Illuminations: Representing Data

Representing Data

Whale Weight

In this lesson, students investigate relationships between numbers, identify number patterns, represent the information in graphic chart form, and generalize the results of an investigation. Specifically, students explore the relationship between a whale's length and its weight.

Learning Objectives
 
Students will:
  • investigate the relationship between pairs of numbers
  • identify number patterns
  • represent the information in graphic chart form
  • generalize the results of an investigation

Materials
 
Whale Weight Activity Sheet

Instructional Plan

Ask students to describe the relationship between inches, feet, and yards. Possible responses will include:

12 inches = 1 foot

3 feet = 1 yard

Ask students to describe the relationship between pounds and tons. One possible response will be:

2000 pounds = 1 ton

Give students some sample problems to complete individually to review how to work within the customary system. For example, you can write the following problems on the chalkboard or overhead:

36 feet = ____ yards [solution: 3 yards]
30 inches = ____ feet [solution: 2.5 feet]
5 1/3 yards = ____ feet [solution: 16 feet]
8,000 pounds = ____ tons [solution: 4 tons]
1.5 tons = ____ pounds [solution: 3,000 pounds]

Distribute the Whale Weight Activity Sheet to each student.

Whale Weight Activity Sheet Whale Weight Activity Sheet

Review the directions, encouraging students to study the information given.

Give students time to complete the chart and make a generalization. This can be done in pairs.

 

 

As a class, discuss the generalization that a gray whale's estimated weight is about 1,000 pounds, or a half ton, for every foot of its length.

Assessment Options
 

You may collect the Whale Weight activity sheet as a means of assessment. The solutions to chart are as follows:

  1. 30 feet; 30,000 pounds (or 15 tons)
  2. 12 yards; 36,000 pounds (or 18 tons)
  3. 48 feet (or 4 yards); 48,000 lbs
  4. 25 feet; 25,000 pounds
  5. 28 feet; 13 tons plus 2,000 pounds
  6. 50 feet; 50,000 pounds
  7. 44 feet; 22 tons
  8. 600 inches; 50,000 pounds (or 25 tons)
  9. 42.5 feet; 42,500 pounds
  10. 38 feet; 38,000 pounds
  11. 15 1/3 yards; 46,000 pounds (or 23 tons)
  12. 39.5 feet; 39,500 pounds

Extensions
 
  1. Express all table lengths in feet and all weights in tons.

  2. Rank the whales by weight from the heaviest to the lightest (note that whales 6 and 8 have equal weights).

NCTM Standards and Expectations
 
Algebra 6-8
  1. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
Measurement 6-8
  1. Understand both metric and customary systems of measurement.
  2. Understand relationships among units and convert from one unit to another within the same system.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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