Classroom Assessment Techniques 'Plausible Estimation' Tasks (Screen 4 of 4)

Variations
The tasks included in this site can be downloaded and used without modification. If you choose to develop your own 'Plausible Estimation' task, you can follow the pattern used in these tools.

• First, select a question whose quantitative answer you can look up in a reference manual (as a check against the students' answers), and which can be derived from fairly simple assumptions or estimates. If the solution process needs a little-known estimate, provide that to the students.

• Then, ask the students to estimate the value, placing an emphasis on their assumptions and chain of reasoning.

An extension to Plausible Estimation tasks is to ask for 'bounded estimates' - what range of values would you give in order to be pretty certain that you have included the true value being estimated? One approach is to consider the effects of taking lower and upper bounds on every estimate made in the calculation, and to see the effects on the final estimate. In the bathtub problem, for example, you could explore the effect on the final estimate of smaller and larger tubs, and smaller and larger liquid intake. Asking about the sensitivity of solutions to initial assumptions is an important thinking skill in science.

The following examples from various disciplines may provide some insight into creating your own variations.

Discipline	Example "Plausible Estimation" task
Astronomy	How many stars are visible to the naked eye in the entire sky?
Biology	How many raccoons are killed by cars in the US each year? How many corn kernels are in an acre of corn? How many fish are in a nearby lake? How many geese migrate through your city each fall?
Chemistry	How many atoms in a grain of sand? How high is a stack of pennies if it's one mole's (6 x 1023) worth? How many oxygen molecules are present in the air in this room? Suppose that your great, great, great grandmother poured a glass of water into the Atlantic Ocean. Suppose that you dip a glass of water from the ocean tomorrow. How many molecules from the first glass of water are in the second glass of water?

Analysis
Student work can be measured against three criteria:

• students can make sensible assumptions relevant to the task;

• students can design a computational strategy that logically estimates the desired quantity from the given quantities; and,

• students can ascertain the reasonableness of the computed estimate and communicate the assumptions upon which the estimate was based.

Category of performance	Typical response
The student needs significant instruction	Student is unable to design a reasonable chain of operations.
The student needs some instruction	Student designs a reasonable chain of operations with the desired results, although there can be computational errors. There may be no attempt to round the results to fit the significant digits of the answer, and the answer may be given without units.
The student's work needs to be revised	Student designs a reasonable chain of operations, and reaches desired results with minimal computational errors and appropriate precision. Assumptions are communicated, but may need to be expanded or clarified.
The student's work meets the essential demands of the task	Student designs a computational strategy that 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.

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Introduction
Description, Purpose, and Limits
Goals, Use, and Instructions
Variations and Analysis
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Tools

Mathematical Thinking CATs || Fault Finding and Fixing || Plausible Estimation
Creating Measures || Convincing and Proving || Reasoning from Evidence