S1+Hardy,+Meng

=Stage 1 - Identify Desired Results=
 * **Establish Goals (MLR or CCSS):** **(G)** ||
 * **Common Core State Standards**
 * Content Area:** Mathematics
 * Grade Level:** 8th Grade
 * Domain:** Geometry
 * Cluster:** Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
 * Standard:** 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. ||

//What understandings are desired?//
•the connections among the angles, sides, lengths, radius, perimeters, circumferences, areas, heights, volumes could be represented through mathematical formulas. •the volumes of cones, cylinders, and spheres could be applied to real-world situations. ||
 * **//Students will understand that://** **(U)** ||
 * •relationships exist among two-dimensional shapes, three-dimensional figures, and between two-dimensional and three-dimensional figures.

//What essential questions will be considered?//
•How are the attributes of 3-D figures connected? •How could the volumes of cones, cylinders, and spheres be applied to real world? ||
 * **Essential Questions:** **(Q)** ||
 * •Why 2-D shapes and 3-D figures are related?

//What key knowledge and skills will students acquire as a result of this unit?//
•Formulas: 2-D shapes and 3-D figures •Critical details: shapes are defined by attributes, in real life volumes of cones, cylinders, spheres could be important || •describe the differences between 2-D and 3-D shapes. •compare the 2-D and 3-D shapes to see the similarities. •illustrate all the attributes of 2-D and 3-D shapes on a graph. •recognize changes in attributes leads to changes in other attributes. •solve mathematical problems using the formulas of volumes of cones, cylinders, and spheres. •imagine the real-world applications of volume formulas. ||
 * **//Students will know://** **(K)** || **//Students will be able to://** **(S)** ||
 * •Definitions: 2-D shapes, 3-D figures and all the attributes related to 2-D and 3-D figures


 * 2004 ASCD and Grant Wiggins and Jay McTighe.**