Georgia standard · Mathematics

`8.GSR.8`Pythagorean Theorem and Volume

Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.

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Expectations

8.GSR.8.1
Explain a proof of the Pythagorean Theorem and its converse using visual models.
8.GSR.8.2
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.
8.GSR.8.3
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.
8.GSR.8.4
Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.

Mathematics Grade 8 (EOG) · Geometric & Spatial Reasoning
Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.
about 14% of the test · 8 points

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

Beginning: Given a drawing, determine the unknown side length of a right triangle.
Developing: Given a description of two sides of a right triangle, determine the unknown side length of the right triangle. Given two coordinate points (x, y) or points graphed in the coordinate plane, use the Pythagorean theorem to determine the distance between the points. Use the formula for the volume of a cone, cylinder, or sphere to determine the volume of a figure.
Proficient: Explain a proof of the Pythagorean theorem and its converse by using visual models. Given a drawing of a polygon or of a three-dimensional figure made up of right triangles, use the Pythagorean theorem to determine an unknown dimension. Use the Pythagorean theorem to find the distance between two points to solve practical, mathematical problems. Find the volumes of cones, cylinders, or spheres to solve relevant problems.
Distinguished: Solve complex or multi-step authentic problems involving the Pythagorean theorem or the volumes of cones, cylinders, or spheres.

Kindergarten · K.GSR.8
Identify, describe, and compare basic shapes encountered in the environment, and form two-dimensional shapes and three-dimensional figures.
Grade 3 · 3.GSR.8
Determine the perimeter of a polygon presented in real-life, mathematical problems.
Grade 4 · 4.GSR.8
Identify and draw geometric objects, classify polygons based on properties, and solve problems involving area and perimeter of rectangular figures.
Grade 5 · 5.GSR.8
Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.
Grade 8 · 8.GSR.8 (this standard)
Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.