HBJ Mathematics Enrichment Workbook. Levels 1-8 by Lola J. May; Shirley M. Frye; DonnaCyrier Jacobs; Carol HartleyReview by: Adele NeubergThe Arithmetic Teacher, Vol. 33, No. 2 (October 1985), pp. 51-52Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192722 .

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Mathematics Activities Course- ware, Level 4. 2 sets of 3 diskettes and teacher's manual. Apple II, Il+, Ile, 48K, DOS 3.3. $150. Houghton Mifflin Co., One Beacon St., Boston, MA 02108.

This collection of fifteen computer mathematics activities is designed to be used in conjunction with Houghton Mifflin' s level-four mathematics curriculum. The activities correlate with specif- ic units of the text and are accordingly se- quenced. They are designed to engage students in problem-solving and concept-developing ac- tivities and estimation. The package contains two sets of three disks, A, B, and C, with five activities on each.

Each activity is designed to be used by more than one student at a time. If only one student is playing, he or she can play against the comput- er. Two teams of two students are recommend- ed for more ** mathematical interaction/1 The activities can be used in a classroom with only one computer or in a lab situation where a load- and-pass routine is necessary.

This package offers a limited amount of teacher control of the programs. The teacher can turn the sound on or off and edit the menu so that only the activities relating to the con- cepts currently being studied can be chosen. No record-keeping or management system is avail- able.

The teacher's manual includes textbook cor- relation, technical information, and descrip- tions and program objectives. An introductory lesson is provided, as well as two student worksheets that reinforce the concepts being taught.

Each of the activities is unique and competi- tive. Many are timed, and one shortcoming of the program is that the teacher cannot control this aspect. When the programs were used by a group of fourth-grade students, the response time on all programs was very short and was the cause of excessive guessing.

Very few directions are given on the disk, so students need explicit directions from the teacher. This is a distinct disadvantage when a classroom has only one computer and students use the programs at different times.

The graphics displays are excellent. They enhance and clarify the concepts and are not distracting.

In summary, these activities can provide quality enrichment experiences for students if they are correlated with the Houghton Mifflin textbook and sufficiently guided by the teach- er. - Eve Juliano, Lovett Elementary School, Houston, TX 77096.

írnral H0W T0 CHOOSE AND CREATE Шш ' GOOD PROBLEMS FOR PRIMARY ^t^ '

children, by Doyal Nelson and Joan Worth. With problem solving the focus of school mathematics in the 1980s, this is a booklet for the decade. Guides the teacher in drawing very young children into the problem-solving way of thinking. 40 pp.; #324, $3. See the NCTM Mate- rials Order Form in the back of this issue.

New Books for Pupils Edited by A. Dean Hendrickson University of Minnesota- Duluth Duluth, MN 55812

Computer Literacy: Bits and Codes; Bytes and Memory Bases and Computation. Marjorie A. Fitting and Roy Dubisch. 1983, 28 pp. ea., $4.25 ea. Midwest Publications, P.O. Box 448, Pacific Grove, CA 93950.

This series of three booklets provides informa- tion and problem-solving activities to enable students to understand more clearly how a computer works.

Bits and Codes (workbook) begins with an introduction of the bit (represented by a 1 or 0). Exercises develop the concept of coding with bits. Powers of two (introducing the terms base and exponent) are then discussed in reference to the coding. Exercises for coding words and decoding messages are included. Ultimately, these coding exercises result in the develop- ment of the ASCII (American Standard Code of Information Interchange) code, which uses a seven-bit code for 128 characters.

Bytes and Memory explains the organization of the computer, the hardware, and how infor- mation is transferred from one place to another. It begins with a clear explanation of how bytes are used to develop a data base. Next the concept of addressing is developed; hexadeci- mal (or base-sixteen) digits are introduced. Many exercises develop students' understand- ing of the hexadecimal system. "The balance of the text explains other ways in which computer memory is used: for storage of programs, for storage of the screen displays, and for character generation."

Bases and Computation develops the con- cept of the binary system (base two). A mythi- cal country, Twobase in "computer world," is described in which currency comes in denomi- nations that are only powers of two. Numerous exercises using base two reinforce the concept of place value by paralleling the binary system with the decimal system (base ten). Counting in base two is facilitated by the suggestion of the use of concrete materials (an egg carton and buttons). Addition in base two is explained using diagrams of the egg cartons; practice exercises follow. The text then returns to the hexadecimal system; however, Bytes and Mem- ory would not be necessary for the use of this booklet.

The authors recommend that this series of booklets be used sequentially. The first two are much more specifically "computer oriented" (particularly, Bytes and Memory). Bases and Computation could be used exclusively to de- velop the concepts of place value through use of bases two, ten, and sixteen. A combination of Bits and Codes and Bases and Computation would seem to be more useful for a greater

number of students than would the use of all three. Bits and Codes does a marvelous job of explaining the ASCII codes for both teachers and students! The series in its entirety would be a perfect resource for students needing a chal- lenge and who are particularly interested in the internal working of computers. - Adele Neu- berg, George Mason University, Fairfax, VA 22030.

Getting More from Your C-64. An- drew Reddekop and Ian Campbell. 1984, 136 pp., $11.95. ISBN 0-88408-329-2. Sterling Swift Publishing Co., 7901 S. IH-35, Austin, TX 78744.

This 136-page BASIC programming guide sum- marizes and simplifies many of the main con- cepts found in the Commodore 64 User* s Guide and the Commodore 64 Programmer's Refer- ence Guide. Although the presentation of mate- rial is probably best suited for middle school students, some of the actual learning projects may be beyond the middle school level.

The major topics covered in this guide in- clude an introduction to the operation of the Commodore 64, simple BASIC statements, low- and high-resolution graphics, flowcharting techniques, and a variety of learning projects. The learning projects involve exploring, writ- ing, predicting, debugging, modifying, and com- pleting programs.

The title of this guide is misleading if the assumption is made that this book will cover concepts beyond those found in the previously mentioned programmer's guide and user's guide. This book is primarily for those who do not have the time or the inclination to work through the more detailed reference manuals. - John W. Frossand, Fauquier County Public Schools, Warrenton, VA 22186.

HBJ Mathematics Enrichment WorkbOOk. Levels 1-8. Lola J. May, Shir- ley M. Frye, Donna Cyrier Jacobs, and Carol Hartley. 1983. ISBN 0-15-352141-4. Harcourt Brace Jovanovich, 757 Third Ave., New York, NY 10017.

These well-designed, visually attractive work- books are directed toward the more able stu- dents in grades 1-8. The work assumes a mas- tery of basic arithmetic skills and provides innovative explorations of the concepts behind those skills. Though they are identified by grade level, these books are certainly not grade-spe- cific.

The format of the workbooks is nonsequen- tial, thus each topic can be used alone or with related topics. The content, most definitely for enrichment, would enable the teacher to intro- duce some rather sophisticated mathematics on a simplified level. Although much of the content would be more appropriate for mathematically gifted children, some of it can be used with students at all ability levels within a classroom. Each workbook offers a variety of puzzles, codes, and tables that are based on the basic arithmetic skills of addition, subtraction, and multiplication. Topics include clock arithmetic,

October 1985 51

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paper folding, word problems, and geometry by drawing. Levels 3 and 4 also cover probability, computer arithmetic, flowcharts, lattice multi- plication, and tangrams. A refreshing emphasis is placed on logic, geometry, and probability.

Level 5 deals with whole-number multiplica- tion shortcuts and puzzles, line designs, num- ber bases, tangrams, construction of magic squares, coordinate graphing, symmetry, bar arithmetic, Pentominoes, Egyptian fractions (using only Уъ and unit fractions), flowcharting (rounding, divisibility, prime numbers), intro- duction to integers, and simple constructions.

Level 6 covers arithmetic and geometric pro- gressions, modular arithmetic, line designs in shapes, order of operations, constructions, cal- culator exercises, factorial computations, square roots, angles in a triangle, fraction puz- zles, introductory algebraic solutions, flow- charts, Venn diagrams, computation with inte- gers, problem solving, and geometric tiles.

Level 7 includes magic squares with whole numbers and fractions, magic triangles, number bases, vectors, algebra (flow diagrams, equali- ties and inequalities, compound sentences),

finding of areas of polygons using the geoboard, more constructions, probability, logic puzzles, matrices, and syllogisms.

Level 8 covers powers of two, base twelve, topology, problem solving, more matrices and more constructions, percentages, probability, algebraic solutions, some factoring, deductive proofs, trigonometric functions (an introduction to tangents, sines, and cosines), Latin squares, logic, and BASIC programming.

Although the directions are clearly written and the terms used are mathematically correct, the average student will still need the teacher's assistance. However, the mathematically gifted student could use the series for self-paced indi- vidual study.

One disadvantage is the lack of any table of contents or index; the content is varied and diverse, and it could be time-consuming for a classroom teacher to identify specific pages to use. Also, no answers are provided. This col- lection need not accompany Harcourt Brace Jovanovich's textbook series, but rather it could be a valuable resource within any elemen- tary or middle school. - Adele Neuberg.

New Books for Teachers Edited by Randall I. Charles Illinois State University Normal IL 61761

Computers in the Mathematics Cur- riculum: Training Materials. i9S4, 175 pp., $35. Minnesota Educational Computing Corp., 3490 Lexington Ave., N., St. Paul, MN 55112.

This set of teacher-training materials was de- signed to be used in workshops concerning the uses of computers in the mathematics curricu- lum, including the skills of analyzing and inter- preting data and the techniques of problem solving. Their goal is to present materials that can be used by a workshop leader to alert

prom the F»«

Computation

HIGH QUOTIENT (two or three players)

Object: To obtain the highest quotient when a four-digit number is divided by a two-digit number

Materials: 1 . A set of forty cards, four each of the digits 0-9 2. Blank sheets of paper and pencils Directions: 1. Each player draws a "blank" division problem of the following form:

DDJDDDD 2. Cards are shuffled and placed upside down in a drawing stack. 3. Play begins with the first player turning over one of the cards from the top of the drawing stack.

This player writes the numeral from the turned-over card someplace in the blanks. The second player turns over a card from the stack and places the corresponding numeral in his or her blanks. This procedure is continued until each player has filled in the blanks.

4. The players do the divisions, and the player with the highest quotient is the winner.

Variation/extension: As each number is turned over, all players write the number somewhere in their blanks. This procedure speeds up the game, but it can also result in more tie games.

From the file of Ruth A. Meyer and James E. Riley, Western Michigan University, Kalamazoo, Ml 49008

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

52 Arithmetic Teacher

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