exponents & roots
factors, factoring, & prime numbers
fractions, decimals &
ratio & proportion
Estimating and measuring are an intrinsic part of our lives. We measure time with watches, weight with scales, and popular opinion using a method known as population sampling. We may think of such measurements as exact, but the accuracy of a measurement depends on the precision of the tool, whether physical or theoretical. In this sense, measurements can be thought of as estimations.
At the middle-school level, students learn how to evaluate the reasonableness of answers to computations that arise within the context of specific problems, and how to decide whether an exact answer or an estimate is appropriate. They practice computing with fractions, decimals, percents, and integers in ways that make sense, explaining why their methods work and seem reasonable. Mental computation and estimation are useful in moving from one representation to another, and can deepen students' understanding of rational numbers and help them to develop flexible thinking. Middle-school students can also think critically about estimation by analyzing the accuracy of various measurements. While rounding (of both rational and irrational numbers) is the underlying theme, students can be challenged to compare estimates, to decide on the degree of accuracy, and to make predictions.
Middle School Problems of the Week that allow students to practice their estimating skills are found below. These problems address the NCTM Number and Operations Standard for Grades 6-8 expectation that students should be able to compute fluently and make reasonable estimates.
To find relevant sites about estimation on the Web, browse and search Estimation in our Internet Mathematics Library; to find middle school sites, go to the bottom of the page, set the searcher for middle school level (6-8), and press the Search button. See also Rules for Significant Figures and Decimal Places in the Dr. Math archives, and Rounding Numbers in the Dr. Math FAQ.
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