Geometry
Grade level: 10-12
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Exploring Geometry |
Building a geometry portfolio; the building blocks of geometry; measuring length; measuring angles; geometry using paper folding; special roots in triangles; motion in geometry; motion in the coordinate plane -Portfolio, Project: Origami Paper Folding |
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Reasoning in Geometry |
An introduction to proofs; an introduction to logic; definitions; building a system of geometry knowledge; conjectures that lead to theorems -Portfolio, Project: Solving Logic Puzzles |
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Parallels and Polygons |
Symmetry in polygons; properties of quadrilaterals; parallel lines and transversals; proving that lines are parallel; The Triangle Sum Theorem; angles in polygons; midsegments of triangles and trapezoids; analyzing polygons using coordinates -Portfolio, Project: String Figures |
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Triangle Congruence |
Congruent polygons; triangle congruence; analyzing triangle congruence; using triangle congruence; proving quadrilateral properties; conditions for special quadrilaterals; compass and straightedge constructions; constructing transformations - Portfolio, Project: Flexagons |
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Perimeter and Area |
Perimeter and area; areas of triangles, parallelograms and trapezoids; circumferences and areas of circles; the Pythagorean Theorem; special triangles and areas of regular polygons; the distance formula and the method of quadrature; proofs using coordinate geometry; geometric probability - Portfolio, Project: Area of a Polygon |
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Shapes in Space |
Solid shapes; spatial relationships; prisms; coordinates in three dimensions; lines and planes in space; perspective drawing -Portfolio, Project: Polyhedra |
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Surface Area and Volume |
Surface area and volume; surface area and volumes of prisms; surface area and volumes of pyramids; surface area and volumes of cylinders; surface area and volumes of cones; surface area and volumes of spheres; three dimensional symmetry - Portfolio, Project: A Three Dimensional Puzzle |
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Similar Shapes |
Dilations and scale factors; similar polygons; triangle similarity Postulates; the Side-Splitting Theorem; Indirect Measurement and Additional Similarity Theorems; area and volume ratios - Portfolio, Project: Indirect Measurement and Scale Models |
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Circles |
Chords and arcs; tangents to circles; inscribed angles and arcs; angles formed by secants and tangents; segments of tangents, secants, and chords; circles in the coordinate plane - Portfolio, Project: Tangent Circles |
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Trigonometry |
Tangent ratios; sines and cosines; extending the trigonometric ratios; The Law of Sines; The Law of Cosines; vectors in geometry; rotations in the coordinate plane - Portfolio, Project: Plimpton 322 Revisited |
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Taxicabs, Fractals, and More |
Golden connections; taxicab geometry; Graph Theory; topology: twisted geometry; Euclid unparalleled; fractal geometry; other transformations: projective geometry - Portfolio, Project: The Tower of Hanoi |
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A Closer Look at Proof and Logic |
Truth and validity of logical arguments; and, or, and not in logical arguments; a closer look at if-then statements; indirect proof; computer logic - Portfolio, Project: Two Famous Theorems |