Geometry EDN 322

NCTM’S STANDARD FOR GEOMETRY  analyze characteristics and properties of two-and three-dimensional geometric objects and develop mathematical arguments about geometric relationships;  specify locations and describe spatial relationships using coordinate geometry and other representational systems; Instructional programs from pre-kindergarten through grade twelve should enable all students to--

NCTM’S STANDARD FOR GEOMETRY  apply transformations and use symmetry to analyze mathematical situations;  use visualization, spatial reasoning, and geometric modeling to solve problems. Instructional programs from pre-kindergarten through grade twelve should enable all students to--

Goals of Geometry for K-6 Students Development of useful intuition and knowledge about shapes in the environment Investigations that are tied to the real world Analysis of shapes for their usefulness and application to solve real world problems

Why Teach Geometry? Useful in everyday situations and it is connected to other mathematical and academic content Allows for orderly representation and description of our world Children are naturally interested in geometry Children’s spatial abilities frequently exceed their numerical skills thus providing motivation for number understanding

LEVEL DESCRIPTION SAMPLE RESPONSES OF CHILDREN 0 VisualizationChildren view a Shown a rectangle and asked to identify geometric shape as ait, the child may say, “It is a rectangle whole. They do notbecause it looks like a book cover.” describe properties of the shape.

LEVEL DESCRIPTION SAMPLE RESPONSES OF CHILDREN 1 AnalysisChildren recognize A child may say that the rectangle has the properties offour sides and square corners. figures. They do not see relations between properties.

LEVEL DESCRIPTION SAMPLE RESPONSES OF CHILDREN 2 InformalStudents see relationsA student may say that since the angles Deductionbetween propertiesof a rectangle are right angles, the of a class of shapes.opposite sides are parallel.

LEVEL DESCRIPTION SAMPLE RESPONSES OF CHILDREN 3 DeductionBoth level 3 (level at which students can use deduction to 4 Rigorprove statements) and level 4 ( level at which students see geometry in the abstract) are beyond the scope of most students in middle school. Level 3 is the level at which a proof-oriented high school geometry course is taught.

Transformations A translation is created by moving an object in a straight line to a new location.

Transformations A reflection is made by picking up the object, turning it over, and sliding it to the new location creating a mirror image.

Transformations A Rotation is created by moving an object around a fixed point.