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Ohio's Academic Content Standards in MathematicsGeometry 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) |
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| | | 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) |
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| | | 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) |
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| | | 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) |
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| | | 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) |
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