Voluntary State Curriculum
2.1.1: The student will analyze the properties of geometric figures.
2.1.1.A: Essential properties, relationships, and geometric models include the following:
2.1.1.A.a: congruence and similarity
2.1.1.A.b: line/segment/plane relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)
2.1.1.A.d: angles and angle relationships (vertical, adjacent, complementary, supplementary, obtuse, acute, right, interior, exterior)
2.1.1.A.e: angle relationships with parallel lines
2.1.1.A.f: polygons (regular, non-regular, composite, equilateral, equiangular)
2.1.1.A.g: geometric solids (cones, cylinders, prisms, pyramids, composite figures)
2.1.1.A.h: circle/sphere (tangent, radius, diameter, chord, secant, central/inscribed angle, inscribed, circumscribed).
188.8.131.52: The student will recognize geometric solids when given the two-dimensional
184.108.40.206: The student will draw two-dimensional representations of three-dimensional solids.
220.127.116.11: The student will analyze the properties and relationships of geometric solids with bases other than rectangles, triangles, or circles.
18.104.22.168: The student will analyze the properties and relationships of oblique solids.
22.214.171.124: The student will analyze the properties and relationships of truncated three-dimensional solids.
126.96.36.199: The student will explore the relationship between the measure of the central angle and the arc length in a circle.
2.1.2: The student will identify and/or verify properties of geometric figures using the coordinate plane and concepts from algebra.
2.1.2.A: ?Verify properties? means to justify solutions using definitions and/or mathematical principles.
2.1.2.B: Properties, relationships, and geometric models include the following:
2.1.2.B.a: congruence and similarity
2.1.2.B.b: line/segment relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)
2.1.2.B.d: angles and angle relationships (obtuse, acute, right)
2.1.2.B.e: polygons (regular, non-regular, equilateral, equiangular)
2.1.2.B.f: circle (tangent, radius, diameter, chord).
2.1.2.D: Concepts from algebra include applications of the distance, midpoint, and slope formulas.
188.8.131.52: The student will locate points on the polar coordinate system including points with rotation greater than 360°.
184.108.40.206: The student will explore the relationship between a point on the coordinate plane with the same point on the polar coordinate system.
220.127.116.11: The student will use the distance and midpoint formulas for segments in three-dimensional space.
2.1.3: The student will use transformations to move figures, create designs, and/or demonstrate geometric properties.
2.1.3.A: Transformations include reflections, rotations, translations, and dilations.
2.1.3.B: Items should go beyond the identification of transformations.
2.1.3.C: Essential properties and relationships include the following: congruence, similarity, and symmetry.
2.1.3.D: The student?s explanation of a transformation must include the following:
2.1.3.D.a: translation ? distance and direction
2.1.3.D.b: reflection ? line of reflection
2.1.3.D.d: dilation ? center and scale factor.
2.1.3.E: Paper folding and the use of Miras? and mirrors are appropriate methods for performing transformations, and their use must be referenced.
2.1.3.a: Given one or more transformations, the student sketches the result of the transformation(s) and/or explains the geometric effect of the transformation(s) on the figure.
18.104.22.168: The student will find transformation images, including rotations, reflections, dilations and translations, using matrices.
22.214.171.124: The student will identify the distance and direction of a given vector.
126.96.36.199: The student will find resultant vectors.
188.8.131.52: The student will describe translations using vectors.
184.108.40.206: The student will find translation images using vector sums.
2.1.4: The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.
2.1.4.A: ?Validate properties? in this indicator, means justifying solutions using definitions, mathematical principles and/or measurement.
2.1.4.B: Students may use a compass, straightedge, patty paper, a Mira?, and/or a mirror as construction tools. Using a ruler or protractor cannot be part of the strategy.
2.1.4.C: Students may use a compass, ruler, patty paper, a Mira?, a mirror and/or a protractor as drawing tools.
2.1.4.D: It is acceptable to do a construction when the item asks for a drawing.
2.1.4.E: Paper folding and the use of Miras? and mirrors are appropriate methods for representing, constructing, and/or analyzing figures, and their use must be referenced.
2.1.4.F: Constructions and drawings are limited to the two-dimensional relationships listed in 2.1.1.
2.2.1: The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts.
2.2.1.A: Students will demonstrate geometric reasoning and justify conclusions. Although the focus is on geometric theory, answers to some items may include a numeric answer.
2.2.1.B: Corresponding measurements include length, angle measure, perimeter, circumference, area, volume, surface area and lateral area.
2.2.1.a: The student recognizes shapes as congruent or similar, calculates corresponding measurements, and/or justifies conclusions.
2.2.1.b: The student uses congruency and similarity statements to identify corresponding parts of figures.
2.2.2: The student will solve problems using two-dimensional figures and/or right-triangle trigonometry.
2.2.2.A: Students will demonstrate geometric reasoning and justify conclusions.
2.2.2.B: Trigonometric functions may be used to find sides or angles.
2.2.2.C: Trigonometric functions will be limited to sine, cosine, and tangent and their inverses.
2.2.2.a: The student solves a problem involving missing parts of two-dimensional figures, which may require the use of right-triangle trigonometry, the Pythagorean theorem, or special right triangle relationships.
220.127.116.11: The student will use geometric mean and relationships between parts of a right triangle and the altitude drawn to the hypotenuse to find missing parts of right triangles.
2.3.1: The student will use algebraic and/or geometric properties to measure indirectly.
2.3.1.A: ?Measure indirectly? means to use mathematical concepts such as congruence, similarity, and ratio and proportion to calculate measurements.
2.3.1.B: Similarity and congruence will be directly stated or implied (scale drawings, enlargements.)
2.3.2: The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two- and three-dimensional figures and their parts.
2.3.2.A: Two-dimensional shapes include polygons, circles, and composite figures.
2.3.2.B: Three-dimensional shapes include cubes, prisms, pyramids, cylinders, cones, spheres, and composite figures.
2.3.2.C: Formulas will be provided.
2.3.2.D: No oblique solids will be used.
2.3.2.E: Items may involve applications of geometric properties and relationships.
2.3.2.a: The student solves a problem involving perimeter, area, surface area, lateral area, circumference, and/or volume expressing solutions with appropriate units.
18.104.22.168: The student will determine properties of oblique solid geometric figures.
22.214.171.124: The student will determine properties of pyramids that have non-square bases.
Correlation last revised: 3/12/2015