5.MD.3
Standard
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.
Student Language:
"I can understand volume."
Explanation
About the Math, Learning Targets, and Rigor
This standard represents the first time that students begin exploring the concept of volume (volume refers to the amount of space that an object takes up). Their prior experiences with volume were restricted to liquid volume. In third grade, students begin working with area and covering spaces. The concept of volume should be extended from area with the idea that students are covering an area (the bottom of cube) with a layer of unit cubes and then adding layers of unit cubes on top of bottom layer.
Students should have ample experiences with concrete manipulatives before moving to pictorial representations. As students develop their understanding of volume they recognize that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. This cube has a length of 1 unit, a width of 1 unit and a height of 1 unit and is called a cubic unit. This cubic unit is written with an exponent of 3 (e.g., in^3 , m^3 ).
Resources
Videos
- Khan Academy
- Scroll to 5.MD.3, click on skill, find videos on left side of each skill
- Learn Zillion
- Virtual Nerd
EngageNY Lessons
Extra Practice
- North Carolina Tasks
- Illustrative Math Tasks
- Howard County Tasks
- Click on 5th grade at bottom, then 5.MD.3
- Common Core Sheets
PARCC
Common Core State Standards
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.
- Measures may include those in whole cubic cm or cubic in.
Performance Indicators: 5.MD.3
Level 5: Exceeds Expectations
Recognizes volume as an attribute of solid figures and understands volume is measured using cubic units and can be found by packing a solid figure with unit cubes and counting them.
Represents the volume of a solid figure as “n” cubic units.
Writes an equation that illustrates the unit cube pattern.
Level 4: Meets Expectations
Recognizes volume as an attribute of solid figures and understands volume is measured using cubic units and can be found by packing a solid figure with unit cubes and counting them.
Critiquing/Reasoning Standards
Base explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response).
(Content Scope: Knowledge and skills articulated in 5.MD.C)
Performance Indicators: 5.C.6
Level 5: Exceeds Expectations
In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on operations using concrete referents such as diagrams--including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which may include:
- a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
- an efficient and logical progression of steps with appropriate justification
- precision of calculation
- correct use of grade-level vocabulary, symbols and labels
- justification of a conclusion
- evaluation of whether an argument or conclusion is generalizable
- evaluating, interpreting, and critiquing the validity of other’s responses, approaches, and reasoning, and providing a counterexample where applicable
Level 4: Meets Expectations
In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on operations using concrete referents such as diagrams--including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which may include:
- a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
- a logical progression of steps
- precision of calculation
- correct use of grade-level vocabulary, symbols and labels
- justification of a conclusion
- evaluation of whether an argument or conclusion is generalizable
- evaluating, interpreting, and critiquing the validity of other’s responses, approaches, and reasoning.