Grade 2 Curriculum Notebook

2nd Grade Curriculum Notebook
2017


Curriculum Notebook Table of Contents
Standards
Standards indicate the broad goals for a student to master in a course. Standards are typically set by a state or district school board.
English Language Arts (ELA) .............................................................................................................. Page 4 Reading Standards for Literature .......................................................................................................... Page 5 Reading Standards for Informational Text ............................................................................................ Page 6 Reading Standards: Foundational Skills................................................................................................. Page 7 Writing Standards ................................................................................................................................. Page 8 Speaking and Listening Standards ......................................................................................................... Page 10 Language Standards .............................................................................................................................. Page 12
Mathematics
Mathematical Practice Standards ......................................................................................................... Page 15 Mathematical Content Standards ......................................................................................................... Page 19
Essential Learning Standards
Particular standards/objectives/indicators that a school/district defines as critical for student learning. In fact, they are so critical that students will receive intervention if they are not learned. Essentials are chosen because they 1. have endurance, 2. have leverage, and 3. are important for future learning. ELA................................................................................................................................................................. Page 22 Math .............................................................................................................................................................. Page 24
Curriculum Resources
The materials teachers use to plan, prepare, and deliver instruction, including materials students use to learn about the subject. Such materials include texts, textbooks, tasks, tools, and media. Sometimes organized into a comprehensive program format, they often provide the standards, units, pacing guides, assessments, supplemental resources, interventions, and student materials for a course. ELA................................................................................................................................................................. Page 26 Math .............................................................................................................................................................. Page 32
Pacing Guide
The order and timeline of the instruction of standards, objectives, indicators, and Essentials over the span of a course (semester or year). ELA................................................................................................................................................................. Page 97 Math .............................................................................................................................................................. Page 100
Units
A plan for several weeks of instruction, usually based on a theme, that includes individual lesson plans. Units often also include: Standards, learning targets/goals, skills, formative and summative assessment, student materials, essential questions, big ideas, vocabulary, questions, and instructional methods.
Understanding By Design .............................................................................................................................. Page 104 ELA................................................................................................................................................................. Page Math .............................................................................................................................................................. Page
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Assessment Standards
A set of criteria to guide the assessment of student learning in a course that is based on Standards/Essentials of the course; this might include formative assessment practices, summative assessments/practices, common assessment plans, feedback practices, and a schedule for testing.
Assessment Standards .......................................................................................................................... Page 105 Ethics ..................................................................................................................................................... Page 107
Intervention Standards
A set of criteria to guide teachers to provide additional instruction to students who did not master the content in Tier 1 instruction. This might include: commercial intervention programs, teacher-developed intervention materials, diagnostic testing, RTI/MTSS processes, and a list of essential knowledge/skills that will prompt intervention if the student does not demonstrate mastery.
RTI ......................................................................................................................................................... Page 109 MTSS...................................................................................................................................................... Page 111
Supplemental Resources
Instructional materials, beyond the main curricular materials, used to strategically fill gaps/weaknesses of the core program materials.
Provo Way Instructional Model ............................................................................................................ Page 114 ELA......................................................................................................................................................... Page 117 Mathematics ......................................................................................................................................... Page 117
Evidence-based Pedagogical Practices
A list of teaching strategies that are supported by adequate, empirical research as being highly effective.
John Hattie ............................................................................................................................................ Page 118
Glossary
Terms and acronyms used in this document ........................................................................................ Page 119
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English Language Arts ELA Standards
College and Career Readiness Anchor Standards for Reading
The K–5 standards on the following pages define what students should understand and be able to do by the end of each grade. They correspond to the College and Career Readiness (CCR) anchor standards below by number.
The CCR and grade-specific standards are necessary complements—the former providing broad standards, the latter providing additional specificity—that together define the skills and understandings that all students must demonstrate.
Key Ideas and Details
1. Read closely to determine what the next text says explicitly and make logical inferences from it; cite specific textural evidence when writing or speaking to support conclusions drawn from the text.
2. Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas.
3. Analyze how and why individuals, events, and ideas develop and interact over the course of a text.
Craft and Structure
4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.
5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.
6. Assess how point of view or purpose shapes the content and style of a text.
Integration of Knowledge and Ideas
7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.
8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.
9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.
Range of Reading and Level of Text Complexity
10. Read and comprehend complex literary and informational texts independently and proficiently.
Note on Range and Content of Student Reading
To build a foundation for college and career readiness, students must read widely and deeply from among a broad range of high–quality, increasingly challenging literary and informational texts. Through extensive reading of stories, dramas, poems and myths from diverse cultures and different time periods, students gain literary and cultural knowledge as well as familiarity with various text structures and elements. By reading texts in history/social studies, science, and other disciplines, students build a foundation of knowledge in these fields that will also give them the background to be better readers in all content areas. Students can only gain this foundation when curriculum is intentionally and coherently structured to develop rich content knowledge within and across grades. Students also acquire the habits of reading independently and closely, which are essential to their future success. The Utah Core Standards include an expectation that students will be introduced to cursive letters and words no later than grade three in order to develop sufficient recognition and reading fluency of
cursive text by the end of grade five.
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Reading standards for literature RL Key ideas and details
1. Askandanswersuchquestionsaswho,what,where,when,why,andhow to demonstrate understanding of key details in a text.
2. Recountstories,includingfablesandfolktalesfromdiversecultures,and determine their central message, lesson or moral.
3. Describehowcharactersinastoryrespondtomajoreventsandchallenges.
Craft and structure
4. Describehowwordsandphrases(e.g.,regularbeats,alliteration,rhymes,
repeated lines) supply rhythm and meaning in a story, poem, or song.
5. Describetheoverallstructureofastory,includingdescribinghowthe
beginning introduces the story and the ending concludes the action.
6. Acknowledgedifferencesinthepointsofviewofcharacters,includingby
speaking in a different voice for each character when reading dialogue
aloud.
Integration of knowledge and ideas
7. Useinformationgainedfromtheillustrationsandwordsinaprintordigital text to demonstrate understanding of its characters, setting, or plot.
8. (Notapplicabletoliterature)
9. Compareandcontrasttwoormoreversionsofthesamestory(e.g.,
Cinderella stories) by different authors or from different cultures.
Range of reading and level of text complexity
10. By the end of the year, read and comprehend literature, including stories and poetry, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range.
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Reading standards for informational text RI Key ideas and details
1. Askandanswersuchquestionsaswho,what,where,when,why,andhow to demonstrate understanding of key details in a text.
2. Identifythemaintopicofamulti-paragraphtextaswellasthefocusof specific paragraphs within the text.
3. Describetheconnectionbetweenaseriesofhistoricalevents,scientific ideas or concepts, or steps in technical procedures in a text.
Craft and structure
4. Determinethemeaningofwordsandphrasesinatextrelevanttoagrade2 topic or subject area.
5. Knowandusevarioustextfeatures(e.g.,captions,boldprint,subheadings, glossaries, indexes, electronic menus, icons) to locate key facts or information in a text efficiently.
6. Identifythemainpurposeofatext,includingwhattheauthorwantsto answer, explain, or describe.
Integration of knowledge and ideas
7. Explainhowspecificimages(e.g.,adiagramshowinghowamachineworks) contribute to and clarify a text.
8. Describehowreasonssupportspecificpointstheauthormakesinatext.
9. Compareandcontrastthemostimportantpointsandkeydetailspresented
in two texts on the same topic.
Range of reading and level of text complexity
10. By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range.
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Reading standards: foundational skills RF Standards 1 and 2 are for kindergarten and grade 1 only
Phonics and word recognition
3. Knowandapplygrade–levelphonicsandwordanalysisskillsindecoding words.
a. Distinguishlongandshortvowelswhenreadingregularlyspelled one-syllable words.
b. Knowspelling-soundcorrespondencesforadditionalcommonvowel teams.
c. Decode regularly spelled tow-syllable words with long vowels.
d. Decodewordswithcommonprefixesandsuffixes.
e. Identifywordswithinconsistentbutcommonspelling-sound
correspondences.
f. Recognize and read grade-appropriate irregularly spelled words.
Fluency
4. Readwithsufficientaccuracyandfluencytosupportcomprehension.
a. Readgrade–leveltextwithpurposeandunderstanding.
b. Readgrade–leveltextorallywithaccuracy,appropriaterate,and
expression on successive readings.
c. Use context to confirm or self-correct word recognition and
understanding, rereading as necessary.
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College and Career Readiness Anchor Standards for Writing
The K–5 standards on the following pages define what students should understand and be able to do by the end of each grade. They correspond to the College and Career Readiness (CCR) anchor standards below by number.
The CCR and grade-specific standards are necessary complements—the former providing broad standards, the latter providing additional specificity—that together define the skills and understandings that all students must demonstrate.
Text Types and Purposes
1. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.
2. Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.
3. Write narratives to develop real or imagined experiences or events using effective technique, well– chosen details, and well–structured event sequences.
Production and Distribution of Writing
4. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
6. Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.
Research to Build and Present Knowledge
7. Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation
8. Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism.
9. Draw evidence from literary or informational texts to support analysis, reflection, and research.
Range of Writing
10. Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.
Note on Range and Content of Student Writing
To build a foundation for college and career readiness, students need to learn to use writing as a way of offering and supporting opinions, demonstrating understanding of the subjects they are studying, and conveying real and imagined experiences and events. They learn to appreciate that a key purpose of writing is to communicate clearly to an external, sometimes unfamiliar audience, and they begin to adapt the form and content of their writing to accomplish a particular task and purpose. They develop the capacity to build knowledge on a subject through research projects and to respond analytically to literary and informational sources. To meet these goals, students must devote significant time and effort to writing, producing numerous pieces over short and extended time
frames throughout the year.
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Writing Standards W Text Types and Purposes
1. Writeopinionpiecesinwhichtheyintroducethetopicorbooktheyare writing about, state an opinion, supply reasons that support the opinion, use linking words (e.g., because, and, also) to connect opinion and reasons, and provide a concluding statement or section.
2. Writeinformative/explanatorytextsinwhichtheyintroduceatopic,use facts and definitions to develop points, and provide a concluding statement or section.
3. Writenarrativesinwhichtheyrecountawell-elaboratedeventorshort sequence of events, include details to describe actions, thoughts, and feelings use temporal words to signal event order, and provide a sense of closure.
Production and Distribution of Writing
4. Thisstandardbeginsingrade3.
5. Withguidanceandsupportfromadultsandpeers,focusonatopicand
strengthen writing as needed by revising and editing.
6. Withguidanceandsupportfromadults,useavarietyofdigitaltoolsto
produce and publish writing, including in collaboration with peers.
Research to Build and Present Knowledge
7. Participateinsharedresearchandwritingprojects(e.g.,readanumberof books on a single topic to produce a report; record science observations). 8. Recallinformationfromexperiencesorgatherinformationfromprovided
sources to answer a question. 9. This standard begins in grade 4
Range of Writing
10. This standard begins in grade 3
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College and Career Readiness Anchor Standards for Speaking and Listening
The K–5 standards on the following pages define what students should understand and be able to do by the end of each grade. They correspond to the College and Career Readiness (CCR) anchor standards below by number.
The CCR and grade-specific standards are necessary complements—the former providing broad standards, the latter providing additional specificity—that together define the skills and understandings that all students must demonstrate.
Comprehension and Collaboration
1. Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.
2. Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.
3. Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric.
Presentation of Knowledge and Ideas
4. Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.
5. Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations.
6. Adapt speech to a variety of contexts and communicative tasks, demonstrating command of formal English when indicated or appropriate.
Note on Range and Content of Student Writing
To build a foundation for college and career readiness, students must have ample opportunities to take part in a variety of rich, structured conversations–as part of a whole class, in small groups, and with a partner. Being productive members of these conversations requires that students contribute accurate, relevant information respond to and develop what others have said; and analyze and synthesize a multitude of ideas in
variousdomains.
New technologies have broadened and expanded the role that speaking and listening play in acquiring and sharing knowledge and have tightened their link to other forms of communication. Digital texts confront students with the potential for continually updated content and dynamically changing combinations of words, graphics, images, hyperlinks, and embedded video and audio.
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Speaking and Listening Standards SL Comprehension and Collaboration
1. Participateincollaborativeconversationswithdiversepartnersaboutgrade 2 topics and texts with peers and adults in small and larger groups.
a. Follow agreed-upon rules for discussions (e.g., gaining the floor in
respectful ways, listening to others with care, speaking one at a time
about the topics and texts under discussion).
b. Build upon others’ talk in conversations by linking their comments to the
remarks of others.
c. Ask for clarification and further explanation as needed about the topics
and texts under discussion.
2. Recount or describe key ideas or details from a text read aloud or
information presented orally or through other media.
3. Ask and answer questions about what a speaker says in order to clarify
comprehension, gather additional information, or deepen understanding of
a topic or issue.
Presentation of Knowledge and Ideas
4. Tell a story or recount an experience with appropriate facts relevant, descriptive details, speaking audibly in coherent sentences.
5. Create audio recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts and feelings.
6. Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 2 language standards 1 and 3 for specific expectations.)
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College and Career Readiness Anchor Standards for Language
The K–5 standards on the following pages define what students should understand and be able to do by the end of each grade. They correspond to the College and Career Readiness (CCR) anchor standards below by number.
The CCR and grade-specific standards are necessary complements—the former providing broad standards, the latter providing additional specificity—that together define the skills and understandings that all students must demonstrate.
Conventions of Standard English
1. Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
2. Demonstrate command of the conventions of Standard English capitalization, punctuation, and spelling when writing.
Knowledge of Language
3. Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.
Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and consulting general and specialized reference materials, as appropriate.
5. Demonstrate understanding of figurative language, word relationships and nuances in word meanings.
6. Acquire and use accurately a range of general
academic and domain specific words and phrases sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression.
Note on Range and Content of Student Writing
To build a foundation for college and career readiness, students Must gain control over many conventions of standard English grammar, usage, and mechanics as well as learn other ways to use language to convey meaning effectively. They must also be able to determine or clarify the meaning of grade–appropriate words encountered through listening, reading, and media use; come to appreciate that words have nonliteral meanings, shadings of meaning, and relationships to other words; and expand their vocabulary in the course of studying content. The inclusion of language standards in their own strand should not be taken as an indication that skills related to conventions, effective language use, and vocabulary are unimportant to reading, writing, speaking, and listening; indeed, they are
inseparable from such contexts.
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Language Standards L
Knowledge of Language
1. Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
a. Fluently, independently and legibly write all upper– and lower–case letters.
b. Produce grade–appropriate text using legible writing.
c. Understand that cursive is different from manuscript.
d. Form and use regular and irregular plural nouns.
e. Use collective nouns (e.g., group).
f. Form and use frequently occurring irregular plural nouns (e.g., feet, children, teeth,
mice, fish).
g. Use reflexive pronouns (e.g., myself, ourselves).
h. Form and use the past tense of frequently occurring irregular verbs (e.b., sat, hid,
told).
i. Use adjectives and adverbs, and choose between them depending on what is to be
modified.
j. Produce, expand, and rearrange complete simple and compound sentences (e.g., The
boy watched the movie; The little boy watched the movie; The action movie was
watched by the little boy).
2. Demonstrate command of the conventions of standard English capitalization,
punctuation, and spelling when writing.
a. Capitalize holidays, product names, and geographic names.
b. Use commas in greetings and closings of letters.
c. Use an apostrophe to form contractions and frequently occurring possessives.
d. Generalize learned spelling patterns with writing words (e.g., cage –>badge; boy–
>boil).
e. Consult reference materials, including beginning dictionaries, as needed to check and
correct spellings.
Knowledge of Language
3. Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Compare formal and informal uses of English.
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Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 2 reading and content, choosing flexibility from an array of strategies.
a. Use sentence-level context as a clue to the meaning of a word or phrase.
b. Determine the meaning of the new word formed when a known prefix is added to a
known word (e.g., happy/unhappy, tell/retell).
c. Use a known root word as a clue to the meaning of an unknown word with the same
root (e.g., addition, additional).
d. Use knowledge of the meaning of individual words to predict the meaning of
compound words (e.g., birdhouse, lighthouse, housefly; bookshelf, notebook,
bookmark).
e. Use glossaries and beginning dictionaries, both print and digital to determine or clarify
the meaning of words and phrases.
5. Demonstrate understanding of word relationships and nuances in word meanings.
a. Identify real-life connections between words and their use (e.g., describe foods that are spicy or juicy).
b. Distinguish shades of meaning among closely related verbs (e.g., toss, throw, hurl) and closely related adjectives (e.g., thin, slender, skinny, scrawny).
6. Use word and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g., When other kids are happy that makes me happy).
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Mathematics
Standards for Mathematical Practice
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
1 Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solutions pathway rather than simply jumping into a solution attempt. The consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and the continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
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2 Reason abstractly and quantitatively
Mathematically proficient students make a sense of the quantities and their relationships in problem situations. Students bring two complimentary abilities to bear on problems involving quantitative relationships: the ability to decontextualize–to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents–and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
3 Construct viable arguments and critique the reasoning of others
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of tow plausible arguments, distinguish correct logic or reasoning form that which is flawed and–if there is a flaw in an argument–explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
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4 Model with mathematics
Mathematically proficient students can apply mathematics the know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity on interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts, and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possible improving the model if it has not served its purpose.
5 Use appropriate tools strategically
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
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6 Attend to precision
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
7 Look for and make use of structure
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y )2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
8 Look for and express regularity in repeated reasoning
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding(x–1)(x +1),(x –1)(x2 +x+1),and(x–1)(x3 +x2 +x +1)might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
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Grade 2 Mathematics
In Grade 2, instructional time should focus on four critical areas:
1. Extending understanding of base-ten system, including ideas of counting in
fives, tens, and multiples of hundreds, tens and ones.
2. Buildingfluencywithadditionandsubtraction,including.
3. Usingstandardunitsofmeasure.
4. Describingandanalyzingshapes.
Operations and Algebraic Thinking
• Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20.
• Work with addition and subtraction equations Number and Operations in Base Ten
• Extend the counting sequence.
• Understand place value.
• Use place value understanding and properties of
operations to add and subtract.
Measurement and Date
• Measure lengths indirectly and by iterating length units.
• Tell and write time.
• Represent and interpret data. Geometry
• Reason with shapes and their attributes
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
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Operations and Algebraic Thinking OA
Represent and solve problems involving addition and subtraction.
1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
Add and subtract within 20.
2. Fluently add and subtract within 20 using mental strategies. By end of grade 2, know from memory all sums of two one digit numbers.
Work with equal groups of objects to gain foundations for multiplication
3. Determine whether a group of objects (up to 20) has an odd or even number of members, write an equation to express an even number as a sum of two equal addends.
4. Use addition to find the total number of objects arranged in rectangular arrays with up
to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Number and Operations in Base Ten NBT
Understand Place Value
1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens – called a “hundred”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900, refer to one, two, three,
four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
2. Count within 1000: skip count by 5s, 10s, and 100s.
3. Read and write numbers to 1000 using base-ten numerals, number names, and
expanded form.
4. Compare two three-digit numbers based on meanings of hundreds, tens, and ones
digits, using >, =, and < symbols to record the results of comparisons.
Use place value understanding and properties of operations to add and subtract.
5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
6. Add up to four two-digit numbers using strategies based on place value and properties of operations.
7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundred and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
8. Mentally add 10 or 100 to a given number 100 – 900, and mentally subtract 10 or 100 from a given number 100-900.
9. Explain why addition and subtraction strategies work, using place value and the properties of operations.
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Measurement and Data MD
Measure and estimate lengths in standard units.
1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the tow measurements relate to the size of the unit chosen.
3. Estimate lengths using units of inches, feet, centimeters, and meters.
4. Measure to determine how much longer one object is than another, expressing the
length difference in terms of a standard length unit.
Relate addition and subtraction to length.
5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units and equations with a symbol for the unknown number to represent the problem.
6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ... , and represent whole-number sums and differences within 100 on a number line diagram.
Work with Time and Money.
7. Tell and write time form analog and digital clocks to the nearest five minutes, using a.m. and p.m.
8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.
Represent and Interpret Data
9. Generate measurement data by using lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole- number units.
10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
Geometry G
Reason with Shapes and their Attributes.
1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
3. Partitions circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
21


ELA Essential Learning Standards
Key Ideas and Details
RL2.1 Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
RL2.2 Recount stories, including fables and folktales from diverse cultures and
determine their central message, lesson, or moral.
Integration of Knowledge and Ideas
RL2.7 Use information from the illustrations and words in a print or digital text to
demonstrate understanding of its characters, setting, or plot.
Key Ideas and Details
RI2.2 Identifythemaintopicofamulti-paragraphtextaswellasthefocusof
specific paragraphs within the text.
Phonics and Word Recognition
RF2.3 Know and apply grade-level phonics and word analysis skills in decoding words.
a. Distinguish long and short vowels when reading regularly spelled one- syllable words.
b. Know spelling-sound correspondences for additional common vowel teams.
c. Decode regularly spelled two-syllable words with long vowels. d. Decode words with common prefixes and suffixes.
e. Identify words with inconsistent but common spelling-sound correspondences.
f. Recognize and read grade-appropriate irregularly spelled words.
Fluency
RF2.4 Read with sufficient accuracy and fluency to support comprehension. c. Use context to confirm or self-correct word recognition and
understanding, rereading as necessary.
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Text Types and Purposes
W1.1 Write opinion pieces in which they introduce the topic or book they are writing about, state an opinion, supply a reason for the opinion, use linking words to connect opinion and reasons, and provide a concluding statement or section.
W1.2 Write informative/explanatory texts in which they name a topic, use facts and definitions to develop points, and provide a concluding statement or section.
W1.3 Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of
closure.
Conventions of Standard English
L2.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Capitalize holidays, product names, and geographic names. b. Use commas in greetings and closing of letters.
c. Use an apostrophe to form contractions and frequently occurring possessives.
d. Generalize learned spelling patterns when writing words
e. Consult reference materials, including beginning dictionaries, as needed to check and correct spellings.
23


Mathematics Essential Learning Standards
Essential Skills List for Mathematics
All 8 Standards for Mathematical Practice are essential.
1. Makesenseofproblemsandpersevereinsolvingthem.
2. Reasonabstractlyandquantitatively.
3. Constructviableargumentsandcritiquethereasoningofothers. 4. Modelwithmathematics.
5. Useappropriatetoolsstrategically.
6. Attendtoprecision.
7. Lookforandmakeuseofstructure.
8. Lookforandexpressregularityinrepeatedreasoning.
The standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout their education.
Essential Skills from Standards for Mathematical Content
Grade 2
In grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.
Operations and Algebraic Thinking (2.OA)
A. Represent and solve problems involving addition and subtraction
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word
problems involving situations of adding to, taking away from, putting together, taking apart, and comparing, with unknowns in all positions.
B. Add and subtract within 20.
2.OA.2 Fluently add and subtract within 20 using mental strategies. By the end of Grade 2, know from memory all sums of two one-digit numbers.
C. Work with equal groups of objects to gain foundations for multiplication
2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
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Number and Operations in Base Ten (2.NBT)
A. Understand place value
2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones.
Count within 1000; skip-count by 5s, 10s, and 100s.
Read and write numbers to 1000 using base-ten numerals, number names and expanded form.
2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
B. Use place value understanding and properties of operations to add and subtract.
2.NBT.5 Fluently add and subtract within 100 using a strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.7 Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction.
Measurement and Data (2.MD)
A. Measure and estimate lengths in standard units.
2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks and measuring tapes.
Geometry (2.G)
A. Reason with shapes and their attributes.
2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2.G.3 Partition circles and rectangles into two, three, or four equal shares, describing the shares using the words halves, thirds, half of, a third of, etc.
2.NBT.2 2.NBT.3
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Curriculum Resources
ELA
Wonders: Comprehensive Reading Program
Provo City School District has adopted McGraw’s Wonders Comprehensive Reading Program for grades 1-6. Classroom teachers have physical materials, including student books and teacher manuals, as well as digital access to all materials.
Directions for logging into Wonders:
For classroom teachers:
Step One: Log into https://connected.mcgraw-hill.com
Step Two: Enter Username: your email address
Step Three: Enter your password: psd###### (your six-digit employee ID number). Step Four: Once you are logged in, choose your teacher edition.
Make sure your Unit and week information is up-to-date.
For anyone without an assigned class:
Step One: Log into https://connected.mcgraw-hill.com
Step Two: Log in using the following username: rw2017
Step Three: Enter the password: 2017readingelem
Step Four: Choose the grade level teacher’s edition and from there locate the dropdown menu to choose the correct Unit and Week.
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From the homepage, choose which components to use during planning and teaching.
27


Language Progressive Skills, by Grade
The following skills, marked with and asterisk (*) in language standards 1–3, are particularly likely to require continued attention in higher grades as they are applied to increasingly sophisticated writing and speaking.
28


Literature
Stories
Dramas Poetry
Range of Text Types for K–5
Includes children’s adventure stories, folktales, legends, fables, fantasy, realistic fiction, and myth
Includes staged dialogue and brief familiar scenes
Includes nursery rhymes and the subgenres of the narrative poem, limerick, and free verse poem
Informational Text
Literary nonfictional and historical, scientific, and technical texts
Includes biographies and autobiographies; books about history, social studies, science, and the arts; technical texts, including directions, forms, and information displayed in graphs, charts, or maps; and digital sources on a range of
topics.
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Texts illustrating the complexity, quality, and range of student reading in Grades 2 – 3
Literature, Stories, Drama, Poetry
“Who Has Seen the Wind?” by Christina G. Rossetti (1893) Charlotte’s Web by E.B. White (1952)
Sarah, Plain and Tall by Patricia MacLachlan (1985)
Tops and Bottoms by Janet Stevens (1995)
Poppleton in Winter by Cynthia Rylant, illustrated by Mark Teague (2001)
Informational Text: Literary Nonfiction and Historical, Scientific, and Technical Texts
A Medieval Feast by Aliki (1983)
From Seed to Plant by Gail Gibbons (1991)
The Story of Ruby Bridges by Robert Coles (1995)
A Drop of Water: A Book of Science and Wonder by Walter Wick (1997) Moonshot: The Flight of Apollo 11 by Brain Floca (2009)
The titles listed above are only meant to show individual titles that are representative of a wide range of topics and genres. At a curricular or instructional level, within and across grade levels, texts need to be selected around topics or themes that generate knowledge and allow students to study those topics or themes in depth.
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Staying on Topic Within a Grade and Across Grades:
How to build knowledge systematically in English Language Arts K–5.
Building knowledge systematically in English language arts is like giving children various pieces of a puzzle in each grade that, overtime, will form one big picture. At a curricular or instructional level, texts–within and across grade levels–need to be selected around topics or themes that systematically develop the knowledge base of students. Within a grade level, there should be an adequate number of titles on a single topic that would allow children to study that topic for a sustained period. The knowledge children have learned about particular topics in early grade levels should then be expanded and developed in subsequent grade levels to ensure an increasingly deeper understanding of these topics. Children in the upper elementary grades will generally be expected to read these texts independently and reflect on them in writing. However, children in the early grades (particularly K–2) should participate in rich, structured conversations with an adult in response to the written texts that are read aloud, orally comparing and contrasting as well as analyzing and synthesizing in the manner called for by the standards.
Preparation for reading complex informational texts should begin at the very earliest elementary school grades. What follows is one example that used domain–specific nonfiction titles across grade levels to illustrate how curriculum designers and classroom teachers can infuse the English language arts block with rich, age–appropriate content knowledge and vocabulary in history/social studies, science, and the arts. Having students listen to informational read–alouds in the early grades helps lay the necessary foundation for students’ reading and understanding of increasingly complex texts on their own in subsequent grades.
Exemplar Texts on Topic Across Grades: The Human Body
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Mathematics
5 Strands of Mathematical Proficiency from NRC’s Adding It Up
Conceptual understanding: Comprehension of mathematical concepts, operations, and relations
Procedural fluency: skill in carrying out procedures flexibly, accurately, efficiently and appropriately
Strategic competence: ability to formulate, represent, and solve mathematical problems
Adaptive reasoning: capacity for logical thought, reflection, explanation, and justification
Productive disposition: habitual inclination to see mathematics as sensible, useful, worthwhile, coupled with a belief in diligence and one's own efficacy
Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content
The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.
The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.
In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics.
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USBE Core Content Guides
Click on a standard to go to the USBE Core Content Guide
2OA1 2OA2 2OA3 2OA4
Use addition and subtraction within 100 to solve one- and two-step problems
Fluently add and subtract within 20 using mental strategies
Determine whether a group of objects (up to 20) has odd or even number of members Use addition to find total number of objects arranged in rectangular arrays up to 5 by 5
2NBT1
2NBT2
2NBT3
2NBT4
2NBT5
2NBT6
2NBT7 Add and subtract within 1000 using concrete models or drawings and strategies 2NMT8 Mentally add or subtract 10 or 100 to a given number 100 -900
Understand the three digits of a number represent amounts of hundreds, tens and ones Count within 1000; skip count by 5s, 10s, and 100s
Read and write numbers to 1000 using base ten numerals
Compare 2 three-digit numbers based on meanings of hundreds, tens and ones
Fluently add and subtract within 100 using various strategies Add up to four two-digit numbers
2NBT9 Explain why addition and subtraction strategies work
2MD1 Measurethelengthofanobjectbyselectingandusingappropriatetools
2MD2 Measurethelengthofanobjecttwiceusinglengthunitsofdifferentlengths
2MD3 Estimatelengthsusingunitsofinches,feet,centimeters,andmeters
2MD4 Measuretodeterminehowmuchlongeroneobjectisthananother
2MD5 Useadditionandsubtractionwithin100tosolvewordproblemsinvolvinglength
2MD6 Representwholenumbersaslengthsfrom0onanumberline
2MD7 Tellandwritetimefromanaloganddigitalclocks
2MD8 Solvewordproblemsinvolvingdollarbills,quarters,dimes,nickelsandpennies
2MD9 Generatemeasurementdatabymeasuringlengthsofseveralobjectstonearestunit
2md10 Draw a picture graph and a bar graph to represent a data set with up to 4 categories
2G1 Recognize and draw shapes having specified attributes
2G2 Partition a rectangle into rows and columns of same-size squares and count to find area
2G3 Partition circles & rectangles into 2, 3 and 4 equal shares, use the words halves, thirds,
fourths, etc.
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34


Operations and Algebraic Thinking 2OA1
Core Content
Cluster Title: Represent and solve problems involving addition and subtraction.
Standard: 1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand how to solve one-step word problems using addition and subtraction within 100.
• Understand how to solve two-step word problems using addition and subtraction within 100. (Could include 2 addition functions, two subtraction functions or both an addition and subtraction function in the same word problem.)
• Understand how to solve word problems with unknowns in all positions using these problem types:
o adding to
o taking from
o putting together/taking apart o comparing
• Understand how to represent the unknown number with a symbol using drawings and equations.
Procedural:
• Solve one and two-step word problems with the unknown in all positions using objects, drawings, number lines or hundreds-charts.
• Write equations for one and two-step word problems for each problem type. Representational:
• Model each one and two-step word problem type using objects, drawings, number lines or hundreds-charts and write the equation for the problem.
35


Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand basic addition and subtraction problem solving strategies.
• Understand how numbers and symbols are used to represent word problems.
• Understand that the unknown number can be in any position in the equation.
• Understand how to efficiently use objects, models and drawings as tools to represent
and solve word problems.
• Standard 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and
subtraction within 10. Use strategies such as counting on, making ten (e.g., 8 + 6 = 8 + 2 + 4 =10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 -4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows that 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1= 13).
Procedural:
• Solve one and two-step word problems for all problem types. o adding to
o taking from
o putting together/taking apart o comparing
• Write equations that represent the problem using a symbol to represent the unknown.
Representational:
• Model addition and subtraction word problems with objects, tools (number lines, hundreds-charts), and drawings.
Academic Vocabulary and Notation
Adding to, Taking from, Putting together, Taking apart, Comparing, Unknown, Position Symbol (plus, minus, equals, unknown symbol), Represent Change
36


Instructional Strategies Used
Resources Used
Teachers could begin instruction by asking students to role play or visualize the situation before solving.
Samples of one-step problem types:
Take From: Result Unknown
Patty had 58 gumballs. She gave 27 gumballs to Susan. How many gumballs does Patty have now?
58 - 27 =£
Add to: Change Unknown
Brock had 27 rocks. His friend gave him some more rocks. Now Brock has 58 rocks. How many rocks did his friend give him?
27 +£= 58
Compare: Result Unknown
Amy has 58 pencils. Jenny has 27 pencils. How many more pencils does Amy have than Jenny? Write an equation for the problem.
58 - 27 =£or 27 +£ = 58
Take From: Start Unknown
Ben had some marbles. He gave 27 to Mike. Now Ben has 31 marbles. How many marbles did Ben start with?
Write an equation for the problem.
£- 27 = 31
Samples of two-step problem types:
These instructional strategies are dealt with in detail in the book Cognitively Guided Instruction by Carpenter, Fennema, Franke and Empsom.
They are also found in Teaching Student Centered Mathematics K - 3 by John Van de Walle
Emily’s First 100 Days of School by Rosemary Wells
http://www.k- 5mathteachingresources.com/support- files/2ndgrade2stepwordproblems.pdf
Add to/ take from:
Result Unknown
There were 67 children on the playground. 20 more children came. Some of the children got on the bus to go home. Now there are 27 children on the playground. How many students got on the bus? Write an equation for the problem.
67 + 20 =£ 87- 27 =£
Compare
Molly has 12 erasers. Jeff has 6 less erasers than Molly. How many erasers do they have all together?
Write the equations used to solve the problem.
12 - 6 =£ 12 + 6 =£
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Assessment Tasks Used
Skill-based Task:
This objective requires a word problem that is embedded into the Problem Task.
Caution: This objective has the intent to help children learn to solve one and two- step word problems and represent their thinking using an algebraic equation. The intent is not to introduce traditional algorithms or rules.
Problem Task:
Use the pattern of problem types given in the Instructional Strategies Section. Create contexts and use numbers that are appropriate for the needs of your learners. Each problem type needs to be assessed separately.
38


Operations and Algebraic Thinking 2OA2
Core Content
Cluster Title: Add and subtract within 20.
Standard: 2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand how to use whole part relationships of numbers to efficiently compose and decompose one digit numbers
• Understand the relationship between addition and subtraction
• Understand that fluency includes accuracy, efficiency and flexibility. Procedural:
• Use mental strategies to add and subtract such as:
* Counting on: 8 + 4 = □ (8 ...9, 10,11,12)
* Counting back: 12 - 4 = □ (12...11, 10, 9, 8)
* Making tens: 5 + 7 = □ (5 = 2 + 3 so 3 + 7 = 10 therefore 10 + 2 = 12) * Doubles: 6 + 6 = □
* Doubles plus/minus one: 6 + 7 = □ (6 + 6 + 1 or 7 + 7 - 1)
* Decomposing a number leading to a ten: 15 - 7 = □, so 15- 5 = 10 therefore 10 - 2 = 8) * Working knowledge of fact families/related facts: 3 + 9 = 12 so 12 - 9 = □
(See Standard 1.OA.6 for a list of mental strategies)
Representational:
• Show and explain addition and subtraction with objects, pictures, words, and numbers
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understands that each number has a unique value.
• Understands what it means to compose and decompose numbers.
• Understands that whole numbers can be decomposed into parts that make them easier to
work with.
• Understands the number combinations of 10.
Procedural:
• Recognizes and forms combinations of 10
• Adds and subtracts two whole numbers
• Adds and subtracts within 20
Representational:
• Draws pictures, uses objects, number line, and/or words to understand and solve addition and subtraction problems.
• Communicate strategy for determining the total number of dots on a given dot card. Academic Vocabulary and Notation
Decompose, Compose, Number Relationships, Mental Strategies, Number Combinations, Doubles, Doubles Plus/Minus One, Equal Part, Expanded notation, Sum, Difference, Addend, Fact Family, Fluency
39


Instructional Strategies Used
Teacher will provide opportunities for students to develop each of the mental strategies. Teachers will encourage students to share their strategies for solving problems. Teacher will model the strategy with concrete or visual materials and allow for sufficient practice using the same materials. Remember the goal is to move them to mental computation strategies. Some suggestions are:
STEP ONE
Develop the strategies using visual representation in “Number Talk” Routine (see resources on right)
• Ten frames and two color counters
• Dot pattern cards
• Rekenrek
• Linking Cubes
STEP TWO
Apply the strategies to given combinations of numbers. Some strategies lend themselves to specific number sets. (Leading to a ten is very helpful for +8 and +9)
STEP THREE
Move students toward using the strategy mentally by solving without the use of concrete items.
Caution: Each of these steps are essential in providing vital foundational understanding. Repeated practice develops the flexibility required to achieve fluency.
Resources Used
Tens Go Fish Game (Go Fish game looking for combinations of ten)
Turn Over Ten (concentration looking for combinations of ten)
Two of Everything by Lily Toy Hong
Thinking with Numbers: Numbers Talks by Kathy Richardson
Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5 by Sherry Parrish
Mental Math in the Primary Grades by Jack A. Hope, Larry Leutzinger, Barbara J. Reys, Robert E Reys
http://www.k-5mathteachingresources.com/2nd- grade-number-activities.html www.mathwire.com/numbersense/bfacts.html
Assessment Tasks Used
Skill-based Task:
Written number fact assessment showing students ability to solve addition and subtraction facts of all two-digit numbers without the aid of objects or tools.
Problem Task:
This objective specifies that the student solves addition and subtraction problems within 20 using mental strategies. This assessment is done without a context to demonstrate
fluency. This could be accomplished in an interview with the student or while observing partner interaction.
40


Operations and Algebraic Thinking 2OA3
Core Content
Cluster Title: Work with equal groups of objects to gain foundations for multiplication.
Standard:3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that an even number can be separated into two equal groups without any left over.
• Understand that an odd number cannot be separated into two equal groups without having a leftover.
• Understand that the number in the ones place shows if a number is odd or even.
• Understands that a group of tens will always be even.
• Understand that an equation with two equal addends will have an even sum.
Procedural:
• Identify an odd number by pairing objects and having one left over.
• Identify an even number by pairing objects.
• Solve problems with two equal addends.
• Count by two’s.
• Write equations showing double facts (e.g., 2 + 2 = 4 5 + 5 = 10) Representational:
• Draw pictures or arrange counters to show even and odd numbers.
• Search for and highlight patterns on a hundred chart.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understands that even means two groups having the same number in each group.
• Understands what it means to put objects in pairs.
• Understands how to use numbers and symbols to make an equation.
Procedural:
• Use objects to represent a number.
• Divide the objects into two groups.
• Determine if the groups have an equal or unequal number of objects.
• Write an addition equation.
Representational:
• Draw a picture to show equal groups.
Academic Vocabulary and Notation
Odd, even, equal, equation, unequal, pair, group, sum, and addend.
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Instructional Strategies Used
• Teach the Doubles Rap to help the students learn the doubles problems. Recognize the sum of each equation is an even number and is the sum of two equal addends.
• Even and Odd Game Show – Write even and odd numbers on index cards. Cover them with a point value. Have two students come
up. One student chooses a point value. The teacher shows the students the number. The first student to answer “Odd or Even” gets the point for their team.
• Give students a group of objects. Have them divide the objects into pairs. Identify if they have an even or odd number.
Resources Used
Even Stephen & Odd Todd by Katheryn Cristaldi
The Doubles Rap -
www.smbsd.org/uploaded/files/Fine_Arts /
Doubles_Rap.doc
If You Were an Even Number
/If You Were an Odd Number by Marcie Aboff
http://www.brainpopjr.com/math /numbersense/evenandodd/grownups.we ml
• Give the students a number line to 20. Color
the odd numbers green and the even numbers
blue. Give each student a group of
cubes. Have them pair the cubes. Determine if Odd and Even Songs –
they have an odd or even number.
• Read The Missing Mitten by Stuart J.
Murphy. Give each student a page with pictures of mittens on it. Have the students draw a string between two mittens to make pairs. Determine if there is an even or odd amount of mittens.
www.thevirtualvine.com/images /math/odd&evensong.pdf
The Missing Mitten by Stuart J. Murphy
Double the Ducks by Stuart J. Murphy
• Put the students in pairs. Have them roll two
Odd and Even Signs –
dice. If both numbers are even or odd, player 1http://www.bainbridgeclass.com/files.htm
gets a point. If one number is even and one
number is odd, player 2 gets a point.
• Determine if the date is odd or even on the
calendar.
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Assessment Tasks Used
Skill-based Task:
Pair the mittens. Determine if there is an odd or even amount of mittens. If it is even, write the doubles problem for the mittens.
Problem Task:
Jenna, Hannah, Jessica, Patty, and Lil eat lunch together at the same table. Are there an odd or even number of girls at the table? Show your thinking with words, pictures or numbers.
For both types of assessment students should be required to explain how they know the sum is odd or even.
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Operations and Algebraic Thinking 2OA3
Core Content
Cluster Title: Work with equal groups of objects to gain foundations for multiplication.
Standard :4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
MASTERY Patterns of Reasoning:
Conceptual:
• Understand what a rectangular array is.
• Understand how to arrange any set of objects into a rectangular array.
• Understand how the rectangular array represents repeated addition.
• Understand how to write an addition equation representing the array.
Procedural:
• Determine the total number of objects in each row or column for arrays with up to 5 rows and up to 5 columns.
• Use addition to find the total number of objects in a rectangular array.
• Write an addition equation to express the total as a sum of equal addends (adding
either columns or rows).
Representational:
• Build a rectangular array with objects.
• Build a rectangular array on a geoboard.
• Draw a rectangular array using grid paper or a pictorial representation.
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Understand the attributes of a rectangle.
• Understand that a rectangle can be divided into rows and columns.
• Understand how to write an addition equation.
• Understand the definition of sum and addend.
Procedural:
• Identify an array as being arranged in rows and columns.
• Identify the number of rows in a rectangular array.
• Identify the number of columns in a rectangular array.
• Identify the number of squares within a row/column.
Representational:
• Write an addition equation and find the sum of the addends. Academic Vocabulary and Notation
Rectangular array, repeated addition, row, column, equation, sum, and addend.
Instructional Strategies Used Resources Used
• Use square color tiles to create an
array. Split the array into rows to The Doorbell Rang by Pat Hutchins
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represent a repeated addition equation.
• Roll two number cubes. One cube will
represent the number of columns in an array. The other cube will represent the number of rows in an array. Create an array with color tiles. Write a repeated addition problem to express the total sum of color tiles in the array.
• Put students into cooperative
groups. Give each group 12 small objects. Challenge the groups to make as many different rectangular arrays as possible. Have them draw a picture to show all the arrays they were able to create. With each picture have them write a repeated addition equation to express the total sum of the objects.
• Give the students dot paper and counters. Have the students arrange the counters in many different
arrays. Next, have the students mark the dots in each array on the dot
paper. Next to each array write a repeated addition equation to show the sum of the dots.
• Read the book The Doorbell Rang by Pat Hutchins. Give the students 12 paper cookies. As the teacher reads the book, have the students arrange their cookies into arrays to match the
story. Write a repeated addition problem for each array. This activity can also be done with One Hundred Hungry Ants by Elinor J. Princzes
One Hundred Hungry Ants by Elinor J. Princzes Plastic Square Color Tiles –
http://www.enasco.com/product/TB15157T
http://www.brainpopjr.com/math /multiplicationanddivision/arrays/grownups.weml
Fit! Game (pg. 24) –
www2.edc.org/thinkmath /lib/samples/G3C2L2TG_Sample.pdf
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Assessment Tasks Used
Skill-based Task:
Write a repeated addition problem for the following array.
Problem Task:
Sally got a box of chocolates for Valentine’s Day. She wants to eat one row of chocolates each day. How many chocolates will she eat in 4 days? Write an addition problem to find the number of chocolates she will eat.
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Number and Operations in Base Ten 2NBT1
Core Content
Cluster Title: Understand place value.
Standard : 1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens — called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
MASTERY Patterns of Reasoning:
Conceptual:
• Understand that one represents a single unit of measurement in counting
• Understand that ten ones can be “bundled” together to make one set of ten; a ten can also
be represented as 10 single units
• Understand that ten sets of ten can be “bundled” together to make a hundred; a hundred
can also be represented as 100 single units.
• Understand that when numbers are bundled into sets of hundreds, there are zero tens and
zero ones
Procedural:
• Identify the value of a given digit in a 3-digit number (e.g., find the value of the 7 in 706; where 7 = 700)
Representational:
• Model a given number using base ten blocks, straws, beans, etc (e.g., of most “efficient” form of base 10 where 706 can be thought of as 7 hundreds and 6 ones)
• Model the same number in different ways (example using 706 again; 706 can be thought of as 6 hundreds, 10 tens, and 6 ones)
Illustrate a given number using a place value drawing in a math notebook.
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Supports for Teachers
Critical Background Knowledge
Conceptual:
• Identifying the value of a given number in hundreds, tens, and ones Procedural:
• Group 10 single units into a bundle of 10; grouping 10 sets of 10 into a bundle of 100
• Identify the value of a digit in a two digit number (e.g., find the value of the 2 in 29;
where the 2 represents 20)
Representational:
• Model various numbers using base ten blocks representing hundreds, tens, and ones.
• Compose a bundle of 10 from ten single units; Decompose a bundle of 10 into 10 single
units.
• Model the same number in different ways.
Academic Vocabulary and Notation
Ones, Tens, Hundreds, Cube, Long, Flat, Decomposing, Composing, Trading, Grouping, Regrouping or Ungrouping
Instructional Strategies Used
1. Teacher models how to represent a 3- digit number with base 10 blocks (suggested use: http://nlvm.usu.edu/ or base 10 manipulatives and document camera)
2. Students model same number using manipulatives or pictorial representations
3. Students need repeated practicing building numbers with a variety of materials. Students should also write the numbers and be asked to label the place value position.
4. Teacher models the concept of grouping 10 single units into a bundle of 10; also groups 10 sets of 10 into a bundle of 100 (suggested use: http://nlvm.usu.edu/ or base 10 manipulatives and document camera).
5. Student models the concept of grouping 10 single units into a bundle of 10; also groups 10 sets of 10 into a bundle of 100 using manipulatives or pictorial representations
6. Students need repeated practice composing and decomposing multi-digit numbers with a variety of materials.
7. Teacher presents 3-digit number with one of the digits underlined. (251 what is the value of the 5 in this number?)
8. Students need repeated practice identifying the value of the underlined
Resources Used
http://www.amathsdictionaryforkids.com /dictionary.html
http://nlvm.usu.edu/
http://mathwire.com/numbersense /placevalue.html
100 Ways to get to 100 – Jerry Pallotta A Place for Zero -
by Kathy Richardson
Angeline Sparagna Lopresti
and Phyllis Hornung
Understanding Numbers: Place Value
Assessing Math Concepts: Grouping Tens, by
Kathy Richardson
Assessing Math Concepts: Two-Digit Addition
and Subtraction, by Kathy Richardson
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digit in a multi-digit number.
Assessment Tasks Used
Skill-based Task:
Student will correctly model three 3-digit numbers using base 10 blocks or pictorial representation:
248; 309; 780
Student will correctly identify the value of an underlined digit in a 3-digit number.
Problem Task:
1. There are 431 animals that need to be transported to the circus. If 10 animals can fit in a trailer and 10 trailers can fit on a truck, how many trucks and trailers will be needed to transport the animals to the circus? Show your thinking with pictures, words or numbers.
2. Given three digit cards build the largest number possible and the smallest number possible. Students should also use a model to build or draw the numbers. Label the place value positions and tell the value of each digit.
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Number and Operations in Base Ten
Core Content
Cluster Title: Understand place value.
Standard :2. Count within 1000; skip-count by 5s, 10s, and 100s.
MASTERY Patterns of Reasoning:
Conceptual:
2NBT2
• Understand that numbers increase through counting patterns
• Understand that counting patterns can start from any number of that pattern’s multiple
• Understand that counting by 5s is just half of counting by 10s
• Understand that when counting by 10s within a hundred, only the digit in the 10s place
increases
• Understand that when counting by 100s within a thousand, only the digit in the 100s
place increases
• Understand that skip counting is the same as repeated addition
Procedural:
• In addition to standard skip counting patterns starting at zero (such as 10, 20, 30, etc.) students need to be able to add 5, 10, or 100 to ANY starting number within the counting pattern and extend the counting pattern (e.g., 425 – count on by 5s: 430, 435, 440, etc.)
• Be able to demonstrate multiple skip counting patterns from the same starting point (example: start at 200 – skip count by 5s, 10s, and 100s)
Representational:
• Model skip counting with objects
• Use hundred chart to skip count by 5s, 10s, or 100s and highlight each pattern (by
coloring or using objects).
• Use number line to skip count.
• Model the relationship between skip counting and monetary units (nickel, dime,
dollar)
Supports for Teachers
Critical Background Knowledge
Conceptual:
• Students should have a conceptual understanding of movement between rows and patterns on a hundreds chart.
Procedural:
• Count to 120 by ones, starting at any number less than 120. Representational:
• Model skip counting with base ten blocks to show the relationship between skip counting and place value
Academic Vocabulary and Notation
Pattern, skip count, extend, repeated addition, inverse, repeated subtraction, multiples
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