Teaching Area and Perimeter

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  • 0:00 Introducing Area and Perimeter
  • 0:27 Presenting the Concepts
  • 1:14 Teaching Area
  • 3:49 Teaching Perimeter
  • 5:07 Practice
  • 6:01 Lesson Summary
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Lesson Transcript
Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

Although students may not believe it, finding the area and perimeter of different shapes and objects can be fun. This lesson will provide strategies and examples for teaching these concepts to your students.

Introducing Area and Perimeter

When you introduce area and perimeter to your students, does their attention begin to wander? It doesn't have to be this way. Area and perimeter really are not difficult. We can make them fun to learn by using concepts that your students can relate to. This lesson is going to present a practical approach for teaching concepts and calculations for area and perimeter.

Presenting the Concepts

Concepts that may be new or challenging to students will be the ideas of a surface versus a line, square measurements versus linear ones, and the calculations involved with the two types of measurements. This lesson uses visualization and active participation to make those concepts interesting and understandable.

For this lesson you'll need:

  • a diagram of the school's football field or playground, including a copy made on graph paper
  • physical access to the playground or football field, if possible
  • a bag of grass seed with the coverage indicated on it, telling how much area the bag of seed will cover. You will want the measurement in square yards for the problem; so, you will want to make sure that number is available for the lesson.

Teaching Area

We'll start with teaching area. Because the area measurement of a surface may be defined as the number of square units that will fit inside it, one of the simplest shapes for area calculation is a rectangle, so an excellent way to introduce area to your students would be to tell your students that their playground or football field needs to be reseeded. If you could take a 'trip' to the field when introducing this concept, that would be great.

Introducing the 'Square' Unit

Displaying the picture or drawing that includes a grid of squares, you can introduce the 'squared unit' idea graphically. Let students know that units, which are the standard divisions for measurements, become square units when the area is calculated. Examples are square feet, square inches, square yards, etc., Let them know that every possible surface has a formula that will determine the size of the area.

The formula for the rectangular field is going to be length x width. If they're out on the field, let them try to visualize which square they're standing in, and how big that square might be on the field. Get them to visualize the size. Let them walk down the field, counting their steps, and then walk across, doing the same thing. Refer to your diagram and have them visualize how many of their 'square-steps' would be on the field. Finally, introduce standard units. They know how many square-steps there are on the field; how many square yards would there be?

A foot length multiplied by a foot width creates a square foot
square foot

Calculating Area

Now, we'll move on to calculating area. Pose the question to your students. For example, you might ask, 'If I have 100 one-yard by one-yard squares along the edge of the field, and each square represents a row of 50 squares across the field, how could I determine the total number of squares on the field?' Once the students suggest multiplying the two numbers, you're on your way. They should resolve that 50 yards multiplied by 100 yards produces an area of 5000 square yards on the field.

Calculating area of a rectangular field
graphic of field

Now you can re-introduce the reseeding problem. If the bag of seed will cover 50 square yards of field, then how can they figure out how many bags they will need? If you're on the field, put the bag down, and have the students visualize how much area that bag will cover. Have them stand in a rough square or rectangle on the field, showing the area that the bag of seed will cover. Now you can ask the questions that will lead them to determining the number of bags they will need. Continuing with our 5000 square yards example, the students will determine that if they divide the total 5000 square yards by the 50 square yards that one bag of seed covers, they will need 100 bags of seed to cover the field!

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