Geometry

The geometry standard addresses the characteristics, properties, and relationships of one-, two-, and three-dimensional geometric figures and objects. Students identify, classify, compare and analyze these characteristics, properties, and relationships. Spatial reasoning, properties of geometric objects, and transformations are used to analyze mathematical situations and solve problems.
 * Geometry Standard**


 * By the end of the K-2 program sudents should be able to:**
 * Describe and create plane figures: circle, rectangle, square, triangle, hexagon, trapezoid, parallellogram, and rhombus, and identify them in the environment.
 * Desribe solid objects: cube, rectangular prism, sphere, cylinder, cone and pyramid, and identify them in the environment.
 * Sort and compare two-dimensional figures and three-dimensional objects according to their characteristics and properties.
 * Identify, explain, and model (superposition, copying) the concept of shapes being congruent and similar.
 * Recognize two- and three-dimensional objects from different positions.
 * Describe location, using comparison (before, after), directional (above, below), and positional (first, last) words.
 * Identify and draw figures with line symmetry.


 * By the end of the 3-4 program students should be able to:**
 * Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects.
 * Describe and identify points, lines, and planes in the environment.
 * Desribe and identify intersecting, parallel and perpendicular lines or segments in the environment.
 * Identify and draw right, obtuse, actue and straight angles.
 * Use attributes to describe, classify and sketch plane figures and build solid objects.
 * Develop definitions of classes of shapes.
 * Find and name locatoins in coordinate systems.
 * Identify and describe line and rotational symmetry in two-dimensional shapes and designs.
 * Desribe, identify and model reflections, rotations and translations, using physical materials.
 * Describe a motion or series of transformations that show two shapes are congruent.
 * By the end of the 5-7 program students should be able to:**
 * Identify and label angle parts and the regions defined within the plane where the angle resides.
 * Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.
 * Specify locations and plot ordered pairs on a coordinate plane.
 * Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.
 * Use proportions to express relationships among corresponding parts of similar figures.
 * Describe and use the concepts of congruence, similarity and symmetry to solve problems.
 * Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.
 * Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.
 * Identify and draw three-dimensional objects from different views (top, side, front and perspective).
 * Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing.


 * By the end of the 8-10 program students should be able to:**
 * Formally define geometric figures.
 * Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.
 * Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.
 * Use coordinate geometry to represent and examine the properties of geometric figures.
 * Draw and construct representations of two- and three-dimensional geographic objects using a variety of tools, such as straightedge, compass, and technology.
 * Represent and model transformations in a coordinate plane and describe results.
 * Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.
 * Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
 * Use right triangle trigonometric relationships to determine lengths and angle measurements.


 * By the end of the 11-12 program students should be able to:**
 * Use trigonometric relationships to verify and determine solutions in problem situations.
 * Represent transformations within a coordinate system using vectors and matrices.


 * Lesson for students in the 5-7 program: [|Describe the Graph]**
 * Lesson for students in the 3-4 program: [|Getting to Know the Solids]**