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

In my Mathematical Methods 1 class yesterday I went back to the topic of solving equations in one variable and of the first degree.

This was just so that they would know the “shortcut” to solving operations dealing with rational expressions without having to resort to expressions of the second degree which is the result of using the method (a/c)+(b/d) = (ad + bc)/cd.

The situation to avoid was what had happened to one of our supposed examples last Monday. Since I had said at the start that we would reserve second degree expressions and more than one variable to a future session, we - or should I say, >I< abandoned the solution right there and then.

The alternative (only brought to their attention two meeting later) used multiplying both sides of the equation by the least common denominator to remove the fractions altogether.

After that I went into another (and hopefully easier to comprehend) method of solving mixture problems, which we had already started on - and stalled - at last time. This used a three-column two-row table of values that involved the mixture.

The two columns pertain to the different parts of the mixture. The third column is the total. The first row dealt with percentages, and the second row is for volume.

The total of the first two cells of the first row totaled a hundred percent, in the upper right hand cell. The first two cells of the second row also added up to the total volume on the lower right hand cell.

Two additional equations are that percentage of the first part of the mixture multiplies by the total volume also results in the volume of the first part of the mixture. The same is done with the second part.

Now a certain volume of one of the two parts is either added or removed to have a new mixture with a different total volume and a different percentage. This is usually what they have to solve for, and is the single variable in the first degree that they assign.

Afterwards we took up uniform motion problems, already gone through by the handful of students who are in my mechanics class.

First I discussed the simplest type, using the relationship speed equals distance divided by time, for one vehicle.

Then we went to two vehicles, with the following scenarios: starting from the same place at the same time in different directions, x distance apart after t time; starting from different places x distance apart at the same time going towards each other, meeting after t time; and a slower vehicle leaving one point, a faster vehicle leaving the same point t time later, and getting overtaken a certain distance from their starting point.

Without having to explain, my mechanics students knew we were only dealing with one-dimensional motion.

My Trig App and mechanics lessons yesterday will have to wait until tomorrow. Class dismissed.