Estimating Unknown Quantities

Estimation is an important aspect of quantitative thinking -- and a critical life skill in a world in which we often need to make decisions on the basis of inexact or undefined information.
Teaching Strategies:
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Updated on: March 15, 2007
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How Can You Stretch Students' Thinking?

Here are some ways of getting students to stretch their estimation skills:

  • Give students increasingly difficult problems. The best problems are ones that are slightly beyond their comfort zone.

  • Have students clearly document their estimations by listing and justifying all of their assumptions, describing their process, and showing all calculations. Have students try alternate methods of estimating, and ask them to share their processes with one another. Encourage students to try a variety of strategies and apply them to new situations.

  • Teach students how to challenge one another's assumptions in a respectful way and how to defend and justify their own estimates to one another.

  • Encourage students to estimate a range of solutions by exploring what happens when they change their assumptions within reasonable bounds.

  • Help students use programmable calculators or spreadsheets to build their own estimation tools. Advanced computer science students can be challenged to build simulation models.

When Can You Use It?

There are many opportunities to use estimation in science, research, history, and economics to quantify amounts when accurate numbers are not needed.


Students can read about estimations in news articles, on Web sites, or in textbooks. Students can analyze the statistics or assumptions that were made to arrive at the estimate and then discuss questions that arise about their estimates.


Have students explain their estimations in writing. Students can describe the process they used to estimate in a given scenario. Have students explain the strategies, assumptions, and benchmarks they used to arrive at their estimate.


Have students estimate using a variety of measures, such as weight, height, and time. Provide students with daily or weekly estimation problems and make them use new operations or estimation strategies.

Social Studies

Discuss the many ways estimates are used in social studies. Discuss how statistics for population, geography, careers, language, and the like were determined. Discuss the sampling, surveying, or other methods that were used to determine the estimates.


Have students make estimations before and during experiments. They can estimate the mass, height, length, or volume of various objects and then find the actual values and compare them.

Lesson Plans

Estimating Angles, Area, and Length
This lesson plan is for students in middle school. Students estimate angles and surface area and perform computational estimation.

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