# Let Your Fingers Do the Estimating

 Subjects Arts & Humanities Language Arts Mathematics Arithmetic, Statistics Grades 3-5, 6-8, 9-12

Brief Description

Students estimate and average phone listings found in the White Pages of the local telephone directory.

Objectives

Students will

• estimate the number of listings in the White Pages of the local telephone directory.
• write an explanation of the math processes used to arrive at the final estimate.

Keywords

telephone, directory, alphabet, estimate, average, chart, table

Materials Needed

• a local phone directory for each student (contact your local phone company for a class set, or collect old phone directories when a new directory is issued)
• chart paper and marker (optional)
• Let Your Fingers Do the Estimating student work sheets

Lesson Plan

Lesson Notes:
• This math activity is designed to be done by hand, but students might use a spreadsheet program to organize and calculate data.
• If you live in a large, urban area, you might figure the total of listings for a handful of specific letters rather than for the entire phone book.

Pose this question to students: How many listings can be found in the White Pages of the local phone directory? Let students consider how they might figure that out. Help them conclude that it would be very difficult to accurately count the listings by hand; however estimating might help them arrive at a number close to the actual number.

Invite students to share their ideas about how they might estimate the number of White Pages listings. Lead them to the conclusion that the easiest way to estimate is to count the number of listings in one column on a page, then add or multiply the number of listings in one column by the number of columns on the page.

Students can use the number of listings on a page (estimated) to figure the total listings for that letter. They can do that by counting the number of pages for a specific letter and multiplying the number of listings on a page by the number of pages.

Tear a sheet of paper into 25 slips. Write a letter of the alphabet on each slip. Omit one letter, for example the letter V. Use that letter as an example as you walk students through the activity. Put the slips in a hat, and let students randomly draw three letters. Students should record the three letters and put the slips back into the hat so the next student can select. Do this until all students have selected three letters. Then write the chart headings below on the board or chart paper:

Assigned Letter Actual Number of Listings in One Column Estimated Number of Listings on One Page Actual Number of Pages for Letter Approximate Number of Listings for Letter

Which letter of the alphabet did you omit when you wrote out the slips in the step above? If it was the letter V, model the exercise students will do using the phone listings in your local phone directory that begin with the letter V.

• Write the letter V in the column with the heading "Assigned Letter."
• Choose a column from the V listings in the White Pages of the phone book, and ask a student to count the number of listings in that column. Write that number in the column "Actual Number of Listings in One Column" on the chart.
• Ask students how they would use that information to derive the number of listings on the entire page.
• Add or multiply to arrive at the estimate, and write students' estimate in the "Estimated Number of Listings on One Page" column.
• Count the number of pages of listings that appear in the V section of your phone book. Write that number in the "Actual Number of Pages for Letter" column.
• Ask students how they would estimate the total number of listings for the letter. Multiply the estimate of listings on one page by the number of pages, and write the product in the "Approximate Number of Listings for Letter" column.

Older students can provide more detail in the last two columns. For example, they might write 17 pages, two extra columns. in the "Actual Number of Pages for Letter" column. To find a total number of listings for the letter in the last column, they can multiply the number of listings on a page (p) by 17, then add the number of listings in a column (c) two times [(p x 17) + (c x 2) = ] to arrive at the total number of listings.

Distribute the Let Your Fingers Do the Estimating student work sheet, and ask students to complete the work sheet for the three letters they drew.

After the students have completed that activity, bring the class together so students who had the same letters can compare their estimates. Did students who drew the letter A come close to one another in their estimates? If the estimates are far apart, let those students share how they arrived at their estimates. Otherwise, write the different estimates on the board or chart paper and let students figure the average. That average will serve as the official class estimate of the number of listings for the letter A.

Do the same thing for the other letters of the alphabet. As you do that, students can record the official class estimates on their work sheets in each of the three columns after each letter.

When students have determined all the estimates, give them time to total the estimates. (This might be a homework assignment.) They should add the estimates once; then they should add them again in reverse. If they arrive at two different answers when figuring the total, they should total the column again to see if that third total matches the total in one of the other columns.

Assessment

Students write a brief paragraph explaining the math processes they used to figure the total number of listings in the White Pages of the local phone book. Invite a handful of students to share what they wrote, and then help them improve on their explanations. Then give all students the opportunity to turn in their explanations for a grade or the opportunity to rework/improve their explanations as homework and turn the revised work in for a grade.

Lesson Plan Source

Education World

Submitted By

Gary Hopkins

National Standards

LANGUAGE ARTS: English

MATHEMATICS: Number and Operations

NM-NUM.3-5.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
NM-NUM.3-5.2 Understand Meanings of Operations and How They Relate to One Another
NM-NUM.3-5.3 Compute Fluently and Make Reasonable Estimates

NM-NUM.6-8.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
NM-NUM.6-8.2 Understand Meanings of Operations and How They Relate to One Another
NM-NUM.6-8.3 Compute Fluently and Make Reasonable Estimates

NM-NUM.9-12.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
NM-NUM.9-12.2 Understand Meanings of Operations and How They Relate to One Another
NM-NUM.9-12.3 Compute Fluently and Make Reasonable Estimates

MATHEMATICS: Problem Solving

NM-PROB.PK-12.2 Solve Problems That Arise in Mathematics and in Other Contexts
NM-PROB.PK-12.3 Apply and Adapt a Variety of Appropriate Strategies to Solve Problems
NM-PROB.PK-12.4 Monitor and Reflect on the Process of Mathematical Problem Solving

MATHEMATICS: Communications

NM-COMM.PK-12.1 Organize and Consolidate Their Mathematical Thinking Through Communication
NM-COMM.PK-12.2 Communicate Their Mathematical Thinking Coherently and Clearly to Peers, Teachers, and Others

MATHEMATICS: Connections

NM-CONN.PK-12.3 Recognize and Apply Mathematics in Contexts Outside of Mathematics

TECHNOLOGY