Estimation is a difficult skill to master. Explain why it is difficulty in the context of measuring height. Suggest an activity to assess that a group of children have mastered the skill for estimation. Explain why this activity is an “assessment activity.
Estimation includes various interrelated concepts and skills, including mental computation, concept development and number sense. In fact, research suggests that number sense, mental computation, and estimation are often very difficult to separate. Further, the development of any one of these abilities often stimulates further growth in the others.
In the Standards estimation is highlighted not as an end in itself but as a means for helping students "develop insights into concepts and procedures, flexibility in working with numbers and measurements, and an awareness of reasonable results". The study of estimation should be integrated with the study of concepts underlying whole numbers, fractions, decimals, and rational numbers so that these concepts can be constructed meaningfully by the learner. The exploration of a wide range of student-generated estimation strategies is recommended. The use of rounding to estimate is singled out for less attention in the Standards. Research and common sense clearly document that traditional rounding rules (rounding to the nearest ten, hundred, thousand, etc.) are often inappropriate and inefficient when estimating. Rather than follow rigid rules for estimating, students should be encouraged to use their knowledge about number to form estimates that are reasonable in the context of the problem. Often this strategy may call for "rounding" to numbers that are more compatible with the computation involved.
Throughout the K-4 and 5-8 sections, the Standards strongly endorses systematically developing estimation skills in grades K-8. The specific recommendations are quoted, and several sample activities are used to illustrate the spirit of the recommendations.
In grades K-4, the curriculum should include estimation so that students can-
- explore estimation strategies;
- recognize when an estimate is appropriate:
- determine the reasonableness of results;
- apply estimation in working with quantities, measurement, computation, and problem solving
Instructional Example Many varied experiences are needed to develop the concept of relative size of numbers and quantities. Although counting is a useful part of many estimation activities, it is not wise to ask students to estimate things that are easy to count. For example, one would not hold a container of three tennis balls and ask a student to estimate the number of tennis balls. However, one might use the same container filled with different objects for an estimation activity.
Figure 3 shows three containers filled with macaroni, rice, and beans. Students might be asked to decide which container contains the most objects. Would an estimate or an exact count be quicker? Do you need to count the number in each container to decide? Tell why or why not.
Students might be asked to "guess" (estimate) the number of items in one container, say, the beans. After all estimates are made, each estimate could be listed from low to high to give students experience in comparing and ordering. Involve all the students in counting the beans by giving each group of two or three students a portion of the beans. Ask them to count their beans and place them in piles of 10. Give the groups plastic bags so that they can put 100 beans into each bag. Ask the whole class to count aloud by 100's, 10's, and 1's to determine the total number of beans.
Once the count is known, review the guesses that were made initially. Which are reasonable? Which are clearly not reasonable? Help students see that several students might have reasonable estimates even though their estimates are different. This knowledge that a range of estimates is acceptable encourages young students to make thoughtful estimates and develop an early tolerance of error, which is an important part of estimation. This activity can
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