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.)
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