Perimeter and Area: why they are important topics, lesson activity

Perimeter and Area are two related topics that are extremely relevant to the “real-

world.” I suppose that when first introducing perimeter, I would use examples of a

basketball court, a fence, or a border of some kind, shapes that were rectangles, but real-

life objects. For teaching area, I would also use such shapes. For perimeter, I would give

students shapes that they could use a ruler to find the perimeter, and for area, I would

give shapes that have unit squared boxes graphed with gridlines so that they could count

the boxes to find the area. I would have students do the arithmetic to figure out the

perimeter and area of a rectangle given the lengths of its sides, and I would then

introduce problems involving variables using the same type of example. This way,

students understand the concepts and definitions before they add algebra into the mix. I

would then have them label the sides with variables where appropriate and have a

connection with algebra. Next, I would have students find perimeter from area, and vice

versa, until they can see how much information one needs to know about a rectangle to

figure it’s area and perimeter (2 sides). When introducing triangles, circles, and other

polygons, we would review what we learned about perimeter and area.

The concepts about perimeter and area that I think are most important are how it is

relevant to students’ everyday lives, whether in the process of measuring (figuring out the

best way to travel), computing (approximately how much wood to buy for a fence), or

just to conceptualize and be able to estimate spaces.

The meanings of perimeter and area are another concept I think is extremely important.

The subjects are precursors to essential topics such as volume, or surface area, so students

must understand more than just computation. The notions of inside, or outside, or border,

terms that might be used by students to try to understand or remember the difference

between the two topics, are concepts in amongst themselves. The intrinsic value in the

two measures, their comparison and contrast especially, is one way of seeing the meaning

of each, the dimension difference and measurement difference. (For instance, why might

perimeter be measured in feet, but area in square feet?) (What does “square feet” really

mean?)(Why are they both in feet, do they have to be?) Many students in college don’t

understand these three concepts.

Lesson: for Prealgebra (first introduction to perimeter, already have been introduced to

rectangles)

Problem: The topic for today is perimeter. (pretend like going off on a tangent) Did any

of you have gym today? When I was in high school, when it was really cold outside, the

gym teacher would have us run in the gym, around the basketball court. He would have

us run 40 laps around the basketball court. I always wondered how many miles that was.

Does anyone have any idea how I could figure that out? (hopefully someone says

something, if not introduce it yourself with picture) So I need the dimensions of the

basketball court (have them already). . .after figured out, have students figure out how

many miles it would be if I ran only around half the court (which half might come up, it’s

down the center line) 40 times (concept of half a rectangle area not having half the

perimeter). Have students draw pictures representing the court.