Did You Know?

1. ?????????????????? Did You Know?

2. WELCOME Mathematics Educators to the Career and College Ready Conference A Quick Look at Critical Topics in Mathematics Reform from Past Academies

3. Remember to: • Reduce Side Chatter • Involve Yourself in the Process • GiveYour Thoughts & Ideas • Open Your Mind on how You Can Change Instruction • Remember to Silence Electronic Devices

4. Outcomes of the Conference • Reflect on how the Standards for Mathematical Practice will be infused into daily instruction. • Become familiar with the Maryland's College and Career-Ready Standards. • Analyze the instructional SHIFTS

5. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others. Model with Mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure. Look for and express regularity in reasoning Apply to every Mathematics Unit in every grade/course

6. Standards for Mathematical Practice (SMP)

7. SMP Placemat Activity Placemat Behavior Cards

8. Standards for Mathematics • Conceptual Categories for • High School: • Number and Quantity • Algebra • Functions • Geometry • Modeling • Probability and Statistics

9. Content Standards for Mathematics Algebra I Arithmetic with Polynomials and Rational Functions • Perform arithmetic operations on polynomials • Understand the relationship between zeros and factors of polynomials • Use polynomial identities to solve problems • Rewrite rational expressions

10. Focus Coherence Rigor SHIFTS in Mathematics • Conceptual Understanding • Procedural Skill • Modeling/Application

11. Shift #1

12. MAJOR SUPPORTING • ADDITIONAL FOCUS

13. FOCUS Final Thoughts FOCUS is largely built into the CCSSM curriculum. The charge for the classroom teacher is to take opportunities to revisit major content frequently and make connections between the major and supporting and additional content.

14. Shift #2 C O H E R E N C E Prior Learning New Learning Shift #2

15. Pythagorean Theorem Connects to Distance Formula Connects to COHERENCE Pythagorean Trig Identities

16. COHERENCE

17. COHERENCE Progression Documents

18. COHERENCE Final Thoughts Instruction in the mathematics classroom of the future must take advantage of every opportunity to make connections between topics both within a course and from course to course if the SHIFT toward COHERENCE is to be a achieved.

19. Shift #3 “Rigoris the goal of helping students develop the capacity to understand content that is complex, ambiguous, provocative, and personally or emotionally challenging.”

20. Non-rigorous Learning Experiences What are some characteristics of RIGOROUS learning experiences? • Awkward, difficult values • Minimal effort required • Focus on quantity, repetition • Scripted, includes pathway to the solution • No links to other mathematics • Routine, rote procedures • Memorized rules without understanding • Teachers do the work while students observe Rigorous Learning Experiences Challenge students Require effort and tenacity Focus on quality Have multiple paths Not always “tidy” Connect ideas in mathematics Develop strategic, flexible thinking Encourage reasoning and sense-making Actively involve students

21. PARCC Model Content Framework documents include Fluency Recommendations Procedural Skill

22. Items Drag into the box exactly three unique items whose sum is less than 10. Drag into the box exactly three unique items whose sum is between 10 and 20. Drag into the box exactly three unique items whose sum is greater than 20. Three unique items whose sum is less than 10 Three unique items whose sum is between 10 and 20 C. Three unique items whose sum is greater than 20 Procedural Skill

23. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Conceptual Category:Algebra Domain: Reasoning with Equations and InequalitiesCluster: Represent and solve equations graphically Standard A-REI.10 Conceptual Understanding

24. To help students develop conceptual understanding provide learning experiences that : • see connections between the mathematics they are learning and what they already know. • use manipulatives to model concepts, • and then verbalize their results. • show different representations of the • same mathematical situation. Conceptual Understanding

25. Conceptual Understanding

26. ModelingMathematics What does it mean to MODEL with mathematics?

27. SMP #4:Model with mathematics • Conceptual Category :Modeling • Modeling Standards: A.CED.1 Modeling/Application

28. Modeling and PARCC Assessments • Tasks assessing modeling / applications • call for modeling/application in a real-world • context or scenario (MP.4) and can also • involve other mathematical practice • standards. • tasks may include a mix of innovative, • machine scored and hand scored responses. • will be included on the PBA component • and generate evidence for measuring • mathematical modeling/application with connections to content.

29. Modeling Cycle Problem Report Formulate Compute Validate Interpret

30. Modeling Cycle Problem Report Formulate Validate Compute Interpret

31. FINAL THOUGHTS ON RIGOR Procedural Skill Conceptual Understanding Modeling/Application

32. RELIABLE RESOURCES Illustrative Mathhttps://www.illustrativemathematics.org/ • Bill McCullum, CCSS lead writer • Sample Lessons that illustrate specific standards Achieve The Core https://achievethecore.org • Jason Zimba, CCSS lead writer • Multiple Resources – e.g. Lesson Plans, Assessments, Professional Development courses, Grade-at-a-Glance PARCChttp://parcconline.org • Information about PARCC Assessments • Sample Lessons • Practice Tests

33. Noticing and Wondering Annie Fetter http://www.youtube.com/watch?v=WFvYZDR4OeY

34. The greatest danger for most of us is not that our aim is too high and we miss it…. But that it is too low and we reach it. -- Michelangelo