# Filling and Wrapping

### Topics

Rectangular prisms, area and circumference of a circle, cylinders, cones, spheres, pyramids, surface area, volume, ratio and proportions.

### Overview of Changes

*Significant change* The area and circumference of circles has been moved from 6th grade to this unit.

### Detailed Description of Changes

Except for some modest reshaping of the mathematical content and repositioning of a few problems, the content of the proposed CMP3 unit is identical to the current CMP2 unit, with the addition of an investigation about circles moved from Grade 6 of CMP2 and some new material on effects of slicing solids to address some CCSSM objectives explicitly.

Surface area and volume for cylinders, spheres are still in this unit. The CMP philosophy has always connected these concepts with the related ideas about prisms and circles. It provides an opportunity for students to extend their understanding of prisms and circles by applying their knowledge to develop strategies for finding the volume of cylinders, cones and sphere. Students find that a strategy for finding the volume of a cylinder is the same for finding the volume of prisms. In so doing, understanding of the volume of prisms, cylinders, cones and spheres are strengthened. Therefore, we have provided a complete and connected presentation of measurement for solids. The volume of cylinders, spheres, and cones is revisited in grade 8.

New Investigation | Changes in CMP2 Investigation |
---|---|

Investigation 1 Building Smart Boxes: Rectangular Prisms |
Since this investigation extends the understanding of volume and surface area of rectangular prisms from the 6^{th} grade Covering and Surrounding, Investigation1 and 2 from CMP 2 have been edited into three problems that now occur in Investigation 1 of CMP3. In addition Problem 5.3 Scaling up Compost Boxes has been added as Problem 1.4 |

Investigation 2 Polygonal Prisms |
Investigation 2, Problems 3.1 and 3.2 are now Problems 2.1 and 2.2. Problem 2.3 is new which looks at slicing prisms and pyramids |

Investigation 3 Area and Circumference of Circles |
This is essentially Investigation 5 from CMP 2’s Covering and Surrounding |

Investigation 4 Cylinders, Cones, and Spheres |
Investigation 4 is similar to Investigation 4 of CMP2 |