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

### Classroom Assessment Techniques 'Plausible Estimation' Tasks

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Description
(an example) are sometimes called 'Fermi' problems after the physicist Enrico Fermi (1901-1954). One favorite problem was, " How many piano tuners are there in Chicago?" Fermi problems have the following characteristics:

• An interesting estimation problem is posed in a simple way.
• Most people instantly respond by saying that it is a problem they could not possibly solve without recourse to reference material.
• An estimate of the solution may be found by a series of simple steps that use only common sense and numbers that are either generally known or are amenable to estimation.

Thus, one way we could estimate an answer to Fermi's question about how many piano tuners are in Chicago is to:

• estimate the size of the population
• estimate the number of households in the population
• estimate the total number of pianos in one's own class, family, street, church etc.
• estimate the frequency of tuning
• estimate the time it takes to tune a piano
• estimate the number of piano tuners.
The downloadable materials for students begin with the sample task and solution that appears below. When we use these tasks for assessment, we are looking for:
• sensible assumptions
• careful reasoning which is carefully communicated, and
• sensible use of units.

Example of a Task and Solution
Plausible estimation tasks are designed to see how well you can develop a chain of reasoning that will enable you to estimate an unknown quantity from things that you already know or can easily guess at. The best way of explaining this is to give an example.

 How much will you drink in your lifetime? How many baths would this fill?