CCSD Proficiency Scale - Language of Geometry

Transcription

1 CCSD Scale - Language of Geometry Content Area: HS Math Grade : Geometry Standard Code: G-CO.1 application G-CO.1 Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc Standard, Create complex figures, when given a description, that incorporates multiple terms with correct notation/labels. Skills/content that encompass the - Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruency, parallel, perpendicular, etc.) - Identify segments, lines, and rays - Classify angles (right, acute, obtuse, congruent) - Identify special angle pairs (vertical, linear, complementary, supplementary) - Classify polygons and their parts (side, vertex, diagonal, convex/concave, congruency, equiangular, equilateral, regular) - Classify triangles (right, acute, obtuse, scalene, equilateral, isosceles) - Classify quadrilaterals (trapezoid, kite, parallelogram, rhombus, rectangle, square) - Classify circles and their parts (radius, chord, diameter, tangent, arc and measure, central angle) - Measure segments and angles - Classify construction vocabulary. - Create geometric constructions using a compass and straightedge. - Interpret and construct points of concurrency. specific vocabulary, point, line, plane, angle, segment, circle, parallel, perpendicular, arc Identify geometric objects in an illustration.

2 CCSD Scales - Reasoning Content Area: HS Math Grade : Geometry Standard Code: G-CO.9 application G-CO.9 Prove theorems about lines and angles. Standard, Prove complex concepts about lines and angles using conjectures. Skills/content that encompass the - Evaluate inductive reasoning techniques - Evaluate & implement deductive reasoning techniques (basic proof) - Use inductive reasoning to extend patterns (sequences, nth-term, etc.) - Develop and apply math models to solve problems - Apply angle conjectures (angle bisector, vertical angles) - Identify angles formed by two lines and a transversal (corresponding, alternate interiors and exteriors) - Use properties and conjectures of parallel lines and their angles - Use transversal to prove or disprove lines are parallel When given a proof with missing statements or reasons, the student will correctly fill in the blanks

3 CCSD Scale - Triangle Congruence Content Area: HS Math Grade : Geometry Standard Code: G-CO.10 application G-CO.10 Prove theorems about triangles Standard, Write proofs to show that two triangles are congruent or that one pair of corresponding parts of congruent triangles are congruent. Skills/content that encompass the - Find measures of angles using triangle interior and exterior angle properties - Apply isosceles triangle conjecture and its converse - Classify and label congruent figures and their corresponding parts - Prove two triangles are congruent using SSS, SAS, ASA, AAS conjectures - Evaluate congruence conjectures as valid or invalid - Use triangle congruence conjectures and CPCTC to prove that parts of two triangles are congruent - Apply the triangle inequality and side-angle inequality conjectures - Apply the vertex angle bisector conjecture specific vocabulary, congruent, angle, side, rigid motion Given two congruent triangles, write congruency statements using correct notation.

4 CCSD Scale - Parallelogram Congruence Content Area: HS Math Grade : Geometry Standard Code: G-CO.11 application G-CO.11 Prove theorems about parallelograms. Standard, Prove complex concepts involving congruence. Skills/content that encompass the - Calculate the measures of the interior angles of polygons - Calculate the measures of exterior angles of polygons - Define and classify special types of quadrilaterals - Apply kite properties and conjectures - Apply trapezoid properties and conjectures - Apply midsegment conjectures to solve problems - Apply parallelogram properties and conjectures - Apply properties and conjectures of rhombi, rectangles, and squares - Prove conjectures using triangle and quadrilateral properties such as: When creating a proof about parallelograms, the student will create a correct sequence of reasoning, using valid triangle congruency to prove the property (some slight structural and/or technical misapplications may be present, as defined in the scoring guide).

5 CCSD Scale - Coordinate Geometry Content Area: HS Math Grade : Geometry Standard Code: G-GPE.4 application G-GPE.4 Use coordinates to prove simple geometric theorems algebraically. Standard, Given four points in a coordinate plane, classify and justify the quadrilateral created by connecting the points in order. Skills/content that encompass the - Use coordinate geometry to classify quadrilaterals - Use coordinate geometry to prove conjectures about quadrilaterals such as: Use the distance formula to find the distance between two points Determine if two lines in the coordinate plane are perpendicular by comparing the slopes of the lines

6 CCSD Scale - Transformations Content Area: HS Math Grade : Geometry Standard Code: G-CO.5 application G-CO.5.a Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Standard, -Create a sequence of transformations to produce a desired image. Skills/content that encompass the - Describe a series of transformations to map one figure onto another - Create a transformation given an algebraic mapping - Generalize the effects of transformations of figures using coordinates - Represent transformations algebraically specific vocabulary, translation, shift, slide, rotation, reflection, symmetry, transform When given two geometric figures, the student will describe the transformation (or combination of transformations) that would map the preimage to the image. The descriptions are not precise.

7 CCSD Scale - Circles Content Area: HS Math Grade : Geometry Standard Code: G-C.2 application G-C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Standard, Solve complex application problems involving topics such as circumference, radius, diameter, area, dimensional analysis, proportionality. Skills/content that encompass the - Solve for missing lengths or angles in and around circles using tangent conjectures - Use congruent chords, arcs, and central angles to find unknown measurements in and around circles - Find the measure of inscribed angles and intercepted arcs of circles - Solve for the measures of angles formed by chords, secants, and tangents - Solve for missing angles in and around circles using cyclic quadrilateral conjecture - Calculate the circumference of a circle and apply to applications - Calculate arc lengths using circumference conjecture specific vocabulary, central angle, inscribed angle, Use information from a single conjecture to answer questions about circles.

8 CCSD Scale - Trigonometry Content Area: HS Math Grade : Geometry Standard Code: G-SRT.8 application G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems Standard, Solve application problems with multiple triangles/steps. Skills/content that encompass the - Apply the Pythagorean Theorem & its converse - Apply & triangle shortcuts - Calculate the area of an equilateral triangle given the side length or altitude (using shortcut) - Calculate the distance between two points - Apply tangent, sine, and cosine ratios to determine side lengths - Use tangent, sine, and cosine inverses to determine angle measurements - Apply tangent ratios to indirect measurement applications specific vocabulary, sine, cosine, tangent, ratio When given a right triangle, write a given trig ratio.

9 CCSD Scale - Volume Content Area: HS Math Grade : Geometry Standard Code: G-GMD.3 application Standard, Maximize the volume of a package while minimizing the area of said package G-GMD.3 Use volume formulas for cylinders, pyramids, cones and spheres to solve problems. Skills/content that encompass the - Calculate the area or missing lengths of polygons (parallelograms, triangles, trapezoids, kits, regular polygons) - Calculate the area or circles, sectors, and segments of circles - Calculate the surface area of three-dimensional objects (prisms, pyramids, cylinders, cones) - Classify polyhedrons and other three-dimensional figures and their parts - Solve for the volume or unknown parts of a prism - Solve for the volume or unknown parts of a cylinder/portion of cylinder - Solve for the volume or unknown parts of a pyramid/cone - Solve for the volume and surface area of a sphere or portions of a sphere Identify 3-D shapes and their volume formulas find the volume of simple 3-D geometric shapes

10 CCSD Scale - Similarity Content Area: HS Math Grade : Geometry Standard Code: G-SRT.5 application G-SRT.5 Use triangle congruence and similarity criteria to solve problems and to prove relationships in geometric figures. Standard, Use similarity to solve indirect measurement problems. Skills/content that encompass the - Write valid ratios and solve proportions using similarity - Identify and apply properties of similar polygons - Apply AA, SAS, and SSS similarity conjectures - Design and solve similarity problems for indirect measurement specific vocabulary, ratio, proportion, Use proportional sides or congruent angles to solve a simple similarity problem with a given diagram