Dodge City Public Schools Grades 7 - 12 August 17, 2011 Elaine Watson, Ed.D .

1. Common Core Standards for Mathematical Practice Dodge City Public Schools Grades 7 - 12 August 17, 2011 Elaine Watson, Ed.D. International Center for Leadership in Education

2. Introductions Introduce yourself: • Name • Instructional Level • On a scale of 1 – 5, with • 1 representing very little knowledge • 5 representing expert knowledge • where do you lie with respect to an understanding of the eight Standards for Mathematical Practice?

3. Desired Outcomes After this three hour presentation, participants will have an introductory understanding of: • The difference and connection between the Standards for Mathematical Practice and the Standards for Mathematical Content • How the Content Standards will be assessed beginning in the 2014-2015 school year • Be familiar with the format and terminology of the Standards for Mathematical Practice • Understand how the ICLE Rigor Relevance Framework can be used as a tool to plan instruction that will reinforce students’ acquisition of the Standards for Mathematic Practice

4. Common Core The new standards support improved curriculum and instruction due to increased: • FOCUS, via critical areas at each grade level • COHERENCE, through carefully developed connections within and across grades • CLARITY, with precisely worded standards that cannot be treated as a checklist • RIGOR, including a focus on College and Career Readiness and Standards for Mathematical Practice throughout Pre K – 12.

5. Common Core Standards for Mathematical Practice Standards for Mathematical Content Same for All Grade Levels Specific to Grade Level

6. Grade 7 Overview

7. Grade 8 Overview

8. High School Overview

9. Structure of Common Core Content Standards K - 5

10. Structure of Common Core Content Standards 6 - 8

11. Structure of Common Core Content Standards HS High School Content Standards are listed in conceptual categories Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability

12. Structure of Common Core Content Standards HS Number and Quantity Overview • The Real Number System • Quantities • The Complex Number System • Vector and Matrix Quantities

13. Structure of Common Core Content Standards HS Algebra Overview • Seeing Structures in Expressions • Arithmetic with Polynomials and Rational Expressions • Creating Equations • Reasoning with Equations and Inequalities

14. Structure of Common Core Content Standards HS Functions Overview • Interpreting Functions • Building Functions • Linear, Quadratic, and Exponential Models • Trigonometric Functions

15. Structure of Common Core Content Standards HS Geometry Overview • Congruence • Similarity, Right Triangles, and Trigonometry • Circles • Expressing Geometric Properties with Equations • Geometric Measurement and Dimension • Modeling with Geometry

16. Structure of Common Core Content Standards HS Statistics and Probability Overview • Interpreting Categorical and Quantitative Data • Making Inferences and Justifying Conclusions • Conditional Probability and the Rules of Probability • Using Probability to Make Decisions

17. Eight Standards for Mathematical Practice Describe practices that mathematics educators should seek todevelopin their students NCTM Process Standards Natl. Resource Council Adding it Up Problem Solving Reasoning and Proof Communication Representation Connections Adaptive Reasoning Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition

18. Eight Standards for Mathematical Practice • Describe ways in which student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity • Provide a balanced combination of procedure and understanding • Shiftthe focus to ensure mathematical understanding over computation skills

19. Quick Common Core Assessment Overview • Adopted by all but 6 States • New assessments are being developed by two consortia (SBAC and PARCC) who are affiliated with member states • Kansas is affiliated with Smarter Balanced Assessment Consortium (SBAC) • New assessments will be administered starting in 2014-15 each year for Grades 3 – 8 and at least once in High School. • Changes in how we instruct students needs to begin NOW!

20. Quick Common Core Assessment Overview Summative Multi-state Assessment Resources for Teachers and Educational Researchers SMARTER Balanced Assessment Consortium (SBAC)

21. Quick Common Core Assessment Overview SBAC Summative Assessments Computer Adaptive Testing (CAT) Performance Events

22. Quick Common Core Assessment Overview Computer Adaptive Testing (CAT) Students are given a short series of moderately difficult grade level test items. Depending upon students initial performance, delivers items that are either more or less difficult. Process continues until the student’s exact level of proficiency is determined.

23. Quick Common Core Assessment Overview Performance Events In-depth performance task Will require students to think critically in order to solve a non-traditional problem Interpret a situation Communicate the solution Develop a plan

24. Quick Common Core Assessment Overview *No grade level was provided for these samples. Practice Tests will be available in the 2013-2014 school year • Look over three SBAC Sample Items* • Discuss reactions in a small group • Report out

25. The International Center for Leadership in EducationRigor/Relevance Framework

26. Thinking Continuum Assimilation of Knowledge Acquisition of Knowledge

27. Knowledge Taxonomy • Awareness • Comprehension • Analysis • Synthesis • Evaluation

28. Action Continuum Application of Knowledge Acquisition of Knowledge

29. Application Model • Knowledge in one discipline • Application within discipline • Application across disciplines • Application to real-world predictable situations • Application to real-world unpredictable situations

30. 6 5 4 3 2 1 Knowledge Application 1 2 3 4 5

31. 6 5 4 3 2 A 1 1 2 3 4 5

32. 6 5 4 3 2 B A 1 1 2 3 4 5

33. 6 C 5 4 3 2 A B 1 1 2 3 4 5

34. 6 D C 5 4 3 2 A B 1 1 2 3 4 5

35. 6 D C 5 4 3 2 A B 1 1 2 3 4 5

36. KNOWLEDGE D C A B A P P L I C A T I O N

37. KNOWLEDGE • Obtain historical data about local weather to predict the chance of snow, rain, or sun during year. • Test consumer products and illustrate the data graphically. • Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event. • Make a scale drawing of the classroom on grid paper, each group using a different scale. • Analyze the graphs of the perimeters and areas of squares having different-length sides. • Determine the largest rectangular area for a fixed perimeter. • Identify coordinates for ordered pairs that satisfy an algebraic relation or function. • Determine and justify the similarity or congruence for two geometric shapes. D C • Calculate percentages of advertising in a newspaper. • Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles. • Determine the median and mode of real data displayed in a histogram • Organize and display collected data, using appropriate tables, charts, or graphs. • Express probabilities as fractions, percents, or decimals. • Classify triangles according to angle size and/or length of sides. • Calculate volume of simple three- dimensional shapes. • Given the coordinates of a quadrilateral, plot the quadrilateral on a grid. A B A P P L I C A T I O N

38. KNOWLEDGE • Obtain historical data about local weather to predict the chance of snow, rain, or sun during year. • Test consumer products and illustrate the data graphically. • Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event. • Make a scale drawing of the classroom on grid paper, each group using a different scale. • Analyze the graphs of the perimeters and areas of squares haingdifferent-length sides. • Determine the largest rectangular area for a fixed perimeter. • Identify coordinates for ordered pairs that satisfy an algebraic relation or function. • Determine and justify the similarity or congruence for two geometric shapes. D C • Express probabilities as fractions, percents, or decimals. • Classify triangles according to angle size and/or length of sides. • Calculate volume of simple three- dimensional shapes. • Given the coordinates of a quadrilateral, plot the quadrilateral on a grid. • Calculate percentages of advertising in a newspaper. • Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles. • Determine the median and mode of real data displayed in a histogram • Organize and display collected data, using appropriate tables, charts, or graphs. A B A P P L I C A T I O N

39. Calculate percentages of advertising in a newspaper. • Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles. • Determine the median and mode of real data displayed in a histogram • Organize and display collected data, using appropriate tables, charts, or graphs. KNOWLEDGE • Obtain historical data about local weather to predict the chance of snow, rain, or sun during year. • Test consumer products and illustrate the data graphically. • Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event. • Make a scale drawing of the classroom on grid paper, each group using a different scale. • Analyze the graphs of the perimeters and areas of squares having different-length sides. • Determine the largest rectangular area for a fixed perimeter. • Identify coordinates for ordered pairs that satisfy an algebraic relation or function. • Determine and justify the similarity or congruence for two geometric shapes. D C • Express probabilities as fractions, percents, or decimals. • Classify triangles according to angle size and/or length of sides. • Calculate volume of simple three- dimensional shapes. • Given the coordinates of a quadrilateral, plot the quadrilateral on a grid. A B A P P L I C A T I O N

40. Analyze the graphs of the perimeters and areas of squares having different-length sides. • Determine the largest rectangular area for a fixed perimeter. • Identify coordinates for ordered pairs that satisfy an algebraic relation or function. • Determine and justify the similarity or congruence for two geometric shapes. KNOWLEDGE • Obtain historical data about local weather to predict the chance of snow, rain, or sun during year. • Test consumer products and illustrate the data graphically. • Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event. • Make a scale drawing of the classroom on grid paper, each group using a different scale. D C • Calculate percentages of advertising in a newspaper. • Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles. • Determine the median and mode of real data displayed in a histogram • Organize and display collected data, using appropriate tables, charts, or graphs. • Express probabilities as fractions, percents, or decimals. • Classify triangles according to angle size and/or length of sides. • Calculate volume of simple three- dimensional shapes. • Given the coordinates of a quadrilateral, plot the quadrilateral on a grid. A B A P P L I C A T I O N

41. KNOWLEDGE • Analyze the graphs of the perimeters and areas of squares having different-length sides. • Determine the largest rectangular area for a fixed perimeter. • Identify coordinates for ordered pairs that satisfy an algebraic relation or function. • Determine and justify the similarity or congruence for two geometric shapes. C • Obtain historical data about local weather to predict the chance of snow, rain, or sun during year. • Test consumer products and illustrate the data graphically. • Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event. • Make a scale drawing of the classroom on grid paper, each group using a different scale. D • Calculate percentages of advertising in a newspaper. • Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles. • Determine the median and mode of real data displayed in a histogram • Organize and display collected data, using appropriate tables, charts, or graphs. • Express probabilities as fractions, percents, or decimals. • Classify triangles according to angle size and/or length of sides. • Calculate volume of simple three- dimensional shapes. • Given the coordinates of a quadrilateral, plot the quadrilateral on a grid. A B A P P L I C A T I O N

42. Standards for Mathematical Practice Students will be able to: • 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 repeated reasoning.

43. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: • Explain to self the meaning of a problem and look for entry points to a solution • Analyze givens, constraints, relationships and goals • Make conjectures about the form and meaning of the solution • Plan a solution pathway rather than simply jump into a solution attempt • Consider analogous problems • Try special cases and simpler forms of original problem

44. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: • Monitorand evaluate their progress and change course if necessary…“Does this approach make sense?” • Persevere in Solving • Transform algebraic expressions • Change the viewing window on graphing calculator • Move between multiple representations: • Equations, verbal descriptions, tables, graphs, diagrams

45. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: • Check their answers • “Does this answer make sense?” • Does it include correct labels? • Are the magnitudes of the numbers in the solution in the general ballpark to make sense in the real world? • Verify solution using a different method • Compare approach with others: • How does their approach compare with mine? • Similarities • Differences

46. 2. Reason Abstractly and Quantitatively Mathematically proficient students: • Make sense of quantities and their relationships in a problem situation • Bring two complementary abilities to bear on problems involving quantitative relationships: • The ability to decontextualize • to abstract a given situation, represent it symbolically, manipulate the symbols as if they have a life of their own • The ability to contextualize • To pause as needed during the symbolic manipulation in order to look back at the referent values in the problem

47. 2. Reason Abstractly and Quantitatively Mathematically proficient students: • Reason Quantitatively, which entails habits of: • Creating a coherent representation of the problem at hand • Considering the units involved • Attending to the meaning of quantities, not just how to compute them • Knowing and flexibly using different properties of operations and objects

48. 3.Construct viable arguments and critique the reasoning of others Mathematically proficient students: • Understand and use… stated assumptions, definitions, and previously established results… when constructing arguments

49. 3.Construct viable arguments and critique the reasoning of others Mathematically proficient students: • Make conjectures and build a logical progression of statements to explore the truth of their conjectures. • Able to analyze situations • by breaking them into cases • by recognizing and using counterexamples • Justify their conclusions, communicate to others, and respond to the arguments of others

50. 3.Construct viable arguments and critique the reasoning of others Mathematically proficient students: • Reason inductively about data, making plausible arguments that take into account the context from which the data arose • Compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed