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* *Reflection: High Expectations
Final Exam Part 1: Open Response - Section 1: Final Exam Part 1: Open Response

I received a lot of positive feedback about the first semester’s final exam; essentially, students said they appreciated working on the harder part of the final (the “Applications/Extension” section) before taking on the more basic level questions (the “Foundations” part) because they started preparing earlier and were able to learn from their feedback for the next part of the exam.

Despite the fact that the “harder” part of the exam came first, students seemed to feel comfortable to take intellectual risks. They communicated their ideas and, because I quickly turned the exams back to students, received feedback that would help them understand their strengths and weaknesses so they could target their studying for the remainder of the final exam.

*Continuous Improvement--Learning from Assessments*

*High Expectations: Continuous Improvement--Learning from Assessments*

# Final Exam Part 1: Open Response

Lesson 3 of 4

## Objective: Students will be able to demonstrate what they know and understand about foundational geometry ideas, constructions, and proof, on the open response portion of the final exam.

In the first part of the final exam, which is all open response, students work through several problems that target their understanding of foundational geometry topics in novel ways. Several of the problems, like problems 4, 5, and 6, require students to synthesize several tools and geometric concepts in order to solve. Some of the problems are my own, but some have been adapted from an NCTM calendar of problems.

- Problem 1: compare the areas of circles and annuluses
- Problem 2: find the perimeter of a heptagon made by right triangles
- Problem 3: determine the number of sides of a regular polygon using angle relationships
- Problem 4: use square properties, the Pythagorean Theorem, and trigonometry to find the area of a slanted rectangle
- Problem 5: apply triangle similarity, trigonometry, proportional reasoning to solve a problem
- Problem 6: construct a regular hexagon and solve using areas of sectors
- Problem 7: prove intersecting chords in a circle create similar triangles
- Problem 8: prove a regular hexagon can be divided into a rectangle and two congruent isosceles triangles such that the rectangle’s area is two-thirds the area of the regular hexagon

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review