Students expand their understanding of geometric measurement and spatial structuring to include volume as an attribute of three‐dimensional space. In this unit, students develop this understanding using concrete models to discover strategies for finding volume, and then later in Unit 9 students generalize this understanding in real‐world problems and apply strategies and formulas. The connection to multiplication and addition provides an opportunity for students to start the year off by applying the multiplication and addition strategies they learned in previous grades in a new, interesting context.
Key Concepts:
 Volume is an attribute of solid figures, and is a measure of space inside the solid figure.
 A cube with the side length of 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
 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.
Prior Knowledge Needed:
 Understand linear measurement and how to measure and estimate lengths with standard units (Grade 2, Unit 2; 2.MD.A.1, 2.MD.A.2)
 Understand that area is the space inside of a 2D figure; (Grade 3, Unit 2; 3.MD.C.5a)
 Understand that a square with a side length of 1 unit is said to have one square unit of area and is used to measure area; (Grade 3, Unit 2; 3.MD.C.5a)
 Use multiplication and division to solve measurement problems, including solving problems and using estimation with liquid volume (Grade 3, Unit 14; 3.OA.A.3, 3.MD.A.2)
Units on the Horizon:
 Solving problems involving volume (Grade 5, Unit 9)
 Problemsolving with volume and surface area (Grade 6, Unit 11)
 3D figures (Grade 7, Unit 12)
Lessons

Lesson objective: Distinguish between shapes with area as their attribute and shapes with volume as their attribute. Students bring prior knowledge of area and shapes from 3.MD.5. This prior knowledge is extended to the understanding of volume as an att...

Lesson objective: Fluently distinguish objects that have volume and those that do not based on their attributes. This lesson helps to build fluency with attributes of volume. Multiple threedimensional figures are used here because it supports the attri...

Lesson objective: Apply understanding of whether shapes have volume to real world situations This lesson provides an opportunity for students to apply their knowledge and understanding of whether or not a shape has volume to a reallife situation. Stude...

Lesson objective: Understand that a cube with side length 1 unit is called a unit cube and measures volume. Students bring prior knowledge of unit squares from 3.MD.5. This prior knowledge is extended to volume as students discover what unit is used to ...

Lesson objective: Practice identifying cubic objects Cubic objects and noncubic objects are used here to support student understanding of the attributes of geometric shapes. This work develops students' understanding that a cube, with the side length 1...

Lesson objective: Understand that volume can be measured by packing objects with unit cubes Students bring prior knowledge of tiling squares from 3.MD.5. This prior knowledge is extended to volume as students develop an understanding of packing to find ...

Lesson objective: Pack rectangular prisms with unit cubes to find volume This lesson helps to build procedural skill with calculating volume of rectangular prisms. Unit cubes are used here to pack the inside of rectangular prisms in order to determine t...

Lesson objective: Decompose and recompose solid figures by partitioning figures into layers This lesson helps to build procedural skill with finding volume of solid figures. Rectangular prisms and irregular figures are used here because it allows studen...

Lesson objective: Solve problems involving volume of solid figures This lesson provides an opportunity for students to apply their knowledge and understanding of finding volume of solid figures to a reallife situation. Students are asked to help a toy ...