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# Capacity

Strand: Shape and Space (Measurement)
Outcome: 5

## 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?
Strand: Shape and Space (Measurement)

 Specific Outcomes 3. 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 by 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. 4. Describe and construct right rectangular and right triangular prisms.

 Specific Outcomes 5. Demonstrate an understanding of capacity by: describing the relationship between mL and L selecting and justifying referents for mL or L units estimating capacity, using referents for mL or L measuring and recording capacity (mL or L).

 Specific Outcomes 2. 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 capacity as "the amount that a container will hold" (p. 265). Standard units of capacity include millilitres (mL) and litres (L). Van de Walle and Lovin (2006) explain that these units are generally used for "liquids as well as the containers that hold them," but "the term volume can also be used to refer to the capacity of a container" (p. 266).

The unit model for capacity is "a small container that is filled and poured repeatedly into the container being measured" (Van de Walle and Lovin 2006, p. 267).

By estimating a measure first and then using measuring instruments to measure, students develop measurement sense. Cathcart (1997) states, "…students should be encouraged to estimate before they measure and to record their results as they find the capacities of a variety of containers using a nonstandard unit" (p. 218). 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/capacity, it is important to discuss the similarities in developing 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). As with other attributes, it is important to understand the attribute of capacity before measuring. 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).

Key ideas in understanding the attribute of capacity 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 unit of capacity to entirely fill a container
• additivity—adding the measures of the capacity for each part of a container to obtain the measure of the entire container
• proportionality—there is an inverse relationship between the size of the unit used to measure capacity and the number of units needed to measure the capacity of a given container; i.e., the smaller the unit, the more you need to measure the capacity of a given container
• transitivity—when direct comparison of two capacities is not possible, use a third item that allows comparison; e.g., to compare the capacity of two containers, find the capacity of one container using non-standard or standard units and compare that measure with the capacity of the other container (if A = B and B = C, then A = C)
• standardization—using standard units for measuring capacity such as millilitre (mL) and litre (L) facilitates communication of measures globally
• unit/unit-attribute relations—units used for measuring capacity must relate to capacity; e.g., mL must be used to measure capacity and not cm or cm2.