149-150 Computer Programming Project Preview

Super exciting computer programming final projects in progress. Here’s one student who’s making a dynamic dragon fractal and working out the math in Desmos before he implements it in processing.

Another student has made a couple of different graphing programs in processing, one that reads in a string, like “y=2x+x^4” and graphs it, and another implicit grapher. Very exciting! More info to come.

 

141-142 Curve Sketching – A beginning

As an introduction to curve sketching, the Precalc h class found out where the derivative of a function was zero, positive and negative. Then I had them draw a set of axes and start their marker at the left side of the grid. Told them to start moving the marker to the right, and gave instructions for “increasing”, “decreasing”, or “0 slope”. Asked them, “what do you notice about the spots where the slope was zero?”

 

139-140 Implicit Differentiation and Difficulty of Math Problems

Megan asked a great question on twitter:

To speak to my response, here’s a problem that we started off today with in PreCalculus H (started calculus early because they have extra time throughout the year).

Tough problem (unless you solve for y first!). Pretty tricky calculus with a product rule inside of a quotient rule, and some tricky algebra too. Here’s some sample work:

Every student made at least one mistake in this problem. BUT, they had a high level of support, they worked next to their peers throughout, and every couple of minutes I’d show my work. This is a small example of a difficult problem that I’d not put on homework or a test because the hurdles are high and numerous without the support.

 

137-138 Derivatives of Trig Functions

To find the derivative of sin(x), they drew tangent lines to sin(x) (printed out on paper), measured their slopes and then graphed the derivative point by point. Here’s a desmos version.

From that derivative fact and noticing that the derivative of cos(x) is -sin(x), they have enough to find the derivatives of tan(x), csc(x), sec(x), and cot(x). Let them at it.