We have had a great year in Trigonometry so far and are getting very close to the midyear exam. As the year has developed, I see more and more how important it is to use visuals to describe certain concepts and how great it is to see how you (my students) describe your understanding in writing. I plan to use this blog to provide roughly a weekly update (T = one week, probably each weekend) about what we learned, any updates about assignments etc. and to preview what is on the horizon. Ideally, it can also be a place to share good links and also hear your thoughts and descriptions about what you have learned. In fact those of you that did not e-mail me last week will be our first commenters! Stay tuned.
To borrow a Trigonometry model, much of what we learn in mathematics is cyclical (it just gets more sophisticated), and as we go through each week we can learn more and more how all the ideas are related.
Last Week
We got back our graded HEP5 tasks. The Ferris Wheel problem really helped me see who understands the relationships between circles, sine/cosine graphs, and how time and height are modeled using a trigonometry function.
Everyone seemed to master the "vertical shift" considering the Ferris Wheel was on top of a building and we had to choose a "middle" height and think about whether cosine or sine could be used to model the changing height over time.
Sine versus Cosine. After we all completed our tasks, there was a learning opportunity to see how either sine or cosine model could be used to model the height at any time ( negative cosine was the most used model because it started at "the bottom"). The graded task transitioned nicely into the idea of a "cofunction", realizing that sine and cosine are the same function, just shifted by a quarter turn (or 90-degrees or pi/2 for you radian purists).
Problem Solving - The most unfamiliar step of the task was using the graph to see how often the ferris wheel was at 40-meters above the ground. This was a great question to recognize the value of our graphical knowledge to estimate how often and when that height occurs and how to use the graphing calculator to find the "actuals". That solving step is just like a systems of equations problem with a horizontal line. The intervals between the 40's ended up happening about every 3 minutes (lower parts of the wheel) and 11 minutes (the longer part of the rotation). Not just a coincidence that 11+3 = 14 minutes, the period of rotation for the Ferris Wheel.
This Week
We are in exam preparation mode. Using our pink topic sheet as a guide, we can review mixed problems to prepare for the exam. Making sure you hit each topic at least 4 times (to follow a topic mastery "rule of 4"). Most of what we learned 2nd quarter can be found in Section 6 of the Algebra2/Trig Page. of http://www.regentsprep.org/ It is up to you to do problems and check yourself. Keep enough evidence of showing your work to be able to show me and another student you have fully prepared yourself. Your completed work should be organized and placed into your folder by the Monday of exam week. (This Friday, is even better!)
50 questions is a minimal expectation (and your final HW assignment). Those of you who are struggling should do more and seek out help for anything you don't understand.
Inverse Functions
One new concept that we will hit this week is the graphing inverse functions. Since you will be at the regentsprep website, take a look at the lesson page for that topic. One reason I assign this website as a review is so you can re-learn or teach yourself any concepts that you may be struggling with. That is what you will be doing in college!
Ok - stop reading now and (1) Scan/upload your tasks (2) attempt the mixed multiple choice Trigonometry problems at the end of Section 6 then (3) check your solutions on the website.
If you finish that, page through each of the topics in Section 6 and attempt the practice pages highlighted in the classroom.
Good luck!
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