Presentation on theme: "Susan Gendron Senior Fellow June 14, 2012"— Presentation transcript:
1 Susan Gendron Senior Fellow June 14, 2012 Transitioning to the Common Core State Standards and Next Generation Assessments Yakima, WASusan GendronSenior FellowJune 14, 2012
2 Common Core State Standards Define the knowledge and skills students need for college and careerDeveloped voluntarily and cooperatively by states; 46 states and DC have adoptedProvide clear, consistent standards in English language arts/Literacy and mathematicsSource:
5 PISA 2009 Overall Math Scale 25th last time 1 Shanghai-China 600 2 Singapore5623Hong Kong-China5554Korea5466Finland5419Japan52910Canada52711Netherlands52613New Zealand51915Australia51416Germany51322France49728United Kingdom49231United States48732Ireland34Spain48338Russian Federation46851Mexico41957Brazil38661Indonesia371PISA 2009Overall Math ScaleSignificantly Above OECD AverageNot Significantly Different(OECD Average 496)Significantly below OECD Average25th last time
6 PISA 2009 Overall Science Scale Last time 21 1 Shanghai-China 575 2 Finland5543Hong Kong-China5494Singapore5425Japan5396Korea5387New Zealand5328Canada52910Australia52711Netherlands52213Germany52016United Kingdom51420Ireland50823United States50227France49836Spain48839Russian Federation47850Mexico41653Brazil40560Indonesia383PISA 2009Overall Science ScaleSignificantly Above OECD AverageNot Significantly Different(OECD Average 501)Significantly below OECD AverageLast time 21
7 Mapping State Proficiency Standards onto NAEP Scales, IES August 2011 Reading RiskWAMapping State Proficiency Standards onto NAEP Scales, IES August 2011
8 Proficiency Grade 4 Reading 2009 ProficientRequiredNAEP ScoreCalifornia60 %202Massachusetts54 %234Missouri47 %229New Hampshire74%211Oregon84 %177Washington73 %205Vermont70%2142nd in the eGrade 4 from Proficient
9 Mapping State Proficiency Standards onto NAEP Scales, IES August 2011 Reading RiskWAMapping State Proficiency Standards onto NAEP Scales, IES August 2011
10 Proficiency Grade 8 Reading 2009 ProficientRequiredNAEP ScoreCalifornia48%259Minnesota67%Missouri50%267Vermont69%Oregon250Washington68%253Missouri number one
11 Mapping State Proficiency Standards onto NAEP Scales, IES August 2011 Math RiskWAMapping State Proficiency Standards onto NAEP Scales, IES August 2011
12 Proficiency Grade 4 Mathematics 2009 ProficientRequiredNAEP ScoreCalifornia65 %220Massachusetts48 %255Hawaii50 %239New Hampshire73 %237New Mexico77 %224Washington52 %243Missouri45 %246Second in the country
13 Math RiskWAMapping State Proficiency Standards onto NAEP Scales, IES August 2011
14 Proficiency Grade 8 Mathematics 2009 ProficientRequiredNAEP ScoreCalifornia41 %270Massachusetts49 %300Missouri47 %287Hawaii39%286Minnesota58 %Oregon71 %266Washington53 %Third in the country
15 Partner Discussion What are your risks? How will you prepare your school for a potential dip in scores?
21 Common Core Research 1900 entry level courses Instructor ratings 25 areas, 14 general education,Reviewed syllabi, assignments and exams
22 Key Findings CCSS applicable to success in a wide range of courses Challenge level is sufficientCoherent representation of knowledge necessaryCore of knowledge is common across general education and career coursesCareer areas tend to have knowledge profiles that differ from general education
23 Lexile Framework® for Reading Study Summary of Text Lexile Measures Interquartile Ranges Shown (25% - 75%)160014001200Text Lexile Measure (L)1000800600PersonalUseEntry-LevelOccupa-tionsHighSchoolLit.CollegeLit.HighSchoolTextsCollegeTextsMilitarySAT 1,ACT,AP** Source of National Test Data: MetaMetrics
24 Content Reading and Writing Strategies that Work for All Students MetaMetrics Survey 2000Arkansas Democrat Gazette1230 LAssociated Press1310 LLA Times1330 LMiami Herald1200 LNew York Post1280 LOakland Tribune1210 LRaleigh News & Observer1220 LWall Street Journal1320 LUSA TodayKuzmich, 2006
25 On-the Job Lexile Requirements National Adult Literacy Study 19921,5001,4001,3001,2001,1001,000900800International Center for Leadership in Education 2009ConstructionCraftsmanNurseSalesSecretary
26 Key to Effective Instruction Is Alignment Organizational LeadershipInstructional LeadershipTeaching
31 Levin and ElmoreEveryone needs to collaborate to ensure that daily teaching and learning practices are the focus of the schoolAll responsible for successPrincipals and teachers are fundamentally evaluatorsLeaders responsible for cultural changes – by displacing specific norms, structures, and processes by others
32 Does your culture do this? Collaboratively build teamsTeam works to solve dilemmas in learningCollectively share and critique the nature and quality of evidence that shows our impact on student learningCooperate in planning and critiquing lessons, learning intentions, and success criteriaHattie, John Visible Learning for Teachers
34 Common Core State Standards All students graduate college and career readyAll students are prepared for all entry-level, credit-bearing, academic college courses in English, mathematics, the sciences, the social sciences, and the humanities.All students enter these classes ready for success (defined for these purposes as a C or better).All American students are prepared for the global economic workplace.
35 DiscussionHow will you create a culture in your schools of ALL students “college and career ready”?
41 Design and Organization Three appendices: A: Research and evidence; glossary of key terms B: Reading text exemplars; sample performance tasks C: Annotated student writing samples
42 Shared Responsibility for Students’ Literacy Development “The Standards insist that instruction in reading, speaking, listening, and language be a shared responsibility within the school” (p. 4).“This division reflects the unique time-honored place of ELA teachers in developing students’ literacy skills while at the same time recognizing that teachers in other areas must have a role in this development as well” (p. 4).Adapted from “Key Design Considerations” (page 4 of the Standards)
44 Increasing Sophistication Reading Anchor Standard #9 Integration of Knowledge and IdeasAnalyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.KindergartenGrades 11-CCRIntegration of Knowledge and Ideas9. Compare and contrast the most important points and key details presented in two texts on the same topic.Integration of Knowledge and Ideas9. Integrate information from diverse sources, both primary and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources.
45 English Language Arts and Literary Shifts Engageny.org
46 Balancing Literature and Informational Text Shift 1Balancing Literature and Informational Text
47 Literary/Informational Text LiteratureInformational TextStoriesDramaPoetryLiterary Nonfiction and Historical, Scientific, and Technical TextsIncludes children’s adventure stories, folktales, legends, fables, fantasy, realistic fiction, and mythIncludes staged dialogue and brief familiar scenesIncludes nursery rhymes and the subgenres of the narrative poem, limerick, and free verse poemIncludes 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
48 Reading Framework for NAEP 2009 GradeLiteraryInformational450%845%55%1230%70%Standards demand a greater focus on informational text literary non fictionMajor focus in 6-12
49 Reading College and Career Readiness Anchor Standards Key Ideas and Details 1. Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual 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.
50 Reading College and Career Readiness Anchor Standards Craft and Structure4. 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.
51 Reading College and Career Readiness Anchor Standards Integration of Knowledge and Ideas7. 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.
52 Building Knowledge in the Disciplines Shift #2Building Knowledge in the Disciplines
53 Shared Responsibility for Students’ Literacy Development “The Standards insist that instruction in reading, speaking, listening, and language be a shared responsibility within the school” (p. 4).“This division reflects the unique time-honored place of ELA teachers in developing students’ literacy skills while at the same time recognizing that teachers in other areas must have a role in this development as well” (p. 4).Adapted from “Key Design Considerations” (page 4 of the Standards)
54 Why Literacy in History/Social Studies, Science and Technical? Students are consistently unable to meet the demands of reading text within a particular discipline.Reading within a discipline is different than reading literature.The ability to read within the discipline is important to citizenship.Being literate across a broad range of disciplines is required to be considered College and Career Ready.
55 History is interpretive. How is reading history/social studies different from other types of reading?History is interpretive.History is an argument in favor of a particular narrative.Who the author is matters. (sourcing)The author’s purpose matters. (bias and perspective)A single text is problematic. (corroboration)
56 Focus is on claims and counter claims How is reading science and technical reading different from other types of reading?Focus is on claims and counter claimsPrecise details, complex details and processesAnalyze results by comparingDetermining what question is being raisedNavigate text, graphs, tables, chartsEvaluate basis for claims
57 Reading College and Career Readiness Anchor Standards Range of Reading and Level of Text Complexity10. Read and comprehend complex literary and informational texts independently and proficiently.
58 Staircase of Text Complexity Shift #3Staircase of Text Complexity
59 Text complexity is defined by: Overview of Text ComplexityReading Standards include over exemplar texts (stories and literature, poetry, and informational texts) that illustrate appropriate level of complexity by gradeText complexity is defined by:QualitativeQualitative measures – levels of meaning, structure, language conventionality and clarity, and knowledge demandsQuantitativeQuantitative measures – readability and other scores of text complexityBest measured by an attentive readerAbility to make an informed decision about the difficulty of a textKnowledge of four factors in developing effective tools:Levels of Meaning or PurposeReader and Task: Determining whether a given text is appropriate for the student:Cognitive abilitiesMotivationTopic knowledgeLinguistic and discourse knowledgeComprehension strategiesExperiences“Reading for Understanding, 2002, The RAND Reading Study group”Quantitative: Word length or frequency (Flesch-Kincaid Grade Level text, Dale-Chall Readability Formula, Lexile)Sentence lengthText cohesion (University of Memphis, Coh-Metrix)Measurement tools ( Lexile exampleStructureLanguage Conventionality & ClarityKnowledge DemandsReader and TaskReader and Task – background knowledge of reader, motivation, interests, and complexity generated by tasks assigned
60 Step 1: Qualitative Measures Measures such as:Levels of meaningLevels of purposeStructureOrganizationLanguage conventionalityLanguage clarityPrior knowledge demands
62 Text Complexity Grade Bands and Associated Lexile Ranges Text Complexity Grade Band in the StandardsOld Lexile RangesLexile Ranges Aligned to CCR expectationsK-1N/A2-34-56-89-1011-CCRMetametrics has realigned its Lexile ranges to match the Standards’ text complexity grade bands and has adjusted upward its trajectory of reading comprehension development through the grades
63 Step 3: Reader and Task Considerations such as: Motivation Knowledge and experiencePurpose for readingComplexity of task assigned regarding textComplexity of questions asked regarding text
65 College and Career Readiness Anchor Writing Standards Text Types and PurposesWrite arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.Write narratives to develop real or imagined experiences or events using effective techniques, well-chosen details, and well-structured event sequences.
67 College and Career Readiness Anchor Writing Standards Production and Distribution of WritingProduce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.
70 College and Career Readiness Anchor Writing Standards Research to Build and Present KnowledgeConduct short, as well as more sustained research projects based on questions, demonstrating understanding of the subject under investigation.Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism.Draw evidence from literary or informational texts to support analysis, reflection, and research.
71 College and Career Readiness Writing Standards Range of WritingWrite 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.
72 Writing and Research the Analyzes and Deploys Evidence Draw evidence from texts to support and develop:AnalysisReflectionResearchIncrease opportunities to write in response to sourcesExtensive practice with short, focused research projects“typically taking a week and occurring—at a minimum—quarterly”Increase focus on argumentation and informative writing, less narrative writing
74 High-quality, Text-dependent Questions & Tasks “Among the highest priorities of the Common Core Standards is that students can read closely and gain knowledge from texts.”“More questions that can be answered only with reference to the text.”“Sequences of questions should elicit a sustained discussion.”Tasks must “require the use of more textual evidence.”
75 College and Career Readiness Anchor Standards for Speaking and Listening Comprehension and Collaboration1. Range of conversations and collaborations, 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.
76 College and Career Readiness Anchor Standards for Speaking and Listening Presentation of Knowledge and Ideas4. 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.
77 College and Career Readiness Anchor Standards for Language Conventions of Standard EnglishWhen writing or speaking.Use capitalization, punctuation, and spelling when writing.Knowledge of LanguageTo comprehend more fully when reading or listening.Vocabulary Acquisition and Use4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts,5. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings6. Acquire and use accurately a range of general academic and domain-specific words
79 Language Progressive Skills Tier I - words of everyday speechTier II - general academic words, typically found in text, ways to communicate simple ideasTier III - domain-specific words (informational text)Handout to be used with language section
80 Reading critical to building knowledge Reading Standards for Literacy in History/Social Studies, Science and Technical Subjects 6-12Reading critical to building knowledgeAppreciation for the norms and conventionsEvidenceUnderstanding of domain specific wordsAnalyze, evaluate intricate argument, synthesizeComplement the disciplines
84 Top Achieving Countries Topic Placement inTop Achieving CountriesTopics (32) that at least 2/3 of the top achieving countries include in their ‘core’ curriculum. Grades 1-8.
85 Topic Placement in the U.S. Composite math standards from 21 states with topics covered by 2/3 of the statesStructure of increasing complexity not seen. Topics are taught repeatedly throughout the grades. Many more topics at each grade level means topics receive less depth. Early introduction of many demanding topics (transformational geometry, measurement error, functions) . Empty rows reflect non-consensus of when to teach a topic, such as properties of common and decimal fractions.Seems to be more of a laundry list approach.Not reflecting the structure of mathematics complexity which requires pre-requisite knowledge
86 K-8 Domain Progressions in CCSS DomainsK12345678Counting and CardinalityOperations and Algebraic ThinkingNumber and Operations in Base TenNumber and Operations - FractionsRatios and Proportional RelationshipsThe Number SystemExpressions and EquationsFunctionsMeasurement and DataGeometryStatistics and ProbabilityFollowing the National Math Panel recommendations, the new standards provide a strong foundation for Algebra by focusing on a strong foundation of number, operations, and fractions in the early grades and bringing in proportionality, probability and statistics in middle school.Many districts in the past, have provided the option for students who are ready to take Algebra I in the 8th grade. This may have been a reaction to the repetition that was seen in the grades 6-8 standards in the past. That repetition was not unique to Massachusetts, and was addressed by the Common Core Standards writers. As a result, the new grade 6-8 standards include more in-depth study of ratio, proportion, and statistics and probability. Many of the topics that commonly were thought of as part of an Algebra I course, such as introducing functions, are now a critical area for grade 8.
88 Focus – Shift # 1 Key ideas, understandings, and skills are identified Deep learning of concepts is stressedThat is, time is spent on a topic and on learning it well. This counters the “mile wide, inch deep” criticism leveled at most current U.S. standards.
89 Critical Areas – similar to NCTM’s Curriculum Focal Points Grade Level OverviewCritical Areas – similar to NCTM’s Curriculum Focal PointsAll K-8 have critical areas – areas that should be emphasized and require more time at the given grade level. This aligns exactly with CFP
90 Coherence – Shift #2Articulated progressions of topics and performances that are developmental and connected to other progressionsConceptual understanding and procedural skills emphasized equallyNCTM states coherence also means that instruction, assessment, and curriculum are aligned
91 Format of Pre-K-8 Standards DomainGrade Level2.NBT (code)ClusterHadingClusterStandard2.NBT.1 (code)Click to show the headings used to categorize the standards. The broadest header is “Domain” which is the larger groups of related standards. There is a code for each grade level with an abbreviation for the domain (2.NBT)Clusters are groups of related standards under the domain.Standards define specifically what students should know and be able to do and are numbers starting with #1.The coherence of the standards at each grade level is demonstrated through the domains and clusters. The standards are grouped first by domain then by cluster. Each grade has up to 6 domains, and each domain is divided into one or more clusters.(The next slide will show the progression of domains through grade 8.)FocusCoherenceClarityRigor
92 Fractions, Grades 3–63. Develop an understanding of fractions as numbers.4. Extend understanding of fraction equivalence and ordering.4. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.4. Understand decimal notation for fractions, and compare decimal fractions.5. Use equivalent fractions as a strategy to add and subtract fractions.5. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.6. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
93 Mathematics/Standards for Mathematical Practice Make sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments and critique the reasoning of othersModel with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated reasoning1.Analyze givens, constraints, relationships and goals
94 The Common Core State Standards offer the possibility of re-orienting school mathematics around a more robust conception of mathematical competence.Deborah BallUniversity of Michigan, Nov 2011
95 Implications for Instruction Mathematical Practices—requires that the Content be taught through the Practices. That way, the connections are real—integrated rather than interspersed.Do activity on slide . . .
96 Viewing Mathematical Practices Choose one lesson and watch approximately 5-7 minutes of instruction using your rubric. Have a discussion on evidence of the mathematical practice.Practice 1Practice 2Practice 3Practice 4Practice 5Practice 6Practice 7Practice 8Say, “This video is from the website, Inside Mathematics, an initiative funded by the Noyce Foundation. The website includes demonstration lessons, tools and resources to support mathematics educators, and a professional learning community to encourage reflective practice.”“The video we are going to watch is not intended to be an exemplar. Instead, it is meant to provide us with a common context so that we can discuss evidence of student proficiency of the practice standards that we are exploring. As you’re watching the video, consider the questions on the slide.”
97 Institute for Advanced Study/Park City Mathematics Institute Secondary School Teachers Program/Visualizing Functions
98 Mathematical practice rubrics RESOURCES TO SUPPLEMENT RUBRICS IMPLEMENTING MATHEMATICAL PRACTICES
100 Rigor -Require fluency, application, and deep understanding Conceptual understanding – solving short conceptual problems, applying math in new situations, and speaking about their understandingProcedural skill and fluency - speed and accuracy in calculation.Application - “real world” situations
101 Reasoning Invite Exploration of important mathematical concepts Allow students to solidify and make connectionsMake connections and develop coherent framework for mathematical ideasProblem formulation, problem solving and mathematical reasoning
102 Reasoning More than one solution Development of all students’ disposition to do math
103 Mathematically proficient students Make conjecturesBuild logical progressions to explore the truth of their conjecturesJustify and communicate their conclusionsRespond to arguments
104 Which number does not belong? Why? Instead of asking which numbers are odd?From: Math for All: Differentiating Instruction, Grades 3-5, Dacey and Lynch
105 Procedural Fluency Knowledgeable about procedures Know when and how to use themSkill in performing procedures flexibly, accurately, efficiently and with understanding
106 Major flow leading to Algebra Operations and Algebraic Thinking leads to explicit work with Expressions and Equations beginning in Grade 6. Grade 6 is also when Base Ten and Fractions are merging to become The Number System. By the end of middle school, Expressions and Equations and The Number System have merged to become high school Algebra.
108 Cognitively-Guided Instruction Process Start the study of a new concept with a rich problem or hypothesisInvite your students to engage in the problemCommunicate multiple representations of solutionsQuestions, justify, and critique thinkingUse your understanding of student thinking to guide further instruction
122 4The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable. 5Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations.
123 Mrs. Olson’s sidewalk (SMARTER) Ms Olsen’s Sidewalk addresses: Content Standards 7.G.6, 7.NS.3, 8.G.7 Practices P1, P5. Claims 1 and 2.In this task students are given a real-world problem whose solution involves determining the areas of two-dimensional shapes as part of calculating the cost of a sidewalk. This particular compound shape could be divided in more than one way and a choice needs to be made as to whether the shape should be considered as a rectangle and trapezoid or a longer rectangle with two smaller right-angles triangles appended near Ash Road (these can be thought of as two halves of a rectangle of width 2ft and diagonal 7.2ft). The dashed line leads towards the former.A common problem with the calculation of the areas of trapezoids is the misuse of the length marked 7.2 ft. Students will need to make use of this dimension but must avoid falling into the error of multiplying 8.5 x 7.2 in an attempt to find the area of the trapezoid. Once the decision has been made regarding how to best deconstruct the figure students will need to apply the Pythagorean Theorem in order to calculate the length of the path contained with the trapezoid.When this has been calculated the remaining length and area calculations can be undertaken. The final stage of this multi-step problem is to calculate the cost of the paving based on the basic fee of $200 plus $12 per square foot.
124 Mrs. Olson’s sidewalk Content Standards 7.G.6, 7.NS.3, 8.G.7 Make sense of problems and persevere in solving them (P1). They will need to analyze the information given and choose a solution pathway. Attend to precision (P6) in their careful use of units in the cost calculations.
125 Note: For scoring purposes, the points for each element can be weighted to reflect the importance of that element relative to the entire task. Further, “Total Points” may be treated in several ways.One approach is to use “value points”, where the total number of points is broken into segments, each accounting for a single score point. For example: if there are a total of 10 points in the rubric, but the task is determined to be valued at 3 points on the test, the rubric may allocate the 10 total points as: 0 value points = Score 0; 1-3 value points = Score 1; 4-7 value points = Score 2; 8-10 value points = Score 3.An alternate scoring scheme simply awards test points on the basis of features of the task. In the “Ms. Olsen’s Sidewalk” task above, if the task is worth 3 points on the test, all 3 points could be awarded if both the final answer for cost and the final square footage are accurate; 2 points could be for only having the square footage is accurate; 1 point for using the Pythagorean Theorem but with an error in calculations; and 0 points for not having any these.
130 HS Pathways1) Traditional (US) – 2 Algebra, Geometry and Data, probability and statistics included in each course 2) International (integrated) three courses including number , algebra, geometry, probability and statistics each year 3) Compacted version of traditional – grade 7/8 and algebra completed by end of 8th grade 4) Compacted integrated model, allowing students to reach Calculus or other college level courses
132 The second part of the pathways shows the clusters and standards as they appear in the courses. Each course contains the following components:• • •An introduction to the course and a list of the units in the course Unit titles and unit overviews (see below) Units that show the cluster titles, associated standards, and instructional notes (below)
133 As Felicia gets on the freeway to drive to her cousin's house, she notice that she is a little low on gas. There is a gas station at the exit she normally takes, and she wonders if she will have to get gas before then. She normally sets her cruise control at the speed limit of 70mph and the freeway portion of the drive takes about an hour and 15 minutes. Her car gets about 30 miles per gallon on the freeway, and gas costs $3.50 per gallon.Describe an estimate that Felicia might do in her head while driving to decide how many gallons of gas she needs to make it to the gas station at the other end.Assuming she makes it, how much does Felicia spend per mile on the freeway? Alignment 1: N-Q.1, N-Q.3
136 ResourcesNational Council of Supervisors of Math:Mathematics Assessment Project (MAP):
137 Item Exemplars: Performance Task Performance Task drawn from the Ohio Performance Assessment Project.
138 Item Exemplars: Performance Task (cont’d) Performance Task drawn from the Ohio Performance Assessment Project.
139 Item Exemplars: Performance Task (cont’d) Performance Task drawn from the Ohio Performance Assessment Project.
140 JUNE ORLANDOCutting-edge approaches from schools that are ahead of the curve in preparing for the Common Core State Standards, Next Generation Assessments, and Teacher Evaluation based on student performance:Leveraging rigor, relevance, and relationships to prepare students for success in theincreasingly technology-driven global economyEmpowering educators to embrace innovation and leverage technology to change theway they teach