About the Core Plus Mathematics Project

1. About the Core Plus Mathematics Project The Core Plus Mathematics Project (CPMP) was funded by the National Science Foundation to develop student and teacher materials for a comprehensive Standards-based high school mathematics curriculum.

2. History of The Core Plus Mathematics Program Core-Plus Mathematics 2 builds on the strengths of the 1st edition which was shaped by multi-year field tests in 36 high schools in Alaska, California, Colorado, Georgia, Idaho, Iowa, Kentucky, Michigan, Ohio, South Carolina, and Texas. Each revised text is the product of a three-year cycle of research and development, pilot testing and refinement, and field testing and further refinement.

3. A Balanced and Unified Curriculum • Replaces the Algebra-Geometry-Advanced Algebra/Trigonometry-Precalculussequence. • Units connected by fundamental ideas such as symmetry, functions, matrices, and data analysis and curve-fitting. • Mathematical habits of mind include visual thinking, recursive thinking, searching for and explaining patterns, making and checking conjectures, reasoning with multiple representations, and providing convincing arguments and proofs.

4. Organization of the Curriculum The first three courses in the Core-Plus Mathematics series provide a significant core of broadly useful mathematics for all students. They were developed to prepare students for success in college, in careers, and in daily life in contemporary society. Course 4: Preparation for Calculus formalizes and extends the core program, with a focus on the mathematics needed to be successful in undergraduate programs requiring calculus.

5. Philosophy of The Core Plus • Developers chose mathematical content that they believe is the most important mathematics that all high school students should have the opportunity to learn • Boxed-off definitions, “worked out” examples, and content summaries are not as prevalent as in conventional texts. Students learn mathematics by doing mathematics. Concept images are developed as students complete investigations; later concept definitions are formalized.

6. Project 2061 Evaluation • CPMP was evaluated by Project 2061 (Contemporary Mathematics in Context) which rated different aspects according to 3 categories: Functions, Variables and Operations • http://www.project2061.org/publications/textbook/algebra/summary/Contempo/ia_Conte.pdf • Functions and Operations were generally good for most aspects • Variables category had many below satisfactory ratings

7. How does Core-Plus Compare to the Standards • Core-Plus is designed to incorporate all eight of the Mathematical Practices into each of the lessons • Core-Plus and the Common Core State Standards: https://www.mheonline.com/assets/gln_download/ccss_alignment_core_plus_math.pdf

8. Teacher Support and Resources • McGraw Hill offers many different resources for teachers • Teacher and Student Editions • Workbooks/Practice books • Activity Materials/Manipulatives • Classroom Resources, Study Guides • Professional Development Ideas • Assessments • Software Tool Kit: http://www.wmich.edu/cpmp/CPMP-Tools/ • Algebra, Geometry, Statistics, Discrete (all Course 2)

9. Publisher and Websites • Core-Plus (McGraw Hill): https://www.mheonline.com/program/view/2/16/647/0078615216/ • Core-Plus benchmarks for Project 2061 evalution: http://www.project2061.org/publications/textbook/algebra/summary/Contempo/ia_Conte.pdf • Core-Plus Comparing to CCSS: https://www.mheonline.com/assets/gln_download/ccss_alignment_core_plus_math.pdf

10. Unit 1 Lesson 3 Tools For Studying Patterns of Change Investigation 1 Communicating with Symbols

11. Suppose that a library loans books free for a week but charges a fine of $0.50 each day the book is kept beyond the first week. To find a rule relating library fines for books to the number of days the book is kept, you might begin by calculating some specific fines, like these: Book Kept 10 Days: Fine = 0.50 ( 10 – 7 ) Book Kept 21 Days: Fine = 0.50 ( 21 – 7 ) The goal is to formulate a symbolic expression relating the amount fined with the number of days kept late. The above strategy is known as specializing. **To Generalize a problem, we may first want to specialize.

12. Suppose that a library loans books free for a week but charges a fine of $0.50 each day the book is kept beyond the first week. Can you create a rule relating library fines for new books to the number of days the book is kept? Write your rule in symbolic form, using F for the fine and d for number of days the book is kept.

13. Midwest Amusement Park charges $25 for each daily admission. The park has daily operating expenses of $35,000. What is the operating profit (or loss) of the park on a day when 1000 admission tickets are sold? On a day when 2,000 admission tickets are sold? b) Write a symbolic rule showing how daily profit p for the park depends on the number of paying visitors n

14. A large jet airplane carries 150,000 pounds of fuel at takeoff. It burns approximately 17,000 pounds of fuel per hour of flight. a) What is the approximate amount of fuel left in the plane after three hours of flight? After seven hours of flight? b) Write a rule showing how the amount of fuel F remaining in the plane’s tanks depends on the elapsed time t in the flight.

15. The costs for a large family reunion party include $250 for renting the shelter at a local park and $15 per person for food and drink. Write a rule showing how the total cost C for the reunion party depends on the number of people n who will attend b) Write another rule showing how the cost per person c (including food, drink, and a share of the shelter rent) depends on the number of people n who plan to attend.

16. Measurement Formulas Many of the most useful symbolic rules are those that give directions for calculating measurements of geometric figures.

17. Figure BCDE is a rectangle For any given rectangle, what is the minimum number of ruler measurements you would need in order to find both its perimeter and area? What set(s) of measurements will meet that condition?

18. What formulas show how to calculate perimeter P and area A of a rectangle from the measurements described in the previous slide?

19. Figure QRST below is a parallelogram For any given parallelogram, what is the minimum number of measurements you would need in order to find both the perimeter and area? What measurements will meet that condition?

20. What formulas show how to calculate perimeter P and area A of a parallelogram from the measurements you described in the previous slide?

21. ABC is a right triangle LMN is an obtuse triangle Using the Pythagorean Theorem, what is the minimum number of ruler measurements you would need in order to find both the perimeter and area of any right triangle? What set(s) of measurements will meet that condition?

22. What formulas show how to calculate perimeter P and area A of a right triangle from the measurements you described in the previous slide

23. What is the minimum number of measurements you would need in order to find both the perimeter and the area of any nonright triangle? What measurements will meet that condition?

24. What formulas show how to calculate perimeter P and area A of a nonright triangle from the measurements you described in the previous slide?

25. The figure below is a circle with center O For any given circle, what is the minimum number of measurements you would need in order to find both the circumference and the area? What measurements will meet that condition?

26. What formulas show how to calculate the circumference C and area A of a circle from the measurements you described in the previous slide?

27. Summary What strategy was found useful for finding algebraic rules when information about the pattern comes in the form of words describing the relationship of the variables?

28. Homework due tomorrow Page 52 “Check Your Understanding”