Liz Baca's CU

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Learning About Native Americans Through Math, Science and Art

Liz Baca

Academic Setting

This lesson was designed to be used in the first grade at Corrales Elementary School. This is a K-5 school with a little less than 600 students. The community is considered a very affluent community, with an abundance of business owners, professionals, and artists. There is also a population of rather impoverished people, some of whom are often just “over the border” from Mexico, and others who are land rich, having moved to Corrales before it became such a trend, but money poor. About 20% of the students qualify for free or reduced lunches. The school is made up of about 34% Hispanics, 62% Anglo, and about 4% “other,” including a handful of Asian, African, and Native Americans. Because of the relative lack of diversity in the Corrales school population, it is very important that they are exposed to as much culture outside their own as possible.

            Academically, Corrales Elementary has been in the top quartile in APS on standard tests, such as the Terra Nova and the New Mexico Writing Assessment. The community is generally supportive and very involved in the school. Many of the students leave Corrales and attend private schools in middle school. The big pressure on elementary teachers at our school is often our lack of time – time to plan, implement, teach, and assess all the things that we are expected to teach. By planning a thematic unit, I will be able to include a variety of curriculum in math, science, social studies, art, literature and writing that supplements what I am already working on in class.

Goals and Objectives

My main goal for this unit is to introduce the students to a diverse population of Native Americans by presenting background information about them and learning about the math, science, and art of those cultures. Much of the Native American culture is unknown outside the particular tribe due to the secrecy imposed upon them by outside forces. These areas will be a way to learn about these cultures without fearing an imposition on the more private religious beliefs, and at the same time going beyond the traditional “cultural” lessons on clothing, food, and celebrations that are often part of elementary multicultural program.

            While planning this unit, I had several things in mind. My first was to be sure anything I included was in tune with the APS District Core Curriculum and Scope and Sequence (DCCSS), and that I wasn’t adding more curriculum to the already packed schedule. Therefore, the math that is the focus of each unit goes directly with the math we will be studying about at the time we do these lessons. This will reinforce the math concepts we are learning, while showing the connections to other Native American cultures throughout time. The lessons are set up as several mini-units, which vary in length from 2-6 lessons. The units are: 1- Petroglyphs and the Anasazi (record keeping), 2- Pueblos and their Art (patterns), 3-Mayas (calendars, cycles, and number systems), 4- Pomo Stick Game (probability), and 5-Seminole Patchwork (patterns and geometry). Each unit is directly connected to our current math program, Investigations in Number, Data and Space, and will be taught during the time period we are working on those math concepts. This means that this curriculum unit will take place throughout the year.

            I have chosen these particular peoples and concepts in order to help me cover my current curriculum. For example, I will be able to share mapping skills in a variety of ways. First we will use a local map to find Petroglyph National Monument in Albuquerque, then a state map to find the Pueblos, a map of North America for the Maya culture, and a USA map for the Pomo and Seminole tribes. Also, since storytelling and the oral tradition is so important in the Native cultures, this was important for me to include. In order to fit with our DCCSS, I am including as much literature as possible. I will also be able to include non-fiction reading in context to include that type of genre. And of course art can be an area that is neglected in a crowded curriculum, so this is included as well.

            Due to the grade level of my students, the information I am including in the Context and Background information may be somewhat basic for older students. This information is geared toward early elementary students. However, these lessons are easily adaptable for use at a variety of grade levels. Here are just a couple of examples how: when looking at the Pomo Stick Game, older students could do an in-depth study of probability, including more advanced concepts like ratios and percentages. The same math concepts could also be taught using examples from other tribes, like the patterns in Navajo rugs or Cherokee beadwork. More in-depth work could also be done studying the cultures, with students responsible for the research.

            In the Context and Background section, I have broken the narrative into 5 different sections, one on each of the main concepts. I begin with a short rationale of the unit to tell some connections. There is information on the culture, and information on the math or science that is the focus of the unit. The objectives of each unit will be included more specifically in the lesson plan part of the paper.

Context and Background

Petroglyphs and the Anasazi

The focus of this unit will be on record keeping. We will be looking on how we record our thinking and keep track of our work in math. We will also be doing beginning journals that record our lives, thoughts, ideas, and plans. We will look at how petroglyphs are an ancient record left behind by people who lived many years ago, focusing specifically on the petroglyphs in New Mexico and learning about the Anasazi Indians, ancestors of the current Pueblo Indians. We will also visit the Petroglyph National Park to get a first-hand look at these ancient records.

Petroglyphs

Petroglyphs are designs and pictures carved into rocks. The tool commonly used to carve is another rock, usually flint, bone or antlers. Petroglyphs differ from painted-on images, which are known as pictographs. Pictographs are much more susceptible to the elements and are therefore more difficult to find. Petroglyphs are found throughout the southwest and North America, but we will be focusing on the petroglyphs of the Anasazi in our area.

Since the Anasazi have no written language, the meaning of various petroglyphs is unknown. There are some common forms found that we can speculate on the meaning based on our current knowledge of the Pueblos. For example, Kokopelli, the flute player, is found in many different forms in petroglyphs. He is known variously as a trickster, a wise man, a trader, a symbol of fertility, and a spiritual being. Handprints are another common petroglyph and are actually found throughout the world on stone. They can be interpreted as a personal signature of the artist, although no one knows for sure. Other common images include corn and corn plants, spirals, and lightning.

Petroglyph National Monument is located in Albuquerque along the West Mesa. This 17 square mile monument, created in 1990, preserves over 15,000 petroglyphs, one of the largest petroglyph sites in North America. These rock carvings were created over a span of thousands of years by the many groups who passed through the area: ancient hunter/gatherers, the Anasazi, farming tribes, and eventually Spanish shepherds (O’Brien, introduction). A visit to the monument will give students a “primary document” from which to study history.

Anasazis

The Anasazis are the ancestors of the current day Pueblo Indians. Their name is a Navajo word (which is ironic since they are not related to the Navajo) that means “Ancient Ones” or “Enemy Ancestor,” depending on the source. Their culture is generally said to have begun about 1400 years ago when they transformed from nomadic hunter-gatherers to basket-making farmers who built permanent structures. Their most famous current ruin is at Chaco Canyon in New Mexico, although there are ruins throughout the four-corners states, including Mesa Verde, Colorado, Bandelier and Snake Canyon, New Mexico and many others.

The Anasazi are known for their work in math and science, in particular astronomy, measurement, architecture, and the study of cycles. Chaco Canyon is an area that has recently been studied extensively. There, archaeo-astronomers are looking at the set up of the buildings and their alignment with the stars. They are amazed at the exact calculations of lunar cycles, eclipses, solstices, comets and other stellar phenomenon that is evidenced in the alignments of buildings, structures within villages, and the placement of villages relative to each other. Without the use of modern tools such as telescopes and computers, they were able to align whole communities with the heavens. An entire unit of study could be done on the astronomy of the Anasazi.

The Anasazi traded with other cultures as far away as Mexico, as well as with tribes from the Pacific and Gulf of Mexico. They built roads that connected communities as far away as sixty miles without the use of modern tools or even the wheel, roads that are still clearly visible from the air today and that are amazingly straight, even through the rough topography of the area.

The Anasazi were hunters as well as farmers. They hunted with a bow and arrow as well as a throwing spear called an atlatl. Even though they lived in the desert, they were able to turn this arid area into a successful farming community, complete with simple irrigation and conservation of rainwater. Their main crops were corn, squash, and beans, which remain the staple of the Pueblo diet today.

Anasazi housing changed over time. Their first type of house was called a pit house. It was built by digging a large hole in the ground and covering it with sticks and mud. These evolved to above-ground structures made of stone that were also single-family dwellings, although many families built these structures close together and formed small villages. Eventually, they built houses in the walls of canyons and built large villages such as those remaining at Chaco Canyon. These are somewhat similar to the more modern Pueblos, in that they both built multi-family, multi-leveled structures with individual rooms and great Kivas for gathering. The Anasazi used stone and mud to build these structures, while the Pueblos use mud and straw (Fisher, 22).

The Anasazi traded with other communities and therefore had access to materials that were not found in the Southwest. They traded with more southern tribes for cotton, which they wove into cloth to make clothing. They also traded for parrot feathers, shells, and other items. Since the area they inhabited was fairly hot in the summer, with somewhat harsh winters, clothing could be made out of cotton, animal hides, and plants to suit their various needs. The most important clothing was their sandals, which kept their feet protected from the hot, rough desert ground. Their sandals were made from strips of split yucca leaves, which were wrapped around their feet with thinner strips of yucca. They adorned themselves with necklaces, buttons, and other ornaments made from shells, bones, seeds, turquoise, and leather.

The Anasazi were very adept at making baskets, pottery, and jewelry. Their baskets were both coil type (sewn) and wicker (woven). They were made so well that some could even hold water. The pottery was also made using a coil that built upon itself until the desired shape and size was achieved. These were fired to harden, and then decorated. Jewelry was worn by men, women, and children and was made with various beads, stones, seeds, and shells. They mostly wore pendants, necklaces, bracelets, and rings (Fisher, 28-30).

Based on the artifacts of game pieces found, games of the Anasazi include dice games similar to those played by other Native American tribes. They also played many running games in which players might run for miles.

Around 1300, the Anasazi abandoned their cites. No one is quite sure why. Some historians speculate drought (based on tree rings). Others say an epidemic of some sort. There is no evidence of battle that may have forced them out of the area. As we learn and come to appreciate this great ancient culture, through the study of their artifacts, perhaps questions such as these can be answered.

Pueblos and Their Art

“Mathematics is a science of pattern and order” (MSEB, 31). A study of pattern in the primary grades often begins by looking for patterns found in our environment. Almost always, these are not numerical patterns but rather patterns found in art, clothing, or other materials. By looking for and describing the patterns we see around us, we are setting the foundation for the life-long study of the patterns of number.

Pueblo Indians

Pueblo Indians are among the earliest people to live in the Southwest. They are the descendents of the Anasazi, who lived in the same area from roughly AD 200-1400. Pueblos were among the first in the area to cultivate food through farming and therefore lived in permanent settlements the Spanish named “pueblos,” which means “towns” (Sife, 34). The word is used to name both the people and the type of housing they live in.

            Pueblos (the villages) are multi-leveled structures built from the earth (mud, straw, and rocks) with many rooms connected together. They are often built around a common area called a plaza where ceremonies take place. Traditionally, the houses were entered from the roof by ladders. These ladders could then be lifted to provide protection from invaders. Various rooms and stories could be accessed from the roof. The pueblos also included one or more kivas, which were used as gathering places and for a variety of ceremonies. These kivas are round and are entered from the roof.

The diet of the Pueblos was based on the three staple crops of corn, beans, and squash. Little corn cobs have been found in caves in Mexico that scientists believe are at least 5000 years old (Aliki, 12). From ancient wild plants to the many varieties cultivated by the Indians later, corn has been a staple in the Pueblo (and most other Native American tribes) diet. The pueblos had many varieties of corn, including flint corn (hard kernels that last for years), flour corn (easy to grind), dent corn (food for cattle), and other varieties in many colors. Farmers often had their own variety, which they passed on to their sons when they married. Corn was carefully separated by color and type, and up to two years worth was stored for times of drought. These staples were supplemented by various herbs, game (buffalo, elk, deer, antelope, rabbit, and prairie dog), birds, pinon nuts, and teas. The Spanish introduced fruits, chile, tomatoes and onions. They also added sheep, goat, cows, horses, mules, pigs, chickens, and oxen to the domesticated dog and turkey native to the Pueblos.

            Pueblo clothing differed from almost all tribes north of what we call Mexico in that their clothing was made of woven cloth rather than hides. The Pueblos had been cultivating, spinning, dying, and weaving cotton since at least AD 800, although some tribes did use hides (those in colder areas). With the arrival of the Spanish, wool was also woven by the Pueblos for clothing. Generally, the Pueblos went barefoot, but by 1300, moccasins were used regularly. The moccasins used by the Pueblos are unique in two ways. First, most tribes made a short shoe, more of a slipper, but the Pueblos wore theirs higher. The men’s came to above the ankle, and the women’s to just below the knee. Second, the hard sole, unlike the sole of other moccasins, was bent up around the side of the foot about a half inch all the way around.

            Every part of Pueblo life is based on spirituality. In every activity, from planting to building to hunting to every day tasks, Pueblo people pray and make offerings. Corn meal is used in almost all prayer as an offering to the spirits. The Pueblos, like other tribes, engage in spiritual dances at various times of the year. Much of the Pueblo religion and beliefs are kept secret, as they were often severely punished by the Spanish for practicing their way of life.

            The first Europeans to visit the Pueblos were the Spanish, who came in 1540, years before the Pilgrims landed at Plymouth Rock. At that time, there were at least 80 Pueblos (Underhill, 17-18). By 1598, they had established a settlement near one of the pueblos. The Spanish forced the Pueblos to abandon their religion (their way of life) and convert to Catholicism. Those who didn’t were punished. The Pueblos were forced to practice their religion secretly.

            In 1680, the Pueblo Revolt took place. Rebelling against the cruel treatment by the Spanish, the various Pueblos united. They killed many Spanish and successfully chased the rest out of the area. Unfortunately for the Pueblos, this respite only lasted 12 years, when the Spanish returned, never to be banished again.

            Today there are 19 tribes of Pueblo Indians. They speak 5 different languages. They live on and off reservations, and make a living in a variety of ways. Some get jobs outside the villages. Others make pottery, silver and gold jewelry, or baskets just as their ancestors did. They have farms on their lands where they grow their crops of corn, beans, and squash, as well as chile, tomatoes, and other vegetables. As with other tribes, they continue to fight against the loss of their language and way of life as outside forces continue to interfere.

Patterns and Geometry

Marilyn Burns states, “The ability to recognize patterns is the key to mathematical thinking. Patterns are basic to the understanding of all concepts in mathematics. Searching for patterns is a way of thinking that is essential for making generalizations, seeing relationships, and understanding the logic and order of mathematics” (Burns,112). As students are taught to observe patterns in their environment, they learn that life generally follows certain orders. It’s logical, and you can often figure out what happens next based on what happens last. There are short repeats in patterns, like day following night, or the evening bedtime routine (bathe, brush, story, water, bed). There are longer cycles that can be more difficult to observe when you’re young, like the year-long seasonal cycle, or the life cycle of people, plants and animals.

            This order is found throughout mathematics. Our entire number system, based on ten, has many patterns. As we study these patterns, we are reinforcing the order of mathematics. This study leads to the concept of functions, the basis for algebra.

            Work with pattern involves reasoning, which is the basis for a deep understanding of mathematics. When we search for a pattern, we are trying to make sense of things. As we describe patterns (and other mathematical ideas) we must share the characteristics that create the pattern in a way others can understand, in a reasonable way.

            In our study of Pueblo art, we will look for, describe, copy, and create patterns as found on pottery and jewelry. Primary students will begin to use vocabulary such as line, curve, angle, reflection and symmetry to discuss objects in their environment. We’ll also be looking at some of the concepts described in the Geometry section of this information. Middle and high school students could extend this study to include angle measurements, a variety of symmetries, spheres and their properties, distortions based on curves, and fractals. There are many geometric designs found on the pottery of the Anasazi and Zuni, as well as that of all Pueblo tribes.

The Maya

Maya Culture

The Mayas are generally considered to be one of the most advanced cultures of the ancient western hemisphere. They lived in the southern part of what we now call North America and in Central America. Their culture was at its developmental peak from about AD 300-900, and was still dominating at the time of the Spanish conquest. There are still Maya who maintain their traditional cultural practices, although many have been greatly influenced by the Spanish.

            The Maya, particularly through the Classic Period (AD 300-900) lived in a society divided by classes. At the top were the royalty, with hereditary kings the head of the hierarchy. The kings also performed the duties of priests. The upper class included nobility and merchants. Merchants were important due to the significance of trade in salt, obsidian, jade, cacao, animal pelts, tropical bird feathers and ceramics throughout different regions of the Maya civilization. Commoners, mostly village farmers who gave 2/3 of their produce to the upper class, made up the majority of the Maya population. At the bottom of society were the slaves. Slaves were criminals, poor commoners who sold themselves into slavery, captives of war, or slaves acquired through trade. They were often sacrificed when their owners died to continue to serve in the afterlife (Fowler, 2-3).

            Maya diet, housing, and clothing varied, depending on the status of the people. The Maya diet included corn, beans, squash, avocados, chile, papaya, pineapple, and cacao. The wealthier classes could supplement their diet with items imported from other areas of the kingdom, including dried fish, venison, turkey, deer, duck, and chocolate.

            The Maya built cities to live in, which were populated by the commoners who paid tribute and sustained the elite working class. Walls and floors were covered with limestone stucco, and the structures included temples, palaces, courtyards, water reservoirs and causeways. Art and sculpture were present throughout the cities. They also built elaborate temples and pyramids to honor their many gods and rulers (Fowler, 2-3).

            Clothing of the nobleman consisted of a cotton loincloth embroidered with feathers, a cotton, feather or fur robe, sandals, and an elaborate feather headdress. As an infant, a nobleman’s head was pressed between boards to make it fashionably elongated, and his eyes intentionally crossed by dangling objects in front of them. As an adult, putty was added to his nose to produce a beak shape. Teeth and ears were inlaid with jade. Noblewomen wore white, embroidered robes. They, too, had elongated heads. They filed their teeth to a point. Common men wore simple cotton tunics and loincloths. Common women wore embroidered cotton blouses, skirts and dresses. They arranged their hair to signal their marital status. Both men and women had elaborately tattooed bodies (Fowler, 3).

            Maya religion revolved around the worship of many gods, including gods of day and night, corn, healing, childbirth, and the four rain gods (Chacs) who controlled the weather. The Maya gathered regularly to honor their gods. They decorated their cities and themselves with feathers, and danced around the plaza to the beat of drums, flutes, bells, and whistles. They partook in hallucinogens, such as mushrooms, blanche (a drink made from fermented honey), and a strong tobacco (Fowler, 4).

            Human sacrifice was often a part of their worship. Children, slaves, or prisoners of war were painted blue and killed on top of the pyramids dedicated to their gods. They were either pierced with arrows or their hearts were removed by the priests with a flint knife. A sacrificial death was considered an honor. Other offerings, such as corn, fruit, game, or blood, were also given to the gods.

            Among the greatest achievements of the Maya were their gains in abstract mathematics and astronomy. Their calendar (see Calendars) was one of the most accurate ever developed and allowed priests to give an exact date of a day thousands of years in the future or the past. They used the concept of zero. They had a system of hieroglyphics, writing that was used in math and science, as well as to record general and historic information (Fowler, 5).

Number Systems

The Maya number system is based on the number 20. This is called vigesimal, as opposed to our decimal system. It is among the earliest of any number systems to use the concept of “zero” which allows for writing very large numbers in a much less cumbersome way. They used many large numbers in their astronomical and calendar systems, so they needed a system that was efficient.

            The Maya number system allows for writing any number with just 3 symbols. They used a shell to mean “zero,” a dot for one, and a line for five. Unlike our number system, which goes horizontally, the Maya number system is arranged vertically, with the smallest values on the bottom. Each step up represents a power of 20, with 20�, which is 1, at the bottom, then 20� above, then 20�, and so on.

Calendars

The Maya calendar had 3 separate ways of keeping track of the days. One was the tzolkin, the Sacred Almanac. This had 20 named days (like our 7 days of the week) but was also given a number from 1 to 13. On the 14^th day, the numbers started again, but the 20 named days continued until the end of that cycle. Therefore, it took 260 days (13x20) until the names and numbers repeated their cycle. The cycle then starts again. This cycle was carefully kept by priests who used it to guide many things. The tzolkin determined lucky and unlucky days for undertaking ventures, based on the gods and numbers each day represented. Birthdays were also thought to determine a person’s fate based on the “luck” of that day (Apfel, 85). The 260-day period coincides with many natural phenomenon, including the gestation period for humans, Venus’ appearance in the evening sky, and the growth cycle of certain types of corn. Perhaps this is the importance of this cycle.

            In addition to the tzolkin cycle, the Maya also had a 365-day calendar, based on the solar year. Unlike other cultures of that time, however, the Maya realized that the year was actually about 365.25 days long, so they added another day every four years to keep the calendar accurate (Fisher, 49). This 365-day solar calendar was broken up into 18 uinals, or months, of 20 days. This left 5 days (or 6 every 4^th year), which were considered unlucky days. The Maya tried to do as little as possible on these “dead” days so as not to tempt the wrath of the gods.

            The final way of keeping track of time historians call the “long count.” Maya numbered all days beginning about 3000 years ago. Because most Mayan documents were destroyed by the Spanish, it’s a mystery what this date represents. The “long count” was based on a 52-year period (the amount of time it takes for the tzolkin and uinal cycles to repeat). This cycle is to end on December 21, 2012, at which time many Maya believe the world will be judged and go through a cleansing. They believe we are currently in the 5^th of 7 cycles.

Pomo Stick Game

Most Native American tribes participated in games of chance. These games of chance are called dice games, although they didn’t use what we traditionally think of as dice. A variety of products, including teeth, bones, cane, rocks, fruit pits, and sticks, are used as game pieces. In many of the games, 4-12 game pieces are decorated on one side and blank on the other. These pieces are tossed or thrown onto the ground, into a basket, or against a blanket. Scoring is determined by the ratio of blank and decorated sides showing, with various scoring systems depending on the tribe (Culin, 5-9). This game will give students a chance to study probability, as well as data collection and representation, while learning about California’s basket makers.

Pomo Indians

The Pomo Indians are a group of tribes that lived along the Pacific Coast of California. In an area known for basket making, the Pomo are considered the finest basket makers of all. They made baskets so tightly woven that a microscope is needed to count the stitches. Their basket making skills were used to make many objects, like cooking pots, cradles, hats, games, fishing traps, and boats. Both males and females participated in basket making. They used both the coiling and the weaving methods to create baskets (Waldman, 197). They were over 450 Pomo settlements at one time, and they spoke 7 languages with many dialects. (Only 3 of the languages are spoken today.)

            The Pomo occupied a large area full of rich and varied resources. Each area had things unique to that place, and so the Pomo were able to trade among themselves a vast array of goods. Their diets could also have a good amount of variety, and they enjoyed the many things the environment had to offer. From the ocean they got fish, snails, sea lions, salt, and shellfish. The forests offered deer, elk, and other small game, as well as certain birds and insects. Vegetation was abundant in that fertile area, so they enjoyed many plants. Acorns played a special role both in their diet and in their religion.

            Pomo housing could vary depending in the resources available in the area. For the most part, the Pomo lived in small, round houses built from bent branches and covered with bark, grass and branches. The houses were temporary. A new house was built twice a year, so they had a winter and a summer house, which allowed them to move easily to the area that provided for their needs at various times of the year. Due to the impermanence of Pomo housing, settlers in that area were easily able to take land from the Pomo tribes, since the Pomo had a hard time claiming they had ancestral rights to the land. There was very little concrete proof of that claim.

            Pomo Indians used a money system, with clam shells that were ground, rounded and polished, and polished magnesite, as currency. The clam shells were strung like beads, made to carefully measured dimensions. The further the beads were from their source the more valuable they became. The magnesite, on the other hand, was traded individually and was more valuable than clam shell beads. The magnesite was fired, turning it banded shades of pink, orange, and buff. The tapered cylinders were traded individually. The Pomo were able to add numbers as high as 40,000 (Waldman, 197-198).

            Although there is little record of life before the Europeans, the Pomo were devastated by contact with outsiders. First came the Mexican-Spanish, who set up missions along the California coast in the early 1700’s. Indians were rounded up and forced to live in the missions and do labor for the Mexican ranchers. During that 100 year period, over 2/3 of all California Indians were killed off by disease and hard labor. Pomo Indians were not as affected by this as other tribes, since they lived further north of the missions.

But by the end of the 18^th century, the Russians had left their mark on the Pomo. These fur-traders treated the Pomo brutally, forcing them to bring in hides of sea otters (now almost extinct). The Russians set up a base called Fort Ross in 1812 at Bodega Bay, one of the most important seacoast sites for the Pomo during the summer. The Russians controlled the Pomo by attacking villages and kidnapping all the women and children. The men were then forced to provide furs, meat and fish to protect the hostages. The women and children were forced to work the hides, and were tortured and killed to ensure compliance. The Russians often raped the Pomo women (Giese, 2).

            There are many stories as well of individuals and small groups of people who abused the Pomo throughout the 1800’s and 1900’s, including the U.S. Army. Ranchers often forced them off their land or enslaved many Pomo. They kept them under control through torture – whipping, starvation, forced labor, hanging. There are also stories of uprisings by the Pomo, but they were generally short-lived due to their small population. Also, acts of revenge for these uprisings were swift and severe, with many tribes being massacred by the U.S. Army (Giese, 4-5).

            The California Gold Rush of the 1850’s pretty much spelled doom for the Pomo. With all the new invaders coming into California, the Pomo and other Native Americans of California were killed or forced off their lands. The Pomo attempted to maintain some small parts of their ancestral lands by purchasing it back. Their baskets, greatly admired by the invaders, were sold to raise money. The tribes pulled their monies to buy small tracts of land, but much of this was lost to taxes and mortgages (more exploitation)(Giese, 8-9).

            Today there are about 4,900 Pomo, according to the 1990 census. There areabout 20 tiny reservations or rancherias. These range in size from 0 to 177 acres, and have populations of 15-400. Most Pomo live off the reservation(Giese, 12).

Probability

Learning about probability and statistics begins informally in childhood, and continues to be important in our daily lives. We are bombarded with statistics involving everything from sports to health to incomes. We see this data represented in a variety of ways as well, in graphs, charts, tables, and, of course, “Government Reports.” As we learn to look for patterns and realize the cyclical nature of life, we can develop an intuition for the likelihood of certain events occurring. Studying probability and statistics, through experiments and data collection, helps this intuition develop.

            The focus in elementary schools has several big ideas. First, the chance of a future event falls in a continuum from impossible to certain, with lots of gray in between. Second, collected data can be analyzed in various ways and will provide different kinds of information, like average, mean, and range. Next, we organize data to help us learn something, like what might happen next, or information about the participants. Finally, analyzed data plays a large role in our lives. It is important that students become informed “consumers” of that information (Van de Walle, 408).

            Data collection is the basis for a study in probability and statistics. We collect informal data without putting much thought to it. For example, we have a pretty good idea about the type of clothes to wear tomorrow because we’ve gathered some data – every day this week has been hot, last September it was hot, etc. – and can decide to wear shorts. When we play dice games, such as backgammon and craps, we pay attention to the seven, because our experience shows us that seven is a common roll. Through our experience and reasoning, we can make more and less certain predictions about future events.

            More formal data collection, with the use of record keeping, can help foster the critical thinking skills necessary to understand probability. Students begin by collecting data. This data is then organized and interpreted. As students work together to draw conclusions, explaining to and questioning each other, they are practicing reasoning skills. They are gaining real world experiences, which build toward understanding more abstract statistical concepts (Burns, 60).

            In studying the Stick Game of the Pomo Indians, students will begin with informal data collection as they play the game with their partner. They will discuss winning strategies with their partner and later with the whole class. (This is a game of chance; therefore, the only “strategy” is luck.) This will lead to a formal collection of data, where each turn is recorded and we observe numerical information. Because the whole class can gather data, the sample will be large, giving realistic data close to the theoretical predictions. Discussions will continue on game-winning strategies, and the difference between games of chance and games of skill. These activities and discussions will reinforce the concepts of data collection and analysis in our Investigations curriculum, while connecting them to concrete experiences.

Seminole Patchwork

The Seminoles have been called “The Unconquerable” because members of their tribe refused to surrender to the pressures of the United States government to be involuntarily relocated. Their culture, created from many groups, exemplifies creativity and adaptability. By studying one part of this adaptability, the patchwork clothing created by the Seminoles, we will combine a study of culture with the mathematics both the Seminoles and our students use.

Seminole Indians

The Seminole history differs from other tribes because we have a record of the entire history. The reason for this is because they are actually a group forced by relocation to form a new tribe. The Seminoles were originally members of the Muskogee tribe (called “Creeks” by Europeans) that lived in southern Georgia and Alabama. (Later, members of other tribes, as well as escaped slaves, joined the tribe.) As more and more White settlers moved into these lands, some of the Muskogee escaped the pressures placed on them by these invaders. In the early 1700, they moved south into Florida and became known as the Seminole.

            But their problems with White settlers didn’t end in Florida. They were eventually involved in what later became known as the Three Seminole Wars. White settlers, led by Andrew Jackson, continued to attack and demand more land. They were moved from the creeks of their native ancestors, to rich farmland, to the swamps of Florida, and eventually to a reservation in Oklahoma! Although some Seminoles refused to leave Florida (which led to the Third Seminole War) they were forced to live in hiding in the swamps of the Everglades.

            They adapted well to this new secluded life. They traveled the waterways in dugout canoes. They planted sweet potatoes, pumpkins, melons and, of course, corn. They used palm leaves and shells to hold food. The women wove baskets from the plants. The men hunted the abundant game. They used many tools for hunting – guns (when ammunition was available), snares, blowguns, bows, and arrowheads. The Seminole built homes called chickees. These open houses with pitched roofs stood about 3 feet off the ground, and provided cool, dry shelters for the tribe.

            Seminole dress also reflects the versatility and adaptability of this tribe. Their clothing was made from cotton they received from the Spanish, which fit the warm Florida climate much better than buckskin. They retained the leather moccasins and leggings, which protected their feet and legs from the spiny plants of the area. Once they acquired the sewing machine, the women created bright patchwork designs, which utilized the scraps of materials that were available. These are the focus of this unit.

            The Third Seminole War, from 1855-1858, was the last attempt by the U.S. government to move the Seminole completely out of Florida. At the end of that final Seminole War, Bolek, the Seminole chief who led them, relocated to Oklahoma, along with 123 others. However, even after this third war, there remained Seminole who never surrendered. Their ancestors still occupy small reservations in Florida, where they attempt to maintain some tradition in today’s modern world.

            The Oklahoma Seminoles, who were given poor farming land, were not able to make a living off their land. Many had to sell their land to provide for their basic needs. These Seminole, however, also maintain their deep spiritual connections to Mother Earth.

            Today, there are Seminole Indians living in both Florida and Oklahoma on and off reservations. They, like other Native Americans, attempt to balance their native beliefs, traditions, and life style with the American culture that so often inundates and overtakes. This tribe is a great example of the adaptability, intelligence, and ingenuity that Native Americans have shown throughout their history, particularly since the forming of the United States of America.

Geometry and Symmetry

In the elementary grades, geometry is often considered a second-class citizen in the math hierarchy. It is often the chapter or the section of the math curriculum that is skipped or taught at the end of the year (if there’s time). Conversely, it’s often a chance for the students who don’t feel strong with the “numbers” part of mathematics to feel confident in math. Young children often have extensive geometric experiences outside of school. They’ve played with blocks and Legos, seen and talked about shapes, sorted toys according to shape, seen how various shapes fit together.

Fortunately, our current curriculum gives ample time to geometry, both 2- and 3-D. In the unit titled Quilt Squares and Block Towns, students explore various concepts in geometry. They name, carefully describe, and discuss attributes of shapes, look for shapes in their environment, create quilt patterns using shapes, use 2-D shapes to create other 2-D and 3-D shapes, and explore 3-D constructions (Klintan, etal., I-17). By introducing the patchwork of the Seminole Indians, those concepts, as well as symmetry, patterns and ratios, can be observed in another culture.

In the study of geometry in the elementary grades, John A. Van de Walle states three big ideas the curriculum should emphasize. First, shapes exist in a wide variety, and there are many ways to describe attributes of these shapes. The more discrete ways these shapes can be defined, the better a student understands them. Second, these varied shapes have properties that can be used to describe and analyze them. And third, analyzing geometric properties leads to deductive reasoning in our world, surrounded by geometry (342). He also states that, “Hands-on, reflective, and interactive experiences are at the heart of good geometric activities at the elementary and middle school levels” (342). This study fits all these requirements.

Seminole patchwork is created by using long, thin strip patterns, often interspaced with bands of solid colors, to create colorful, geometric designs. These are used on the skirts, vests, and shirts of women, as well as the shirts, vests, and jackets of men. In my primary class, a study of these various designs will allow us to look for and describe in detail the various shapes and patterns present in the clothing. It will give students a chance to manipulate and create new shapes. For example, two diamonds might become a chevron, or a rectangle can be made from two or four triangles. We will also be reinforcing the concepts discussed and described in the Patterns section of the Background information.

We can also look at the concept of symmetry. What type of pattern do we create when we repeat a pattern using identical strips (a translation)? The ideas of translation, rotation (180� turn around a point), and reflection (mirror image) can all be demonstrated and created in the patchwork. In fact, an in-depth study of symmetry could be conducted with students in middle or high school. There are only seven types of symmetries strip patterns can create. The classification system to describe the translations, reflections (glide, perpendicular and/or parallel), and rotations in strip patterns was invented by Russian crystallographers. All seven of the symmetries are found in Seminole quilts (Preston, 1-3). Older students could also look at fractions, ratios, and percentages.

By creating both paper (for practice) and cloth (final project) designs, students are exploring a variety of shapes, analyzing their properties, and using the analysis to create an aesthetically pleasing, geometric patchwork.

Implementation

These lessons were planned to coincide with the mathematics curriculum I will be using, Investigations in Number, Data and Space. They will be used throughout the first semester of school, and will reinforce the math concepts we are studying while introducing social studies and art concepts.

            These lessons are set up as mini-units. Each of the units focuses on a different Native North American culture and shows how these groups used the mathematical concepts we study in their math, art, and science. The units begin with a lesson on the culture. As the oral tradition is crucial in passing on the traditions of these groups without written languages (except the Maya), their background will be shared in the form of a story. As the written tradition is crucial in our modern world, books may also be used to share information on the groups or their work. After learning something about them, we will continue to study that group through one or more studio lessons focusing on math, science, and/or art practiced by that culture.

            The Content Standards are from the A.P.S. web page.

Pre-Assessment

Based on experiences in my own life, through my classes as well as my young nieces and nephews, many young children (and adults J) have a very limited view of who Native Americans are. Much of it is based on the media, which seem to portray the Plains Indians of the 1800’s as the only tribe of Native Americans. As we work through these lessons, I hope to dispel this mythical portrayal and give students a more realistic vision of these diverse people.

            Although this unit is based on the mathematics curriculum, I also want an idea of the learning taking place in social studies. I will begin by discussing with the students what they know about Native Americans, or Indians. We’ll make a list of their ideas. I will then ask them to draw a picture of a Native American and write one or two sentences about them. (As an elementary school teacher at the beginning of the year, this will also give me a drawing and writing sample to save.) These will be collected and saved until the end of the unit. We will repeat the same activity at the end. At that point, I will be able to see if their ideas have changed, and how.

Mini-Unit 1: Petroglyphs

Content Standards: Language Arts, Strand II, Performance Standards 1,2,5,7,9,11, Strand VI, Performance Standard 3.

Lesson 1: What, How and Why Do We Record?

Materials: chart paper, markers

This lesson will begin on one of the first days of school. We will start a chart to keep track of the things we record. The chart will have three sections. One will be labeled WHAT, one HOW and one WHY. We will brainstorm all the things we can think of at the time. This chart will remain posted in a conspicuous place, and will be referred to and added to frequently. We will then have a list of many records and the reasons for them.

Lesson 2: The Anasazi

Materials: Before You Came This Way, other books on the Anasazi, paper, pencil, USA map, timeline

The students will be introduced to the Anasazi, the ancestors of the Pueblo Indians. They will hear the book Before You Came This Way by Byrd Baylor. This book tells of southwest rock paintings and shows many examples of petroglyphs. It gives ideas about who wrote the messages, and shows several common images. I will share other information about the Anasazi (discussed in Context and Background). We will look at the map of the USA, identify the four-corner states, and find the area of the Anasazi. Some sites, such as Bandelier, Chaco Canyon, Mesa Verde, and Snake Canyon, will be located. We will look at a timeline and see what else was happening in the world at the time of the Anasazi.

            As a closing, students will be asked to draw/write (record) what they know about the Anasazi.

Lesson 3: Field Trip to Petroglyph National Monument

Materials: notebook, pencils, water bottles

We will take a field trip to the Petroglyph National Monument. On this trip, we will be able to observe many petroglyphs created and preserved in this area. As we visit the area, we will observe the climate and landscape of the area. We’ll talk about how this environment (the desert Southwest) influenced the lives of the Anasazi. As students observe the various petroglyphs, they can draw (record) in their journals.

            After the trip, we’ll speculate on the meanings of the petroglyphs. We’ll talk about WHAT, WHY and HOW these petroglyphs keep records. We’ll share our records from our journals.

Lesson 4: “Mock Rock” Petroglyphs

Materials: Plaster of Paris, paper clips, dried-out pens, pictures of petroglyphs, paper, pencils, string or jute, black or brown shoe polish, paper towels

Students will use the information they’ve learned to create a “petroglyph.” To prepare for this, I will create “rocks” out of Plaster of Paris by mixing the Plaster of Paris (following the package directions) and spooning blobs of various shapes and sizes onto wax paper. While the “rock” is still wet, I’ll stick a paper clip into the side so the “petroglyph” can be hung and displayed at the end.

            First, the students should select a “rock”. They trace the shape onto a piece of paper and practice drawing a design, either one they’ve seen or one they create. When they are satisfied with their drawing, they reproduce it lightly on the “rock.” Using paper clips or dried pens, they peck out their petroglyph. It should be carved fairly deep, rather than a thin scratch.

            To blacken the design, students will put shoe polish over the entire surface. This will fill in the holes with color. They use a damp paper towel to rub some of the color on the surface into a more natural color. We’ll use jute or string tied to the embedded paper clip to hang the “petroglyphs.” The students will tell the story of their petroglyph, and record the story in their journal with pictures and words.

Mini-Unit 2: The Pueblos and their Art

Content Standards: Math, Strand I, Performance Standards 8, 9, and 15, Strand III, Performance Standards 1, 2, 4, 6, 7 and 10, Strand V, Performance Standard 1. Language Arts, Strand II, Performance Standards 2, 5, 7, 9 and 11.

Lesson 1: The Pueblos, Modern Descendents of the Anasazi

Materials: journals, pencils, examples of Pueblo pottery and jewelry (real and pictures), books about Pueblos, NM map, A Heart Full of Turquoise

Students will learn about Pueblo Indians. I will share the Background information with them. We will locate some of the Pueblos on a NM map. Students can share what they know about the Pueblos. I will pass around some of the Pueblo pottery and jewelry I have, as well as sharing the books and pictures. To include story, I will read one of the Pueblo Indian tales in the book A Heart Full of Turquoise by Joe Hayes. As the story concludes, we will discuss any lessons it might teach, and then there will be time once again to record in journals.

Lesson 2: Pueblo Pottery

Materials: clay, small containers of water, newspaper, paints, paintbrushes, When Clay Sings (a kiln will also be needed to fire the pots)

Students will listen to the story When Clay Sings by Byrd Baylor. This book tells of the pottery found at different sites and what it tells about the people who left it. They will then make coil pots similar to those created by the Pueblos. They will begin by rolling clay into long coils. They will make a base for their pottery by creating a spiral with their coil. They will then build up the sides by continuing to add coils to the sides of the pottery. Finally, the coils will be smoothed out using their fingers and water. Some may decide to carve designs into the sides of their pots.

            Once the pottery has dried and been fired, students will paint designs and patterns onto the sides of their pots (or inside, if they create plates). They will describe their design to their classmates, noting any repeating patterns or known shapes, and sharing where they got their ideas. They will record their work in their journals, and we will display the pottery for everyone to enjoy.

Lesson 3: Pueblo Jewelry

Materials: cardboard squares, circles and other shapes, toothpicks, turquoise-colored rocks, foil, jute or leather strips, jewelry samples and pictures, paper, pencils, glue, bolo backs.

Students will make a bolo tie, based on the designs of the Pueblos. They will first look at the examples that are shown. They will choose a cardboard shape for their bolo tie. Tracing this shape on a piece of paper, the students will practice on that until they are pleased with their design. They will cover their shape with two or three layers of foil, and use the toothpicks to etch their design into the shape. They may choose to use a piece of turquoise in their bolo, which should be glued onto the foil. We will glue the backs in place and add the cord. Again, they will describe their design to their classmates, sharing where they got their ideas. They will record their work in their journals, and we will display their bolo ties for everyone to enjoy.

Mini-Unit 3: The Maya

Content Standards: Math, Strand II, Performance Standards 1, 4, 5 and 7, Strand III, Performance Standard 18, Strand V, Performance Standard 2. Language Arts, Strand 2, Performance Standards 2, 9 and 11.

Lesson 1: Meet the Maya

Materials: globe/map of North and South America, pictures of glyphs, journals, pencils, The Boy Who Wouldn’t Obey: A Mayan Legend

Students will listen to The Boy Who Wouldn’t Obey: A Mayan Legend. We will discuss similarities between this story and other legends we’ve heard. This book tells of Chac, four of the Maya gods who rule over the square that forms heaven and earth, controlling rain, wind, lightning, and thunder. We will look again at the book, paying special attention to the glyphs decorating each page of text. I’ll show them other examples of hieroglyphic writing, including the “month” symbols. They will learn about the math and science advancements of the culture, including the use of “zero,” architecture, and precise calculations in astronomy. We will find their communities on a map or globe (or both) and discuss the climate in that part of the world. Students will practice drawing some of the glyphs of the Maya, discussing possible meanings. They will record in their journals.

Lesson 2: The Importance of 20

Materials: unifix cubes, paper, pencil

In this lesson, students will explore the importance of the number 20 in the Maya culture. We will begin by brainstorming all the things we know of that come in groups of 20. They will use unifix cubes to see how many ways 20 can be divided up evenly (its factors). As a group, we will practice counting by 20’s, and students can list the multiples of 20 to look for patterns. (Note: students who are ready for a challenge can look at the factors of 60, which is an important number to the Babylonians.)

Lesson 3: Perpetual Calendars (Maya Calendar)

Materials:

Just as any cycle repeats itself, the Maya calendar also repeats itself. For this lesson, students will make two perpetual calendars, one that coincides with our calendar, the Gregorian calendar, and one based on the Maya calendar, the tzolkin (see Context and Background). This Sacred Almanac is a 260-day cycle. We will make two wheels for the tzolkin, one for the 20-day signs, and one for the 13-day number cycle. There will be three for the Gregorian, one for the 7 days of the week, one for the 31 (or 28 or 30) days in a month, and one for the 12 months. These wheels will be put together with brads, and will show the date as long as students remember to change them each day.

Lesson 4: Race to the Maya Sun (Maya Number System)

Materials: game disks, dice marked with Maya numbers

This game is similar to other math games we’ve played to learn place value, including Race to a Quarter, or Race to 100. For this game, students will play against a partner. The goal of the game will be to get the Maya Sun, which has a value of 60 (This number is a fairly high number for first graders, although it could be adapted to use a higher or lower number). The dice will have numbers from 1-10, written in the Maya system. Students will take game pieces (circular disks) to show how much they have accumulated. They will trade 20 small disks for one larger disk. They will eventually need 3 of the larger disks to trade for the Maya Sun. The first person to get the Maya Sun is the winner.

Mini-Unit 4: Pomo Stick Game

Content Standards: Math, Strand I, Performance Standards 1, 4, 5, 6, 7, 8, 10 and 11, Strand II, Performance Standards 4, 6 and 10, Strand III, Performance Standards 1, 2, 3, 5, 6 and 7.

Lesson 1: The Pomo, California Basket Makers

Materials: map/globe, paper, pencil, crayons

As with the other groups, the students will learn about the Pomo Indians of California. Since so many of the students in my class have been to California (based on past experience), they should be able to tell about the climate there, make some predictions about the types of food, clothing, and housing that is available there, and what might be needed. After sharing the information on the Pomo, I will ask students to do a drawing with two sides. One side will be labeled “Pomo Indians of California” and the other “California Today.” I will ask students to show in their drawing what they’ve learned about the California Indians and about California today, and to label their drawings.

Lesson 2: Creating Sticks

Materials: pictures of game pieces, markers, craft sticks

Students will be shown the examples of the designs the Pomo Indians used on their game sticks. We will talk about the various designs, describing the patterns and shapes we see. Students will then be given 6 craft sticks to decorate for themselves to play the game. They will use markers, and will have a chance to share their designs at the end.

Lesson 3: Playing the Stick Game

Materials: game sticks (from previous lesson), counters

Students will be told to how to play the stick game (see task card). They will have several chances to play, and will play against different opponents. As they play, I will ask them to think about and discuss strategies for winning. What can they do to get better at this game? We will end with a discussion on winning strategies.

Lesson 4: Data Collection and Organization

Materials: game sticks, class graph, score sheets for partners, pencil

Students will be asked to play the Stick Game again, but this time they will keep track of their turns. They will mark an X in the column that coincides with their throw. For example, if it’s one blank and five colored, they will put an X in that column. I will demonstrate how to mark their throw on a class graph. They will play with their partner, with the main goal being to collect data. Each time they roll 10 times, they should report their data to me, where I can record it onto the class graph.

            After collecting data, we will meet for a class discussion. We will look at the data and see what it tells us. We will again discuss winning strategies. Hopefully, by this point, they will see that this game of chance does not have a strategy to help them, and we can discuss the difference between chance and luck. We will use the numerical information from the graph to help us see the chance of certain throws coming up.

Mini-Unit 5: Seminole Patchwork

Content Standards: Math, Strand II, Performance Standard 18, Strand III, Performance Standards 1, 2, 3, 4 and 10, Strand V, Performance Standard 2.

Lesson 1: The Seminoles: The Unconquerable

Materials: books on the Seminole, pictures of patchwork clothing

The story of the Seminoles is an exciting drama that leads itself to oral story telling. I will tell the history of this tribe in the form of a story, including lots of information on the adaptability of the tribe. I will ask lots of questions about the ways their environments dictated their lifestyles. Again, at the end of the lesson, children will record what they’ve learned about the Seminole.

Lesson 2: Practicing Designs

Materials: paper, scissors, glue, paper cutter, mirrors

Students will be shown how to create simple patchwork designs using paper (see task card). They will get lots of chances to practice making different designs by cutting at angles, using different sizes of strips, and using a variety of colors. They will be encouraged to look at each other’s designs for ideas, and will be expected to share any new knowledge about different constructions that they learn. As we look at designs, we will talk informally about symmetry. We will observe what happens when we slide to get our pattern (transformation). I will have mirrors for them to see if there is mirror symmetry (reflection). At the end of the lesson, they will get a chance to describe their favorite design to the class.

Lesson 3: Creating a Patchwork Design

Materials: cloth, scissors, glue

We will get one last chance to make a patchwork design, this time using cloth. Students will be given a set amount of cloth and will be asked to make a patchwork design from this. They will again be asked to describe their design, including any symmetry they see, and any shapes they recognize. We will collect them at the end, and make a patchwork panel for the class to hang and admire.

Documentation

Teacher Resources

Brandon, William. Indians. Boston: Houghton Mifflin Company, 1961.

Burns, Marilyn. About Teaching Mathematics: A K-8 Resource. White Plains, NY: Math                  Solutions Publications, 1992.

Culin, Stewart. Games of the North American Indians. NY: Dover Publications, Inc., 1973.                  Reprint of original published in 1844.

Fowler, William R. “Maya Civilization.” Microsoft Encarta Encyclopedia 2000. 1993-1999.

Giese, Paula. “Pomo People: Brief History.” 6 June 1997.
               <http://www.kstrom.net/isk/art/basket/pomohist.html>

Mathematical Sciences Education Board, National Research Council. Everybody Counts: A report                 to the nation on the future of mathematics education. Washington, D.C.: National                 Academy of Science Press, 1989.

O’Brien, Karen and Robin White. Petroglyph National Monument, Teacher’s Guide, Grades                 K-8. Albuquerque: Petroglyph National Monument. (No date given).

Preston, Vera and Mary Hannigan. “Symmetries of Culture.”
             <http://www2.austin.cc.tx.us/hannigan/Presentations/NSFMar1398/SPTopics.html>.

Russell, Susan Jo, etel. Investigations in Number, Data and Space, Grade 1. Menlo Park, CA:                Dale Seymour Publications, 1998.

Underhill, Ruth. Life in the Pueblos. Santa Fe: Ancient City Press, 1991.

Van de Walle, John A. Elementary and Middle School Mathematics: Teaching
             Developmentally, 3^rd edition. NY: Longman, 1998.

Waldman, Carl. Encyclopedia of Native American Tribes, Revised Ed. NY: Checkmark Books,                1999.

Student Resources

Petroglyphs and the Anasazi

Arnold, Caroline. The Ancient Cliff Dwellers of Mesa Verde. NY: Clarion Books, 1992.

Dewey. Jennifer Owings. Stories on Stone. Boston: Little Brown and Co., 1996.

Fisher, Leonard Everette. Anasazi. NY: Atheneum Books for Young Readers, 1997.

Gustafson, Sarah. Exploring Bandelier National Monument. Southwest Parks and Monuments              Association, 1997.

Peterson, David. The Anasazi. Chicago: Children’s Press, 1991

---. Chaco Canyon National Park. NY: Children’s Press, 1999.

Pueblos and their Art

Aliki. Corn is Maize: The Gift of the Indians. NY: Thomas Y. Crowell, 1976.

Baylor, Byrd. Before You Came This Way. NY: EP Dutton & Co., Inc., 1969.

Falwell, Catheryn. Shapes Space. NY: Clarion Books, 1992.

Flanagan, Alice. The Zunis. NY: Children’s Press, 1998.

--- The Pueblos. NY: Children’s Press, 1998.

Grossman, Virginia. Ten Little Rabbits. San Francisco: Chronicle Books, 1991.

Hayes, Joe. A Heart Full of Turquoise. Santa Fe: Mariposa Publishing, 1988.

Keegan, Marcia. Pueblo Girls. Santa Fe: Clear Light Publications, 1999.

King, Andrew. Math for Fun: Exploring Shapes. Brookfield, Connecticut: Copper Beech Books,              1998.

Mott, Evelyn Clarke. Dancing Rainbows. NY: Cobblehill Books, 1996.

Powell, Suzanne I. The Pueblos. NY: Franklin Watts, 1993.

Sita, Lisa. Indians of the Southwest. Milwaukee: Gareth Stevens Publications, 1997.

Maya Culture

Apfle, Necia H. Calendars. NY: Franklin Watts, 1985.

Bruchac, Joseph and Jonathan London. Thirteen Moons on Turtle’s Back: A Native American              Year of Moons. NY: Philomel Books, 1992

Burr, Claudia. Broken Shield. Toronto: Groundwood Books, 1994.

Chapman, Gillman and Pam Robson. Exploring Time. Brookfield, CN: The Millbrook Press,              1994.

Fisher, Leonard Everette. Calendar Art: Thirteen days, weeks, months and years from around              the world. NY: Four Winds Press, 1987.

Ganeri, Anita. The Story of Numbers and Counting. NY: Oxford University Press, 1996.

Pluckrose, Henry Arthur. Math Counts: Numbers. Chicago: Children’s Press, 1995.

Rockwell, Anne. The Boy Who Wouldn’t Obey: A Mayan Legend. Hong Kong:
            Greenwillow Books, 1986.

Steinecker, David L. Discovering Math: Numbers. NY: Benchmark Books, 1996.

Weiss, Malcolm E. Skywatchers of Ages Past. Boston: Houghton Mifflin Co., 1982.

Pomo Indians and Probability

Wood, Marion. The World of Native Americans. NY: Peter Bedrick Books, 1997.

Wyler, Rose and Mary Elting. Math Fun: Test Your Luck. NY: Julian Messner, 1992.

Seminole Patchwork Designs

Garbarino, Merwyn S. The Seminole. NY: Chelsea House Publishers, 1989.

Naylor, P.R. To Walk the Sky Path. NY: Dell Publishing, 1973.

Sitomer, Mindel and Harry. What is Symmetry? NY: Thomas Y. Crowell Co., 1972.

Sneve, Virginia Driving Hawk. The Seminole. NY: Holiday House, 1994.

Temko, Florence. Traditional Crafts from Native North America. Minneapolis: Learner                   Publications Co., 1997.

Task Card – Pomo Stick Game

You Need:        6 sticks, decorated on one side              10 counters
                        A partner

1.      Take turns tossing all 6 of the sticks onto the floor. Notice which sides are showing (the plain side or the decorated side).

2.      Scoring is as follows:

All 6 decorated side up – take 3 counters
All 6 plain side up – take 2 counters
3 plain and 3 decorated – take 1 counter
Anything else – take 0 counters

3.      Take the counters from the pile at first. When the pile runs out, you can take counters from your partner. The winner is the first one to collect all 10 counters.

Task Card – Seminole Patchwork

You Need:        9” paper strips in many colors       glue                   pencil
                        scissors                                         ruler                  white paper

1.      Choose several of the strips of paper. Carefully glue them together, with just the edges touching. Make a rectangle that is 9” x 12”.

2.      With your ruler, measure 1” marks across the color strips of paper. Mark them with your pencil.

3.      Cut along your lines. You should have 12 multi-colored strips.

4.      Now put your design together at a 45� angle. Try turning some of your strips upside down, or putting them backwards. Keep experimenting until you find a pleasing design.

5.      Glue your final design onto plain white paper.

6.      Share your design with your classmates.

*Note: for more information on this (if the directions don’t seem clear) see Traditional Crafts from Native North America by Florence Temko.