5. Understands and applies basic and advanced properties of the concepts of geometry.
· Within this standard, achievement at grade level is as follows:
Primary (grades k-2)
- Understands basic properties of, similarities of, and differences between geometric shapes.
- Understands the language of spacial concepts (ex. "inside," "between").
- Understands that geometric shapes are useful for representing and describing real-world situations.
- Understands that patterns can be made by putting different shapes together or taking them apart.
Upper Elementary (grades 3-5)
- Knows basic geometric language for describing and naming shapes (ex. parallelogram, cone).
- Understands the basic properties of figures.
- Predicts and verifies the effects of combining, subdividing, and changing basic shapes.
- Understands that shapes can be congruent or similar.
- Uses motion geometry (ex. turning, flipping, sliding) to understand geometric relationships.
- Understands characteristics of lines and angles.
- Understands how scale in maps and drawings shows relative distance and size.
Middle School/Junior High (grades 6-8)
- Uses geometric methods to complete geometric constructions.
- Understands the defining properties of three-dimensional figures.
- Understands the defining properties of triangles.
- Understands the geometric transformations of figures.
- Understands the relationships between two- and three-dimensional representations of a figure.
- Understands the concept of tessellation (ex. repetitive patterns of polygons that fit together without gaps/holes).
- Understands the basic concept of the Pythagorean theorem.
High School (grades 9-12)
- Understands that objects and relations in geometry correspond directly to objects and relations in algebra.
- Uses the Pythagorean theorem and its converse and properties of special right triangles (30-60-90 and 45-45) to solve mathematical and real-world problems.
- Uses synthetic representations (ex. drawings) and analytic methods to solve problems involving symmetry and transformation of figures.
- Understands the characteristics and uses of vectors (velocity and force).
- Uses geometric constructions to complete simple proofs, to model, and to solve mathematical and real-world problems.
- Uses basic operations on vectors.
- Understands the basic concepts of right-triangle trigonometry.
- Uses trigonometric ration methods to solve mathematical and real-world problems.
- Understands the basic properties and uses of polar coordinates.
- Uses inductive and deductive reasoning to make observations about, verify properties of, and see relationships among figures.
- Uses properties of and relationships between geometric figures to solve mathematical and real-world problems.
6. Understands and applies basic and advanced concepts of statistics and data analysis.
· Within this standard, achievement at grade level is as follows:
Primary (grades k-2)
- Understands that observations about objects or events can be organized and displayed in simple graphs.
