Area
The definition for area is the amount of space in an enclosed figure. This is not meaningful to students when they don’t understand the concept. Therefore, one meaningful way of understanding the definition is for students to investigate area. Squares are easy to quantify because they are distinct quantities. If a shape is made of unit squares (that is, squares of area 1), the measurement of its area simply takes the form of counting the squares. If the region is a rectangle with sides of whole number length, and if students have seen that a rectangle can be decomposed into an array of squares (as in the 2 by 3 example above), then the multiplication method to find the area can be used. For instance, if we use the simple shape of a rectangle with a width of 3 units and a length of 4 units using square unit tiles, we see 3 rows of 4 tiles. To find the area of this shape we can count each unit tile, 1,2,3,4,5,6,7,8,9,10,11,12 units or add all the units 1+1+1+1+1+1+1+1+1+1+1+1 = 12 units or multiply the dimensions, 3 length units x 4 length units = 12 square units. Hence, the formula for the area of a rectangle is A= l × w or Area equals length times the width, with the units of each term understood.
Another important component when I teach measurement is to make sure that students use appropriate units. They should state their units of length when computing area and perimeter, and use units of area when explaining measures of area. Measures must be labeled with a unit or they lose their meaning. A unit is a fixed, reference amount. For instance, if a measurement is a big number, we need to know the quantity of the units and what unit is being used as measurement. In other words, the measurement of 10 inches is smaller than the measurement of 10 feet because of the unit of measure being used. Therefore, it’s important to have students write the solution of the measurement using the appropriate unit of measure.
So far we have gone over the measurement of perimeter and area. How are these related to surface area and volume? We know that all real world objects have several different measurable attributes such as length, area and volume. Length is a measure of the object that is one-dimensional such as a line segment. When we measured the perimeter of a planar shape we are actually finding the length or the one dimensional distance around the shape. The area of the shape was then measured by square units, which in other words means how many square units does it take to cover the shape. We will now move into our next content objective, of surface area.
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