This post is a quick hitter about the way I have approached grading tests for several years. I purposefully try not to stretch the point total to 100 or some other tidy multiple of 10 or 20. Instead, I assign points to each problem based on sub-steps. I use my trusty TI-84 to compute values quickly for grade book entry.
Suppose a test turns out to be worth 68 points. Here's what I do.
This is the linear function with slope 1/68 and y-intercept 0. One approach is to construct a table of values like below.
But the trouble occurs when grades vary wildly. Say some students are getting poor scores, like a 41 out of 62. Then we have to either reset the initial table value or, even slower, scroll up.
Instead, I set the viewing window and make a graph.
Just ignore the delta-x and TraceStep at the bottom of the screen. I set the window to have an Xmin of 0, an Xmax of 68 (because these x-values span all possible raw scores), and then set the Xscl to 1. The Xscl assigns integer values to tick marks on the graph, but for our purposes, this is really a personal preference, not a requirement.
Setting Ymin = 0 and Ymax = 1 with Yscl = .1 computes the percentage for the student's score. I could obviously do a little extra work by graphing Y = (X/68)*100 and make window adjustments accordingly, but for the sake of speed, I will just mentally convert the decimal to a percent.
By pressing the TRACE key, I can now manually enter any score and see the decimal corresponding to the student's percentage instantly. For example, suppose a student answered 44 items of 68 correctly.
I know there are other ways to do this... but, this way works well for me. This is another of the many things that students in math teacher ed programs may not see or talk about before student teaching experience, or in some cases, at all before entering the classroom.