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Geometry End-of-Course Assessment
Achievement Level Descriptions
Florida Department of Education/Office of Assessment
December 2012
Geometry End-of-Course Assessment Reporting Category ─ Two-Dimensional Geometry
Students performing at the mastery level of this reporting category will be able to solve and analyze real-world problems involving segments, lines,
angles, polygons, and circles. In addition, students will be able to find measures of angles, sides, perimeters, and areas of polygons and determine the
effect of changes in dimensions. Students will be able to apply transformations to polygons to determine congruence, similarity, and symmetry.
Students will be able to justify and prove properties of triangles and quadrilaterals.
Achievement Level
Level 5
Achievement Level Descriptions
Students will consistently be able to
• find the length, midpoint, and one of the endpoints of a segment;
• identify and use the relationship between special pairs of angles formed by parallel lines and transversals to
solve mathematical and real-world problems;
• determine measures of interior and exterior angles of regular polygons and justify the method used;
• identify, describe, and classify triangles and polygons;
• identify, describe, and classify medians, altitudes, angle bisectors, and perpendicular bisectors of a triangle
and the centers of a triangle;
• use properties of congruent and similar polygons to solve mathematical and real-world problems;
• solve problems by applying theorems involving segments divided proportionally;
• apply transformations to polygons to determine congruence, similarity, and symmetry in mathematical and
real-world contexts;
• solve problems by using and deriving formulas for perimeter and area of polygons and composite figures;
• determine how changes in dimensions affect the perimeter and area of common geometric figures;
• use coordinate geometry to justify measures and characteristics of congruent, regular, and similar
quadrilaterals;
• compare and contrast special quadrilaterals on the basis of their properties;
• use formal proofs to prove theorems involving rectangles, squares, parallelograms, rhombi, trapezoids, and
kites;
• use geometric properties to justify measures and characteristics of congruent and similar triangles;
• prove that triangles are congruent or similar and use the concept of corresponding parts of congruent
triangles;
• apply the inequality theorems to determine relationships about sides and angles within and between
triangles;
• solve real-world problems of right triangles by applying one or more of the following: the Pythagorean
theorem, geometric mean, and properties of 30-60-90 triangles or 45-45-90 triangles;
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Level 5 (continued)
Level 4
• solve problems related to circles and find measures of arcs and angles related to arcs;
• identify the center, radius, and graph of a circle given its equation and identify the equation of a circle given
its center and radius or graph; and
• provide statements and reasons in formal or informal proofs of a geometric idea and distinguish between the
proof of a conjecture and an example that supports a conjecture.
Students will usually be able to
• find the length, midpoint, and one of the endpoints of a segment;
• identify and use the relationship between special pairs of angles formed by parallel lines and transversals to
solve mathematical problems;
• determine measures of interior and exterior angles of regular polygons;
• identify, describe, and classify triangles and quadrilaterals;
• identify and classify medians, altitudes, angle bisectors, and perpendicular bisectors of a triangle and the
centers of a triangle;
• use properties of congruent and similar polygons to solve mathematical or real-world problems;
• solve problems by applying theorems involving segments divided proportionally;
• apply transformations to polygons to determine congruence, similarity, and symmetry in mathematical or
real-world contexts;
• solve problems by using or deriving formulas for perimeter and area of polygons and composite figures;
• determine how changes in dimensions affect the perimeter and area of common geometric figures with a
maximum of six sides;
• use coordinate geometry to find measures and determine characteristics of congruent, regular, and similar
quadrilaterals;
• compare special quadrilaterals on the basis of their properties;
• use formal proofs to prove theorems involving rectangles, squares, parallelograms, and rhombi;
• use geometric properties to find measures and determine characteristics of congruent and similar triangles;
• prove that triangles are congruent or similar and use the concept of corresponding parts of congruent
triangles;
• apply the inequality theorems to determine relationships about sides and angles within and between
triangles;
• solve real-world problems of right triangles by applying one or more of the following: the Pythagorean
theorem, geometric mean, and properties of 30-60-90 triangles or 45-45-90 triangles;
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Level 4 (continued)
Level 3
• solve problems related to circles and find measures of arcs;
• identify the center, radius, or graph of a circle given its equation and identify the equation of a circle given its
center and radius or graph; and
• provide statements and reasons in formal or informal proofs of a geometric idea and provide an example
that supports a conjecture.
Students will generally be able to
• find the length and midpoint of a segment;
• identify and use the relationship between special pairs of angles formed by parallel lines and transversals to
solve simple problems;
• determine measures of interior or exterior angles of regular polygons;
• identify and classify triangles and quadrilaterals;
• identify and classify medians, altitudes, angle bisectors, and perpendicular bisectors of a triangle;
• use properties of congruent and similar polygons to solve simple problems;
• solve problems by applying theorems involving segments divided proportionally;
• apply transformations to polygons to determine congruence, similarity, or symmetry;
• solve problems by using or deriving formulas for perimeter and area of polygons;
• determine how changes in dimensions affect the perimeter or area of triangles or quadrilaterals;
• use coordinate geometry to find measures or determine characteristics of congruent, regular, and similar
quadrilaterals;
• identify or compare special quadrilaterals on the basis of their properties;
• use formal proofs to prove theorems involving parallelograms;
• use geometric properties of triangles to find measures or to justify characteristics of triangles;
• prove that triangles are congruent and use the concept of corresponding parts of congruent triangles;
• apply the inequality theorems to determine relationships about sides and angles within triangles;
• solve real-world problems of right triangles by applying one of the following: the Pythagorean theorem or
properties of 30-60-90 triangles or 45-45-90 triangles;
• solve problems related to circles;
• identify the center, radius, or graph of a circle given its equation; and
• provide statements and reasons in informal proofs of a geometric idea and provide an example that supports
a conjecture.
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Level 2
Students may demonstrate limited ability to
• find the length or midpoint of a segment;
• identify or use the relationship between special pairs of angles formed by parallel lines and transversals to
solve simple problems;
• determine measures of interior angles of regular polygons;
• use properties of congruent or similar polygons to solve simple problems;
• identify and classify triangles;
• apply one transformation to polygons to determine congruence, similarity, or symmetry;
• solve problems using formulas for perimeter or area of polygons;
• determine how changes in dimensions affect the perimeter of common triangles or quadrilaterals;
• use coordinate geometry to justify measures and characteristics of congruent, regular, and similar
quadrilaterals;
• identify special quadrilaterals on the basis of their properties;
• use geometric properties to find measures of congruent or similar triangles;
• identify that triangles are congruent;
• apply the inequality theorems to determine relationships about sides and angles within a triangle;
• solve simple problems of right triangles by applying one of the following: the Pythagorean theorem or
properties of 30-60-90 triangles or 45-45-90 triangles;
• solve simple problems related to circles involving circumference and area; and
• identify the center or radius of a circle given its equation.
Level 1
Performance at this level indicates an inadequate level of success with the challenging content of the Next
Generation Sunshine State Standards for mathematics.
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Geometry End-of-Course Assessment Reporting Category ─ Three-Dimensional Geometry
Students performing at the mastery level of this reporting category will be able to simplify rational and radical expressions. In addition, students will
be able to add, subtract, multiply, and divide radical expressions and simplify results. Students will be able to solve algebraic proportions. Students
will be able to interpret the graph of a quadratic function and solve quadratic equations over the set of real numbers. Students will be able to
perform set operations including union and intersection, complement, and cross product. Students will be able to interpret Venn diagrams.
Achievement Level
Level 5
Level 4
Achievement Level Descriptions
Students will consistently be able to
• identify a net for a regular, nonregular, or oblique polyhedron and identify the regular, nonregular, or
oblique polyhedron for a given net;
• identify and determine types of faces and the number of faces, edges, or vertices of a given polyhedron;
• justify and apply formulas to determine surface area, lateral area, and volume of solids;
• identify and use properties of congruent and similar solids to solve problems;
• identify chords, tangents, radii, and great circles of spheres;
• determine how changes in up to three parameters affect the surface area and volume and how changes in
surface area and volume affect the parameters; and
• determine how changes in up to two parameters affect the other parameter(s) when surface area and
volume are held constant.
Students will usually be able to
• identify a net for a regular or nonregular polyhedron and identify the regular or nonregular polyhedron for a
given net;
• identify and determine types of faces or the number of faces, edges, or vertices of a given polyhedron;
• explain and apply formulas to determine surface area, lateral area, and volume of solids;
• identify and use properties of congruent or similar solids to solve problems;
• identify chords, tangents, radii, or great circles of spheres;
• determine how changes in no more than two parameters affect the surface area and volume; and
• determine how changes in one parameter affect the other parameter(s) when surface area and volume are
held constant.
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Level 3
Students will generally be able to
• identify a net for a regular polyhedron and identify the regular polyhedron for a given net;
• identify and determine types of faces or the number of faces or edges of a given polyhedron;
• apply formulas to determine surface area, lateral area, or volume of solids;
• identify and use properties of congruent or similar solids to solve simple problems;
• identify chords, tangents, or radii of spheres;
• determine how changes in one parameter affect the surface area or volume; and
• determine how changes in one parameter affect the other parameter(s) when volume is held constant.
Level 2
Students may demonstrate limited ability to
• identify a net for a regular polyhedron;
• identify or determine the number of faces, edges, or vertices of a given polyhedron;
• use formulas to determine surface area or volume of solids;
• identify congruent or similar solids to solve simple problems; and
• determine how changes in one parameter affect the volume.
Level 1
Performance at this level indicates an inadequate level of success with the challenging content of the Next
Generation Sunshine State Standards for mathematics.
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Geometry End-of-Course Assessment Reporting Category ─ Trigonometry and Discrete Mathematics
Students performing at the mastery level of this reporting category will be able to use trigonometry to solve real-world problems involving right
triangles. In addition, students will be able to identify a conditional statement and write the converse, inverse, and contrapositive.
Achievement Level
Level 5
Level 4
Level 3
Level 2
Level 1
Achievement Level Descriptions
Students will consistently be able to
• identify the converse, inverse, and contrapositive of a given statement;
• determine whether two propositions are logically equivalent in mathematical and real-world contexts; and
• solve problems using the trigonometric ratios sine, cosine, and tangent to determine side lengths and angle
measures.
Students will usually be able to
• identify the converse, inverse, or contrapositive of a given statement;
• determine whether two propositions are logically equivalent in mathematical or real-world contexts; and
• solve problems using the trigonometric ratios sine, cosine, or tangent to determine side lengths or angle
measures.
Students will generally be able to
• identify the converse and inverse of a given statement in if-then form;
• determine whether two propositions are logically equivalent in mathematical contexts; and
• solve problems using no more than one trigonometric ratio to determine side lengths or angle measures.
Students may demonstrate limited ability to
• identify the converse or inverse of a given statement in if-then form; and
• solve problems using no more than one trigonometric ratio to determine side lengths.
Performance at this level indicates an inadequate level of success with the challenging content of the Next
Generation Sunshine State Standards for mathematics.
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