## Unit 12: Chapter 12 - Volume (Grade 8 Focus)

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### Learning Targets/Performance Indicators

Grade 8 Geometry PI #4: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

• Substitute values into formulas and solve algebraically to find missing values for the volume of cylinders, cones, and spheres
• Solve real-world and mathematical problems involving area, volume, and surface area

Essential Questions:

• What is the relationship between the volume of a prism and the volume of a pyramid with the same base area and height?
• How can you find the volume of a composite figure?
• What is the relationship between the volume of a cylinder and a cone?
• Why is the area of a circle needed to find the volume of a cylinder, sphere, and cone?
• When would you need to find the volume of a cylinder in the real world?
• When would you need to find the volume of a sphere in the real world?
• When would you need to find the volume of a cone in the real world?

Prior Learning:

In grade 6, students found the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. Using these methods, students discussed, developed, and justified formulas for areas of triangles and parallelograms. Work toward meeting the standard drew together grades 3â€“6 work with geometric measurement.

In grade 6, students found areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces they could determine. They represented three-dimensional figures using nets made up of rectangles and triangles and used the nets to find the surface area of these figures. Students applied these techniques in the context of solving real-world and mathematical problems. They reasoned about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths.

In grade 6, students found the area of triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. They applied techniques in the context of solving real-world and mathematical problems. Students used nets to find surface area. They used cubes to find volume and compared results using formulas.

Current Learning:

Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross sections. They solve real-world and mathematical problems involving surface area as well as volume of three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. This is a critical area and an additional cluster for PARCC.

In grade 8, this is an additional cluster. Students know the formulas for the volume of cones, cylinders, and spheres. They use the formulas to work and solve mathematical and real-world problems.

Future Learning:

In this unit, students will extend their knowledge to solve problems involving volume of cylinders, cones, and spheres. All of studentsâ€™ previous knowledge will be applied in high school geometry when they learn and apply geometric theorems. Students will be expected to explain volume formulas and use them to solve problems while also applying geometric concepts in modeling situations.

In high school, students will explain volume formulas and use them to solve problems. They will give informal arguments for the volume of a cylinder, pyramid, cone, spheres, and other solid figures. Students will use volume formulas to solve problems. These skills, along with proportional reasoning and multistep numerical problem solving, can be combined and used in flexible ways as part of modeling during high school.