Badge Overview

Explorations in Geometry  Explorations in Geometry

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Explorations in Geometry

Explorations in Geometry

Issued by Hood College

Badge Description

The Exploration in Geometry badge offers a look at basic geometry from a more sophisticated point of view, including more advanced Euclidean and non-Euclidean geometries. Topics covered may include analytic geometry, spherical geometry, hyperbolic geometry, fractal geometry and transformational geometry. Dynamic geometry software will be an integral part of the course.

Skills Problem Solving Perseverance Reasoning Communication Mathematical Arguments

Badge Criteria

This FOUNDATIONAL level badge is equivalent to a 3-credit, master's-level course. A final grade of B or better is required to earn this badge.

1. Core concepts including angle, parallel, perpendicular, and principles of Euclidean geometry in two and three dimensions. 2. Transformations including dilations, translations, rotations, reflections and glide reflections; compositions of transformations; and the expression of symmetry and regularity in terms of transformations. 3. Congruence, similarity and scaling, and their development and expression in terms of transformations. 4. Basic geometric figures in one, two and three dimensions (line segments, lines, rays, circles, arcs, polygons, polyhedral solids, cylinders, cones and spheres) and their elements (vertices, edges and faces). 5. Identification, classification into categories, visualization, two- and three-dimensional representations, and formula rationale and derivation (perimeter, area, and volume) of two- and three-dimensional objects (triangles; classes of quadrilaterals such as rectangles, parallelograms and trapezoids; regular polygons; rectangular prisms; pyramids; cones; cylinders; and spheres). 6. Geometric measurement and units (linear, area, surface area, volume and angle), unit comparison, and the iteration, additivity and invariance related to measurements. 7. Geometric constructions, axiomatic reasoning, and making and proving conjectures about geometric shapes and relations. 8. Coordinate geometry including the equations of lines and algebraic proofs (e.g., Pythagorean Theorem and its converse). 9. Historical development and perspectives of geometry and measurement including contributions of significant figures and diverse cultures. 10. Non-Euclidean Geometries such as Taxicab Geometry and Spherical Geometry. 11. Common Core State Standards and Maryland College and Career Ready Standards relevant to Geometry and Measurement.

Aligned Outcomes