Gizmos for Pennsylvania - Mathematics: Geometry (Keystone Exams Assessment Anchors and Eligible Content adopted 2010)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

G.1: : Geometric Properties and Reasoning

G.1.1: : Properties of Circles, Spheres, and Cylinders

G.1.1.1: : Identify and/or use parts of circles and segments associated with circles, spheres, and cylinders.

G.1.1.1.1: : Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle.

G.1.1.1.2: : Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle.

G.1.1.1.3: : Use chords, tangents, and secants to find missing arc measures or missing segment measures.

G.1.1.1.4: : Identify and/or use the properties of a sphere or cylinder.

G.1.2: : Properties of Polygons and Polyhedra

G.1.2.1: : Recognize and/or apply properties of angles, polygons, and polyhedra.

G.1.2.1.1: : Identify and/or use properties of triangles.

G.1.2.1.2: : Identify and/or use properties of quadrilaterals.

G.1.2.1.3: : Identify and/or use properties of isosceles and equilateral triangles.

G.1.2.1.4: : Identify and/or use properties of regular polygons.

G.1.2.1.5: : Identify and/or use properties of pyramids and prisms.

G.1.3: : Congruence, Similarity, and Proofs

G.1.3.1: : Use properties of congruence, correspondence, and similarity in problem-solving settings involving two- and three-dimensional figures.

G.1.3.1.1: : Identify and/or use properties of congruent and similar polygons or solids.

G.1.3.1.2: : Identify and/or use proportional relationships in similar figures.

G.1.3.2: : Write formal proofs and/or use logic statements to construct or validate arguments.

G.1.3.2.1: : Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).

G.2: : Coordinate Geometry and Measurement

G.2.1: : Coordinate Geometry and Right Triangles

G.2.1.1: : Solve problems involving right triangles.

G.2.1.1.1: : Use the Pythagorean theorem to write and/or solve problems involving right triangles.

G.2.1.1.2: : Use trigonometric ratios to write and/or solve problems involving right triangles.

G.2.1.2: : Solve problems using analytic geometry.

G.2.1.2.1: : Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane.

G.2.1.2.2: : Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).

G.2.2: : Measurements of Two-Dimensional Shapes and Figures

G.2.2.1: : Use and/or compare measurements of angles.

G.2.2.1.1: : Use properties of angles formed by intersecting lines to find the measures of missing angles.

G.2.2.1.2: : Use properties of angles formed when two parallel lines are cut by a transversal to find the measures of missing angles.

G.2.2.2: : Use and/or develop procedures to determine or describe measures of perimeter, circumference, and/or area. (May require conversions within the same system.)

G.2.2.2.2: : Find the measurement of a missing length, given the perimeter, circumference, or area.

G.2.2.2.3: : Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon.

G.2.2.3: : Describe how a change in one dimension of a two-dimensional figure affects other measurements of that figure.

G.2.2.3.1: : Describe how a change in the linear dimension of a figure affects its perimeter, circumference, and area (e.g., How does changing the length of the radius of a circle affect the circumference of the circle?).

G.2.2.4: : Apply probability to practical situations.

G.2.2.4.1: : Use area models to find probabilities.

G.2.3: : Measurements of Three-Dimensional Shapes and Figures

G.2.3.1: : Use and/or develop procedures to determine or describe measures of surface area and/or volume. (May require conversions within the same system.)

G.2.3.1.1: : Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheet.

G.2.3.1.2: : Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheet.

G.2.3.1.3: : Find the measurement of a missing length given the surface area or volume.

G.2.3.2: : Describe how a change in one dimension of a three-dimensional figure affects other measurements of that figure.

G.2.3.2.1: : Describe how a change in the linear dimension of a figure affects its surface area or volume (e.g., How does changing the length of the edge of a cube affect the volume of the cube?).

Correlation last revised: 7/13/2022

Pennsylvania - Mathematics: Geometry

Keystone Exams Assessment Anchors and Eligible Content | Adopted: 2010

G.1: : Geometric Properties and Reasoning

G.2: : Coordinate Geometry and Measurement