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| Analyze characteristics and properties of two- and three-dimensional geometric shapes
and develop mathematical arguments about geometric relationships |
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• Analyze properties and determine attributes of two- and three-dimensional objects |
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3.01 - 3.17, 3.21, 5.4, 5.7, 5.21-5.28, 5.01-5.05, 5.08-5.09, 5.10-5.16 (triangles) |
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8.01-8.09, 8.15, 8.21-8.30 (other polygons)
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8.01 - 8.17 (circles)
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11.1 - 11.28 (three dimensional objects)
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• Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them,
and solve problems involving them |
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1.19, 1.23, 1.26, 2.01 - 2.05, 2.07-2.08, 2.12, 2.31-2.32, 3.03-3.17,3.21, 4.01-4.08,4.17-4.32, 4.38 (congruence)
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1.07-1.11, 6.01-6.22 (similarity)
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• Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others
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1.15-1.18, 1.25, 2.05-2.06, 5.29-5.30 |
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note: Many, many more sections contain proofs. Above sections focus on explaining reasoning processes
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• Use trigonometric relationships to determine lengths and angle measures |
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7.01-7.14, 7.16 - 7.18, 7.21 - 7.28 |
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| Specify locations and describe spatial relationships using coordinate geometry and other representational systems |
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• Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations |
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2.14-2.16, 2.22-2.36, 3.02, 4.01-4.40, 5.17-5.22, 7.15 - 7.20, 8.26, 10.02, 10.24-10.25
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•Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates
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note: many other sections include the use of coordinates |
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| Apply transformations and use symmetry to analyze mathematical situations |
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• Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices
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4.01-4.40, 6.17-6.23, 7.15-7.20, 10.01-10.06 |
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• Use various representations to help understand the effects of simple transformations and their compositions |
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4.11, 4.13-4.14, 4.17-4.21, 4.24-4.30, 4.38, 6.17-6.21 |
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| Use visualization, spatial reasoning, and geometric modeling to solve problems |
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• Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools |
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1.10-1.12, 10.01,10.24-10.25, 11.08-11.09
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• Visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections
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10.22-10.25 |
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• Use vertex-edge graphs to model and solve problems
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• Use geometric models to gain insights into, and answer questions in, other areas of mathematics
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3.22 |
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• Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture
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