1. Core Plus Mathematics Stefanie Buckner Buncombe County Schools Stefanie.buckner@bcsemail.org

2. Core Plus Mathematics Project Essential Features • Courses organized around interwoven mathematical strands • Mathematical strands developed in coherent, focused units connected by fundamental unifying idea • Mathematics developed in context with an emphasis on applications and mathematical modeling • Student-centered investigations that promote active learning through problem solving • Full and appropriate use of technology tools

3. Course One (“blue” book) • Unit 1: Patterns of Change • Unit 2: Patterns in Data • Unit 3: Linear Functions • Unit 4: Vertex-Edge Graphs • Unit 5: Exponential Functions • Unit 6: Patterns in Shape • Unit 7: Quadratic Functions • Unit 8: Patterns in Chance

4. Common Core Math 1 How Buncombe County Does CCSS Math 1 using Core Plus Materials (somewhat exclusively)

6. Course Two (“green” book) • Unit 1: Functions, Equations, and Systems • Unit 2: Matrix Methods • Unit 3: Coordinate Methods • Unit 4: Network Optimization • Unit 5: Nonlinear Functions and Equations • Unit 6: Regression and Correlation • Unit 7: Trigonometric Methods • Unit 8: Probability Distributions

7. Common Core Math 21 How Buncombe County plans to do CCSS Math 2 using Core Plus Materials (somewhat exclusively)

9. Course Three (“purple” book) • Unit 1: Reasoning and Proof • Unit 2: Inequalities and Linear Programming • Unit 3: Similarity and Congruence • Unit 4: Samples and Variation • Unit 5: Polynomial and Rational Functions • Unit 6: Circles and Circular Functions • Unit 7: Recursion and Iteration • Unit 8: Inverse Functions and Logarithms

10. Course Four (“orange” book) • Unit 1: Families of Functions • Unit 2: Vectors and Motion • Unit 3: Algebraic Functions and Equations • Unit 4: Trigonometric Functions and Equations • Unit 5: Exponential Functions, Logarithms, and Equations • Unit 6: Surfaces and Cross Sections • Unit 7: Rates of Change • Unit 8: Counting Methods and Induction • Unit 9: Binomial Distributions and Statistical Inference • Unit 10: Mathematics of Information Processing and the Internet

11. Instructional Support Materials TeacherWorks CD StudentWorks CD ExamView Pro Resource Masters Teacher Editions (different approach)

12. Launch – Think About the Situation (TATS) • Full class discussion of a problem situation and related questions to think about; purpose is both affective and cognitive. • Explore – Investigation • Group investigation of focused problems and questions related to the launching situation. • Share and Summarize - Summarize the Mathematics (STM) • Class discussion of the mathematical ideas, strategies and reasoning developed in their groups leads to a summary of important ideas. • Apply (CYU) • Tasks students complete individually to check and reinforce their developing understanding. Core Plus Instructional Model

13. Collaboration Based Student to student discourse and student to teacher discourse is at the heart of CPMP investigations.

14. Everyone has a job

15. Collaborative Group Guidelines Each member of the group: • contributes to the group’s work; • is responsible for listening carefully when another group member is talking; • has the responsibility and the right to ask questions; • should help others in the group when asked; • should be considerate and encouraging. • All members should work together until everyone in the group understands and can explain the group’s results.

16. On Your Owns A new “twist” on practice problems Each LESSON is followed by an extensive set of On Your Owns (OYOs)

17. On Your Own Tasks • Applications • Provide opportunities for students to use and strengthen their understanding of ideas they have learned in the lesson. • Connections • Help students to build links between mathematical topics in the lesson and to connect those topics with other mathematics that they know. • Reflections • Provide opportunities for students to re-examine their thinking about ideas in the lesson. • Extensions • Provide opportunities for students to explore further or more deeply the mathematics they are learning. • Review • Provide opportunities for just-in-time review and distributed practice of skills to maintain procedural fluency.

18. Core Math Tools Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful. . . . Common Core State Standards for Mathematics, 2010, p. 7

19. Core Math Tools Core Math Tools is freely available at: www.nctm.org/coremathtools Core Math Tools is accompanied by user support and resources at a CMT portal within the NCTM website. Core Math Tools is designed for use with any CCSSM‐ oriented high school textbook series. BUT Core Plus Data sets are all preloaded. The text often times references CPMP tools. Can be used online in mathematics classrooms, in school and local libraries, or any other place offering Internet access. Can be freely downloaded to user’s class or home computer and is self‐updating whenever connected to the Internet. aka CPMP tools

20. General Purpose Tools

21. Algebra Tools Electronic spreadsheet, computer algebra system (CAS) that produces tables and graphs, manipulates algebraic expressions, and solves equations inequalities. Also includes custom apps supporting mathematical modeling.

22. Geometry Tools Interactive drawing tools for constructing, measuring, manipulating, and transforming geometric figures. Ability to turn off/on coordinate plane. Includes simple programming language for custom applications. Custom apps specifics to geometric properties.

23. Statistics Tools Tools for graphic display and analysis of both univariate and bivariate data, simulation of probabilistic situations and mathematical modeling of quantitative relationships. Spreadsheet capability has built in data sets (correlate to CPMP text) and the ability to enter your own data. Customs apps are key in developing key statistical ideas.

24. Modeling with Core Math Tools • Optimal Refinery Location: Drilling teams from oil companies search around the world for new sites to place oil wells. Increasingly, oil reserves are being discovered in offshore waters. The Gulf Oil Company has drilled two high-capacity wells in the Gulf of Mexico about 5 km and 9 km from shore. The company wants to build a refinery to pipe oil from the two wells to a single new refinery on shore. Assume the 20 km of shoreline is nearly straight. • What are important considerations in locating the refinery? • What is your best estimate for the location of the refinery? How did you decide on that location?

25. Interactive Geometry Approach

26. Multiple Algebraic Approaches

27. A Reflection Approach