Correlations to the Secondary Mathematics Benchmarks

KEY:

Geometry

G.A.1 Angles and triangles.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know the definitions and basic properties of angles and triangles in the plane and use them to solve problems. D.1 PK.C.1 K2, K2.3, K3, K5 8, 21
b. Know and prove basic theorems about angles and triangles. F.1 PK.C.2 K2, K2.3, K3

G.A.2 Rigid motions and congruence.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Represent and explain the effect of translations, rotations, and reflections of objects in the coordinate plane. F.2 E.1 K6
b. Identify corresponding sides and angles between objects and their images after a rigid transformation. F.2 E.1
c. Show how any rigid motion of a figure in the plane can be created by some combination of translations, rotations, and reflections. F.2 E.1 K6

G.A.3 Measurement.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Make, record, and interpret measurements. C.1 PK.B.1 K8.2
b. Apply units of measure in expressions, equations, and problem situations. C.1 PK.B.1 K8.1
c. Use measures of weight, money, time, information, and temperature. C.1 PK.B.1
d. Record measurements to reasonable degrees of precision, using fractions and decimals as appropriate. C.1 PK.B.1 K8 24

G.A.4 Length, area, and volume.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Identify and distinguish among measures of length, area, surface area, and volume. C.2 PK.B.2 K8.2
b. Calculate the perimeter and area of triangles, quadrilaterals, and shapes that can be decomposed into triangles and quadrilaterals that do not overlap. C.2 PK.B.2 K8.2 17, 19
c. Determine the surface area of right prisms and pyramids whose base(s) and sides are composed of rectangles and triangles. C.2 part PK.B.2 part D.1 E.1 part K8.2 19
d. Know, and apply formulas for the surface area of right circular cylinders, right circular cones, and spheres. C.2 part PK.B.2 part D.1 part E.1 part K8.2 7
e. Know, and apply formulas for the volume of right prisms, right pyramids, right circular cylinders, right circular cones, and spheres. C.2 part PK.B.2 part D.1 part E.1 part K8.2 7
f. Estimate lengths, areas, surface areas, and volumes of irregular figures and objects. C.2 part PK.B.2 part E.1 K9

G.B.1 Angles in the plane.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know and distinguish among the definitions and properties of vertical, adjacent, corresponding, and alternate interior angles. D.1 PK.C.1 K2.1, K2.3 8
b. Identify pairs of vertical angles and explain why they are congruent. D.1 PK.C.1 K2.3 8
c. Identify pairs of corresponding, alternate interior, and alternate external angles in a diagram where two parallel lines are cut by a transversal and show that they are congruent. D.1 PK.C.1 K2.3 8
d. Explain why, if two lines are intersected by a third line in such a way as to make the corresponding angles, alternate interior angles, or alternate exterior angles congruent, then the two original lines must be parallel. D.1 B.2 K2.3 8
e. Apply properties of lines and angles to perform basic geometric constructions. D.2 B.3 K2, K2.1, K2.3

G.B.2 Coordinates and slope.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Represent and interpret points, lines, and two-dimensional geometric objects on a coordinate plane. G.3 E.2 K10 19
b. Determine the area of polygons in the coordinate plane. G.3 E.2 K10
c. Know how the word slope is used in common non-mathematical contexts, give physical examples of slope, and calculate slope for given examples. G.3 E.2 K10.1
d. Calculate the slope of a line in a coordinate plane. G.3 E.2 K10.1
e. Interpret and apply slope of parallel and perpendicular lines in a coordinate plane. G.3 E.2

G.B.3 Pythagorean theorem.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Interpret and prove the Pythagorean theorem and its converse. A.4 A.3 K1.2, K5
b. Determine distances between points in the Cartesian coordinate plane. A.4 A.3 K10.3
c. Apply the Pythagorean theorem and its converse to solve problems. A.4 A.3 K5 1

G.B.4 Circles.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Identify and explain the relationships among the radius, diameter, circumference, and area of a circle. D.2 F.1 K4 25
b. Show that for any circle, the ratio of the circumference to the diameter is the same as the ratio of the area to the square of the radius and that these ratios are the same for different circles. D.2 F.1
c. Know and apply formulas for the circumference and area of a circle. D.2 F.1 K4, K8.2 7, 25

G.B.5 Scaling, dilation, and dimension.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Analyze and represent the effects of multiplying the linear dimensions of an object in the plane by a constant scale factor, r. B.2 G.2 K8.3 19
b. Describe the effect of a scale factor r on length, area, and volume. B.2 G.2 A.2 part K8.3 19
c. Recognize and use relationships among volumes of common solids. A.3 E.1 K8.2
d. Interpret and represent origin-centered dilations of objects in the coordinate plane. A.4 C.4 19

G.B.6 Similarity and congruence.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Interpret the definition and characteristics of similarity for triangles in the plane. B.3 G.3 K3, K7 1
b. Apply similarity in practical situations. B.3 G.3 K3, K7 1
c. Identify and apply conditions that are sufficient to guarantee similarity of triangles. A.5 C.1 K3 1
d. Explain why congruence is a special case of similarity; determine and apply conditions that guarantee congruence of triangles. A.6 C.2 K3 8
e. Apply the definition and characteristics of congruence to make constructions, solve problems, and verify basic properties of angles and triangles. A.6 C.2 K3, K7 8
f. Extend the concepts of similarity and congruence to other polygons in the plane. A.7 C.3 K7

G.B.7 Visual representations.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Relate a net, top-view, or side-view to a three-dimensional object that it might represent. E.1 PK.D.1 K9 7
b. Draw two-dimensional representations of three-dimensional objects by hand and using software. E.1 PK.D.1 K9
c. Visualize, describe, or sketch the cross-section of a solid cut by a plane that is parallel or perpendicular to a side or axis of symmetry of the solid. E.1 PK.D.1 K9

G.B.8 Geometric constructions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Carry out and explain simple straightedge and compass constructions. D.2 B.3 K2, K2.1, K2.2, K2.3 4
b. Use geometric computer or calculator packages to create and test conjectures about geometric properties or relationships. D.2 B.3 4

G.C.1 Geometry of a circle.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know and apply the definitions and properties of a circle and the radius, diameter, chord, tangent, secant, and circumference of a circle. B.1 D.1 K4
b. Recognize and apply the fact that a tangent to a circle is perpendicular to the radius at the point of tangency. B.2 D.1 K4 25
c. Recognize, verify, and apply statements about the relationships between central angles, inscribed angles, and the circumference arcs they define. B.2 D.1 K4 7, 21
d. Recognize, verify, and apply statements about the relationships between interior and exterior angles of a circle and the arcs and segments they define. B.2 D.1 K4 25
e. Determine the length of line segments and arcs, the size of angles, and the area of shapes that they define in complex geometric drawings. B.3 D.2 K2, K8 21, 25

G.C.2 Axioms, theorems, and proofs in geometry.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Use geometric examples to illustrate the relationships among undefined terms, axioms/postulates, definitions, theorems and various methods of reasoning. A.1 B.1 K1, K1.1, MR3 8
b. Present and analyze direct and indirect geometric proofs using paragraphs, two-column, or flow-chart formats. D.1 A.2 B.2 K1.2, MR1, MR3 21
c. Use coordinates and algebraic techniques to interpret, represent, and verify geometric relationships. D.1 A.2 part, D.3 part K10, K2, K2.1, K2.2, K2.3, K3, K4
d. Interpret and use locus definitions to generate two- and three-dimensional geometric objects. B.4 A.2
e. Recognize that there are geometries other than Euclidean geometry in which the parallel postulate is not true. B.8 E.5 K2.1

G.D.1 Triangle trigonometry.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know the definitions of sine, cosine, and tangent as ratios of sides in a right triangle and use trigonometry to calculate the length of sides, measure of angles, and area of a triangle. D.3 C.5 K11, K11.2 25
b. Show how similarity of right triangles allows the trigonometric functions sine, cosine, and tangent to be properly defined as ratios of sides. D.3 C.5 K11.1 25
c. Derive, interpret, and use the identity sin2θ + cos2θ = 1 for angles θ between 0° and 90°. D.3 C.5 K12.2*

G.D.2 Three-dimensional geometry.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Analyze cross-sections of basic three-dimensional objects and identify the resulting shapes. B.5 E.2 K9
b. Describe the characteristics of the three-dimensional object traced out when a one- or two-dimensional figure is rotated about an axis. B.6 E.3
c. Analyze all possible relationships among two or three planes in space and identify their intersections. B.7 E.4

G.E.1 Spherical geometry.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Know and apply the definition of a great circle. B.9 opt E.6 opt K1.3
b. Use latitude, longitude, and great circles to solve problems relating to position, distance, and displacement on the earth’s surface. B.9 opt E.6 opt
c. Interpret various two-dimensional representations for the surface of a sphere (e.g., two-dimensional maps of the Earth), called projections, and explain their characteristics. B.9 opt E.6 opt
d. Describe geometry on a sphere as an example of a non-Euclidean geometry. B.9 opt E.6 opt K1.3

G.E.2 Vectors.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Use vectors to represent quantities that have both magnitude and direction. M4.a
b. Add and subtract vectors, find their dot product, and multiply a vector by a scalar; interpret the results. M4.b
c. Use vectors to describe lines in two- and three-dimensional Euclidean space.
d. Use vectors and their operations to represent situations and solve problems.
e. Use vectors to represent motions of objects in two and three dimensions. M4.a
f. Apply parametric methods to represent motion of objects.

G.E.3 Conic sections.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Develop and represent conic sections from basic properties. C1.a, C1.b, C1.c J4.6*
b. Describe how the intersection of a plane with a cone can form a circle, an ellipse, a parabola, or a hyperbola depending on the orientation of the plane with respect to the axis of the cone.
c. Apply conic sections in modeling real-world phenomena. C1.d