Site Planning Phase II, Maximum Buildable Area, is the second part of this lesson and explores mathematical concepts such as area and constraints using a realistic building site development project. Through site analysis, calculation, and site drawing, students will discover and analyze the maximum buildable area on a given site.
Materials needed for this activity include:
a calculator, and a ruler with marked 1/16". To introduce
this activity the teacher should discuss the definitions in the
introduction, and the concept of drawing to scale with the class.
The students can then work on this activity in small groups and
complete the remaining problems for homework. A follow up class
discussion of the activity will be necessary to identify key mathematical
ideas within the lesson and address any student difficulties.
Each student can share their site plan drawings with the class
for discussion.
Lesson Prerequisites
Before beginning this lesson, students will already be familiar with several necessary mathematical concepts. As in Phase I of this lesson, student must understand the concept of area. It is important for them to use this knowledge to explore the given site and find the maximum size of area that can be built on. Students must also be familiar with general ruler measurements in terms of inches, and fractions of an inch. For example, students should understand the difference visually and mathematically between 1/4", and 1/2."
Students should understand the concept and mathematical process of percents and percent increase. During the activity, students will be required to use this knowledge to understand and compute the area needed for parking requirements.
Most importantly, student should have basic
algebra skills such as using variables to represent a quantity
in an algebraic expression. Students should be able to use this
knowledge to solve for those variables to determine a specific
quantity. Conceptually, students must be able to extract mathematical
information from applied text problems and represent this information
as a basic mathematical expression.
Difficult Concepts
There are several mathematical concepts in this workplace that students may have difficulty understanding. Scale conversions are important for professionals to communicate through drawings in the design and construction industry, and may be confusing to students. Scale conversion relies practically on operations with fractions and conceptually on representing a measurement in feet as parts of inches. Additional instruction in this process may be necessary for students to be comfortable with this process.
Also, students may have difficulty understanding
how constraints can limit the development plans and options in
the design industry, as well as how to represent these constraints
mathematically. Given a realistic situation, or a zoning code,
students may not understand how these values dictate a certain
area requirement for the site. It is important to understand the
implications of design constraints on a site so students can evaluate
the situation and discover the maximum buildable area on the given
site.
Lesson
Goals
The goal of this lesson is to utilize and develop student's prerequisite knowledge. For example, given a specific area, students will be able to find the length and width to determine the boundaries. This information will then be translated into inches, as students are required to use scale measurements to visually represent this area on the site drawing. Knowledge of fractions of inches will be fundamental to the discovery process as students represent a distance of feet in terms of inches.
This lesson will also build on student's ability
to construct general mathematical expressions from situations
presented in text. Information from this activity will allow students
to constructively analyze and present data mathematically as well
as graphically. This lesson combines practical reasoning with
mathematical constraints to relate to the process of developing
a realistic and functional construction site.
Activity Summary
As students progress through this activity, they will be required to use and develop their prerequisite knowledge as they explore a realistic situation that applies relevant mathematical concepts and procedures. They are visualizing given situational and mathematical constraints and translating that information in terms of area and boundaries on the site. By requiring the students to draw their results on the given site, they are able to clearly see the relationship between feet and inches in scale measurement, as well as the relationship between the area represented by constraints and by the buildable area.
This lesson utilizes the problem solving strategy
of breaking a large problem into smaller parts. General mathematical
expressions are built over a period of leading questions as students
complete the activity. These general expressions help students
with the difficult task of constructing algebraic formulas from
written text. They also give students an understanding of how
these formulas can be applied to easily determine a desired outcome.
Possible
Extensions
This activity has possible extensions for further student development and exploration. One possible extension is exploring the notion of fractions as scale measurements. Students could be asked to represent different feet measurements in terms of inches, or fractions of inches, for a given scale prior to the activity. For example, given the scale 1/4" = 20'-0" students can be asked to determine how large 5', 50' or even 100' are in terms of fractions of inches. A small exercise in fractions could be developed to allow students to explore this concept.
An additional extension of this activity could
involve Geometer's Sketchpad as a tool for exploring scale measure,
or to design the site electronically. Students can use this program
to visually represent area and given mathematical constraints
as a classroom activity.
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