GRADE LEVEL EDUCATION MATHEMATICS ELEMENTARY Salmon Fishing 6/7 K1234567 Investigations into Probability Math in a Cultural Context: Lessons Learned from Yup’ik Picking Berries: Connections Between Data Salmon Fishing Eskimo Elders is the result of a long-term collaboration. Collection, Graphing, and Measuring (2nd grade) These supplemental math modules for grades 1-6 bridge Students engage in a series of hands-on activities the unique knowledge of Yup’ik elders with school-based that help them explore measuring, data, and graphic Aishath Shehenaz Adam mathematics. This series challenges students to commun- representation. The complete package includes a Jerry Lipka icate and think mathematically as they solve problems. CD-ROM, posters, two story books: Big John and LIBERTY Problems are inquiry-oriented and the problems are con- Little Henry, about using traditional Yup’ik body Barbara L. Adams 1998 structed so that the possibilities are constrained and the measurements to build kayaks; and Berry Picking, students can understand mathematical relationships, prop- about a Yup’ik family’s berry picking trip, which Anthony Rickard LIBERTY erties of geometrical shapes, develop place value under- incorporates a traditional story about mosquitoes. 1998 standing, and state conjectures and provide proofs. Curr- Kay Gilliland ED STA NIT TE Building a Fish Rack: Investigations into Proof, U S o f A M iculum taps into students’ creative, practical, and O E R Investigations into Probability Properties, Perimeter, and Area (6th Grade) Joan Parker Webster N I C analytical thinking. Our classroom-based research strongly E A Students will explore what happens when the perimeter is CENT 5% suggests that students engaged in this curriculum can held constant and area changes, and what happens 1.20 S develop deeper mathematical understandings than students TATE of A S M D E when area is held constant and perimeter changes. E R T I I C who engage with the more procedure-oriented paper and N A Through model building, students explore properties of 15% 1.00 U pencil curriculum. MCC’s research has shown that these O various quadrilaterals, including measurements of perimeter NE NT modules have been effective in enhancing students’ mathe- and area. The complete package includes posters and a CD- 0.80 CE matical learning. ROM. 55% 25% 0.60 ES Forthcoming in this series: TAT of A S M Also in this series: D E E R T I I C N A Going to Egg Island: Adventures in Grouping and Place Patterns and Parkas (tentative title) 0.40 U Values (2nd Grade) The traditional repeating geometric border pattern O Students learn to group objects in a variety of ways. In particular, 0.20 N T sewn on Yup’ik fur parkas provide the basis for a E CEN they learn the Yup’ik system of counting and grouping (base series of activities on patterns and shapes. After Each Flip Probability 20 and sub-base 5). Students compose and decompose 0.00 Rhombi Patterns: Investigations into Properties, numbers. This hands-on and evidence-based approach to 0246810 12 14 16 18 20 teaching numeration has produced good results. The complete Geometrical Relationships, and Area (tentative package includes an accompanying story book called Egg Island, title, 3rd-5th grade) Number of Flips Students learn how to cut a rhombus from a folded 11 Flipspin 22 Flipsspins 33 Flipsspins posters, two CD-ROMs, and a coloring book. K K rectangle, learning the properties of rhombus and a K R LIBERTY 1998 rectangle and the lines of symmetry of the rec- King K K K tangle, the cut out rhombus, and the four congruent R R R triangles. They explore part-to-whole and part- K K K Red R R R to-part relationships, construct a rhombus pattern K R LIBERTY puzzle, and create a linear pattern of their own. R R 1998 The Supplemental Math Modules curriculum was developed at the University MCC MCC of Alaska Fairbanks. Part of the series Math in a Cultural Context: Lessons Learned from Yup’ik Eskimo Elders Part of the series Math in a Cultural Context: Lessons Learned from Yup’ik Eskimo Elders MATH IN A CULTURAL CONTEXT© Salmon Fishing Investigations into Probability Part of the Series Math in a Cultural Context: Lessons Learned from Yup’ik Eskimo Elders Grade 6 & 7 Aishath Shehenaz Adam Jerry Lipka Barbara Adams Anthony Rickard Kay Gilliland Joan Parker Webster Developed at University of Alaska Fairbanks, Fairbanks, Alaska Salmon Fishing: Investigations into Probability © 2005 University of Alaska Fairbanks Library and Archives Canada Cataloguing in Publication Salmon fishing : investigations into probability / Aishath Shehenaz Adam . [et al.]. (Math in a cultural context: lessons learned from Yup’ik Eskimo elders) Includes bibliographical references. ISBN 1-55059-305-6 1. Mathematics—Study and teaching (Elementary). 2. Probabilities—Study and teaching (Elementary). 3. Salmon fishing. 4. Yupik Eskimos—Alaska. I. Adam, Aishath Shehenaz II. Series. QA135.6.S24 2005 372.7’044 C2005-904881-6 Math in a Cultural Context: Lessons Learned from Yup’ik Eskimo Elders© was developed at the University of Alaska Fairbanks. This material is based upon work supported by the National Science Foundation under grant #9618099, Adapting Yup’ik Elders’ Knowledge: Pre-K-to-6th Math and Instructional Materials Development, and U.S. Department of Education grant #S356A030033, Developing and Implementing Culturally Based Curriculum and Teacher Preparation. University of Alaska Fairbanks, 2019 © 2019 University of Alaska Fairbanks. Salmon Fishing: Investigations into Probability is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License. This material may be shared and adapted, provided that appropriate credit is given, a link to the license is provided, and any changes made are indicated. Commercial use is prohibited. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/. Any opinions, findings, conclusions, or recommendations in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF) or the U.S. Department of Education. This project was also sponsored, in part, by the University of Alaska Fairbanks, Alaska Schools Research Fund and the Bristol Bay Curriculum Project. ISBN: 1-55059-305-6 SAN: 113-0234 Printed in Canada. iii MATH IN A CULTURAL CONTEXT© MCC Principal Investigator, Writer, and Teacher Piloting the Module: Series Editor: Tom Dolan Jerry Lipka Teachers Piloting the Test: Project Mathematician: Tom Dolan Barbara Adams Thad Keener Terry McCarthy Project Manager: Kathleen Meckel Flor Banks Gretchen Murphy Project Illustrator: Editing: Putt (Elizabeth) Clark Shane Dayton Loretto Jones Project Layout: Sue Mitchell Sue Mitchell Yup’ik Elders: Folklorist: Mary Active Ben Orr Henry Alakayak Julia Apalayaq Literacy Specialist: Mary E. Bavilla Joan Parker-Webster Annie Blue Frederick George Yup’ik Consultants: Mary George Dora Andrew-Ihrke Samuel Ivan Mary Beans Anuska Nanalook Sassa Peterson Ferdinand Sharp Yup’ik Translators: Mike and Anecia Toyukak Dora Andrew-Ihrke Evelyn Yanez Eliza Orr Ferdinand Sharp Evelyn Yanez Table of Contents Introduction: Math in a Cultural Context. .ix Introduction to Salmon Fishing: Investigations into Probability . 1 Section 1—Deciding on the Fishing Gear: Experimental and Theoretical Probability Activity.1:.Preparing.to.Fish:.Experimental.and.Theoretical.Probability. 33 Activity.2:.What.Type.of.Gear.to.Bring:.The.Law.of.Large.Numbers . 45 Activity.3:.Chances.of.Being.Trapped:.A.Literacy.Activity . 55 Section 2—Catching Multiple Salmon in a Row: Sample Space Activity.4:.Catching.Multiple.Salmon.in.a.Row:.Creating.Sample.Spaces . 67 Activity.5:.Catching.Multiple.Salmon.in.a.Row:.Finding.the.Probabilities .. .. .. .. .. .. .. .. .. .. .. .. ... 77 Activity.6:.Falling.Sticks.Game:.Reviewing.Sample.Space,.Experimental.. and.Theoretical.Probability . 85 Section 3—Integrating Knowledge and Skills: Additional Probability Concepts Activity.7:.Sampling.the.River:.Equally.Likely.and.Unequally.Likely.Events. 95 Activity.8:.Knowledge.and.Skills.Changes.the.Probability. 107 Section 4—Project Activity.9:.Creating.a.Game.of.Chance. 117 Appendix: Games of Chance. 121 ii Acknowledgements From Jerry Lipka, Series Editor The supplemental math series Math in a Cultural Context: Lessons Learned from Yup’ik Eskimo Elders is based on traditional and present-day wisdom and is dedicated to the late Mary George of Akiachak, Alaska, and her late father George Moses of Akiachak, and to the late Lilly Gamechuk Pauk of Manokotak, Alaska. Mary con- tributed to every aspect of this long-term project, from her warm acceptance of people from all walks of life to her unique ideas and ways of putting together traditional Yup’ik knowledge with modern Western knowledge. Mary’s contribution permeates this work. Without the dedication and perseverance of Mary and her husband, Frederick George, who tirelessly continues to work with this project, this work would not be possible. George Moses was always eager and willing to teach and share his knowledge of the land and river. He was particularly concerned with the well-being of the next generation and hoped that this project would help connect community knowledge to schooling. Lilly cheerfully worked with this project even when she was ill. She would make sure that she first told her story to the group before she attended to other personal concerns. Her dedication, laughter, and spirit of giving formed a foundation for this project. For more years than we care to remember, I have had the pleasure to work with and learn from Evelyn Yanez of Togiak, Alaska; Nancy and Ferdinand Sharp of Manokotak, Alaska; Sassa Peterson of Manokotak, Alaska; and Dora Andrew Irhke of Aleknagik and Anchorage, Alaska. Their contributions are immeasurable, as is their friendship. Our long-term relationship with elders who embraced this work wholeheartedly has made this difficult endeavor pleasurable as we learn from each other. In particular, I would like to acknowledge Henry Alakayak of Manokotak and Annie Blue of Togiak, whose dedication and commitment to cultural continuity has much inspired our project.