==================== KINDERGARTEN ====================

English Language Arts (ELA) standards

■ Naming upper- and lower-case letters, matching those letters with their sounds, and printing them
■ Comparing the adventures and experiences of characters in familiar stories, such as fairy tales and folktales
■ Retelling familiar stories and talking about stories read to them using details from the text
■ Using a combination of drawing, dictating, and writing to describe an event, including his or her reaction to what happened
■ Stating an opinion or preference about a topic or book in writing (e.g., “My favorite book is . . .”)
■ Taking part in classroom conversations and following rules for discussions (e.g., learning to listen to others and taking turns when speaking)
■ Speaking clearly to express thoughts, feelings, and ideas, including descriptions of familiar people, places, things, and events
■ Asking and answering questions about key details in stories or other information read aloud
■ Understanding and using question words (e.g., who, what, where, when, why, how) in discussions
■ Learning to recognize, spell, and properly use those little grammatical words that hold the language together (e.g., a, the, to, of, from, I, is, are)

ELA Enrichment

■ Read with your child every day, books like Are You My Mother by P.D. Eastman or Green Eggs and Ham by Dr. Seuss. Ask your child to explain his or her favorite parts of the story. Share your own ideas. To find more books for your child to read, visit www.corestandards.org/assets/Appendix_B.pdf.
■ Encourage your child to tell you about his or her day at school. Keep paper, markers, or crayons around the house for your child to write letters or words or draw a picture about his or her day. Have your child describe the picture to you.
■ Play word games like I Spy, sing songs like Itsy Bitsy Spider, and make silly rhymes together.

Math standards

■ Counting objects to tell how many there are
■ Comparing two groups of objects to tell which group, if either, has more; comparing two written numbers to tell which is greater
■ Acting out addition and subtraction word problems and drawing diagrams to represent them
■ Adding with a sum of 10 or less; subtracting from a number 10 or less; and solving addition and subtraction word problems
■ Adding and subtracting very small numbers quickly and accurately (e.g., 3 + 1)
■ Correctly naming shapes regardless of orientation or size (e.g., a square oriented as a “diamond” is still a square)

Math Enrichment

Look for “word problems” in real life. Some kindergarten examples might include:
■ Play “Write the next number.” You write a number, and your child writes the next number.
■ Ask your child questions that require counting as many as 20 things. For example, ask, “How many books do you have about wild animals?”
■ Ask your child questions that require comparing numbers. “Who is wearing more bracelets, you or your sister?” (Your child might use matching or counting to find the answer.)


==================== FIRST GRADE ====================

English Language Arts (ELA) standards

■ Using phonics (matching letters and sounds) and word analysis skills to figure out unfamiliar words when reading and writing
■ Describing characters, settings, and major events in a story, using key details
■ Getting facts and information from different writings
■ Writing about a topic, supplying some facts, and providing some sense of opening and closing
■ Participating in shared research and writing projects (e.g., exploring a number of “how-to” books and using them to write a sequence of instructions)
■ Taking part in conversations about topics and texts being studied by responding to the comments of others and asking questions to clear up any confusion
■ Describing people, places, things, and events with relevant details, expressing ideas and feelings clearly and with complete sentences
■ Producing and expanding complete simple and compound statements, questions, commands, and exclamations
■ Identifying the correct meaning for a word with multiple meanings, based on the sentence or paragraph in which the word is used (e.g., deciding whether the word bat means a flying mammal or a club used in baseball)
■ Learning to think about finer distinctions in the meanings of near-synonyms (e.g., marching, prancing, strutting, strolling, walking)

ELA Enrichment

■ Encourage your child to read to you books such as Little Bear by Else Holmelund Minarik. Help him or her sound out difficult words. To find more books for your child to read, visit www.corestandards.org/assets/Appendix_B.pdf.
■ Act out stories together from books, television, or your child’s imagination.
■ Pick a “word of the day” each day starting with a different letter. Have your child write the word and look for other things beginning with the same letter.
■ Visit the library with your child every week. Have your child sign up for a library card.

Math standards

■ Solving addition and subtraction word problems in situations of adding to, taking from, putting together, taking apart, and comparing (e.g., a taking from situation would be: “Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?”)
■ Adding with a sum of 20 or less, and subtracting from a number 20 or less, for example by using strategies based around the number 10 (e.g., to solve 13 – 4, one can start with 13, subtract 3 to reach 10, and then subtract 1 more to reach 9)
■ Quickly and accurately adding with a sum of 10 or less, and quickly and accurately subtracting from a number 10 or less (e.g., 2 + 5, 7 – 5)
■ Understanding what the digits mean in two-digit numbers (place value)
■ Using understanding of place value to add and subtract (e.g., 38 + 5, 29 + 20, 64 + 27, 80 – 50)
■ Measuring lengths of objects by using a shorter object as a unit of length
■ Making composite shapes by joining shapes together, and dividing circles and rectangles into halves or fourths

Math Enrichment

Look for “word problems” in real life. Some 1st grade examples might include:
■ If you open a new carton of a dozen eggs, and you use four eggs to cook dinner, close the carton and ask your child how many eggs are left.
■ While putting away toys into bins, count the number of toys in two bins and ask your child how many more are in one bin compared to the other.
■ Play the “I’m thinking of a number” game. For example, “I’m thinking of a number that makes 11 when added to 8. What is my number?”


==================== SECOND GRADE ====================

English Language Arts (ELA) standards

■ Paying close attention to details, including illustrations and graphics, in stories and books to answer who, what, where, when, why, and how questions
■ Determining the lesson or moral of stories, fables, and folktales
■ Using text features (e.g., captions, bold print, indexes) to locate key facts or information efficiently
■ Writing an opinion about a book he or she has read, using important details from the materials to support that opinion
■ Writing stories that include a short sequence of events and include a clear beginning, middle, and end
■ Participating in shared research projects (e.g., read books on a single topic to produce a report)
■ Taking part in conversations by linking his or her comments to the remarks of others and asking and answering questions to gather additional information or deepen understanding of the topic
■ Retelling key information or ideas from media or books read aloud
■ Producing, expanding, and rearranging sentences (e.g., “The boy watched the movie”; “The little boy watched the movie”; “The action movie was watched by the little boy”)
■ Determining the meaning of the new word formed when a known prefix or suffix is added to a known word (happy/unhappy; pain/painful/painless)

ELA Enrichment

■ Read at home every day and assist your child by reading every other paragraph. Encourage your child to read to younger siblings, cousins, or other children you know. To find recommendations of books for your child to read, visit www.corestandards.org/assets/Appendix_B.pdf.
■ Have your child write a thank you note or letter to family members or friends.
■ Ask your librarian to suggest books about people or places that are important to your child or family that you can read together. Encourage your child to explain what he or she has just read.

Math standards

■ Solving challenging addition and subtraction word problems with one or two steps (e.g., a “one-step” problem would be: “Lucy has 23 fewer apples than Julie. Julie has 47 apples. How many apples does Lucy have?”)
■ Quickly and accurately adding with a sum of 20 or less (e.g., 11 + 8); quickly and accurately subtracting from a number 20 or less (e.g., 16 – 9); and knowing all sums of one-digit numbers from memory by the end of the year
■ Understanding what the digits mean in three-digit numbers (place value)
■ Using understanding of place value to add and subtract three-digit numbers (e.g., 811 – 367); adding and subtracting two-digit numbers quickly and accurately (e.g., 77 – 28)
■ Measuring and estimating length in standard units
■ Solving addition and subtraction word problems involving length (e.g., “The pen is 2 cm longer than the pencil. If the pencil is 7 cm long, how long is the pen?”)
■ Building, drawing, and analyzing 2-D and 3-D shapes to develop foundations for area, volume, and geometry in later grades

Math Enrichment
Look for “word problems” in real life. Some 2nd grade examples might include:
■ When saving for a purchase, compare the cost of the item to the amount of money you have; then ask your child to determine how much more money he or she needs to buy the item.
■ When measuring your child’s height, ask how many inches he or she has grown since the very first measurement.
■ Play “draw the shape.” For example, ask your child to draw a hexagon with one side longer than the others, or ask him or her to shade in a quarter of a rectangle.


==================== THIRD GRADE ====================

English Language Arts (ELA) standards

Reading closely to find main ideas and supporting details in a story
■ Describing the logical connection between particular sentences and paragraphs in stories (e.g., first, second, third; cause and effect)
■ Comparing the most important points and key details presented in two books on the same topic
■ Writing opinions or explanations that group related information and develop topics with facts and details
■ Writing stories that establish a situation and include details and clear sequences of events that describe the actions, thoughts, and feelings of characters
■ Independently conducting short research projects that build knowledge about various topics
■ Asking and answering questions about information he or she hears from a speaker or while participating in classroom discussions, offering appropriate elaboration and detail that build on what others have said
■ Reading stories and poems aloud fluently, without pausing to figure out what each word means
■ Distinguishing the literal and nonliteral meanings of words, such as something’s fishy and cold shoulder
■ Spelling correctly and consulting dictionaries to clarify meanings of words

ELA Enrichment

■ Make reading for fun a part of your child’s daily routine. Set aside quiet time, with no phones, computers, or other distractions, when your child can read for pleasure, books such as Amos & Boris by William Steig or The Fire Cat by Esther Averill. To find more books for your child to read, visit www.corestandards.org/assets/Appendix_B.pdf.
■ Encourage your child to find a picture from a newspaper or magazine, cut it out, paste it on paper, and write a story about it.
■ Start a family vocabulary box or jar. Have everyone write down new words they discover, add them to the box, and use the words in conversation.

Math standards

■ Multiplying and dividing up to 10 × 10 quickly and accurately, including knowing the times tables from memory
■ Solving word problems using addition, subtraction, multiplication, and division
■ Beginning to multiply numbers with more than one digit (e.g., multiplying 9 × 80)
■ Understanding fractions and relating them to the familiar system of whole numbers (e.g., recognizing that 3 ⁄1 and 3 are the same number)
■ Measuring and estimating weights and liquid volumes, and solving word problems involving these quantities
■ Reasoning about shapes (e.g., all squares are rectangles but not all rectangles are squares)
■ Finding areas of shapes, and relating area to multiplication (e.g., why is the number of square feet for a 9-foot by 7-foot room given by the product 9 × 7?)

Math Enrichment

Look for “word problems” in real life. Some 3rd grade examples might include:
■ Notice those everyday occasions when you find yourself using your times tables — such as to determine how many days there are in four weeks. Ask your child for the answer.
■ Involve your child when you notice yourself using division to “work backward” in the times tables — such as determining how many candies each child will get if 36 candies are shared equally among nine children at a party, or determining how many six-inch lengths can be cut from a string 18 inches long.


==================== FOURTH GRADE ====================

English Language Arts (ELA) standards

Describing the basic elements of stories — such as characters, events, and settings — by drawing on specific details in the text
■ Paying close attention to key features of informational books and articles: these include understanding the main and supporting ideas; being able to compare and contrast information; and explaining how the author uses facts, details, and evidence to support particular points
■ Comparing ideas, characters, events, and settings in stories and myths from different cultures
■ Writing summaries or opinions about topics supported with a set of well-organized facts, details, and examples
■ Independently conducting short research projects on different aspects of a topic using evidence from books and the Internet
■ Paraphrasing and responding to information presented in discussions, such as comparing and contrasting ideas and analyzing evidence that speakers use to support particular points
■ Reporting orally on a topic or telling a story with enough facts and details
■ Writing complete sentences with correct capitalization and spelling
■ Relating words that are common in reading to words with similar meanings (synonyms) and to their opposites (antonyms)

ELA Enrichment

■ Urge your child to use logical arguments to defend his or her opinion. If your child wants a raise in allowance, ask him or her to research commonsense allowance systems and, based on that research, explain reasons why, supported by facts and details.
■ Talk about the news together. Pick one story in the news, read it together, and discuss with your child what it means.
■ Keep books, magazines, and newspapers at home. Make sure your child sees you reading.

Math standards

■ Using whole-number arithmetic to solve word problems, including problems with remainders and problems with measurements
■ Adding and subtracting whole numbers quickly and accurately (numbers up to 1 million)
■ Multiplying and dividing multi-digit numbers in simple cases (e.g., multiplying 1,638 × 7 or 24 × 17, and dividing 6,966 by 6)
■ Understanding and applying equivalent fractions (e.g., recognizing that 1⁄4 is less than 3⁄8 because 2⁄8 is less than 3⁄8)
■ Adding, subtracting, and multiplying fractions in simple cases (such as 2 3⁄4 − 1 1⁄4 or 3 × 5⁄8), and solving related word problems
■ Understanding simple decimals in terms of fractions (e.g., rewriting 0.62 as 62⁄100)
■ Measuring angles and finding unknown angles in a diagram

Math Enrichment

■ Urge your child to use logical arguments to defend his or her opinion. If your child wants a raise in allowance, ask him or her to research commonsense allowance systems and, based on that research, explain reasons why, supported by facts and details.
■ Talk about the news together. Pick one story in the news, read it together, and discuss with your child what it means.
■ Keep books, magazines, and newspapers at home. Make sure your child sees you reading.


==================== FIFTH GRADE ====================

English Language Arts (ELA) standards

■ Summarizing the key details of stories, dramas, poems, and nonfiction materials, including their themes or main ideas
■ Identifying and judging evidence that supports particular ideas in an author’s argument to change a reader’s point of view
■ Integrating information from several print and digital sources to answer questions and solve problems
■ Writing opinions that offer reasoned arguments and provide facts and examples that are logically grouped to support the writer’s point of view
■ Writing stories, real or imaginary, that unfold naturally and developing the plot with dialogue, description, and effective pacing of the action
■ Coming to classroom discussions prepared, then engaging fully and thoughtfully with others (e.g., contributing accurate, relevant information; elaborating on the remarks of others; synthesizing ideas)
■ Reporting on a topic or presenting an opinion with his or her own words, a logical sequence of ideas, sufficient facts and details, and formal English when appropriate
■ Expanding, combining, and reducing sentences to improve meaning, interest, and style of writing
■ Building knowledge of academic words with an emphasis on those that signal a contrast in ideas or logical relationships, such as on the other hand, similarly, and therefore
■ Producing writing on the computer

ELA Enrichment

Invite your child to read his or her writing out loud to other family members. Ask questions about your child’s word choices and ideas.
■ Discuss your family stories and history. Encourage your child to ask relatives questions about their lives. Put the information together in an album or brainstorm different ways to tell family tales, such as poems or short stories.
■ Go to a play or musical with your child. Discuss the way the actors bring the words to life.

Math standards

■ Adding and subtracting fractions with unlike denominators (e.g., 21⁄4 – 11⁄3), and solving word problems of this kind
■ Multiplying fractions; dividing fractions in simple cases; and solving related word problems (e.g., finding the area of a rectangle with fractional side lengths; determining how many 1⁄3-cup servings are in 2 cups of raisins; determining the size of a share if 9 people share a 50-pound sack of rice equally or if 3 people share 1⁄2 pound of chocolate equally)
■ Generalizing the place-value system to include decimals, and calculating with decimals to the hundredths place (two places after the decimal)
■ Multiplying whole numbers quickly and accurately, for example 1,638 × 753, and dividing whole numbers in simple cases, such as dividing 6,971 by 63
■ Understanding the concept of volume, and solving word problems that involve volume
■ Graphing points in the coordinate plane (two dimensions) to solve problems
■ Analyzing mathematical patterns and relationships

Math Enrichment

Look for “word problems” in real life. Some 5th grade examples might include:
■ Doing arithmetic with decimals, for example when balancing a checkbook.
■ Multiplying with fractions — for example, if you used about 2⁄3 of a 3⁄4-cup measure of vegetable stock, then how much stock did you use? About how much is left?
■ Using the length, width, and depth of a garden plot to determine how many bags of garden soil to buy


==================== SIXTH GRADE ====================

English Language Arts (ELA) standards

■ Analyzing how chapters of a book, scenes of a play, or stanzas of a poem fit into the overall structure of the piece and contribute to the development of ideas or themes
■ Gaining knowledge from materials that make extensive use of elaborate diagrams and data to convey information and illustrate concepts
■ Evaluating the argument and specific claims in written materials or a speech, and distinguishing claims that are supported by reasons and evidence from claims that are not
■ Presenting claims and findings to others orally, sequencing ideas logically, and accentuating main ideas or themes
■ Writing arguments that provide clear reasons and relevant evidence, using credible sources
■ Writing brief reports that examine a topic, have a clear focus, and include relevant facts, details, and quotations
■ Conducting short research projects to answer a question, drawing on several sources and sharpening the focus based on the research findings
■ Reviewing and paraphrasing key ideas and multiple perspectives of a speaker
■ Recognizing variations from standard English in his or her own and others’ writing and speaking, and using this knowledge to improve language use
■ Determining the correct meaning of a word based on the context in which it is used (e.g., the rest of the sentence or paragraph; a word’s position or function in a sentence)

ELA Enrichment

■ Listen with your child to a television reporter, politician, or other speaker. Ask your child to tell you the speaker’s main points. Was the speaker trying to convince the audience of something? How?
■ Visit a library or book store together and ask the librarian or bookseller to recommend young adult books, such as Roll of Thunder, Hear My Cry by Mildred D. Taylor. To find more books for your child to read, visit www.corestandards.org/assets/Appendix_B.pdf.
■ Invite your child to participate in an adult gathering, such as a meal with friends, to practice listening skills and making conversation.
■ Encourage your child to learn at the library or on the Internet what life in your community was like 100 years ago. Have your child write a story, poem, or play about that time.

Math standards

■ Understanding ratios and rates, and solving problems involving proportional relationships (e.g., if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)
■ Dividing fractions and solving related word problems (e.g., how wide is a rectangular strip of land with length 3⁄4 mile and area 1⁄2 square mile?)
■ Using positive and negative numbers together to describe quantities; understanding the ordering and absolute values of positive and negative numbers
■ Working with variables and expressions by generalizing the way numbers work (e.g., when adding numbers, the order doesn’t matter, so x + y = y + x; likewise, properties of addition and multiplication can be used to rewrite 24x + 18y as 6(4x + 3y), or y + y + y as 3y)
■ Understanding the process of solving simple equations
■ Writing equations to solve word problems and describe relationships between quantities (e.g., the distance D traveled by a train in time T might be expressed by an equation D = 85T, where D is in miles and T is in hours)
■ Reasoning about relationships between shapes to determine area, surface area, and volume

Math Enrichment

Look for “word problems” in real life. Some 6th grade examples might include:
■ Determining the average speed of a family trip, based on the distance traveled and the time taken; or estimating the time that a trip will take, given the distance and an estimate of the average speed. (Examples can also come from the news — for example, a swimmer crossing the English Channel or a space probe traveling to another planet.)
■ Finding the surface area of the walls and ceiling in a room to determine the cost of painting the room.


==================== SEVENTH GRADE ====================

English Language Arts (ELA) standards

Citing several sources of specific evidence from a piece when offering an oral or written analysis of a book, essay, article, or play
■ Analyzing works of fiction to see how events advance the plot and how setting shapes the characters
■ Determining an author’s point of view or purpose in a nonfiction work and analyzing how the author takes a position different from other authors
■ Organizing and focusing his or her own writing, including supporting statements and conclusions with evidence and showing that the evidence is accurate and reliable
■ Conducting research in response to a specific question by drawing on evidence from several credible literary or informational sources to support an analysis or reflection
■ Avoiding plagiarism and following a standard format for citations (e.g., footnotes, bibliography)
■ Evaluating a speaker’s key points and reasoning, asking questions, and stating his or her own wellsupported ideas in discussions
■ Presenting claims and findings to others emphasizing main points, making eye contact, speaking loudly enough, pronouncing words clearly, and using formal English when the situation calls for it
■ Using common, grade-appropriate Greek or Latin affixes and roots as clues to defining the meaning of a word (e.g., semi-, semiannual, semicircle)

ELA Enrichment

Visit a local art museum together. Take time to closely observe the details of the paintings or other art objects and talk about what you see there.
■ Have your child help plan a family outing, using the Internet or library to research a place he or she is interested in.
■ Ask your child who his or her favorite authors are. Why does your child like their books? What ideas does the author write about? Who are his or her favorite characters? Why? To find recommendations of books for your child to read, visit www.corestandards.org/assets/Appendix_B.pdf.

Math standards

■ Analyzing proportional relationships (e.g., by graphing in the coordinate plane), and distinguishing proportional relationships from other kinds of mathematical relationships (e.g., buying 10 times as many items will cost you 10 times as much, but taking 10 times as many aspirin will not lower your fever 10 times as much)
■ Solving percent problems (e.g., tax, tips, and markups and markdowns)
■ Adding, subtracting, multiplying, and dividing positive and negative numbers, and solving related word problems
■ Solving word problems that have a combination of whole numbers, fractions, and decimals (e.g., a woman making $25 per hour receives a 10% raise; she will make an additional 1⁄10 of her salary an hour, or $2.50, for a new salary of $27.50)
■ Solving equations such as 1⁄2 (x – 3) = 3⁄4 quickly and accurately, and writing equations of this kind to solve word problems (e.g., “I knocked over a carton of milk, and 3 cups were spilled before I set the carton upright again. When I poured out the remaining milk equally into two measuring cups, there was 3⁄4 of a cup of milk in each one. How much milk was originally in the carton?”)
■ Solving problems involving scale drawings
■ Using statistics to draw inferences and make comparisons (e.g., deciding which candidate is likely to win an election based on a survey)

Math Enrichment

Look for “word problems” in real life. Some 7th grade examples might include:
■ Figuring the amount of a 15% tip or determining what percentage of weekly income goes to pay taxes.
■ Using a scale diagram in a manual or a newspaper article to determine lengths, areas, distances, or other measures.
■ For a long-term project, help your child choose a stock and follow its value on the stock market using the newspaper or the Internet. Have your child calculate the stock’s percent increase or decrease each month.


==================== EIGHTH GRADE ====================

English Language Arts (ELA) standards

■ Citing the evidence that most strongly supports an analysis of what is explicitly stated and/or implied from a book, article, poem, or play
■ Analyzing where materials on the same topic disagree on matters of fact, interpretation, or point of view
■ Learning how authors support their ideas through word choice, sentence and paragraph structure, and other methods
■ Building writing around strong central ideas or points of view; supporting the ideas with sound reasoning and evidence, precise word choices, smooth transitions, and different sentence structures
■ Planning and conducting research projects that include several steps and use many credible and documented print and digital sources
■ Analyzing the purpose of information presented in diverse media (e.g., print, TV, web) and evaluating its social, political, or commercial motives
■ Presenting findings and claims to others, emphasizing key points with relevant evidence and sound reasoning, adapting speech to the audience and the formality of the setting, and responding to questions and comments with relevant observations and ideas
■ Using strong, active verbs to create a clear picture for the reader (e.g., walk, skip, meander, lurch, limp)
■ Interpreting figures of speech (e.g., irony, puns) and developing a large vocabulary of general academic words and phrases

ELA Enrichment

■ Make time in everyone’s busy schedule for family discussions about things going on around the world. Weekends can be a chance for everyone to catch up.
■ Visit the campus of a local college with your teen. Begin talking about college early. What does he or she expect from college? What high school courses will your child need to pass to prepare for college?
■ Make sure to keep books and magazines around the house that your child will enjoy reading and learning from. For a list of book recommendations, visit www.corestandards.org/assets/Appendix_B.pdf.

Math standards

■ Understanding slope, and relating linear equations in two variables to lines in the coordinate plane
■ Solving linear equations (e.g., –x + 5(x + 1⁄3) =2x – 8); solving pairs of linear equations (e.g.,x + 6y = –1 and 2x – 2y = 12); and writing equationsto solve related word problems
■ Understanding functions as rules that assign a unique output number to each input number; using linear functions to model relationships
■ Analyzing statistical relationships by using a bestfit line (a straight line that models an association between two quantities)
■ Working with positive and negative exponents, square root and cube root symbols, and scientific notation (e.g., evaluating √36 + 64; estimating world population as 7 x 109)
■ Understanding congruence and similarity using physical models, transparencies, or geometry software (e.g., given two congruent figures, show how to obtain one from the other by a sequence of rotations, translations, and/or reflections)
■ Understanding and applying the Pythagorean Theorem (a2 + b2 = c2) to solve problems

Math Enrichment

Ask your child to share with you any work he or she is doing in math class that strikes him or her as interesting. Some possibilities might include:
■ Solving interesting problems involving cylinders and spheres, such as figuring out how much water fits inside a garden hose, or how many earths would fit inside the sun.
■ Analyzing data with a scatterplot, for example to decide whether exercise and obesity are related.
■ Solving “just for fun” algebra puzzles, such as: “I’m thinking of two numbers. The difference between the numbers is 40. Twice the smaller number is 20 more than the larger number. What are my numbers?”


==================== HIGH SCHOOL / SECONDARY SCHOOL ====================

ENGLISH LANGUAGE ARTS (ELA)

ELA: Reading

■ Understanding more from and making fuller use of written materials, including using a wider range of evidence to support an analysis
■ Making more connections about how complex ideas interact and develop within a book, essay, or article
■ Evaluating arguments and specific claims; assessing whether the reasoning is valid and the evidence is sufficient; and as appropriate, detecting inconsistencies and ambiguities
■ Analyzing the meaning of foundational U.S. documents (the Declaration of Independence, the Preamble to the Constitution, the Bill of Rights)

ELA: Writing
■ Making an argument that is logical, well-reasoned, and supported by evidence
■ Writing a literary analysis, report, or summary that develops a central idea and a coherent focus and is well supported with relevant examples, facts, and details
■ Conducting several research projects that address different aspects of the same topic, using more complex books, articles, and other sources

ELA: Speaking and Listening
■ Responding thoughtfully to diverse perspectives; synthesizing comments, claims, and evidence made on all sides of an issue; and resolving contradictions when possible
■ Sharing research, findings, and evidence clearly and concisely
■ Making strategic use of digital media (e.g., animations, video, websites, podcasts) to enhance understanding of findings and to add interest

ELA: Language
■ Determining or clarifying the meaning of words and phrases, choosing flexibly from multiple strategies, such as using context, Greek and Latin roots (e.g., bene as in benefactor or benevolent), patterns of words (conceive, conception, conceivable), and consulting specialized reference materials (e.g., dictionaries, glossaries, thesauruses)
■ Interpreting figures of speech (e.g., hyperbole, paradox) in context and analyzing their role in the written materials


MATH

Math: Number and Quantity

■ Working with rational and irrational numbers, including working with rational exponents (e.g., rewriting (53)1/2 as 5√5)
■ Solving problems with a wide range of units and solving problems by thinking about units (e.g., “The Trans Alaska Pipeline System is 800 miles long and cost $8 billion to build. Divide one of these numbers by the other. What is the meaning of the answer?”; “Greenland has a population of 56,700 and a land area of 2,175,600 square kilometers. By what factor is the population density of the United States, 80 persons per square mile, larger than the population density of Greenland?”)

Math: Algebra

■ Solving real-world and mathematical problems by writing and solving nonlinear equations, such as quadratic equations (ax2 + bx + c = 0)
■ Interpreting algebraic expressions and transforming them purposefully to solve problems (e.g., in solving a problem about a loan with interest rate r and principal P, seeing the expression P(1+r)n as a product of P with a factor not depending on P)

Math: Functions

■ Analyzing functions algebraically and graphically, and working with functions presented in different forms (e.g., given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum)
■ Working with function families and understanding their behavior (such as linear, quadratic, and exponential functions)

Math: Modeling

■ Analyzing real-world situations using mathematics to understand the situation better and optimize, troubleshoot, or make an informed decision (e.g., estimating water and food needs in a disaster area, or using volume formulas and graphs to find an optimal size for an industrial package)

Math: Geometry

■ Proving theorems about triangles and other figures (e.g., that the angles in a triangle add to 180º)
■ Solving applied problems involving trigonometry of right triangles
Using coordinates and equations to describe geometric properties algebraically (e.g., writing the equation for a circle in the plane with specified center and radius)

Math: Statistics and Probability

■ Making inferences and justifying conclusions from sample surveys, experiments, and observational studies
■ Working with probability and using ideas from probability in everyday situations (e.g., comparing the chance that a person who smokes will develop lung cancer to the chance that a person who develops lung cancer smokes)