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John R. Kasich, Governor Paolo DeMaria, Superintendent of Public Instruction Standard Number Original Standard Key: Red shows added words. Purple shows a footnote addition. Words that have been deleted are not shown in the New Standard column. Gray boxes show vertical alignment changes that were impacted by the white standard box directly above it. The symbol G means the word is now in the glossary. Revised Standard Rationale or Action Standards/ Courses Impacted GEOMETRY K.G.4 Analyze, compare, create, and compose shapes. K.G.4 Analyze and compare two- and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). K.G.6 Analyze, compare, create, and compose shapes. Describe, compare, create, and compose shapes. K.G.6 Compose simple shapes to form larger K.G.6 Combine simple shapes to form larger shapes. shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” 1.G.2 Reason with shapes and their attributes. 1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. Geometry (Grades K-8)-DRAFT Clarity Describe, compare, create, and compose shapes. K.G.4 Describe and compare two- or three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts and other attributes. Clarity Footnote added Reason with shapes and their attributes. 1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. Students do not need to learn formal names such as "right rectangular prism." 1 7/5/2016 John R. Kasich, Governor Paolo DeMaria, Superintendent of Public Instruction Key: Red shows added words. Purple shows a footnote addition. Words that have been deleted are not shown in the New Standard column. Gray boxes show vertical alignment changes that were impacted by the white standard box directly above it. The symbol G means the word is now in the glossary. Standard Number Original Standard Revised Standard 1.G.3 Reason with shapes and their attributes. 1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. Clarity Reason with shapes and their attributes. 1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters, and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares in real-world contexts. Understand for these examples that decomposing into more equal shares creates smaller shares. 2.G.3 Reason with shapes and their attributes. 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Vertical alignment Reason with shapes and their attributes. 2.G.3 Partition circles and rectangles into two, three or four equal shares, describe the shares using the words halves, thirds, fourths and quarters, and use the phrases half of, third of, fourth of and quarter of. Describe the whole as two halves, three thirds, four fourths in real-world contexts. Recognize that equal shares of identical wholes need not have the same shape. 2.G.1 Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Reason with shapes and their attributes. 2.G.1 Recognize and/or draw triangles, quadrilaterals, pentagons and hexagons based on the number of sides or vertices. Recognize and identify cubes, rectangular prisms, cones and cylinders. Geometry (Grades K-8)-DRAFT 2 Rationale or Action Standards/ Courses Impacted 2.G.3 Clarity Grade level appropriateness 7/5/2016 John R. Kasich, Governor Paolo DeMaria, Superintendent of Public Instruction Key: Red shows added words. Purple shows a footnote addition. Words that have been deleted are not shown in the New Standard column. Gray boxes show vertical alignment changes that were impacted by the white standard box directly above it. The symbol G means the word is now in the glossary. Standard Number Original Standard Revised Standard 3.G.1 Reason with shapes and their attributes. 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Clarity Reason with shapes and their attributes. 3.G.1 Understand that quadrilaterals may share attributes, and that the shared attributes can define a subcategory (parallelograms, trapezoids, rhombuses, rectangles, and squares). Attributes include sides, parallel sides, and right angles. Draw examples of two-dimensional figures that do not belong to a given subcategory of quadrilaterals. Either of the following definitions for a trapezoid is acceptable: a trapezoid is a quadrilateral with at least one pair of parallel sides, or a trapezoid is a quadrilateral with exactly one pair of parallel sides. 4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Draw and identify lines and angles, and classify shapes by Vertical alignment properties of their lines and angles. 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Either of the following definitions for a trapezoid is acceptable: a trapezoid is a quadrilateral with at least one pair of parallel sides, or a trapezoid is a quadrilateral with exactly one pair of parallel sides. 5.G.4 Classify two-dimensional figures into categories based on their properties. 5.G.4 Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures into categories based on Vertical alignment their properties. 5.G.4 Use graphic organizers to compare and contrast rhombuses, squares, triangles, rectangles, trapezoids and parallelograms based on properties. Either of the following definitions for a trapezoid is acceptable: a trapezoid is a quadrilateral with at least one pair of parallel sides, or a trapezoid is a quadrilateral with exactly one pair of parallel sides. Geometry (Grades K-8)-DRAFT 3 Rationale or Action Standards/ Courses Impacted 4.G.2 5.G.4 7/5/2016 John R. Kasich, Governor Paolo DeMaria, Superintendent of Public Instruction Standard Number Original Standard 4.G.3 Draw and identify lines and angles, and classify Deleted Standard shapes by properties of their lines and angles. 4.G.3 Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. 5.G.4 Classify two-dimensional figures into categories based on their properties. 5.G.4 Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures into categories based on Grade level appropriateness their properties. 5.G.4 Use graphic organizers to compare and contrast rhombuses, squares, triangles, rectangles, trapezoids and parallelograms based on properties. Either of the following definitions for a trapezoid is acceptable: a trapezoid is a quadrilateral with at least one pair of parallel sides, or a trapezoid is a quadrilateral with exactly one pair of parallel sides. 6.G.1 Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Solve real-world and mathematical problems involving area, Clarity surface area, and volume. 6.G.1 Through composition into rectangles or decomposition into triangles, find the area of right triangles, other triangles, special quadrilaterals and polygons; apply these techniques in the context of solving real-world and mathematical problems. Geometry (Grades K-8)-DRAFT Revised Standard Key: Red shows added words. Purple shows a footnote addition. Words that have been deleted are not shown in the New Standard column. Gray boxes show vertical alignment changes that were impacted by the white standard box directly above it. The symbol G means the word is now in the glossary. 4 Rationale or Action Standards/ Courses Impacted Vertical alignment 7/5/2016 John R. Kasich, Governor Paolo DeMaria, Superintendent of Public Instruction Key: Red shows added words. Purple shows a footnote addition. Words that have been deleted are not shown in the New Standard column. Gray boxes show vertical alignment changes that were impacted by the white standard box directly above it. The symbol G means the word is now in the glossary. Standard Number Original Standard Revised Standard 6.G.2 Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Solve real-world and mathematical problems involving area, Content Error surface area, and volume. 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Clarity Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.1 Solve problems involving scale drawings of right triangles, other triangles and special quadrilaterals. a. Represent proportional relationships in scale drawings. b. Compute actual lengths and areas from a scale drawing and reproduce a scale drawing at a different scale. Geometry (Grades K-8)-DRAFT 5 Rationale or Action Standards/ Courses Impacted 7/5/2016 John R. Kasich, Governor Paolo DeMaria, Superintendent of Public Instruction Key: Red shows added words. Purple shows a footnote addition. Words that have been deleted are not shown in the New Standard column. Gray boxes show vertical alignment changes that were impacted by the white standard box directly above it. The symbol G means the word is now in the glossary. Standard Number Original Standard Revised Standard Rationale or Action 7.G.4 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Solve real-life and mathematical problems involving angle measure, circles, area, surface area, and volume. 7.G.4 Work with circles. a. Know that a circle is created by connecting all of the points equidistant from a point (center). b. Explore and understand the relationships among the circumference, diameter, and radius of a circle. c. Explore and understand how the area relates to the circumference of a circle. d. Informally derive and know the formulas for the area and circumference of a circle and use them to solve real-world and mathematical problems. Clarity Grade level appropriateness 8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.1 Verify experimentally the properties of rotations, reflections, and translations (include examples both with and without coordinates): a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. Clarity Geometry (Grades K-8)-DRAFT 6 Standards/ Courses Impacted 8.G.2 8.G.4 7/5/2016 John R. Kasich, Governor Paolo DeMaria, Superintendent of Public Instruction Key: Red shows added words. Purple shows a footnote addition. Words that have been deleted are not shown in the New Standard column. Gray boxes show vertical alignment changes that were impacted by the white standard box directly above it. The symbol G means the word is now in the glossary. Standard Number Original Standard Revised Standard Rationale or Action 8.G.2 Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. (Include examples both with and without coordinates.) Vertical alignment 8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. Vertical alignment Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. (Include examples both with and without coordinates.) 8.G.6 Understand and apply the Pythagorean Theorem. 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. Understand and apply the Pythagorean Theorem. 8.G.6 Analyze and justify an informal proof (for example, pictorially, narratively, geometrically, etc.) of the Pythagorean Theorem and its converse. Clarity Vertical alignment from high school 8.G.9 Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 8.G.9 Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres. Clarity Geometry (Grades K-8)-DRAFT 7 Standards/ Courses Impacted 7.G.4 7/5/2016 John R. Kasich, Governor Paolo DeMaria, Superintendent of Public Instruction Key: Red shows added words. Purple shows a footnote addition. Words that have been deleted are not shown in the New Standard column. Gray boxes show vertical alignment changes that were impacted by the white standard box directly above it. The symbol G means the word is now in the glossary. Standard Number Original Standard Revised Standard Rationale or Action 7.G.4 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Solve real-life and mathematical problems involving angle measure, circles, area, surface area, and volume. 7.G.4 Work with circles. a. Know that a circle is created by connecting all of the points equidistant from a point (center). b. Explore and understand the relationships among the circumference, diameter, and radius of a circle. c. Explore and understand how the area relates to the circumference of a circle. d. Informally derive and know the formulas for the area and circumference of a circle and use them to solve real-world and mathematical problems. Vertical alignment Geometry (Grades K-8)-DRAFT 8 Standards/ Courses Impacted 7/5/2016