Area

Strand: Shape and Space (Measurement)
Outcome: 2

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 6

Grade 7

Grade 8

Specific Outcomes

Develop and apply a formula for determining the:

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

Specific Outcomes

Develop and apply a formula for determining the area of:

triangles
parallelograms
circles.

Specific Outcomes

Determine the surface area of:

right rectangular prisms
right triangular prisms
right cylinders

to solve problems.

Develop and apply formulas for determining the volume of right rectangular prisms, right triangular prisms and right cylinders.

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. 240).

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:

conservation—an object retains its size when the orientation is changed or when it is rearranged by subdividing it in any way
iteration—the repetitive use of identical nonstandard or standard units of area to cover the surface of the region entirely
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 units are needed 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 rearranging as necessary
transitivity—when direct comparison of two areas is not possible, a third item is used 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, and similarly for inequalities
standardization—using standard units for measuring area, such as cm² and m², facilitates communication of measures globally
unit/unit–attribute relations—units used for measuring area must relate to area; e.g., cm² must be used to measure area and not cm or mL.

Adapted from Alberta Education, Measurement: Activities to Develop Understanding (Research section) (unpublished workshop handout) (Edmonton, AB: Alberta Education, 2005), pp. 2–4.

Formulas for finding areas of 2-D shapes provide a method of measuring area by using only measures of length (Van de Walle and Lovin 2006, p. 230). The areas of rectangles, parallelograms, triangles and circles are related, with the area of rectangles forming the foundation for the areas of the other 2-D shapes.