 Mathematics Grade 8

Strand: GEOMETRY (8.G)

Understand congruence and similarity using physical models, transparencies, or geometry software (Standards 8.G.1-5). Understand and apply the Pythagorean Theorem and its converse (Standards 8.G.6-8). Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres (Standard 8.G.9).

Standard 8.G.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

• Comparing Snow Cones
This task asks students to use formulas for the volumes of cones, cylinders, and spheres to solve a real-world problem.
• Comparing Volumes of Cylinders, Spheres, and Cones
This interactive explains how to calculate the volumes of cylinders, cones and spheres. Students then apply this understanding to an activity where cylinders, cones and spheres are filled with water so that their volumes can be compared. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Flower Vases
The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.
• Glasses
This task gives students an opportunity to work with volumes of cylinders, spheres and cones.
• Grade 8 Unit 3: Geometric Applications of Exponents (Georgia Standards)
In this unit students will distinguish between rational and irrational numbers; find or estimate the square and cubed root of non-negative numbers, including 0; interpret square and cubed roots as both points of a line segment and lengths on a number line; use the properties of real numbers (commutative, associative, distributive, inverse, and identity) and the order of operations to simplify and evaluate numeric and algebraic expressions involving integer exponents, square and cubed roots; work with radical expressions and approximate them as rational numbers; solve problems involving the volume of a cylinder, cone, and sphere; determine the relationship between the hypotenuse and legs of a right triangle; use deductive reasoning to prove the Pythagorean Theorem and its converse; apply the Pythagorean Theorem to determine unknown side lengths in right triangles; determine if a triangle is a right triangle, Pythagorean triple; apply the Pythagorean Theorem to find the distance between two points in a coordinate system; and solve problems involving the Pythagorean Theorem.
• Modeling: Making Matchsticks
This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods, interpret and evaluate the data generated, and communicate their reasoning clearly.
• Shipping Rolled Oats
Given different scenarios, students will generate dimensions of boxes and calculate the different surface areas.
In this task, students will determine how many matchsticks can be made from a tree with a trunk with a base radius of 1 foot and a height of 80 feet. http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.