Discovering Geometry

In this course students will use an inquiry approach, whereby students work with the tools of geometry and investigate geometric properties by experimentation and observation. In the class students are encouraged to take responsibility for their own learning.

The essential questions for the course are:
• What is Geometry
•What is its function in the world?

1. Inductive Reasoning: How do we use inductive reasoning to look at sequence and patterns to determine a generalization? Using situations, word problems and number patterns where inductive reasoning can be practiced in order to arrive at solutions.

Guidelines for effective group work discussed.

Group work: In groups of four, students will be given and required to create situations, word problems and number patterns where they will cooperatively use inductive reasoning to determine a conjecture.

2. Building Blocks of Geometry: How do the building blocks of geometry help to organize the world?

- Definitions : a point, a line, a plane, line segment, a ray, and an angle.
- Different angles defined: Right , Acute, obtuse, complementary, supplementary angles.
- Defining line and ale relationships: Angle bisector, parallel lines, perpendicular lines and perpendicular bisectors.
- Polygons and their classification.
- Constructions of the building blocks of geometry: Skills: learning how to use the ruler and protractor to construct these geometric figures

- PROJECT: Drawing and constructing a model of geometric solids: Prism, Cylinder, Pyramid and a Sphere.

3. Observations of the Building Blocks of Geometry in the world ( inside and outside the classroom).
- Shapes and patterns in Architecture
- Shapes and patterns in Art
- Shapes and Patterns in general objects in the home.

4. Geometric Constructions: How do we construct geometric shapes using a compass and a ruler? (Creating geometric constructions through investigations and making conjectures at the conclusion of these investigations)

1. Duplicating segments and angles
2.Constructing perpendicular bisectors and perpendiculars,
3. Constructing angle bisectors,
4.Constructing Triangles, quadrilaterals, and parallel lines,
5. Construction Problems: Using the conjectures attained, students construct a set of geometric problems and write a refection about the connection this has to the real world.

- Group Project : Representations of geometric constructions with real pictures and their drawings of them.

5. Circles and their Function: What is the relationship of the circle to humans?
- The zero.
- Cycles of life.
- The clock.
- The Human cell.
- The planets, Lunar and Solar systems.
- The wheel.
- The Mandalas design.

Skills: Use of compass, ruler and formulas to construct, measure and determine radius, and circumference of circles.

5. Portfolio Preparation: Students will write a reflective essay on the concepts learned, and the steps and the process used to accomplish one of the projects. A set of questions will guide the students in this essay.

6. Observing Symmetry in Nature: How is symmetry defined in geometry? Observing reflectional, vertical, horizontal, and rotational symmetry in the body, insects, plants and animals

7. Areas People Occupy: How do we determine the size of the areas in which we live? Investigating area formulas to calculate the areas of polygons. Group project: Creating a model of a selected area

8. Pythagorean Theorem: How does the pythagorean theorem help us to calculate the distance between two points?
•Discovering properties of right triangles and its applications
•A series of hands on and written activities will be used to prove the theorem

Final Class Project
Portfolio Piece selected: Student selects two projects to use as a portfolio presentation piece. The project must include a written reflection explaining the project.