This course examines ideas associated with two- and three-dimensional geometric figures, including polygons, polyhedra, circles, cylinders, and spheres. Topics include the vocabulary of geometric figures; spatial visualization, representation by nets and isometric drawings; basic notions and constructions of Euclidean geometry; isometric transformations, congruence, and similarity; length, area, and volume; and perimeter and surface area. Prerequisite: Intermediate Algebra

GETTING STARTED (GS-GEO)
Participants get started by meeting and greeting each other as they examine some properties of quadrilaterals. They learn about institute expectations.

TANGRAM POLYGONS (TANG)
Participants examine vocabulary, attributes, and properties of two-dimensional figures using tangram polygons. They become familiar with the shapes through a paper-tearing activity. They continue to explore relationships through a coordinate graphing and proportional drawing investigation.

SPATIAL VISUALIZATION (SPATVIS)
Participants develop spatial concepts and skills in two and three dimensions. They explore the ideas of isometric transformation, congruence, and symmetry. They compare various methods for representing three-dimensional structures with two-dimensional drawings and descriptions. They use models, isometric drawings, and orthographic drawings to represent cube structures, prisms, and pyramids.

NETS AND POLYHEDRA (3D)
Participants use two-dimensional drawings (nets) to represent polyhedra, and common objects to build them. They review geometry vocabulary and examine relationships among the parts of the polyhedral figures. An investigation of the relationship among vertices, faces, and edges is included.

THE PATTERN BLOCK PROTRACTOR AND PROPERTIES OF PARALLEL LINES (PPP)
Participants find the interior angle measures for the six pattern block pieces and the sum of the interior angles of polygons. They then use pattern blocks to construct a protractor, which is used to measure angles and to conjecture about properties of parallel lines.

CONGRUENCE (CONG)
Participants practice congruency theorems (SAS, AAS, ASA, SSS, HA) and learn to apply CPCTC.

CLASSIC CONSTRUCTIONS (CONST)
Participants perform basic Euclidean constructions with straightedge and compass, and “folding constructions” with patty paper. Participants use properties of congruent triangles to justify the constructions. They learn about points of concurrency of various lines associated with triangles.

GEOMETRY: LENGTH AND AREA (GEO4)
Participants focus on common properties of length, area, and volume as they find lengths of polygonal paths, areas of polygonal regions, and volumes of prisms. Participants find perimeters of regions and contrast perimeter and area. They create nets for prisms to explore the meaning of surface area.

PERIMETER AND AREA (PA)
Participants examine properties of length and area. They investigate the relationship between the perimeter and the area of rectangles drawn on grid paper. Participants estimate areas of more complicated regions. They verify area formulas for parallelograms, triangles, and trapezoids, and they apply the formulas to more complicated regions.

EVERYONE LIKES A LITTLE PI: AN EXPLORATION OF CIRCLES (PI)
Participants measure parts of circles to determine a relationship between diameter and circumference. They explore the concept of area of a circle. They use circumference and area formulas to solve application problems.

SURFACE AREA AND VOLUME (SAV)
Participants investigate surface area and volume of rectangular boxes built from cubes. They experiment to find formulae for the volume of more complicated shapes, such as pyramids, cones, and spheres.

THE JUICE CONTAINER (JUICE)
Participants examine the properties of a juice container as well as some unconventionally shaped “cans,” reviewing such concepts as constructing nets, making orthogonal and isometric drawings, and finding surface area and volume. They examine the “cans” with proportional dimensions and explore the resulting changes that occur in the new surface areas and volumes.

CAHSEE: MEASUREMENT AND GEOMETRY (CAHSEE:MG)
Participants become familiar with the topics tested on the California High School Exit Exam (CAHSEE). Anchor problems and released items for geometry and measurement are included.

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