Online Math Academy – K-2 Course 1:
Counting and Number Relationships Pilot – Nov 7–Dec 12, 2022

The CORE Online Math Academy K-2 course, Counting and Number Relationships, is a highly interactive, robust course that looks deeply at teaching and learning about numbers in the primary grades. The focus of Course 1 is on the development of counting and early number relationships. The course includes the pedagogical practices needed to advance students’ mathematical competencies.

Educators take this asynchronous online course with a cohort of their peers, engaging with the online coursework and participating in moderated weekly online discussions. The course facilitator will answer questions, monitor progress, and monitor and add to course discussion boards. The course is self-paced within a flexible schedule.

Online Math Academy – K-2 Course 1: Counting and Number Relationships Pilot: November 7 – December 12, 2022Online Math Academy

Purpose and Cost of Pilot Course

The purpose of this pilot is to verify the flow, timing, engagement, accessibility, understandability, do-ability, usefulness, and depth of this course in terms of both content and pedagogy. We will collect feedback from participants that will allow us to refine the course to improve it for a formal launch in the winter of 2023. 

The cost of pilot participation is $100 per participant (the normal cost of the course is $225 per person). As a token of our appreciation, participants who complete the course and complete our pilot feedback form will receive a $50 Amazon gift card.

The pilot will run from November 7 through December 12, 2022. An additional week may be added to accommodate participants’ needs. The week of November 24 is off, though participants are free to continue working in the course during that week if they like.

Course Format, Outcomes, and Content

Each module in the course focuses on one or two big ideas around counting and number relations in grades K-2. The course, modules, and sections generally follow a launch-explore-summarize instructional model. Within the focus on each big idea, a standard routine is followed (though sometimes there may be slight variations to this routine):

  1. Vignettes for initial reflection
  2. Ideas, information, research, and resources to increase understanding of big ideas
  3. Student-facing activities that participants can adapt and use with their own students
  4. Prompts for participant reflection accompany activities and videos
  5. Knowledge checks or discussions focused on deepening learning, not checking for understanding

Course Outcomes

Content and Concepts In this course, you will:

  • Learn how concepts of counting and cardinality develop in early grades.
  • Recognize the relationship between counting and a student’s understanding of numbers.
  • Develop an understanding of how counting supports place value, composing and decomposing, and how numbers relate to one another.
  • Connect counting strategies to how students solve addition and subtraction problems.

Pedagogy In this course, you will:

  • Apply and connect the Concrete, Pictorial, and Abstract (CPA) sequence and strategies to build an understanding of numbers.
  • Recognize the importance of varied and consistent practice with models, explanations, number relations, and counting.
  • Create equity by focusing on practices that promote all students reaching proficiency with mathematics in grades K-2.
  • Learn strategies to address common challenges.
  • Gain ideas for activities you can use in the classroom.
  • Connect to valuable resources to enhance your knowledge and provide additional ideas and activities for teaching and learning.

Course Modules

The course is divided into seven modules to be completed over a four-week period. Each module in this course integrates best practice strategies which include modeling, language supports, connections to instruction, and connections to big ideas. Best practices and models are taken from the most current research.

Module 0: Orientation

  • The focus is two-fold. First, orientation to the online format of the course and interactives within the course. Secondly, to establish a common pedagogical frame of reference.

Module 1: Counting and Subitizing in the Emergent Phase

  • The focus is on emergent counting and subitizing. This includes examining students learning to count to 100 by ones and tens, count to 120 starting at any number; and count within 1000.

Module 2: Learning in the Matching Phase

  • The focus is on the progression of counting in grades K-2: Counting Small Collections to tell how many; Cardinality; One-to-One Correspondence; One More, One Less; and Equal Shares.

Module 3: Counting in the Quantifying Phase

  • The focus is on how students’ reason about quantities (understanding number conservation and the difference between a number representing a quantity vs. a number representing a position, such as first, second, or third). We examine effective practices to develop counting strategies, such as counting on, counting back, and skip counting.

Module 4: Comparing and Relating Numbers in the Quantifying Phase

  • The focus is on how students move from fair sharing of quantities of objects to recognizing a part-whole relationship between quantities. This lays the foundation for comparing and changing quantities (joining and separating amounts).

Module 5: Extending Foundational Number Concepts

  • In this module, we will revisit the counting strategies of counting on, counting back, skip counting, and subitizing. These strategies build toward an understanding of addition, subtraction, and multiplicative thinking.

Module 6: Course Review and Wrap Up

  • Review highlighting key points in the course. Tables are provided that list activities and resources shared throughout the course.

Who should attend

  • Teachers (most appropriate for grades K-2)
  • Math specialists
  • Principals/assistant principals
  • Math instructional coaches
  • Special Education and intervention teachers
  • Pre-service teachers or classes


There are no required materials for the course. All necessary materials are provided within the course.

Fee per course

The standard cost for this course is $225 per participant. The pilot is being offered for $100 per participant. A certificate of completion citing 16 hours of professional development time devoted to study will be provided at the end of each course. Graduate continuing education credit is available for an additional fee.

Group discounts are not available for the pilot.

Custom cohorts

If you would like to host your own district-specific cohort of 20 or more people, please contact With a custom cohort, you will choose your own dates and pacing of the course. You will also receive a dedicated instructor.

Graduate continuing education credit option

Participants may receive one (1) graduate-level semester extension unit for an additional cost of $109 per course. Units are typically used for salary advancement. There are no additional requirements beyond successful completion of the course. Participants may register and pay for this unit once the course has started.

Refund information

A full refund of registration fees is available for cancellations 30 days or more prior to the course start date. A 50% refund is available for cancellations less than 30 days but more than 14 days prior to course start date.

Contact to cancel a registration 14 or more days prior to course start date.

No refunds are available 13 days or less prior to course start date or anytime on or after course start date.