Upper Elementary (9-12 Years)

The History of Mathematics during the six Elementary years

The “Great Lesson” of humankind’s invention of numeration and measurement systems is a key that opens the door of the imagination to the world of mathematics and geometry. At the Lower Elementary level, students often investigate the number systems of civilizations as diverse as that of the Egyptians, the Romans, and the Mayans. Ancient measurements such as the cubit and the span are presented and used. Upper Elementary students research mathematics, geometry, and invention in the Hellenic world (with a particular focus on ancient Alexandria) and elsewhere.

The Decimal System: The Four Operations of Arithmetic in Upper Elementary

Students tackle more complex problems such as using two and three-digit multipliers and divisors. They still use materials when needed but are now often working solely on paper. Practice with the four operations of arithmetic continues as they work on their speed and accuracy. Non-decimal bases are also worked with beginning with manipulative materials. As students now move towards greater abstraction, they also work in a math textbook and take periodic mastery tests.

Multiples and Factors during the six Elementary years

Lower Elementary students begin the study of multiples and begin finding the least common multiple and greatest common factor. The rules for divisibility are introduced. At the Upper Elementary level, they further explore divisibility and the concepts of least common multiple, greatest common factor, prime numbers and prime factorization.

Geometry in Upper Elementary

The formulae for area and volume are derived and mastered during the Upper Elementary years. These formulae are a point of arrival after much exploration, not a point of departure. The work involves a lot of investigation of the equivalency relationships of various figures and includes a deep study of the Pythagorean Theorem (arithmetical, geometrical and Euclidean proofs) using Montessori materials specially prepared for this purpose. Students learn to describe their proofs using precise terminology. They also practice a graduated series of geometric constructions using compass and straight edge. Once the number line is mastered, students are introduced to the concept of the coordinate plane. The concepts of ordered pairs, slope and intercept are presented.

Fractions, Decimals, Percents, Money, and Ratio and Probability in Upper Elementary

Upper Elementary students learn the more complex operations with fractions, such as division of a fraction by a fraction. These are first explored with manipulatives and then the rules of the operations are memorized. Working with decimals and percents and their conversions to fractions is a focus of the Upper Elementary years. Money problems such as calculating a tip, sales tax, interest problems are undertaken. Students learn about the concepts of ratio and proportion and problem solve using these concepts. Probability is also explored.

Powers of Numbers and Roots of Numbers in Upper Elementary

Further exploration of the powers of ten in the Upper Elementary classroom leads to the study of scientific notation. Squaring and cubing work prepares students for the extraction of square roots and cube roots. They may explore other polynomials according to interest. Montessori mathematics materials allow students to do this complex work in a very concrete way and gradually work their way towards abstraction.

Measurement in Upper Elementary

US customary and metric measures are memorized and the temperature scales are introduced. Students explore the concepts of area and volume and derive formulae using hands-on Montessori materials. Unit conversions within and between systems are learned and practiced.

Statistics and Graphs during the six Elementary years

Data collecting and organization begins at the Lower Elementary level with surveys and learning to find the mean. Students learn how to represent data using a variety of graphs. At the Upper Elementary level, students learn other central tendency measures such as mode and median, and the interpretation and reading of all kinds of graphs.

Pre-Algebra and Order of Operations during the six Elementary years

During the Lower Elementary years, students explore the commutative, associative, and distributive properties using various math materials. They work with positive and negative numbers using special materials. At the Upper Elementary level, they begin to work with integers and are introduced to the concept of “order of operations”. They learn all pre-algebra skills, and students who demonstrate readiness will begin to work in an Algebra I text.

Students delve deeper into physical geography by learning to identify more and varied physical features of both the United States and the world. They create many maps to accompany their various researches and studies. They also learn map-reading skills such as location using latitude and longitude, reading a map scale and legend, and becoming familiar with many types of maps (historical, contour, etc.). The students are introduced to the skill of orienteering using compass and topographical map. They undertake studies of the U.S. regions from both economic and cultural perspectives. They explore worldwide production, consumption and trade of various resources and goods. Students participate in the National Geographic Bee each year from 4th through 6th grade.

Elementary History: Overview

History is the central organizing discipline during the Montessori elementary years. Every subject is encountered in relation to its historical origins and evolution. We strive through a sequence of inspiring tales to help students see where they fit into the great chain of history from the beginning of time. In particular, our interdisciplinary approach to the history of the universe, planet earth, and the contributions of the great civilizations gives our students a deep awareness of the grandeur of the human endeavor. Humans are seen as adaptive, inventive, and resourceful. A sense of gratitude for the contributions of all our ancestors is fostered.

We appeal to the emerging reasoning mind and powerful imagination of this developmental plane by telling great stories framed in the form of fables, but with rich scientific and historical content. Students use concrete organizational frameworks as an aid to understanding relationships and sequences over time. These include timelines of the development of life on Earth and the progress of the early humans and their civilizations, as well as charts illustrating key scientific or historical principles. We also use core classification materials that guide the research of any culture or civilization in any time or place. These materials focus on how different people throughout history fulfilled their fundamental needs. These would include their types of food, shelter, clothing, artistic expression, religion, government, and education.

Upper Elementary History

Upper Elementary students also begin their history studies with the study of the formation of the Universe and the earth, and specific periods of earth’s history. These time periods are now approached at a second and more detailed level, building on the work of the Lower Elementary years. All of this study is integrated with the disciplines of chemistry, astronomy, geology and biology.

Students study the classical civilizations in greater depth, especially the Hellenic and Roman as connected to their Latin language studies, which begin at this time. They are introduced to European Medieval and Renaissance times and contemporaneous civilizations of the Americas and Africa. The Age of Exploration is presented through story and maps. The movements and mass migrations of peoples are presented and their contributions to our global economy and cultural heritage are featured.

American History is studied in depth over the three years. The pre-Colonial, Colonial, and Revolutionary War Periods are reviewed in greater depth. The text “A History of US” by Joy Hakim is used to present an interesting and complete narrative of U.S. history to the 21st century. Students use an American History Time Line as they focus on periods such as the Civil War, the Industrial Revolution, or the Information Age. They hear stories from Connecticut State History. Field trips to places such as Dinosaur State Park, Sturbridge Village, Mystic Seaport, Historic Deerfield, and other local historical sites are punctuated throughout the three-year cycle. Students also learn about the structure of U.S. government and are introduced to the fundamental powers and workings of the various branches.

Science in the Elementary: Introduction

During the elementary years, every aspect of science is introduced through stories of discovery and with reference to the etymology of the scientific words (i.e., Gk. bios – life; logos – speech – literally “to talk about life”). Various scientific disciplines emerge from and relate back to the Great Lessons of the origin of the universe and the earth, the story of life on earth, and the ingenuity of humans throughout history. The adventure of scientific discoveries is seen as part of a Great Story reaching back to the beginning of time and the student is empowered through activity and research to see himself as an actor in this story.

Upper Elementary Physical Science

Astronomy

Students look deeper into the early history of the universe and solar system through the lens of our study of chemistry. They begin to look at topics such as the life cycle of a star, the role of supernovas, and concepts such as light years and black holes. Students do various researches on these topics. They learn about constellations, eclipses, famous astronomers, the history of space exploration, and they hear stories of astronomical discoveries.

Earth Science

Students work with materials to aid their understanding of the geological ages, tectonic plates, and the theory of continental drift. They study the classification of physical features according to their formation by ice, wind, and running water. They build on the earlier work in geology by studying the rock cycle and the physical and chemical processes involved in the formation of rocks. Students study meteorology more thoroughly, learning to interpret weather maps and looking at both local weather patterns and global atmospheric and oceanic phenomena.

Chemistry and Physics

Students explore in detail the periodic table of the elements, its classification and use. They use hands-on material to create atoms, molecules, and chemical equations such as that for photosynthesis. They conduct experiments, further exploring concepts such as acids and bases. They do field work testing both local soil and water. Study of simple machines is also a focus during the Upper Elementary years. Examples of areas studied include gears and levers, pulleys, inclined plane. Students also use hands-on material especially designed for classroom use to explore electric circuits and electric motors.

The history of technology and inventions into modern times continues to be presented by means of story, and is explored through independent reading and research. As an extension to the earth and physical science work, each year we attend programs at Talcott Mountain Science Center. Rocketry, and a plate tectonics/rocks and minerals programs are given by a visiting expert. Meteorology and astronomy programs are also held at the Science Center. We also may take a field trip to a garnet quarry and quartz vein, where students learn how to hammer out specimens and identify rocks and minerals on outcrops.

Upper Elementary Life Science

Taxonomy during the six Elementary years

Students enter the Montessori Lower Elementary classes from our Primary program with knowledge of significant Life Science classified nomenclature, particularly in the areas of botany and zoology. We build on the great developing interest in living things by opening the students’ minds to the whole span of the Time Line of Life on the Earth. From this historical perspective, we introduce them right away to the Five Kingdoms of Life. This grand scheme of biological classification is explored in a systematic and rigorous fashion over the six years of our Elementary program, culminating in the Chinese Box material, which classifies the major life forms on earth.

Zoology

Upper Elementary students continue the study of the Animal Kingdom. They look in more detail at the internal anatomy of the various phyla and classes of animals. They use Montessori zoology materials, create drawings and write about the various systems. In addition, they now study in greater depth the work of Kingdoms Fungi, Protista, and Bacteria through prepared Montessori story materials and lessons using the Chinese Box of Life. As always, we relate these studies to the Time Line of Life and key events in earth’s history, such as the invention of photosynthesis. Students also begin the study of cells. They are introduced to the basic parts of both the prokaryotic and eukaryotic cell.

Botany

Students explore the classification of the plant kingdom and learn about monocotyledons, dicotyledons, angiosperms etc. Students look in more detail at important processes, such as pollination and seed dispersal. They study humankind’s uses of plants for medicines, and the importance of the great ecosystems, such as tropical rainforests and grasslands. They are introduced to the art of botanical drawing and often use these drawings to illustrate their botanical research work. Students use world and continent maps to identify the geographic locations of the great grasslands, boreal forests, and other plant ecosystems. They continue to plant, tend, and harvest classroom gardens.

Human Biology

Students study the composition of various types of cells. They learn the relationship between cells, tissues, organs and systems. Students undertake an overview of all the major systems of the human body. They review the systems learned in the Lower Elementary program at a deeper level, looking at, for example, the chemistry involved in the digestive and circulatory systems. At this age, the brain and nervous system, and the reproductive system are presented. Other systems are introduced or researched according to interest. Students look at nutrition in greater detail, exploring the function of carbohydrates, proteins, fats, and their molecular structures. They begin to analyze the nutritional content of a meal according to the various food groups.

Over the course of the six Elementary years of Montessori education, students learn how to observe from nature and from experiment, gather data, and record their observations. They learn how to use various measuring tools, such as scales and thermometers. They are taught how to use a hand lens and microscope, including how to prepare a microscope slide. Older students are introduced to the basics of writing a lab report and such skills as recording data on a table and using scientific notation. Books are always available in both the classroom and school libraries, as well as ready Internet access in the classroom and library.

Elementary Spanish Curriculum: Introduction

Spanish is taught in both the Lower and Upper Elementary. Total physical response (TPR) activities help to reinforce vocabulary comprehension. Students learn to follow simple directions. Activities include acting out infinitives with partners who will guess the verb, role-playing to improvise conversation, recorded tapes to study pronunciation and food preparation to practice and create enthusiasm with the language. Students are encouraged to work as a team to read the recipes and follow directions in Spanish. The “Symtalk Card” method involves students in building sentences using these specially designed cards. This practice also helps them develop and improve their writing and reading skills.

Upper Elementary Spanish

During the Upper Elementary years, the number of reading and writing activities increases. Students are given the choice to work with the material displayed on the Spanish-designated shelf. This material has been designed to improve conversation skills, verb conjugations, grammar understanding, and vocabulary retention. As some of the students start to show confidence in their ability with the language, they are encouraged to perform a play in Spanish. Assigned work is given once a week to review topics covered during the past group lesson. Students are also introduced to the cultures of some countries in which Spanish is spoken. Students are exposed to Spanish literature through short stories and poetry. To improve their reading skills, students can borrow books in Spanish each week. By the end of the sixth year, the goal is for students to have gained a solid foundation in conversation, writing, and reading. This includes the vocabulary necessary to ask and answer questions, the use of adjectives, correct articles, personal pronouns, and conjugation of verbs in simple tenses.

Upper Elementary Music

Elementary students engage in a rich and creative music program. They sing, read music, and compose using the Montessori tone bars. Each Elementary classroom has a set of tone bars and the accompanying materials for the reading and writing of music. The specialist music curriculum utilizes the strengths of various music education approaches. Musical concepts are explored through movement/dance, singing and playing instruments. The core philosophy of the music curriculum is derived from the Orff-Schulwerk approach. The elemental aspects of music are explored through the natural behavior of children. Literacy in music is further supported by the Kodaly approach to music education in which students make visual and aural connections to music. Development of the ear is further enhanced by Edwin Gordon’s Music Learning Theory, an approach emphasizing audiation (thinking music in the mind with understanding). These various approaches complement each other and provide a strong fabric for musical learning and understanding. We have a music program with a strong global aspect in its curriculum and repertoire.

Using teaching methods from various cultures as well as music from around the world, students are part of a holistic musical experience without borders. The synthesis of known best practices all center around experiencing and exploring musical concepts and expression by creating, performing and responding to music – the essential artistic processes. The structure of the music program involves weekly lessons with a music specialist. Lower Elementary students meet once each week. First year students meet as their own group, while second and third year students have music class together. The Upper Elementary students have two classes per week. One class is a general music class emphasizing creative movement and expression and singing. The second Upper Elementary music class is dedicated to instrumental ensemble work.

General Music Class

All general music classes involve a combination of movement and music. Students sing, dance and play as they explore various concepts. Key to their musical experience is the idea of creative expression. Students explore, imitate, improvise and compose. Student-created poems and songs are incorporated into lessons. Multicultural games, songs and dances provide a global repertoire. Integration is woven by connecting the music curriculum to classroom content – from history and literature to art and Spanish language. Students move, sing, listen and play in each class session. They create music and movement, respond to music and movement linguistically and kinesthetically and perform movement and music (vocally and on instruments).

Instrumental Ensemble

This ensemble rotates throughout the academic year. Students work in Orff Ensembles made up of xylophones and other barred instruments. The Orff Ensemble uses a multicultural approach. At times, it represents traditional western style music, at other times it acts as an Indonesian Gamelan Ensemble or an African Marimba group. The instrumental ensemble at times functions as a drumming ensemble. In particular, students work as a Japanese Taiko group, playing traditional Taiko drums. In all classes, students are able to explore and create.

Opera

As an annual tradition, all elementary students participate in a student opera. The composer (or a director he personally chooses) and a choreographer, come for a week’s residency, ending with a grand theatrical performance off-site at a local theater. This performance acts as an opportunity for integration, as the general music curriculum and classroom curriculum is adjusted to reflect the culture and key aspects of the chosen opera. Extended Day children also participate by singing opening songs on stage.

Elementary Art: Overview

All elementary classrooms have a range of materials available to the students. Many art projects take place in the classrooms. The students may also illustrate and create clay or other artistic expressions as part of their research projects. Our elementary art specialist is an artist-in-residence and as such works at the school five full days a week. This allows students extensive studio access during their classroom work periods. The art process is a rewarding experience that allows each student the freedom to explore and experiment with various media and techniques. It is through this process of self-exploration that they begin to make connections between the artistic world and their natural environment. Students begin with the basic elements of art (line, shape, color, texture, space, value, and form) and progress to the more complex throughout the elementary program. These basic elements are the building blocks of art and are incorporated into every lesson. Over time, students begin to make connections between them and begin to develop their own visual vocabulary. Each lesson is given a name, and demonstrations are used to ensure the use of materials in a safe and responsible manner. Once the art lesson has been demonstrated, students are allowed the freedom to create and express themselves in an individual way.

Framed reproductions of famous artist’s works are hung while the artist’s style is being studied. This provides inspiration and further reinforces the various innovations, concepts, styles and techniques used by artists throughout history. Over time, students begin to question what they see and create their own art-related projects. By sharing these experiences, they increase their understanding and appreciation of art.

Art classes are structured to allow students of different ages and abilities to interact in a safe and productive manner. Students with a more advanced skill level are encouraged to act as mentors and assist others. As a result, a sense of community develops among caring, confident, and compassionate peers.

Upper Elementary Art

In the Upper Elementary program, the focus of the study of the elements of art is on exploring the expressive qualities or meanings implied by the elements in student art activities and in artists’ works. Concepts relating to the elements of art and principles of design are taught in context, rather than in isolation. Students are guided to reflect on how the elements of art are used to convey meaning in works of art.

Students begin to examine sources of ideas and make connections between ideas and visual art works. Students are encouraged to brainstorm, problem-solve, research, explore and experiment when creating works of art. Sketchbooks are given to each student to collect and store ideas that will become starting points for works of art in the future. These visual journals allow students to enhance their skills of observation and image making in order to process more detailed information. Some examples of sketchbook activities are illustrating poems and short stories, designing and illustrating commercial advertisements, observational drawings, photo collages, and mixed media experimentation.

Students are encouraged to research, discuss and share information about past and present artists and artworks. Through this research, they discover how artistic trends developed in relation to the events of the time, geographic location and historical periods and cultures. To further their understanding of this concept, students visit museums and galleries pertaining to an area of study. This also allows them to view diverse arts such as music, costume and set design, architecture, mass media and popular culture. Occasionally, a guest artist will come to visit the classroom to demonstrate a unique craft or skill. This experience further develops their understanding that art is an integral part of life.

Finally, the Upper Elementary art program encourages students to develop critical thought and to support their interpretations and opinions when responding to art. This is achieved through group critiques and discussions. When studying a particular artist, we will display various works of art and engage in open discussions. Students will then perceive, describe, and interpret these works of art to make informed judgments. Each critique supports an open-minded approach to diversity of ideas and artistic style, and students are taught to respect opinions that differ from their own. This same approach is used when discussing the artwork of their classmates. After completion of the Upper Elementary art program, students are equipped with the necessary skills to become active contributors to the visual arts community.

Elementary Physical Education: Overview

Physical education lessons are designed to be student-centered and self-directed. As a guide, the physical education specialist provides the initial task and then assists students as needed. They are trusted to act responsibly and encouraged to work at their own rate and ability level. The physical education environment allows students of different ages and abilities to interact in a safe and productive manner. The result is a class of focused individuals working towards mastery of a particular skill or movement. Each class is structured to allow full participation of every student, with the emphasis placed on a particular movement or skill. At the end of the activity, students are given a few minutes for cool down time and stretching. The goal is to develop responsible, contributing citizens who possess good character and a strong sense of self-worth. Skills and themes are chosen to help students better understand the key concepts and movements involved in physical activity and various sports.

The physical education specialist introduces specific skills related to motor coordination. The youngest students work to master the skills while the older students use the skills learned in previous lessons to play a game or sport. When working with younger students, the skill is isolated within an activity so they can develop the proper mechanics and coordination of movements. If the theme is, for example, soccer, younger students practice skills to perfect eye-foot coordination, while older students learn the rules specific to the game of soccer.

Upper Elementary Program

Students are now beginning to demonstrate more advanced manipulative skills, which contribute to movement proficiency. These types of skills also allow more competitive sports to be played, such as baseball, volleyball, basketball, soccer, and hockey. Lacrosse or tennis classes are offered in the spring. Students are now able to apply rules and safety procedures while participating in a wide range of physical activities. The core themes at this level are communication, cooperation, appreciating diversity, conflict resolution, problem solving, and self-esteem.

Another big component of physical fitness at this level is the students’ ability to acquire the knowledge and skills necessary to engage in an active lifestyle. They can now identify the main components of fitness, which are muscular strength, muscular endurance, flexibility, and body composition. Students are encouraged to monitor self-progress and to participate in fitness assessments.

A great deal of emphasis is placed on reducing health risks and living safely. For example, students are educated about abuse and risky situations and how they can behave in ways that are safe and prevent injury at home, school, and in the community. Issues such as bullying, teasing, threatening, and harassment are defined and students are taught ways to act and communicate responsibly and safely.

Circus Smirkus

Each year, Cobb School students experience the magic and joy of the circus acts with a one week Circus Smirkus Residency program.

Standardized Testing

The Cobb School administers the Stanford Achievement Test each year in the fourth, fifth, and sixth grades. The tests are independently scored and the results are sent to parents. All parents are invited to an optional additional conference to review the results.

We conduct a test preparation course in all three years of Upper Elementary. The focus is on the techniques and psychology of test taking. Our goal is that the students are very familiar and comfortable with this form of assessment by the time they graduate in sixth grade. The standardized test results are not used as part of the students’ permanent record.