Geometry A
MA.09.GeometryATFv2.Bnet4copy
In this course, students will develop a thorough understanding of the principles of geometry. Students will develop an understanding that geometry is important to a wide range of scientific and technological fields of study such as engineering, physics, and cartography. The course will make connections to the real world while they are learning concepts in such areas as: surveying, global positioning systems (GPS) and bridge design. The course is aligned to Pennsylvania State Standards and National Standards.
Enduring Understanding
The student will understand:
- The language of geometry allows us to communicate in a precise and efficient manner.
- Logical reasoning creates a higher lever of thinking used throughout geometry
- Relationships exist among the angles, sides, lengths, perimeters, areas and volumes of geometric figures and can be used to prove theorems
- A variety of representations, tools and technology can be used to solve meaningful problems by representing and transforming figures and analyzing relationships.
- Specifying locations and describing spatial relationships using coordinate geometry and other representational systems can solve meaningful problems.
Essential Questions
- Why are symbols important in geometry?
- How does finding a midpoint apply to real world situations?
- Why are there different classifications of angles?
- If I'm going to be a doctor, how can geometry help me?
- When is winning an argument not really winning an argument?
- How are the properties of algebra and geometry related?
- When are lines parallel? Perpendicular?
- How are triangles classified?
- When are triangles congruent?
- How are unknowns found in triangles?
- What do we need to know about two triangles to know if they are congruent, and once we know they are, what else do we know?
- Why are some triangles special?
Additional Resources Needed
- Ruler (straightedge)
- Protractor
- Tracing paper
- Adobe Reader
- Adobe Flash Player
- Adobe Shockwave Player
- Quicktime
- Java Media Player
Content Topics
Unit 1
Foundations for Geometry
Unit 2
Proof and Reasoning
Unit 3
Congruence
Unit 4
Similarity
Unit 5
Triangles
Key Skills
- Spatial awareness, geometrical intuition and the ability to visualize
- Use of conjecture, deductive reasoning and proof
- Apply geometry through problem solving
- Knowledge and understanding of and the ability to use geometrical properties and theorems
Assessments
- Essays
- Tests and Quizzes
- Projects
Standards Alignment:
National Council of Teachers of Mathematics Standards:
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationship
Specify locations and describe spatial relationships using coordinate geometry and other representational systems
Pennsylvania State Science Anchors
M11B2 Apply appropriate techniques, tools and formulas to determine measurements (M11B211, M11B221, M11B222, M11B224, M11B231)
M11C12 Recognize and apply properties of angles, triangles and quadrilaterals (M11C121, M11C122, M11C123)
M11C13 Use properties of congruence, correspondence and similarity in problem solving settings involving 2- and 3-D figures (M11C131)
M11C14 Solve problems involving right triangles using the Pythagorean Theorem (M11C141)