Unit 5 Overview:

Within this unit, students study volume as an attribute of solid figures. Students develop an understanding of volume and explore ways to measure it. Students explore the concept of volume by first filling solid containers with cubes and then observing and discovering the mathematical formula. Students compare volume by using cubes to build rectangular prisms. Students discover that the volume of a right rectangular prism can be calculated by multiplying the area of its base by its height. Students discover that the volume of a right rectangular prism can be found by multiplying its lengths, width, and height. Students work with determining the volume of composite figures that are composed of rectangular prisms.

1. Students will use parentheses, brackets, or braces in a numerical expressions and evaluate expressions with these symbols. (OA.A.1)
2. Students will write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product. (OA.A.2)
3. Students will recognize a cube with side lengths 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. (MD.C.3, MD.C.3a).
4. Students will recognize a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. (MD.C.3b)
5. Students will measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units. (MD.C.4)
6. Students will find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. (MD.C.5a)
7. Students will apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. (MD.C.5b)
8. Students will recognize volume as additive. Find volumes of solid figures of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. (MD.C.5c)