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Volume

Strand: Shape and Space (Measurement)
Outcome: 4

Step 3: Plan for Instruction

Guiding Questions

• What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
• What teaching strategies and resources should I use?
• How will I meet the diverse learning needs of my students?

A. Assessing Prior Knowledge and Skills

Before introducing new material, consider ways to assess and build on students' knowledge and skills related to counting.

Ways to Assess and Build on Prior Knowledge

B. Choosing Instructional Strategies

Consider the following general strategies for teaching volume (Van de Walle 2001):

• Access prior knowledge on using perimeter and area in the real world.
• Introduce volume by drawing on familiar and accessible contexts to illustrate uses of volume (NCTM 2000).
• Review the process used in developing understanding of perimeter and area and use a similar process in developing understanding of volume, stressing that the attribute changes but the process is similar:
  • Explain that the attribute to be measured is volume.
  • Check for conservation of volume; e.g., rearrange a given object and determine if the student realizes that the volume of the object remains unchanged.
  • Always estimate prior to comparing or measuring volumes.
  • Make direct comparisons; e.g., compare the volume of two boxes by placing one box inside the other box, if possible.
  • Estimate the volume of an object using nonstandard units of measure; e.g., sugar cubes. Use various techniques for estimating volume:
    • Referents—use a referent for the single unit of measure and iterate this unit mentally to obtain the estimate; e.g., use the size of the end of your smallest finger or a student's fore finger including the fingernail as a referent for 1 cm³.
    • Chunking—estimate the volume of a smaller portion of an object initially and use this chunk to estimate the volume of the entire object; e.g., estimate the volume of a smaller section of a box and then multiply that answer by the number of these sections in the entire box.
    • Iteration—iterate a unit mentally or physically; e.g., use a single unit repeatedly to visually estimate the volume of an object.
      (Van de Walle and Lovin 2006)
  • Have the students share their strategies for estimating volume.
  • Accept a range of estimates—within 30% of the actual measure is reasonable (Van de Walle and Lovin 2006, p. 279).
  • Encourage the students to measure the volume after each estimate so that they develop a better sense of volume.
  • Use nonstandard units of measure that have the same attribute as the item being measured; e.g., use sugar cubes to measure volume of a box.
  • Make indirect comparisons using a nonstandard unit of measure that has the same attribute as the item being measured; e.g., use sugar cubes to measure the volumes of boxes for the purpose of comparison.
  • Measure the volume of an object using larger then smaller nonstandard units of measure to establish that the smaller the unit of measure, the more you need to measure the volume of a given object; e.g., more small wooden cubes are needed than larger wooden cubes to measure the volume of a given object.
  • Explain the need to use standard units to measure volume to facilitate communicating various areas globally.
  • Measure the volume of a given object using an appropriate instrument with standard units of measure; e.g., use centimetre cubes that each have a volume of 1 cm³ to measure the volume of a box.
• Integrate the strands by:
  • using patterns to develop understanding of volume
  • using multiplication and division of whole numbers in building or removing layers of cubes in a rectangular prism.

C. Choosing Learning Activities

Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.

Teaching Conservation of Volume
Shapes Made from Plasticine	Download Activities
Shapes Made from Cubes	Download Activities

Teaching Volume Measured in Nonstandard Units
Concept of Volume	Download Activities
Using Nonstandard Units to Measure Volume	Download Activities

Teaching the Comparison of Volumes and the Justification for Cubic Units
Focus on Comparing Volumes	Download Activities
Focusing on the Cubic Unit and Proportionality	Download Activities

Teaching the Use of Referents for cm3 or m3 in Estimating Volume and Then Finding the Actual Volume Using Standard Units
Standard Units for Volume	Download Activities
Referents for Volume and Estimating Volume; Finding the Actual Volume	Download Activities
Estimate–Measure–Estimate–Measure Sequences	Download Activities
Estimate and Compare Volumes Using Standard Units	Download Activities

Teaching that Many Different Rectangular Prisms can be Constructed for a Given Volume (cm3 or m3)
Constructing Rectangular Prisms for a Given Volume Focusing on Layers	Download Activities
Constructing Rectangular Prisms for a Given Volume, Focusing on the Inverse Relationship Between the Area of the Base and the Height of the Prism	Download Activities
Frayer Model for Volume	Download Activities