Volume

Strand: Shape and Space (Measurement)
Outcome: 4

Step 1: Identify Outcomes to Address

Guiding Questions

What do I want my students to learn?
What can my students currently understand and do?
What do I want my students to understand and be able to do, based on the Big Ideas and specific outcomes in the program of studies?

See Sequence of Outcomes from the Program of Studies

Strand: Shape and Space (Measurement)

Grade 4

Grade 5

Grade 6

Specific Outcomes

Demonstrate an understanding of area of regular and irregular 2-D shapes by:

recognizing that area is measured in square units
selecting and justifying referents for the units cm² or m²
estimating area, using referents for cm² or m²
determining and recording area (cm² or m²)
constructing different rectangles for a given area (cm² or m²) in order to demonstrate that many different rectangles may have the same area.

Describe and construct right rectangular and right triangular prisms.

Specific Outcomes

Demonstrate an understanding of volume by:

selecting and justifying referents for cm³ or m³ units
estimating volume, using referents for cm³ or m³
measuring and recording volume (cm³ or m³)
constructing right rectangular prisms for a given volume.

Specific Outcomes

Develop and apply a formula for determining the:

perimeter of polygons
area of rectangles
volume of right rectangular prisms.

Big Ideas

Van de Walle and Lovin (2006) define volume as "the amount of space that an object takes up" (p. 265). Volume is measured in units such as cubic centimetres (cm³) or cubic metres (m³), which are based on linear measures.

By estimating a measure first and then using measuring instruments to measure, students develop measurement sense. Estimation in measurement is defined as follows:

"Measurement estimation is the process of using mental and visual information to measure or make comparisons without the use of measuring instruments. It is a practical skill" (Van de Walle and Lovin 2006, p. 278).

In using any type of measurement, such as length, area or volume, it is important to discuss the similarities between them in developing an understanding of the different measures. First identify the attribute to be measured, then choose an appropriate unit and finally compare that unit to the object being measured (NCTM 2000, p. 171). An attribute of an object is an aspect of that object that can be measured. "The measure of an attribute is a count of how many units are needed to fill, cover or match the attribute of the object being measured" (Van de Walle and Lovin 2006, p. 253). As with other attributes, it is important to understand the attribute of volume before measuring.

Key ideas in understanding the attribute of volume include:

conservation—an object retains its size when the orientation is changed or it is rearranged by subdividing it in any way
iteration—the repetitive use of an identical non-standard or standard units of volume to entirely fill or construct an object
additivity—add the measures of the volume for each part of an object to obtain the measure of the entire object
proportionality—there is an inverse relationship between the size of the unit used to measure volume and the number of units needed to measure the volume of a given object; i.e., the smaller the unit, the more you need to measure the volume of a given object
transitivity—when direct comparison of two volumes is not possible, use a third item that allows comparison; e.g., to compare the volume of two boxes, find the volume of one box using non-standard or standard units and compare that measure with the volume of the other box (if A = B and B = C, then A = C)
standardization—using standard units for measuring volume such as cm³ and m³ facilitates communication of measures globally
unit/unit-attribute relations—units used for measuring volume must relate to volume; e.g., cm³ must be used to measure volume and not cm or cm².