enVision Mathematics Topic 11
5th Grade; March (2 weeks); 3rd Trimester
Embedded Files
Topic Title(s):
Understand Volume Concepts
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP5. Use appropriate tools strategically.
MP7. Look for and make use of structure.
Standard(s):
3. Data, Statistics, and Probability
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
5.MD.C. Measurement & Data: Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. (CCSS: 5.MD.C.3)
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. (CCSS: 5.MD.C.3.a)
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. (CCSS: 5.MD.C.3.b)
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (CCSS: 5.MD.C.4)
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. (CCSS: 5.MD.C.5)
Model 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. (CCSS: 5.MD.C.5.a)
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. (CCSS: 5.MD.C.5.b)
Use the additive nature of volume to 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. (CCSS: 5.MD.C.5.c)
Solve real-world problems involving volume. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
Make connections between the values being multiplied in a volume formula, the concept of cubic units, and the context within which volume is being calculated. (MP2)
Use unit cubes as a tool for finding or estimating volume and compare those results with those obtained with formulas. (MP5)
Extend the structure of two-dimensional space and the relationship between arrays and area to three-dimensional space and the relationship between layers of cubes and volume. (MP7)
Inquiry Questions
How are volume and area related in a solid figure?
Why is multiplication used when computing the volume of a solid figure, instead of another operation?
Coherence Connections
This expectation represents major work of the grade.
In previous grades, students connect area to the operation of multiplication and understand how to represent area problems as multiplication equations.
In Grade 6, students solve real-world and mathematical problems involving area of right rectangular prisms with fractional side lengths, using fractional cubic units.
Academic Vocabulary & Language Expectations:
Volume, cubic unit, cube, rectangular prism, unit cube, formula
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 11
Additional enVision Mathematics Resources
Let's Investigate! Shipping Blocks (TE) (supports Lessons 11-2, 11-3)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Volume Concepts, Measure Volume, Calculate Volume
Coherence Map/Concept Progressions: 5.MD.C.4, 5.MD.C.5.b
Page updated
Report abuse