# Geometry

**Unit of Study * from Springboard**

Unit 1: Proof, Parallel and Perpendicular Lines | Students study formal definitions of basic figures, the axiomatic system of geometry and the basics of logical reasoning. They are then introduced to mathematical proof by applying formal definitions and logical reasoning to develop proofs about basic figures. Finally, students learn how to write equations of parallel and perpendicular lines. |

Unit 2: Congruence, Triangles, and Quadrilaterals | Students explore transformations of figures in the coordinate plane. They relate the transformations to congruence, and study the properties of triangles and special quadrilaterals. |

Unit 3: Similarity, Right Triangles, and Trigonometry | Students use knowledge of congruent figures to develop similarity rules for triangles and other polygons. In addition, students will expand their knowledge of right triangles through the use of the Pythagorean Theorem, special right triangles, and trigonometric ratios. |

Unit 4: Circles and Constructions | Students study angles in a circle and lengths of chords and tangents. They are introduced to coordinate proofs and write equations of circles and parabolas. Then they apply what they have learned about circles to basic straightedge-and-compass constructions. |

Unit 5: Extending two dimensions to three dimensions | Students study various properties of two-dimensional and three-dimensional figures. Students develop various formulas for perimeter and area. They develop surface area and volume formulas for prisms, cylinders, pyramids, cones, and spheres. Students also explore the effects of changing dimensions and investigate spherical geometry. |

Unit 6: Probability | Students focus on applications of probability. They use Venn and tree diagrams to model situations involving probability to analyze probable results |

**Math Practice Standards**

- Make sense of problems and persevere in solving them
- Reason abstractly and quantitatively
- Construct viable arguments and critique the reasoning of others
- Model with mathematics
- Use appropriate tools strategically
- Attend to precision
- Look for and make use of structure
- Look for and express regularity in repeated reasoning

**SpringBoard**

This year all Algebra 1, Geometry, and Algebra 2 mathematics classes at Hollywood High School are using the SpringBoard program developed by The College Board. The College Board is also responsible for creating the SAT and the Advanced Placements Exams. The program is a research-based program that puts the learning in the students’ hands. Each lesson is designed to teach students content in the context of a problem, as opposed to content with no immediate relevance. This course is going to push you to think in ways that many have not done previously. There will be a lot of emphasis put on student input and collaboration in class. Things may start out a little frustrating and slow, but once the class has the feel for the program the results will be well worth the effort.

**Textbook: SpringBoard: Geometry. CollegeBoard**

This textbook is different from most others in that it is completely consumable by the student. This means that you will take notes and do classwork directly in the text. Since the books are consumable, they are not hardbound and can be messed up fairly easily. For this reason I suggest that you get a three ring binder to protect your book (see class materials). If a book is lost, the cost to have a new book will be $20. Ordering a replacement book will be mandatory.

**KhanAcademy**The website www.khanacademy.org is a world famous tool for learning math. It has videos for students to watch when they are absent or need extra examples as well as exercises to practice and achieve mastery. Students in Algebra 1 should seek to master all skills in the KhanAcademy Algebra 1 Mission. Springboard has published a document that correlates the activities in class to KhanAcademy videos that students should take advantage of when they are struggling or want to work ahead. That document and the video link is below.