## GIS + GPS = Illinois State Standards

 Illinois Mathematics State Standard #9 - Geometry

STATE GOAL 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

Why This Goal Is Important: Geometry provides important methods for reasoning and solving problems with points, lines, planes and space. The word "geometry" comes from Greek words meaning "measurement of the Earth." While we use modern technology and employ a wider variety of mathematical tools today, we still study geometry to understand the shapes and dimensions of our world. The applications of geometry are widespread in construction, engineering, architecture, mapmaking and art. Historically, geometry is a way to develop skill in forming convincing arguments and proofs. This goal of developing a means of argument and validation remains an important part of our reasons for studying geometry today.

Illinois Mathematics Standards covered: ( 9A, 9B, & 9C)

 Learning Standard 9A. Demonstrate and apply geometric concepts involving points, lines, planes and space. Early Elementary 9.A.1a Identify related two- and three-dimensional shapes including circle-sphere, square-cube, triangle-pyramid, rectangle-rectangular prism and their basic properties. Late Elementary 9.A.2a Build physical models of two- and three-dimensional shapes. Late Elementary 9.A.2b Identify and describe how geometric figures are used in practical settings (e.g., construction, art, advertising). Late Elementary 9.A.2c Describe and draw representations of geometric relationships, patterns, symmetries, and designs in two- and three-dimensions with and without technology. Middle & Junior High School 9.A.3b Draw transformation images of figures, with and without the use of technology. Early High School 9.A.4a Construct a model of a three-dimensional figure from a two-dimensional pattern. Late High School 9.A.5 Use geometric figures and their properties to solve problems in the arts, the physical and life sciences and the building trades, with and without the use of technology. Learning Standard 9B. Identify, describe, classify and compare relationships using points, lines, planes and solids. Early Elementary 9.B.1a Identify and describe characteristics, similarities and differences of geometric shapes. Early Elementary 9.B.1b Sort, classify and compare familiar shapes. Late Elementary 9.B.2 Compare geometric figures and determine their properties including parallel, perpendicular, similar, congruent and line symmetry. Middle & Junior High School 9.B.3 Identify, describe, classify and compare two- and three- dimensional geometric figures and models according to their properties. Early High School 9.B.4 Recognize and apply relationships within and among geometric figures. Late High School 9.B.5 Construct and use two- and three-dimensional models of objects that have practical applications (e.g., blueprints, topographical maps, scale models). Learning Standard 9C. Construct convincing arguments and proofs to solve problems Early Elementary 9.C.1 Draw logical conclusions and communicate reasoning about simple geometric figures and patterns using concrete materials, diagrams and contemporary technology. Late Elementary 9.C.2 Formulate logical arguments about geometric figures and patterns and communicate reasoning. Middle & Junior High School 9.C.3a Construct, develop and communicate logical arguments (informal proofs) about geometric figures and patterns Early High School 9.C.4a Construct and test logical arguments for geometric situations using technology where appropriate. Early High School 9.C.4b Construct and communicate convincing arguments for geometric situations. Late High School 9.C.5a Perform and describe an original investigation of a geometric problem and verify the analysis and conclusions to an audience. Late High School 9.C.5b Apply physical models, graphs, coordinate systems, networks and vectors to develop solutions in applied contexts (e.g., bus routing, areas of irregular shapes, describing forces and other physical quantities).