id: 06512815
dt: j
an: 2016a.00628
au: Havens, Rick
ti: Grass for goats (the silo version).
so: Math. Teach. (Reston) 107, No. 7, 553-557 (2014).
py: 2014
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G43 G63 N53 I54 G44 N54
ut: problem solving; student activities; project method; calculus; area;
definite integrals; elementary geometry; plane geometry; circles;
regular polygons; approximation; pre-calculus; trigonometry;
calculators; sum of squares; discovery learning; different approaches
ci:
li: http://www.nctm.org/Publications/mathematics-teacher/2014/Vol107/Issue7/Delving-Deeper_-Grass-for-Goats-%28The-Silo-Version%29/
ab: From the text: The Grazing Goat problem, familiar to many teachers and
students, has several variations. The version presented here provides a
rich opportunity for engaging students in a project spanning several
weeks. Three solutions are discussed, one suitable for a calculus
class, one suitable for a geometry class, and one suitable for a
pre-calculus class. Although we start with a calculus approach, most of
the article uses only algebra and geometry concepts. Also discussed are
the didactics of using projects to open ever-larger fields of
mathematics to students. The problem maybe stated as follows: A retired
mathematics professor has decided to raise a goat. He owns a silo and a
barn. The barnâ€™s front wall is tangent to the silo at the corner. The
silo has a circular base with a radius of 10 feet. The professor has
decided to tether the goat to a chain that is anchored at the corner of
the barn, the point of tangency. He has also cut the chain so that it
is long enough to wrap around the silo exactly once-that is, the length
of the chain equals the circumference of the silo. Help the professor
calculate the grazing area of the goat. Present a solution, complete
with diagrams and calculations, explaining your answer. You are
encouraged to use calculators and computers.
rv: