Inspiration & Ideas

An image of the Inspirations & Ideas Textbook

Course Design

Inspirations & Ideas is designed to support students in CPM’s Core Connections, Course 3 who sometimes struggle with mathematics. The expectation is that students in Inspirations & Ideas will be concurrently enrolled in Core Connections, Course 3, and therefore will have two math classes daily. Ideally, Inspirations & Ideas is a non-graded course, with no homework, and no summative assessments.

Course Structure

Inspirations & Ideas is a compilation of lessons, arranged appropriately in units, that convey multiple objectives. Although each unit may not fully address a single objective, as a compilation the objectives are met. The course does not attempt to address every content standard in the 8th grade curriculum. Rather the math content in the course is used as a vehicle to change students’ beliefs and attitudes about math. Inspirations & Ideas focuses on the following themes:

Incorrect ideas are often necessary to develop correct ideas.

  • Honoring mistakes
  • Trial and error/Guess and Check

Mathematics is visual.

  • Multiple representations
  • Patterns

Effective communication in mathematics should be practiced.

  • Giving and receiving effective math feedback
  • Justifying mathematics verbally and in writing

Problem solving strategies make problems accessible.

  • Working backwards
  • Making the problem smaller
  • Organize information

Building relationships is vital to a positive classroom environment.

  • Individual progress checks with the teacher
  • Student reflection journals
  • Goal setting

Students can re-engage with mathematics in new ways.

  • Ratio
  • Proportion
  • Equivalence
  • Solving
  • Numeracy
  • Patterns
  • Graphing
  • Fractions
  • Exponents

Professional Learning Requirement

New teachers of Inspirations & Ideas must attend the virtual professional learning event. Teachers will need to successfully complete the learning in order to use the curriculum. Event dates and locations can be found in the CPM Event Catalog.


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Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.


Building on Instructional Practice Series

This series contains three different courses, taken in either order. The courses are designed for schools and teachers with a minimum of one year of experience teaching with CPM curriculum materials. Teachers will develop further understanding of strategies and tools for instructional practices and assessment.

Building on Equity

In this course, participants will learn how to include equitable practices in their  classroom and support traditionally underserved students in becoming leaders of their own learning. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for implementing Chapter 1 that creates an equitable classroom culture and curate strategies for supporting all students in becoming leaders of their own learning. Follow-up during the school year will support ongoing implementation of equitable classroom practices.

Building on Assessment

In this course, participants will apply assessment research to develop methods to provide feedback to students and to inform equitable assessment decisions. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

This professional learning builds upon the Foundations for Implementation Series by improving teachers’ ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rigorous, team-worthy tasks with all elements of the Effective Mathematics Teaching Practices.