Illuminations: Mathematics and Children's Literature

Mathematics and Children's Literature

Estimating Volume by Counting on Frank

In this lesson, students read the book Counting on Frank. They use information in the book to make estimates involving volume. In particular, students explore the size of humpback whales.

Learning Objectives
 
Students will:
  • predict and find the average size of humpback whales
  • solve problems involving estimation of volume

Materials
 
Book: Counting on Frank, by Rod Clement
One calculator per group
Getting The Facts Activity Sheet

Instructional Plan

Story Summary

The narrator likes to collect facts with the help of his dog, Frank.  Each two-page spread of this book includes a different fact involving such mathematical topics as counting, size comparison, and ratio along with delightful illustrations.

Structuring the Investigation

Ask students to brainstorm what they already know about humpback whales. If they do not know a great deal about this topic, discuss where this information can be found. Two internet resources include:

Next, ask students to predict the size of a humpback whale. Students should explain their estimates.

 

 

Read the book, Counting on Frank, by Rod Clement aloud. Divide the class into small, cooperative working groups. Provide each student with a copy of the Getting The Facts activity sheet.

Getting The Facts Activity Sheet

Ask students to calculate how large a box is needed to hold the average humpback whale. Because the data they have collected will most likely include weight and length, students will have to make inferences about several dimensions of the box. These decisions should be justified in questions 1 and 2 of the Getting The Facts activity sheet.

After estimating the size of the boy's house, encourage each group to describe the process they used to find the answer. Discuss the information needed to determine the number of whales that would fit inside the house.

Direct each group to complete the remainder of the activity sheet.

Assessment Options
 
  1. You may wish to judge the reasonableness of the students' estimates. For example, based upon several internet resources, most humpbacks have an average length of 40-45 feet. The image shown suggests that the whale is about 4-5 times as long as it is tail, so 8-10 feet seems a fairly accurate estimate for the whale's width. And if the diver shown in that picture is assumed to be 6 feet tall, about 1.5 to 2 of him would fit in the height of the whale, so the height of a whale could be 9-12 feet. Once again, these are estimates only.

NCTM Standards and Expectations
 
Measurement 3-5
  1. Understand that measurements are approximations and how differences in units affect precision.
  2. Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes.

References
 
  • Hopkins, Martha. "Ideas: Mathematics and Children’s Literature." The Arithmetic Teacher. May, 1993.  pp 512 - 520.
  • Clement, Rod. Counting on Frank. Milwaukee, Wis.: Gareth Stevens Children’s Books, 1991.
  
1 period   

NCTM Resources

Exploring Mathematics Through Literature

National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
© 2000 National Council of Teachers of Mathematics
Use of this Web site constitutes acceptance of the Terms of Use

The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.