Goal-directed Instructional Design Plan - Mathematics: Area of Regular Polygons
Author - Ashley Bartkowiak
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A problem or a need – The goal for this lesson is to provide students with an
understanding of how to find the area of any regular polygon.
A real-world performance – Students are asked to explain how a contractor would
estimate the amount of flooring needed to cover one level of a regular polygonal shaped
building, such as the United States Pentagon.
An instructional objective – the objectives are based on the final outcome, activity or
test. These objectives will each be different for the four types of knowledge; performing
skills, recalling facts, identifying examples of concepts, and applying principles.
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Students will develop and share a method for finding the area of The Pentagon
Building (a regular pentagon) with their peers.
b. Students will test their method and generate a formula for finding the area of any
regular polygon.
c. Students will use their generated formula to solve basic and complex real-world
problems.
A set of essential content – Students must have a basic understanding of area and the
properties of regular polygons. They will also need to know the order of operations for
solving complex problems.
An evaluation consisting of a test or observation –
● Student understanding will be evaluated based on the level of discussion - are students
able to comprehend the key concepts, use correct vocabulary, and make mathematical
connections?
● Student achievement will be informally assessed during individual work time and
formally assessed through homework and quiz responses.
A method to help participants learn –
● A picture of the United States Pentagon will be displayed on the front board. Students
are asked to name the shape and list the properties of that shape. As a bonus
question, they are asked to provide the name of the building and describe its purpose.
● Students are shown two short videos about The Pentagon Building.
● Students are given a template of a regular pentagon (representing the floor plan of
one level of The Pentagon) and asked to individually think about how they would find
the area of that pentagon using prior knowledge.
● Students will discuss their findings with a partner and test their methods using the
Cabri geometry software. As a pair, the students will generate a formula for finding the
area of the regular pentagon.
● As a class, the students will share what they have discovered and generate a formula
for finding the area of any regular polygon.
● Students will be assigned practice problems for homework.
Michigan State University, Educational Technology Programs
http://edutech.msu.edu
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Motivation:
○ Meaningfullness – Students will have a basic understanding of how contractors
calculate how much flooring a polygonal building needs.
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Pleasant consequences – Students will generate a formula for finding the area
of any regular polygon so that they do not have to analyze each regular polygon
individually and go through all of the steps over again. Students will simply have to
plug the necessary information into the formula and calculate their answers. This
will reduce the amount of time needed to solve each problem.
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Novelty – Students are asked to think of other oddly shaped buildings in the world
in which it may be difficult to find the area of the flooring.
Socialization - This is a discovery-based lesson in which students are able to work
with their peers and use technology to test their findings. They are responsible for their
learning and are given the chance to explore their ideas with little teacher interference.
Audience – For what audience are you designing this lesson? Consider the following:
○ Age:
○ High School Geometry Students- 10th grade
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Skill level (including technology skills):
○ Varied understanding of the Cabri geometry software
○ The ability to solve problems using order of operations
○ A basic understanding of the properties of regular polygons
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Prerequisite knowledge (including technology background):
○ Basic Cabri software skills
○ Algebra skills - order of operations
○ Basic computational skills - adding, subtracting, multiplying, dividing
○ Knowledge of the properties of regular polygons
Technology Needs – Overhead Projector, Document Camera, Computer Lab or Laptop
Cart, Internet access, and Cabri Geometry Software
Michigan State University, Educational Technology Programs
http://edutech.msu.edu