Standards Detail
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Subject Area - CC.2:
Mathematics
Mathematics
- 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.
- Standard Area - CC.2.3: Geometry
- Assessment Anchor - G.2.3:
Measurements of Three-Dimensional Shapes and Figures
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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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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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Anchor Descriptor - M08.C-G.3.1 Apply volume formulas of cones, cylinders, and spheres.
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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.
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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.2Understand and apply congruence, similarity, and geometric transformations using various tools.
- Standard Area - CC.2.3: Geometry
- Assessment Anchor - G.1.2:
Properties of Polygons and Polyhedra
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Eligible Content - G.1.2.1.1 Identify and/or use properties of triangles
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Eligible Content - G.1.2.1.2 Identify and/or use properties of quadrilaterals
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Eligible Content - G.1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles.
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Eligible Content - G.1.2.1.4 Identify and/or use properties of regular polygons
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Eligible Content - G.1.2.1.5 Identify and/or use properties of pyramids and prisms.
- Assessment Anchor - G.2.2:
Measurements of Two-Dimensional Shapes and Figures
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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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Anchor Descriptor - M08.C-G.1.1 Apply properties of geometric transformations to verify congruence or similarity.
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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.
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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.
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Eligible Content - M08.C-G.1.1.2 Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.
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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.
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Eligible Content - M08.C-G.1.1.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
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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.3Understand and apply the Pythagorean Theorem to solve problems.
- Standard Area - CC.2.3: Geometry
- Assessment Anchor - G.2.1:
Coordinate Geometry and Right Triangles
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Eligible Content - G.2.1.1.1 Use the Pythagorean Theorem or trigonometric ratios to write and/or solve problems involving right triangles.
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Eligible Content - G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles.
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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.
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Eligible Content - G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).
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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.
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Anchor Descriptor - M08.C-G.2.1 Solve problems involving right triangles by applying the Pythagorean theorem.
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Eligible Content - M08.C-G.2.1.1 Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.
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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.)
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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.
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Eligible Content - M08.C-G.2.1.3 Apply the Pythagorean theorem to find the distance between two points in a coordinate system.
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