In the teacher edition, the section before the investigation starts is divided into the following sections:

• Launch
  • Launch Video
  • Connect Prior Knowledge
  • Present Challenge
• Explore
  • Provide for Individual Needs
  • Planning for Summary
• Summary
  • Orchestrate Discussion
  • Reflect on Student Learning

The underlying design of the materials does distinguish between problems and exercises meeting the expectations for this indicator.

The investigations are divided into problem sets, and they typically follow a sequence. For example, Investigation 1 could be divided into the following problems set: 1.1, 1.2, and 1.3.

At the beginning of each investigation problem set, there are some explanations and definitions given. Next, there is a set of problems to be completed within the class period. 

At the end of each investigation, there is a homework section. This section is divided into Application, Connection, and Extension sections. 

There is also a mathematical reflection section at the end of each investigation where students reflect on the mathematics content they have learned. During this section, there is also a connection between the mathematical practices used throughout the investigation.

The design of assignments is not haphazard; exercises do seem to be given in intentional sequences meeting the expectations for this indicator.

On page 12 of A Guide to Connected Mathematics, the three phases of the CMP model are explained: launching, exploring, and summarizing. 

In the first phase, the teacher launches the problem with the whole class. Launches include connecting to prior knowledge as well as presenting the challenge of the problem.  

For the Explore phase, the nature of the problem suggests whether students work individually, in pairs, in small groups, or occasionally as a whole class to solve the problem. As students work, they gather data, share ideas, look for patterns, make conjectures, and develop problem solving strategies. 

It is during the Summarize phase that the teacher guides the students to reach the mathematical goals of the problem and to connect their new understanding to prior mathematical goals and problems in the unit. The Summarize phase begins when most students have gathered sufficient data or made sufficient progress toward solving the problem. In this phase, students present and discuss their solutions and the strategies they used to understand the problem, organize the data, and find the solution. During the discussion, the teacher helps students enhance their conceptual understanding of the mathematics in the problem and guides them in refining their strategies into more efficient, generalizable problem-solving techniques, or algorithms.

There is a variety in what students are asked to produce, meeting the expectations for this indicator.

• Throughout various investigations and within the problem sets, students are asked to produce answers and solutions as well as to describe their answers, discuss ideas, make conjectures, explain their work and reasoning, make sketches and diagrams, justify their reasoning, and use appropriate models.
• Sometimes only one aspect is specified, such as only requiring an answer, and other times a problem requires students to provide an answer, provide an explanation or steps, include a diagram and/or use a model.

Because problems require different responses, the type of response is intentional, like requiring models when a concept is introduced and then not requiring the same model when a more procedural method for solving similar problems is developed.

The manipulatives are almost always faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models, meeting the expectations for this indicator.

On page 40 of A Guide to Connected Mathematics, an explanation is provided for the use of manipulatives in the instructional materials. Manipulatives are used only when they can help students develop understanding of the mathematical ideas.  

For example, in Filling and Wrapping, students find all the different rectangular arrangements possible for a given number of cubes. They find the surface area of each arrangement by creating a net (covering) for the arrangement that require the least and the most material to wrap. This activity sets the stage for developing the ideas of surface area and volume of rectangular prisms. 

Most of the manipulatives used in CMP are commonly available, and many schools may already have them. Included are rulers, protractors, angle rulers, cubes, square tiles, counters, spinners, and dice.

Two manipulatives are unique to CMP:

Polystrips are plastic strips that can be pieced together with brass fasteners to form polygons. They are used in Grade 7 to investigate the relationship among the side lengths of triangles and quadrilaterals. They also are useful in the Grade 8 Geometry unit, “Butterflies, Pinwheels, and Wallpaper.”  

The CMP Shapes Set is a set of polygons used in Grade 7 to explore sides, angles, and tilings.

Materials support teachers in planning and providing effective learning experiences through teacher questioning. This is a strength of the program with multiple questions for each lesson/problem throughout all of the Grade 8 units. 

• Lesson sections that include questions are Launch, Presenting the Challenge, Explore and Summarize.
• Additionally, teachers are prompted to reflect on student learning after the lesson in order to prepare for the next daily lesson or unit.

The teacher’s edition has many suggestions on presenting the content to students. 

• The Launch section and Connecting to Prior Knowledge are the two beginning sections of each lesson.
• The purple book contains ideas for technology implementation for student learning.

The teacher’s edition is an excellent resource for mathematics teachers to understand the mathematics of the unit and for teachers to expand their understanding of the mathematical concepts.

• Mathematical background is included at the beginning of each unit. In the It’s in the System book, there are 13 pages of mathematical background for teachers to understand.

It’s in the System includes problems, explanations of problems, examples, and connections to CCSSM. 

The teacher’s edition clearly explains the role of specific grade-level mathematics in the context of the overall mathematics for grades 6-12.

• Standards are aligned in Grades 6-12 (curriculum is only written for these grade levels--K-5 is not an option)
• Teacher’s editions connect the learning from previous grade levels and explain how standards build on one another throughout the program.

In the first phase of each lesson, the teacher launches the problem with the whole class.  Launches include connecting to prior knowledge. 

Materials provide very few strategies for teachers to identify and address common student errors and misconceptions.

• In the Teacher Planning section, there were occasionally “Notes” about potential student errors.

They present situations and ask students to identify mistakes or provide rationale based on common misconceptions.

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

• The materials provide several opportunities for ongoing review and practice, such as Notebook, Mathematical Reflection, Looking Back, Check Up, Partner Quiz, Unit Test, Self-Assessment, Project, and Group Work/Discussion.
• Within a unit the set of practice problems includes Application, Connection, and Extension to promote both increased understanding of a concept as well as developing procedural skill/fluency.
• Beyond a lesson, future lessons/units typically expand practice and depth of previous learning.

Teacher Planning offers a multitude of prompts to orchestrate discussion.

Assessments clearly denote which standards are being emphasized.

• Each standard is aligned to one or more lessons as noted at the beginning of each topic.
• The Check up and Unit Test appear to be developed to fully assess a particular standard and the scoring guidelines specify which item aligns to which standard.
• However, reflections and problem sets—which could be used as formative assessment tasks—are not aligned to a specific standard or group of standards.