Brought to you by
A mathematics resource for parents, teachers, and students
Further investigations:
Here are some activities you and your
student can do together:
Practice measuring large and small
items using both metric and customary
measurement. For example, measure the
dimensions of a room or the dimensions
of a book.
Choose two rectangular prisms (such as
cereal and cracker boxes). Predict which
box has the greater volume. Then measure length, width, and height to find the
volumes
(V = l × w × h).
Calculate distance to nearby cities using a
map and its scale.
Compare a toy such as a car or a dollhouse to the actual object it represents.
Is the toy a scale model? If so, what is its
scale factor?
Terminology:
Dimensions: The measure of the
magnitude, or size, of an object.
Proportion: An equation which states that
two ratios are equal.
Ratio: A comparison of two quantities that
have the same unit of measure.
Scale drawings: Drawings that represent
relative sizes and placements of real
objects or places.
Scale factor: The ratio of corresponding
lengths of the sides of two similar figures.
Similar figures: Figures that have the
same shape but not necessarily the same
size.
Unit: A fixed amount that is used as a
standard of measurement.
Scale Factor
Students will:
•
•
•
•
•
•
Kathy Cox, State Superintendent of Schools
Sixth Grade 7 of 10
Select and use appropriate units to measure length, perimeter, area, and volume
Measure lengths to the nearest 1/2, 1/4, 1/8, and 1/16 inch
Convert one unit of measure to another in the same system of measurement
Use ratio, proportion, and scale factor to describe relationships between similar figures
Interpret and create scale drawings
Solve problems using scale factors, ratios, and proportions
Classroom Cases:
1. Amir is 1.6 meters tall. How tall is he in centimeters?
Case Closed - Evidence:
x cm = 100 cm
1.6 m 1m
x = 100 × 1.6 = 160 cm
2. How long is the pencil?
Measure to the nearest 1/2 inch.
Then measure to the nearest 1/8 inch.
Case Closed - Evidence:
There are 16 divisions (little lines) in each inch. The eraser of the pencil is aligned with 0 and
the point of the pencil is aligned with the 7th line past the 4 inch mark. So the pencil measures
4 7/16 inches. To the nearest 1/2 inch, 4 7/16 is closer to 4 1/2 inches than to 4 inches.
(4 1/2 = 4 8/16). To the nearest 1/8 inch, 4 7/16 is between (4 6/16 = 4 3/8)
and 4 8/16 (= 4 4/8)
3. Anna’s living room floor is a rectangle 12 feet by 15 feet.
How many feet of baseboard will she need to go around the room?
How many square feet of carpeting will she need to cover the floor?
If the room is 10 feet high, how many cubic feet of space will it contain air will it hold?
How will your answers change if you know the door is 2 1/2 feet wide and 7 1/2 feet tall?
Case Closed - Evidence:
To go around the room means to find the perimeter: 12 + 15 +12 + 15 = 54 feet.
Anna will need 54 feet of baseboard. She can subtract 2 1/2 feet from this
sum to account for the door (54-2 1/2 = 51 1/2 feet of baseboard.) To find square feet means
to find the area: 12 × 15 = 180 sq. ft. Anna will need 180 sq. ft. of carpet. To find how much it
will hold means to find the volume: 12 × 15 × 10 = 1800 cu. ft. of space in the room
4. At left is a scale drawing of Carlos’ living room. If the scale factor is 1 in.: 12 feet, how
many cubic feet of air will Carlos’ living room hold?
Case Closed - Evidence:
The dimensions of the scale drawing are 1 1/4 by 7/8 by 9/16 inches. I first find the actual
measurements:
1 inch = 12 feet
Related Files:
www.ceismc.gatech.edu/csi
Produced by the Center for Education Integrating Science, Mathematics, and Computing at Georgia Tech in cooperation with the Georgia DOE. ©2008 Georgia Institute of Technology