. The school system aims to increase the number of high school students taking courses such as calculus and statistics.
The new direction comes as part of a sweeping set of recommended changes in the math curriculum released Thursday. Some of the recommendations cost money and require school board approval. Others, including the change in math acceleration, do not, and will be implemented quickly, officials said.
“Some students were placed in classes, and perhaps they weren’t as prepared as they should have been,” said Frieda Lacey, deputy superintendent of Montgomery schools, who sat on the work group that wrote the report. She said it was better to tackle topics in greater depth.
And I wonder if this will be a growing trend. Are other math teachers out there sensing a turning of the tide in curriculum? I know the new Common Core standards make this move, toward a more in-depth approach. So perhaps this is a national turning of the tide. On the face, I think this seems like a good direction in which to go.
I just ordered this book. I’m excited to see what it’s like. And of course, I’ll be sure to let you know how it is!
Here are a few noteworthy posts I’ve seen in the math blogosphere recently:
Dr. Robert Ghrist, professor of mathematics at U Penn is writing a Calculus text–the Funny Little Calculus Text (FLCT for short). The FLCT not your typical Calculus text. Check out his incredible, artistic, funny, and mathematically elegant work-in-progress here. He currently has completed these short little chapters, all of which are a delightful read:
Ghrist lectures in a similar style, with a tablet PC. And yes, his handwriting is really awesome.
NOTE: I’m updating this post today (1-10-2013) because I’ve just noticed that Ghrist has placed these files behind a (very low) pay-wall. They are STILL worth checking out!! Pay for them for goodness sake! 🙂
Everyone should go enter this giveaway @ the Wild About Math blog. In order to qualify, though, you have to submit a solution to the problem Sol created for us. I just submitted mine!
Today we had a “Tower of Terror” competition in our Calculus classes (just for Halloween fun :-)). The rules are: You get 5 pieces of 8.5″x11″ paper and 8″ of masking tape. The goal is to build the tallest free-standing tower.
Here’s a photo of the best tower from all the classes, standing at an amazing 57″. Great job, ladies!
Check this well-produced rap by Montgomery Blair math teacher Jake Scott. Cool!
Good job, Mr. Scott! We’ll look forward to more videos!
Reposted from Wired.com:
Designing a good roller-coaster loop is a balancing act. The coaster will naturally slow down as it rises, so it has to enter the loop fast enough to make it up and over the top. The curving track creates a centripetal force, causing the cars to accelerate toward the center of the loop, while momentum sweeps them forward. Loose objects like riders are pinned safely to their seats. The acceleration gives the ride its visceral thrill, but it also puts stress on the fragile human body—and the greater the velocity, the greater the centripetal acceleration.
Coney Island’s Flip-Flap Railway, built in 1895, reached a neck-snapping 12 times the force of gravity at the bottom of its loop—more than enough to induce what pilots call G-LOC, or gravity-induced loss of consciousness. In other words, riders often passed out. In fact, any vehicle trying to get around a perfectly circular loop has to hit at least 6 g’s—enough to render most people unconscious.
To solve the problem, modern designers adopted an upside-down teardrop shape called a clothoid, in which the track curves more sharply up top than at the bottom. Then most of the turn happens at the peak, when the coaster is moving the slowest and the acceleration is least. Result: no G-LOC, just screams. The formula that helped them do it? ac = v2⁄ r.
Random Walks 