Geometry and Volume
Unit description: Students will build on their understanding of area from fourth grade to consider 3-D shapes and their volumes. Students will develop methods for finding the volume of rectangular prisms that include multiplying the area of the base times the height, multiplying length by the width by the height, and counting unit cubes.
Essential Outcomes of the Unit
Measurement and Data- Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
- 5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
- 5.MD.5a 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.
- 5.MD.5b 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.
- 5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Other Standards Addressed in the Unit
Measurement and Data- Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
- 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
- 5.MD.3a Recognize that 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
- 5.MD.3b Recognize that 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.
Geometry- Classify two-dimensional figures into categories based on their properties.
- 5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
- 5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
Essential Questions and Big Ideas
- How do I classify quadrilaterals?
- Quadrilaterals can be classified in multiple ways.
- Trapezoids and parallelograms are classified based on parallel sides.
- Rectangles and squares are classified based on right angles.
- Squares and rhombi are classified based on equal side lengths.
- What is volume?
- Volume represents the amount of 3-D space a 3-D shape takes up.
- Volume is measured in cubic units.
- What is a “unit cube” and how do I use it to measure volume?
- A “unit cube” represents one cubic unit.
- “Unit cubes” can be combined together to represent a volume.
- How is volume related to area?
- Rectangular prisms are built of layers of areas of unit cubes.
- The area of a base can be multiplied by a height to find a volume.
Download the complete Grade 5 Math Unit 5 framework to customize for your own planning.