Math 2 8-12
- 1. Vertical Alignment Professional Development February 8, 2012 Northern Vance High School
- 2. Where We’ve Been Introduction to Common Core/NC Essential Standards Mathematical Practices CLOSE Reading Technique
- 3. What’s Next Today’s Purpose To explore the format of the Common Core State Standards for Mathematics To examine the vertical alignment of instruction and assessments to ensure that course expectations (2012-2013) are appropriately aligned to Common Core State Standards.
- 4. Key ideas Common core state standards are research based. The sequence of topics respects what is known about how children learn and develop over time. The intent is for students to “understand”, not just do. All students must have the opportunity to learn the same high standards.
- 5. Naming the standards What does 7.G.3 tell you? Grade level Standard number 7.G.3 Domain This is the third 7th grade Geometry standard.
- 6. High school standards (math 1) These standards have a slightly different naming convention. Conceptual category Standard number A-CED.3 Domain This standard is from the Algebra category and the Creating Equations domain. It is standard #3.
- 7. Accessing YOUR Standards Go to the VCS Moodle site Click on Instructional Technology from the Course Categories Click on Common Core & NC Essential Standards Select Common Core State Standards for Math from the Mathematics
- 8. CLOSE Read Closely read p. 5 of the CCSS, “How to read the grade level standards”. List 3 key ideas from the page. Share your ideas with others at your table. Each table will report 2 ideas.
- 9. Key fact!!!! “These standards are not intended to be new names for old ways of doing business.” The standards for mathematical practice are crucial here.
- 10. Our standards are organized into FIVE Conceptual Categories: •Number and Quantity •Algebra •Functions •Geometry •Statistics and Probability Modeling Standards Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear the high school standards indicated by a star symbol (★).
- 11. A Close Look at the Knowing where to find information is just as important as knowing the information. Using the Common Core State Standards in Mathematics, search with others around you to navigate through the conceptual categories and answer the questions on the handout provided
- 12. A Close Look at the Approximately HIGH SCHOOL 5 mins. INTRODUCTION
- 13. High School Introduction p.57 1. What symbol indicates the mathematics that students need to take advanced courses? The symbol, “+” 2. What does a * symbolize in the standards? Modeling standard 3. What does it mean if a cluster heading has a *? All standards in that cluster are modeling standards
- 14. A Close Look at the Approximately NUMBER AND 13 mins. QUANTITY
- 15. Number & Quantity p.58 – 59 4. …how will the numbers systems be extended for high school students? Imaginary and complex numbers are introduced 5. …what are the two ways that number systems remain the same? They all have communicative, associative, and distributive properties Their new meanings are consistent from before. 6. Read the subsection Quantities and explain the process of quantification. The analysis of attributes of interests by determining their quantity (value) as determined by the context of the problem.
- 16. Number & Quantity cont. p.58 – 59 7. No. of No. of Domain Cluster Standards Advanced Standards The Real Number • Extend the properties of exponents to rational 2 0 System exponents N-RN • Use properties of rational and irrational numbers. 1 0 Quantities N-Q • Reason quantitatively and use units to solve problems 3 0 The Complex Number System • Perform arithmetic operations with complex numbers 2 1 N-CN • Represent complex numbers and their operations on 0 3 the complex plane • Use complex numbers in polynomial identities and 1 2 equations Vector and Matrix Quantities • Represent and model with vector quantities. 0 3 N-VM • Perform operations on vectors. 0 2 • Perform operations on matrices and use matrices in 0 7 applications.
- 17. Number & Quantity p.58 – 59 8. List one standard or cluster that indicates a strong correlation to the MODELING standard. N-Q #1-3 (Quantities Cluster) Approximately 17 mins. ALGEBRA
- 18. Algebra pg. 62 – 63 9. What are the three subsections highlighted in the introduction? Expressions Equations & inequalities Connections to Functions and Modeling
- 19. Algebra cont. pg. 62 – 63 No. of No. of Advanced Domain Cluster Standards Standard s Seeing Structure in Expressions • Interpret the structure of expressions 2 0 A-SSE • Write expressions in equivalent forms to solve 2 0 problems Arithmetic with Polynomials and • Perform arithmetic operations on polynomials 1 0 Rational Expressions A-APR • Understand the relationship between zeros and 2 0 factors of polynomials • Use polynomial identities to solve problems 1 1 • Rewrite rational expressions 1 1 Creating Equations • Create equations that describe numbers or A-CED 4 0 relationships Reasoning with Equations and • Understand solving equations as a process of 2 0 Inequalities reasoning and explain the reasoning A-REI • Solve equations and inequalities in one variable 2 0 • Solve systems of equations 3 2 • Represent and solve equations and inequalities 3 0 graphically
- 20. Algebra cont. pg. 62 – 63 11. List one standard or cluster that indicates a strong correlation to the MODELING standard. A-SSE #1, 3, & 4 A-CED #1-4 A-REI #11
- 21. Approximately FUNCTIONS 10 mins.
- 22. 12. No. of No. of Domain Cluster Standards Advanced Standards Interpreting Functions • Understand the concept of a function and use F- IF function notation 3 0 • Interpret functions that arise in applications in terms of the context 3 0 • Analyze functions using different representations 3 1 (#7d) Building Functions • Build a function that models a relationship F-BF 2 1 (#1c) between two quantities 2 (#4b-d & • Build new functions from existing functions 2 5) Linear, Quadratic, and Exponential • Construct and compare linear, quadratic, and Models 4 0 exponential models and solve problems F-LE • Interpret expressions for functions in terms of 1 0 the situation they model Trigonometric Functions • Extend the domain of trigonometric functions F- TF using the unit circle 2 2 • Model periodic phenomena with trigonometric functions 1 2 • Prove and apply trigonometric identities 1 1
- 23. Functions cont. pg. 67 – 68 13. List one standard or cluster that indicates a strong correlation to the MODELING standard. F – IF #4-7 F – BF #1 & 2 F – LE (all) F – TF #5 & 7
- 24. Approximately MODELING 13 mins.
- 25. Modeling pg. 72 – 73 14. Complete the sentence from the first paragraph on pg. 72 Modeling is the process of CHOOSING _ and USING appropriate mathematics and statistics to analyze EMPIRICAL situations. 15. Complete the sentence from the second paragraph on pg. 72 Real-world situations are not ORGANIZED and LABELED for analysis; formulating tractable MODELS , representing such MODELS , and analyzing them is appropriately a CREATIVE process.
- 26. Modeling pg. 72 – 73 16. VALIDATE REPORT PROBLEM FORMULATE COMPUTE INTERPRET 17. Compare descriptive modeling and analytic modeling as described on page 73 Descriptive – describes or summarizes existing phenomena Analytic – explain data based on theoretical ideas with parameters based on the situational model.
- 27. DELING Approximately GEOMETRY 10 mins.
- 28. 20. No. of No. of Domain Cluster Advanced Standards Standards Congruence • Experiment with transformations in the plane 5 0 G-C • Understand congruence in terms of rigid motions 3 0 • Prove geometric theorems 3 0 • Make geometric constructions 2 0 Similarity, Right Triangles, • Understand similarity in terms of similarity 3 0 and Trigonometry transformations G-SRT • Prove theorems involving similarity 2 0 • Define trigonometric ratios and solve problems involving 3 0 right triangles • Apply trigonometry to general triangles 0 3 Circles • Understand and apply theorems about circles 3 1 G-C • Find arc lengths and areas of sectors of circles 1 0 Expressing Geometric • Translate between the geometric description and the 2 1 Properties with Equations equation for a conic section G-GPE • Use coordinates to prove simple geometric theorems 4 0 algebraically Geometric Measurement • Explain volume formulas and use them to solve problems 2 1 and Dimension G-GMD • Visualize relationships between two-dimensional and 1 0 three-dimensional objects Modeling with Geometry G-MD • Apply geometric concepts in modeling situations 3 0
- 29. Geometry cont. pg. 74 – 75 19.List one standard or cluster that indicates a strong correlation to the MODELING standard. G – SRT #8 G – GPE #7 G – GMD #3 G – MG #1-3
- 30. DELING STATISTICS & Approximately 7 mins. PROBABILITY
- 31. 20.Why is there a star (*) in the title of this strand on page 79? ALL STATISTICS AND PROBABILITY STANDARDS ARE 21 Domain ALSO MODELING STANDARDS Cluster No. of No. of Advanced Standards Standards Interpreting Categorical and • Summarize, represent, and interpret data Quantitative Data 4 0 on a single count or measurement variable S-ID • Summarize, represent, and interpret data 2 0 on two categorical and quantitative variables • Interpret linear models 3 0 Making Inferences & Justifying • Understand and evaluate random Conclusions 2 0 processes underlying statistical experiments S - IC • Make inferences and justify conclusions from sample surveys, experiments and 4 0 observational studies Conditional Probability and the • Understand independence and conditional Rules of Probability 5 0 probability and use them to interpret data S-CP • Use the rules of probability to compute probabilities of compound events in a 2 2 uniform probability model Using Probability to Make • Calculate expected values and use them to Decisions 0 4 solve problems S-MD • Use probability to evaluate outcomes of 0 3 decisions
- 32. FINAL SUMMATION TIME! Domains Cluster No. of No. of Adv. Standards Standards Number and 4 9 9 18 Quantity Algebra 4 11 23 4 Functions 4 10 22 9 Geometry 6 15 37 6 Probability & 4 9 22 9 Statistics Grand Total! 22 54 113 46
- 34. The Current Dilemma Inch-deep Lengthy coverage review Re-teaching Definition at next level of insanity
- 35. The Solution VERTICAL ALIGNMENT Establishing and/or recognizing the scope and sequence of course content to ensure… DAILY instructional An appropriate Unnecessary activities/lessons amount of time is repetitions are are aligned to state devoted to removed standards instruction Gaps are Assessments are indentified appropriate (Cohen, 1987; English & Steffy, 2001; Moss-Mitchell, 1998; Neidermeyer & Yelon, 1981; Porter et al., 1994; Porter & Smithson, 2001; Price-Braugh, 1997; Wishnick, 1989)
- 36. Activity: Building a Map • In two separate groups, remove the content of the envelope and place them on the table so that all members can read its statements • Discuss what statements should be learned and/or mastered at each grade band (K- 2, 3-5, 6-8 and 9-12) in regards to the Geometry Domain
- 37. Activity: Building a Map • Have one group member keep notes of the conversations and/or questions that arise • Once a group consensus has been made, arrange them on the table under the appropriate grade band • Make note of how one statement may contribute to the understanding of another
- 38. Activity: Building a Map • Have a group member share out the group’s progression map and discussions with the whole group
- 39. Compare your maps to the Common Core State Standards for Mathematics 1.G.3 Partition circles and rectangles 2.G.2 K.G.2 into two and four Partition a Correctly name equal rectangle into shapes shares, describe rows and regardless of the shares using columns of their orientations the words same-size or overall size. halves, fourths, an squares and d quarters, and count to find the use the phrases total number of half of, fourth them. of, and quarter of.
- 40. 5.G.2 Represent real world and 3.G.1 4.G.1 mathematical Understand that Draw points, problems by shapes in lines, line graphing points different segments, rays, in the first categories angles quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation
- 41. 7.G.5 8.G.4 Use facts about Understand that a 6.G.3 supplementary, two-dimensional Draw polygons in figure is similar to complementary, the coordinate another if the vertical, and plane given second can be adjacent obtained from the coordinates for angles in a first by a the vertices multi-step sequence of problem to write rotations, and solve reflections, transl simple ations, and equations for an dilations; unknown angle in a figure.
- 42. G.CO.3 G.GPE.5 Given a rectangle, Prove the slope parallelogram, G.C.1 criteria for parallel and trapezoid, or Prove that all perpendicular lines regular polygon, circles are similar. and use them to solve describe the geometric problems rotations and reflections that carry it onto itself.
- 43. HOW DID YOUR GROUP DO? Discuss your reactions and any misconceptions that you/your group may have had.
- 44. Where We’re Going On next/last early release session will be on Wednesday, March 21 at Northern We will begin Unit/Assessment Planning and Locating Resources There will be two days of Common Core/NC Essential Standards training for core teachers this summer – Dates TBA
- 45. Before you GO… To submit an evaluation on today’s professional development session: •Return to the 1:1 Professional Development VCS Moodle http://moodle.vcs.k12.nc/moodle •Under the EVALUATION topic, select “Professional Development *Hard copies are available for those without (Feb. 8, 2012) EVALUATION” laptops/internet connection