Using Visual Representations to Explore Addition, Subtraction, Multiplication, and Division


Student Voices in Mathematics is a series of four workshops that focus on developing mathematical reasoning through the use of representations. These workshops will explore how representations can enable students to model, make sense of, and analyze the mathematics and procedures they are learning.

Participation in these workshops will enhance teachers’ ability to draw on a variety of visual representations, understand and explain why mathematical procedures work, and nurture the development of the Common Core Standards for Mathematical Practice in their students.

This workshop is the first in a series of four workshops. Follow the links in the list below to learn more about the other workshops:

  1. Using Visual Representations to Explore Addition, Subtraction, Multiplication, and Division
  2. Using Representations to Teach Fraction Concepts and Procedures 
  3. What Are My Students Telling Me? Using Representations to Focus on a Range of Learners
  4. How to Use Argument and Discussion to Help Students Learn Mathematics

Participation in all four workshops is encouraged, but each workshop is designed to stand independently. PDPs are available for educators attending two or more workshops. See below for details.

Participants in this workshop will explore a variety of representations of addition, subtraction, multiplication, and division to enhance their understanding of the properties of these operations and to facilitate their work with students who are developing computational fluency. Emphasis will be placed on learning to support students’ ability to reflect on and explain their work. Participants will come out of this workshop knowing how to use representations to help students make the transition from the concrete to the abstract.

Audience and Grade Level

Teachers of Mathematics, Grades K-8.


A Certificate of Attendance for 6 hours is available to participants in a single workshop. For educators taking two or more of the four workshops, PDPs are available as follows: two workshops - 12 PDPs; three workshops - 18 PDPs; four workshops - 24 PDPs.


Future training dates will be announced here. If you have questions or are interested in offering this training on-site, please contact us.

For more information, contact:
Events Coordinator
413.586.4900 x5981