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

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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 x-value

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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.

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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.