Grade 1 – 12

CURRICULUM FRAMEWORK

Overview of the Integrated Curriculum Model

The Integrated Curriculum Model (ICM), a theoretical model of curriculum design for gifted learners (Figure 1), emphasizes the inclusion of advanced processes, advanced content, and connections to overarching concepts through themes and issues as the foundation for curriculum development.

The greatest student learning occurs when emphases are given to each of these dimensions within a given curriculum unit (VanTassel-Baska, 2001). The ICM was derived based on the characteristics of gifted students and how curriculum may be designed to best match the characteristics of these learners. For example, since gifted students are precocious learners, advanced content within a given subject area will provide opportunities for students to develop expertise in the content domains.

The intensity of gifted students can be addressed through the provision of advanced processes and organizers that help them reason through situations and think critically about given advanced topics and real world  issues. Moreover, since many gifted students thrive on complexity, the provision of interdisciplinary connections and the linkage of content to issues and themes is a necessary component of curriculum for these students

The three components of the ICM (advanced content, issues/themes connected to overarching concepts, and advanced processes/products) comprise a framework for curriculum design and differentiation.

Advanced Content Dimension

A curriculum for the gifted needs to be designed with an advanced content focus that incorporates subject matter that is two to three grade levels above what is normally expected of a typical learner. Advanced content is derived based on standards within a given discipline. These educational  standards serve as the basis for content inclusion.

In addition to advanced content standards, students need to understand how the advanced content is used to develop expertise within a given domain by using tools of the discipline and developing skills used by experts.

Process-Product Dimension

Gifted learners show great intensity and the process-product dimension of the ICM supports students’ concentration and passion by providing students with higher-level thinking challenges and reasoning skills. Advanced processes and products  that would be appropriate for any content-based curriculum for gifted learners include problem-based learning, issue-based research, real-world  connections, oral and written presentations to real-world audiences, and situation or issue reasoning and analysis.

Issues/Themes Dimension: Connecting to Overarching Concepts

Students who are gifted thrive on complex and ambiguous  situations. These students need a curriculum that helps them integrate isolated pieces of information in a cohesive way. The issues/themes dimension provides a framework for students to connect observations and facts to an overarching concept. These concepts span multiple disciplines and allows students to gain an in-depth understanding of their world (American Association for the Advancement of Science, 1993).

Overarching concepts provide students with a framework to guide learning and bring order to the complex and often ambiguous information they gather (National Research Council, 2005). Sample overarching concepts include change, systems, and cause and effect. Specific generalizations that are associated with each concept help to provide additional understanding.

Grades : 1-2
Curriculum Overview:  Noble Academy Language Arts curriculum currently consists of 16 units for high-ability learners in grades 1-12. All curriculum materials emphasize literature, writing, oral communication, and language study. Each unit represents a semester of work.

Noble Academy language arts units focus on analytic and interpretive skills in literature, persuasive writing skills, linguistic competency, listening/oral communication skills, reasoning skills, and understanding an overarching concept.

Through the use of graphic organizers, students are better able to write persuasively, analyze and interpret literature, understand and enhance vocabulary, develop issue-based research products and presentations, and analyze situations within a fiction or nonfiction text.

Advanced Content

The essential understandings of each language arts unit have been aligned to national standards within a given grade level as well as two to three grades above the current grade. Besides addressing the regular language arts standards, Noble Academy language arts curricula also focus on analyzing and interpreting literature, issue-based research skills, vocabulary development and analysis, and persuasive writing. Reading selections were chosen because of their readability levels, connection to an overarching concept, and multicultural emphases.

The language arts units incorporate advanced content-based thinking models such as a literature web and a vocabulary web to help students understand and analyze text and words. Students are introduced to the literature web early in each unit. For example, after reading a short story or poem, students analyze and justify key words and feelings. They are asked to describe images and symbols, identify structural elements within the story and how they contribute to the meaning, and elaborate on main ideas of the selected piece. Discussion and reflection are critical components of this advanced content organizer. Students are asked to reflect individually about a passage, share ideas with a partner, and then discuss findings in a small or whole group setting with teacher guidance and feedback.

Advanced Process-Product

Noble Academy language arts units use a variety of advanced processes and models to guide students’ thinking, writing, and research as they explore quality literature and current issues. After identifying an issue, students may examine it through the lens of Paul’s Reasoning Model.

Issues and Research

Advanced issue-based research opportunities are part of the advanced process/product dimension within the language arts curriculum. The issue-based research model features real-world problems and authentic data collection such as interviews and surveys. Students are taught how to distinguish between a topic and an issue and then led through a process to help them collect, analyze, and report data. Within the language arts units often the research topic is based on student choice. Sample topics may stem from an issue presented in a novel or from a current event within the school or world.

Persuasive Writing

By using a persuasive writing model, students learn to articulate ideas by providing at least three key ideas, evidence or elaboration, and an appropriate introduction and conclusion. Students who are more sophisticated in their writing and thinking may add counterpoints within the model as part of reasoning and elaboration.

Issues and Themes: Connecting to Overarching Concepts

Most of the language arts units focus on the overarching concept of change. Progressing through the units, students learn that change is everywhere, change is linked to time, change may be positive or negative, change may be perceived as orderly or random, and change may happen naturally or may be caused by people. As students read literature, they identify examples of how change generalizations are illustrated in different reading passages.

Textbook / Unit Titles:

A Wild, Wacky, Wonderful World of Words—Grades 1 – 2

This unit is designed to engage primary students with high abilities in the verbal domain in challenging reading, writing, and interpretation skills in the language arts. It reflects talented young learners’ need for greater exposure to higher-level thinking activities sooner in their school years than other students. The unit specifically focuses on literature that uses extensive figurative language in order to support young children’s development of metaphoric competence in the areas of both comprehension and production.

Beyond Words—Grades 1 – 2

This literature unit, organized around the study of figurative language, explores the idea that language can change the way we think about the world by creating new images and connections in our minds. The unit uses poetry and picture books as the basis for analyzing different types of figurative language, including simile, metaphor, and personification, and gives opportunities for students to create their own literary images. In addition, the unit introduces students to persuasive writing and to advanced word study, as well as providing an opportunity for students to explore how language changes over time.

Journeys & Destinations—Grades 2 – 3

This unit uses an inquiry-based approach to investigate literature in an interdisciplinary, multicultural curriculum. The guiding theme of this unit is the recognition of change as a concept that affects people and their relationships to the world around them. An open-ended approach to the discussion process is emphasized in the search for meaning in selected literature selections. Vocabulary development, writing activities, oral communication, research, and reasoning are also integrated into the unit.

Explore, Discover, Reveal—Grades 3 – 4

This unit is organized around the idea that our world has many exciting places and ideas to explore. Students learn that exploration can be done both physically and cognitively, and will come to realize that exploration and new discoveries affect people as well as the world around them. As literature, history, music, and art are studied, students will also grow to understand that each of us explores the world in many different ways.

Literary Reflections—Grades 4 – 5

While all four language arts strands of literature, writing, language study, and oral communication are integrated into this unit, the core of the unit involves students interacting with literature while enhancing reading comprehension and textual analysis skills. The literature selections serve as a basis for discussion.

Perspectives—Grades 4 – 5

The guiding theme of this unit is the recognition that people have their own perspectives based on their experiences in the world around them. The literature selections in the unit will allow students the opportunity to view and study multiple perspectives. Students will reflect on their own individual perspectives as well as the perspectives of characters in and authors of classical literature.

Mind Your Time – Grades 4-5

Each of us has experienced the effects of time on various phases of our life. Many individuals take time for granted and do not understand its important role in their lives. Both the reading selections and instructional activities in Mind Your Time, for grades

4-5, were designed to intrigue and challenge high ability students. Students will work independently and in groups doing classwork as well as homework outside of the classroom.

Patterns of Change—Grades 4 – 6

The concept of cyclic patterns of change was chosen as the unifying theme for this unit. Selected literary works deal with cycles in nature, knowledge, history, and human life. Students are introduced to some of the important approaches and ideas of literary criticism. Students are encouraged to use journals, literature webs, essays, and visual projects to organize and express their ideas about various literary selections.

Autobiographies—Grades 5 – 6

In this unit, students study the concept of change by reading autobiographies of writers and by looking at change in the lives of writers and other artists. As they examine life stories and self-portraits, they study literature and examine works of art from various cultures. In order to gain insight into the development of talent, students are encouraged to explore their own identities as talented learners through discussions, research, oral presentations, and reflective writing.

Persuasion—Grades 6 – 7

This unit highlights elements of persuasion, especially as it relates to oral communication. Students must cite passages from literature to defend their points of view in discussion as well as in written arguments. Literature selections such as “The Valiant,” “The Pied Piper of Hamelin,” and the “Declaration of Independence” frame the basis for exploring the reasoning process through analysis and interpretation. Opportunities are presented for impromptu, informative, and persuasive speeches, debate, small and large group discussion, and critical reasoning.

Courage: Connections and Reflections—Grades 7 – 8

Courage: Connections and Reflections offers students the chance to compare and contrast their own lives with those of others. The unit explores social and historical issues by studying people, historical time periods and events, and students’ own lives. Novels, short stories, poetry, art, and music will be the avenues for addressing unit goals. Students will be given numerous opportunities for reading, writing, listening, and speaking.

The Pursuit of Justice—Grades 7 – 8

This unit is about the path man has taken in his desire for justice. Students will explore the South of the 1930s in the perennial classic To Kill a Mockingbird by Harper Lee; they will also read some of her short stories and essays that have intrigued readers. The plight of the Little Rock Nine becomes a first- person account in Warriors Don’t Cry by Melba Pattillo Beals. Students will read the primary source newspapers of the day to get other perspectives on how Civil Rights and integration shook the nation.

They will also travel the path of the migrant ranch hand in John Steinbeck’s Of Mice and Men. Students will also have a chance to examine poetry, songs, essays, and art that portray the pursuit of justice. Vocabulary and grammar will align with the readings. Opportunities to research, write expository pieces, and creative meaning for themselves will abound in this unit.

The 1940’s: A Decade of Change—Grades 7 – 9

This unit looks at the historical events and social issues of the 1940s through the literature of the decade, including novels, short stories, poetry, essays, letters, and newspapers. Numerous opportunities for reading, writing, listening, linguistic competency, and speaking are incorporated into the unit. Each student is required to pose a hypothesis and conduct research concerning some issue of significance that arises from the literature that is studied.

Utopia—Grades 7 – 9

This unit provides an overview of utopia as seen by various individuals, groups, and countries and gives students an opportunity to examine why ideas about utopia undergo change. Through the study of literature, art, music, and other classroom activities, students learn about the search through the ages for utopia and the struggles to grasp and maintain it on both personal and societal levels. Exploring utopia through personal dreams and goals allows students to analyze the literature they read more thoroughly throughout this unit.

Threads of Change in 19th Century American Literature—Grades 8 – 10

This unit uses literature of the 19th century to explore five historical movements: romanticism, transcendentalism, abolitionism, industrialism, and feminism. Each of the five “isms” has its own “literature box” containing appropriate documents to serve as a resource for teams of students. The “isms” are investigated as change agents in American life through the study of key writings of the period.

The American Dream—Grades 9 – 10

This unit explores how humans’ quest for peace, prosperity, and progress leads them towards a sometimes-elusive goal. It provides an overview of the “American Dream” relative to various individuals, groups, and regions. Through classroom activities and the study of rich, challenging literature, students will learn that pursuit of the American Dream can cause joy and despair as well as other emotional and physical reactions in humans. Exploring that journey through both current and historic documents, literature, art, photography, and music will provide students with an avenue to compare and contrast their own ideas with those of peers, communities, and society.

Change Through Choices—Grades 10 – 12

Choices and the consequences of choices that people make have an important impact on life and the success of individuals. This unit focuses on catalytic choices that determine change in a variety of situations. Rich in content, the world literature chosen can be analyzed and synthesized for depth in understanding cultural similarities and differences. This unit attempts to give the student a chance to question real world choices and problems and decide what valuable lessons can be learned through careful individual examination of options.

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Grade: 2-8

Curriculum Overview:  Noble Academy science curriculum features ambiguous, problem-based learning scenarios. As active investigators, students must take on the role of scientists to solve problems through scientific inquiry. Advanced, in-depth content and a connection to an overarching concept, such as systems, are also emphasized in all unit materials.

Advanced Content

Advanced content is infused within the science curriculum to help students develop expertise in science based on research standards. For example, the National Research Council (2005) has outlined three key practices for developing expertise in science. These are included  within Noble Academy science units: 1) address preconceptions  and concepts by connecting the content to the outside world and outline appropriate content and understanding; 2) engage students in practice  as to what it means to “do” science through inquiry and investigation; and 3) encourage metacognition and reflection through guided teacher feedback, student discussion, and personal reflection.

Unit content has been aligned to national standards and meets national grade level standards as well as standards for grades that are two to three levels above the current grade.

Goals for science units include the following process and concept goals in addition to essential understandings of specific content areas:

1) To understand the concept of systems or change;

2) To understand and apply the basic principles of experimental design and investigation, and

3) To develop reasoning skills with real-world applications to science.

Advanced Process-Product

Problem-based learning is a primary vehicle to help students develop scientific understanding in an in-depth, sophisticated way, by experiencing the processes and tools a scientist may use when presented with a difficult problem.

Noble Academy science units introduce real-world problems to initiate scientific investigation. All units incorporate a problem-based learning scenario as the catalyst for initiating the discussion of content and scientific investigation.

Students not only focus on specific content learning in science, but they also develop scientific investigation skills as a way to develop the thinking skills of a scientist. Students pose questions, then conduct experiments to answer those questions. They also identify independent and dependent variables, constants, and controls as a guide for quality investigations.

Issues and Themes: Connecting to Concepts

The science units incorporate the overarching concept of systems as a way to link unit components together, add depth to the content, and connect students’ learning to essential interdisciplinary understandings.

Examples of systems discussions and applications within the science units include how an acid spill affects the environmental system, how electrical systems impact one another, or how the human body systems are interrelated.

Using these real-world system discussions students learn generalizations about systems and how to identify the inputs, outputs, and interactions among parts, and identify positive and/or dysfunctional systems. Students learn to conceptualize how larger systems can encompass smaller systems, understand the interdependence of systems, and explain how systems exhibit patterns.

Textbook / Unit Titles:

Where’s the Beach?—Grades 2-4

Plans for building a children’s camp at the beach are on hold because the town council is worried about beach erosion. Since the camp received a large donation to develop nature-themed  experiences, designed to teach children how to protect the environment, the camp manager wants to cooperate with the council. The problem is that she must begin construction quickly to be ready for the summer season. Acting as members of the town council, the students must develop scientifically-based regulations that will satisfy the long-term needs of the town and the plans for the new camp.

What A Find! —Grades 2-4

What an appropriate title for an exploration of the field of archaeology! Students are put in the role of junior archaeologists at a research museum and discover that construction work has been halted on a new school because historic artifacts were discovered. To determine whether or not the dig is important enough to halt building the school entirely, students learn to excavate and actually conduct the dig—carefully seeded with “historic artifacts.”

Acid, Acid Everywhere—Grades 4-6

Acid, Acid Everywhere presents the structure of systems through chemistry, ecological habitats, and transportation.  This unit poses an ill-structured problem that leads students into an interdisciplinary inquiry about the structure and interaction of several systems, centering around the study of an acid spill on a local highway.

Electricity City—Grades 4-6

Electricity City provides a creative and interdisciplinary approach to introducing fourth through sixth grade students to electricity. In this simulated activity, a large recreational complex is being built in the middle of a city, and the students’ role is to plan the site’s electrical needs, as well as create additional backup plans. This “real world” problem requires students to analyze the situation, determine what type of research is needed, conduct experiments, and evaluate solutions.

Animal Populations—Grades 6-8

This curriculum unit integrates population biology and mathematics. The ill-structured problem puts students in the stakeholder role of assistant to the mayor of a small town in which residents are demanding that something be done about the deer that are eating their landscaped plants. Throughout the unit, students deal with physical models, conceptual models, and mathematical models as they tackle the deer problem and the complication of Lyme Disease.

Nuclear Energy—Grades 6-8

This unit creatively explores the effects of nuclear power waste. The topic is introduced through the eyes of a mayor of a town where a nuclear power plant is located. She must decide if the facility can expand its waste disposal techniques. What are the biological implications of radiation? What are the trade-offs with which society must live as we accept nuclear technologies into our lives? These questions are explored by students as they prepare to make recommendations about the use of the nuclear power plant in their fictitious town.

Something Fishy—Grades 6-8

This unit poses an ill-structured problem that will lead students into an interdisciplinary study about several individual systems and their interactions. The content of the unit focuses on the various systems involved in the pollution of a local body of water: the aquatic ecosystem, chemical reaction systems, government systems, and economic systems. Students are challenged to grapple with real world concerns and develop recommendations through simulation activities based on the scientific process.

No Quick Fix—Grades 6-8

No Quick Fix uses systems as the fundamental concept to help students understand cell and tuberculosis biology. In a series of widening concentric circles, students learn that the cells are elements in larger systems, such as the immune system and the even larger system of the human body. Students also interact with the human social systems: health care and public education. Students take on the role of physician and begin to search for the cause and resolution of the problem. While unraveling the interactions among various systems, students can appreciate the complexities of staying healthy in the modern world.

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Grade: 2-10

Curriculum Overview:  Noble Academy social studies units were designed with the goal of meeting the specific learning needs of the advanced learner, yet also maintaining focus on mainstream learning standards such that they can be used in heterogeneous classrooms.

The major emphases of the units on concept development, critical thinking, and primary source analysis within the context of high-level content reflect the focus of national standards in social studies on historical thinking and research and on the integration of major concepts across disciplines.

The units have been successfully implemented in heterogeneous classrooms and in special classes for the gifted. Foundational principles that are learned in the early units (grades 2-3) are cultivated as students’ progress to higher grades, maximizing learning potential.

Advanced Content

Unit content has been aligned to national standards and meets grade level standards as well as standards for grades that are two to three levels above the current class grade. Advanced content is also incorporated through the use of primary source documents. Rather than having students read about historical events, Noble Academy social studies units provide learners with primary source documents as learning tools to develop historical perspectives.

When analyzing primary source documents, students establish a context and intent for each piece (author, time written, related culture and events, purpose, intended audience), work to understand the source (issues/events and values reflected in document), and evaluate or interpret the source (reliability, representativeness, potential and actual consequences).

Advanced Process-Product

When students encounter events within curriculum readings, Noble Academy social studies units guide students in analyzing the situation by looking at different points of view. Students may reason through a situation using a graphic organizer to analyze an historical situation or event through multiple stakeholder perspectives. After analyzing a situation, students may be required to take a side or write a persuasive essay from the perspective of one of the stakeholders, thus, incorporating the additional advanced process of articulating the perspectives in a cohesive manner. Persuasive writing opportunities vary by unit content.

Issues and Themes: Connecting to Overarching Concepts

Noble Academy social studies units develop a broad understanding of concepts, such as systems and cause and effect. Students examine relationships to events and eras in history as an essential area of focus. Sample systems discussions include the exploration of the silk trade as a type of economic system, comparison of European colonist and Native American social systems, and comparison of the American political system with that of other democracies.

Sample cause and effect discussions are: causes of the American Revolution, effects of the Declaration of Independence, causes of the stock market crash, and effects of the Dust Bowl.

Textbook / Unit Titles:

Ancient Egypt:  Gift of the Nile, Second Edition—Grades 2-3

Gift of the Nile is designed around the idea that human civilizations develop and sustain themselves as a collection of interdependent systems. The civilization of ancient Egypt forms the central content of the unit, with exploration of systems of agriculture, economics, language, and leadership in this ancient culture. Students broaden their understanding by comparing the ancient Egyptian civilization with aspects of their own lives and communities.  Teacher guide now has accompanying student guide.

Ancient China: The Middle Kingdom—Grades 2-3

The concept of systems is the foundation for The Middle Kingdom, which explores ancient China to demonstrate the interdependent systems that develop and sustain a civilization. The unit explores systems of agriculture, language, leadership, and trade in ancient China, using models for reasoning and document analysis to support student understanding. This unit may be used in conjunction with Ancient Egypt.

Building a New System: Colonial America 1607-1763—Grades 4-5

Building a New System begins with an in-depth study of the interrelationships between the Chesapeake Bay system and both the Native Americans and the early English colonists in Virginia. The unit then turns to an exploration of the economic, social, and political systems of early America across the colonies, comparing and contrasting lifestyles of different groups in different regions.

The World Turned Upside Down:  The American Revolution—Grades 4-5

Intensive document analysis and exploration of the concept of cause and effect form the foundation of this unit exploring the Revolutionary period in American history. The World Turned Upside Down explores the chronology and major events leading up to and during the Revolutionary War and uses primary sources to demonstrate the social and political context.

A House Divided?   The Civil War:  Its Causes and Effects, Second Edition—Grades 5-6

The concept of cause and effect serves as a central organizing theme of A House Divided? This unit explores the events and perspectives leading to the American Civil War and the chronology and context of the war itself. Using primary source documents, students investigate the social, political, and economic influences that were significant in this period of history. Teacher guide now has accompanying student guide.

The 1920s in America: A Decade of Tensions—Grades 6-7

Centered on a variety of primary sources including music, advertisements, and traditional documents, the 1920s in America provides insight into the events, values, lifestyles, and experiences of the 1920s period. Students explore the concept of cause and effect and how it relates to the events of the time, and gain a level of appreciation and understanding as they look at the ways different aspects of the era interact with and influence one another.

The 1930s in America: Facing Depression—Grades 6-7

The 1930s in America explores Depression-era America from the perspective of many different groups of people, utilizing a variety of primary sources to illustrate events and the social-political context. The unit emphasizes the interplay of changes in geography, government, the economy, and the influence of particular individuals and groups.

The Road to the White House: Electing the American President, Second Edition—Grades 6-8

The concept of systems forms the basis for this exploration of American government, and focuses on the processes involved in the election of the President, and the constitutional context of these processes. Students investigate the chronology of campaign and election, and study documents and statistics related to Presidential elections in American history. Teacher guide now has accompanying student guide.

Defining Nations—Grades 9-10

This unit is designed around the concepts of nationalism and identity as interrelated ideas that affect events and decisions throughout the world. Unit lessons explore recent changes and conflicts, giving students multiple opportunities to analyze events based on a developing understanding of how the ideas of nationalism and identity apply to specific situations.

The Renaissance and Reformation in Europe—Grades 9-10

This unit focuses on the concept of authority and how the Renaissance and Reformation period was defined by changing notions of political and religious authority. The unit traces the background of the Renaissance and Reformation through exploration of the Mediterranean world in medieval times, then engages students in analysis of various influences on changing conceptions of the church and of political leadership and authority. In addition, the unit explores the cultural changes occurring in the Renaissance and their influence on the past and present. Students engage in extensive primary source analysis and structured reasoning as they explore how political, religious, and economic authority were constituted and legitimized throughout the period.

Primary Sources and Historical Analysis—Grades 9-10

This unit is intended to support students in their development of the skills of the historian, particularly in the area of document analysis. It provides a collection of primary source documents and strategies for engaging students with these documents that will deepen and extend their skills in analyzing and interpreting written historical contributions. The unit lessons may be used as stand-alone pieces as +they fit throughout a year’s curriculum or addressed as a whole unit on the historical analysis process.

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Primary (Grade 3-6)

Geometry and Measurement (Grade 3-4):

In this unit on measurement, students are actively engaged in the measurement process and connect it to their own personal worlds. Students go “In Search of the Yeti” as they learn about perimeter, area, and volume.

Geometry and Measurement (Grade 5-6):

What Are Your Chances? Probability in Action

Students begin their exploration of probability as a measurement of the likelihood of events. They move beyond performing simple probability experiments to an understanding of experimental and theoretical probability and the Law of Large Numbers. Students also experience what it means for a game to be fair as they create their own games.

Middle School (Grade 6-8)

Middle School focuses on Pre-Algebra, which leads to the Algebra

Grade (6-7)

1. Let’s Be Rational: Focusing on Fractions, Decimals and Integers
2. Accent on Algebra: Focusing on Equations, Tables and Graphs
3. Puzzling Proportions: Focusing on Rates, Percent and Similarity
4. Sizing Up Solids: Focusing on Angles, Surface Area and Volume
5. Driven by Data: Focusing on Probability and Data Analysis

Grade (7-8)

Discovering Algebra

Balancing conceptual and procedural understanding

With Discovering Algebra, students solve problems, make sense of complex situations, and develop mathematical skills in a meaningful and retrievable way.

Grade (8-9)

GEOMETRY

Building your students’ reasoning and proof abilities

Discovering Geometry helps students develop inductive and deductive reasoning skills by creating conjectures and reporting and justifying conclusions as they explore the principles of geometry. Congruence, similarity, and symmetry are studied from the perspective of geometric transformation to create connections within the mathematics. Digital & print editions now available with probability.

Grade (9-10)

ALGEBRA 2

Modeling with mathematics

Discovering Advanced Algebra builds upon the foundation of Discovering Algebra to help all learners further develop algebraic skills along with a strong, conceptual understanding of Algebra 2. The investigative approach keeps students engaged as they use mathematical functions to model real-world data, answer questions, and make predictions.

Grade (10-12)

Precalculus

Students will review the various of functions, from linear to trigonometric, which already discussed in Algebra II and learn about the application of the functions.

Statistics in Action

Students will learn the fundamental logic and tools of statistics and its actual practice of statistics in real-world situations

Algebra I:

Units:

• Data Exploration
• Proportional Reasoning and Probability
• Variation and Graphs
• Linear Equations
• Line Fitting
• Equations and Inequalities
• Exponents and Exponentials Models
• Functions
• Transformations of functions
• Quadratics

Geometry:

Units:

• Introduction of Geometry
• Reasoning in Geometry
• Tools of Geometry
• Triangle Properties
• Polygon Properties
• Circle Properties
• Transformation and Tesselations
• Area
• Pythagorean Theorem
• Volume
• Similiarity
• Trigonometry

Algebra II:

Units:

• Patterns
• Data Description
• Linear Models and Systems from Linear Functions
• Functions, Relations and Its transformations
• Exponential,Power, and Logarithmic Functions
• Matrices and Linear Systems
• Quadratics and Polynomial
• Parameters in Trigonometry
• Conic and Rational Functions
• Trigonometric Functions
• Series
• Probability

PreCalculus:

Units:

• Functions and Mathematical Models
• Periodic Functions and Right Triangle
• Application of trigonometric and circular functions
• Trigonometric Function Properties and its parametric
• Combinations of sinusoids
• Triangle Trigonometry
• Review of essential functions
• Data fitting to functions
• Probability and random variable
• Vectors
• Matrix transformation and Fractals
• Conic
• Complex numbers
• Sequences and series

Statistics:

Units:

• Data
• Distributions
• Relationship between variables
• Sampling
• Sampling distributions
• Probability Models
• Probability Distributions
• Inference
• Means
• Testing for data fitting (Chi-Square)
• Regression

Grade:

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Grade:  4 – 12

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