Challenge Questions with SBG

One thing that I’ve always struggled with is adding challenging questions to my assessments within a SBG scheme. Like a lot of people using SBG, I use a 4 point scale. The upper limit on this scale is similar to an A, and for the sake of the post I’ll refer to the top proficiency as “mastery”. If a student were to get an A in a course I teach, roughly speaking they would have to be at the mastery level in at least half of the learning objectives, and then only if they don’t have any level 2 grades.

The problem with asking a good and interesting challenge question is that only one or two students would likely solve these questions correctly. This means one of two things. Either only one or two students would ever get an A in a course I teach, or I would sort of “ignore” the challenge question in terms of determining mastery. If it’s the former there would be a valid argument that the hardest challenging questions shouldn’t be used to determine mastery, they are a better indicator for something like “sophisticated excellence.” (You can choose your own descriptor here). If it’s the latter, the typical somewhat cynical teen would see through the assessment and naturally ask what the point of the question is, if it doesn’t count towards the grade.

For what it’s worth, here are a couple examples of challenging questions. Question 1 would be from a Physics 11 course (intro physics) and Question 2 could be Pre-Calculus 11 (algebra 1? algebra 2?).

  1. Two people 120 m apart run towards each other. One person runs at a constant velocity of 5.5 m/s while the other person accelerates at a rate of 0.11 m/s/s. Where do they meet?
  2. $$ \frac{x^2+2}{x}^2-6(\frac{x^2+2}{x})+5=0 $$

Neither is fantastically difficult but I would estimate that maybe 2 out of 30 kids in a typical class of mine may get these. If we practiced questions just like these, the number of students that get these correct would increase but then it takes away from the idea of asking new, interesting challenge questions.

How can we go about stretching/challenging all of our students but still use a 4pt grading system?