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Subject Area - CC.2:
Mathematics
  • Standard Area - CC.2.3: Geometry
  • Grade Level - CC.2.3.PREK: GRADE Pre-Kindergarten
Standard - CC.2.3.PREK.A.1

Identify and describe shapes.

Materials & Resources
Standard - CC.2.3.PREK.A.2

Analyze, compare, create, and compose shapes.

Materials & Resources
  • Standard Area - CC.2.3: Geometry
  • Grade Level - CC.2.3.K: GRADE K
Standard - CC.2.3.K.A.1

Identify and describe two- and three-dimensional shapes.

PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
Standard - CC.2.3.K.A.2

Analyze, compare, create, and compose two- and three-dimensional shapes.

Assessments
Materials & Resources
  • Standard Area - CC.2.3: Geometry
  • Grade Level - CC.2.3.1: GRADE 1
Standard - CC.2.3.1.A.1

Compose and distinguish between two- and three-dimensional shapes based on their attributes.

PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
Standard - CC.2.3.1.A.2

Use the understanding of fractions to partition shapes into halves and quarters.

PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
  • Standard Area - CC.2.3: Geometry
  • Grade Level - CC.2.3.2: GRADE 2
Standard - CC.2.3.2.A.1

Analyze and draw two- and three-dimensional shapes having specified attributes.

PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
Standard - CC.2.3.2.A.2

Use the understanding of fractions to partition shapes into halves, quarters, and thirds.

Assessments
Materials & Resources
  • Standard Area - CC.2.3: Geometry
  • Grade Level - CC.2.3.3: GRADE 3
Standard - CC.2.3.3.A.1

Identify, compare, and classify shapes and their attributes.

Eligible Content:
3 Total
PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
  • Anchor Descriptor - M03.C-G.1.1 Analyze characteristics of polygons.
    • Eligible Content - M03.C-G.1.1.1 Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category. Example 1: A rhombus and a rectangle are both quadrilaterals since they both have exactly four sides. Example 2: A triangle and a pentagon are both polygons since they are both multi-sided plane figures.
      • Alternate Eligible Content - M03.C-G.1.1.1a Identify similarities between two polygons.
        Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
    • Eligible Content - M03.C-G.1.1.2 Recognize rhombi, rectangles, and squares as examples of quadrilaterals and/or draw examples of quadrilaterals that do not belong to any of these subcategories.
    • Eligible Content - M03.C-G.1.1.3 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Example 1: Partition a shape into 4 parts with equal areas. Example 2: Describe the area of each of 8 equal parts as 1/8 of the area of the shape.
      • Alternate Eligible Content - M03.C-G.1.1.3a Partition a rectangle into parts with equal areas.
        Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
Standard - CC.2.3.3.A.2

Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole.

Eligible Content:
3 Total
PASA DLM
Essential Elements (EE)
Assessments
Materials & Resources
  • Anchor Descriptor - M03.C-G.1.1 Analyze characteristics of polygons.
    • Eligible Content - M03.C-G.1.1.1 Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category. Example 1: A rhombus and a rectangle are both quadrilaterals since they both have exactly four sides. Example 2: A triangle and a pentagon are both polygons since they are both multi-sided plane figures.
      • Alternate Eligible Content - M03.C-G.1.1.1a Identify similarities between two polygons.
        Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
    • Eligible Content - M03.C-G.1.1.2 Recognize rhombi, rectangles, and squares as examples of quadrilaterals and/or draw examples of quadrilaterals that do not belong to any of these subcategories.
    • Eligible Content - M03.C-G.1.1.3 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Example 1: Partition a shape into 4 parts with equal areas. Example 2: Describe the area of each of 8 equal parts as 1/8 of the area of the shape.
      • Alternate Eligible Content - M03.C-G.1.1.3a Partition a rectangle into parts with equal areas.
        Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
      • Standard Area - CC.2.3: Geometry
      • Grade Level - CC.2.3.4: GRADE 4
      Standard - CC.2.3.4.A.1

      Draw lines and angles and identify these in two-dimensional figures.

      Eligible Content:
      3 Total
      PASA DLM
      Essential Elements (EE)
      Assessments
      Materials & Resources
      • Anchor Descriptor - M04.C-G.1.1 List properties, classify, draw, and identify geometric figures in two dimensions.
        • Eligible Content - M04.C-G.1.1.1 Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
        • Eligible Content - M04.C-G.1.1.2 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.
          • Alternate Eligible Content - M04.C-G.1.1.2a Classify two-dimensional shapes based on attributes.
            Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
        • Eligible Content - M04.C-G.1.1.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry).
          • Alternate Eligible Content - M04.C-G.1.1.3a Recognize a line of symmetry in a two-dimensional figure.
            Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
      Standard - CC.2.3.4.A.2

      Classify two-dimensional figures by properties of their lines and angles.

      Eligible Content:
      3 Total
      PASA DLM
      Essential Elements (EE)
      Assessments
      Materials & Resources
      • Anchor Descriptor - M04.C-G.1.1 List properties, classify, draw, and identify geometric figures in two dimensions.
        • Eligible Content - M04.C-G.1.1.1 Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
        • Eligible Content - M04.C-G.1.1.2 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.
          • Alternate Eligible Content - M04.C-G.1.1.2a Classify two-dimensional shapes based on attributes.
            Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
        • Eligible Content - M04.C-G.1.1.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry).
          • Alternate Eligible Content - M04.C-G.1.1.3a Recognize a line of symmetry in a two-dimensional figure.
            Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
      Standard - CC.2.3.4.A.3

      Recognize symmetric shapes and draw lines of symmetry.

      Eligible Content:
      3 Total
      PASA DLM
      Essential Elements (EE)
      Assessments
      Materials & Resources
      • Anchor Descriptor - M04.C-G.1.1 List properties, classify, draw, and identify geometric figures in two dimensions.
        • Eligible Content - M04.C-G.1.1.1 Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
        • Eligible Content - M04.C-G.1.1.2 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.
          • Alternate Eligible Content - M04.C-G.1.1.2a Classify two-dimensional shapes based on attributes.
            Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
        • Eligible Content - M04.C-G.1.1.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry).
          • Alternate Eligible Content - M04.C-G.1.1.3a Recognize a line of symmetry in a two-dimensional figure.
            Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
          • Standard Area - CC.2.3: Geometry
          • Grade Level - CC.2.3.5: GRADE 5
          Standard - CC.2.3.5.A.1

          Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and mathematical problems.

          Eligible Content:
          2 Total
          PASA DLM
          Essential Elements (EE)
          Assessments
          Materials & Resources
          • Anchor Descriptor - M05.C-G.1.1 Identify parts of a coordinate grid and describe or interpret points given an ordered pair.
            • Eligible Content - M05.C-G.1.1.1 Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I.
              • Alternate Eligible Content - M05.C-G.1.1.1a Identify an ordered pair (x,y) in quadrant I.
                Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
            • Eligible Content - M05.C-G.1.1.2 Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation.
              • Alternate Eligible Content - M05.C-G.1.1.2a Graph an ordered pair(x,y)in quadrant I.
                Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
          Standard - CC.2.3.5.A.2

          Classify two-dimensional figures into categories based on an understanding of their properties.

          Eligible Content:
          1 Total
          PASA DLM
          Essential Elements (EE)
          Assessments
          Materials & Resources
          • Anchor Descriptor - M05.C-G.2.1 Use basic properties to classify two-dimensional figures.
            • Eligible Content - M05.C-G.2.1.1 Classify two-dimensional figures in a hierarchy based on properties. Example 1: All polygons have at least three sides, and pentagons are polygons, so all pentagons have at least three sides. Example 2: A rectangle is a parallelogram, which is a quadrilateral, which is a polygon; so, a rectangle can be classified as a parallelogram, as a quadrilateral, and as a polygon.
              • Alternate Eligible Content - M05.C-G.2.1.1a Identify a two-dimensional figure with specific attributes.
                Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
              • Standard Area - CC.2.3: Geometry
              • Grade Level - CC.2.3.6: GRADE 6
              Standard - CC.2.3.6.A.1

              Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume.

              Eligible Content:
              6 Total
              PASA DLM
              Essential Elements (EE)
              Assessments
              Materials & Resources
              • Anchor Descriptor - M06.C-G.1.1 Find area, surface area, and volume by applying formulas and using various strategies.
                • Eligible Content - M06.C-G.1.1.1 Determine the area of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid). Formulas will be provided.
                  • Alternate Eligible Content - M06.C-G.1.1.1a Find the area of a quadrilateral given the dimensions.
                    Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                • Eligible Content - M06.C-G.1.1.2 Determine the area of irregular or compound polygons. Example: Find the area of a room in the shape of an irregular polygon by composing and/or decomposing.
                • Eligible Content - M06.C-G.1.1.3 Determine the volume of right rectangular prisms with fractional edge lengths. Formulas will be provided.
                  • Alternate Eligible Content - M06.C-G.1.1.3a Solve a real-world problem involving volume using unit cubes or multiplication.
                    Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                • Eligible Content - M06.C-G.1.1.4 Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). Formulas will be provided.
                • Eligible Content - M06.C-G.1.1.5 Represent three-dimensional figures using nets made of rectangles and triangles.
                  • Alternate Eligible Content - M06.C-G.1.1.5a Classify three-dimensional figures.
                    Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                • Eligible Content - M06.C-G.1.1.6 Determine the surface area of triangular and rectangular prisms (including cubes). Formulas will be provided.
                • Standard Area - CC.2.3: Geometry
                • Grade Level - CC.2.3.7: GRADE 7
                Standard - CC.2.3.7.A.1

                Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.

                Eligible Content:
                4 Total
                PASA DLM
                Essential Elements (EE)
                Assessments
                Materials & Resources
                • Anchor Descriptor - M07.C-G.2.1 Identify, use, and describe properties of angles and their measures.
                  • Eligible Content - M07.C-G.2.1.1 Identify and use properties of supplementary, complementary, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
                    • Alternate Eligible Content - M07.C-G.2.1.1a Use angle relationships to find the missing angle.
                      Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                  • Eligible Content - M07.C-G.2.1.2 Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).
                • Anchor Descriptor - M07.C-G.2.2 Determine circumference, area, surface area, and volume.
                  • Eligible Content - M07.C-G.2.2.1 Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided.
                  • Eligible Content - M07.C-G.2.2.2 Solve real-world and mathematical problems involving area, volume, and surface area of twoand three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.
                    • Alternate Eligible Content - M07.C-G.2.2.2a Use a conversion table to identify equivalent standard measurements of length or mass.
                      Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                Standard - CC.2.3.7.A.2

                Visualize and represent geometric figures and describe the relationships between them.

                Eligible Content:
                4 Total
                PASA DLM
                Essential Elements (EE)
                Assessments
                Materials & Resources
                • Anchor Descriptor - M07.C-G.1.1 Describe and apply properties of geometric figures.
                  • Eligible Content - M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area.
                    • Alternate Eligible Content - M07.C-G.1.1.1a Solve a 1-step real-world problem related to scaling.
                      Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                  • Eligible Content - M07.C-G.1.1.2 Identify or describe the properties of all types of triangles based on angle and side measures.
                    • Alternate Eligible Content - M07.C-G.1.1.2a Identify the properties of a right triangle.
                      Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                  • Eligible Content - M07.C-G.1.1.3 Use and apply the triangle inequality theorem.
                  • Eligible Content - M07.C-G.1.1.4 Describe the two-dimensional figures that result from slicing three-dimensional figures. Example: Describe plane sections of right rectangular prisms and right rectangular pyramids.
                    • Alternate Eligible Content - M07.C-G.1.1.4a Identify athree-dimensional figure with specific attributes.
                      Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                    • Standard Area - CC.2.3: Geometry
                    • Grade Level - CC.2.3.8: GRADE 8
                    Standard - CC.2.3.8.A.1

                    Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.

                    Eligible Content:
                    4 Total
                    PASA DLM
                    Essential Elements (EE)
                    Assessments
                    Materials & Resources
                    • Standard Area - CC.2.3: Geometry
                    • Assessment Anchor - G.2.3:

                      Measurements of Three-Dimensional Shapes and Figures

                      • Eligible Content - G.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.
                        Assessments
                        Materials & Resources
                      • Eligible Content - G.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.
                        Assessments
                        Materials & Resources
                      • Eligible Content - G.2.3.1.3 Find the measurement of a missing length given the surface area or volume.
                        Assessments
                        Materials & Resources
                        • Eligible Content - 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?).
                          Assessments
                          Materials & Resources
                          • Anchor Descriptor - M08.C-G.3.1 Apply volume formulas of cones, cylinders, and spheres.
                            • Eligible Content - M08.C-G.3.1.1 Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided.
                              • Alternate Eligible Content - M08.C-G.3.1.1a Complete the formula for volume to solve a real-world or mathematical problem.
                                Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                              Standard - CC.2.3.8.A.2

                              Understand and apply congruence, similarity, and geometric transformations using various tools.

                              Eligible Content:
                              11 Total
                              PASA DLM
                              Essential Elements (EE)
                              Assessments
                              Materials & Resources
                              • Standard Area - CC.2.3: Geometry
                              • Assessment Anchor - G.1.2:

                                Properties of Polygons and Polyhedra

                                • Eligible Content - G.1.2.1.1 Identify and/or use properties of triangles
                                  Assessments
                                  Materials & Resources
                                • Eligible Content - G.1.2.1.2 Identify and/or use properties of quadrilaterals
                                  Assessments
                                  Materials & Resources
                                • Eligible Content - G.1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles.
                                  Assessments
                                  Materials & Resources
                                • Eligible Content - G.1.2.1.4 Identify and/or use properties of regular polygons
                                  Assessments
                                  Materials & Resources
                                • Eligible Content - G.1.2.1.5 Identify and/or use properties of pyramids and prisms.
                                  Assessments
                                  Materials & Resources
                                • Assessment Anchor - G.2.2:

                                  Measurements of Two-Dimensional Shapes and Figures

                                  • Eligible Content - G.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing angles.
                                    Assessments
                                    Materials & Resources
                                  • Eligible Content - 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.
                                    Assessments
                                    Materials & Resources
                                    • Eligible Content - G.2.2.2.1 Estimate area, perimeter or circumference of an irregular figure.
                                      Assessments
                                      Materials & Resources
                                    • Eligible Content - G.2.2.2.2 Find the measurement of a missing length given the perimeter, circumference, or area.
                                      Assessments
                                      Materials & Resources
                                    • Eligible Content - G.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon.
                                      Assessments
                                      Materials & Resources
                                    • Eligible Content - G.2.2.2.4 Develop and/or use strategies to estimate the area of a compound/composite figure.
                                      Assessments
                                      Materials & Resources
                                    • Eligible Content - G.2.2.2.5 Find the area of a sector of a circle.
                                      Assessments
                                      • Eligible Content - 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?).
                                        Assessments
                                        Materials & Resources
                                        • Eligible Content - G.2.2.4.1 Use area models to find probabilities.
                                          Assessments
                                          Materials & Resources
                                          • Anchor Descriptor - M08.C-G.1.1 Apply properties of geometric transformations to verify congruence or similarity.
                                            • Eligible Content - M08.C-G.1.1.1 Identify and apply properties of rotations, reflections, and translations. Example: Angle measures are preserved in rotations, reflections, and translations.
                                              • Alternate Eligible Content - M08.C-G.1.1.1a Identify a rotation, reflection, or translation of a two- or three-dimensional figure.
                                                Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                                            • Eligible Content - M08.C-G.1.1.2 Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.
                                              • Alternate Eligible Content - M08.C-G.1.1.2a Identify figures that are congruent/similar.
                                                Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                                            • Eligible Content - M08.C-G.1.1.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
                                            • Eligible Content - M08.C-G.1.1.4 Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.
                                            Standard - CC.2.3.8.A.3

                                            Understand and apply the Pythagorean Theorem to solve problems.

                                            Eligible Content:
                                            6 Total
                                            Assessments
                                            Materials & Resources
                                            • Standard Area - CC.2.3: Geometry
                                            • Assessment Anchor - G.2.1:

                                              Coordinate Geometry and Right Triangles

                                              • Eligible Content - G.2.1.1.1 Use the Pythagorean Theorem or trigonometric ratios to write and/or solve problems involving right triangles.
                                                Assessments
                                                Materials & Resources
                                              • Eligible Content - G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles.
                                                Assessments
                                                Materials & Resources
                                                • Eligible Content - G.2.1.2.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane.
                                                  Assessments
                                                  Materials & Resources
                                                • Eligible Content - G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).
                                                  Assessments
                                                  Materials & Resources
                                                • Eligible Content - G.2.1.2.3 Use slope, distance and/or midpoint between 2 points on a coordinate plane to establish properties of a 2-dimensional shape.
                                                  Assessments
                                                  Materials & Resources
                                                  • Anchor Descriptor - M08.C-G.2.1 Solve problems involving right triangles by applying the Pythagorean theorem.
                                                    • Eligible Content - M08.C-G.2.1.1 Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.
                                                    • Eligible Content - M08.C-G.2.1.2 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.)
                                                      • Alternate Eligible Content - M08.C-G.2.1.2a Apply the Pythagorean theorem to determine length/distance in a real-world problem.
                                                        Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
                                                    • Eligible Content - M08.C-G.2.1.3 Apply the Pythagorean theorem to find the distance between two points in a coordinate system.
                                                    • Grade Level - CC.2.3.HS: GRADE High School
                                                    Standard - CC.2.3.HS.A.1

                                                    Use geometric figures and their properties to represent transformations in the plane.

                                                    Eligible Content:
                                                    2 Total
                                                    PASA DLM
                                                    Essential Elements (EE)
                                                    Assessments
                                                    Materials & Resources
                                                    • Standard Area - CC.2.3: Geometry
                                                    • Assessment Anchor - G.1.3:

                                                      Congruence, Similarity, and Proofs

                                                      • Eligible Content - G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
                                                        Assessments
                                                        Materials & Resources
                                                      • Eligible Content - G.1.3.1.2 Identify and/or use proportional relationships in similar figures.
                                                        Assessments
                                                        Materials & Resources
                                                        • Eligible Content - G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).
                                                          Assessments
                                                          Materials & Resources
                                                        Standard - CC.2.3.HS.A.2

                                                        Apply rigid transformations to determine and explain congruence.

                                                        Eligible Content:
                                                        2 Total
                                                        PASA DLM
                                                        Essential Elements (EE)
                                                        Assessments
                                                        Materials & Resources
                                                        • Standard Area - CC.2.3: Geometry
                                                        • Assessment Anchor - G.1.3:

                                                          Congruence, Similarity, and Proofs

                                                          • Eligible Content - G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
                                                            Assessments
                                                            Materials & Resources
                                                          • Eligible Content - G.1.3.1.2 Identify and/or use proportional relationships in similar figures.
                                                            Assessments
                                                            Materials & Resources
                                                            • Eligible Content - G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).
                                                              Assessments
                                                              Materials & Resources
                                                            Standard - CC.2.3.HS.A.3

                                                            Verify and apply geometric theorems as they relate to geometric figures.

                                                            Eligible Content:
                                                            13 Total
                                                            Assessments
                                                            Materials & Resources
                                                            • Standard Area - CC.2.3: Geometry
                                                            • Assessment Anchor - G.1.2:

                                                              Properties of Polygons and Polyhedra

                                                              • Eligible Content - G.1.2.1.1 Identify and/or use properties of triangles
                                                                Assessments
                                                                Materials & Resources
                                                              • Eligible Content - G.1.2.1.2 Identify and/or use properties of quadrilaterals
                                                                Assessments
                                                                Materials & Resources
                                                              • Eligible Content - G.1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles.
                                                                Assessments
                                                                Materials & Resources
                                                              • Eligible Content - G.1.2.1.4 Identify and/or use properties of regular polygons
                                                                Assessments
                                                                Materials & Resources
                                                              • Eligible Content - G.1.2.1.5 Identify and/or use properties of pyramids and prisms.
                                                                Assessments
                                                                Materials & Resources
                                                              • Assessment Anchor - G.1.3:

                                                                Congruence, Similarity, and Proofs

                                                                • Eligible Content - G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
                                                                  Assessments
                                                                  Materials & Resources
                                                                • Eligible Content - G.1.3.1.2 Identify and/or use proportional relationships in similar figures.
                                                                  Assessments
                                                                  Materials & Resources
                                                                  • Eligible Content - G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).
                                                                    Assessments
                                                                    Materials & Resources
                                                                  • Assessment Anchor - G.2.2:

                                                                    Measurements of Two-Dimensional Shapes and Figures

                                                                    • Eligible Content - G.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing angles.
                                                                      Assessments
                                                                      Materials & Resources
                                                                    • Eligible Content - 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.
                                                                      Assessments
                                                                      Materials & Resources
                                                                      • Eligible Content - G.2.2.2.1 Estimate area, perimeter or circumference of an irregular figure.
                                                                        Assessments
                                                                        Materials & Resources
                                                                      • Eligible Content - G.2.2.2.2 Find the measurement of a missing length given the perimeter, circumference, or area.
                                                                        Assessments
                                                                        Materials & Resources
                                                                      • Eligible Content - G.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon.
                                                                        Assessments
                                                                        Materials & Resources
                                                                      • Eligible Content - G.2.2.2.4 Develop and/or use strategies to estimate the area of a compound/composite figure.
                                                                        Assessments
                                                                        Materials & Resources
                                                                      • Eligible Content - G.2.2.2.5 Find the area of a sector of a circle.
                                                                        Assessments
                                                                        • Eligible Content - 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?).
                                                                          Assessments
                                                                          Materials & Resources
                                                                          • Eligible Content - G.2.2.4.1 Use area models to find probabilities.
                                                                            Assessments
                                                                            Materials & Resources
                                                                          Standard - CC.2.3.HS.A.4

                                                                          Apply the concept of congruence to create geometric constructions.

                                                                          Materials & Resources
                                                                          Standard - CC.2.3.HS.A.5

                                                                          Create justifications based on transformations to establish similarity of plane figures.

                                                                          Eligible Content:
                                                                          2 Total
                                                                          Assessments
                                                                          Materials & Resources
                                                                          • Standard Area - CC.2.3: Geometry
                                                                          • Assessment Anchor - G.1.3:

                                                                            Congruence, Similarity, and Proofs

                                                                            • Eligible Content - G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
                                                                              Assessments
                                                                              Materials & Resources
                                                                            • Eligible Content - G.1.3.1.2 Identify and/or use proportional relationships in similar figures.
                                                                              Assessments
                                                                              Materials & Resources
                                                                              • Eligible Content - G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).
                                                                                Assessments
                                                                                Materials & Resources
                                                                              Standard - CC.2.3.HS.A.6

                                                                              Verify and apply theorems involving similarity as they relate to plane figures.

                                                                              Eligible Content:
                                                                              3 Total
                                                                              Assessments
                                                                              Materials & Resources
                                                                              • Standard Area - CC.2.3: Geometry
                                                                              • Assessment Anchor - G.1.3:

                                                                                Congruence, Similarity, and Proofs

                                                                                • Eligible Content - G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
                                                                                  Assessments
                                                                                  Materials & Resources
                                                                                • Eligible Content - G.1.3.1.2 Identify and/or use proportional relationships in similar figures.
                                                                                  Assessments
                                                                                  Materials & Resources
                                                                                  • Eligible Content - G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).
                                                                                    Assessments
                                                                                    Materials & Resources
                                                                                  Standard - CC.2.3.HS.A.7

                                                                                  Apply trigonometric ratios to solve problems involving right triangles.

                                                                                  Eligible Content:
                                                                                  2 Total
                                                                                  Assessments
                                                                                  Materials & Resources
                                                                                  • Standard Area - CC.2.3: Geometry
                                                                                  • Assessment Anchor - G.2.1:

                                                                                    Coordinate Geometry and Right Triangles

                                                                                    • Eligible Content - G.2.1.1.1 Use the Pythagorean Theorem or trigonometric ratios to write and/or solve problems involving right triangles.
                                                                                      Assessments
                                                                                      Materials & Resources
                                                                                    • Eligible Content - G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles.
                                                                                      Assessments
                                                                                      Materials & Resources
                                                                                      • Eligible Content - G.2.1.2.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane.
                                                                                        Assessments
                                                                                        Materials & Resources
                                                                                      • Eligible Content - G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).
                                                                                        Assessments
                                                                                        Materials & Resources
                                                                                      • Eligible Content - G.2.1.2.3 Use slope, distance and/or midpoint between 2 points on a coordinate plane to establish properties of a 2-dimensional shape.
                                                                                        Assessments
                                                                                        Materials & Resources
                                                                                      Standard - CC.2.3.HS.A.8

                                                                                      Apply geometric theorems to verify properties of circles.

                                                                                      Eligible Content:
                                                                                      6 Total
                                                                                      PASA DLM
                                                                                      Essential Elements (EE)
                                                                                      Assessments
                                                                                      Materials & Resources
                                                                                      • Standard Area - CC.2.3: Geometry
                                                                                      • Assessment Anchor - G.1.1:

                                                                                        Properties of Circles, Spheres, and Cylinders

                                                                                        • Eligible Content - G.1.1.1.1 Identify, determine and/or use the radius, diameter, segment and/or tangent of a circle.
                                                                                          Assessments
                                                                                          Materials & Resources
                                                                                        • Eligible Content - G.1.1.1.2 Identify, determine and/or use the arcs, semicircles, sectors, and/or angles of a circle.
                                                                                          Assessments
                                                                                          Materials & Resources
                                                                                        • Eligible Content - G.1.1.1.3 Use chords, tangents, and secants to find missing arc measures or missing segment measures.
                                                                                          Assessments
                                                                                          Materials & Resources
                                                                                        • Eligible Content - G.1.1.1.4 Identify and/or use the properties of a sphere or cylinder.
                                                                                          Assessments
                                                                                          Materials & Resources
                                                                                        • Assessment Anchor - G.1.3:

                                                                                          Congruence, Similarity, and Proofs

                                                                                          • Eligible Content - G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
                                                                                            Assessments
                                                                                            Materials & Resources
                                                                                          • Eligible Content - G.1.3.1.2 Identify and/or use proportional relationships in similar figures.
                                                                                            Assessments
                                                                                            Materials & Resources
                                                                                            • Eligible Content - G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).
                                                                                              Assessments
                                                                                              Materials & Resources
                                                                                            • Assessment Anchor - G.2.2:

                                                                                              Measurements of Two-Dimensional Shapes and Figures

                                                                                              • Eligible Content - G.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing angles.
                                                                                                Assessments
                                                                                                Materials & Resources
                                                                                              • Eligible Content - 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.
                                                                                                Assessments
                                                                                                Materials & Resources
                                                                                                • Eligible Content - G.2.2.2.1 Estimate area, perimeter or circumference of an irregular figure.
                                                                                                  Assessments
                                                                                                  Materials & Resources
                                                                                                • Eligible Content - G.2.2.2.2 Find the measurement of a missing length given the perimeter, circumference, or area.
                                                                                                  Assessments
                                                                                                  Materials & Resources
                                                                                                • Eligible Content - G.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon.
                                                                                                  Assessments
                                                                                                  Materials & Resources
                                                                                                • Eligible Content - G.2.2.2.4 Develop and/or use strategies to estimate the area of a compound/composite figure.
                                                                                                  Assessments
                                                                                                  Materials & Resources
                                                                                                • Eligible Content - G.2.2.2.5 Find the area of a sector of a circle.
                                                                                                  Assessments
                                                                                                  • Eligible Content - 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?).
                                                                                                    Assessments
                                                                                                    Materials & Resources
                                                                                                    • Eligible Content - G.2.2.4.1 Use area models to find probabilities.
                                                                                                      Assessments
                                                                                                      Materials & Resources
                                                                                                    Standard - CC.2.3.HS.A.9

                                                                                                    Extend the concept of similarity to determine arc lengths and areas of sectors of circles.

                                                                                                    Eligible Content:
                                                                                                    10 Total
                                                                                                    Assessments
                                                                                                    Materials & Resources
                                                                                                    • Standard Area - CC.2.3: Geometry
                                                                                                    • Assessment Anchor - G.1.1:

                                                                                                      Properties of Circles, Spheres, and Cylinders

                                                                                                      • Eligible Content - G.1.1.1.1 Identify, determine and/or use the radius, diameter, segment and/or tangent of a circle.
                                                                                                        Assessments
                                                                                                        Materials & Resources
                                                                                                      • Eligible Content - G.1.1.1.2 Identify, determine and/or use the arcs, semicircles, sectors, and/or angles of a circle.
                                                                                                        Assessments
                                                                                                        Materials & Resources
                                                                                                      • Eligible Content - G.1.1.1.3 Use chords, tangents, and secants to find missing arc measures or missing segment measures.
                                                                                                        Assessments
                                                                                                        Materials & Resources
                                                                                                      • Eligible Content - G.1.1.1.4 Identify and/or use the properties of a sphere or cylinder.
                                                                                                        Assessments
                                                                                                        Materials & Resources
                                                                                                      • Assessment Anchor - G.2.1:

                                                                                                        Coordinate Geometry and Right Triangles

                                                                                                        • Eligible Content - G.2.1.1.1 Use the Pythagorean Theorem or trigonometric ratios to write and/or solve problems involving right triangles.
                                                                                                          Assessments
                                                                                                          Materials & Resources
                                                                                                        • Eligible Content - G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles.
                                                                                                          Assessments
                                                                                                          Materials & Resources
                                                                                                          • Eligible Content - G.2.1.2.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane.
                                                                                                            Assessments
                                                                                                            Materials & Resources
                                                                                                          • Eligible Content - G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).
                                                                                                            Assessments
                                                                                                            Materials & Resources
                                                                                                          • Eligible Content - G.2.1.2.3 Use slope, distance and/or midpoint between 2 points on a coordinate plane to establish properties of a 2-dimensional shape.
                                                                                                            Assessments
                                                                                                            Materials & Resources
                                                                                                          • Assessment Anchor - G.2.2:

                                                                                                            Measurements of Two-Dimensional Shapes and Figures

                                                                                                            • Eligible Content - G.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing angles.
                                                                                                              Assessments
                                                                                                              Materials & Resources
                                                                                                            • Eligible Content - 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.
                                                                                                              Assessments
                                                                                                              Materials & Resources
                                                                                                              • Eligible Content - G.2.2.2.1 Estimate area, perimeter or circumference of an irregular figure.
                                                                                                                Assessments
                                                                                                                Materials & Resources
                                                                                                              • Eligible Content - G.2.2.2.2 Find the measurement of a missing length given the perimeter, circumference, or area.
                                                                                                                Assessments
                                                                                                                Materials & Resources
                                                                                                              • Eligible Content - G.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon.
                                                                                                                Assessments
                                                                                                                Materials & Resources
                                                                                                              • Eligible Content - G.2.2.2.4 Develop and/or use strategies to estimate the area of a compound/composite figure.
                                                                                                                Assessments
                                                                                                                Materials & Resources
                                                                                                              • Eligible Content - G.2.2.2.5 Find the area of a sector of a circle.
                                                                                                                Assessments
                                                                                                                • Eligible Content - 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?).
                                                                                                                  Assessments
                                                                                                                  Materials & Resources
                                                                                                                  • Eligible Content - G.2.2.4.1 Use area models to find probabilities.
                                                                                                                    Assessments
                                                                                                                    Materials & Resources
                                                                                                                  Standard - CC.2.3.HS.A.10

                                                                                                                  Translate between the geometric description and the equation for a conic section.

                                                                                                                  Eligible Content:
                                                                                                                  8 Total
                                                                                                                  Assessments
                                                                                                                  Materials & Resources
                                                                                                                  • Standard Area - CC.2.3: Geometry
                                                                                                                  • Assessment Anchor - A2.2.1:

                                                                                                                    Patterns, Relations, and Functions

                                                                                                                    • Eligible Content - A2.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.
                                                                                                                      Assessments
                                                                                                                      Materials & Resources
                                                                                                                    • Eligible Content - A2.2.1.1.2

                                                                                                                      Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).
                                                                                                                      Assessments
                                                                                                                      Materials & Resources
                                                                                                                    • Eligible Content - A2.2.1.1.3 Determine the domain, range or inverse of a relation.
                                                                                                                      Assessments
                                                                                                                      Materials & Resources
                                                                                                                    • Eligible Content - A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increasing/decreasing, intercepts, zeros, and asymptotes).
                                                                                                                      Assessments
                                                                                                                      Materials & Resources
                                                                                                                    • Assessment Anchor - A2.2.2:

                                                                                                                      Applications of Functions

                                                                                                                      • Eligible Content - A2.2.2.1.1 Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).
                                                                                                                        Assessments
                                                                                                                        Materials & Resources
                                                                                                                      • Eligible Content - A2.2.2.1.2 Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).
                                                                                                                        Assessments
                                                                                                                        Materials & Resources
                                                                                                                      • Eligible Content - A2.2.2.1.3

                                                                                                                        Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.
                                                                                                                        Assessments
                                                                                                                        Materials & Resources
                                                                                                                      • Eligible Content - A2.2.2.1.4

                                                                                                                        Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).
                                                                                                                        Assessments
                                                                                                                        Materials & Resources
                                                                                                                        • Eligible Content - A2.2.2.2.1

                                                                                                                          Identify or describe the effect of changing parameters within a family of functions (e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).
                                                                                                                          Assessments
                                                                                                                          Materials & Resources
                                                                                                                        • Assessment Anchor - G.2.1:

                                                                                                                          Coordinate Geometry and Right Triangles

                                                                                                                          • Eligible Content - G.2.1.1.1 Use the Pythagorean Theorem or trigonometric ratios to write and/or solve problems involving right triangles.
                                                                                                                            Assessments
                                                                                                                            Materials & Resources
                                                                                                                          • Eligible Content - G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles.
                                                                                                                            Assessments
                                                                                                                            Materials & Resources
                                                                                                                            • Eligible Content - G.2.1.2.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane.
                                                                                                                              Assessments
                                                                                                                              Materials & Resources
                                                                                                                            • Eligible Content - G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).
                                                                                                                              Assessments
                                                                                                                              Materials & Resources
                                                                                                                            • Eligible Content - G.2.1.2.3 Use slope, distance and/or midpoint between 2 points on a coordinate plane to establish properties of a 2-dimensional shape.
                                                                                                                              Assessments
                                                                                                                              Materials & Resources
                                                                                                                            Standard - CC.2.3.HS.A.11

                                                                                                                            Apply coordinate geometry to prove simple geometric theorems algebraically.

                                                                                                                            Eligible Content:
                                                                                                                            3 Total
                                                                                                                            PASA DLM
                                                                                                                            Essential Elements (EE)
                                                                                                                            Assessments
                                                                                                                            Materials & Resources
                                                                                                                            • Standard Area - CC.2.3: Geometry
                                                                                                                            • Assessment Anchor - G.2.1:

                                                                                                                              Coordinate Geometry and Right Triangles

                                                                                                                              • Eligible Content - G.2.1.1.1 Use the Pythagorean Theorem or trigonometric ratios to write and/or solve problems involving right triangles.
                                                                                                                                Assessments
                                                                                                                                Materials & Resources
                                                                                                                              • Eligible Content - G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles.
                                                                                                                                Assessments
                                                                                                                                Materials & Resources
                                                                                                                                • Eligible Content - G.2.1.2.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane.
                                                                                                                                  Assessments
                                                                                                                                  Materials & Resources
                                                                                                                                • Eligible Content - G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).
                                                                                                                                  Assessments
                                                                                                                                  Materials & Resources
                                                                                                                                • Eligible Content - G.2.1.2.3 Use slope, distance and/or midpoint between 2 points on a coordinate plane to establish properties of a 2-dimensional shape.
                                                                                                                                  Assessments
                                                                                                                                  Materials & Resources
                                                                                                                                Standard - CC.2.3.HS.A.12

                                                                                                                                Explain volume formulas and use them to solve problems.

                                                                                                                                Eligible Content:
                                                                                                                                3 Total
                                                                                                                                PASA DLM
                                                                                                                                Essential Elements (EE)
                                                                                                                                Assessments
                                                                                                                                Materials & Resources
                                                                                                                                • Standard Area - CC.2.3: Geometry
                                                                                                                                • Assessment Anchor - G.2.3:

                                                                                                                                  Measurements of Three-Dimensional Shapes and Figures

                                                                                                                                  • Eligible Content - G.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.
                                                                                                                                    Assessments
                                                                                                                                    Materials & Resources
                                                                                                                                  • Eligible Content - G.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.
                                                                                                                                    Assessments
                                                                                                                                    Materials & Resources
                                                                                                                                  • Eligible Content - G.2.3.1.3 Find the measurement of a missing length given the surface area or volume.
                                                                                                                                    Assessments
                                                                                                                                    Materials & Resources
                                                                                                                                    • Eligible Content - 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?).
                                                                                                                                      Assessments
                                                                                                                                      Materials & Resources
                                                                                                                                    Standard - CC.2.3.HS.A.13

                                                                                                                                    Analyze relationships between two-dimensional and three-dimensional objects.

                                                                                                                                    Eligible Content:
                                                                                                                                    10 Total
                                                                                                                                    PASA DLM
                                                                                                                                    Essential Elements (EE)
                                                                                                                                    Assessments
                                                                                                                                    Materials & Resources
                                                                                                                                    • Standard Area - CC.2.3: Geometry
                                                                                                                                    • Assessment Anchor - G.1.1:

                                                                                                                                      Properties of Circles, Spheres, and Cylinders

                                                                                                                                      • Eligible Content - G.1.1.1.1 Identify, determine and/or use the radius, diameter, segment and/or tangent of a circle.
                                                                                                                                        Assessments
                                                                                                                                        Materials & Resources
                                                                                                                                      • Eligible Content - G.1.1.1.2 Identify, determine and/or use the arcs, semicircles, sectors, and/or angles of a circle.
                                                                                                                                        Assessments
                                                                                                                                        Materials & Resources
                                                                                                                                      • Eligible Content - G.1.1.1.3 Use chords, tangents, and secants to find missing arc measures or missing segment measures.
                                                                                                                                        Assessments
                                                                                                                                        Materials & Resources
                                                                                                                                      • Eligible Content - G.1.1.1.4 Identify and/or use the properties of a sphere or cylinder.
                                                                                                                                        Assessments
                                                                                                                                        Materials & Resources
                                                                                                                                      • Assessment Anchor - G.1.2:

                                                                                                                                        Properties of Polygons and Polyhedra

                                                                                                                                        • Eligible Content - G.1.2.1.1 Identify and/or use properties of triangles
                                                                                                                                          Assessments
                                                                                                                                          Materials & Resources
                                                                                                                                        • Eligible Content - G.1.2.1.2 Identify and/or use properties of quadrilaterals
                                                                                                                                          Assessments
                                                                                                                                          Materials & Resources
                                                                                                                                        • Eligible Content - G.1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles.
                                                                                                                                          Assessments
                                                                                                                                          Materials & Resources
                                                                                                                                        • Eligible Content - G.1.2.1.4 Identify and/or use properties of regular polygons
                                                                                                                                          Assessments
                                                                                                                                          Materials & Resources
                                                                                                                                        • Eligible Content - G.1.2.1.5 Identify and/or use properties of pyramids and prisms.
                                                                                                                                          Assessments
                                                                                                                                          Materials & Resources
                                                                                                                                        • Assessment Anchor - G.2.3:

                                                                                                                                          Measurements of Three-Dimensional Shapes and Figures

                                                                                                                                          • Eligible Content - G.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.
                                                                                                                                            Assessments
                                                                                                                                            Materials & Resources
                                                                                                                                          • Eligible Content - G.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.
                                                                                                                                            Assessments
                                                                                                                                            Materials & Resources
                                                                                                                                          • Eligible Content - G.2.3.1.3 Find the measurement of a missing length given the surface area or volume.
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                                                                                                                                            • Eligible Content - 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?).
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                                                                                                                                            Standard - CC.2.3.HS.A.14

                                                                                                                                            Apply geometric concepts to model and solve real world problems.

                                                                                                                                            Eligible Content:
                                                                                                                                            4 Total
                                                                                                                                            PASA DLM
                                                                                                                                            Essential Elements (EE)
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                                                                                                                                            • Standard Area - CC.2.3: Geometry
                                                                                                                                            • Assessment Anchor - G.2.2:

                                                                                                                                              Measurements of Two-Dimensional Shapes and Figures

                                                                                                                                              • Eligible Content - G.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing angles.
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                                                                                                                                              • Eligible Content - 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.
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                                                                                                                                                • Eligible Content - G.2.2.2.1 Estimate area, perimeter or circumference of an irregular figure.
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                                                                                                                                                • Eligible Content - G.2.2.2.2 Find the measurement of a missing length given the perimeter, circumference, or area.
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                                                                                                                                                • Eligible Content - G.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon.
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                                                                                                                                                • Eligible Content - G.2.2.2.4 Develop and/or use strategies to estimate the area of a compound/composite figure.
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                                                                                                                                                • Eligible Content - G.2.2.2.5 Find the area of a sector of a circle.
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                                                                                                                                                  • Eligible Content - 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?).
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                                                                                                                                                    • Eligible Content - G.2.2.4.1 Use area models to find probabilities.
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                                                                                                                                                    • Assessment Anchor - G.2.3:

                                                                                                                                                      Measurements of Three-Dimensional Shapes and Figures

                                                                                                                                                      • Eligible Content - G.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.
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                                                                                                                                                      • Eligible Content - G.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.
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                                                                                                                                                      • Eligible Content - G.2.3.1.3 Find the measurement of a missing length given the surface area or volume.
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                                                                                                                                                        Materials & Resources
                                                                                                                                                        • Eligible Content - 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?).
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                                                                                                                                                          Materials & Resources
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