Mystery Mathematician Contest ending soon...
Pi fact for today? Try explaining why the imaginary number i raised to the power of i is REAL without mentioning π somewhere! Of course, you could just ask Google to do it for you!
You'd think that the deafening silence from the 5-7-8 triangle post would discourage me - NOT! Here is an investigation for middle schoolers and up.
Typical Content Standard: Patterns, Relations, Algebra
(1) Developing strategies for comparing sums
(2) Developing algebraic generalizations
(3) A few dozen more!
Where might the first question in the title of this post be asked?
(b) End of Course Test for Algebra 2?
(c) Other standardized tests?
(d) Math contests? If so, what grade level? 7th? 8th? Higher?
If you value a question such as this, would you introduce it to middle schoolers in 6th? 7th? Prealgebra? Would you use a very different instructional approach with students in higher math courses who have reasonable algebra background? Even if you don't like this question, try it with one of your groups tomorrow and let me know what happens!
Since I have personally posed this type of question to both middle schoolers and older students, I can tell you that even strong math students often have not seen the 'compare differences of corresponding terms method'. I made up that designation but, hopefully, you can make sense of it. Do you think many high school students would attempt to find two separate sums by some method/formula (or using their calculator if allowed) they've seen?
Well, I won't give any more away, but I believe the issues of pedagogy here may transcend the problem and the math strategies:
How does one introduce this? Do you simply have this question on the white board as students enter the room and allow them to work on it individually or in small groups for 5-10 minutes? We all hear about our re-defined role as 'guides on the side' but what exactly does this look like for this activity? How do we facilitate? When do we ask leading questions? What questions would be highly effective here? I haven't even mentioned the calculator issue yet!
So many questions. So few answers...
Actually I was going to do a short video presentation of this question to demonstrate one instructional model, but, unfortunately, my dog ate my main computer which has all my files and applications. Wait - let me apologize to my pooch. He really didn't eat it or even bless it with his bodily functions. But my iBook is very sick and will need intensive care from Apple. In the meantime, I'm on a backup machine, with limited memory and lacking many of my files and applications. Excuses, excuses, excuses! Please bear with me!
Wednesday, March 12, 2008
51+52+53+...+100 is how much more than 1+2+3+...+50? Why, 50^2 of course! Now Explain and Generalize...