STAINED GLASS WINDOW
Enduring Understanding: Develop a better understanding of how to use the properties of special
triangles and regular polygons to answer a question. Develop a better understanding of how to
develop a persuasive mathematical argument both orally and in written form.
Essential Questions:
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What is a regular hexagon?
What is an itemized bill?
What are the properties of an equilateral triangle that aligns with the properties of a 30-60-90
triangle?
How does one convert square inches to square feet?
What are the special properties of a regular polygon?
What is the difference between area and perimeter?
How is a persuasive argument developed?
Lesson Overview:
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Before allowing the students the opportunity to start the activity: access their prior knowledge
regarding how to work with the special properties of triangles and regular polygons. How
many have given persuasive oral presentations? How many have written a persuasive
argument? Have you ever tried to persuade your parents and/or friends to allow you to do
something that they didn’t want you to do? How did you go about trying to persuade them?
A good warm-up for this activity is Landscape Architect.
Some artistic license can be allowed to assist the students’ ability to be more creative.
Give the students the presentation rubric prior to their development of their presentations.
Introduce this activity on a Monday with the turn-in and presentations on Friday. Allow for
some time during class during the week for the students to work on this activity.
Provide the students with several copies of the template of the regular hexagon. The template
given to the students should be on card stock so that the hexagon is sturdy when the students
trace the template onto a sheet of blank paper.
How is a problem situation decoded so that a person understands what is being asked?
What mathematical information should be used to support a particular conclusion?
How will the students make their thinking visible?
Use resources from your building.
EALRs/GLEs
1.1.4
1.1.6
1.2.3
1.2.5
1.3.2
2.2.1
2.2.2
3.3.1
4.2.1
4.2.2
5.1.1
Item Specifications: NS02; NS04; ME02; ME03; GS01; SR02; SR05; CU02; MC01
Assessment:
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Use WASL format items that link to what is being covered by the classroom activity
Include multiple choice questions
Stained Glass Window
1. You are the great stained glass architects of the Western World. You have been commissioned to
create a hexagonal stained glass window for the National Math Institute. You will design the window
meeting the Mathematicians following specifications:
 The window must fit the hexagon EXACTLY.
 The only shapes that may be used in the window are 30-60-90 triangles and smaller regular
hexagons.
 At least 4 colors must be used.
 You must submit a scale drawing (each side of the regular hexagon should be 4”).
 The drawing needs to be completely colored to match what your regular-sized window.
 Write the dimensions of your regular-sized window.
 You must submit an itemized bill using the following information:
COSTS:
lead strips (between pieces of glass)…………………………………$3.08/ft.
blue/brown glass……………………………………………………...$7.67/sq. ft.
green/purple glass…………………………………………………….$8.23/sq. ft.
red/yellow glass………………………………………………………$10.47/sq. ft.
all other colors………………………………………………………..$9.88/sq. ft.
labor…………………………………………………………………..$30.36/sq. ft.
2. You must figure the areas and lengths exactly in order to submit an accurate itemized bill.
3. You must turn in your itemized bill, the drawing of the “stained glass” and a written report that
includes the method you used to figure the costs and the reasons(s) that your window is the best. The
written part of the proposal is a persuasive argument designed to persuade us to use your window.
4. At the same time that you turn in your written work and your window, you will give an oral
presentation to the class to try to persuade them why they should purchase your window.
Itemized Bill
Name: _______________________________________
Date: ______________________
Dimensions of the window: __________________________________________________________
Cost for the lead: ________________feet @ $3.08 per foot
Total Cost: _________________
Cost for glass:
 Color __________________
________________sq. feet @ ______________ per sq. foot
Total Cost: _________________
 Color __________________
________________sq. feet @ ______________ per sq. foot
Total Cost: _________________
 Color __________________
________________sq. feet @ ______________ per sq. foot
Total Cost: _________________
 Color __________________
________________sq. feet @ ______________ per sq. foot
Total Cost: _________________
 Color __________________
________________sq. feet @ ______________ per sq. foot
Total Cost: _________________
Cost for Labor: ________________sq. feet @ $30.36/sq. ft
Total Cost: _________________
OVERALL TOTAL COST FOR THE WINDOW: _____________________________________
5. For an original graphic design, Lee charges a fixed fee of $50 plus $25 for each hour that he
works. His main competitor charges a fixed fee of $40 plus $30 for each hour that he works on a
design. Lee’s competitor advertises that his rates are cheaper.
Is Lee’s competitor correct?
Support your answer using words, numbers and/or diagrams.
Is Lee’s competitor correct? _____________
6. The regular hexagon below has the same perimeter as a square with a side of twelve inches.
Which is the length of each side of the hexagon?
O A.
2 inches
O B.
3 inches
O C.
6 inches
O D.
8 inches
7. The grass in Lindsay’s lawn in dying, and she has decided to replant the lawn. She made a scale
drawing to help her determine the area of her lawn.
Lindsay’s vegetable garden and flower bed are congruent.
Which is the area of her lawn?
O A.
350 ft²
O B.
425 ft²
O C.
475 ft²
O D.
600 ft²