Fifth Grade Standards
Mathematics
By the end of grade five, students increase their facility with the four basic arithmetic operations applied to fractions, decimals, and positive and negative numbers. They know and use common measuring units to determine length and area and know and use formulas to determine the volume of simple geometric figures. Students know the concept of angle measurement and use a protractor and compass to solve problems. They use grids, tables, graphs, and charts to record and analyze data.
Number Sense
1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers:
1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.
1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.
1.3 Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication.
1.4 Determine the prime factors of all the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2x2x2x3 =23 x 3).
1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.
2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals:
2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.
2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.
2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form.
2.4 Understand the concept of multiplication and division of fractions.
2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.
Algebra and Functions
1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results:
1.1 Use information taken from a graph or equation to answer questions about a problem situation.
1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.
1.3 Know and use the distributive property in equations and expressions with variables.
1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane.
1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid.
Measurement and Geometry
1.0 Students understand and compute the volumes and areas of simple objects:
1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram).
1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects.
1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm 3], cubic meter [m3], cubic inch [in3] cubic yard [yd3]) to compute the volume of rectangular solids.
1.4 Differentiate between, and use appropriate units of measures for, two- and three-dimensional objects (i.e., find the perimeter, area, volume).
2.0 Students identify, describe, and classify the properties of, and the relation-ships between, plane and solid geometric figures:
2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software).
2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems.
2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.
Statistics, Data Analysis, and Probability
1.0 Students display, analyze, compare, and interpret different data sets, including data sets of different sizes:
1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ.
1.2 Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets.
1.3 Use fractions and percentages to compare data sets of different sizes.
1.4 Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph.
1.5 Know how to write ordered pairs correctly; for example, (x, y).
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
1.2 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.4 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.
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual under-standing of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and apply them in other circumstances.
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.
Word Recognition
1.1 Read aloud narrative and expository text fluently and accurately and with appropriate pacing, intonation, and expression.
Vocabulary and Concept Development
1.2 Use word origins to determine the meaning of unknown words.
1.3 Understand and explain frequently used synonyms, antonyms, and homographs.
1.4 Know abstract, derived roots and affixes from Greek and Latin and use this knowledge to analyze the meaning of complex words (e.g., controversial).
1.5 Understand and explain the figurative and metaphorical use of words in context.
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 five, students make progress toward this goal.
Structural Features of Informational Materials
2.1 Understand how text features (e.g., format, graphics, sequence, diagrams, illustrations, charts, maps) make information accessible and usable.
2.2 Analyze text that is organized in sequential or chronological order.
Comprehension and Analysis of Grade-Level-Appropriate Text
2.3 Discern main ideas and concepts presented in texts, identifying and assessing evidence that supports those ideas.
2.4 Draw inferences, conclusions, or generalizations about text and support them with textual evidence and prior knowledge.
Expository Critique
2.5 Distinguish facts, supported inferences, and opinions in text.
3.0 Literary Response and Analysis
Students read and respond to historically or culturally significant works of literature. They begin to find ways to clarify the ideas and make connections between 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 Identify and analyze the characteristics of poetry, drama, fiction, and nonfiction and explain the appropriateness of the literary forms chosen by an author for a specific purpose.
Narrative Analysis of Grade-Level-Appropriate Text
3.2 Identify the main problem or conflict of the plot and explain how it is resolved.
3.3 Contrast the actions, motives (e.g., loyalty, selfishness, conscientiousness), and appearances of characters in a work of fiction and discuss the importance of the contrasts to the plot or theme.
3.4 Understand that theme refers to the meaning or moral of a selection and recognize themes (whether implied or stated directly) in sample works.
3.5 Describe the function and effect of common literary devices (e.g., imagery, metaphor, symbolism).
Literary Criticism
3.6 Evaluate the meaning of archetypal patterns and symbols that are found in myth and tradition by using literature from different eras and cultures.
3.7 Evaluate the author's use of various techniques (e.g., appeal of characters in a picture book, logic and credibility of plots and settings, use of figurative language) to influence readers' perspectives.
Writing
1.0 Writing Strategies
Students write clear, coherent, and focused essays. The writing exhibits the 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 multiple-paragraph narrative compositions:
a. Establish and develop a situation or plot.
b. Describe the setting.
c. Present an ending.
1.2 Create multiple-paragraph expository compositions:
a. Establish a topic, important ideas, or events in sequence or chronological order.
b. Provide details and transitional expressions that link one paragraph to another in a clear line of thought.
c. Offer a concluding paragraph that summarizes important ideas and details.
Research and Technology
1.3 Use organizational features of printed text (e.g., citations, end notes, bibliographic references) to locate relevant information.
1.4 Create simple documents by using electronic media and employing organizational features (e.g., passwords, entry and pull-down menus, word searches, the thesaurus, spell checks).
1.5 Use a thesaurus to identify alternative word choices and meanings.
Evaluation and Revision
1.6 Edit and revise manuscripts to improve the meaning and focus of writing by adding, deleting, consolidating, clarifying, and rearranging words and sentences.
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. Student 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 five outlined in Writing Standard 1.0, students:
2.1 Write narratives:
a. Establish a plot, point of view, setting, and conflict.
b. Show, rather than tell, the events of the story.
2.2 Write responses to literature:
a. Demonstrate an understanding of a literary work.
b. Support judgments through references to the text and to prior knowledge.
c. Develop interpretations that exhibit careful reading and understanding.
2.3 Write research reports about important ideas, issues, or events by using the following guidelines:
a. Frame questions that direct the investigation.
b. Establish a controlling idea or topic.
c. Develop the topic with simple facts, details, examples, and explanations.
2.4 Write persuasive letters or compositions:
a. State a clear position in support of a proposal.
b. Support a position with relevant evidence.
c. Follow a simple organizational pattern.
d. Address reader concerns.
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 this grade level.
Sentence Structure
1.1 Identify and correctly use prepositional phrases, appositives, and independent and dependent clauses; use transitions and conjunctions to connect ideas.
Grammar
1.2 Identify and correctly use verbs that are often misused (e.g., lie/lay, sit/set, rise/raise), modifiers, and pronouns.
Punctuation
1.3 Use a colon to separate hours and minutes and to introduce a list; use quotation marks around the exact words of a speaker and titles of poems, songs, short stories, and so forth.
Capitalization
1.4 Use correct capitalization.
Spelling
1.5 Spell roots, suffixes, prefixes, contractions, and syllable constructions correctly.
Listening and Speaking
1.0 Listening and Speaking Strategies
Students deliver focused, coherent presentations that convey ideas clearly and relate to the background and interests of the audience. They evaluate the content of oral communication.
Comprehension
1.1 Ask questions that seek information not already discussed.
1.2 Interpret a speaker's verbal and nonverbal messages, purposes, and perspectives.
1.3 Make inferences or draw conclusions based on an oral report.
Organization and Delivery of Oral Communication
1.4 Select a focus, organizational structure, and point of view for an oral presentation.
1.5 Clarify and support spoken ideas with evidence and examples.
1.6 Engage the audience with appropriate verbal cues, facial expressions, and gestures.
Analysis and Evaluation of Oral and Media Communications
1.7 Identify, analyze, and critique persuasive techniques (e.g., promises, dares, flattery, glittering generalities); identify logical fallacies used in oral presentations and media messages.
1.8 Analyze media as sources for information, entertainment, persuasion, interpretation of events, and transmission of culture.
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 five outlined in Listening and Speaking Standard 1.0, students:
2.1 Deliver narrative presentations:
a. Establish a situation, plot, point of view, and setting with descriptive words and phrases.
b. Show, rather than tell, the listener what happens.
2.2 Deliver informative presentations about an important idea, issue, or event by the following means:
a. Frame questions to direct the investigation.
b. Establish a controlling idea or topic.
c. Develop the topic with simple facts, details, examples, and explanations.
2.3 Deliver oral responses to literature:
a. Summarize significant events and details.
b. Articulate an understanding of several ideas or images communicated by the literary work.
c. Use examples or textual evidence from the work to support conclusions.
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