Ohio Resource Center

# Ohio's Academic Content Standards in Mathematics

## Benchmarks

Geometry and Spatial Sense Standard
Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects, and transformations to analyze mathematical situations and solve problems.

By the end of the K - 2 program:
 A. Describe and create plane figures: circle, rectangle, square, triangle, hexagon, trapezoid, parallelogram and rhombus, and identify them in the environment. (ORC Resources) B. Describe solid objects: cube, rectangular prism, sphere, cylinder, cone and pyramid, and identify them in the environment. (ORC Resources) C. Sort and compare two-dimensional figures and three-dimensional objects according to their characteristics and properties. (ORC Resources) D. Identify, explain and model (superposition, copying) the concept of shapes being congruent and similar. (ORC Resources) E. Recognize two- and three-dimensional objects from different positions. (ORC Resources) F. Describe location, using comparative (before, after), directional (above, below), and positional (first, last) words. (ORC Resources) G. Identify and draw figures with line symmetry. (ORC Resources)

By the end of the 3 - 4 program:
 A. Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects. (ORC Resources) B. Describe and identify points, lines and planes in the environment. (ORC Resources) C. Describe and identify intersecting, parallel and perpendicular lines or segments in the environment. (ORC Resources) D. Identify and draw right, obtuse, acute and straight angles. (ORC Resources) E. Use attributes to describe, classify and sketch plane figures and build solid objects. (ORC Resources) F. Develop definitions of classes of shapes. (ORC Resources) G. Find and name locations in coordinate systems. (ORC Resources) H. Identify and describe line and rotational symmetry in two-dimensional shapes and designs. (ORC Resources) I. Describe, identify and model reflections, rotations and translations, using physical materials. (ORC Resources) J. Describe a motion or series of transformations that show two shapes are congruent. (ORC Resources)

By the end of the 5 - 7 program:
 A. Identify and label angle parts and the regions defined within the plane where the angle resides. (ORC Resources) B. Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference. (ORC Resources) C. Specify locations and plot ordered pairs on a coordinate plane. (ORC Resources) D. Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties. (ORC Resources) E. Use proportions to express relationships among corresponding parts of similar figures. (ORC Resources) F. Describe and use the concepts of congruence, similarity and symmetry to solve problems. (ORC Resources) G. Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles. (ORC Resources) H. Predict and describe results (size, position, orientation) of transformations of two-dimensional figures. (ORC Resources) I. Identify and draw three-dimensional objects from different views (top, side, front and perspective). (ORC Resources) J. Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing. (ORC Resources)

By the end of the 8 - 10 program:
 A. Formally define geometric figures. (ORC Resources) B. Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence. (ORC Resources) C. Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines. (ORC Resources) D. Use coordinate geometry to represent and examine the properties of geometric figures. (ORC Resources) E. Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology. (ORC Resources) F. Represent and model transformations in a coordinate plane and describe the results. (ORC Resources) G. Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system. (ORC Resources) H. Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others. (ORC Resources) I. Use right triangle trigonometric relationships to determine lengths and angle measures. (ORC Resources)

By the end of the 11 - 12 program:
 A. Use trigonometric relationships to verify and determine solutions in problem situations. (ORC Resources) B. Represent transformations within a coordinate system using vectors and matrices. (ORC Resources)