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Christine
Fairless Connects With Her Students
Twenty
five seventh graders at Bernard-White School in Union City were
designing research stations for Antarctic researchers last week.
After designing floor plans on computers, students investigated
which insulation level was the best buy for reducing building
and heating costs at the south pole.
Major
projects in MMAP/Pathways ask students to take on the role of
a math-using professional and carry out a design project from
beginning to end. Memos from their fictional employer—along
with other paper materials and computer software— aid students
in their work. Students learn mathematics as they use it in
their design and analysis of their design. Then Side Trips focus
on the same content from a more pure mathematics point of view.
Antarctica is a 5-week project in which students design and
analyze a research station for scientists working and living
in the frozen south. Memo 3 asks students to find the level
of insulation (measured in R-value) that minimizes total building
and 20-year heating costs for their research station. Students
create tables, rules in word and symbols, and graphs to investigate
the problem and support their choice. Students learn how to
build a formula from variables that represents the total cost.
They use functions in which the variables are linearly and inversely
related. The move from stating patterns such as “as R value
goes up, heating costs go down” to more precise expressions
such as T=B+20(12)H where T is total cost, B is building cost
and H is monthly heating cost. They interpret the graph of this
function to make their choice of the best R value for their
design in the Antarctic climate.
The Side Trip, Direct and Inverse Variation, introduces students
to the families of functions for the two relationships they
uncovered in the R value problem. They explore the mathematical
properties of these two families through examination of many
examples.
So, within these lessons, students are learning significant
mathematics aligned with the NCTM PSSM 2000, specifically with
understanding functions through use of tables, graphs and verbal
and symbolic rules. They identify graphs as linear or non-linear
and contrast their properties. They learn about uses of variables,
dependent and independent, and as parts of an equation. They
solve a problem from a architectural and engineering context
and draw inferences from the mathematical model and the real-life
context to solve the problem.
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