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

In yesterday’s Mathematical Methods 1 class I finished on the word problems regarding work.

I only concentrated on the type of example though were the times that two different workers finishing the job alone and together are given, and one is asked for.

I did not give the type of problem where one worker starts a job and another one joins in after a certain amount of time. That would have taken a deeper understanding of the (pardon the pun) working equation than the students could accept.

After that we started with solving quadratic equations in one variable.

For the first part of this one, which is solving for the solution set or roots of the variable, they had to call on their previous knowledge of factoring polynomial expressions and the zero-factor property, including the special products like the difference of two squares and the perfect square trinomial.

These were the simplest types of quadratic equations to solve because given that the coefficients of the variables with decreasing degree (from 2 to zero) are a, b and c, these were the cases where sometimes b or c are equal to zero.

After this we worked on the method of completing the square. This obviously assumes that the quadratic equation is not a perfect square trinomial. This even works if the equation can be factored into two binomials of degree one. In fact, they could have tried both methods and the answer would have come out the same.

Unfortunately, they could not comprehend the purpose of the method, and I had to restrict the written exercise near the end of the period to the two types of factoring we had discussed earlier while I thought of a way to rework the topic to be easier for them to understand.

In my Trig App class I discussed the word problems involving trigonometric functions. Just like the problems in MM1 regarding uniform motion, I told them that is recommended that they draw an illustration of their understanding of the problem first before attempting to come up with an equation.

Their diagram then should have the given length, the given angle and length to be computed as parts of a right triangle.

The first examples were easy, because they only referred to one triangle. This was also where they got introduced to the angle of elevation and the angle of depression.

After that, we had examples that involved two right triangles, and had two angles given, but sometimes only one length required. This was where a bit more analysis came in, and where they found out how to determine a structure’s height or depth without having to bring a long enough tape measure.

And since we have an exam on Thursday that means that they will have to perform the actual measurements on Monday next week, when I told them to bring the materials for obtaining angles of elevation and depression.

I’ll talk about my mechanics class tomorrow. For now, class dismissed.