College Preparatory Mathematics

1. College Preparatory Mathematics 6th Grade: Foundations for Algebra Year 1

2. Philosophy • Students can be successful in mathematics if they use materials focused on: • Understanding • Building Mastery Over Time • This is accomplished by using stages in learning mathematics: • Problem Solving • Beginning Concept • Skill Building • Clearer Concept

3. IncompleteLearning Cycle • OLD teaching approach : • Conceptual Definitions • Sample Exercises • Drill and Practice • Created an incomplete learning cycle: In several studies in which students were asked questions that required them to use their skills, less than fifty percent of the best students could give reasonable responses. (Bell, 1995)

4. CPM for 6th Grade • CPM Foundations for Algebra, Yr. 1: • Embraces recommendations of the National Council of Teachers of Mathematics (NCTM) Standards • Develops students’ understanding and skills in 5 key areas: • Operations with integers • Properties and areas of geometric figures • Ratio and proportion • Operations with fractions • Probability

5. Full Learning Cycle Using CPM • Key Components of course: • Use real situations or questions • Use problem solving strategies • Introduce algebraic concepts and build in complexity • Teacher-supported study teams • Use calculator when valuable tool—discourage use when not needed Full Learning Cycle

6. Teacher’s Responsibilities • Overarching: • Give each student the opportunity to learn • Do his/her best to assure that each student reaches acceptable level of understanding of each topic • During Class: • Set the stage for lesson and assign the problems for study teams • Circulate, listen, and respond • Address whole class during or after team study as deemed necessary to move the topic forward or receive clarifying questions from students • Assign Homework/provide answers

7. Student’s Responsibilities • Actively contribute in whole class and study team work and discussions • Complete or attempt all assigned problems and turn in assignments in a timely manner • Check and correct problems on assignments (usually with study team) based on answers and solutions provided in class • Ask for help when needed from study team or teacher/attempt to help when asked by other students • Take notes and make Tool Kit entries when recommended by teacher or text • Keep a well-organized notebook • Do not distract other students

8. The Art of Questioning • Most important—JUST ASK! There is no complete list of questions to ask students who find themselves “stuck” on a problem. Ask any question at all, even if it seems too simple to you. It might be an easy question for the student to answer, but verbalizing the response might make the idea clear in the student’s mind.

9. The Art of Questioning • Simple and helpful starter questions when helping a student with a problem: • What is the problem about? • What is the problem asking you to do? • Ask the student to read the problem to you, and then ask the student again what the problem is asking them to do.

10. The Art of Questioning • Additional Questions to get the student moving on the topic. • Questions to ask if the student has made a start at the problem. • Questions to try if the student is not making any progress. What have you tried? What is still left to be done? Did you work on this IN CLASS?Show me what you did.

11. REMEMBER… • Don’t let your child pass the responsibility for learning to you. • Learning must take place within your child. • By giving answers directly or providing step by step directions, you shift the learning from your child to yourself. • Use questioning, offer help and encouragement, and lead your child to learn on their own. • Your child will be more likely to understand and to be able to use the ideas he/she has learned in practical application and daily use. • Students and parents can get assistance with homework at the following: www.cpm.org/students/hotmath.htm(Be sure to select “Foundations for Algebra: Year 1” from drop-down list.)