Footprints: Take a
Step into Estimation
photo: Blackhawk College

Author:
Kathleen Kruthoff,
Washington School, 3500 Prais St.,
Stevens Point, WI 54481
kkruthof@wisp.k12.wi.usa

Grades:
3-6

Overview of Lesson:
This lesson gives students a chance to compare the sizes of their footprints with those of elephants and sauropod dinosaurs. They will make estimations of the areas of irregular shapes. Students will use grids to make and explain estimates within low and high ranges.

Suggested Time:
Three 45-minute class periods

Students' Prior Knowledge:
Students should be familiar with the concepts of perimeter and area and also with using a grid for measuring. (Previous lessons on mapping and scale from this site are helpful.)

Background Information:
Recently there has been a renewed interest in dinosaur tracks and trackways. As part of this field experience, participants found a site on private land in Colorado where they mapped the site and traced the sauropod (large, quadrapedal dinosaurs, like apatosaurus) imprints they found. There are scale map drawings of some of these walkways and an elephant trackway found under Classroom Resources on the Student Activity page.

There is an area in the Comanche National Grasslands in Colorado, about 23 miles south of La Junta, known as the Picket Wire Canyonlands. The area is managed by the U.S.D.A. Forest Service and is located along the banks of the Purgatoire River. It contains the largest dinosaur tracksite found in North America.
http://www.fs.fed.us/r2/psicc/coma/palo/autotour_brochure.pdf
#xml=http://www.fs.fed.us/cgi-bin/texis/searchallsites/
search.allsites/xml.txt?query=dinosaur+
tracks&db=allsites&id=424892d60

Materials:

• scissors
• overhead projector pens (at least 2 colors for each group)
• colored construction paper (12 x 18, assorted colors, 2 pieces for each child)
• overhead transparencies of scaled grids: square inch and/or square centimeter (at least one for each group, better if one per child)
• cut-outs of the elephant and sauropod footprints (could be made from plastic sheet trackways or enlarged from the resource page, whichever is available to you)
• Dinosaur Lake: The Story of the Purgatoire Valley Dinosaur Tracksite Area
  by Martin G. Lockley, Barbara J. Fillmore, Lori Marquart
  (ISBN 1-884216-53-6) (Nice to have for more information and trackway diagrams, but not necessary for this lesson.)

Student Activity:
Part 1

1. Make a tracing of your bare foot.
2. Cut it out and make 10 – 12 copies (also cut out).
3. Estimate how many of your feet it would take to fill in the elephant print. (Actually use your cut-outs to help you, after predicting.) (See Teacher Note.)
4. Estimate how many of your feet it would take to fill in the sauropod print.

Part 2 ( This may be done independently from Part 1)

1. Recall how you’ve found the area of regular rectangles and polygons that could be divided into rectangles.
2. Make a tracing of your bare foot (or use a copy of one from Part 1). This is an “irregular” shape.
3. Place your footprint under the grid transparency.
4. Using an overhead pen, trace a copy of your foot on the transparency.
5. Draw x’s in all the squares that are completely filled by the colored paper (this is the “low” estimate).
6. Take a pen of a different color and draw x’s on any square which shows a partial piece of your foot (this is the “high” estimate). (See Teacher Notes - Part 2 a.)
7. Estimate the area of a sauropod footprint. Record the steps in the method you used. (See Teacher Notes – Part 2 b.)

Teacher Notes:
Part 1: A discussion about whether to count only “whole” feet or “partial” feet may arise. Decide ahead of time or let the class discuss how they think these estimates should be made.

Part 2a: Explain to students that both estimates of area are valid and that they create an area “range”. The actual area is somewhere in between. Explain how difficulties arise when trying to figure “exact” areas with irregular shapes. Let them discuss which number they’d like to use, low or high, or come to some consensus on an alternative. They might suggest counting “filled and at least half-filled”. All answers are estimates.

Part 2b: Students may employ a variety of methods based on previous activities. Accept any answer that follows a step-by-step process that they can justify. Have the class groups explain how they came to their answers. Display a class “range” of areas. Have students explain why there might be variables with answers, and why estimation is OK.

Vocabulary:
perimeter, area, grid, rectangle, regular, irregular, trackway, variables

Interdisciplinary Connections:
Math: estimation, area, measurement
Language Arts: writing an explanation of a process, using resources
Social Studies: mapping and scale

Extension Activities:
Have students read more about dinosaur trackways in various books like Dinosaur Lake. They could also do research on the internet to various linking web sites mentioned in this site. Students could measure distances between footprints on a trackway and do various scale model drawing on paper or plastic. Comparing walking vs. running prints can be fun, too. Compare the prints of theropods, like Tyrannosaurus rex or grallators vs. sauropods. Compare skeletons of foot and leg structures of animals past and present. Tell stories by looking at trackways of past or present day animals.

Wisconsin State Science Standards:
A4.2
http://www.dpi.state.wi.us/standards/scia4.html
When faced with a science-related problem decide what evidence, models, or explanations previously studied can be used to better understand what is happening now.

C4.2
http://www.dpi.state.wi.us/standards/scic4.html
Use the science content being learned to ask questions, plan investigations, make observations, make predictions, and of explanations.

C4.4
http://www.dpi.state.wi.us/standards/scic4.html
Use simple science equipment (including rulers, and computers) safely and effectively to collect data relevant to questions and investigations.

C4.5
http://www.dpi.state.wi.us/standards/scic4.html
Use data they have collected to develop explanations and answer questions generated by investigations.

C4.6
http://www.dpi.state.wi.us/standards/scic4.html
Communicate results of their investigations in ways their audiences will understand by using charts, graphs, drawings, written descriptions, and various other means.

Wisconsin State Math Standards:
A.4.3
http://www.dpi.state.wi.us/standards/matha4.html
Connect mathematical learning with other subjects, personal experiences, current events, and personal interests: use math in a way to understand the other areas of the curriculum (e.g., measurement in science, map skills in social studies).

D.4.5
http://www.dpi.state.wi.us/standards/mathd4.html
Determine measurements by using basic relationships (such as perimeter and area) and approximate measurements by using estimation techniques.