8.6
Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to:
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(A) describe the volume formula V = Bh of a cylinder in terms of its base area and its height;
(B) model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas; and
(C) use models and diagrams to explain the Pythagorean theorem.
8.7
Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to:
(A) solve problems involving the volume of cylinders, cones, and spheres;
(B) use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders;
(C) use the Pythagorean Theorem and its converse to solve problems; and
(D) determine the distance between two points on a coordinate plane using the Pythagorean Theorem.
8.8
Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:
(A) write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants;
(B) write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants;
(C) model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants; and
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(D) use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
8.9
Expressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to:
(A) identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations.
