South Williamsport Area School District
Course Plan Template
Teacher: Chris Lusk/Dave Rovenolt / School Year: 2014-2015Course: Geometry / Intended Grade Level: 10/9
Course Summary: The Geometry course is designed so that students are challenged to develop 21st century skills such as critical thinking and creative problem solving, while engaging in exciting careers within science, Technology, Engineering and Mathematics related fields. The topics that will be covered will include, but not be limited to, Geometric structure, congruence, similarity and measurement.
Course Outcomes:
By the end of the course, students will know:
- The basic tools that make up the foundation of geometry.
- What makes two objects congruent and the different relationships that present themselves when objects are congruent.
- What makes two object similar. and the different relationships that present themselves when objects are similar.
- Ways to find different measurements in geometric figures.
By the end of the course, students will be able to:
- Use the definitions, postulates and theorems to write paragraph and two column proofs.
- Prove that two figures are congruent or use congruent figures to prove other relationships within figures.
- Prove that two figures are similar or use similar figures to prove other relationships within figures.
- Calculate area, surface area and volume.
Standards Targeted[1]
- Common Core State Standards.
Units of Study
Unit Topic / Primary Learning Outcome
Unit 0 – Preparing for Geometry / - Review Basic Algebra Skills to prepare for Geometry
Unit 1 – Tools of Geometry / - The students will be able to find different measurements from distance to perimeters, areas, and volumes.
Unit 2 – Reasoning and Proof / - Make conjectures and find counterexamples for statements.
- Use deductive reasoning to reach valid conclusions.
- Write proofs involving segment and angle theorems.
Unit 3 – Parallel and Perpendicular Lines / - Identify and prove angle relationships that occur with parallel lines and a transversal
- Use slope to analyze a line and to write its equation.
- Find the distance between a point and a line and between two parallel lines.
Unit 4 – Congruent Triangles / - Apply special relationships about interior and exterior angles of triangles.
- Identify corresponding parts of congruent triangles and prove triangles are congruent.
- Learn about the special properties of isosceles and equilateral triangles.
Unit 5 – Relationships in Triangles / - Learn about special segments and points related to triangles.
- Learn about relationships between the sides and angles of triangles.
- Learn to write indirect proofs.
Unit 6 – Quadrilaterals / - Find and use the sum of the measures of the interior and exterior angles of a polygon.
- Recognize and apple properties of quadrilaterals.
- Compare quadrilaterals.
Unit 7 – Proportion and Similarity / - Identify similar polygons and use ratio and proportions to solve problems.
- Identify and apply similarity transformations.
- Use scale models and drawings to solve problems.
Unit 8 – Right Triangles and Trigonometry / - Use the Pythagorean Theorem
- Use properties of special right triangles.
- Use trigonometry to find missing measures of triangles.
Unit 9 – Transformations and Symmetry / - Name and draw figures that have been reflected, translated, rotated and dilated.
- Recognize and draw compositions of transformations.
- Identify symmetry in two and three dimensional figures.
Unit 10 – Circles / - Learn the relationships between central angles, arcs and inscribed angles in a circle.
- Define and use secants and tangents.
- Use an equation to identify or describe a circle.
Unit 11 – Areas of Polygons and Circles / - Find areas of polygons.
- Solve problems involving areas and sectors of circles.
- Find scale factors using similar figures.
Unit 12 – Extending Surface Area and Volume / - Find lateral areas, surface areas, and volumes of various solid figures.
- Investigate Euclidean and Spherical Geometries
- Use Properties of Similar Solids.
Unit 13 – Probability and Measurement / - Represent sample spaces.
- Use permutations and combinations with probability.
- Find probabilities by using length and area.
- Find probabilities of compound events.
Advanced Learner Recommendations
*Advanced Learners with GIEPs: All Specially Design Instruction is followed as outlined by the student's Gifted Individualized Education Plan.
Struggling Learner Recommendations
*Struggling Learners with IEPs: All accommodations/modifications are followed as outlined by the student's Individualized Education Plan. Examples: extended time, small group testing, study guides, test read aloud, and modifications made to the regular education curriculum.
*Struggling Learners without IEPs: Available during the daily FLEX period to ask questions or review materials, restating of directions, and instruction that incorporates the different types of learning modalities (ex: visual, auditory, or kinesthetic).
*Implement Note Cards to help with learning the postulates and theorems.
Revised - November 17, 2014
Course plans represent district curriculum. They will be posted to building web pages accessible to the school and community.
[1] Indicate primary Standards emphasis:
- PA Core - Math / ELA / Science & Technology / History & Social Studies
- National Content Standards (Name and Type)
- Industry Recognized Standards (Name and Type)