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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Malcolm Swan
Mathematics Education, University of Nottingham
Malcolm.Swan@nottingham.ac.uk

Jim Ridgway
School of Education, University of Durham
Jim.Ridgway@durham.ac.uk

Plausible Estimation tasks involve students in an activity central to modelling in science, other areas of intellectual activity, and in everyday life. The core skill is to create (or check) estimates of quantities that, at first glance, seem unknowable. Students are also required to communicate their assumptions and results and check the plausibility of their answers - important thinking processes for all science, math, and engineering fields. These tasks (an example) show students that many seemingly impossible-to-estimate quantities (such as the number of new cars sold in the United States) can be reasonably derived using basic, known quantities and simple reasoning. In addition, Plausible Estimation tasks practice arithmetic fluency, ability to handle large numbers, and conversion of units.

A 'Plausible Estimation' task consists of a one or two easily-stated questions which at first glance seem impossible to answer without reference material, but which can be reasonably estimated by following a series of simple steps that use only common sense and numbers that are generally known or are amenable to estimation. One such example is, "How many babies are born in the United States each minute?" To answer this question, students must identify and estimate the relevant pieces of information, such as the U.S. population and the age distribution of the U.S. population. With these estimates, and simple multiplication (mindful of units), students can make a reasonable estimate of this quantity.

WHAT IS INVOLVED?

 Instructor Preparation Time: Minimal if use existing tasks. Preparing Your Students: Students will need some coaching on their first task. Class Time: 45 minutes. Disciplines: Appropriate for all, requires very little mathematical knowledge beyond fluency in basic skills. Class Size: Any. Special Classroom/Technical Requirements: None. Individual or Group Involvement: Either. Analyzing Results: Intensive for formal scoring for large classes. Best used as an informal way to get your students thinking mathematically. Other Things to Consider: Fairly demanding task for students who are unfamiliar with open-ended problems.