Showing posts with label problem-solving. Show all posts
Showing posts with label problem-solving. Show all posts

Wednesday, September 30, 2009

Two Trains and a Tunnel! Is There Room For This In The Tunnel And In Your Curriculum?

At the same instant of time, trains A and B enter the opposite ends of a tunnel which is 1/5 mile long. Don't worry -- they are on parallel tracks and no collision occurs!

Train A is traveling at 75 mi/hr and is 1/3 mile long.
Train B is traveling at 100 mi/hr and is 1/4 mile long.

When the rear of train B just emerges from the tunnel, in exactly how many more seconds will it take the rear of train A to emerge?

Click on More to see answer (Feed subscribers should see answer immediately).

Comments
1. Appropriate for middle schoolers even before algebra? Exactly when are middle schoolers in your district introduced to the fundamental Rate_Time_Distance relationship?
2. What benefits do you think result from tackling this kind of exercise? If it's not going to be tested on your standardized tests, is it worth all the time and effort?
3. How much "trackwork" needs to be laid before students are ready for this level of problem-solving?
4. As an instructional strategy, would you have the problem acted out with models in the room or use actual students to represent the trains and the tunnel? OR just have them draw a diagram and go from there? Do a simulation on the TI-Inspire or TI-84 using graphics and parametric equations for the older students?
5. If you believe there is still a place for this type of problem-solving, should it be given only to the advanced classes and depicted as a math contest challenge?
6. I'm dating myself but I remember seeing problems like this in my old yellow Algebra 2 textbook? Uh, I believe this was B.C. -- before calculators! Can you imagine! Do you recall these kinds of problems? Do you recall the author or publisher?
7. Of course, the proverbial "two trains and tunnel" problems are frequently parodied and used as emblematic of the "old math"! They've been replaced by "real-world" applications. "Progress makes perfect!"

YOUR THOUGHTS...





Answer: 9.4 seconds (challenge this if you think I erred!)

...Read more

Sunday, October 19, 2008

A 'Mean' Problem to Ponder

It's that time of year folks! Here's a problem for you or your students to think about as a warm-up for this week or for the SATs or for just developing logical thinking. It might also deepen student thinking about the distribution of data. You might find this question trivial but don't be too quick to judge this until your students try it! I would allow a calculator to be used. Observe how students approach this: Guess-Test, consideration of the 'mean', etc...

In a certain high school election, there were 12 candidates for President of the Student Council. If 1600 votes were cast and Denise received more votes than any of the others (i.e., she received a plurality), what is the least number of votes she could have received?

Wednesday, April 23, 2008

A Very Big Number Question...

What is the sum of the digits of (googol + 1)(googol - 1) when expanded?

Comments:
(1) Google 'googol' if you need some background!
(2) Does the strategy of 'make it simpler' work well here?
(3) Can you invent a similar problem or, better, have your students devise their own!
(4) Oh, BTW, NO CALCULATORS!!
(5) I felt I needed a change of pace from the heavy math ed stuff from the past few days. You too?

Posted by Dave Marain at 3:31 PM 12 comments

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Tuesday, January 30, 2007

Problems 1-31-07

Tomorrow's problems focus on sequences and are of varying levels of difficulty. Although #4 may be more appropriate for Algebra 1/2 students, middle schoolers should be able to handle the others. Again, read the comments later in the evening for the answers, comments and solutions. There were some profound ideas expressed about today's questions particularly that innocent-looking quadrilateral problem with the 60 degree angles!


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