Enduring Understanding

 

The student will understand:

  • Polygons are classified by examining their sides and angles.
  • Polygons can be described by their perimeter and area.
  • Geometric solids can be measured using lateral area, surface area and volume.
  • Geometric models help to gain insights into, and answer questions in, other areas of Mathematics.
  • Geometric ideas help to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.
  • How to establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others.
  • The properties of angles, arcs, chords, tangents and secants can be used to solve problems involving circles.

 

 

Essential Questions

 

  • How are polygons measured? What strategies and formulas can be used to find perimeter and area of polygons?
  • How are geometric solids measured? How do you know which measure to use?
  • How can we use the properties of polygons to describe their sides and angles?
  • What are the relationships between a circle and its arcs, lines, segments and angles? How do we use those relationships to solve problems?
  • How do we solve problems involving congruence in a variety of contexts?
  • How do we identify and apply transformations of figures in the coordinate plane and discuss the results of these transformations?

 

 

Additional Resources Needed


  • Pencil
  • Notebook
  • Scratch Paper.

 

Content Topics

 

Unit 1

Exploring Quadrilaterals

 

Unit 2

Geometric Measurement of Two Dimensional Figures

 

Unit 3

Geometric Measurement of Three Dimensional Figures

 

Unit 4

Analyzing Circles

 

Unit 5

Transformations/Tessellations

 

 

Key Skills

 

  • Geometric terms & definitions
  • Apply geometry through problem solving
  • Cooperative Learning
  • Visual/graphic formats
  • Knowledge and understanding of and the ability to use geometrical properties and theorems

       

       

Assessments

 

  • Quizzes & Unit Assessments
  • Math Journals Performance
  • Tasks (GRASP Assessments)
  • Unit Projects
  • Discussion Boards

 

 

Standards Alignment:

 

State Standards: 2.9.11

A. Construct geometric figures using dynamic geometry tools (e.g., Geometer's Sketchpad, GeoGebra).

B. Prove two triangles or two polygons are congruent or similar using algebraic, coordinate and deductive proofs.

C. Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles and diagonals using deductive proofs.

E. Solve problems involving inscribed and circumscribed polygons.

F. Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles.

H. Construct a geometric figure and its image using various transformations. I. Model situations geometrically to formulate and solve problems.

J. Analyze figures in terms of the kinds of symmetries they have.