the math machine series: pentomino puzzles, tangram puzzles, pattern block puzzles. complete series...

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The Math Machine Series: Pentomino Puzzles, Tangram Puzzles, Pattern Block Puzzles. complete series consisting of 6 sets Review by: Virginia Horak The Arithmetic Teacher, Vol. 34, No. 2 (October 1986), pp. 52, 28 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41192996 . Accessed: 14/06/2014 16:57 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 185.44.79.40 on Sat, 14 Jun 2014 16:57:50 PM All use subject to JSTOR Terms and Conditions

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The Math Machine Series: Pentomino Puzzles, Tangram Puzzles, Pattern Block Puzzles.complete series consisting of 6 setsReview by: Virginia HorakThe Arithmetic Teacher, Vol. 34, No. 2 (October 1986), pp. 52, 28Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192996 .

Accessed: 14/06/2014 16:57

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 185.44.79.40 on Sat, 14 Jun 2014 16:57:50 PMAll use subject to JSTOR Terms and Conditions

mative anecdotes and teaching suggestions. For the teacher inexperienced in working with learning disabled students, this book will be both interesting and useful. It is one book you will read and keep as a reference. - Sandra Pryor Clarkson, Hunter College of CUNY, New York, NY 10021.

Practical Mathematics: Appraisal of the Learning Disabled. John f. Cawiey, ed. 1985, x + 292 pp. ISBN 0-89443-559-0. Aspen Systems Corp., 1600 Research Blvd., Rockville, MD 20850.

This book explores the practical aspects of appraising the learning disabled child. Each author of this edited text examines a different aspect of the topic and, where appropriate, uses the context of the teaching or learning of math- ematics.

The three components of appraisal - mea- surement, assessment, and diagnosis - are dis- cussed throughout the book. However, mea- surement (testing of educational aptitude and achievement) receives the least attention. The more practical parts of the process, assessment and diagnosis, comprise the majority of the discussion.

Chapter 1 gives an overview of appraisal and distinguishes among the components of mea- surement, assessment, and diagnosis. Chapter 2 discusses measurement, paying particular at- tention to domain-referenced achievement tests. Chapter 3 discusses assessment with a particular focus on how it influences curricular and instructional decisions in mathematics. Chapters 4, 5, and 6 explore assessment in the early grades, in grades 5-12, and in the real world. Chapter 7 discusses the more general topic of nonmathematical appraisal, and chap- ter 8 develops an interdisciplinary approach to the assessment and diagnosis of a mathematical learning disability. Chapter 9 considers behav- ior in the appraisal process, and chapter 10 considers approaches in mathematics for the severely handicapped. Chapter 11 describes methods of evaluating students' growth and the effectiveness of the mathematics program to aid in making decisions for future programming efforts.

This book goes beyond the depth of under- standing necessary for the mathematics teacher in the mainstream classroom. It is more appro- priate for special education students in the college classroom. Also, it could certainly be a valuable resource for the mathematics teacher of learning disabled children and, as the editor says, as a general resource for "those inter- ested in the field of learning disability." It is a practical and useful text with discussion of numerous facets of appraisal, including, for example, discussions of tests for mathematics appraisal with respect to the learning disabled child and the particular difficulties that learning disabled children experience with mathematics. The book explores a very narrow field of edu- cation, but it offers a depth of understanding that is extremely valuable. - Karen Schultz, Georgia State University, Atlanta, GA 30303.

Etcetera Game Bag 2, 4, and 6. Each set contains 6 game boards, instructions, game cards, dice. 1984, $20.95 ea. or $108.95 for complete set of 6 levels. Creative Publications, P.O. Box 10328, Palo Alto, CA 94303.

The Game Bag series consists of six storage boxes of games, one for each grade level 1-6. Each kit includes six brightly colored game boards printed on a file folder, dice, game cards, and spinners. Directions for students are on the front of the file folder, and instructions for the teacher are on the back. Answer keys are usually provided for the students. Game preparation is minimal, requiring only packag- ing the game cards or making the dice.

Each game is designed to offer extra practice in computational skills. All games are for two players and have familiar game formats, such as bingo, checkers, and trail games. The game boards have appealing illustrations for students at each level.

Game Bag 2. The games in this kit are all easy to play, and the mathematical topics ap- pear appropriate for most students at this level. Teachers should be aware that the primary focus of these activities is practicing isolated computational skills without the use of manip- ulative materials. The game Clowns Around uses a spinner with pictures of tens and ones. The student spins the spinner and covers the appropriate number.

The topics in level 2 include comparing num- bers; counting by 2s, 5s, and 10s; place value of tens and ones; addition and subtraction facts; word problems; and telling time.

Game Bag 4. An interesting variety of games gives the students a chance to practice compu- tational skills without using paper and pencil. The game boards have especially appealing illustrations and themes for students at this level. The topics for grade 4 include identifying multiples, learning division facts, multiplying by 10 and 100, rounding to the nearest ten, telling time, comparing and matching equiva- lent fractions, and solving word problems. One game, Destination Earth, requires the use of strategy to win and does not just reinforce a skill. After rolling the two game cubes, the student must decide which of the possibilities would be the best choice. For example, a roll of 2 and 5 could result in any of the following:

520 (52 x 10) 5200 (52 x 100) 250 (25 x 10) 2500 (25 x 100)

The student then decides which number would yield the most advantageous position on the game board. Thus the student is involved in decision making as well as computation.

Edited by Carol Novillis Larson University of Arizona Tucson, AZ 85721

Game Bag 6. Four of the six games in the sixth-grade kit require students to compute with pencil and paper at each play of the game. Students would need a fairly good grasp of the concepts of comparing fractions, finding place value to hundredths and thousandths, rounding and ordering decimals, and understanding per- cents before playing the game.

Given the purpose for which the Game Bag series was designed - to sharpen students' com- putational skills - the games do give students who have already developed these concepts a chance to practice what they have learned in a motivating atmosphere. - Carol D. Brooks, Tucson Unified School District, Tucson, AZ 85717.

The Math Machine Series: Pento- mino Puzzles ($20.95), Tangram Puz- zles ($20.95), and Pattern Block Puzzles ($30.95). 1984, complete series consisting of 6 sets $139.95. Creative Publications, P.O. Box 10328, Palo Alto, CA 94303.

The Math Machine series is a collection of six activity sets, three of them designed as games and three with a puzzle format. The three puzzle sets are reviewed here. Each of these sets comes in a storage box that contains twen- ty-four task cards (printed on both sides), the puzzle pieces named by the title, and a solution key.

The Pattern Blocks Puzzles set is designed for the primary grades, although it could be used in open-ended activities at the intermedi- ate school level. The 100 pattern blocks pro- vided are made of sturdy plastic in the six standard colors and shapes. Each side of the task cards is printed with one or two figures that the children are to copy. They may do this by placing the blocks on the figure or by producing the figure beside the card. The task cards progress from easy puzzles, on which the indi- vidual blocks are drawn, to more difficult shapes without the blocks indicated. As the tasks get more difficult, the puzzle pieces to be used are specified. For example, a task card might say "Use: 2 yellow O , 1 blue o, and 2 green A." On the most advanced cards, the instructions read, "Use 19 blocks."

The Tangram Puzzles kit contains two sets of tangram pieces in addition to the task cards. Designed for grades 1-6, these cards accommo- date a range of abilities in a manner similar to that of Pattern Blocks Puzzles. The easiest shapes to copy outline the tangram pieces within the shape. A worthwhile pedagogical feature of Tangram Puzzles is its inclusion of shapes that are geometric figures. Many of the task cards have rectangles, triangles, penta- gons, and hexagons for the children to repro- duce. From the cards, a student is led to make, for example, triangles from two, three, four, or all seven tangram pieces.

The Pentomino Puzzles kit, for grades 2-8, contains the task cards and two twelve-piece sets of pentominoes. The shapes on the cards progress from very easy, using only three or four pieces, to very challenging, using all

(Continued on page 28)

52 Arithmetic Teacher

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RaxriacDing and '?kza>ing

(Continued from page 52)

twelve pentominoes. Several of the shapes in these puzzles have "holes" in them, which the other sets do not. On some shapes the hole is indicated, whereas for others a note on the card simply tells the student that holes will appear

somewhere in the shape. Six of the cards con- tain only rectangles of different dimensions and sizes. Some of the rectangles use all twelve pieces, whereas others use only three.

The Math Machine puzzle kits are worth- while hands-on geometry materials for students at all grade and ability levels. For younger children, the puzzles aid in developing their ability to match, copy, and visualize shapes within a self-checking context. For older chil- dren, the more difficult puzzles offer challenges to which more than one solution can often be found. - Virginia Horak, University of Arizona, Tucson, AZ 85721. W

28 Arithmetic Teacher

hi is not permissible. b. All fractions should have a one- digit numerator and a one-digit de- nominator. It is not permissible to write

86 1 '

c. In this game,

are the same solution and do not count as two separate examples. 3. Students working together can help develop logical arguments for sorting solutions. Extensions

Ask students the following: "If you could choose one additional number to add to the present set of numbers, which would you choose?" Encour- age them to compare notes to see which new number(s) yield the most additional solutions to A, B, C, D, and E.

Answers

Pool classroom results at the end of each exercise. Accept any reasonable answer.

Sample answers

A- A 2 4 16 £1 II A- A 3 6"' 4 8' 8 X6' 6 X8

o 3 6 £ 2 8. 2 1 8 B- o

TX 8' 3 I' 4 3' 2 3

L ̂ I i. - §. I - ?- 1 - 6- C- 8 ^ ' 2' 6

- ' 3' 4

- ' 3' 4 - ' 2

3__1 Í-1 1-1 2^£ U42'6'8'8'6'3'8

1 ¡I 6' ¡2 . 6' 24« 'F

+ Tj

or ^8 "J

.

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