Seventh Grade Standards
Mathematics
By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. Students know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students make conversions between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another. They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest. They graph linear functions and understand the idea of slope and its relation to ratio.
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
1.4 Differentiate between rational and irrational numbers.
1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.
1.6 Calculate the percentage of increases and decreases of a quantity.
1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
2.0 Students use exponents, powers, and roots and use exponents in working with fractions:
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
2.2 Add and subtract fractions by using factoring to find common denominators.
2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
Algebra and Functions
1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:
1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2 .
1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.
1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
2.0 Students interpret and evaluate expressions involving integer powers and simple roots:
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
3.0 Students graph and interpret linear and some nonlinear functions:
3.1 Graph functions of the form y = nx2 and y = nx 3 and use in solving problems.
3.2 Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths).
3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio ("rise over run") is called the slope of a graph.
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantity.
4.0 Students solve simple linear equations and inequalities over the rational numbers:
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
Measurement and Geometry
1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
1.2 Construct and read drawings and models made to scale.
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.
2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.
2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1in3] = [16.38 cm3]).
3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.
3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.
3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
3.5 Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.
3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).
Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.
1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).
1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.
Mathematical Reasoning
2.0 Students make decisions about how to approach problems:
2.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
2.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
2.3 Determine when and how to break a problem into simpler parts.
3.0 Students use strategies, skills, and concepts in finding solutions:
3.1 Use estimation to verify the reasonableness of calculated results.
3.2 Apply strategies and results from simpler problems to more complex problems.
3.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
3.4 Make and test conjectures by using both inductive and deductive reasoning.
3.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
3.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
3.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
3.8 Make precise calculations and check the validity of the results from the context of the problem.
4.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:
4.1 Evaluate the reasonableness of the solution in the context of the original situation.
4.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
4.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
Reading/Language Arts Standards
READING
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students use their knowledge of word origins and word relationships, as well as historical and literary context clues, to determine the meaning of specialized vocabulary and to understand the precise meaning of grade-level-appropriate words.
Vocabulary and Concept Development
1.1 Identify idioms, analogies, metaphors, and similes in prose and poetry.
1.2 Use knowledge of Greek, Latin, and Anglo-Saxon roots and affixes to understand content-area vocabulary.
1.3 Clarify word meanings through the use of definition, example, restatement, or contrast.
2.0 Reading Comprehension (Focus on Informational Materials)
Students read and understand grade-level-appropriate material. They describe and connect the essential ideas, arguments, and perspectives of the text by using their knowledge of text structure, organization, and purpose. The selections in Recommended Readings in Literature, Kindergarten Through Grade Eight illustrate the quality and complexity of the materials to be read by students. In addition, by grade eight, students read one million words annually on their own, including a good representation of grade-level-appropriate narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information). In grade seven, students make substantial progress toward this goal.
Structural Features of Informational Materials
2.1 Understand and analyze the differences in structure and purpose between various categories of informational materials (e.g., textbooks, newspapers, instructional manuals, signs).
2.2 Locate information by using a variety of consumer, workplace, and public documents.
2.3 Analyze text that uses the cause-and-effect organizational pattern.
Comprehension and Analysis of Grade-Level-Appropriate Text
2.4 Identify and trace the development of an author's argument, point of view, or perspective in text.
2.5 Understand and explain the use of a simple mechanical device by following technical directions.
Expository Critique
2.6 Assess the adequacy, accuracy, and appropriateness of the author's evidence to support claims and assertions, noting instances of bias and stereotyping.
3.0 Literary Response and Analysis
Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They clarify the ideas and connect them to other literary works. The selections in Recommended Readings in Literature, Kindergarten Through Grade Eight illustrate the quality and complexity of the materials to be read by students.
Structural Features of Literature
3.1 Articulate the expressed purposes and characteristics of different forms of prose (e.g., short story, novel, novella, essay).
Narrative Analysis of Grade-Level-Appropriate Text
3.2 Identify events that advance the plot and determine how each event explains past or present action(s) or foreshadows future action(s).
3.3 Analyze characterization as delineated through a character's thoughts, words, speech patterns, and actions; the narrator's description; and the thoughts, words, and actions of other characters.
3.4 Identify and analyze recurring themes across works (e.g., the value of bravery, loyalty, and friendship; the effects of loneliness).
3.5 Contrast points of view (e.g., first and third person, limited and omniscient, subjective and objective) in narrative text and explain how they affect the overall theme of the work.
Literary Criticism
3.6 Analyze a range of responses to a literary work and determine the extent to which the literary elements in the work shaped those responses.
Writing
1.0 Writing Strategies
Students write clear, coherent, and focused essays. The writing exhibits students' awareness of the audience and purpose. Essays contain formal introductions, supporting evidence, and conclusions. Students progress through the stages of the writing process as needed.
Organization and Focus
1.1 Create an organizational structure that balances all aspects of the composition and uses effective transitions between sentences to unify important ideas.
1.2 Support all statements and claims with anecdotes, descriptions, facts and statistics, and specific examples.
1.3 Use strategies of notetaking, outlining, and summarizing to impose structure on composition drafts.
Research and Technology
1.4 Identify topics; ask and evaluate questions; and develop ideas leading to inquiry, investigation, and research.
1.5 Give credit for both quoted and paraphrased information in a bibliography by using a consistent and sanctioned format and methodology for citations.
1.6 Create documents by using word-processing skills and publishing programs; develop simple databases and spreadsheets to manage information and prepare reports.
Evaluation and Revision
1.7 Revise writing to improve organization and word choice after checking the logic of the ideas and the precision of the vocabulary.
2.0 Writing Applications (Genres and Their Characteristics)
Students write narrative, expository, persuasive, and descriptive texts of at least 500 to 700 words in each genre. The writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in Writing Standard 1.0. Using the writing strategies of grade seven outlined in Writing Standard 1.0, students:
2.1 Write fictional or autobiographical narratives:
a. Develop a standard plot line (having a beginning, conflict, rising action, climax, and denouement) and point of view.
b. Develop complex major and minor characters and a definite setting.
c. Use a range of appropriate strategies (e.g., dialogue; suspense; naming of specific narrative action, including movement, gestures, and expressions).
2.2 Write responses to literature:
a. Develop interpretations exhibiting careful reading, understanding, and insight.
b. Organize interpretations around several clear ideas, premises, or images from the literary work.
c. Justify interpretations through sustained use of examples and textual evidence.
2.3 Write research reports:
a. Pose relevant and tightly drawn questions about the topic.
b. Convey clear and accurate perspectives on the subject.
c. Include evidence compiled through the formal research process (e.g., use of a card catalog, Reader's Guide to Periodical Literature, a computer catalog, magazines, newspapers, dictionaries).
d. Document reference sources by means of footnotes and a bibliography.
2.4 Write persuasive compositions:
a. State a clear position or perspective in support of a proposition or proposal.
b. Describe the points in support of the proposition, employing well-articulated evidence.
c. Anticipate and address reader concerns and counter-arguments.
2.5 Write summaries of reading materials:
a. Include the main ideas and most significant details.
b. Use the student's own words, except for quotations.
c. Reflect underlying meaning, not just the superficial details.
Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.
1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to the grade level.
Sentence Structure
1.1 Place modifiers properly and use the active voice.
Grammar
1.2 Identify and use infinitives and participles and make clear references between pronouns and antecedents.
1.3 Identify all parts of speech and types and structure of sentences.
1.4 Demonstrate the mechanics of writing (e.g., quotation marks, commas at end of dependent clauses) and appropriate English usage (e.g., pronoun reference).
Punctuation
1.5 Identify hyphens, dashes, brackets, and semicolons and use them correctly.
Capitalization
1.6 Use correct capitalization.
Spelling
1.7 Spell derivatives correctly by applying the spellings of bases and affixes.
Listening and Speaking
1.0 Listening and Speaking Strategies
Deliver focused, coherent presentations that convey ideas clearly and relate to the background and interests of the audience. Students evaluate the content of oral communication.
Comprehension
1.1 Ask probing questions to elicit information, including evidence to support the speaker's claims and conclusions.
1.2 Determine the speaker's attitude toward the subject.
1.3 Respond to persuasive messages with questions, challenges, or affirmations.
Organization and Delivery of Oral Communication
1.4 Organize information to achieve particular purposes and to appeal to the background and interests of the audience.
1.5 Arrange supporting details, reasons, descriptions, and examples effectively and persuasively in relation to the audience.
1.6 Use speaking techniques, including voice modulation, inflection, tempo, enunciation, and eye contact, for effective presentations.
Analysis and Evaluation of Oral and Media Communications
1.7 Provide constructive feedback to speakers concerning the coherence and logic of a speech's content and delivery and its overall impact upon the listener.
1.8 Analyze the effect on the viewer of images, text, and sound in electronic journalism; identify the techniques used to achieve the effects in each instance studied.
2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver well-organized formal presentations employing traditional rhetorical strategies (e.g., narration, exposition, persuasion, description). Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0. Using the speaking strategies of grade seven outlined in Listening and Speaking Standard 1.0, students:
2.1 Deliver narrative presentations:
a. Establish a context, standard plot line (having a beginning, conflict, rising action, climax, and denouement), and point of view.
b. Describe complex major and minor characters and a definite setting.
c. Use a range of appropriate strategies, including dialogue, suspense, and naming of specific narrative action (e.g., movement, gestures, expressions).
2.2 Deliver oral summaries of articles and books:
a. Include the main ideas of the event or article and the most significant details.
b. Use the student's own words, except for material quoted from sources.
c. Convey a comprehensive understanding of sources, not just superficial details.
2.3 Deliver research presentations:
a. Pose relevant and concise questions about the topic.
b. Convey clear and accurate perspectives on the subject.
c. Include evidence generated through the formal research process (e.g., use of a card catalog, Reader's Guide to Periodical Literature, computer databases, magazines, newspapers, dictionaries).
d. Cite reference sources appropriately.
2.4 Deliver persuasive presentations:
a. State a clear position or perspective in support of an argument or proposal.
b. Describe the points in support of the argument and employ well-articulated evidence.
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