

The
fourphase cycle of classroom activities,
is designed to actively engage students in investigating and making sense of problem situations, in constructing important mathematical concepts and methods, in generalizing and proving mathematical relationships, and in communicating, both orally and in writing, their thinking and the results of their efforts. Most classroom
activities are designed to be completed by students working collaboratively
in groups of two to four students. 
Short clips of classrooms are available at Parent Support: CPMP Classrooms. 

LAUNCH class discussion Think About
This Situation Sample launch 
EXPLORE group investigation Investigation Sample exploration 

SHARE AND SUMMARIZE class discussion Summarize
the Mathematics Sample Summarize
the Mathematics 
APPLY individual tasks Check
Your Understanding Sample Check Your Understanding 
In addition to the classroom investigations, CorePlus Mathematics provides sets of On Your Own tasks, which are designed to engage students in applying, connecting, reflecting on, extending, and reviewing their evolving mathematical knowledge. On Your Own tasks are provided for each lesson in the materials and are central to the learning goals of each lesson. These tasks are intended primarily for individual work outside of class. Selection of homework tasks should be based on student performance and the availability of time and technology. Also, students should exercise some choice of tasks to pursue, and, at times should be given the opportunity to pose their own problems and questions to investigate. The chart below describes the types of tasks in a typical On Your Own set.
On Your Own: Homework Tasks  
Applications  These tasks provide opportunities for students to use and strengthen their understanding of the ideas they have learned in the lesson. 
Connections  These tasks help students to build links between mathematical topics they have studied in the lesson and to connect those topics with other mathematics that they know. 
Reflections  These tasks provide opportunities for students to reexamine their thinking about ideas in the lesson. 
Extensions  These tasks provide opportunities for students to explore further or more deeply the mathematics they are learning. 
Review  These tasks provide opportunities for justintime review and distributed practice of mathematical skills to maintain procedural fluency. 
Review and
Practice
CorePlus Mathematics includes review tasks in
the homework sets. The purpose of the review tasks is twofold.
Some tasks are justintime review of concepts and skills needed
in the following lesson. These tasks will be designated by
a clock icon near the solution. Some tasks provide distributed
practice of mathematical skills to maintain procedural fluency.
These tasks should be completed outside of class by students.
If a few students are identified as needing additional assistance
with specific skills, they should be given additional assistance
outside of class.
Practicing
for Standardized Tests
Opportunities for additional review
and practice are provided in the Practicing for Standardized
Tests masters in each Unit Resources booklet. Each Practicing
for Standardized Tests master presents 10 questions that draw on all content
strands. The questions are presented in the form of test items similar to how
they often appear in standardized tests such as state assessment tests, the
Preliminary Scholastic Aptitude Test (PSAT), SAT, ACT PLAN, or ACT. We
suggest using these practice sets following the unit assessment so students can
become familiar with the formats of standardized tests and develop effective
testtaking strategies for performing well on such tests.
Preparing for Undergraduate Mathematics Placement Tests
Most colleges and universities administer a mathematics placement test to incoming students. The results of this test together with grades in high school mathematics courses and intended undergraduate major are used to advise students regarding the first college mathematics course they study. About half of these postsecondary institutions allow students the use of technology (e.g., a graphing calculator) while completing the test. But you may wish to ensure that your students are prepared to take placement tests with and without technology.
To perform well on these tests, there are a number
of skills and reasoning techniques that need to be automatic. Developing that
level of proficiency requires practice. Thus, you will find two Preparing
for Undergraduate Mathematics Placement (PUMP) sets in the unit resources
for each of the Course 4 units.
Additional
Summarizing Activities
In CorePlus Mathematics, students
learn mathematics by doing mathematics. However, it is important
that students prepare and maintain summaries of important concepts
and methods that are developed. Students should create a Math
Toolkit that organizes important classgenerated ideas and
selected Summarize the Mathematics responses as they complete
investigations. Math Toolkit Prompts are provided in this Teacher's Guide to
assist in identifying and summarizing key concepts and methods as they are
developed by students.
In addition, the final lesson in each unit is a
Looking Back lesson that helps students review and synthesize the key mathematical
concepts and techniques developed in the unit. The Summarize the Mathematics
questions in this lesson are focused on key ideas of the unit. The Check
Your Understanding asks students to prepare a summary of the important
concepts and skills developed in the unit. Templates to guide preparation of
these unit summaries can be found in the Unit Resource Masters. Completed
Unit Summaries should become part of students' Math Toolkits.
Students should retain their Math Toolkits as they
continue on to later courses. In some districts, teachers collect these resources
at the end of the school year and return them to students in the fall.
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