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© 2003 by
Cobb County School District
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Scantron Corporation.
All Rights Reserved.
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Scantron Corporation
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Cobb County School District |
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Mathematics (Updated July 2003) |
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Mathematics - Geometry |
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Goals and Descriptions |
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PS1: ATTRIBUTES AND UNITS
The learner will be able to
select appropriate standard units for measuring.
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M.GEOM.1.1 Units of Measurement: Appropriate
The learner will be able to
define and differentiate among perimeter, area, and volume, and the appropriate units for each.
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PS2: TOOLS AND FORMULAS
The learner will be able to
estimate, measure, and compute with formulas in problem solving.
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M.GEOM.2.1 Area: 2D
The learner will be able to
find area of triangles, parallelograms, rectangle, squares, (M/R) trapezoids, rhombi, kites, regular polygons, circles and sectors.
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M.GEOM.2.2 Three-Dimensional Solids: Area
The learner will be able to
find the lateral and total surface areas of right prism, regular pyramids, right circular cylinders, cones, and spheres.
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M.GEOM.2.3 Three-Dimensional Solids: Volume
The learner will be able to
find the volume of solids composed of prisms, pyramids, cylinders, cones and spheres.
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M.GEOM.2.4 Perimeter: Area: Volume
The learner will be able to
solve problems involving perimeter, area, and volume.
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M.GEOM.2.5 Triangles: Find/Midsegment Triangles
The learner will be able to
find segment lengths by applying the midsegment theorem for triangles.
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M.GEOM.2.6 Formulas: Deriving/Area/Circles
The learner will be able to
find the perimeter of polygons, the circumference of circles, and arc lengths.
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M.GEOM.2.7 Coordinate Geometry: Find/Coordinates
The learner will be able to
find coordinates that would complete a specific figure.
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M.GEOM.2.8 Formula: Distance and Midpoint
The learner will be able to
apply the distance and midpoint formulas.
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M.GEOM.2.9 Coordinate Plane: Graph/Plot
The learner will be able to
identify and graph ordered pairs on the coordinate plane.
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PS3: FIGURES IN SPACE
The learner will be able to
analyze properties of geometric shapes, develop related mathematical arguments, and solve related problems.
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M.GEOM.3.1 Figures: Find/Necessary/Part
The learner will be able to
find the parts that are necessary to make a particular figure given some of the figure's properties.
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M.GEOM.3.2 Properties: State/Apply
The learner will be able to
state and apply properties of triangles and quadrilaterals such as parallelograms, rectangles, rhombi, squares, and trapezoids.
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M.GEOM.3.3 Properties: Quadrilaterals
The learner will be able to
use properties of quadrilaterals to establish and/or test relationships involving sides, medians (trapezoids), diagonals, angles, and lines of symmetry.
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M.GEOM.3.4 Circles: Identify/Define
The learner will be able to
identify and define circles and their parts,( center, arc, interior, exterior); segments and lines associated with circles (chord, diameter, radius, tangent, secant): properties of circles (congruent, concentric, tangent); congruence of polygons and circles (inscribed and circumscribed).
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M.GEOM.3.5 Angles: Identify
The learner will be able to
identify and define angles (central; inscribed; formed by tangents, chords, and secants.
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M.GEOM.3.6 Solids: Polyhedrons/Spheres
The learner will be able to
identify polyhedrons and their components including prisms, pyramids, cubes, tetrahedrons, cylinders, cones, spheres, faces, edges, vertices, bases, diagonals, and lateral edges.
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M.GEOM.3.7 Geometric Terms: Identify
The learner will be able to
identify the geometric term when given a definition or description.
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M.GEOM.3.8 Angles: Understand
The learner will be able to
name, identify, classify, describe, and measure segments and angles (acute, obtuse, right, straight, adjacent, vertical, linear pair, complementary, supplementary, congruent).
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M.GEOM.3.9 Lines/Angles: Identify
The learner will be able to
identify, name, and define or describe properties associated with points (distance, between, collinear, coplanar), segments (midpoint, congruence, bisector) angle (bisector, congruence, interior, exterior) and lines and planes (perpendicular, parallel, intersecting).
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M.GEOM.3.10 Planes/Points/Lines: Recognize
The learner will be able to
identify, describe, and contrast points, lines, planes, segments and rays.
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M.GEOM.3.11 Triangles: Sorting
The learner will be able to
classify triangles by sides and angles.
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PS4: SPATIAL RELATIONSHIPS
The learner will be able to
make, test, and validate conjectures associated with spatial relationships in problem solving.
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M.GEOM.4.1 Reasoning: Apply/Formal/Informal
The learner will be able to
apply formal and/or informal logical reasoning methods to geometric, algebraic, or non-mathematical scenarios.
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M.GEOM.4.2 Proof: Recognize/Complete/Statement
The learner will be able to
recognize a statement or justification necessary to complete an informal proof.
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M.GEOM.4.3 Reasoning: Inductive/Deductive
The learner will be able to
uses inductive and deductive reasoning to prove conjectures in written form such as paragraph, two-column or flow chart.
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M.GEOM.4.4 Planes/Points/Lines: Apply/Facts
The learner will be able to
apply basic facts about points, lines and planes, and about perpendicular and parallel lines and planes.
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M.GEOM.4.5 Theorems: Apply/State
The learner will be able to
state and apply the triangle sum theorem.
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M.GEOM.4.6 Congruence: Identify
The learner will be able to
identify congruent figures and recognize congruence in practical applications.
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M.GEOM.4.7 Right Triangles: Identify
The learner will be able to
identify congruent triangle and right triangles using basic congruence postulates and theorems.
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M.GEOM.4.8 Triangles: Identify/Congruent
The learner will be able to
use properties of congruence to test conjectures involving triangles.
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M.GEOM.4.9 Similarity: Properties
The learner will be able to
recognize and apply properties of similar polygons using ratio and proportion.
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M.GEOM.4.10 Parallel Lines: Use/Properties
The learner will be able to
apply properties dealing with parallel lines and proportion.
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M.GEOM.4.11 Problem Solving: Polygons
The learner will be able to
solve problems involving similar polygons.
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M.GEOM.4.12 Pythagorean Theorem: State/Apply
The learner will be able to
state and apply the Pythagorean Theorem and its converse.
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M.GEOM.4.13 Right Triangles: Recognize
The learner will be able to
recognize a statement that is true given a right triangle.
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M.GEOM.4.14 Problem Solving: Trigonometry
The learner will be able to
use the tangent, sine and cosine ratios for right triangles to solve problems such as indirect-measurement problems.
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M.GEOM.4.15 Problem Solving: Circles
The learner will be able to
apply geometric relationships to solve problems, such as relationships between lines and segments associated with circles.
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M.GEOM.4.16 Problem Solving: Arcs
The learner will be able to
applies geometric relationships to solving problems such as relationships between lines and angles they form, and the arcs they subtend and the measures of these arcs, angles, and segments.
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M.GEOM.4.17 Polygons: Classify
The learner will be able to
classify polygons as being regular, convex, and congruent.
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M.GEOM.4.18 Angles: Parallel lines
The learner will be able to
recognize parallel lines and planes, skew lines, and pairs of angles when two lines are cut by a transversal (alternate and same side, interior and exterior, corresponding).
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M.GEOM.4.19 Lines/Angles: Identify/Use
The learner will be able to
recognize and apply inequality properties with the measurements of segments in triangles and angles in triangles.
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M.GEOM.4.20 Angles: Sum of Angles of a Polygon
The learner will be able to
state and apply the exterior and interior polygon angle sum theorems.
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M.GEOM.4.21 Congruence/Symmetry/Similar
The learner will be able to
recognize an explanation of the symmetry, similarity, or congruence of geometric figures.
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M.GEOM.4.22 Similarity: Triangles
The learner will be able to
identify similar figures in practical applications; identify similar triangle polygons by using their properties.
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M.GEOM.4.23 Lines: Find/Length/Transversals
The learner will be able to
find segment lengths on the transversals of 3 or more parallel lines.
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M.GEOM.4.24 Right Triangles: Use/Properties
The learner will be able to
state and apply properties of special right triangles such as 30-60-90 and 45-45-90 triangles.
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M.GEOM.4.25 Right Triangles: Identify/Evaluate
The learner will be able to
identify and evaluate tangent, sine, and cosine ratios for an acute angle of a right triangle and apply a table, calculator, or computer to determine the ratio for a given angle or the angle for a given ratio.
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M.GEOM.4.26 Circumference: Recognize/Circle
The learner will be able to
estimate and recognize the circumference of circles using regular, irregular, and combined inscribed and circumscribed figures.
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M.GEOM.4.27 Compare: similar 2D and 3D
The learner will be able to
compare the areas of similar polygons and the volumes of similar solids.
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M.GEOM.4.28 Constructions: Use/Tools
The learner will be able to
use tools such as compass and straight edge, paper folding, tracing paper, Mira, or computer to construct segments, angles, triangle, and circles, an angle bisector, a perpendicular bisector, a perpendicular line from a point on a line; parallel lines, proportional segments; tangents; and inscribed and inscribed polygons.
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M.GEOM.4.29 Spatial Thinking: Identify
The learner will be able to
find the image of figures under preserving transformations such as line reflection, translation and rotations.
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M.GEOM.4.30 Transformations: Dilations
The learner will be able to
find the image of figures under dilations.
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M.GEOM.4.31 Transformations: Examine/Apply
The learner will be able to
examine and apply basic properties of line reflections, translations, rotations, dilations, and/or their compositions.
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M.GEOM.4.32 Transformations: Use
The learner will be able to
use transformations to examine symmetry, similarity, and/or congruence of geometric figures.
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PS5: ALGEBRAIC MODELS/PROBLEM SOLVING
The learner will be able to
use symbolic algebra and reasoning to solve problems.
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M.GEOM.5.1 Connecting: Algebra/Geometry
The learner will be able to
use algebraic skills and concepts to solve geometric problems throughout geometry, especially when given data about relationships between angles and lines.
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M.GEOM.5.2 Coordinate Geometry: Explore
The learner will be able to
use coordinate methods to explore, conjecture, or prove properties of geometric figures using tools of algebra, graphing, and/or suitable technology.
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M.GEOM.5.3 Coordinate Geometry: Find Coordinates
The learner will be able to
find and recognize the coordinates of the point of intersection of two lines using algebra, graphing, and/or appropriate technology.
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M.GEOM.5.4 Linear Equations: Write
The learner will be able to
find the slope of a line: write an equation of a line: graph equation of a line.
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PS6: PATTERNS/RELATIONS/FUNCTIONS
The learner will be able to
identify, analyze, and represent relations and functions.
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M.GEOM.6.1 Patterns: Number/Determine/Missing
The learner will be able to
determine a specific missing element from a numerical pattern.
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PS7: PROBLEM SOLVING
The learner will be able to
solve routine and nonroutine problems, including real world problems, that involve math concepts and skills associated with the Pre-Algebra math curriculum.
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M.GEOM.7.1 Inductive/Deductive: Prove/Conclusions
The learner will be able to
apply inductive and deductive reasoning to reach conclusions, verify conjectures and counterexamples and describe the nature of a deductive conclusions system.
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M.GEOM.7.2 Reasoning: Recognize
The learner will be able to
recognize valid deductive reasoning; constructs and use of if-then, converse, inverse and contrapositive statements.
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M.GEOM.7.3 Geometric Relationships: Problems
The learner will be able to
solve problems and practical applications using appropriate approaches and tools (including calculators and computer) and judges the reasonableness of the results.
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M.GEOM.7.4 Problem Solving: Visualization
The learner will be able to
use visualization skills to explore and interpret both two and three-dimensional geometric figures using such topics as projections, cross sections, and locus problems.
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й 2003 Cobb County School
District. All Rights Reserved
514 Glover Street | Marietta, Ga. 30060 | (770) 426-3300
Send your comments to Sue Brown
visitors since July 18, 2003
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