DOCUMENT RESUME ED 382 467 SE 056 167 TITLE 5-8 Mathematics Interim Guide. INSTITUTION Manitoba Dept. of Education and Training, Winnipeg. REPORT NO ISBN-0-7711-1222-X PUB DATE 94 NOTE 237p. PUB TYPE Guides Classroom Use Teaching Guides (For Teacher) (052) EDRS PRICE MF01/PC10 Plus Postage. DESCRIPTORS Arithmetic; Data Analysis; *Elementary School Mathematics; Foreign Countries; Geometry; Intermediate Grades; Junior High Schools; *Mathematics Instruction; *Mathematics Materials; Number. Concepts; Problem Solving; *Secondary School Mathematics IDENTIFIERS Canada; Manitoba; *Mathematics Activities; Patterns (Mathematics) ABSTRACT This document contains the revisions to the 5-8 Mathematics curriculum produced for Manitoba (Canada) teachers. It contains an introduction and seven content sections: Problem Solving, Algebra, Data Managemenc, Geometry. Measurement, Number Concepts, and Number Operations. The introduction includes discussion of: rationale, goals, big ideas (mathematical reasoning; patterns and problem solving; mental mathematics; communication; connections; and review, drill, and practice), the seven strand areas, instructional practices, use of technology, changes from previous curriculum guides, assessment and evaluation, resources, and information for parents. Each of the seven strand sections contains a discussion of the topic, goals, and examples. Appendices include: "Kinds of Problem Solving," "Principles to be Used in Calculation," "Subtraction Algorithms," and "Division Algorithms." (MKR) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** ,%,,,,,:,. Mathematics N 00 Cfn '''''''''' ''''''''''''''''''''''''''''''''''' U.S. DEPARTMENT OfEDUCATION On.cs of Educsnonal firarch andIntorovtnnt EDUCATIONAL RESOURCESINFORMATION CENTER IER/CI this document has beenreproduced as )(4.....r.0 Iron the OrOn orPgantaallon onomanno d 0 Mnor changes nay* beenm00 to omprov rOr0Ouctton Quenty V' in this cloCt Pants ofVNW r/ 00111.0fill$11114110 mint do not nCSsanlyntorfient 04hc41 NNW OERI 00thon or PohCy Interim Guide REPRODUCE THIS "PERMISSION TO BY MATERIAL HASBEEN GRANTED L.-DazKACt4 Manitoba Education and Training RESOURCES EDUCATIONAL TO THE (ERIC)." INFORMATION CENTER BEST COPYAVAILABLE r 1994 5-8Mathematics ................................................ .................. + Interim Guide Manitoba Education and Training 3 ISBN 0 -771 1- 1222 -X 4 Contents Acknowledgements v Introduction to 5-8 Mathematics I Problem Solving 19 Appendix A, Kinds of Problem Solving 22 Algebra 41 Data Management 61 Geometry 79 Measurement 103 Number Concepts 131 Number Operations 165 Appendices 225 Appendix A, Kinds of Problem Solving 22 Appendix B, Principles To Be Used in Calculation226 Appendix C, Subtraction Algorithms 231 Appendix D, Division Algorithms 233 iii 5 Acknowledgements of the 5-8 Mathematics Manitoba Education and Training wishes toacknowledge and to thank members and the 5-8 Mathematics Pilot Revision Committee, the 5-8Mathematics Regional Reaction Panels, modification, and identification of Teachers. Without their feedbackand support, suggestions for additional examples, this documentwould be less complete. Members of the 5-8 MathematicsRevision Committee Rhineland S.D. #I8 Braun, Barry West Park School Manitoba Education and Training Carbotte, Roger Bureau de reducation francaise Winnipeg S.D. #1 Clifford, Terry Prince Charles ERC Winnipeg S.D. #1 Hill, Peggy (Writer) Prince Charles ERC Pelly Trail S.D. #37 Kaskiw, Dennis Oakburn Elementary LaRue-van Es, Joan Researcher Winnipeg University of Manitoba MacPherson, Eric Faculty of Education Portage la Prairie S.D. #24 McRae, Bonnie Fort la Reine School Seven Oaks S.D. #10 Oster, Dave O.V. jewitt School Parcey-Westhaver, Snow Lake S.D. #2309 Suzanne Joseph H. Kerr School St. Boniface S.D. #4 Talpash, Verna General Vanier School Manitoba Education and Training Watt, Wayne Program Development Woloshyn, Deb Samuel Burland School St Vital S.D. #6 Members of the 5-8 MathematicsRegional Reaction Panels South Central Steppler, Patsy Midland S.D. #25 Woods, Don Midland S.D. #25 Hildebrand, Brian Garden Valley S.D. #26 Sawatzky, Art Garden Valley S.D. #26 Frisch, Carol Pembina Valley S.D. #27 Shewchuk, Laurel Pembina Valley S.D. #27 Bridgeman, Joy Mountain S.D. #28 Friesen, Lynn Western S.D. #47 Kormilo, Donna Western S.D. #47 South Western Johannson, Doug Rolling River S.D. # 39 Sansome, Cathy Rolling River S.D. #39 Braun, Angela Brandon S.D. #40 Sefton, Mark Brandon S.D. #40 Rout ledge, Murray Fort La Bosse S.D. #41 Pettinger, Karen Souris Valley S.D. #42 North, Blake Souris Valley S.D. #42 Sutton, Laurie Souris Valley S.D. #42 White, Brad Turtle Mountain S.D. #44 Smith, Ray Turtle Mountain S.D. #44 North Western Joss, Gerry Dauphin Ochre Area S.D. #33 Rudy, Dennis Dauphin Ochre Area S.D. #33 Fass, Bill Duck Mountain S.D. #34 Shewchuk, Elaine Duck Mountain S.D. #34 Marshall, Agnes Swan Valley S.D. #35 Buchanan, Rob Swan Valley S.D. #35 Wyatt, Gladys Swan Valley S.D. #35 Kalechyn, Tony Intermountain S.D. #36 Drysdale, Brian Fort La Bosse S.D. #41 Winnipeg Area Bergman, Glen Winnipeg S.D. #1 Brown, Jackie Winnipeg S.D. #1 Thiry, Irene St. James-Assiniboia S.D. #2 Asu, Vicki St. James-Assiniboia S.D. #2 Scott, Barb Assiniboine South S.D. #3 Wolodarsky, Terri-Mae Assiniboine South S.D. #3 Dziedzic, Richard St. Boniface S.D. #4 Feir, Dennis St. Boniface S.D. #4 Labelle, Audrey St. Boniface S.D. #4 Laferty, Jack St. Boniface S.D. #4 Bannatyne, Ross Fort Garry S.D. #5 Munro, Sophie Fort Garry S.D. #5 Holmes, Roberta St. Vital S.D. #6 Mathews, John St. Vital S.D. #6 Hitchen, Bob Norwood S.D. #8 Kazina, Stan Norwood S.D. #8 Gould, Carla River East S.D. #9 Sernyk, Pat River East S.D. #9 Taylor, Gord Seven Oaks S.D. #I0 vi 7 Winnipeg Area (Continued) Kinaschuk, Faith Seven Oaks S.D. #10 Sprange, Joanne Lord Selkirk S.D. #I I Perry, John Lord Selkirk S.D. #I Elke, Grace Transcona-Springfield S.D. #I2 Bernhard, Lionel White Horse Plain S.D. #20 Bielus, Kathy White Horse Plain S.D. #20 Kolafa, Nancy Frontier S.D. #48 Osadchuk, Peter Frontier S.D. #48 Pauls, Fred Independent Schools Members of the 5-8 MathematicsPilot Project Winnipeg S. D. #1 Backe, Ralph Sargent Park School Winnipeg S. D. #1 Fillingham, Ian Isaac Newton Junior High Winnipeg S. D. #1 Hayes, Darlene King Edward School Sharrow, Cathy Sargent Park School Winnipeg S. D. #1 Winnipeg, S. D. #1 Zacharias, Kathy Robert H. Smith School St. James-Assiniboia S. D. #2 Hooper, Brenda Brooklands School St. James-Assiniboia S. D. #2 Lawrence, Judy Strathmillan School St. James-Assiniboia S. D. #2 Switzer, Maureen Sansome School Toews, Dick Phoenix Elementary St. James-Assiniboia S. D. #2 Assiniboine South S. D. #3 Manson, Shiriey Van Walleghem School Assiniboine South S. D. #3 Rollins, Val Linden Meadows School Wolodarsky, Terri-Mae Laidlaw School Assiniboine South S.D. #3 Dyal, Harry Marion School St. Boniface S. D. #4 St Boniface S. D. #4 Dziedzic, Richard Niakwa Place School Ziprick, Will Shamrock School St. Boniface S. D. #4 Fort Garry S. D. #5 Broeska, Rozann Oakenwald School Palien, Gretha Arthur A. Leach Junior High Fort Garry S. D. #5 Schmidt, Jim General Byng School Fort Garry S. D. #5 White, Bob Arthur A. Leach Junior High Fort Garry S. D. #5 Bird, Vivian Prince Edward School River East S. D. #9 Neumann, Laura Munroe Junior High River East S. D. #9 River East S. D. #9 Strachan, Barbara Maple Leaf School Wohlschlager, Linda Poison School River East S. D. #9 Burns, Robert James Nisbet School Seven Oaks S. D. #10 Swick, Maxine West St. Paul School Seven Oaks S. D. #10 Lord Selkirk S. D. #1 I Grahame, Stephen Selkirk Junior High Mulholland, Sandra St. Andrews School Lord Selkirk S. D. #1 I Lord Selkirk S. D. #1 I Perry, John Lockport School Procyshyn, Rita Selkirk Junior High Lord Selkirk S.D. #11 vii Members of the 5-8 Mathematics Pilot Project(Continued) Belanger, Mary Jane Arthur Day School Transcona-Springfield S. D. #12 Proskurnik, Tim Oakbank Elementary Transcona-Springfield S. D. #12 Penner, Cheryl Green Valley School Hanover S. D. #15 Moir, Maureen Green Vally School Hanover S. D. #I5 Dowsett, Joanne Woodlands School Interlake S. D. #21 Waldbauer, Darlene Teulon Elementary Interlake S. D. #21 Waldvogel, Gregg Oakville Elementary Portage la Prairie S. D. #24 Williams, Pat Oakville Elementary Portage la Prairie S. D. #24 Kirchner, Adriana Fort la Reine School Portage la Prairie S. D. #24 McKetiak, Billy Miami Elementary Midland S. D. #25 Hand, Marg Carman Elementary Midland S. D. #25 Woods, Don Elm Creek School Midland S. D. #25 Anderson, Clara Manitou Elementary Pembina Valley S. D. #27 Holliston, Dean Manitou Elementary Pembina Valley S. D. #27 Mueller, Ella Manitou Elementary Pembina Valley S. D. #27 Ramage, Wayne Cartwright School Pembina Valley F. D. #27 Drummond, Janice Holland Elementary Tiger Hillis S. D. #29 Greenlay, Georgina Glenboro School Tiger Hills S. D. #29 Smart, Scott Treherne Elementary Tiger Hills S. D. #29 Boden, Gary Austin Elementary Pine Creek S. D. #30 Wolfe, Beverley Austin Elementary Pine Creek S. D. #30 McKinnon, Bruce MacGregor Elementary Pine Creek S. D. #30 Wainikka, Brad MacGregor Elementary Pine Creek S. D. #30 Joss, Jerry Whitmore School Dauphin Ochre Area S. D. #33 Rudy, Dennis Mackenzie Junior High Dauphin Ochre Area S. D. #33 Stock, Robert Swan River Junior High Swan Valley S. D. #35 Wyatt, Gladys Mafeking School Swan Valley S. D. #35 Dunham, Wayne Major Pratt School Pelly Trail S. D. #37 Ferg, Dan Major Pratt School Pelly Trail S. D. #37 McNabb, Glen Shoal Lake School Birdtail River S.D. #38 Garbolinsky, Garry Tanner's Crossing School Rolling River S. D. #39 Geseron, Richard Rivers Collegiate Rolling River S. D. #39 Fawcett, Howard Kirkcaldy Heights School Brandon S. D. #40 Joss, Norman Vincent Massey High Brandon S. D. #40 Lee, Robert George Fitton School Brandon S.