Estimation

Abstract

This lesson is designed to show students how to make estimations.

Objectives

Upon completion of this lesson, students will:

• have worked with estimations of quantity, length and area.
• have practiced making comparison estimations of two different items and estimating whether an amount is greater or less than a specified amount.

Standards

The activities and discussions in this lesson address the following NCTM Standards:

Measurement Standard

Apply appropriate techniques, tools, and formulas to determine measurements.

• use common benchmarks to select appropriate methods for estimating measurements;

Compute fluently and make reasonable estimates.

• develop and use strategies to estimate the results of rational number calculations and judge the reasonableness of the results;

Links to other standards.

Student Prerequisites

• Arithmetic: Students must be able to:
  • perform integer and fractional arithmetic
• Technological: Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Students will need:

• Access to a browser
• pencil and paper
• Copies of supplemental materials for the activities:
  • Estimator Worksheet
  • Comparison Estimator Worksheet
  • More or Less Estimator Worksheet

Key Terms

• estimate
• tolerance

Lesson Outline

1. Focus and Review

   Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

   • Ask the students what an estimate is and to think of an example. Have a student share an example with the class. A starter example might be, "How many inches long is this chalkboard?"

     Review the comparison terms, greater than, less than, and almost the same as, when giving examples of estimates. For example, "Is the size of the window greater than the size of the chalkboard?"

2. Objectives

   Let the students know what it is they will be doing and learning today. Say something like this:

   • Today we are going to study estimates.

   • We are going to use the computers to learn about making estimations, but please do not turn your computers on or go to this page until I ask you to.

3. Teacher Input

   In this part of the lesson you will explain to the students how to do the assignment. You should model or demonstrate it for the students, especially if they are not familiar with how to use our computer applets.

   • You may want to lead a discussion on Making Estimates.

   • When you are satisfied your students are familiar with estimates, open your browser (but don't let the students open theirs yet) to the Estimator activity in order to demonstrate it to the students.

   • Show students the first estimation question and ask them to give you the answer. Enter their number, and show them that if they are not close enough, they will be prompted to refine their answer, either higher or lower. Demonstrate the "hint" button if students are struggling.

   • Pass out the Estimator Worksheet. Complete the worksheet with the students. As you demonstrate and discuss the problems, ask some students to explain orally how they arrive at their estimates.

4. Guided Practice
   • The next activity is the Comparison Estimator.
     • Pass out the Comparison Estimator Worksheet.

     • Do the first problem together, but let the students direct your actions:
       • Show students the first estimation and the menu of choices: greater than, less than, almost the same as.

       • Let the students give you the answers to one or two problems, then direct them to do more and work on answering the questions on the worksheet.

5. Independent Practice
   • Give students a chance to work independently on the More or Less Estimator.

   • Pass out the Comparison Estimator Worksheet. Circulate through the room, giving help as needed, while students complete the worksheet.

6. Closure

   Just before the end of class, bring the students together and ask if any of them still have questions about estimation.

   • Asking students which problems gave them the most trouble might be a way to spark conversation.

   • You might want to ask students to share their strategies for making estimates.

   • To evaluate students' comprehension of the class, collect their worksheets.

Alternate Outlines

This lesson can be rearranged in several ways.

• If the students pick up the concept of estimation right away, you may want to work together with them on the first worksheet, but then give them the other two to do independently.

• If students need more time to absorb the material, you might decide to give them only one or two of the estimation activities, or take two or more days to cover all the activities.

Suggested Follow-Ups or Extensions

• As an extension, and if the students are proficient with addition and multiplication using decimals, you may want to have the students work in pairs with the Fraction Four Estimator activity. In it they take turns estimating addition and multiplication problems.