AUTHOR: Kirsten Davis, Salt Lake City, UT

Date: 1994

Grade Level(s): 8, 9, 10, 11, 12

Subject(s):

• Mathematics/Geometry

OVERVIEW: Students will explore properties of similarity using models, measurement, and calculation.

OBJECTIVES: The students will:
1. Measure the dimensions of a rectangular solid to the nearest millimeter.
2. Create a scale drawing of the box.
3. Calculate surface area and volume for the original and the scaled down rectangular solids.
4. Calculate and interpret scale factors for length, area and volume of two similar objects.
5. Use correct dimensions for units.

RESOURCES/MATERIALS:

• boxes (full or empty)
• centimeter rulers
• pencil
• graph paper
• scissors
• tape
• calculator

ACTIVITIES AND PROCEDURES:
1. Divide class into groups of two or three.
2. Give materials to student teams.
3. Have students make a table or chart that has columns for length, width, height, total surface area, and volume for both the original box and the mini-box.
4. Have students measure the original box and record length, width and height in mm.
5. Have students make a scale drawing of the original box (graph paper helps keep segments straight).
6. Have students record measurements for the mini-box in mm. Cut out, fold, and tape the scale drawing together.
7. Have students calculate total surface area and volume for the two rectangular solids.
8. Have students find scale factors for length, surface area, and volume and write conclusions about findings.

TYING IT ALL TOGETHER:
1. Discuss findings about scale factors for similar objects with regard to the length, area and volume.
2. Discuss careers that would use scale drawings.
3. Have students share in writing the technique(s) that they used to make their scale drawing.
4. Encourage students to share learned knowledge with parents.