Parents: Boston Public Schools Grade 10

Learning Standards

This information is from the Boston Public Schools Citywide Learning Standards.

ENGLISH LANGUAGE ARTS

Oral Presentation and Discussion
Students will be able to:

  • Use agreed upon rules for informal and formal discussions in small and large groups such as Book Club, Literature Circles, and Buddy Reading.
  • Facilitate discussion groups independent from the teacher; identify and practice techniques to improve group productivity such as discussion guidelines, setting time limits for speakers and deadlines for decision-making.
  • Organize and present ideas in a logical order.
  • Ask for clarification when others' responses are unclear.
  • Actively listen, respond to, and build on ideas generated during group discussions.
  • Use information to inform or change their perspectives.
  • Support their responses with evidence or details; expect and request the same of others.
  • Summarize and evaluate what they have learned from the discussion.
  • Evaluate the productivity of group discussion using group created criteria and make suggestions to address the needs of the group.
  • Deliver informal and formal presentations, giving consideration to audience, purpose, content.
  • Identify elements and organizational structures of effective speeches made for a variety of purposes; work collaboratively to create and use an appropriate rubric or criteria to prepare, improve, and assess presentations.
  • Conduct interviews for research projects and writing.
Language
  • Identify and use correctly idioms, cognates, literary terms, and words with literal and figurative meanings.
  • Demonstrate an understanding of how patterns of words change their meanings or functions.
  • Use knowledge of Greek, Latin, and Norse mythology and the Bible to understand the meaning of new words.
  • Identify rhetorically functional sentence structure.
  • Identify and correctly use mechanics, usage, and sentence structure in oral and written responses.
  • Describe the origins and meanings of common words or phrases used in written English.
  • Identify and use content-specific vocabulary and terminology in oral and written responses.
  • Identify differences between the voice, tone, diction, and syntax used in different media presentations.
Reading and Literature
  • Develop fluency, accuracy, and understanding when reading different genres and complex texts.
  • Select books for independent reading.
  • Develop a language for effectively talking about books they are reading.
  • Use before, during, and after reading strategies to enhance their understanding of texts.
  • Use background knowledge to make inferences and predictions and to make personal connections with what they are reading.
  • Set a purpose for reading and monitoring their progress.
  • Listen critically and ask questions to clarify information.
  • Summarize information to check understanding.
  • Visualize information in text to support comprehension.
  • Apply their knowledge of topic and main idea to evaluate different texts.
  • Understand genres and organizational structure and apply that knowledge to their reading and responding to different texts.
  • Use their knowledge of text features and organizational structure in informational and nonfiction texts to make meaning of what they are reading.
  • Understand when comprehension breaks down; know and use self-correcting strategies to make meaning of what they are reading.
  • Apply their knowledge of patterns of imagery or symbolism in different literary texts.
  • Respond orally and in writing to the logic and use of evidence in an author's argument in informational and expository texts.
  • Compare and contrast the presentation of a theme or topic across genres to explain how the selection of genre shapes the message.
  • Demonstrate an understanding of intertextuality and different literary theories (i.e., reader response, historical, biographical, structuralism, post-structuralism) and utilize them when interpreting literary texts.
  • Apply and evaluate their knowledge of theme (a view or comment on life) to identify themes in text and support with evidence from the text.
  • Apply and evaluate their knowledge of the structure and elements of fiction in their oral and written response to a variety of literature from different cultures and provide evidence from the text to support their understanding.
  • Apply and evaluate their knowledge of the purpose, structure, and elements of nonfiction or informational materials in oral and written response, providing evidence from the text to support their understanding.
  • Apply their knowledge of the effects of sound, form, figurative language, graphics, diction, and dramatic structure of poems in oral and written responses to what they read.
  • Sound (alliteration, onomatopoeia, rhyme scheme, consonance, assonance).
  • Form (ballad, sonnet, heroic couplet).
  • Figurative language (personification, metaphor, simile, hyperbole, symbolism).
  • Evaluate their understanding of the importance of sentence variety in the overall effectiveness of an imaginary/literary or informational/expository work.
  • Evaluate how an author's choice of words advances the theme or purpose of a work.
  • Identify and analyze characters, structure, and themes in classical Greek drama and epic poetry.
  • Apply their knowledge of how dramatic conventions support, interpret, and enhance dramatic text.
Composition
  • Collect ideas for writing from different texts and sources (dialogue, artifacts, memories, images, etc.).
  • Maintain a process for recording, collecting, referring to, and sharing their ideas for writing, as well as more formal writing products, including drafts.
  • Write for different purposes and for different audiences.
  • Understand different genres and organizational structures.
  • Select appropriate genres and organizational structures for drafts.
  • Select appropriate strategies for developing ideas into drafts.
  • Select appropriate strategies for revising the organization and ideas in drafts.
  • Use literary language to talk about pieces of writing (e.g., craft, focus, structure, genre, voice, audience).
  • Use their knowledge of standard English conventions (mechanics, grammar, and spelling) to edit work.
  • Reflect on and self-monitor their development as a writer.
  • Write well-organized stories or scripts with an explicit or implicit theme and details that contribute to a definite mood or tone.
  • Write poems using a range of poetic techniques, forms (sonnet, ballad), and figurative language.
  • Write well-organized essays (persuasive, literary, personal) that have a clear focus, logical development, effective use of detail, and variety in sentence structure.
  • Evaluate their use of different levels of formality, style, and tone when composing for different audiences.
  • Use various strategies for revision to improve their writing by attending to topic/idea development, organization, level of detail, language/style, sentence structure, grammar and usage, and mechanics.
  • Use knowledge of types of clauses (main and subordinate), verbals (gerunds, infinitives, participles), mechanics (semicolons, colons, hyphens), usage (tense consistency), sentence structure (parallel structure), and standard English spelling when writing and editing.
  • Create a piece of literature that integrates all elements of fiction to emphasize the theme and tone.
  • Organize ideas for a critical essay about literature or a research report with an original thesis statement in the introduction, well constructed paragraphs that build an effective argument, transition sentences to link paragraphs into a coherent whole, and a conclusion.
  • Formulate open-ended research/inquiry questions and apply steps for obtaining and evaluating information from a variety of sources, organizing information, documenting sources in a consistent and standard format, and presenting research.
  • Use group-generated MCAS-like criteria for evaluating different forms of writing and explain why these are important before applying them.
Media
  • Analyze and evaluate visual or aural techniques used in a media message.
  • Create media presentations that effectively use graphics, images, and/or sound to present a distinctive point of view on a topic or theme from literature.
  • Establish criteria for assessing the effectiveness of the presentation, style, and content of films and other forms of electronic communication.
HISTORY

World History II - 1800 to the Present

Section I: Imperialism & the Rise of Modern Asia, Africa & South America in the 19th and 20th Centuries

Topic 1: Rising European Nationalism and New Western Imperialism

    Students will be familiar with:
  • The causes of 19th century European Imperialism.
Topic 2: In Depth Study - India
  • British colonialism in India.
  • The physical characteristics and resources of India.
  • The economic relationship between India and Britain.
  • The development of the Indian infrastructure (e.g., roads, canals, railroads and universities).
  • The social position of Indian subjects in relationship to the British.
  • The rise of nationalism in India and the influence and ideas of Ghandi.
  • The development and goals of the nationalist movement in India including the ideas and significance of nationalist leaders such as Jawaharial Nehru.
  • Colonialism in India, its decline, and long-lasting effects.
Topic 3: In Depth Study - China
  • China's interaction with colonialism and the central events and developments in Chinese History in the 19th and early 20th century.
  • The physical characteristics and resources of China.
  • China's population growth between 1750 and 1850.
  • The decline of the Manchu dynasty and its effects on the growth and development of China.
  • The causes and results of the Opium War.
  • The significance of the Taiping and Boxer Rebellions.
  • Sun Yat-Sen; the 1911 Nationalist Revolution.
  • The Chinese Civil War, the rise of Mao Tse-tung, the triumph of the Communist Revolution in China in 1949.
  • The major political and economic upheavals in China after the Chinese Revolution, to the present.
Topic 4: In Depth Study - Africa
  • The major developments if African History in the 19th and 20th centuries.
  • The physical characteristics and resources of Africa.
  • Territorial "claims" to the African continent by the Britain, Belgium, Germany and France.
  • The impact of European domination over African people as it relates to: the loss of personal rights, cheap or forced labor, taxation, uniting of warring people into single colonies, "reserves" or towns, cultural disruption, including detribalization, diminished status of African women and the law.
  • The European and African perspective on imperialism.
  • The causes and goals of nationalist movements.
  • The rise and results of Black Nationalism in Angola, Chad, Ghana, Kenya, Nigeria or Sudan. (Select two or more nations for close study and comparison.)
  • The long lasting impact of European imperialism on the African continent.
  • The impact of enslavement during the 15th and 16th centuries to imperialism.
  • Students will focus on South Africa past and present.
  • How South Africa became a Republic.
  • The meaning and limitations of apartheid and apartheid laws.
  • The establishment of Bantustans and living conditions for its residents.
  • Black resistance to apartheid including the work of the African National Congress.
  • The international position regarding South Africa, apartheid and growing violence.
  • The significance of the Sharpeville Riot and riots in Soweto.
  • How apartheid ended; P. W. Botha, F. W. de Klerk, Nelson Mandela.
  • The significance of the Presidency of Nelson Mandela; the problems facing South Africa.
Topic 5: In Depth Study - Central and South America
  • The major developments in South American History during the 19th and 20th centuries.
  • European nations who had laid claim to South America.
  • The causes of the wars for independence including leaders, their goals, and results.
  • The causes and goals of nationalist movements.
  • The significance of economic and social stratification created by imperialism and colonialism.
  • The role of the church in South American history and its effect on South American development.
  • The importance of trade and the influence of the United States in the region.
  • Economic and political conditions today regarding the stability or instability of the nation.
Section II: The World in the Era of Great Wars (1900-1945)

Topic 6: World War I: Causes, Military Course, and Consequences

  • The relative importance of economic and imperial competition, Balkan nationalism, German militarism and aggression in causing World War I.
  • Major events and the consequences of World War I.
Topic 7: The Great Depression: Causes and Worldwide Consequences
  • The causes and consequences of the global depression of the 1930s; how people and governments responded to the Depression.
Topic 8: International Fascism; Nazi Totalitarianism; Liberal Democracies in Danger; Origins and Responsibilities for World War II:
  • The rise and goals of fascism in Italy, totalitarianism in Germany, and communism in the Soviet Union; the policies and main ideas of Lenin, Stalin, Hitler and Mussolini.
  • The German, Italian and Japanese drive for empire in the 1930s.
  • The difference between fascism and democracy and their contribution to the start of WWII.
Topic 9: World War II - Geography, Leaders, Military Factors, and Turning Points
  • Key battles and events of World War II, including the Battle of Britain, Pearl Harbor, the Bataan Death March, El Alamein, Midway, Stalingrad, D-Day, Battle of the Bulge, Iwo Jima, Okinawa. (Note: Teachers should select five of the ten for study.)
  • The goals, leadership and post-war plans of the allied leaders to include: Winston Churchill, Franklin D. Roosevelt, Joseph Stalin, Charles DeGaulle.
  • The consequences of World War II to include the physical and economic destruction, support in Europe for political reform and de-colonization, the emergence of the United States and the Soviet Union as the world's two superpowers.
  • The changes to the political boundaries of nations in Europe and beyond.
Topic 10: The Holocaust and Atomic Warfare
  • The causes and consequences of the Holocaust.
  • The reasons for and impact of the dropping of atomic bombs on Hiroshima and Nagasaki.
Topic 11: Democracy and Human Rights; Advances and Retreats Since 1945
  • The establishment of the United Nations; the main ideas of the Universal Declaration of Human Rights; the role of the United Nations in world affairs.
Section III: The Cold War Era & the Contemporary World, 1945-Present

Topic 12: Cold War in Europe; Marshall Plan; NATO; Iron Curtain; Warsaw Pact

  • The factors that contributed to the Cold War, including Soviet expansion in Eastern Europe and the philosophical differences between communism and democracy.
  • The term containment; Truman Doctrine; the Marshall Plan; NATO.
Topic 13: New Nations in Africa and Asia; the End of European Colonialism
  • See topics 2, 3, 4, and 5 above.
  • The causes and goals of the nationalist movement in Viet Nam; the ideas and significance of Ho Chi Minh.
Topic 14: Israel - Statehood, Military and Political Conflicts
  • The establishment of the modern state of Israel in 1948; the subsequent, key military and political conflicts between Israel and the Arab World, to the present.
Topics 15: Russia - from Revolution to the Collapse of the Soviet Union
  • The key consequences of Soviet Communism to 1945.
  • The causes for the decline and collapse of the Soviet Union and the Communist regimes of Eastern Europe.
  • The role of various leaders in bringing about a transformation in the Soviet Union and Eastern Europe to include: Mikhail Gorbachev, Vaclav Havel, Andrei Sakharov, Aleksander Solzhenitsyn, Lech Walesa.
  • The consequences of the Soviet Union breakup (e.g., market economies, political instabilities within the former Soviet Union and in former Eastern Block nations, danger of the spread of nuclear technology and other technologies of mass destruction).
Topic 16: The Changing World Economy
  • The global surge in and consequences of economic productivity during the Cold War.
  • The rise of living standards.
  • The economic development of Germany and Japan.
  • The various factors that contributed to post-war economic growth.
Topic 17: Persistent Nationalism, Militarism; Conflict of Race, Religion, and Ethnicity
  • The sources of ethnic and religious conflict in Northern Ireland, the Balkans, Sudan, Rwanda, Sri Lanka; conflict between India and Pakistan over Kashmir (Select two for study and comparison.).
Topic 18: Into the 21st Century
  • The reasons for the rise of Islamic Fundamentalism in the last half of the 20th century and the major events and forces in the Middle East over the last several decades.
  • The implications of attacks on the United States September 11, 2001 including international response to the attacks and possible long-term consequences for all world nations.
MATH: ALGEBRA 1A, COURSE 45A

Number Sense and Operations

  • Understand numbers and ways of representing numbers, relationships among numbers, and number systems.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Understand numbers, ways of representing numbers, relationships among numbers.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive numbers for any positive integer n.
  • Express and simplify numerical expressions involving real numbers.
  • Understand and demonstrate algebraically and graphically the relationship between operations and their inverses, including exponential.
  • Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
  • Express real numbers in fractional and radical form as well as in exponential form using integral and fractional exponents.
  • Use logical reasoning as well as estimation and mental computation to determine the validity of a solution in algebraic, and statistical problems.
Data Analysis, Statistics, and Probability
  • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
  • Select and use appropriate statistical methods to analyze data.
  • Develop and evaluate inferences and predictions that are based on data.
  • Understand and apply basic concepts of probability.
  • Formulate questions that can be answered with data and collect, organize and display relevant data to answer them.
  • Select and use appropriate statistical methods to analyze data.
  • Develop and evaluate inferences and predictions that are based on data.
  • Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plot, box-and-whisker plot, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.
  • Collect and graph data (using graphing calculators and/or computers when appropriate) and express relationships between variables, both verbally and symbolically.
  • Collect, organize, and analyze data from real problems using graphing calculators and other technology to create tables and graphs.
  • Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.
  • Use scatter plots of sets of data points to graph a line of best fit.
  • Use the basic set of operations with the help of Venn diagrams.
  • Solve counting problems using Venn diagrams.
  • Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.
  • Understand and apply basic concepts of probability.
  • Use tree diagrams, tables, organized lists, basic combinations ("fundamental counting principle"), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice.
  • Carry out probability experiments and discuss the results.
  • Conduct experiments to determine experimental probabilities.
Patterns, Relations, and Algebra
  • Understand patterns, relations, and functions.
  • Represent and analyze mathematical situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative relationships.
  • Analyze change in various contexts.
  • Represent and analyze mathematical situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative relationships.
  • Analyze change in various contexts.
  • Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), and linear functional relationships.
  • Use properties of the real number system to judge the validity of equations and inequalities, to prove or disprove statements, and to justify every step in a sequential argument.
  • Translate between different representations of functions and relations: graphs, equations, point sets, and tabular.
  • Demonstrate an understanding of the relationship between various representations of a line.
  • Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "slope y-intercept" formulas.
  • Explain the significance of a positive, negative, zero, or undefined slope.
  • Find linear equations that represent lines parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.
  • Solve equations apply to the solution of everyday problems.
Discussion, Presentation, Composition
  • Use agreed upon rules to participate in discussions in large and small groups.
  • Express ideas in an organized way.
  • Explain their mathematical thinking in writing.
  • Maintain a system for collecting, referring to, and sharing their work.
MATH: ALGEBRA, COURSE 451

Number Sense and Operations

  • Understand numbers and ways of representing numbers, relationships among numbers, and number systems.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number.
  • Recognize when and how to apply the field properties in problems using real numbers.
  • Express and simplify numerical expressions involving real numbers.
  • Pose and solve problems using operations on whole numbers, integers, rational, irrational, and complex numbers.
  • Simplify numerical expressions, including those involving positive integer exponents or the absolute value; apply such simplifications in the solution of problems.
  • Express and simplify numerical expressions involving real numbers.
  • Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator. e.g., .
  • Understand and demonstrate algebraically and graphically the relationship between operations and their inverses, including exponential.
  • Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
Data Analysis, Statistics, and Probability
  • Formulate questions that can be answered with data and collect, organize and display relevant data to answer them.
  • Select and use appropriate statistical methods to analyze data.
  • Develop and evaluate inferences and predictions that are based on data.
  • Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plot, box-and-whisker plot, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.
  • Use logical reasoning as well as estimation and mental computations to determine the validity of a solution in algebraic, geometric, and statistical problems.
  • Collect, organize, analyze and graph data from real problems (using graphing calculators and/or computers when appropriate) and express relationships between variables, verbally, graphically and symbolically.
  • Collect, organize, and analyze data from real problems using graphing calculators and other technology to create tables and graphs.
  • Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.
  • Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.
Patterns, Relations, and Algebra
  • Understand patterns, relations, and functions.
  • Represent and analyze mathematical situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative relationships.
  • Analyze change in various contexts.
  • Represent and analyze mathematical situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative relationships.
  • Analyze change in various contexts.
  • Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive linear, quadratic, functional relationships.
  • Demonstrate an understanding of relations and functions. Identify the domain, range, dependent, and independent variables of functions.
  • Translate between different representations of functions and relations: graphs, equations, point sets, and tabular.
  • Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.
  • Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.
  • Solve equations and apply to the solution of problems.
  • Evaluate exponential functions and compare the effects of different growth rates.
  • Describe compounding situations using exponential functions.
  • Evaluate exponential functions and draw their graphs with a graphing calculator. Construct examples of functions on finite sets using diagrams and tables.
  • Describe a sequence recursively and use that description to list its terms with a graphing calculator.
  • Describe a sequence algebraically and use that description to find specific terms.
  • Identify and describe real world examples of step functions.
  • Explain restrictions on the domains of functions.
  • Use graphs to represent functions and to find images of domain elements.
  • Interpret graphs of step function in real world situations.
Discussion, Presentation, Composition
  • Use agreed upon rules to participate in discussions in large and small groups.
  • Express ideas in an organized way.
  • Explain their mathematical thinking in writing.
  • Maintain a system for collecting, referring to, and sharing their work.
MATH: ALGEBRA /GEOMETRY, COURSE 452

Number Sense and Operations

  • Understand numbers and ways of representing numbers, relationships among numbers, and number systems.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Understand numbers, ways of representing numbers, relationships among numbers.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive numbers for any positive integer n.
  • Express and simplify numerical expressions involving real numbers.
  • Understand and demonstrate algebraically and graphically the relationship between operations and their inverses, including exponential.
  • Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
  • Express real numbers in fractional and radical form as well as in exponential form using integral and fractional exponents.
  • Use logical reasoning as well as estimation and mental computation to determine the validity of a solution in algebraic, and statistical problems.
Patterns, Relations, and Functions
  • Understand patterns, relations, and functions.
  • Represent and analyze mathematical situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative relationships.
  • Analyze change in various contexts.
  • Represent and analyze mathematical situations including geometric situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative relationships including geometric relationships.
  • Analyze change in various contexts.
  • Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive linear, quadratic, functional relationships.
  • Demonstrate an understanding of relations and functions. Identify the domain, range, dependent, and independent variables of functions.
  • Translate between different representations of functions and relations: graphs, equations, point sets, and tabular.
  • Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.
  • Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.
  • Solve equations and apply to the solution of problems including geometric problems.
  • Evaluate exponential functions and compare the effects of different growth rates.
  • Describe compounding situations using exponential functions.
  • Evaluate exponential functions and draw their graphs with a graphing calculator. Construct examples of functions on finite sets using diagrams and tables.
  • Describe a sequence recursively and use that description to list its terms with a graphing calculator
  • Describe a sequence algebraically and use that description to find specific terms.
  • Identify and describe real world examples of step functions.
  • Explain restrictions on the domains of functions.
  • Use graphs to represent functions and to find images of domain elements.
  • Interpret graphs of step function in real world situations.
Geometry
  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
  • Apply transformations and use symmetry to analyze mathematical situations.
  • Use visualization, spatial reasoning, and geometric modeling to solve problems.
  • Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry.
  • Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solution of problems.
  • Recognize special types of polygons (e.g., isosceles triangles, parallelograms, and rhombuses). Apply properties of sides, diagonals, and angles in special polygons; identify their parts and special segments (e.g., altitudes, mid-segments); determine interior angles for regular polygons. Draw and label sets of points such as line segments, rays, and circles. Detect symmetries of geometric figures.
  • Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of constructions. Justify the conjectures by logical arguments.
  • Use compass and straightedge to measure geometric figures to a high degree of accuracy.
  • Draw congruent and similar figures using a compass, straightedge, protractor, or computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments.
  • Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle.
  • Identify congruence and similarity correspondences and properties of the figures to find missing parts of geometric figures, and provide logical justification.
  • Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean Theorem.
  • Use the properties of special triangles (e.g., isosceles, equilateral, 30-60-90, 45-45-90) to solve everyday problems.
  • Using rectangular coordinates, calculate the midpoints of segments, slopes of lines, and distances between two points. Apply the results of these calculations to find the solution to everyday problems.
  • Demonstrate an understanding of the relationship between various representations of a line.
  • Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.
  • Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.
  • Explore and use properties of parallel and perpendicular lines, bisectors of angles and segments, triangles and circles through constructions.
  • Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems
  • Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.
  • Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems.
Measurement
  • Understand measurable attributes of objects and the units, systems, and processes of measurement.
  • Apply appropriate techniques, tools, and formulas to determine measurements.
  • Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
  • Use diagrams, models, and other manipulatives to determine methods of finding relationships and measurements of the two and three dimensional shapes.
  • Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements.
  • Use appropriate measurement tools along with calculators and computers to solve problems in science, technology, consumer education, and other areas as well.
Data Analysis, Statistics, and Probability
  • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
  • Select and use appropriate statistical methods to analyze data.
  • Develop and evaluate inferences and predictions that are based on data.
  • Understand and apply basic concepts of probability.
  • Use the basic set of operations with the help of Venn diagrams.
  • Solve counting problems using Venn diagrams.
  • Solving counting problems using Venn diagrams.
  • Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.
  • Understand and apply basic concepts of probability.
  • Use tree diagrams, tables, organized lists, basic combinations ("fundamental counting principle"), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice.
  • Carry out probability experiments, discuss the results.
  • Conduct experiments to determine experimental probabilities.
Discussion, Presentation, Composition
  • Use agreed upon rules to participate in discussions in large and small groups.
  • Express ideas in an organized way.
  • Explain their mathematical thinking in writing.
  • Maintain a system for collecting, referring to, and sharing their work.
MATH: GEOMETRY, COURSE 454

Number Sense and Operations

  • Understand numbers and ways of representing numbers, relationships among numbers, and number systems.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Understand numbers, ways of representing numbers, and relationships among numbers.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive numbers for any positive integer n.
  • Express and simplify numerical expressions involving real numbers.
  • Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
  • Express real numbers in fractional and radical form.
  • Use logical reasoning as well as estimation and mental computation to determine the validity of a solution in algebraic, geometric, and statistical problems.
Patterns, Relations, and Functions
  • Understand patterns, relations, and functions.
  • Represent and analyze mathematical situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative relationships.
  • Analyze change in various contexts.
  • Represent and analyze geometric situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative geometric relationships.
  • Analyze change in various contexts.
  • Use properties of the real number system to judge the validity of equations and inequalities, to prove or disprove geometric statements, and to justify every step in a sequential, geometric argument.
  • Translate between different geometric and algebraic representations of functions and relations: graphs, equations, point sets, and tabular.
  • Demonstrate an understanding of the relationship between various representations of a line.
  • Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "slope y-intercept" formulas.
  • Explain the significance of a positive, negative, zero, or undefined slope.
  • Find linear equations that represent lines parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.
  • Solve equations apply to the solution of everyday geometric problems.
Data Analysis, Statistics, and Probability
  • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
  • Select and use appropriate statistical methods to analyze data.
  • Develop and evaluate inferences and predictions that are based on data.
  • Understand and apply basic concepts of probability.
  • Use the basic set of operations with the help of Venn diagrams.
  • Solve counting problems using Venn diagrams.
  • Solving counting problems using Venn diagrams.
  • Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.
  • Understand and apply basic concepts of probability.
  • Use tree diagrams, tables, organized lists, basic combinations ("fundamental counting principle"), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice.
  • Carry out probability experiments, discuss the results.
  • Conduct experiments to determine experimental probabilities and construct a table to establish theoretical
Geometry
  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
  • Apply transformations and use symmetry to analyze mathematical situations.
  • Use visualization, spatial reasoning, and geometric modeling to solve problems.
  • Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry.
  • Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solution of problems.
  • Recognize special types of polygons (e.g., isosceles triangles, parallelograms, and rhombuses). Apply properties of sides, diagonals, and angles in special polygons; identify their parts and special segments (e.g., altitudes, midsegments); determine interior angles for regular polygons. Draw and label sets of points such as line segments, rays, and circles. Detect symmetries of geometric figures.
  • Apply congruence and similarity correspondences and properties of the figures to find missing parts of geometric figures and to provide logical justifications.
  • Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of constructions. Justify the conjectures by logical arguments.
  • Use compass and straightedge to measure geometric figures to a high degree of accuracy
  • Draw congruent and similar figures using a compass, straightedge, protractor, or computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments.
  • Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle.
  • Apply properties of angles, parallel lines, arcs, radii, chords, tangents and secants to solve everyday problems.
  • Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean Theorem.
  • Use the properties of special triangles (e.g., isosceles, equilateral, 30-60-90, 45-45-90) to solve everyday problems.
  • Using rectangular coordinates, calculate the midpoints of segments, slopes of lines, and distances between two points. Apply the results of these calculations to find the solution to everyday problems.
  • Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.
  • Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.
  • Explore and use properties of parallel and perpendicular lines, bisectors of angles and segments, triangles and circles through constructions.
  • Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems.
  • Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.
  • Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems.
  • Demonstrate an understanding of the relationship between geometric and algebraic representations of circles.
  • Apply algebraic and geometric principles and practices to solve everyday problems involving circles.
  • Demonstrate the ability to visualize solid objects and to recognize their projections and cross sections.
Measurement
  • Understand measurable attributes of objects and the units, systems, and processes of measurement.
  • Apply appropriate techniques, tools, and formulas to determine measurements.
  • Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
  • Use diagrams, models, and other manipulatives to determine methods of finding relationships and measurements of the two and three-dimensional shapes.
  • Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements.
  • Relate geometric and algebraic representations of lines, simple curves, and conic sections.
  • Use appropriate measurement tools along with calculators and computers to solve everyday geometric problems in science, technology, consumer education, and other areas as well.
Discussion, Presentation, Composition
  • Use agreed upon rules to participate in discussions in large and small groups.
  • Express ideas in an organized way.
  • Explain their mathematical thinking in writing.
  • Maintain a system for collecting, referring to, and sharing their work.
MATH: ADVANCED ALGEBRA, COURSE 456

Number Sense and Operations

  • Understand numbers and ways of representing numbers, relationships among numbers, and number systems.
  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.
  • Define complex numbers (e.g., a + bi) and operations on them, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers.
  • Simplify numerical expressions with powers and roots, fractional and negative exponents.
Patterns Relations and Algebra
  • Understand patterns, relations, and functions.
  • Represent and analyze mathematical situations and structures using algebraic symbols.
  • Use mathematical models to represent and understand quantitative relationships.
  • Analyze change in various contexts.
  • Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive patterns.
  • Identify arithmetic and geometric sequences and finite arithmetic and geometric series. Use the properties of such sequences and series to solve problems, including finding the formula for the general term and the sum, recursively and explicitly.
  • Demonstrate an understanding of the binomial theorem; use it in the solution of problems.
  • Demonstrate an understanding of polynomial and rational functions.
  • Apply polynomial and rational functions to solve "real world" problems.
  • Demonstrate an understanding of the exponential and logarithmic functions.
  • Apply exponential and logarithmic functions to solve "real world" problems.
  • Perform operations on functions, including composition.
  • Find inverses of functions.
  • Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential.
  • Find solutions to quadratic equations (with real coefficients and real or complex roots) and apply to the solutions of problems.
  • Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula; use graphing calculator technology where appropriate. Include polynomial, exponential, and logarithmic functions; expressions involving the absolute values; and simple rational expressions.
  • Use matrices to solve systems of linear equations; apply to the solution of everyday problems.
  • Use symbolic, numeric, and graphical methods to solve systems of equations and/or inequalities involving algebraic, exponential, and logarithmic expressions; use technology where appropriate.
  • Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, and step functions, absolute values and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include growth and decay; logistic growth; joint (e.g., I = Prt, y = k(w1 + w2)), and combined (F = G(m1m2)/d2) variation.
  • Identify maximum and minimum values of functions in simple situations; apply to the solution of everyday problems.
  • Describe the translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = af (b(x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, and logarithmic functions.
Geometry
  • Analyze characteristics and properties of two-dimensional and three-dimensional geometric shapes and develop mathematical arguments about geometrical relationships.
  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
  • Apply transformations and use symmetry to analyze mathematical situations.
  • Use visualization, spatial reasoning, and geometric modeling to solve problems.
  • Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.
  • Find values of trigonometric functions for acute angles.
  • Solve everyday problems involving right triangles.
  • Derive and apply basic trigonometric identities (e.g., sin2q + cos2q = 1, tan2q + 1 = sec2q) and the laws of sines and cosines.
  • Relate geometric and algebraic representations of lines, simple curves, and conic sections.
  • Change radian measure to degree measure and vice versa.
  • Identify coterminal angles.
  • Find values of trigonometric functions for general angles.
  • Use reference angles to find the values of trigonometric functions.
  • Solve everyday problems using the Law of Sines and the Law of Cosines.
Data Analysis, Statistics, and Probability
  • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
  • Select and use appropriate statistical methods to analyze data.
  • Develop and evaluate inferences and predictions that are based on data.
  • Understand and apply basic concepts of probability.
  • Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data.
  • Find measures of variation for a set of data.
  • Use combinatorics (e.g., "fundamental counting principle," permutations, combinations) to compute probabilities of compound events and solve other problems; use technology as appropriate.
  • Find the probability of two independent events; of two dependent events.
  • Solve everyday problems involving the probability of independent or dependent events.
  • Determine whether a set of data appears to be normally distributed of skewed.
  • Solve everyday problems involving normally distributed data.
Discussion, Presentation, Composition
  • Use agreed upon rules to participate in discussions in large and small groups.
  • Express ideas in an organized way.
  • Explain their mathematical thinking in writing.
  • Maintain a system for collecting, referring to, and sharing their work.
SCIENCE

Earth and Space Science

  • Explain how the transfer of energy through radiation, conduction, and convection contributes to global atmospheric processes, e.g., storms, winds.
  • Explain how the revolution of the earth and the inclination of the axis of the earth cause the earth's seasonal variations (equinoxes and solstices).
  • Explain the dynamics of oceanic currents, including upwelling, density and deep water currents, the local Labrador Current, and the Gulf Stream, and their relationship to global circulation within the marine environment and climate.
  • Describe how glaciers, gravity, wind, temperature changes, waves, and rivers cause weathering and erosion. Give examples of how the effects of these processes can be seen in our local environment.
  • Describe the absolute and relative dating methods used to measure geologic time, e.g., index fossils, radioactive dating, law of superposition, and cross-cutting relationships.
  • Trace the development of a lithospheric plate from its growing margin at a divergent boundary (mid-ocean ridge) to its destructive margin at a convergent boundary (subduction zone). Explain the relationship between convection currents and the motion of the lithospheric plates.
  • Explain how the sun, earth, and solar system formed from a nebula of dust and gas in a spiral arm of the Milky Way Galaxy about 4.6 billion years ago.
Biology
  • Describe the composition and functions of the four major categories of organic molecules (carbohydrates, lipids, proteins, and nucleic acids).
  • Relate cell parts/organelles to their function.
  • Distinguish between plant and animal cells.
  • Explain the role of cell membranes as a highly selective barrier (diffusion, osmosis, and active transport).
  • Describe and compare the processes of mitosis and meiosis, and their role in the cell cycle.
  • Describe the structure and function of DNA, and distinguish among replication, transcription, and translation.
  • Use a Punnett Square to determine the genotype and phenotype of monohybrid crosses.
Chemistry
  • Identify and explain some of the physical properties that are used to classify matter, e.g., density, melting point, ad boiling point.
  • Explain the difference between mixtures and pure substances.
  • Describe the four states of matter (solid, liquid, gas, plasma) in terms of energy, particle motion, and phase transitions.
  • Identify the major components of the nuclear atom (protons, neutrons, and electrons) and explain how they interact.
  • Compare nuclear fission and nuclear fusion and mass defect.
  • Explain the relationship al an element's position on the periodic table to its atomic number and mass.
  • Explain how atoms combine to form compounds through both ionic and covalent bonding.
  • Identify and explain the factors that affect the rate of dissolving, i.e., temperature, concentration, and mixing.
Physics
  • Explain the relationship between mass and inertia.
  • Interpret and apply Newton's first law of motion.
  • Interpret and apply Newton's second law of motion to show how an object's motion will change only when a net force is applied.
  • Interpret and provide examples that illustrate the law of conservation of energy.
  • Differentiate between wave motion (simple harmonic nonlinear motion) and the motion of objects (nonharmonic).
  • Recognize the measurable properties of waves (e.g., velocity, frequency, wavelength) and explain the relationships among them.
  • Distinguish between mechanical and electromagnetic wave.
Scientific Inquiry
  • Use simple tools such as rulers, magnifiers, balances, thermometers, graduated cylinders, etc to observe and measure things carefully.
  • Design and conduct simple science experiments using appropriate controls, variables, equipment and measuring tools. Some questions may be posed by the student and some will be posed by the teacher.
  • Predict, observe, classify and record results clearly in journals or logs.
  • Use technology and mathematics to improve investigations and communications.
  • Communicate scientific procedures and explanations using presentations, charts, simple graphs, discussions and writing.
  • Develop descriptions, explanations, predictions, and models using evidence.
  • Compare results and explanations with scientific knowledge.
Discussion and Presentation
  • Participate in formal and informal discussions in large and small groups, using agreed upon rules to conduct and facilitate them.
  • Organize and present their thoughts in a logical manner.
  • Support their ideas with evidence or details; expect and request the same of others.
  • Actively listen, respond to, and build on ideas generated during discussions.
  • Use the information to inform or change their perspectives.
  • Ask for clarification when others' responses are unclear.
  • Summarize and evaluate what they have learned from the discussion.
  • Evaluate the productivity of discussions using established criteria; make suggestions to improve the discussions.
  • Give oral presentations, using established criteria to prepare, assess, and improve their presentations.
Composition
  • Write frequently in response to readings, other presentations, and observations (e.g., summaries, questions, reactions, connections, predictions, reports).
  • Maintain a system for collecting, referring to, and sharing their thoughts, observations, writings, illustrations, and other work.
  • Write occasional, brief research reports to extend their knowledge beyond classroom presentations; include a clear focus and supporting details.
  • Write, share, assess, and revise frequent responses to MCAS-like, open response (key) questions posed by the teacher.