College Preparatory Mathematics

6th Grade:Foundations for Algebra

Year 1

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

Philosophy

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)

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:1. Operations with integers

2. Properties and areas of geometric figures

3. Ratio and proportion

4. Operations with fractions

5. Probability

Full Learning CycleUsing 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

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

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

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.

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.

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.

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.)