Common Core Mathematics
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Prepared for21st Century Instructional LeadershipJune 17, 2013Common Core Mathematics
Mission StatementEast Central University's mission is to foster a learning environment in which students, faculty, staff and community interact to educate students for life in a rapidly changing and culturally diverse society. Within its service area, East Central University provides leadership for economic development and cultural enhancement.
Administrator AND Curriculum LeaderThe same only differentDont forget: You can copy-paste this slide into other presentations, and move or resize the poll.Press F5 or enter presentation mode to view the pollIn an emergency during your presentation, if the poll isn't showing, navigate to this link in your web browser:http://www.polleverywhere.com/free_text_polls/71eHLs9YsaVSuGf
If you like, you can use this slide as a template for your own voting slides. You might use a slide like this if you feel your audience would benefit from the picture showing a text message on a phone.4EMPOWERINGENGAGING
http://www.ok.gov/sde/sites/ok.gov.sde/files/OC3%20Math%20Standards%20Overview.pdfCommon Core State Standards: Mathematics ShiftsFocus strongly where the Standards focusCoherence think across grades, and link to major topics within gradesRigor in major topics pursue:Conceptual understandingProcedural skill and fluencyApplicationwith equal intensityhttp://www.achievethecore.org/files/6213/6880/2802/2-pager_update_05.16.13.pdfEMPOWERINGENGAGING
Articulating CurriculumFocus, Coherence, RigorThe role of leadershipGet every mathematics teacher teaching the intended curriculum every day (coherence/curriculum alignment)Break the dominant techniqueLectureDemonstrationIndependent PracticeEmphasize focus
ThinkHow do you engage teachers about mathematics curriculum?How do you address all personalities?How do you address the spectrum of mathematics proficiency and/or fluency proficiency?EMPOWERINGENGAGING
Implementing CurriculumA volume problem from textbook to Common Core application.Math Problem
Find the volumeReal World Application
Calculate the amount of water needed to fill the fountain.Problem BasedCalculate the amount of water needed to fill the pool and prepare a budget for the necessary upkeep (chemicals, cleaning, etc.).
Common CoreThe administration will host a forum to consider the continued maintenance of the fountain or recommendations for replacing the fountain. Plan a proposal and presentation to either support or replace the fountain. Include budget, aesthetic and social considerations.
CCSS Prototypeshttp://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html The role of leadershipEnsure curriculum implementation throughStudent/Parent communicationVisibility of learning objectivesReview of curriculum documentsClassroom visits and observations
WILLINGABLEThinkWhy does this category (implementing) fall under engagement instead of empowerment?How do you address all personalities?How do you address the spectrum of mathematics proficiency and/or fluency proficiency?How do you get them to open the door?EMPOWERINGENGAGING
Incorporating Effective StrategiesStudent collaboration, strategies for all students, alignmentSample Lessonshttp://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html http://www.parcconline.org/samples/item-task-prototypes
Teaching Channelhttps://www.teachingchannel.org/videos/class-warm-up-routine?fd=1https://www.teachingchannel.org/videos/carousel-activity-math-lesson?fd=1https://www.teachingchannel.org/videos/real-world-geometry-lesson?fd=1https://www.teachingchannel.org/videos/surface-area-lesson Handy PARCCingOverview of Mathematics Task TypesPARCC mathematics assessments will include three types of tasks. Task TypeDescription of Task TypeI. Tasks assessing concepts, skills and procedures Balance of conceptual understanding, fluency, and applicationCan involve any or all mathematical practice standardsMachine scorable including innovative, computer-based formatsWill appear on the End of Year and Performance Based Assessment componentsII. Tasks assessing expressing mathematical reasoning Each task calls for written arguments / justifications, critique of reasoning, or precision in mathematical statements (MP.3, 6).Can involve other mathematical practice standardsMay include a mix of machine scored and hand scored responsesIncluded on the Performance Based Assessment componentIII. Tasks assessing modeling / applications Each task calls for modeling/application in a real-world context or scenario (MP.4) Can involve other mathematical practice standards.May include a mix of machine scored and hand scored responsesIncluded on the Performance Based Assessment componentFor more information see PARCC Item Development ITN Appendix D. Grade 7 Illustrative Sample Item
Aligns to the Standards and Reflects Good PracticeGrade 7 Sample Illustrative Item: SpeedTask Type I: Tasks assessing concepts, skills and procedures Alignment: Most Relevant Content Standard(s)7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.In addition, see 7.RP.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. (The explain portion is not required in the task, but the task involves some of the concepts detailed here.)Alignment: Most Relevant Mathematical Practice(s)MP.2 enters (Reason abstractly and quantitatively), as students must relate the graphs and tables to each other via the unit rate and then to the context at hand.
Aligns to the Standards and Reflects Good PracticeGrade 7 Sample Illustrative Item Key Features and Assessment AdvancesThe PARCC assessment will seek to preserve the focus of the Standards by thoroughly exploring the major work of the grade. In this case, a multi-point problem is devoted to a single standard about proportional relationships, which are a major focus in grades 6 and 7. Unlike traditional multiple choice, it is difficult to guess the correct answer or use a choice elimination strategy. Variants of the task could probe understanding of unit rates and representations of proportional relationships by showing different scales on the two graphs, and/or by presenting the data in tables C and D with the ordered pairs not equally spaced in time.High School Illustrative Sample ItemSeeing Structure in a Quadratic Equation
Aligns to the Standards and Reflects Good PracticeHigh School Sample Illustrative Item: Seeing Structure in a Quadratic EquationTask Type I: Tasks assessing concepts, skills and procedures Alignment: Most Relevant Content Standard(s)A-REI.4. Solve quadratic equations in one variable.Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p)2 = q that has the same solutions. Derive the quadratic formula from this form.Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a bi for real numbers a and b.Alignment: Most Relevant Mathematical Practice(s)Students taking a brute-force approach to this task will need considerable symbolic fluency to obtain the solutions. In this sense, the task rewards looking for and making use of structure (MP.7).
Aligns to the Standards and Reflects Good Practicehttp://www.achievethecore.org/files/3013/6863/6129/CCSS_Evidence_Guide_Over_the_Year_Math_K-8_v051313.pdf
ReferencesOne-Page Overview of OC3-Mhttp://www.ok.gov/sde/sites/ok.gov.sde/files/OC3%20Math%20Standards%20Overview.pdfThe Common Core Shifts At a Glancehttp://www.achievethecore.org/files/6213/6880/2802/2-pager_update_05.16.13.pdfPublishers Criteria for the CCSS in Mathematicshttp://www.achievethecore.org/files/6913/6545/6063/Math_Publishers_Criteria_K-8_Spring_2013_FINAL.pdf Elementary Math Specialist & Teacher Leader Projecthttps://sites.google.com/site/emstlonline/ Inside Mathematicshttp://insidemathematics.org/index.php/exemplary-lessons-integrating-practice-standards
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