# Area

**Strand:** Shape and Space (Measurement)

**Outcome:** 3

## 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

### Big Ideas

Van de Walle and Lovin define area as "a measure of the space inside a region or how much it takes to cover a region" (2006, p. 234).

In using any type of measurement, such as length, area or volume, 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 area before measuring.

Key ideas in understanding the attribute of area include the following:

- 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 a identical nonstandard or standard units of area to entirely cover the entire surface of the region
- tiling—the units used to measure the area of a region must not overlap and must completely cover the region, leaving no gaps
- additivity—add the measures of the area for each part of a region to obtain the measure of the entire region
- proportionality—there is an inverse relationship between the size of the unit used to measure area and the number of units needed to measure the area of a given region;

i.e., the smaller the unit, the more you need to measure the area of a given region
- congruence—comparison of the area of two regions can be done by superimposing one region on the other region, subdividing and rearrangement as necessary
- transitivity—when direct comparison of two areas is not possible, use a third item that allows comparison; e.g., to compare the area of two windows, find the area of one window using nonstandard or standard units and compare that measure with the area of the other window; i.e., if A = B and B = C, then A = C
- standardization—using standard units for measuring area such as cm
^{2} and m^{2} facilitates communication of measures globally
- unit/unit-attribute relations—units used for measuring area must relate to area; e.g., cm
^{2} must be used to measure area and not cm or mL. (Alberta Education 2006, pp. 2–4)

Adapted from Alberta Education, *Teaching Measurement Concepts, Grades 4–6* (unpublished workshop handout) (Edmonton, AB: Alberta Education, 2006), Research section, pp. 2–4.