Prepare to WOrk With Area

Define area: Discuss the concept of area with the class. Have students answer these questions in small groups first or as a think-pair-share: What about an object is being measured? How would you define area?

Units of area: Discuss standard (e.g. square units or acre) and nonstandard units (e.g. soccer field) of area. Have students discuss these questions: What is a square unit? What kind of nonstandard unit could be used to measure the area of a parking lot or a classroom floor?

Discussion about Area

Define area: Students should be able to articulate the concept of area as measuring the amount of space an object takes up in two dimensions. In the current context we are focused on quantifying the space occupied by flat surfaces but the more general concept of surface area can be used to quantify the amount of two-dimensional space that a surface takes up in three or more dimensions.

Units of area: Square units are a natural way to measure area because squares are formed when two one-dimensional unit lengths extended in perpendicular directions, into two-dimensions, from a single origin point. We can, therefore, measure two-dimensional space by seeing how many squares can cover a flat surface. The dimensions of a square unit are commonly measured in units of length like inches, feet, yards, miles, or meters. 

An acre is a typical measurement of the area of property but is not necessarily familiar in terms of what it's size looks like. An acre is a fraction (one 640th) of a square mile or 4,840 square yards but is not a perfect square. An acre was traditionally defined as a 66 ft by 660 ft rectangle that was originally measured in chains (1 chain by 1 furlong, or 10 square chains, because 1 furlong is equivalent to 10 chains). An acre has also been described, in the Middle Ages, as the amount of land that one man and a team of 8 oxen could plow in one day.

A soccer field is a helpful non-standard unit of measurement that can help visualize the size of an area. For example, a soccer field is about 1.75 acres while the area of Vatican city is approximately the size of 62 soccer fields.

The area of a parking lot might naturally be measured by the number of cars that could cover it or a classroom area measured by the number of student desks or tables that could cover the floor. The main takeaway is that area is a measurement of two-dimensional space so anything that also fills two-dimensional space can be used to quantify the area of another object in comparison.

The area can be also be arrived at by using multiplication to count the total of unit squares making up the figure. In our example, we have six rows of six square units for a total of 36 square units.