*
Ken Schmarge
Spring, 2015
* Teacher of Math at Ramsey High School
* Geometry, Calculus, Computer Science
* Infuse technology to coursework to enhance
student understanding
*
* Geometry Honors Course (10th grade)
* Perimeter & area of a regular polygon
* Develop formulas
* Use a spreadsheet to implement formulas
* Use graphing capabilities of the software to
recognize a pattern
*
*
1.
Apply trigonometry to a new
problem
2.
Apply knowledge of circles and
triangles to a new problem
3.
Solve a complex problem by
breaking it into bite-sized pieces
4.
Apply statistical analysis
techniques to repeated calculations
*

CCSS.MATH.CONTENT.HSG.GMD.A.1
(Give an informal argument for the
formulas for the circumference of a
circle, area of a circle…)

CCSS.MATH.CONTENT.HSG.SRT.C.6
(Understand that by similarity, side
ratios in right triangles are
properties of the angles in the
triangle, leading to definitions of
trigonometric ratios for acute
angles)

CCSS.MATH.CONTENT.HSG.SRT.C.8
(Use trigonometric ratios and the
Pythagorean Theorem to solve right
triangles in applied problems.
*
•
•
2 days total
•
1 day in the computer lab
to complete excel work
1 day for students to
complete pre-work
*Pre-work
 The “look” of a
regular polygon as the
# of sides increase
 Introductory problem –
find the area of an
isosceles triangle
*Excel piece
 Set up columns
 Enter formulas
 Populate the chart
 Build the graphs
 Percent error analysis
 Find the area of
regular 3-gon, 4-gon,
& 5-gon
 Develop needed
formulas for general
case
*

Data in rows &
columns

Column widths
and text alignment
customized
*

Color utilized
to highlight
perimeters and
areas that are
within a specified
tolerance
*
* Formulas created by using cell references on
same sheet – ex: central angle = 360 / n
* Formulas created by using cell references
across different sheets – ex: calculation results
from “Perimeter and Area” sheet called in
“Percent Error” analyis
* Formulas created using Excel’s built=in
functions – ex: PI()
* Formula created by an absolute reference – ex:
Circumference = 2*PI() and Area = PI()
* Conditional formatting – ex: shading cells
within a certain tolerance
*
* Fill Series feature utilized – ex: number of
sides in the polygon auto-filled from 3-50
* Headers and print titles used – ex: both sheets
have a title header and, due to the length of
the sheet, print titles
*
* Graph of polygon perimeter
*
* Graph of polygon area
*
* Dropdown menu created for user to pick a
tolerance
*
* Students will connect the concepts of trigonometry,
area, statistics, and graphical analysis to demonstrate
that the perimeter and area of regular polygon
inscribed in a circle approach the circumference and
area of the circle.
* Students can pick a tolerance to visually identify how
many sides are needed for the approximation to be
“close enough” to the known answer – this is a building
block of calculus (concept of limit introduced).
* Students will develop a concrete association with the
irrational number pi through table and graphical
analysis.
*
Category
0
1-3
4-5
Pre-work
Work is not done, or
shows little to no
effort
Work is partially
complete and contains
mathematical and
conceptual errors.
Work is completed
with little or no
mathematical or
conceptual errors
Excel Sheet 1
Sheet is not
completed
Sheet is completed,
but formulas either
have errors or have
not been entered.
Sheet is completed
with all formulas
correct and properly
expanded to fill all
cells. Sheet has been
appropriately named.
Excel Sheet 2
Sheet is not
completed
Sheet is completed,
but formulas either
have errors or have
not been entered.
Sheet is completed
with all formulas
correct and properly
expanded to fill all
cells. Sheet has been
appropriately named.
Graphs
Graphs are not
completed
Graphs are
constructed, but have
no title, axis labels,
may have incorrect
data selected, and
may not be properly
located
Graphs are correctly
constructed with
titles, labels, and
correctly located on
their own page.
Sheets have been
appropriately named.
*
* Concrete Sequential
learners will benefit
from the programmed
instructions and
application of known
topics to a new area
* Concrete Random
learners are curious
and follow their
instincts. They will
benefit from the
problem-solving aspect
to this lesson and the
ability to work
independently through
the guide.
*
*
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Target graphic: blog.7gees.com
•
Sousa, David. How the Brain Learns, 4th. Thousand Oaks:
Corwin Press, 2011. 1-120. Kindle Edition.
•
Diagrams created in Geometer Sketchpad
Common Core graphic: johnstonpublicschools.org
Clock image: metro.co.uk
Common Core Standards:
www.corestandards.org/Math/Content/HSG/introduction/