Elementary Mathematics

5th Grade Unit 2 Overview and Standards

Use these links to access resources for this unit.

 Before You Begin this Unit…   Unit at a Glance

In grade 3, students began recognizing area as an attribute of plane figures, measured area by counting square units and related area to the operations of multiplication and addition. Students explored with both rectangular and non rectangular figures. This work continued in grade 4 as students applied the area and perimeter formulas for rectangles in real world mathematical problems. Grade 5 "represents the first time that students begin exploring the concept of volume. This concepts should be an extension from area with the idea that students are covering an area (bottom of cube) with a layer of unit cubes on top of bottom layer (see picture below). Students should have ample experience with concrete manipulatives before moving to pictorial representations." (5th Grade Mathematics- Unpacked Content, page 50).

Rationale for pacing change- The work of volume is better supported by the work of multiplication. Measurements that involve fractional side lengths will be moved to the end of Unit 4 (The fraction Unit for grade 5).

Suggested Dates:

September 22-October 8

Estimated Duration: 13 days (12 lessons)

*Investigation 1: 
8 lessons (Including 1.5A) 

*Investigation 2: 
4 lessons/5 days (Including 2.4A)

*Investigation 3: SKIP this investigation

*Performance Task-Messy Desk

 Standards Addressed in the Unit

Link to CCSS Unpacking Document- Updated Sept. '15

5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

b. 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.

5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems 

a. 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.

b. Apply the formulas V = l × w × h and V = b × 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.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.