DOCUMZNT RESUME ED 025 437 By-Zimmerman, Joseph Central Iowa Low Achiever MathematicsProject ESP. Central Iowa Low-Achiever MathematicsProject, Des Moines. Elementary and Secondary Education. Spons Agency-Office of Education(DHEW), Washington, D.C. Bureau of Pub Date (Nov 68] Grant- OEG- 3965 Note- 64p EDRS Price MF-$0.50 HC-$3.30 *Instructional Materials, Descriptors-Curriculum, Curriculum Development,*Elementary School Mathematics, *Low Achievers, *Mathematics,*Problem Solving. SecondarySchool Mathematics Identifiers-Central Iowa Low AchieverMathematics Project The materials in this EnrichmentStudent Project (ESP) aredesigned especially for the low achiever student inmathematics. The booklet is aselfontained unit consisting of fourelements--a mathematicalpuzzle, a set of instructions,response sheets, and a suitable containerfor keeping the unittogether. ESP is amotivational the student's interest andpromoting hisinvolvement in a idea aimed at attracting been collected portion of mathematicsthat can be enjoyed. Thematerials which have for this ESP, complete with solutionof problems for the teacher'sconvenience involve prepared under ESEATitle peg, dissection,cube, and topologypuzzles. This work was III contract. (RP) Central Iowa LowAchiever Mathematics Project U.S. DEPARTMENT Of HEALTH, EDUCATION & WELFARE OFFICE Of EDUCATION THIS DOCUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROM THE ED025437 PERSON OR ORGANIZATION ORIGINATING II.POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRESENT OFFICIAL OFFICE OF EDUCATION POSITION OR POLICY. The work presented or rennrted herein was performed our, suant to a Grant, OE No. 3969, from the U.S. Office of Educe. tion, Deprirtment of Hei Ith. Ed,initi-n, and Welfare.However, the opinions exnrer,sed hrTiin do not necesssrily reflect the positionorpolicy of the U.S. Office of Education, and no official endorsement by the U.S. Office of Education shoultl.be Inferred. 1164 26th Street Des Moines, Iowa 50311 1,". riTripssereroMMIOTP t -, - .444090 f-2'.3e ;".," ".-t JOSEPH ZEINNIERMAK MAL IOWA LOWACHIEVER MATHEMATICSPENEI (CILAMP) 1164 - 26th Street tagEsulgajw 1111011111111M11000011111PIP sodPIIPSIMPNINIMMINIMINI0W 'VD 10111111111MtliaM ,,..."172.M.OrMi. TABLE OF CONTENTS Page Section I. INTRODUCTION PEG PUZZLES 1 1)Ten Men In A Boat 5 2)Reversal 7 3)Quadrix 8 4)Elimination Plus 10 5)Elimination Square 11 6)Elimination Triangle 12 7)Garage Shuffle III. DISSECTION PUZZTJES 1 1)Tanagrasm 4 2)Dissected Square 6 3)Dissected "T" 7 4)Cross Dissections 8 5)Star Trick 9 6)Butterfly Puzzle 11 7)Hexed 12 8)Voodoo IV. CUBE PUZZLES 0 1 1) Soma Cube 4 2) Combo 5 3) Gambler's Die 6 4) Paper Cube 7 5) Oriental Cube V. TOPOLOGY PUZZLES 1 1) Wire Heart 2 2) Shoestring Puzzle 3 3) Kite Knot 4 4) The Gordian Knot 5 5)Another Knot 6 6)Ring Release VI. MISCELLANEOUS PUZZLES 1 1) Tower of Hanoi 4 2) Puzzling Pyramid 5 3) Double Cross 6 4) Three X Three 7 5) Five X Five 8 6)Stick Puzzles 11 7) Loco 12 8) Digit 13 9) Mystery Maze i tipxeli 1IrileA X X Xx X X a -14 44 - .... 44 94 apavH X X X X 440 v-I .....- ta) iiPa X XXXXXX a - )4 X XXXX XX XXXXXX XXXXX SSPTO X X X X X X XXXXXXX . .... 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An EnrichmentStudent Project is a self-containedunit composed of four sheets, and elements: a mathematical puzzle, aset of instructions, response a suitable container. The puzzle can be almostanything that is a problem commercially made solving situation. There are hundreds of possibilities, some and others hoemade. A few of the possibilities aregiven in the pages which The user follow, buthese are intended only as anintroduction or beginning. 'The instruc- should feelfree to add new ones as well as toalter the old ones. From tions, typd on index cards, should be asclear and as brief aspossible. puzzle, the the instctions a student should be able tolearn the object of the questions that should rules that govern or restrict asolution, and any pertinent be answered in the process. student The response sheetis just a blank half-sheetof paper which the questions. And, uses,if he so desires, to record hissolution or to answer the enclosed in a finally, the puzzlefinstructioncardsfand response sheets are manilla envelope, orother small box suitable container. A cigar box, shoe box, element of mystery tothe makes it possible to keep theunit together and adds an puzzle. Why use it? Student As the name wouldimply, one of the reasonsfor using Enrichment But more than that Projects is to enrich the student'sstudy of mathematics. interest and involv- E S P is a motivational idea aimed atcatching the student's One of the biggest ing him in a portion ofmathematics that can beenjoyed. attitude many studens problems any mathematics teacherfaces is the negative dealt with before have towards mathematics ingeneral. This attitude must be interest has been arousedby any learning cantake place. Once the student's 2 the puzzle, then the related mathematics can be drawn out.Also, E S P serves as an incentive for students to work,since it can be used as a reward when the normal work has been completed. And, finally, E S P is a way of providing for the individual differences of the students. There are many puzzles where a slow student is on an equal footing with a good student when it comes tofinding a solution, and as a result is in as good aposition to find success. In summary, then, E S P is a way of enriching, motivating, involving, changing attitudes, rewarding, and providing for success. How can it be used? There are as many different ways of using E S P as there are teacherswho have used it. The following are but a few of the ways which teachers havefelt were successful. First of all, E S P can be used on an individual basis, when a student finishes an assignment before the majority of the class and asks,"What can I do now?" Keeping the set of E S P's in a convenien corner will make it possible for a student to get the teacher's permission and to find apuzzle with as little confusion as possible. Requiring a student to get permission first discourages a student from rushingthrough anddoing his work in a slipshod manner. Some teachers keep a chart with a class list on one sideand the list of E S P's across the top. Each student is assigned one of the puzzlesand when he has solved it a check mark is recorded.The chart serves as an incentive to master a given puzzle and in so doing to receiverecognition. The same kinl of recognition can be given by putting up signs on abulletin board naming the first one to solve a given puzzle orthe champion on one of the puzzles, forexample: Mary Kay -- 1st to solve the Tower ofHanoi with 8 discs, or John Brown -- 20 Men in a Boat. Secondly, E S P can be used with an entire class. Sometimes the whole class needs a pick-me-up or a shot-in-the-armbefore anything can be accomplished. If you have a classroom set ofEnrichment Student Projects you can have them passed out and allow fifteen or twenty minutes for each studentto become familiar with a different puzzle. I is xecreational and the students enjoy it, but it is also mathematical and the students learn from it. Some of the E S P's are such that the same puzzle can beused by the whole class at the same time. Most of these involve the student in makingthe puzzle first, and then in trying to solve it. This method emphasizes the importance of following instructions accurately, and introduces theelement of group competition. Making classroom sets of some of the puzzles such asTower of Hanoi or 10 Men in a Boat could serve as agood shop project for a student whosetalents lie in that direction.