Geometry SPI’s
SPI 3108.1.1 Give precise mathematical descriptions or definitions of geometric shapes in the plane and space.
SPI 3108.1.2 Determine areas of planar figures by decomposing them into simpler figures without a grid.
SPI 3108.1.3 Use geometric understanding and spatial visualization of geometric solids to solve problems and/or create drawings.
SPI 3108.1.4 Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems.
SPI 3108.2.1 Analyze, apply, or interpret the relationships between basic number concepts and geometry (e.g. rounding and pattern identification in measurement, the relationship of pi to other rational and irrational numbers)
SPI 3108.2.2 Perform operations on vectors in various representations.
SPI 3108.3.1 Use algebra and coordinate geometry to analyze and solve problems about geometric figures (including circles).
SPI 3108.3.2 Use coordinate geometry to prove characteristics of polygonal figures.
SPI 3108.3.3 Describe algebraically the effect of a single transformation (reflections in the x or yaxis, rotations, translations, and dilations) on twodimensional geometric shapes in the coordinate plane.
SPI 3108.4.1 Differentiate between Euclidean and nonEuclidean geometries.
SPI 3108.4.2 Define, identify, describe, and/or model plane figures using appropriate mathematical symbols (including collinear and noncollinear points, lines, segments, rays, angles, triangles, quadrilaterals, and other polygons).
SPI 3108.4.3 Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other polygons.
SPI 3108.4.4 Analyze different types and formats of proofs.
SPI 3108.4.5 Describe solids and/or surfaces in threedimensional space when given twodimensional representations for the surfaces of threedimensional objects.
SPI 3108.4.6 Use various area of triangle formulas to solve contextual problems (e.g., Heron’s formula, the area formula for an equilateral triangle and A = ½ ab sin C).
SPI 3108.4.7 Compute the area and/or perimeter of triangles, quadrilaterals and other polygons when one or more additional steps are required (e.g. find missing dimensions given area or perimeter of the figure, using trigonometry).
SPI 3108.4.8 Solve problems involving area, circumference, area of a sector, and/or arclength of a circle.
SPI 3108.4.9 Use right triangle trigonometry and crosssections to solve problems involving surface areas and/or volumes of solids.
SPI 3108.4.10 Identify, describe, and/or apply transformations on two and three dimensional geometric shapes.
SPI 3108.4.11 Use basic theorems about similar and congruent triangles to solve problems.
SPI 3108.4.12 Solve problems involving congruence, similarity, proportional reasoning and/or scale factor of two similar figures or solids.
SPI 3108.4.13 Identify, analyze and/or use basic properties and theorems of circles to solve problems (including those relating right triangles and circles).
SPI 3108.4.14 Use properties of right triangles to solve problems (such as involving the relationship formed when the altitude to the hypotenuse of a right triangle is drawn).
SPI 3108.4.15 Determine and use the appropriate trigonometric ratio for a right triangle to solve a contextual problem.
SPI 3108.5.1 Use area to solve problems involving geometric probability (e.g. dartboard problem, shaded sector of a circle, shaded region of a geometric figure).
