FOCUS ISSUE: CALCULATORS || Readers' Dialogue

Readers' DialogueAuthor(s): Dormalee Harrington Lindberg, Lyn English, Joan Yares Schussheim, Jean M. Shawand Donnie BainSource: The Arithmetic Teacher, Vol. 34, No. 6, FOCUS ISSUE: CALCULATORS (February 1987),pp. 5-6, 15Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193085 .

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Rccickzry Dialogue

Numbers = words

On a calculator the following numbers can be read as letters when the calculator is turned upside down.

8- B 3- E 6- g A- h 1-1 0- o 5- S

These letters can be used to form words that are answers to "numberical" questions such as the following: 1. What do you call big pigs?

(500 x 10) + (20 x 30) + (22)

2. You're a good . (2 x 3) x 100 + (7x9)

Besides creating questions like these, students can create stories in which the blanks are words that are solutions to problems.

Dormalee Harrington Lindberg Southern Illinois University

at Carbondale Carbondale, IL 62901

Two tips

Two activities help students understand place value and gain experience with a calculator. The first is called "Wipe-Out." Children are given a number to enter and are instructed to wipe out a particular digit within that number. For example, to delete the digit 7 in 207 654, children must subtract 7000.

The second activity stresses the relationship between each place in our numeration system through use of the calculator's constant feature. Beginning with any number, such as 0.003 (or just 3, for younger children), and

Because of space limitations, letters may be subject to abridgment. Although we are unable to acknowledge those letters that cannot be published, we appreciate the interest and value the views of those who take the time to send us their comments. Readers who are commenting on articles are encouraged to send copies of their correspondence to the authors. Please double-space all letters that are to be considered for publication.

using the constant feature to repeatedly multiply by ten, it can be shown that each time a digit is moved one place to the left, its value increases ten times.

Lyn English Brisbane College

of Advanced Education Carseldine Campus Brisbane, Queensland Australia 4034

Calculating presents

We have used an activity called "Holiday Shopping" in our remedial mathematics labo- ratory for grades 3-5. Students work through a variety of shopper's problems using a calculator and the prices that appear in current holiday catalogs from local department stores. Apart from questions about which items are the most and least expensive, we ask ones like, "How many different items can you list and still get change from a $100 bill?" and "Create a holiday list for your family where price is no object." Each question is discussed in small groups before it is solved individually. All those who complete the sea- sonal activity get a holiday sticker, along with their "in the lab" shopping experience.

Joan Yares Schussheim ' Lake vil le School Great Neck, NY 11020

Personalized problems

Problems personalized with individualized measurements appeal to children because each person's answer is unique. Such problems intrigue middle school children and in- volve them in the problem-solving process. Aided with calculators to perform the computations, children can concentrate on the pro- cesses of figuring out what to do and compar- ing their answers. Children can further personalize problems by changing the problems to fit their own interests.

Teachers can start children on personalized problems by having them work in groups of four or five. Then each group can choose a different problem and can figure out ways to solve the problem. Next, individuals in the groups should take the needed measurements and figure their answers on the calculator. Group members can work together using a single calculator if one is not available for each person. When all are finished, group members can share their problems, strategies, and individual answers with the entire class. The range of answers for any single problem can be noted. Some examples are as follows:

1 . Take your pulse for three or four minutes. Find your average number of heart beats a minute. Now use your calculator to com- pute (a) the number of times your heart beats in an hour, (b) the number of times your heart beats in a day, and (c) the number of times your heart will beat between your birth and age forty.

2. Time your breathing for three or four minutes. Then figure your average number of breaths a minute. On the basis of your average, (a) how many breaths do you take in a day, (b) how many breaths have you taken so far in your life, and (c) how many breaths will you take between now and Christmas?

3. Measure your height in centimeters. Use your calculator to help you find (a) how many

February 1987 5



of your heights make 1 km, (b) how many of your heights would stretch from New York to Los Angeles (about 4460 km), and (c) how many of your heights would stretch from to (fill in some places).

After a few examples, children can create their own personalized problems. Each can write a problem on a notecard and put it on a bulletin board for others to choose and solve. Students can also vary the contents of problems by changing such factors as distances, times, or body measurements. Although answers to problems will vary, authors of problems might write a strategy or two for solutions on the back of each notecard to help classmates check their work.

Jean M. Shaw University of Mississippi University, MS 38677

Word displays

My students have enjoyed creating problems whose solutions are words that can be read from a calculator's display when it is turned upside down. This activity helps children become more familiar with the calculator's keyboard. It encourages children to "problem solve" in a unique fashion, as they seek the mathematical computations they need to proceed from step to step in their "solutions," which make their calculators "talk"! A file of these problems is stored on 5x8 cards for other students to use. A sam- ple from one fifth-grade student is included here.

What animal lays golden eggs? 1. Start with 1000. 2. Multiply by 20 because she laid 20 eggs. 3. Subtract 2000 because the farmer sold

2000 of them. 4. Multiply by 2 because 2 eggs hatched. 5. Subtract 1000 because 1000 got smashed. 6. Add 6 because the farmer glued 6 back

together.

(Answer: goose) Joan Yares Schussheim Lakeview School Great Neck, NY 11020

Shopping spree

This year give your students a $1000.00 shopping spree and at the same time practice with discounts and sales tax. All you need are some catalogs from mail-order houses or local retail stores and a recording sheet for purchases. Make sure the catalogs have a wide variety of items and prices that will interest your students.

The goal of this activity is to buy at least ten items of different prices and spend exactly $1000.00. It sounds easy so far but here is the

(Continued on page 15)

from the File

| Computation |

TRIPLE CHECK A 85 A

/ '10° Usually by the first of March, my sixth- / ' grade pupils have demonstrated that giv- / ' en a rational number in any of the three / ' forms, fraction, decimal, or percent, they / ' can quickly give the two equivalent names / ' for commonly used fractions and can find 85°// / 'n ft* equivalents for other fractions, decimals, / 'U-o5 ft*

or percents. To maintain and increase that knowledge, we use Triple Check at various

intervals throughout the rest of the school year. On the last day of each month, pupils give their daily attendance, reading and mathematics grades, and spelling scores in 'Triple Check." Usually we begin with a fraction, for example, for 17 days of attendance of a possible 20 days, we would write 17/20 = 85/100 = 85% = 0.85. However, if you are working with decimals or percents, name them first.

Triple Check encourages pupils to check their answers in a reasonable and an exact manner. It reinforces the idea that fractions, decimals, and percents communicate the same information about rational numbers.

From the file of Celestine Wyatt, , 10629 S. Emerald, Chicago, IL 60628

-Readers are encouraged to send two copies of their classroom-tested ideas for "From the File" to the managing editor for review.-

6 Arithmetic Teacher



Rcadary Dialogua

(Continued from page 6)

twist- different prices receive different rates of discount, and sales tax must be added to the discount price. I use the following table for discount rates:

If the item's cost is -

$0.00-$24.99, the discount is 10%; $25.0O-$74.99, the discount is 15%; $75.00-$149.99, the discount is 20%; $150.00 or over, the discount is 25%.

Sales tax is always 4 percent for each item.

I also give students a recording sheet like the one below to keep track of their purchases. To save space I have abbreviated the number of lines that normally fill a full page. Although the columns appear vertically here for publication purposes, use a horizontal treatment and include a spot for totaling the costs.

Page#

Item

Catalog price

Amount of discount

Discount price

Amount of sales tax

Your cost

As you can imagine, buying the first eight or nine items is relatively easy, but finding the right items and prices to reach $1000.00 can be pretty challenging. All my students do this activity individually; I allow them to use their calculators. Each student will receive a grade according to how close they can get to $1000.00. The scale I use is as follows:

Exactly $1000.00-100 within $0.25-95 within $0.40-85 within $0.50-75 within $1.00-70 within $2.00-65 Allow four or five days for your students to

complete this activity. Lively discussions oc- cur, and interesting items are purchased to reach that $1000.00 mark. Some students enjoy trying to figure out an equation to give them the final price they need to spend $1000.00. An ideal time in the year to use this activity is just before your December holi- days.

All in all this is an enjoyable activity that does not require much preparation and pro- vides practice with both percents and problem solving. I hope your students enjoy this activity as much as mine have over the years.

Donnie Bain 124 Rock Hill Avenue Hendersonville, NC 28739

J RME Monograph #1 |

LEARNING AND MATHEMATICS GAMES By George W. Bright, John G. Harvey,

and Margariete Montague Wheeler

Focuses on game-related instruction and the resulting learning. Describes elemen- tary and secondary classroom studies that investigated the use of selected games to promote the learning of mathematics. Presents research on the cogni- tive effects of mathematics instructional

i games, the design of the studies and the data-gathering instruments used in each study, the results of analyzing the data gathered in the studies, and conclusions on the effectiveness of games. Numerous references and appendices that suggest games for specific grade levels. 1985, 199 pp., #357, $7.50.

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24 ready-to-use activities dedicated to the proposition that calculators free children to think out problem solutions. 42 pp 1981 ISBN 0-87353-175-2 $4.00

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February 1987 15

MATHEMATICS TEACHER'S

Complete Calculator Handbook

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GEOMETRY- Ratios & proportion / Polygons & area / Circles / Lateral area & volume

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PLUS 25 full-page, reproducible worksheets in- volve students in estimation, problem-solving, and number pattern activities like: Estimate Check • Missing Factor Game • A Tall Tale (words are formed by turning the calculator upside down) • Prime Time • Decimal Mazes • Bogus Fractions • Chart Your Course • Mystery Sequences • Power Power • Number Picks • One-Zero-One • more!

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FOCUS ISSUE: CALCULATORS || Readers' Dialogue