Maybe I shouldn't have started this blog now, not with everything that's been going on.

Last Thursday in my Mathematical Methods 1 class, we discussed word problems involving quadratic equations. Obviously, this just involved having two expressions with the variable multiplied together, such as the numbers of rows and number of items per row in a rectangular arrangement, and finding the length and the width of rectangle given the area.

At least the first type of problem was very easy for the students because the answer not only needed to be whole numbers, but positive as well, as it pertained to a physical quantity. That meant eliminating any negative and rational roots.

The second was almost as easy because they could disregard negative roots that do not represent width or length, but only those. It is still possible for either measurement to be a rational number.

The last type of problem, that described two “generic” numbers whose product is given, is the one where they had the most work, because for these negative and rational roots are possible.

So they not only had to accept both roots that represented two possibilities for one of the numbers, but they also had to give the two other possibilities for the second number. That meant that their answer here had to be two pairs.

At least for the word problems they had the choice of which method for getting the roots to use. After all, they seem to have a large aversion for completing the square.

Thankfully, David had agreed that that is the end of our coverage for the usual Friday quiz this week.

In my Trigonometric Applications class, for the first part I had a graded recitation for finding out if they had already memorized the trigonometric functions (in terms of relative position to the reference angle and in terms of standard position) but also the trigonometric functions of the special acute angles.

Then we had some more board work problems, this time focusing on the types of problems I knew were going to come out in the exam, including finding the other two sides of a right triangle whose second side is given to be one of the special acute angles (30, 45 or 60 degrees). There were also word problems that need the use of the included arc equation, such as the distance a wheel with a given radius and a given angle of turning travels.

I also allowed them time to ask any previous topics to be reviewed, but they didn’t come up with any, so we ended early.

In my mechanics class, I gave them their first hundred point long exam, which only had eleven number/letter problems, again all taken from their textbook. So far, I have heard no complaints about this, but I have yet to see proof that it provokes them to get the book and study the problems therein.

Afterwards, realizing that this is the only lecture class this term that does not need to be coordinated with another teacher handling the same subject, I gave them the same questions as their problem set due on Thursday next week, shades of electricity and magnetism class last term.

That’s all for today. In fact, that’s all for this week. Class dismissed.