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  1. An Overview of CCSSM-oriented Core Math Tools Wisconsin Math Council Annual Conference Green Lake, WI Patrick Hopfensperger University of Wisconsin-Milwaukee hopfensp@uwm.edu

  2. Goals for the Session Overview of Core Math Tools CAS Spreadsheet Synthetic Geometry Coordinate Geometry Data Analysis & Probability Simulation Mini-Lesson using Core Tools

  3. Genesis of Core Math Tools In spite of the considerable promise that computer technology provides for the improvement of school mathematics and student learning, the fulfillment of that promise has been stymied by issues of finance, access, and equity, among others. Heid 1997, 2005

  4. Common Core State Standards for Mathematics Mathematical Practice: Use appropriate tools strategically. 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. . . . They are able to use these tools to explore and deepen their understanding of concepts. Common Core State Standards for Mathematics 2010, p. 7

  5. Translating the CCSSM into practice will require “meaningful curriculum organizations that are problem-based, informed by international models, connected, consistent, coherent, and focused on both content and mathematical practices. These new models should exploit the capabilities of emerging digital technologies … with due attention to equity.” Confrey & Krupa A Summary Report from the Conference “Curriculum Design, Development, and Implementation in an Era of Common Core State Standards,” 2010

  6. Access and Equity 95% of youth aged 14–17 are online; 92% of families have a computer at home; 93% of teens use a desktop or laptop; and 76% report having high-speed Internet access. Parent-Teen Cell Phone Survey, September 2009 Pew Internet & American Life Project

  7. Core Math Tools Use Use by Teachers and Students: Core Math Tools can be saved on computers and USB drives, making it possible to use them without internet access. Files can be saved and reloaded by students and teachers. Its portability allows easy access for students, teachers and parents outside the classroom. Core Math Tools will automatically check for updates when launched and Internet access is available.

  8. Three Families of Software Algebra & Functions—The software for work on algebra problems includes an electronic spreadsheet and a computer algebra system (CAS) that produces tables and graphs of functions, manipulates algebraic expressions, and solves equations and inequalities.

  9. Algebra toolsinclude an electronic spreadsheet and a computer algebra system (CAS) that produces tables and graphs of functions, manipulates algebraic expressions, and solves equations and inequalities;

  10. and custom apps supporting mathematical modeling.

  11. Geometry & Trigonometry—The software for work on geometry problems includes an interactive drawing program for constructing, measuring, and manipulating geometric figures and a set of custom apps for exploring properties of two- and three-dimensional figures.

  12. Geometry toolsinclude an interactive drawing tool for constructing, measuring, manipulating, and transforming geometric figures, a simple object-oriented programming language for creating animation effects,

  13. and custom apps for studying geometric models of contextual situations, physical mechanisms, tessellations, and special shapes.

  14. Statistics & Probability—The software for work on data analysis and probability problems provides tools for graphic display and analysis of data, simulation of probabilistic situations, and mathematical modeling of quantitative relationships.

  15. Statistics toolsinclude tools for graphic display and analysis of univariate and bivariate data, simulation of probabilistic situations

  16. and mathematical modeling of quantitative relationships. Spreadsheets allow easy insert of class data or data available from other sources. CMT includes pre-loaded data sets for developing key statistical ideas.

  17. www.nctm.org/coremathtools

  18. Overview of CAS

  19. Algebra Tools

  20. Graphing

  21. Points of Intersection

  22. Trig Functions

  23. Overview of Spreadsheet App

  24. Graph of Population Growth Model

  25. Overview of Synthetic Geometry

  26. Circumcenter of a Circle

  27. Coordinate Geometry

  28. Simulation Tool

  29. Simulation

  30. Example Aaron Rodgers – QB for Green Bay Packers completes about 65% of passes that he throws. Suppose he makes 10 passes in a game. Estimate the probability that he completes at least 7 of the 10 passes.

  31. Custom Event Editor

  32. Count number of successes

  33. Conduct the Simulation

  34. Repeat a large number of times

  35. Donating Blood In the United States, approximately 10% of the population has type B blood. On a certain day, a blood center needs 1 donor with type B blood. How many donors, on average, should they have to see in order to obtain exactly 1 with type A blood?

  36. Setting Up the Simulation

  37. One Trial

  38. Summary of 101 trials

  39. Fire Alarms SimulationFrom Navigating Through Probability 9-12 (NCTM) A local high school installed 3 fire alarms in the cafeteria. Each alarm is estimated to sound the alarm for a fire 75% of the time. What is the probability that at least one of the alarms will go off if a fire starts in the cafeteria?

  40. Build Custom Event

  41. Conduct trials

  42. Data Analysis tool

  43. Analyzing Bivariate Data • Health and Nutrition • The data in the table show how average daily food supply (in calories) is related to life expectancy (in years) and infant mortality rates (in deaths per 1,000 births) in a sample of countries in the western hemisphere. (Source: World Health Organization Global Health Observatory Data Repository; www.populstat.info/Americas)

  44. Relationship between daily calories and Life expectancy

  45. Scatterplot