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

• Identifying scenarios that can be modeled with arithmetic sequences

• Finding the nth term of a visual pattern

• Writing explicit rules for arithmetic and non-arithmetic sequences

• Interpreting sigma notation and finding a partial sum by hand

• Finding a term value and a partial sum in context (and differentiating between the two!)

• Given an average value of an arithmetic sequence, finding the sum

• Writing a recursive rule for a sequence

• Solving for the value of n that gives a particular term value or partial sum

​

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

Our students were able to show mastery of the learning targets for the most part, but still struggled with using the partial sum formula for arithmetic sequences. When asked which expression would give the sum up to the 12th term students were not able to identify expressions that were equivalent to the sum formula they had learned. We were very pleased with their ability to use equations to model visual patterns, especially for quadratic patterns! We enjoyed seeing many equivalent forms based on how the students saw the pattern grow.