# Modules

Math in a Cultural Context (MCC) is a supplemental elementary school math series. The math modules that compose MCC are the result of a rather extraordinary collaboration of educators, Yup’ik elders and teachers, mathematicians and math educators, and Alaskan school districts. This collaboration spans nearly two decades of work: forming meaningful relationships between the parties of this work to producing not only culturally relevant materials that connect local knowledge to school knowledge, include integrated materials (literacy, geography, and science), and according to rigorous experimental and quasi-experimental designs used in numerous studies found MCC to be effective. This website introduces you to this work.

To order an MCC module, please visit the publisher.

### Modules Grades 1 - 3

#### Going to Egg Island: Adventures in Grouping and Place Values

##### Mathematics Content

Elementary number concepts. Students learn how to group objects, decompose and compose numbers using addition or subtraction, develop the concepts of place value and numeration, learn to use a two-dimensional coordinate system. For example, students learn how to form groups of five (grouping), how to express a number in terms of a number of groups of five (composing and decomposing numbers) and/or five groups of groups of five (group of 25), record the number of units, groups of 5, and groups of 25 and make connections to the Yup’ik counting system and the base 10 system (place value and numeration), and how to find and designate objects or locations on a simple map (two-dimensional coordinates).

##### Yup'ik Cultural Context

Egging, which is the subsistence practice of gathering eggs, particularly that of the Black-Legged Kittiwake (a ground-nesting bird common to southwest Alaska), is the central cultural context of the module. However, in the module students also learn to count in Yup’ik and they study the mathematical structure of the traditional Yup’ik number system, which is a base 20 (with sub-base 5) number system. To reinforce the concepts of grouping, place value, and numeration, students also learn how to use different abaci from different cultures (e.g., western base 10, Chinese) and then construct their own Yup’ik abacus to correspond to the Yup’ik number system.

##### General Information

Author: Jerry Lipka

Complete Kit:

• ISBN 978-1-55059-257-3 \$56.95
• Curriculum ISBN: 978-1-55059-245-0 \$28.95
• Egg island Storybook (the reader) ISBN: 978-1-55059-246-7 \$14.95
• Egg Island coloring book master
• 5 posters: Map of Alaska, Map of North America, Map of Egg Island with grid, Map of Egg Island without grid, Whole Body Counting
• Annie Blue CD-ROM
• Yup'ik Glossary CD-ROM

#### Patterns and Parkas: Investigating Geometric Principles, Shapes, Patterns and Measurement

##### Mathematics Content

Fundamental geometry concepts. Students learn how to identify and construct geometric patterns, and study properties of geometric shapes.

##### Yup'ik Cultural Context

Making border patterns for the hood, cuffs, and hemline of a traditional parka provides the overall cultural context for the module. Students learn traditional Yup’ik ways to make patterns for parkas by constructing, manipulating, and repeating geometric figures.

##### General Information

Authors: Sandi Pendergrast, Jerry Lipka, Daniel Lynn Watt,
Kay Gilliland, Nancy Sharp
Complete Kit:

• ISBN: 978-1-55059-308-2 \$55.95
• Curriculum ISBN: 978-1-55059-325-9 \$34.95
• Iluvaktuq story ISBN: 978-1-55059-307-5 \$17.95
• 7 posters: Yup'ik Border Patterns, Yup'ik Pattern Posters (Parka with Pretend Boxes, Parka with Pretend Boxes on Top of Each Other and Connected, Parka with Pretend Braids, Parka with Pretend Mountains with Reflections, Parka with Pretend Teeth or Mountains, Parka with Pretend Windows)
• Tumartat: Gathering the Pieces to make the Whole DVD
• Yup'ik Glossary CD-ROM

#### Picking Berries: Connections Between Data Collection, Graphing, and Measuring (2nd - 3rd Grades)

##### Mathematics Content

Key concepts from statistics. Students learn how to collect, organize, display, and interpret data. For example, students learn how to determine an appropriate unit for measuring and how to use a measuring device, like a ruler (collecting data), how to put the data into a table (organizing data), how to construct a line graph or bar graph of the data (displaying data), and to explain what a graph means (interpret data). Students also learn about identifying patterns in data and how to use data to formulate and test conjectures.

##### Yup'ik Cultural Context

The subsistence practice of picking berries provides the overall cultural context for the module. Yup’ik names of the berries found in southwest Alaska are taught. How the seasons, weather, and temperature affect the growth and harvest of berries are explored, as well as the role of berry picking in Yup’ik culture and traditional Yup’ik recipes for using berries in cooking. Students also learn Yup’ik units for measuring length, which correspond to measures of the body (e.g., arm span or hand width).

##### General Information

Authors: Jerry Lipka, Janice Parmelee, Rebecca Adams

Complete Kit:

• ISBN: 978-1-55059-294-8 \$68.95
• Curriculum ISBN: 78-1-55059-282-5 \$34.95
• Berry Picking storybook (reader) ISBN: 978-1-55059-283-2 \$17.95
• Big John and Little Henry storybook ISBN: 978-1-55059-284-9 \$9.95
• Berry coloring book master
• 2 posters: Berries and Yup'ik Measures
• Yup'ik Glossary CD-ROM

### Modules Grades 3 - 5

#### Designing Patterns: Exploring Shapes and Area

##### Mathematics Content

Geometric properties of polygons (esp. rectangles, rhombi) and introduction to area. Rectangles and rhombi are decomposed into triangles and properties such as symmetry and congruence are explored. Introduction to proof and how to make and justify a mathematical conjecture and opportunities are provided to make connections to fractions.

##### Yup'ik Cultural Context

Students study patterns found in traditional Yup’ik headdresses. By cutting and folding rectangles to make decorative linear strips to make a headdress, students learn how Yup’ik seamstresses develop geometric patterns for headdresses. The Yup’ik cultural role of headdresses is that they are used in traditional dances and ceremonies.

##### General Information

Authors: Daniel L.Watt, Jerry Lipka, Joan Parker Webster,
Evelyn Yanez, Dora Andrew-Ihrke, Aishath Shehenaz Adam
Complete Kit:

• ISBN: 978-1-55059-306-8 \$49.95
• Curriculum ISBN: 978-1-55059-318-1 \$34.95
• Iluvaktuq and Paluqtalek stories ISBN: 978-1-55059-328-0 \$14.95
• Tumartat: Gathering the Pieces to make the Whole DVD
• Yup'ik Glossary CD-ROM

### Modules Grades 5 - 7

#### Star Navigation: Explorations into Angles and Measurement

##### Mathematics Content

Measurement concepts of units, distance, and the process of measuring. Number concepts of ratio and proportion, geometric concept of similarity.

##### Yup'ik Cultural Context

The traditional Yup’ik practice of using angles and stars (or the sun) to determine location, direction, and distance provides the overall cultural context of this module.

##### General Information

Authors: Barbara L Adams, Melissa Kagle, Frederick George
Complete Kit:

• ISBN: 978-1-55059-337-2 \$45.95
• Curriculum ISBN: 978-1-55059-326-6 \$32.95
• 2 posters: Sky Map and Sun and Earth Facts
• Yup'ik Glossary CD-ROM

#### Kayak Design: Scientific Method and Statistical Analysis

##### Mathematics Content

Measurement concepts of units, distance, and the process of measuring. Number concepts of ratio and proportion, geometric concept of similarity.

##### Yup'ik Cultural Context

The traditional Yup’ik practice of using angles and stars (or the sun) to determine location, direction, and distance provides the overall cultural context of this module.

##### General Information

Authors: Jerry Lipka, Carrie Jones, Nicolle Gilsdorf, Karen Remick and Anthony Rickard
Complete Kit ISBN: 978-1-55059-404-1 \$54.95
Kit includes:

• Curriculum ISBN: 978-1-55059-401-0 \$32.95
• 2 posters
• Kukugyarpak by Annie Blue: ISBN: 978-1-55059-360-0 \$13.95

#### Building a Fish Rack: Investigations into Proofs, Properties, Perimeter and Area

##### Mathematics Content

Measurement concepts of perimeter and area; introduction to proving and disproving mathematical conjectures (e.g., use of reasoning, counterexamples). Exploration of the relationships between measures of rectangles (e.g., constant perimeter, varying area).

##### Yup'ik Cultural Context

The subsistence practices of harvesting, preparing, and constructing a fish rack to dry salmon is the overall cultural context for this module. Students learn about fish camp, the role of subsistence in Yup’ik culture, and traditional ways of building a fish rack.

##### General Information

ISBN: 978-1-55059-258-0 \$34.95
Kit includes:

• Curriculum
• 3 posters: Fish Racks, Salmon Life Cycle, the Five Salmon Species
• Yup'ik Glossary CD-ROM

#### Building a Smokehouse: The Geometry of Prisms

##### Mathematics Content

Introduction to threedimensional geometric figures, particularly rectangular prisms and properties of prisms. The measurement concepts of surface area and volume of rectangular prisms is explored. Relationships between volume and surface area in rectangular prisms is also studied (e.g., fixed volume, varying surface area).

##### Yup'ik Cultural Context

Designing a smokehouse to use to prepare salmon at fish camp provides the overall Yup’ik cultural context for the module. Students use cubes to build models of smokehouses (which are in the shape of a rectangular prism), record their properties (e.g., surface area, volume) and select the best smokehouse design for particular criteria.

##### General Information

Authors: Melissa Kagle, Valerie Barber, Jerry Lipka, Ferdinand Sharp, Anthony Rickard
ISBN: 978-1-55059-331-0 \$31.95
Kit includes:

• Curriculum
• 1 poster: Smokehouses
• Yup'ik Glossary CD-ROM

#### Salmon Fishing: Investigations into Probability

##### Mathematics Content

Introduction to probability concepts, including sample space, experimental and theoretical probability, equally likely and not equally likely outcomes, law of large numbers, and probabilistic reasoning.

##### Yup'ik Cultural Context

Salmon fishing, particularly in the Kuskokwim, Yukon, and other major rivers in southwest Alaska (as well as in Bristol Bay) provide the major cultural context for the module. Students develop and apply their knowledge of probability to select suitable fishing gear, predict the salmon harvest, learn how state agencies regulate subsistence and commercial salmon fishing. Some traditional Yup’ik games are also provided and students apply probability to analyze the games, as well as develop and refine strategies for playing the games.

##### General Information

Authors: Aishath Shehenaz Adam, Jerry Lipka, Barbara L Adams, Anthony Rickard, Kay Gilliland, Joan Parker Webster
ISBN: 978-1-55059-305-1 \$32.95
Kit includes:

• Curriculum
• 2 posters: The Salmon Life Cycle, The Five Salmon Species
• Excel template CD-ROM
• Yup'ik Glossary CD-ROM

#### Drying Salmon: Journeys into Proportional and Pre-Algebraic Thinking

##### Mathematics Content

The relationship between body proportions, fish racks, and salmon sizes establishes proportional thinking. Body measures are transformed into mathematical symbols. This begins explorations into algebraic thinking. Other topics include variables, constants, proportions, ratios, and patterns.

##### Yup'ik Cultural Context

Built around the Yup'ik subsistence activity of salmon fishing and drying salmon, The late Mary George of Akiachak, Alaska used a unique system of body measure to estimate the relationship of the different types of salmon and their size to her body measure and to the fish rack pole for drying. This formed the major insight into this module.

##### General Information

Authors: Barbara L. Adams, Jerry Lipka
ISBN: 978-1-55059-330-3 \$35.95
Kit includes:

• Curriculum
• 3 posters: Hanging Salmon to Dry, Body measurements and Fish Cuts
• Yup'ik Glossary CD-ROM

### Other Story Books

#### The Story of a Giant

From the back cover: This story, like all of the Yup’ik stores in the Math in a Cultural Context (MCC) series, presents a glimpse into Yup’ik culture and life as it was lived in the past, but the values and joy that underlie this story carry into the present. The Giant was told to us by the late Mary George of Akiachak, Alaska.

The Giant represents a literature genre that has features of oral story telling accompanied by “performance.” In this case, the performance is storyknifing. Storyknifing symbols are akin to action characters in that they animate the oral presentation. The young children’s story stresses the Yup’ik value of listening to your elders in a fun and entertaining way. The Yup’ik symbols for houses, children, the Giant, and actions such as singing, talking or moving is what makes this particular story genre unique. Elementary school children anywhere will enjoy this story.

Connections to mathematics can also be made by emphasizing perspective, what the symbols represent, and the importance of those symbols. These connections enrich the story with the inherent mathematics of the Yup’ik culture. Most importantly, however, we hope you enjoy this wonderful story.

This story book is included with the Going to Egg Island module set.

From the back cover: Iluvaktuq is a traditional Yup’ik story, told by Annie Blue and Mary E. Bavilla. It accompanies the curriculum module Patterns and Parkas: Investigating Geometric Principles, Shapes, Patterns, and Measurement, which part of the series Math in a Cultural Context (MCC): Lessons Learned from Yup’ik Eskimo Elders. MCC is the result of a long-term collaboration with Yup’ik elders, Yup’ik teachers and Alaskan school districts. These supplemental math modules for grades 1-7 bridge the unique knowledge of Yup’ik elders with school-based mathematics. Our classroom-based research strongly suggests that students engaged in this curriculum can develop deeper mathematical understanding that students who engage with the more procedure-oriented paper and pencil curriculum. MCC’s research has shown that these modules have been effective in enhancing students’ mathematical learning. MCC also produces stories that embed both mathematical concepts and unique cultural, geographical, or historical information about southwest Alaska.

This story is about a famous historical Yup’ik warrior who lived during the Great War, during the Russian occupation of Alaska. The story tells about the importance of family lineage to Yup’ik people and the history behind the design of the parkas that his descendents still wear today. Stories are an important part of the MCC series, as a way for students to relate to Alaska and some of its unique characteristics. These two stories help connect to the math of the module through parka pattern designs.

#### Two Yup'ik Warrior Stories

From the back cover: Iluvaktuq and Paluqtalek: Two Yup’ik Warrior Stories are traditional Yup’ik stories, told by Annie Blue and Mary E. Bavilla. It accompanies the curriculum module Designing Patterns: Exploring Shapes and Area, which part of the series Math in a Cultural Context (MCC): Lessons Learned from Yup’ik Eskimo Elders. MCC is the result of a long-term collaboration with Yup’ik elders, Yup’ik teachers and Alaskan school districts. These supplemental math modules for grades 1-7 bridge the unique knowledge of Yup’ik elders with school-based mathematics. Our classroom-based research strongly suggests that students engaged in this curriculum can develop deeper mathematical understanding that students who engage with the more procedure-oriented paper and pencil curriculum. MCC’s research has shown that these modules have been effective in enhancing students’ mathematical learning. MCC also produces stories that embed both mathematical concepts and unique cultural, geographical, or historical information about southwest Alaska.

These two stories are about two Yup’ik warriors who were part of a group or warriors living during the Great War, during the Russian occupation of Alaska. Stories are an important part of the MCC series, as a way for students to relate to Alaska and some of its unique characteristics. These two stories help connect to the math of the module through parka pattern designs.

From the back cover: Mary Makes a Qaspeq is a fictionalized account of a typical relationship between a young girl and her grandmother. The story was developed from the childhood experiences of Evelyn Yanez and Dora Andrew-Ihrke who grew up in Togiak and Aleknagik respectively, two villages in southwest Alaska. The story chronicles Mary visiting with her grandmother. Her grandmother is making a qaspeq , a versatile women’s garment that can be worn in the house and outside while berry picking. Mary not only observes her grandmother make a qaspeq , but she begins to make an outfit for a doll ( sugaq ). Mary makes the doll for her best friend Christine, who will be spending the summer at fish camp.

Mary Makes a Qaspeq is part of the Math in a Cultural Context (MCC) series. This story, like others in the series, highlights everyday activities of Yup’ik people connecting Yup’ik culture, math and pedagogy. In this story, the importance of relationships is highlighted as well as a way of teaching; mathematically the story embeds measuring, folding (symmetry), and putting pieces together to make a product.

#### Told by Annie Blue

From the back cover: When the young hunter Kukugyarpak gets lost on the icy ocean while out on his kayak, he begins an epic journey filled with fantasy, adventure and unforgettable sights. Kukugyarpak’s travels take him to a land of giants, a village where the people have no mouths, and a strange place where all the women have beards. Along the way, Kukugyarpak learns the value of helping those in need and how to face the unexpected with grace and dignity.

A traditional Yup’ik tale passed down through the generations and recounted by famed storyteller Annie Blue, this rollicking adventure provides a glimpse into an ancient way of life uniquely adapted to the North. As part of the Math in a Cultural Context series, this story can be used with the Kayak Design module or enjoyed on its own.

#### Akagyugnarli

From the back cover: Annie Blue, a revered ninety-four-year-old elder and wonderful storyteller from Togiak, Alaska, continues to contribute to the Math in a Cultural Context (MCC) series and to the next generation through storytelling. Annie’s deep cultural knowledge, dedication and caring attitude were recognized by the University of Alaska Fairbanks in 2009 when she was awarded an honorary doctorate.

The Raven Story has become a favorite of Eva Evelyn Yanez, who has listened to Annie telling stories since her childhood. Evelyn has often retold Annie’s story at meetings in Anchorage, Fairbanks, elsewhere in the United States, and internationally. It has always been well received.

In this book, the story is told twice: once as Annie has told it and a second time as an illustrated “storyknife” version. Storyknifing is a literary form that combines an oral presentation with quickly drawn illustrations that represent a particular scene. As soon as the scene has been completed and told, the teller will erase the scene and draw the new illustration to align it with the spoken word. In the form presented here, the spoken word has been replaced by the written word, and the scenes are not erased. The story is first told by Annie Blue and translated by both Eva Evelyn Yanez and Dora Andrew-Ihrke and the second storyknife version was retold by Eva Evelyn Yanez.

Each Yup’ik story in the MCC series has embedded Yup’ik values about how to live. This story is no different. Also, MCC has typically integrated Yup’ik stories to further establish the context and also make connections to the mathematics of the module. This story can be used independently, or it can be used with the MCC module Going to Egg Island: Adventures in Grouping and Place Values.

From the back cover: Annie Blue, a revered elder and marvelous storyteller from Togiak, Alaska, presents Slave Girl . Annie Blue continues to contribute to the education of the next generation through her vast cultural knowledge and her dedication to people. Annie was honored in 2009 with a honorary doctorate from the University of Alaska Fairbanks.

This story takes place during the beginning of the period of time known as the Yup’ik wars. As Annie notes, it was a difficult time especially for young women. This story begins and ends with the importance of family symbols, identity, place, and patterns on parkas that symbolize a person’s lineage and family. The story follows the adventures and misadventures of Slave Girl as her life dramatically changes after she is captured during this time of war.

Her journey provides a view back in time. Students will learn about how Yup’ik people lived during those times, acquire a glimpse of the land, and gain some of the knowledge required to live on and off the land. Elders are keen to point out that these stories provide life lessons for younger generations.

This story, like others in the Math in a Cultural Context (MCC) series, can be told or read independently of any MCC modules; or Slave Girl can be integrated into the Patterns and Parkas module and the Designing Patterns module. These two MCC modules stress the mathematics behind the construction and design of meaningful Yup’ik symbols which adorn parkas and other clothing.