MEASUREMENT

Activity 4 (Small-Group Activity)
Scale Drawings

Students learn about scale while working with scale drawings of floor plans. Use with the Student Copy and the Reference Copy.

Introduction

Obtain pairs of items where one can be considered a scaled version of the other. Flower pots, picture frames, and objects that students know the dimensions of work well. Start the discussion with something like the following. I have two flower pots. One is 10 cm high, the other is 30 cm high. How many times higher is the larger pot? What is the scale to get from the larger to the smaller pot? I have a toy car that is 20 cm long. A real car is about 6 meters long. What is the scale to get from the smaller to the larger car? Put another way, how many centimeters represent each meter.

As part of this lesson, students convert square feet to square yards, so you may wish to discuss how to do this. Drawing a square yard on the blackboard (or identifying one on your floor if you have a tile floor) and showing why you divide by 9 to convert will be helpful to students.

• To extend understanding of the process of measurement.
• To understand the concept of a scale for scale drawings.

A 3-Bedroom Apartment

 Room Length (ft) Width (ft) Floor Area (ft2) Bedrooms 14.5 10.1 11.9 15 13.7 9 217.5 138.4 107.1 Bathrooms 8 5 8 5 40 40 Living room 11.3 23.7 267.8 Kitchen 8 8 64 Storage 4 5 20 Balcony 12 6 72
1. The area to be carpeted is 730.8 sq. ft. The cost for this amount of carpet is \$2030. In practice, however, measurements are often rounded; the cost will actually be higher. Allow answers that take rounded measurements into account.

2. The cost of 144 sq. ft. of linoleum is \$160. The cost of 12 boxes is \$96.

3. The surface area of the wall is about 560 sq. ft.

4. The apartment appears to be about 23.7 feet by 52.8 feet for a total of about 1251 sq. ft. Therefore, the balcony is not part of the advertised living space of 1253 sq. ft.

A 1-Bedroom Apartment

The scale is displayed on the floor plan as 3/8"= 1'.

Including the balcony, the living space is about 928 sq. ft. The living space can be divided into 3 rectangles and a triangle, less a small rectangle in the upper right. Rectangle #1 includes the den, master bedroom, bathroom, and closet for about 429 sq. ft. (less the rectangle in the upper right). Rectangle #2 includes the living room, kitchen, and part of the den for about 324 sq. ft. Rectangle #3 includes the rest of the den and space above the living room for about 56 sq. ft. The triangle includes the storage area, entry, and miscellaneous space for about 119 sq. ft.

 Room Lenth(ft) Width(ft) Bedroom 12.5 18 Living Room 12 13.5 Bathroom 8 12 Walk-in closet 7 7 Dining Room 9 9 Kitchen 8 8 Den 9 10 Storage 9 9 Balcony 4 13.5

 Room Implied Area (ft2) Actual Area (ft2) Bedroom 225 225-7.5-20=197.5 Living Room 162 ---------- Bathroom 108 108-15=93 Walk-in closet 49 --------- Dining Room 81 --------- Kitchen 64 --------- Den 90 90-7.5=82.5 Storage 40.5 --------- Balcony 54 ---------

Closing Discussion

Suppose that the toy car actually belongs to an elf. How tall is the elf? How would you estimate the elf's height without actually seeing her or him? One possibility is to consider the scale of the car and find the size of the elf using the same scale. The discussion could be extended with other objects. For example, suppose your largest flower pot was a coffee cup for a giant. How tall is the giant?

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Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.

Last updated on 1/30/1999
Comments: egalindo@indiana.edu
http://www.indiana.edu/~atmat/units/measurement/mea_t4.htm