GEOMETRY STANDARDS BASED RUBRIC

Transcription

1 GEOMETRY STANDARDS BASED RUBRIC LOCAL STANDARD: KNOW AND APPLY THE BASIC DEFINITION AND UNDEFINED TERMS OF GEOMETRY. Unable to construct (straight edge and compass) the midpoint of a segment, the triangle bisection, and the perpendicular bisections of a Unable to derive the equation of a line through two given points and derive the equation of a line perpendicular to the original line through a given point. Unable to identify or give examples of the three undefined terms of geometry (point, line, and plane). Inconsistently constructs (straight edge and compass) the midpoint of a segment, the triangle bisection, and the perpendicular bisections of a Inconsistently able to derive the equation of a line through two given points and derive the equation of a line perpendicular to the original line through a given point. Inconsistently identifies or gives examples of the three undefined terms of geometry (point, line, and plane). Unable to identify or classify Inconsistently identifies or classifies Unable to classify triangles as acute, Inconsistently classifies triangles as obtuse, or right. acute, obtuse, or right. Unable to identify the midpoint, bisection, and perpendicular bisection of a given Inconsistently identifies the midpoint, bisection, and perpendicular bisection of a given Constructs (straight edge and compass) the midpoint of a segment, the triangle bisection, and the perpendicular bisections of a Derives the equation of a line through two given points and derives the equation of a line perpendicular to the original line through a given point. Identifies or gives examples of the three undefined terms of geometry (point, line, and plane). Applies the construction to other problems. Takes the equation defined in proficient column and change it to another form, standard, point, slope or general. Explains the necessity for the undefined terms. Identifies or classifies angles Uses the classification of angles to solve other problems. Classifies triangles as acute, obtuse, Uses the classification of triangles to or right solve other problems. Identifies the midpoint, bisection, Uses the properties of midpoint, and perpendicular bisection of a bisection, and perpendicular given bisections of a given PROVE, USE AND ANALYZE PARALLEL LINES. Identify the types of angles created by a transversal passing through two lines. Identifies parallel lines based on angles created by a transversal. Construct a copy of a given angle. Demonstrates knowledge of parallel line construction but not correctly completed. Proves (formally or informally) lines are parallel using postulates and theorems. Constructs a line parallel to a given line and passing through a given point not on the given line. Formally proves lines are parallel. Constructs and justifies parallel lines in multiple ways based on parallel line theorems. 1

2 PERFORM BASIC TRANSFORMATIONS ON VARIOUS GEOMETRIC FIGURES. Unable to identify and perform translations, reflections, and rotations of line segments and Inconsistently identifies and performs translations, reflections, and rotations of line segments and May be able to perform, but not both. Identifies and performs translations, reflections, and rotations of line segments and Identifies and performs combinations of two or more transformations. PROVE, USE, AND ANALYZE TRIANGLES. Unable to solve for the missing side of a right triangle using the Pythagorean theorem. Inconsistently will solve for the missing side of a right triangle using the Pythagorean theorem. Solves for the missing side of a right triangle using the Pythagorean theorem. Applies to a word problems the use of the Pythagorean theorem and its converse. Unable to prove, formally or Inconsistently able to prove, formally Proves triangles congruent line SAS, Formally proves and applies triangles informally, triangles congruent line SAS, SSS, ASA, AA s, and/or numbers. or informally, triangles congruent line SAS, SSS, ASA, AA s, and/or SSS, ASA, AA s, and/or numbers. being congruent. Unable to calculate lengths and angles related to triangles including the mid-segment and the corresponding parts. Unable to prove two triangles similar by AA, SAS and/or SSS. Unable to use the triangle inequality theorem. numbers. Inconsistently calculates lengths and angles related to triangles including the mid-segment and the corresponding parts. Inconsistently able to prove two triangles similar by AA, SAS and/or SSS. Inconsistently able to use the triangle inequality theorem. Calculates lengths and angles related to triangles including the midsegment and the corresponding parts. Proves two triangles similar by AA, SAS and/or SSS. Applies the mid-segment theorem and corresponding parts of triangles to other problems. Applies the proof of similar triangles to prove other problems. Uses the triangle inequality theorem. Applies the triangle inequality theorem. ABLE TO USE AND APPLY TRIGONOMETRIC FUNCTIONS. 2

3 Unable to evaluate the sine, cosine, Inconsistently able to evaluate the Evaluates the sine, cosine, and Finds the degree measure of an acute and tangent of a given angle. sine, cosine, and tangent of a given tangent of a given angle. angle given its sine, cosine or Unable to evaluate the sine, cosine, and tangent of a given angle. Unable to use the trigonometric functions to solve for unknown parts of a triangle. angle. Inconsistently able to evaluate the sine, cosine, and tangent of a given angle. Inconsistently able to use the trigonometric functions to solve for unknown parts of a triangle. Unable to apply the law of sines. Inconsistently applies the law of sines. Unable to recognize the identity of Inconsistently recognizes the identity Tan A=sin A of Tan A=sin A Unable to use the special right triangle, e.g., 30, 60, 90 ; 45 m 45, 90 to solve for missing parts of a right triangle. Unable to use the special right triangles to calculate the sine, cosine, and tangent. Unable to identify the relationship of the various sides of Inconsistently able to use the special right triangle, e.g., 30, 60, 90 ; 45, 45, 90 to solve for missing parts of a right triangle. Inconsistently able to use the special right triangles to calculate the sine, cosine, and tangent. Inconsistently able to identify the relationship of the various sides of Evaluates the sine, cosine, and tangent of a given angle. Uses the trigonometric functions to solve for unknown parts of a triangle. tangents. Finds the degree measure of an acute angle given its sine, cosine or tangents. Uses the trigonometric functions to solve a word problem. Applies the law of sines. Applies and proves the law of sines. Recognizes the identify of Tan A=sin A Uses the special right triangle, e.g., 30, 60, 90 ; 45, 45, 90 to solve for missing parts of a right triangle. Uses the special right triangles to calculate the sine, cosine, and tangent. Identifies the relationship of the various sides of Uses the identify of Tan A=sin A Applies the special right triangle, e.g., 30, 60, 90 ; 45, 45, 90 in other problems. Applies the special right triangles to calculate the sine, cosine, and tangent to other problems. Uses the relations of various sides and POLYGONS IDENTIFIES AND WORKS WITH POLYGONS AND THEIR RELATED GEOMETRIC FEATURES. Recognizes a quadrant has four sides. Recognizes different types of quadrants. Identifies types of quadrants based on sides and angles of Identifies quadrant based on properties of diagonals. Calculates perimeter given all side measurements. Inconsistently calculates perimeter and area of Calculates perimeter and area of Applies perimeter and area to real-life situations. Unable to identify polygons by Identifies types of polygons by Identifies types of polygons by Identifies word origins. sides and Unable to calculate interior and exterior angles and angle sums using informal methods (dividing into triangles). sides and angles with assistance. Inconsistently calculates interior and exterior angles and angle sum using informal methods (dividing into triangles). sides and Calculates interior and exterior angles and angle sum using informal methods (dividing into triangles). Calculates interior and exterior angles using formal methods (using formulas). CIRCLES 3

4 ABLE TO IDENTIFY AND WORK WITH CIRCLES AND THEIR RELATED GEOMETRIC FEATURES. Unable to identify parts of a circle such as chords, secants, tangents, major arcs, minor arcs, central and inscribed Inconsistently identifies parts of a circle such as chords, secants, tangents, major arcs, minor arcs, central and inscribed Identifies parts of a circle such as chords, secants, tangents, major arcs, minor arcs, central and inscribed Unable to calculate measures of circles such as area, circumference, and central Inconsistently calculates measures of circles such as area, circumference, and central Calculates measures of circles such as area, circumference, and central Gives the names for parts of circles in more than one way. Knows the background behind the names. Proves calculations and supports their solutions. THREE-DIMENSIONAL FIGURES ABLE TO SOLVE PROBLEMS INVOLVING THREE-DIMENSIONAL FIGURES. Unable to find volume of solids. Unable to find surface area of solids. Unable to determine how changes in dimensions affect perimeter, area, and volume (e.g., r:r 3 :r 3 ). Inconsistently able to find volume of solids. Inconsistently able to find surface area of solids. Inconsistently determines how changes in dimensions affect perimeter, area, and volume (e.g., r:r 3 :r 3 ). Finds the volume of solids. Finds the surface area of solids. Determines how changes in dimensions affect perimeter, area, and volume (e.g., r:r 3 :r 3 ). Finds the volume of combinations of solids. Finds the surface area of combinations of solids. Applies to real-life situations. STUDENTS UNDERSTAND AND EXHIBIT THE RIGHTS AND EXHIBIT THE RIGHTS AND INDIVIDUAL RESPONSIBILITIES OF CITIZENSHIP (L.S.) 4

5 Rarely completes or turns in documents when due. Occasionally turns in complete or partially completed documents when due. Turns in completed documents when due. Submits completed documents on time and shows a willingness to revise and redo assignments to improve score. Frequently is disrespectful of people and/or property. Fails to show proper respect for people and property. Shows respect for people and property. Is respectful and helpful to classmates and handles property with care. Lacks an interest in learning. Shows moderate interest in learning. Shows a high interest in learning and a strong work ethic. Maintains a high interest in learning and is willing to work hard to accomplish difficult tasks or to master difficult concepts. Is disorganized and unprepared for class. Fails to always be prepared and organized for class. Is always prepared and organized for class. Is well prepared for class and maintains personal organization to ensure that class requirements can be met. Excessive tardiness and/or absences interfere with academic success. Irregular attendance and/or frequent tardiness affect academic success. Attends school and class regularly and on time. Attends school and class regularly and on time and is willing to work outside of the regular school day to improve performance and master concepts. Rarely completes or turns in classroom work. Inconsistently turns in completed work. Classroom work completed in a timely manner. Completes classroom work in a timely manner and maintains an academic focus in class. T:\website\WORD\RUBRICS\MATH, 7-12\GEOMETRY.doc 5