Geometric Concepts

Goal:The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used. The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

Geometric Content

Shapes and Properties

study of properties of shapes in 2d and 3d

Polygon

Area of a Polygon: A=bh (base X height)perimeter: all sides added together

Circle

The Area of a Circle is: A = π × r2

Box, Cylinder, and Cube

Box or Cube:V=l X w X hCylinder:V = πr2h

Pythagorean Theorem and special properties of isosceles, equilateral, and right triangles

Properties of parallel and perpendicular lines

Coordinate geometry

To introduce the idea, consider the grid on the right. The columns of the grid are lettered A,B,C etc.The rows are numbered 1,2,3 etc from the top. We can see that the X is in box D3; that is, column D, row 3.D and 3 are called the coordinates of the box. It has two parts: the row and the column.There are many boxes in each row and many boxes in each column. But by having both we can find one single box,where the row and column intersect

Geometric visualization

Slope

Transformations

Main topic

Similarity

Figures shown in the same color are similar Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

Van Hiele Levels

Level 0: Visualization

The objects of thought at level 0 are shapes and what they "look like"

Level 1: Analysis

The objects of thoughts at level 1 are classes of shapes rather than individual shapes.

Level 2: Informal Deduction

The objects of thought at level 2 are the properties of shapes.*Students can develop relationships between these poperties

Level 3: Deduction

The objects of thought at level 3 are relationships between properties of geometric objects.

Level 4: Rigor

The objects of thought at level 4 are deductive axiomatic systems for geometry.

Characteristics of the van Hiele Levels:

Levels are not age dependentadvancement through the levels requires geometric experiences.