Quiz (Sections 9.19.3)
Unit 9  Day 8
Unit 9
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
Day 15
Day 16
Day 17
Day 18
Day 19
Day 20
Day 21
All Units
Writing a Precalculus Assessment

Include questions in multiple representations (graphical, analytical, tabular, verbal)

Write questions that reflect learning targets and require conceptual understanding

Include multiple choice and short answer or free response questions

Determine scoring rubric before administering the assessment (see below)

Offer opportunities to practice with and without calculators throughout the year
Questions to Include

Calculating average rate of change from a graph, table, or equation

Estimating instantaneous rate of change from a graph or table

Calculating instantaneous rate of change using the limit definition

Interpreting a negative derivative in context

Writing the equation of a tangent line

Comparing average and instantaneous rates of change using slopes of secant lines and tangent lines from a graph

Given a piecewise linear graph, interpret a limit of a difference quotient as asking for the slope of the graph at a particular xvalue
Grading Tips
Look for more than just correct answers. Give students feedback on their justifications, communication, and mathematical thinking. We recommend that you prepare a rubric for the free response and short answer items before you begin grading your quizzes or tests. Know what information is necessary for a complete and correct response and award points when a student presents that information. Many of the “Why did I get marked down?” questions are eliminated when you share the components that earn points.
Reflections
Overall students did well distinguishing between average and instantaneous rates of change and estimating instantaneous rate of change from a graph or table. Students also demonstrated an understanding of tangent lines as being distinct from derivative equations, as this can be a common misconception for students. Calculating the average or instantaneous rate of change from an equation was still a struggle for some students. Algebra errors abounded.
Proper limit notation was sparse in student responses. Students either did not include the limit at all, or wrote that the limit as h approaches 0 was equal to the difference quotient instead of taking the limit OF the difference quotient. This is something that we will continue to work on throughout the unit.