Background:

This activity is intended to reinforce concepts of ratios and proportions by applying them to scale drawings. It will also give practice in solving proportions.

Prior to attempting this activity, students should have mastered identifying equivalent fractions by cross-multiplication. They should also have had minimal exposure to ratios and proportions.

Resources Needed:

• Computer with Internet access and projection capability, or large United States road map;
• Computer(s) with Internet access for student use;
• Rulers (preferably flexible rulers);
• Graph paper and tape are needed for the assignment, which may be given as homework.
  

Exposition:

1. Review concepts of ratios and proportions.

• A ratio is a comparison between two numbers.
• A ratio comparing a to b may be written as "a:b" or as "a/b".
• A proportion is a statement that two ratios are equivalent (e.g. a/b = c/d).
• We solve proportions by cross-multiplication and division. (E.g. 3/4 = x/16 iff (3)(16) = 4x iff (3)(16)/4 = x iff x = 12.)

2. Introduce map scale as one application of ratios.

Experience/Procedure:

3. On the Internet "MapBlast!" site (www.mapblast.com/mblast/mAdr.mb), request driving directions from Los Angeles, CA to Washington, DC. The "MapBlast!" program will return a United States road map. Open a "notepad" window alongside the map to take notes while working through questions such as:

• What is the map scale?
• What is the map distance from LA to DC?
• How far is LA from DC?
• How far is Omaha from Chicago?
• If we map Omaha to Chicago, what will the new scale be?
  

Critical Thinking:

4.             What would happen if the same scale was not used consistently across an entire map?

Which units of measure are most appropriate for maps or floor plans? Why?

How could you use proportions to convert a scale from one unit of measure to another?

Interactive Learning:

5. With a partner or cooperative learning group, students locate their school on a "MapBlast!" map (www.mapblast.com/mblast/mAdr.mb). They use the map scale and a ruler to compute the actual distance between the school and some given landmark several blocks from the school. Students then zoom in or out and observe the change in the map scale. Have students calculate the distance on the map between the school and the landmark by solving a proportion relating the new scale to the measurements from the previous map. Students can check their answers by measuring with the ruler.

6. If time permits, students may visit Internet site http://pezboy.hypermart.net/swblue.html to see a blue print of a Star Wars Y-wing Longprobe spacecraft and calculate the scale of this drawing as viewed on the computer monitor.

Students may also learn about large scale vs. small scale maps by visiting Cynthia Lanius's "Mathematics of Cartography" web page at http://math.rice.edu/~lanius/pres/map.

Assignment:

7. Make scale drawings of a bedroom and essential bedroom furniture. Use the scale models to experiment with various furniture arrangements. As a homework assignment, students may measure their own bedrooms and bedroom furniture. Alternatively, they may visit a web site such as www.gshomedesign.com/plans.html to find realistic bedroom dimensions and an online furniture catalog such as www.funrniturefind.com/bedroom.htm for furniture dimensions. A worksheet is provided to assist students in organizing their data and computations.

Resources:

"A long time ago, in a galaxy far, far, away...PezBoy's Star Wars blueprints corner." [Online]. Available: http://pezboy.hypermart.net/swblue.html.

FurnitureFind.com. "The bedroom department." [Online]. Available: http://www.furniturefind.com/bedroom.htm.

G.S. Home Design. "House plans/floor plans by G.S. Home Design." [Online]. Available: http://www.gshomedesign.com/plans.html.

Lanius, C. "Mathematics of Cartography." [Online]. Available: http://math.rice.edu/~lanius/pres/map/.

"MapBlast!" [Online]. Available: http://www.mapblast.com/mblast/mAdr.mb.

Roles Names

Computer Operator: Types on the keyboard and maneuvers the mouse ___________________

Navigator: Determines site addresses and links to follow ___________________

Measurer: Takes measurements with a ruler ___________________

Recorder: Records final answers on the group worksheet ___________________

1. Go to the MapBlast! web site at http://www.mapblast.com/mblast/mAdr.mb. Enter the school address to get a map of our town, with the school at the center of the map.

What is the zoom level of the map?

2. What is the scale of miles at this zoom level? Measure the scale box and write the scale of miles as a ratio.

3. With your ruler, measure the distance from the school to the nearest highway intersection.

4. Use a proportion to calculate the distance in miles from the school to the highway. (All group members should perform the calculation on scratch paper. When you reach a consensus, write your final answer here. Show your work.)

5. Zoom in or out on the map. What is the new scale?

6. Use a proportion to convert the scale to miles if necessary. The ratio of feet to miles is 5280:1. (All group members should perform the calculation on scratch paper. Write your final answer here, showing how you got it.)

7. Use a proportion to calculate the distance on the map from the school to the highway, using the new scale of miles. Show your work.

8. Use the ruler to check your answer. What is the actual measurement?

9. Was your predicted measurement reasonably close to the actual measurement? Justify any discrepancy.

Is it time to give your bedroom a new look? Experiment with a new furniture arrangement the way the professionals do, with scale drawings.

Interior decorators use scale drawings of rooms and furniture to experiment with different ways of arranging a room. There are computer programs that enable decorators to map a room, enter the dimensions of the furniture, and drag the furniture into various arrangements within the room. The same thing can be accomplished by hand using graph paper, pencil and scissors.

Your assignment is to create scale drawings of (1) a bedroom floor plan and (2) at least two pieces of bedroom furniture. Cut out the furniture drawings and tape them to the floor plan in your recommended furniture arrangement.

You may choose to measure your own bedroom and furniture at home, or you may use a bedroom from a model blueprint on the Internet and furniture dimensions from an online furniture catalog. Here are two sites you might visit:

Home plans by G. S. Home Design: www.gshomedesign.com/plans.html

FurnitureFind.com online catalog: www.furniturefind.com/bedroom.htm

First complete the data sheet below. Then use graph paper to make your scale drawings.

Room Dimensions:

Wall Length Position of door, window or indentation

1

2

3

4

Furniture Dimensions:

Description Shape Length Width