After using a trig identity to re-write sin(x/2) in terms of cos(x), you needed to square both sides of the equation. Squaring both sides can always introduce extraneous solutions - which is what 180 +360k turns out to be. So in this case, checking possible solutions is something that MUST be done to solve the original equation - not something that is optional.
Another quick check that can be done is by graphing both equations simultaneously and locating the intersection points by using a graphing calculator. You will be able to quickly verify all non- extraneous solutions.
For a proposal my colleagues and I intend to submit to the U.S. Department of Education on September 4, we are looking for high school math teachers at schools anywhere in the U.S. who teach a course in "problem solving" using the "Crossing the River with Dogs" book. Alternatively, they could be teachers who use the book in another math course, as part of their curriculum, or even high school math teachers in general who would be willing to work with us and have their kids participate. It is my hope that you might be able to point me to some teachers, given your connection with this book.
The idea we have in mind is to have students work in collaborative groups, discussing and debating different solutions to the challenging problems presented in the problem solving course and textbook. We are aiming to build an Internet-based system to support the process and, eventually, for kids to collaborate at a distance with kids from other schools (but we will start within individual schools).
So, we need forward thinking high school math teachers who either teach the problem solving course or are willing to include some of the content from the book in one of their math courses. Would you be able to help?
Thanks for any help and suggestions you might have.
Dr. Bruce M. McLaren Senior Systems Scientist Carnegie Mellon University
I've got a primo job here for anybody that wants to teach Math or Physics at a really good high school in Taiwan (Yunlin County). The pay is super high. The school is great. The benefits are wonderful. They even pay for you to come over. Let me know if you or anyone you know is interested. [email removed]
I am seeking help from any Texas teachers who had success on the 4th grade math STAAR this past year. My students did not do so well. Looking for any programs or success stories to bring their scores up this year. Thank you for any help.
I teach 5th grade math. This year I will have a mixed ability group...co teaching with the LSTeacher for the inclusion students. Would love ideas/suggestions on how you enhance/enrich the higher level math students. Thanks!
On 8/10/13, Kelly wrote: >...See MoreWe create 3 sections in the lesson/worksheet (with cute names), but essentially Easy, Med, Hard. Many of our students want to get to the Hard, but they don't always have time. All students start at Easy and keep working - during Independent Practice. The higher level students will get to those harder problems.
On 8/10/13, Kelly wrote: > I teach 5th grade math. This year I will have a mixed > ability group...co teaching with the LSTeacher for the > inclusion students. Would love ideas/suggestions on how you > enhance/enrich the higher level math students. Thanks!
hello, we create iPad math application for primary and secondary school. application is explaining math problems connected with motion. there are about 200 motion problems in first level. we are almost ready to release the first level and look for teachers who can review prerelease version