Changing Grades - Task

A math teacher graded student exams on a scale of 0-100. After finishing, the teacher decided to raise the grades. Students could choose one of the following methods to have their grades raised:
method 1 method 2 method 3
Adding 10 points to the gradeIncreasing the grade by 25%Adding to the grade half the difference between the grade and 100
Method 1 is shown below in three representations: a computing machine that calculates the updated grade, a graph, and a value table.
  • Construct computing machines to help students compute their updated grades according to methods 2 and 3. Use the Representation of Functions tool to present graphs and value tables of functions that describe the dependence of the updated grade on the original grade.
  • Suggest a way to determine the best grade-correction method for each student without having to compute their grades using all three methods.
  • What will be the range of grades after the correction?
  • Propose another method for raising the grades, which all students will prefer over the existing methods.