Mathematics Content Expectations
|Form A: Math Alignment Table
|Alignment to Math High School Content Expectations
|Math High School Content Expectations
Math 050 to
Math 050 to
|STRAND 3: GEOMETRY AND TRIGONOMETRY (G)
|In Grades K–5, students study figures
such as triangles, rectangles, circles, rectangular solids, cylinders,
and spheres. They examine similarities and
differences between geometric shapes. They learn to quantify geometric figures by measuring and calculating lengths , angles, areas and volumes. In
Grades 6-8, students broaden their understanding of area and volume and develop the basic concepts of congruence, similarity, symmetry and the
Pythagorean Theorem. They apply these ideas to solve geometric problems, including ones related to the real world.
In Grades 9–12, students see geometry developed as a coherent, structured subject. They use the geometric skills and ideas introduced earlier, such as
congruence and similarity, to solve a wide variety of problems. There is an emphasis on the importance of clear language (e.g. for postulates, definitions and
theorems) and on learning to construct geometric proofs. In this process, students build geometric intuition and facility at deductive reasoning. They use
elements of logic and reasoning as described in the Quantitative Literacy and Logic strand, including both direct and indirect proof presented in narrative
form. They begin to use new techniques, including transformations and trigonometry. They apply these ideas to solve complex problems about two- and
three-dimensional figures, again including ones related to the real world. Their spatial visualization skills will be developed through the study of the
relationships between two- and three-dimensional shapes.
|STANDARD G1: FIGURES AND THEIR
PROPERTIES Students represent basic geometric
figures, polygons, and conic sections and apply their
definitions and properties in solving problems and
justifying arguments, including constructions and
representations in the coordinate plane. Students
represent three-dimensional figures, understand the
concepts of volume and surface area, and use them
to solve problems. They know and apply properties
of common three-dimensional figures.
|G1.1 Lines and Angles ; Basic Euclidean and
|G1.1.1 Solve multi- step problems and construct
proofs involving vertical angles, linear pairs of angles
supplementary angles, complementary angles, and
|G1.1.2 Solve multi-step problems and construct
proofs involving corresponding angles, alternate
interior angles, alternate exterior angles, and sameside
(consecutive) interior angles.
|G1.1.3 Perform and justify constructions,
midpoint of a line segment and bisector of an angle,
using straightedge and compass.
|G1.1.4 Given a line and a point, construct a line
through the point that is parallel to the original line
using straightedge and compass; given a line and a
point, construct a line through the point that is
perpendicular to the original line; justify the steps of
|G1.1.5 Given a line segment in terms of its
endpoints in the coordinate plane, determine its
length and midpoint.
|G1.1.6 Recognize Euclidean Geometry as an axiom
system ; know the key axioms and understand the
meaning of and distinguish between undefined terms
(e.g., point, line, plane), axioms, definitions, and
|G1.2 Triangles and Their Properties
|G1.2.1 Prove that the angle sum of a triangle is
and that an exterior angle of a triangle is the sum of
the two remote interior angles.
|G1.2.2 Construct and justify arguments and solve
multi-step problems involving angle measure, side
length, perimeter, and area of all types of triangles.
|G1.2.3 Know a proof of the Pythagorean Theorem
and use the Pythagorean Theorem and its converse
to solve multi-step problems
|G1.2.4 Prove and use the relationships among the
side lengths and the angles of 30º- 60º- 90º triangles
and 45º- 45º- 90º triangles.
|G1.2.5 Solve multi-step problems and construct
proofs about the properties of medians, altitudes, and
perpendicular bisectors to the sides of a triangle, and
the angle bisectors of a triangle; using a straightedge
and compass, construct these lines.
|G1.3 Triangles and Trigonometry
|G1.3.1 Define the sine, cosine, and tangent of
angles in a right triangle as ratios of sides ; solve
problems about angles, side lengths, or areas using
trigonometric ratios in right triangles.
|G1.3.2 Know and use the Law of Sines and the Law
of Cosines and use them to solve problems; find the
area of a triangle with sides a and b and included
angle using the formula Area = (1÷ 2) a b sin.
|G1.3.3 Determine the exact values of sine ,
and tangent for 0°, 30°, 45°, 60°, and their integer
multiples , and apply in various contexts.
|G1.4 Quadrilaterals and Their Properties
|G1.4.1 Solve multi-step problems and construct
proofs involving angle measure, side length, diagonal
length, perimeter, and area of squares, rectangles,
parallelograms, kites, and trapezoids.
|G1.4.2 Solve multi-step problems and construct
proofs involving quadrilaterals (e.g., prove that the
diagonals of a rhombus are perpendicular) using
Euclidean methods or coordinate geometry.
|G1.4.3 Describe and justify hierarchical
among quadrilaterals, (e.g. every rectangle is a
|G1.4.4 Prove theorems about the interior and
exterior angle sums of a quadrilateral.
|G1.5 Other Polygons and Their Properties
|G1.5.1 Know and use subdivision or
methods to find areas of polygons (e.g., regular
octagon, non-regular pentagon).
|G1.5.2 Know, justify, and use formulas for the
perimeter and area of a regular n -gon and formulas
to find interior and exterior angles of a regular n -gon
and their sums.
|G1.6 Circles and Their Properties
|G1.6.1 Solve multi-step problems involving
circumference and area of circles.
|G1.6.2 Solve problems and justify arguments about
chords (e.g., if a line through the center of a circle is
perpendicular to a chord, it bisects the chord) and
lines tangent to circles (e.g., a line tangent to a circle
is perpendicular to the radius drawn to the point of
|G1.6.3 Solve problems and justify arguments about
central angles, inscribed angles and triangles in
|G1.6.4 Know and use properties of arcs and
and find lengths of arcs and areas of sectors.
|G1.7 Conic Sections and Their Properties
|G.1.7.1 Find an equation of a circle given its
and radius; given the equation of a circle, find its
center and radius.
|G1.7.2 Identify and distinguish among geometric
representations of parabolas , circles, ellipses, and
hyperbolas; describe their symmetries, and explain
how they are related to cones.
|G1.7.3 Graph ellipses and hyperbolas with axes
parallel to the x- and y-axes, given equations.
|G1.8 Three- Dimensional Figures
|G1.8.1 Solve multi-step problems involving
area and volume of pyramids, prisms, cones,
cylinders, hemispheres, and spheres.
|G1.8.2 Identify symmetries of pyramids, prisms,
cones, cylinders, hemispheres, and spheres.
|11/15/2006 bls BUSINESS and ED