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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.
| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Prekindergarten | | 1. | Match identical two- and three-dimensional objects found in the environment in play situations (e.g., 2 squares of same size, 2 stop signs). (ORC Resources) | | 2. | Sort and classify similar two- and three-dimensional objects in the environment and play situations (e.g., paper shapes, 2 balls of different size). (ORC Resources) | | 3. | Identify, name, create and describe common two-dimensional shapes in the environment and play situations (e.g., circles, triangles, rectangles, and squares). (ORC Resources) | | 4. | Identify, name and describe three-dimensional objects using the child's own vocabulary (e.g., sphere-"ball", cube-"box", cylinder-"can" or "tube", and cone-"ice cream cone" (ORC Resources) | | 5. | Demonstrate and begin to use the language of the relative position of objects in the environment and play situations (e.g., up, down, over, under, top, bottom, inside, outside, in front, behind, between, next to, right side up and upside down). (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Kindergarten | | 1. | Identify and sort two-dimensional shapes and three-dimensional objects. For example:
a. Identify and describe two-dimensional figures and three-dimensional objects from the environment using the child's own vocabulary.
b. Sort shapes and objects into groups based on student-defined categories.
c. Select all shapes or objects of one type from a group.
d. Build two-dimensional figures using paper shapes or tangrams; build simple three-dimensional objects using blocks. (ORC Resources) | | 2. | Name and demonstrate the relative position of objects as follows:
a. place objects over, under, inside, outside, on, beside, between, above, below, on top of, upside-down, behind, in back of, in front of; and
b. describe placement of objects with terms such as on, inside, outside, above, below, over, under, beside, between, in front of, behind. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 1 | | 1. | Identify, compare, and sort two-dimensional shapes; i.e., square, circle, ellipse, triangle, rectangle, rhombus, trapezoid, parallelogram, pentagon, and hexagon. For example:
a. Recognize and identify triangles and rhombuses independent of position, shape or size; and
b. Describe two-dimensional shapes using attributes such as number of sides and number of vertices (corners, or angles). (ORC Resources) | | 2. | Create new shapes by combining or cutting apart existing shapes. (ORC Resources) | | 3. | Identify the shapes of the faces of three-dimensional objects. (ORC Resources) | | 4. | Extend the use of location words to include distance (near, far, close to) and directional words (left, right). (ORC Resources) | | 5. | Copy figures and draw simple two-dimensional shapes from memory. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 2 | | 1. | Identify, describe, compare, and sort three-dimensional objects (i.e., cubes, spheres, prisms, cones, cylinders and pyramids) according to the shape of the faces or the numbers of faces, edges, or vertices. (ORC Resources) | | 2. | Predict what new shapes will be formed by combining or cutting apart existing shapes. (ORC Resources) | | 3. | Recognize two-dimensional shapes and three-dimensional objects from different positions. (ORC Resources) | | 4. | Identify and determine whether two-dimensional shapes are congruent (same shape and size) or similar (same shape different size) by copying or using superposition (lay one thing on top of another). (ORC Resources) | | 5. | Create and identify two-dimensional figures with line symmetry; e.g., what letter shapes, logos, polygons are symmetrical? (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 3 | | 1. | Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face. (ORC Resources) | | 2. | Identify and describe the relative size of angles with respect to right angles as follows:
a. Use physical models, like straws, to make different sized angles by opening and closing the sides, not by changing the side lengths.
b. Identify, classify and draw right, acute, obtuse and straight angles. (ORC Resources) | | 3. | Find and name locations on a labeled grid or coordinate system; e.g., a map or graph. (ORC Resources) | | 4. | Draw lines of symmetry to verify symmetrical two-dimensional shapes. (ORC Resources) | | 5. | Build a three-dimensional model of an object composed of cubes; e.g., construct a model based on an illustration or actual object. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 4 | | 1. | Identify, describe and model intersecting, parallel and perpendicular lines and line segments; e.g., use straws or other material to model lines. (ORC Resources) | | 2. | Describe, classify, compare and model two- and three-dimensional objects using their attributes. (ORC Resources) | | 3. | Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids. (ORC Resources) | | 4. | Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles). (ORC Resources) | | 5. | Describe points, lines and planes, and identify models in the environment. (ORC Resources) | | 6. | Specify locations and plot ordered pairs on a coordinate plane, using first quadrant points. (ORC Resources) | | 7. | Identify, describe and use reflections (flips), rotations (turns), and translations (slides) in solving geometric problems; e.g., use transformations to determine if two shapes are congruent. (ORC Resources) | | 8. | Use geometric models to solve problems in other areas of mathematics, such as number (multiplication/division) and measurement (area, perimeter, border). (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 5 | | 1. | Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of  . (ORC Resources) | | 2. | Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. (ORC Resources) | | 3. | Label vertex, rays, interior and exterior for an angle. (ORC Resources) | | 4. | Describe and use properties of congruent figures to solve problems. (ORC Resources) | | 5. | Use physical models to determine the sum of the interior angles of triangles and quadrilaterals. (ORC Resources) | | 6. | Extend understanding of coordinate system to include points whose x or y values may be negative numbers. (ORC Resources) | | 7. | Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side. (ORC Resources) | | 8. | Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 6 | | 1. | Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides. (ORC Resources) | | 2. | Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse, etc. (ORC Resources) | | 3. | Use multiple classification criteria to classify triangles; e.g., right scalene triangle. (ORC Resources) | | 4. | Identify and define relationships between planes; i.e., parallel, perpendicular and intersecting. (ORC Resources) | | 5. | Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations. (ORC Resources) | | 6. | Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other. (ORC Resources) | | 7. | Build three-dimensional objects built with cubes and sketch the two-dimensional representations of each side; i.e., projection sets.
(ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 7 | | 1. | Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. (ORC Resources) | | 2. | Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example:
a. Determine when one set of figures is a subset of another; e.g., all squares are rectangles.
b. Develop a set of properties that eliminates all but the desired figure; e.g., only squares are quadrilaterals with all sides congruent and all angles congruent. (ORC Resources) | | 3. | Use and demonstrate understanding of the properties of triangles. For example:
a. Use Pythagorean Theorem to solve problems involving right triangles.
b. Use triangle angle sum relationships to solve problems. (ORC Resources) | | 4. | Determine necessary conditions for congruence of triangles. (ORC Resources) | | 5. | Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures. (ORC Resources) | | 6. | Determine and use scale factors for similar figures to solve problems using proportional reasoning. (ORC Resources) | | 7. | Identify the line and rotation symmetries of two-dimensional figures to solve problems. (ORC Resources) | | 8. | Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper). (ORC Resources) | | 9. | Draw representations of three-dimensional geometric objects from different views. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 8 | | 1. | Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects. (ORC Resources) | | 2. | Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal. (ORC Resources) | | 3. | Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures). (ORC Resources) | | 4. | Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex. (ORC Resources) | | 5. | Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations. (ORC Resources) | | 6. | Draw nets for a variety of prisms, pyramids, cylinders and cones. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 9 | | 1. | Define the basic trigonometric ratios in right triangles: sine, cosine and tangent. (ORC Resources) | | 2. | Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle sizes in similar figures. (ORC Resources) | | 3. | Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 10 | | 1. | Formally define and explain key aspects of geometric figures, including:
a. interior and exterior angles of polygons;
b. segments related to triangles (median, altitude, midsegment);
c. points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter); and
d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle). (ORC Resources) | | 2. | Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane. (ORC Resources) | | 3. | Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:
a. prove the Pythagorean Theorem;
b. prove theorems involving triangle similarity and congruence;
c. prove theorems involving properties of lines, angles, triangles and quadrilaterals; and
d. test a conjecture using basic constructions made with a compass and straightedge or technology. (ORC Resources) | | 4. | Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software. (ORC Resources) | | 5. | Construct congruent or similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software. (ORC Resources) | | 6. | Identify the reflection and rotation symmetries of two- and three-dimensional figures. (ORC Resources) | | 7. | Perform reflections and rotations using compass and straightedge constructions and dynamic geometry software. (ORC Resources) | | 8. | Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane. (ORC Resources) | | 9. | Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable. (ORC Resources) | | 10. | Solve problems involving chords, radii, and arcs within the same circle. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 11 | | 1. | Use polar coordinates to specify locations on a plane. (ORC Resources) | | 2. | Represent translations using vectors. (ORC Resources) | | 3. | Describe multiplication of a vector and a scalar graphically and algebraically, and apply to problem situations. (ORC Resources) | | 4. | Use trigonometric relationships to determine lengths and angle measures; i.e., Law of Sines and Law of Cosines. (ORC Resources) | | 5. | Identify, sketch and classify the cross sections of three-dimensional objects. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 12 | | 1. | Use matrices to represent translations, reflections, rotations, dilations and their compositions. (ORC Resources) | | 2. | Derive and apply the basic trigonometric identities; i.e., angle addition, angle subtraction, and double angle. (ORC Resources) | | 3. | Relate graphical and algebraic representations of lines, simple curves and conic sections. (ORC Resources) | | 4. | Recognize and compare specific shapes and properties in multiple geometries; e.g., plane, spherical and hyperbolic. (ORC Resources) |
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