Mr. Slater's Blog

Making Money Learning Task

Students worked collaboratively in groups on the Making Money Learning Task, which leads students step-by-step through the mental process of a linear programming problem - identify what needs to be maximized (or minimized), define your variables, write an objective function equation, identify any limitations and write inequalities for these constraints, graph the constraints and find the feasible region to consider, identify the vertices of this region, plug the coordinates of each vertex into the objective function written earlier and see which produces the maximum value.  This task needs to be completed for checking in class tomorrow.  (In case you left it as school unfinished, click to download Making Money to the Max Learning Task)

Taylor Series

Writing a function as a Taylor Series gives one an opportunity to rewite an "awkward" function as an infinite series of polynomial terms, which are much, much simpler to work with.  Basically, this is an extension of Linear Approximations we studied back in the fall - i.e., we can approximate a curve by using the tangent to that function at a given point, which will give us a quite good approximation for values very close to the point of tangency.  If these approximations work well with linear functions, they should work even better with higher degree polynomials - the basic idea of Taylor Series.  Students should read through Section 10-7 tonight, and then do the problems on Pages 614-615:  #1-16 all.  We are tentatively looking at our Test over Series being on this Thursday, April 15th.

Linear Programming - finding max/min values

Using the feasible regions students graphed on Practice Worksheet 3.5 last night, we proceeded to test vertices of the feasible region in the linear objective funtion to determine where the maximum or minimum values occurred.  In particular, we worked on problems #4-10 to find these optimal values. 

In addition, we also looked at any issues that have arisen as students have been starting to work on the Conics Face Lab, which is due on April 16th (after Spring Break).  Specifically, we addressed how to limit the domain of a function on your calculator (enter Y1=(equation)/(domain, using 2nd Test menu) on your calculator), and how to save a partially completed picture if you need to use more that ten equations or just want to "play" with possible equations (go to Draw menu and go to Sto to StorePic).  Spring Break gives everyone lots of time to get creative with this major test grade project - Have fun! 

Area and Volume ReTest analyzed

Students got their ReTests back today for those who took yesterday's ReTest over Area and Volume.  Since this is such a common application of integrals (usually tested in 5-6 test questions on the AP Calculus Exam), we went over every one of these ReTest problems for the entire class and discussed them in detail.  As usual, some students improved 35-40 points on their ReTest, and others showed a much smaller change in grade - the key to success continues to be preparation and practice!

Linear programming

Linear programming is the process of finding a maximum or minimum value of a linear objective function, subject to a system of linear inequalities (called constraints).  Today we looked in particular at the constraints - the system of inequalities that produces the feasible region to consider.  On Practice Worksheet 3.5 Linear Programming, students are graphing the feasible regions in problems #1-3 and 7-10, and finding the coordinates of all the vertices.  They should also do the Matthew Lovett baking cookies problem on the back, which is an application of inequalites which leads you through the problem step-by-step.

Power Series problem demonstrations

As a summary of looking at power series and deciding when they converge, students worked in groups during class to prepare a problem to be demonstrated to the class.  In particular, problems to be demonstrated from Section 10-6 included #36, 37, 40, 52, 53, and examples 6 and 7.