Welcome to CPM Educational Program,an educational non-profit organization dedicated to improving grades 6-12 mathematics instruction. CPM offers professional development and curriculum materials. We invite you to learn more about the CPM mathematics program by clicking the "Learn about CPM" link at left. The other sections offer support materials for teachers, parents and students.
CPM Releases Statistics Supplements –
The statistics and probability lessons from the CPM Core Connections series have been posted here. This series of Core Connections Statistics Supplements replaces the Statistics and Probability Resource that was previously available. These files are available for download free of charge.
Lessons aligned to the statistics and probability content standards of the CCSS
For a class not using Common Core State Standards (CCSS)–aligned curriculum materials, these lessons supplement the statistics and probability content to meet the statistics and probability standards of the CCSS. Even if CCSS-aligned curriculum is being used in the classroom, in the transition period to CCSS, it is possible, even likely, that a class will not cover all of the statistics and probability content standards. This content will have to be taught in a subsequent course. These CPM Statistics Supplements provide the materials for any delayed statistics content.
The CPM Statistics Supplements are complete lessons that include the content, learning strategies, teacher notes and methodologies, resource pages, closure activities, review problems, and Checkpoints.
CPM releases Common Core series, Core ConnectionsClick on "Learn About CPM" at left to see tables of contents.
Teachers, for an eBook preview, click here.
Curriculum coordinators in charge of district wide adoptions email Lorrayne Graham.
Digital Math Environment Test GroupAccess feedback survey here. [link]
CPM to offer Integrated I-IIICPM will develop an Integrated series based on the Appendix A pathway. Click here for full details.
Middle School acceleration pathways now availableThe timelines, pacing guides and tables of contents for acceleration to take algebra in 8th grade are now available here.
Conference Handouts and ResourcesView sample course problems and handouts from CPM presentations here.
CPM August 2013 Newsletter "News You Can Use"(download here.)
New curriculum and technical support availableThree CPM mentor teachers are now available to help parents, students and teachers who have questions about the CPM program. This support is primarily for questions about using the program, its technology and the website. To use CPM's support service, go to http://www.cpm.org/support to see the available services. Follow the prompts to get help. Note that this service is not a "homework helpline." That support is at http://www.cpm.org/students/homework.
The CPM mentors are:
Middle grades courses: Susan Hoffmier, Auburn, CA
High school core courses: Melissa Thomley, Madison, WI
Transition to college courses: Sarah Morrison, Glendale, CA
Common Core State Standards (CCSS):CPM now offers a new series of textbooks to meet the grade 6-8 and high school CCSS content and practice standards: Core Connections, Courses 1 - 3 and Core Connections Algebra 1 & 2 and Geometry. Learn how this series as well as the original Connections series of CPM textbooks are fully aligned with the CCSS Content and Mathematical Practice Standards. CPM can also provide professional development centered around embedding the eight CCSS Mathematical Practices into your current lessons and current textbook from any publisher. Start moving on the path to the CCSS today!
Parent e-book licenses are now available!Parents may purchase a one-year e-book license of their student's book for $10 by calling CPM and using a credit card. See order form for a complete list of available one-year licenses. Contact CPM at (209) 745-2055.
Core Connections Geometry : 4.2.5: How much can I expect to win?
Different cultures have developed creative forms of games of chance. For example, native Hawaiians play a game called Konane, which uses markers and a board and is similar to checkers. Native Americans play a game called To-pe-di, in which tossed sticks determine how many points a player receives.
When designing a game of chance, attention must be given to make sure the game is fair. If the game is not fair, or if there is not a reasonable chance that someone can win, no one will play the game. In addition, if the game has prizes involved, care needs to be taken so that prizes will be distributed based on their availability. In other words, if you only want to give away one grand prize, you want to make sure the game is not set up so that 10 people win the grand prize!
Today your team will analyze different games to learn about expected value, which helps to predict the result of a game of chance.
4-101 - TAKE A SPIN
Consider the following game: After you spin the wheel at right, you win the amount spun.
a.) If you play the game 10 times, how much money would you expect to win? What if you played the game 30 times? 100 times? Explain your process. [answer]
b.) What if you played the game n times? Write an equation for how much money someone can expect to win after playing the game n times. [answer]
c.) If you were to play only once, what would you expect to earn according to your equation in part (b)? Is it actually possible to win that amount? Explain why or why not. [answer]