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Cognitive Delays in Processing

Students who have the ability to engage with the mathematics but need more time and supports may struggle to keep up.

Supporting Question to Ask:
Can assignments be extended or modified to allow more time? Are there opportunities for extra help available?

Collaborative Learning

Research says students learn ideas more deeply when they discuss ideas with classmates.

Collaborative learning is evident in a classroom when

  • Students and teachers are aware of the purpose for and value of working in teams. 
  • Students and teachers are familiar with team norms and roles.

Concept Goals

Concept Goals are those focused on the mathematics students learn.  Teachers may have particular success criteria attached to these Learning Goals that explain how and when students may demonstrate their proficiency level.

Connect-Extend-Challenge protocol

This is a reading strategy used for longer passages where students are asked to make connections to things they already know, extend their thinking by finding new ideas in the material, identify ideas that challenge them, and then share these with their group or the class.


  • Craft questions to make the math visible.
  • Compare and contrast 2 or 3 students' work. What are the mathematical relationships?
  • What do parts of a student's work represent in the original problem? The solution? Work done in the past?

Connecting is Step 5 of the 5 Practices for Orchestrating Productive Math Discussions

Construct viable arguments and critique the reasoning of others

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.

Content Goals

A content goal is linked to a specific content standard or objective.  A content goal example might be "creating equations and inequalities in one variable and using them to solve problems."

Core Problems

If time is limited, use these problems to meet the lesson objectives and the Common Core State Standards.  A problem that is not listed as part of the core is either an extension, an opportunity for deeper understanding, or further practice. Core Problems for each lesson are listed in the Teacher Notes.

Course Notebook

Your course notebook is the place where you record solutions to all of your classwork and Review & Preview problems.  Some teachers ensure that their written solutions are complete with the intent of sharing them with their students.  Some teachers use this area to take notes about formative and summative assessments, including questioning.  You will also want to think about how your students should organize their own Course Notebook. How will you support your students with their notebook organization throughout the school year?

CPM Principles of Assessment

Teachers understand that students learn at different rates and through different experiences. The CPM materials have been designed to support mastery over time through a student-centered, problem-based course, and this approach supports students’ different learning styles. But when changing the materials and changing the methodology, teachers must also change their assessment practices. Teachers cannot tell students they want them to explain their thinking during class and then assess them with only a multiple choice test. Students will quickly realize that “explaining” is not valued enough to be given the time to be assessed.

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