Activity 1: Square Logo

Activity 1: Square Logo

You have been contracted (hired) to produce a logo for a new company. The company is so new that the founder (owner) has not decided on a name. The company founder wants to represent the company with a logo that must have these characteristics:

· The outline of the logo will be a square;

· There must be at least two non-overlapping squares, two non-overlapping rectangles, and two non-overlapping triangles inside the logo;

· The triangles must be congruent (having the same shape and size) 45°- 45°- 90° triangles;

· All squares must be congruent to all other squares.

1. How are you going to know that a triangle in your logo is a 45°- 45°- 90° triangle?

Describe at least two characteristics of a 45°- 45°- 90° triangle.

______

2. On graph paper or 1 cm grid paper, draw a square with side lengths of 20 centimeters. Within the square, draw a logo that meets these requirements:

· The outline of the logo will be a square;

· A plastic frame will surround the square that is 20 cm on each side;

· There must be at least two non-overlapping squares, two non-overlapping rectangles, and two non-overlapping triangles inside the logo;

· The triangles must be congruent 45°- 45°- 90° triangles;

· All squares must be congruent to all other squares.

**Before proceeding too far along with your design, check with your teacher (initials) ______

Student: Ch 20 “Creating A Logo”

3. You may notice that, since the triangles are all congruent and the squares are all congruent, you can use transformations (reflections (a mirror view), rotations (move in circular direction), translations (slide or move) to move one of the figures to the location of the other(s). This is a common way that computer programmers create congruent figures in designs.

· For your logo, describe a transformation or combination (blend) of transformations that you could use to move one triangle to the location of another triangle. If you used a transformation, make sure you label your transformed figure.

______

4. For your logo, describe a different transformation or combination of transformations that you could use to move one square to the location of another square.

______

Student: Ch 20 “Creating A Logo”

5. For your logo, is it possible to use a transformation or combination of transformations to move

one rectangle to the location of another rectangle? ______

--If it is possible, describe a transformation or combination of transformations you could use.
--If it is not possible, describe why you cannot use a transformation or combination of transformations to move one rectangle to the location of another rectangle.

______

Activity 2: Glass Logo

6. You need to be able to describe your design to the founder of the company over the phone before you work on putting it into an electronic format for printing.
Write a description of your image. You must use correct mathematical language including language about the transformations (reflections, rotations, translations) for your logo.

______

7. The founder is going to make a glass version of your logo to hang in the window of her office. She is going to use different colors of glass for the squares, rectangles, and triangles in the logo. The different colors of glass have different costs per square centimeter. She will put a plastic frame around the perimeter of the logo to keep the glass from chipping or breaking. She will also put lead stripping between the various shapes of the glass within the logo.
The founder wants to know, for your design, the total area and perimeter of the outside of the logo, and the perimeter and areas of each of the squares, rectangles, and triangles within the logo.

a. Describe a strategy (a plan) you could use to determine the total area of the logo.

______

b. What is the area of one of the triangles inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

c. What is the total area of all of the triangles inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

d. What is the area of one of the squares inside your logo? ______

Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

e. What is the total area of all of the squares inside your logo? ______

Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

f. What is the area of one of the rectangles inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

g. What is the total area of all of the rectangles inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

h. What is the total area of the colored glass inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

i. Describe a strategy you could use to determine the total perimeter of the outside of the logo and the total perimeter of the figures inside of the logo.

______

j. What is the perimeter of one of the triangles inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

k. What is the total perimeter of all of the triangles inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

l. What is the perimeter of one of the squares inside your logo? ______

Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

m. What is the total perimeter of all of the squares inside your logo? ______

Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

n. What is the perimeter of one of the rectangles inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

o. What is the total perimeter of all of the rectangles inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

p. What is the total perimeter of the figures inside your logo? ______
Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

q. What is the perimeter around the outside of your logo? ______

Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

r. The area within the logo that is not a square, rectangle, or 45°- 45°- 90° triangle of colored glass will be filled with clear glass.

· Describe a strategy you could use to determine the area of clear glass that would be used for your logo.

______

s. What is the area of clear glass that would be used for your logo? ______

Support your answer using words, numbers and/or diagrams. Be sure to include appropriate units.

Activity 3: Itemized Bill

8. Here are the costs of the thin plastic frame, the clear glass, the different colors of glass and the lead stripping that will go between the various colors.

Material / Cost
Plastic frame / $0.24 per cm
Clear glass / $0.88 per square cm
Purple glass / $1.42 per square cm
Green glass / $1.14 per square cm
Yellow glass / $0.96 per square cm
Blue glass / $1.35 per square cm
Red glass / $0.85 per square cm
Labor Cost / $0.36 per square cm
Lead stripping for between the glass / $0.87 per cm

All of the squares within the logo must to be filled with one color of glass. All of the triangles must to be filled with a second color of glass that is different than the color chosen for the squares, and all of the rectangles need to be filled with a third color of glass, different from the triangles and the squares.

a. Determine which colors you are going to use for the squares, triangles, and rectangles. On your graph paper, color the logo with the appropriate colors.

b. Determine the total cost for your logo by filling in the Itemized Bill on the next page.

Itemized Bill

Name: ______Date: ______

Dimensions of the window: ______

Cost for the lead: ______cm @ $0.87 per cm Material Cost: ______

Cost for the plastic frame: ______cm @ $0.24 per cm Material Cost: ______

Cost for glass (Round measurement calculations to the nearest hundredth (second decimal place)):

v Color ______sq. cm @ ______per sq. cm

Material Cost: ______

v Color ______sq. cm @ ______per sq. cm

Material Cost: ______

v Color ______sq. cm @ ______per sq. cm

Material Cost: ______

v Color ______sq. cm @ ______per sq. cm

Material Cost: ______

Cost for Labor: ______sq. cm @ $0.36/sq. cm Labor Cost: ______

TOTAL COST FOR THE LOGO: ______

Activity 4: Stained Glass Window

You are the greatest stained glass architects of the Western World. You have been commissioned (hired) to create a hexagonal stained glass window for the National Mathematics Institute. You will design the window to meet the Institute’s guidelines (requirements):

1.) The window design must be a regular hexagon;

2.) You must submit a drawing of the window design with hexagon side lengths of 4 inches;

3.) The only shapes that may be used in the window design are 30-60-90 triangles and smaller regular hexagons;

4.) At least 4 different colors of glass must be used;

5.) The drawing needs to be colored to match the color of the stained glass window;

6.) You must include a scale factor of 2:3 for your drawing and stained glass window;

7.) You must submit an itemized bill using these costs:

Material / Cost
lead strips (between pieces of glass and around entire window) / $3.08 per foot
blue/brown glass / $7.67 per square foot
green/purple glass / $8.23 per square foot
red/yellow glass / $10.47 per square foot
all other colors of glass / $9.88 per square foot
labor for entire window / $215.36 per square foot

1. Design a drawing of a hexagonal stained glass window. You may use grid paper to help you.

· Be sure your drawing follows the first three of the Institute’s guidelines.

2. Determine all relevant measurements of your drawing to an appropriate level of precision (accuracy). Use those measurements to determine the measurements of the actual window.

· Be sure to follow the sixth guideline.

3. Determine the colors you will be using for your window design and color your window design accordingly.

· Be sure to follow the fourth and fifth guidelines.

4. Write a report to present to the National Mathematics Institute. Be sure to include:

· How your window meets the Institute’s guidelines for the window;

· The process you used to determine the total cost of the window, including the cost of the lead strips, the different colors of glass, and the labor for the entire window;

· A persuasive argument on why the Institute should choose your window design.

5. You must present an itemized bill to the Institute for the cost of your window. Use this template and the costs from the seventh guideline to create your itemized bill.

6. At the same time that you turn in your written report, itemized bill, and design for a stained glass window, you will give an oral presentation to the class to persuade them why the Institute should purchase your window.

Supporting Calculations

Calculations dealing with the lead (Be sure to convert units):

Calculations dealing with the glass (Be sure to convert units):

Calculations dealing with the labor:

Calculations dealing with determining the actual size of the window:

Itemized Bill

Name: ______Date: ______

Dimensions of the window: ______

Cost for the lead: ______feet @ $3.08 per foot Material Cost: ______

Cost for glass (Round measurement calculations to the nearest hundredth):