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Grade Level: Senior
This task asks students to make estimates of weights, volumes and numbers using either general knowledge or information readily obtainable from reference sources.
Grouping: Students may work individually or in pairs.
Materials: Pencil and paper, calculator, reference books
Estimated time: 30-40 minutes
Pick one part (either a or b) from each of the following three questions, and make the best possible estimate for the situation. Your answer will be a combination of several quantities. Be sure to specify what assumptions you have made in arriving at your estimate.
1. a. How long do you think it would take you to eat your weight in food?
or
b. What is the weight of all the trash produced in your house in a year?
Assumptions:
Calculation:
2. a. How many hot dogs do you think are sold in a baseball season at
Fenway Park?
or
b. How many times does a person's heart beat in a lifetime?
Assumptions:
Calculation:
3. a. What do you think is the volume of gasoline your car uses in a
year? How does this compare to the volume of liquid (water, soda, coffee, etc.)
you drink in a year?
or
b. What do you think is the volume occupied by one million dollars in single dollar bills? How does this volume compare to your own body's volume?
Assumptions:
Calculation:
1a. Assumptions:
an average food intake: 5 lbs/day
an average weight of a person: 150 lbs
Computation:
150 lbs / (5 lbs/day) = 30 days
The answer is: about a month.
1b. Assumptions:
10 lbs of garbage/week (for a family of 4)
10 lbs of recyclable
materials/week (for a family of 4)
total: 20 lbs of trash/week (for a family
of 4)
Computation:
50 weeks/year . 20 lbs of trash/week = 1,000 lbs of trash/ year
The answer is: about 1,000 lbs of trash/year.
2a. Assumptions:
there are 80 home games/season
attendance: 35,000 people/game (usually sold
out)
1 hot dog/person (some people buy more than one, some don't buy any)
Computation:
(80 games/season) . (35,000 people/game) . (1 hot dog/person) =
2,800,000
hot dogs/person
The answer is: about 3,000,000 hot dogs/season.
2b. Assumptions:
a heart beats about 60 times/minute
an average life span: 75 years
Computation:
75 years . (60 heart beats/minute) = 75 years .(31,536,000 heart beats/year) = 2,365,200,000 heart beats.
The answer is: about 2,400,000,000 beats
3a. Assumptions:
the average capacity of a gas tank: 12 gallons/1 filling
1 filling/week
8
additional fillings/year for vacation times
Computation:
(52 weeks/year) . (1 filling/week) . (12 gallons/filling)
+ (8
fillings/year) . (12 gallons/filling)
The answer is: about 700 gallons/ year.
3b. Assumptions:
an average person drives: 15,000 miles/year
an average car's efficiency: 20
miles/gallon
Computation:
(15,000 miles/year) / (20 miles/gallon) = 750 gallons/year
The answer is: about 700 gallons/year.
For informal classroom use, you may want to suggest to the students that they make use of available reference materials such as encyclopedias, almanacs, newspapers, etc. They should also be reminded to state their assumptions clearly and explicitly.
This section offers a characterization of student responses and provides indications of the ways in which the students were successful or unsuccessful in engaging with and completing the task. The descriptions are keyed to the Core Elements of Performance. Our global descriptions of student work range from "The student needs significant instruction" to "The student's work meets the essential demands of the task." Samples of student work that exemplify these descriptions of performance are included below, accompanied by commentary on central aspects of each student's response. These sample responses are representative; they may not mirror the global description of performance in all respects, being weaker in some and stronger in others.
The characterization of student responses for this task is based on these `Core Elements of Performance':
The student is unable to design a reasonable chain of operations for any of the three parts.
Student A
This student has misinterpreted question 1, given only a partial list of the necessary assumptions for question 2, and made no effort to answer question 3.
The student designs a reasonable chain of operations with the desired result in one of the three parts, although there may be computational errors. There is no attempt to round the results of computation, and numerical results are communicated without units.
Student B
This student has developed a reasonable chain of operations for question 1, but not for questions 2 or 3. There is no clarifying information about the assumptions used to arrive at the answer for question 3, and no labels are given.
The student designs reasonable chains of operations, and reaches desired results with minimal computation errors and appropriate precision in the statement of the answers. Assumptions are communicated, but may need to be expanded or clarified.
Student C
This student has used a very orderly approach and stated assumptions clearly, but the computational strategy for question 2 is flawed. In addition, each answer is stated with an inappropriate level of precision.
The student designs a computational strategy that, in each case, logically estimates the desired quantity from the given information. The reasonableness of the computed estimate is ascertained, and the assumptions upon which the estimate is based are clearly communicated.
Student D
This student presents all work in an orderly, logical fashion. All assumptions are clearly stated, the calculations are correct, and expressed with an appropriate degree of precision, and in each case a general formula is presented.
This Senior assessment package was designed and developed by members of the Balanced Assessment Project team, particularly Judah Schwartz, Kevin Kelly, Joan Kenney, Teresa Sienkeiwicz, Victor Steinbok and Malcolm Swan. The editor was Joan Kenney.
Many others have made helpful comments and suggestions in the course of the development. We thank them all. The project is particularly grateful to administrators, teachers and students at high schools in Boston MA, Brighton MA, Brookline MA, Holt MI, Little Rock AR, Somerville MA, Worcester MA and Wrentham MA, with whom these tasks were developed and tested.
The project was directed by Alan Schoenfeld, Hugh Burkhardt, Phil Daro, Jim Ridgway, Judah Schwartz and Sandra Wilcox.
The package consists of materials compiled or adapted from work done at the four sites of the Balanced Assessment Project.
The work of this project was supported by a grant from the National Science Foundation. The opinions expressed in these materials do not necessarily represent the position, policy, or endorsement of the Foundation.
Copyright (c) 1995 Regents of the University of California. All rights reserved.
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Page updated 4 March 1998 For further information please contact wilcoxs@pilot.msu.edu |
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